|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_log10abserr, > glob_start, > glob_warned, > glob_no_eqs, > glob_hmax, > glob_clock_sec, > glob_log10normmin, > glob_smallish_float, > glob_relerr, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_max_hours, > glob_max_trunc_err, > glob_max_iter, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_last_good_h, > glob_optimal_done, > hours_in_day, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_reached_optimal_h, > sec_in_min, > djd_debug, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_dump_analytic, > glob_h, > glob_initial_pass, > years_in_century, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_current_iter, > glob_warned2, > glob_small_float, > glob_log10_abserr, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_iter, > glob_hmin, > glob_disp_incr, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_max_minutes, > glob_not_yet_finished, > days_in_year, > glob_display_flag, > glob_almost_1, > min_in_hour, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_1st_rel_error, > array_y_init, > array_y, > array_x, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_last_rel_error, > array_pole, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_poles, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global INFO, glob_iolevel, glob_max_terms, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_log10abserr, glob_start, glob_warned, glob_no_eqs, glob_hmax, glob_clock_sec, glob_log10normmin, glob_smallish_float, glob_relerr, centuries_in_millinium, glob_percent_done, glob_normmax, glob_max_hours, glob_max_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_subiter_method, glob_optimal_clock_start_sec, glob_last_good_h, glob_optimal_done, hours_in_day, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_reached_optimal_h, sec_in_min, djd_debug, glob_log10relerr, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_dump_analytic, glob_h, glob_initial_pass, years_in_century, glob_dump, glob_html_log, MAX_UNCHANGED, glob_current_iter, glob_warned2, glob_small_float, glob_log10_abserr, glob_max_opt_iter, glob_optimal_expect_sec, glob_iter, glob_hmin, glob_disp_incr, glob_not_yet_start_msg, glob_clock_start_sec, glob_max_minutes, glob_not_yet_finished, days_in_year, glob_display_flag, glob_almost_1, min_in_hour, djd_debug2, array_const_1, array_const_0D0, array_1st_rel_error, array_y_init, array_y, array_x, array_m1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_last_rel_error, array_pole, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_poles, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_log10abserr, > glob_start, > glob_warned, > glob_no_eqs, > glob_hmax, > glob_clock_sec, > glob_log10normmin, > glob_smallish_float, > glob_relerr, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_max_hours, > glob_max_trunc_err, > glob_max_iter, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_last_good_h, > glob_optimal_done, > hours_in_day, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_reached_optimal_h, > sec_in_min, > djd_debug, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_dump_analytic, > glob_h, > glob_initial_pass, > years_in_century, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_current_iter, > glob_warned2, > glob_small_float, > glob_log10_abserr, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_iter, > glob_hmin, > glob_disp_incr, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_max_minutes, > glob_not_yet_finished, > days_in_year, > glob_display_flag, > glob_almost_1, > min_in_hour, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_1st_rel_error, > array_y_init, > array_y, > array_x, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_last_rel_error, > array_pole, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_poles, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global INFO, glob_iolevel, glob_max_terms, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_log10abserr, glob_start, glob_warned, glob_no_eqs, glob_hmax, glob_clock_sec, glob_log10normmin, glob_smallish_float, glob_relerr, centuries_in_millinium, glob_percent_done, glob_normmax, glob_max_hours, glob_max_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_subiter_method, glob_optimal_clock_start_sec, glob_last_good_h, glob_optimal_done, hours_in_day, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_reached_optimal_h, sec_in_min, djd_debug, glob_log10relerr, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_dump_analytic, glob_h, glob_initial_pass, years_in_century, glob_dump, glob_html_log, MAX_UNCHANGED, glob_current_iter, glob_warned2, glob_small_float, glob_log10_abserr, glob_max_opt_iter, glob_optimal_expect_sec, glob_iter, glob_hmin, glob_disp_incr, glob_not_yet_start_msg, glob_clock_start_sec, glob_max_minutes, glob_not_yet_finished, days_in_year, glob_display_flag, glob_almost_1, min_in_hour, djd_debug2, array_const_1, array_const_0D0, array_1st_rel_error, array_y_init, array_y, array_x, array_m1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_last_rel_error, array_pole, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_poles, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_log10abserr, > glob_start, > glob_warned, > glob_no_eqs, > glob_hmax, > glob_clock_sec, > glob_log10normmin, > glob_smallish_float, > glob_relerr, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_max_hours, > glob_max_trunc_err, > glob_max_iter, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_last_good_h, > glob_optimal_done, > hours_in_day, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_reached_optimal_h, > sec_in_min, > djd_debug, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_dump_analytic, > glob_h, > glob_initial_pass, > years_in_century, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_current_iter, > glob_warned2, > glob_small_float, > glob_log10_abserr, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_iter, > glob_hmin, > glob_disp_incr, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_max_minutes, > glob_not_yet_finished, > days_in_year, > glob_display_flag, > glob_almost_1, > min_in_hour, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_1st_rel_error, > array_y_init, > array_y, > array_x, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_last_rel_error, > array_pole, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_poles, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, glob_iolevel, glob_max_terms, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_log10abserr, glob_start, glob_warned, glob_no_eqs, glob_hmax, glob_clock_sec, glob_log10normmin, glob_smallish_float, glob_relerr, centuries_in_millinium, glob_percent_done, glob_normmax, glob_max_hours, glob_max_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_subiter_method, glob_optimal_clock_start_sec, glob_last_good_h, glob_optimal_done, hours_in_day, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_reached_optimal_h, sec_in_min, djd_debug, glob_log10relerr, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_dump_analytic, glob_h, glob_initial_pass, years_in_century, glob_dump, glob_html_log, MAX_UNCHANGED, glob_current_iter, glob_warned2, glob_small_float, glob_log10_abserr, glob_max_opt_iter, glob_optimal_expect_sec, glob_iter, glob_hmin, glob_disp_incr, glob_not_yet_start_msg, glob_clock_start_sec, glob_max_minutes, glob_not_yet_finished, days_in_year, glob_display_flag, glob_almost_1, min_in_hour, djd_debug2, array_const_1, array_const_0D0, array_1st_rel_error, array_y_init, array_y, array_x, array_m1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_last_rel_error, array_pole, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_poles, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_log10abserr, > glob_start, > glob_warned, > glob_no_eqs, > glob_hmax, > glob_clock_sec, > glob_log10normmin, > glob_smallish_float, > glob_relerr, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_max_hours, > glob_max_trunc_err, > glob_max_iter, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_last_good_h, > glob_optimal_done, > hours_in_day, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_reached_optimal_h, > sec_in_min, > djd_debug, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_dump_analytic, > glob_h, > glob_initial_pass, > years_in_century, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_current_iter, > glob_warned2, > glob_small_float, > glob_log10_abserr, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_iter, > glob_hmin, > glob_disp_incr, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_max_minutes, > glob_not_yet_finished, > days_in_year, > glob_display_flag, > glob_almost_1, > min_in_hour, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_1st_rel_error, > array_y_init, > array_y, > array_x, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_last_rel_error, > array_pole, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_poles, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global INFO, glob_iolevel, glob_max_terms, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_log10abserr, glob_start, glob_warned, glob_no_eqs, glob_hmax, glob_clock_sec, glob_log10normmin, glob_smallish_float, glob_relerr, centuries_in_millinium, glob_percent_done, glob_normmax, glob_max_hours, glob_max_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_subiter_method, glob_optimal_clock_start_sec, glob_last_good_h, glob_optimal_done, hours_in_day, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_reached_optimal_h, sec_in_min, djd_debug, glob_log10relerr, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_dump_analytic, glob_h, glob_initial_pass, years_in_century, glob_dump, glob_html_log, MAX_UNCHANGED, glob_current_iter, glob_warned2, glob_small_float, glob_log10_abserr, glob_max_opt_iter, glob_optimal_expect_sec, glob_iter, glob_hmin, glob_disp_incr, glob_not_yet_start_msg, glob_clock_start_sec, glob_max_minutes, glob_not_yet_finished, days_in_year, glob_display_flag, glob_almost_1, min_in_hour, djd_debug2, array_const_1, array_const_0D0, array_1st_rel_error, array_y_init, array_y, array_x, array_m1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_last_rel_error, array_pole, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_poles, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_log10abserr, > glob_start, > glob_warned, > glob_no_eqs, > glob_hmax, > glob_clock_sec, > glob_log10normmin, > glob_smallish_float, > glob_relerr, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_max_hours, > glob_max_trunc_err, > glob_max_iter, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_last_good_h, > glob_optimal_done, > hours_in_day, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_reached_optimal_h, > sec_in_min, > djd_debug, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_dump_analytic, > glob_h, > glob_initial_pass, > years_in_century, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_current_iter, > glob_warned2, > glob_small_float, > glob_log10_abserr, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_iter, > glob_hmin, > glob_disp_incr, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_max_minutes, > glob_not_yet_finished, > days_in_year, > glob_display_flag, > glob_almost_1, > min_in_hour, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_1st_rel_error, > array_y_init, > array_y, > array_x, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_last_rel_error, > array_pole, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_poles, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global INFO, glob_iolevel, glob_max_terms, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_log10abserr, glob_start, glob_warned, glob_no_eqs, glob_hmax, glob_clock_sec, glob_log10normmin, glob_smallish_float, glob_relerr, centuries_in_millinium, glob_percent_done, glob_normmax, glob_max_hours, glob_max_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_subiter_method, glob_optimal_clock_start_sec, glob_last_good_h, glob_optimal_done, hours_in_day, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_reached_optimal_h, sec_in_min, djd_debug, glob_log10relerr, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_dump_analytic, glob_h, glob_initial_pass, years_in_century, glob_dump, glob_html_log, MAX_UNCHANGED, glob_current_iter, glob_warned2, glob_small_float, glob_log10_abserr, glob_max_opt_iter, glob_optimal_expect_sec, glob_iter, glob_hmin, glob_disp_incr, glob_not_yet_start_msg, glob_clock_start_sec, glob_max_minutes, glob_not_yet_finished, days_in_year, glob_display_flag, glob_almost_1, min_in_hour, djd_debug2, array_const_1, array_const_0D0, array_1st_rel_error, array_y_init, array_y, array_x, array_m1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_last_rel_error, array_pole, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_poles, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_log10abserr, > glob_start, > glob_warned, > glob_no_eqs, > glob_hmax, > glob_clock_sec, > glob_log10normmin, > glob_smallish_float, > glob_relerr, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_max_hours, > glob_max_trunc_err, > glob_max_iter, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_last_good_h, > glob_optimal_done, > hours_in_day, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_reached_optimal_h, > sec_in_min, > djd_debug, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_dump_analytic, > glob_h, > glob_initial_pass, > years_in_century, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_current_iter, > glob_warned2, > glob_small_float, > glob_log10_abserr, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_iter, > glob_hmin, > glob_disp_incr, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_max_minutes, > glob_not_yet_finished, > days_in_year, > glob_display_flag, > glob_almost_1, > min_in_hour, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_1st_rel_error, > array_y_init, > array_y, > array_x, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_last_rel_error, > array_pole, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_poles, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre tan $eq_no = 1 > array_tmp1_a1[1] := sin(array_x[1]); > array_tmp1_a2[1] := cos(array_x[1]); > array_tmp1[1] := (array_tmp1_a1[1] / array_tmp1_a2[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre tan $eq_no = 1 > array_tmp1_a1[2] := att(1,array_tmp1_a2,array_x,1); > array_tmp1_a2[2] := -att(1,array_tmp1_a1,array_x,1); > array_tmp1[2] := (array_tmp1_a1[2] - ats(2,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre tan $eq_no = 1 > array_tmp1_a1[3] := att(2,array_tmp1_a2,array_x,1); > array_tmp1_a2[3] := -att(2,array_tmp1_a1,array_x,1); > array_tmp1[3] := (array_tmp1_a1[3] - ats(3,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre tan $eq_no = 1 > array_tmp1_a1[4] := att(3,array_tmp1_a2,array_x,1); > array_tmp1_a2[4] := -att(3,array_tmp1_a1,array_x,1); > array_tmp1[4] := (array_tmp1_a1[4] - ats(4,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre tan $eq_no = 1 > array_tmp1_a1[5] := att(4,array_tmp1_a2,array_x,1); > array_tmp1_a2[5] := -att(4,array_tmp1_a1,array_x,1); > array_tmp1[5] := (array_tmp1_a1[5] - ats(5,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit tan $eq_no = 1 > array_tmp1_a1[kkk] := att(kkk-1 ,array_tmp1_a2,array_x,1); > array_tmp1_a2[kkk] := -att(kkk-1,array_tmp1_a1,array_x,1); > array_tmp1[kkk] := (array_tmp1_a1[kkk] - ats(kkk ,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global INFO, glob_iolevel, glob_max_terms, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_log10abserr, glob_start, glob_warned, glob_no_eqs, glob_hmax, glob_clock_sec, glob_log10normmin, glob_smallish_float, glob_relerr, centuries_in_millinium, glob_percent_done, glob_normmax, glob_max_hours, glob_max_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_subiter_method, glob_optimal_clock_start_sec, glob_last_good_h, glob_optimal_done, hours_in_day, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_reached_optimal_h, sec_in_min, djd_debug, glob_log10relerr, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_dump_analytic, glob_h, glob_initial_pass, years_in_century, glob_dump, glob_html_log, MAX_UNCHANGED, glob_current_iter, glob_warned2, glob_small_float, glob_log10_abserr, glob_max_opt_iter, glob_optimal_expect_sec, glob_iter, glob_hmin, glob_disp_incr, glob_not_yet_start_msg, glob_clock_start_sec, glob_max_minutes, glob_not_yet_finished, days_in_year, glob_display_flag, glob_almost_1, min_in_hour, djd_debug2, array_const_1, array_const_0D0, array_1st_rel_error, array_y_init, array_y, array_x, array_m1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_last_rel_error, array_pole, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_poles, glob_last; array_tmp1_a1[1] := sin(array_x[1]); array_tmp1_a2[1] := cos(array_x[1]); array_tmp1[1] := array_tmp1_a1[1]/array_tmp1_a2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1_a1[2] := att(1, array_tmp1_a2, array_x, 1); array_tmp1_a2[2] := -att(1, array_tmp1_a1, array_x, 1); array_tmp1[2] := ( array_tmp1_a1[2] - ats(2, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1_a1[3] := att(2, array_tmp1_a2, array_x, 1); array_tmp1_a2[3] := -att(2, array_tmp1_a1, array_x, 1); array_tmp1[3] := ( array_tmp1_a1[3] - ats(3, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1_a1[4] := att(3, array_tmp1_a2, array_x, 1); array_tmp1_a2[4] := -att(3, array_tmp1_a1, array_x, 1); array_tmp1[4] := ( array_tmp1_a1[4] - ats(4, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1_a1[5] := att(4, array_tmp1_a2, array_x, 1); array_tmp1_a2[5] := -att(4, array_tmp1_a1, array_x, 1); array_tmp1[5] := ( array_tmp1_a1[5] - ats(5, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1_a1[kkk] := att(kkk - 1, array_tmp1_a2, array_x, 1); array_tmp1_a2[kkk] := -att(kkk - 1, array_tmp1_a1, array_x, 1); array_tmp1[kkk] := ( array_tmp1_a1[kkk] - ats(kkk, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 2.0 - log(abs(cos((x)))) > end; exact_soln_y := proc(x) 2.0 - log(abs(cos(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 > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_log10abserr, > glob_start, > glob_warned, > glob_no_eqs, > glob_hmax, > glob_clock_sec, > glob_log10normmin, > glob_smallish_float, > glob_relerr, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_max_hours, > glob_max_trunc_err, > glob_max_iter, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_last_good_h, > glob_optimal_done, > hours_in_day, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_reached_optimal_h, > sec_in_min, > djd_debug, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_dump_analytic, > glob_h, > glob_initial_pass, > years_in_century, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_current_iter, > glob_warned2, > glob_small_float, > glob_log10_abserr, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_iter, > glob_hmin, > glob_disp_incr, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_max_minutes, > glob_not_yet_finished, > days_in_year, > glob_display_flag, > glob_almost_1, > min_in_hour, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_1st_rel_error, > array_y_init, > array_y, > array_x, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_last_rel_error, > array_pole, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_poles, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ALWAYS := 1; > glob_log10abserr := 0.0; > glob_start := 0; > glob_warned := false; > glob_no_eqs := 0; > glob_hmax := 1.0; > glob_clock_sec := 0.0; > glob_log10normmin := 0.1; > glob_smallish_float := 0.1e-100; > glob_relerr := 0.1e-10; > centuries_in_millinium := 10.0; > glob_percent_done := 0.0; > glob_normmax := 0.0; > glob_max_hours := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_max_iter := 1000; > glob_log10_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_subiter_method := 3; > glob_optimal_clock_start_sec := 0.0; > glob_last_good_h := 0.1; > glob_optimal_done := false; > hours_in_day := 24.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_abserr := 0.1e-10; > glob_look_poles := false; > glob_reached_optimal_h := false; > sec_in_min := 60.0; > djd_debug := true; > glob_log10relerr := 0.0; > glob_curr_iter_when_opt := 0; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_unchanged_h_cnt := 0; > glob_optimal_start := 0.0; > glob_dump_analytic := false; > glob_h := 0.1; > glob_initial_pass := true; > years_in_century := 100.0; > glob_dump := false; > glob_html_log := true; > MAX_UNCHANGED := 10; > glob_current_iter := 0; > glob_warned2 := false; > glob_small_float := 0.1e-50; > glob_log10_abserr := 0.1e-10; > glob_max_opt_iter := 10; > glob_optimal_expect_sec := 0.1; > glob_iter := 0; > glob_hmin := 0.00000000001; > glob_disp_incr := 0.1; > glob_not_yet_start_msg := true; > glob_clock_start_sec := 0.0; > glob_max_minutes := 0.0; > glob_not_yet_finished := true; > days_in_year := 365.0; > glob_display_flag := true; > glob_almost_1 := 0.9990; > min_in_hour := 60.0; > djd_debug2 := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/tanpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"2.0 - log(abs(cos((x))))"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_tmp1_a1:= Array(1..(max_terms + 1),[]); > array_tmp1_a2:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_a1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_a2[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_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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_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 <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_a2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_a1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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 := 0.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := 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 ) = tan ( 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,"2012-06-16T01:47:51-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tan") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( 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,"tan diffeq.mxt") > ; > logitem_str(html_log_file,"tan 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 INFO, glob_iolevel, glob_max_terms, DEBUGL, DEBUGMASSIVE, ALWAYS, glob_log10abserr, glob_start, glob_warned, glob_no_eqs, glob_hmax, glob_clock_sec, glob_log10normmin, glob_smallish_float, glob_relerr, centuries_in_millinium, glob_percent_done, glob_normmax, glob_max_hours, glob_max_trunc_err, glob_max_iter, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_subiter_method, glob_optimal_clock_start_sec, glob_last_good_h, glob_optimal_done, hours_in_day, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_reached_optimal_h, sec_in_min, djd_debug, glob_log10relerr, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_dump_analytic, glob_h, glob_initial_pass, years_in_century, glob_dump, glob_html_log, MAX_UNCHANGED, glob_current_iter, glob_warned2, glob_small_float, glob_log10_abserr, glob_max_opt_iter, glob_optimal_expect_sec, glob_iter, glob_hmin, glob_disp_incr, glob_not_yet_start_msg, glob_clock_start_sec, glob_max_minutes, glob_not_yet_finished, days_in_year, glob_display_flag, glob_almost_1, min_in_hour, djd_debug2, array_const_1, array_const_0D0, array_1st_rel_error, array_y_init, array_y, array_x, array_m1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_last_rel_error, array_pole, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_poles, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; glob_iolevel := 5; glob_max_terms := 30; DEBUGL := 3; DEBUGMASSIVE := 4; ALWAYS := 1; glob_log10abserr := 0.; glob_start := 0; glob_warned := false; glob_no_eqs := 0; glob_hmax := 1.0; glob_clock_sec := 0.; glob_log10normmin := 0.1; glob_smallish_float := 0.1*10^(-100); glob_relerr := 0.1*10^(-10); centuries_in_millinium := 10.0; glob_percent_done := 0.; glob_normmax := 0.; glob_max_hours := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_max_iter := 1000; glob_log10_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_subiter_method := 3; glob_optimal_clock_start_sec := 0.; glob_last_good_h := 0.1; glob_optimal_done := false; hours_in_day := 24.0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_look_poles := false; glob_reached_optimal_h := false; sec_in_min := 60.0; djd_debug := true; glob_log10relerr := 0.; glob_curr_iter_when_opt := 0; glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_unchanged_h_cnt := 0; glob_optimal_start := 0.; glob_dump_analytic := false; glob_h := 0.1; glob_initial_pass := true; years_in_century := 100.0; glob_dump := false; glob_html_log := true; MAX_UNCHANGED := 10; glob_current_iter := 0; glob_warned2 := false; glob_small_float := 0.1*10^(-50); glob_log10_abserr := 0.1*10^(-10); glob_max_opt_iter := 10; glob_optimal_expect_sec := 0.1; glob_iter := 0; glob_hmin := 0.1*10^(-10); glob_disp_incr := 0.1; glob_not_yet_start_msg := true; glob_clock_start_sec := 0.; glob_max_minutes := 0.; glob_not_yet_finished := true; days_in_year := 365.0; glob_display_flag := true; glob_almost_1 := 0.9990; min_in_hour := 60.0; djd_debug2 := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/tanpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "2.0\t- log(abs(cos((x))))"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_1st_rel_error := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_tmp1_a1 := Array(1 .. max_terms + 1, []); array_tmp1_a2 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_poles := Array(1 .. 2, 1 .. 4, []); term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_a2[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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_a2[term] := 0.; term := term + 1 end do; array_tmp1_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_a1[term] := 0.; term := term + 1 end do; 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 := 0.; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := 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 ) = tan ( 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, "2012-06-16T01:47:51-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tan"); logitem_str(html_log_file, "diff ( y , x , 1 ) = tan ( 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, "tan diffeq.mxt"); logitem_str(html_log_file, "tan 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/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 2.0 - log(abs(cos((x)))) end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 2.0000005000000833333555555623016 y[1] (numeric) = 2.0000005000000833341333337650796 absolute error = 7.777782027780e-19 relative error = 3.8888900416673275460398341155912e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 2.0000020000013333347555572825419 y[1] (numeric) = 2.0000020000013333363111228897218 absolute error = 1.5555656071799e-18 relative error = 7.7778202580740567069070092666832e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 2.0000045000067500162000442608434 y[1] (numeric) = 2.0000045000067500185334196965844 absolute error = 2.3333754357410e-18 relative error = 1.1666850928251035718785034776957e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 2.0000080000213334243559976657853 y[1] (numeric) = 2.000008000021333427467218577436 absolute error = 3.1112209116507e-18 relative error = 1.5556042333918232500865325541196e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 2.0000125000520836805581907455634 y[1] (numeric) = 2.0000125000520836844473060047022 absolute error = 3.8891152591388e-18 relative error = 1.9445454761095347727033886322501e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 2.0000180001080010368113308750952 y[1] (numeric) = 2.0000180001080010414784025789558 absolute error = 4.6670717038606e-18 relative error = 2.3335148501706374526463930489112e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 2.0000245002000859477944457038803 y[1] (numeric) = 2.000024500200085953239549177164 absolute error = 5.4451034732837e-18 relative error = 2.7225183855192585533055095227649e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.40 NO POLE x[1] = 0.008 y[1] (analytic) = 2.0000320003413391588687375355708 y[1] (numeric) = 2.0000320003413391650919613326443 absolute error = 6.2232237970735e-18 relative error = 3.1115621130118928125033443772702e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 2.0000405005467618100904021720563 y[1] (numeric) = 2.0000405005467618170918480795355 absolute error = 7.0014459074792e-18 relative error = 3.5006520645782808601498198261310e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 2.0000500008333555562301806003859 y[1] (numeric) = 2.0000500008333555640099636401063 absolute error = 7.7797830397204e-18 relative error = 3.8897942733825746004771347525727e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 2.0000605012201227028016840979645 y[1] (numeric) = 2.000060501220122711359932530338 absolute error = 8.5582484323735e-18 relative error = 4.2789947739843876378198997400085e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 2.0000720017280663581008055881231 y[1] (numeric) = 2.0000720017280663674376609158806 absolute error = 9.3368553277575e-18 relative error = 4.6682596024995288319818110847309e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 2.0000845023801906012588024023147 y[1] (numeric) = 2.0000845023801906113744193746364 absolute error = 1.01156169723217e-17 relative error = 5.0575947967616670194546566606891e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 2.000098003201500666311908004791 y[1] (numeric) = 2.0000980032015006772064546218228 absolute error = 1.08945466170318e-17 relative error = 5.4470063964831750205509381123829e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.015 y[1] (analytic) = 2.0001125042190031422906027186064 y[1] (numeric) = 2.0001125042190031539642602363635 absolute error = 1.16736575177571e-17 relative error = 5.8365004434165009664432807214222e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 2.0001280054617061893319460661503 y[1] (numeric) = 2.0001280054617062017849090018085 absolute error = 1.24529629356582e-17 relative error = 6.2260829815157650133196724771829e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 2.0001445069606197708186460110779 y[1] (numeric) = 2.0001445069606197840511221486518 absolute error = 1.32324761375739e-17 relative error = 6.6157600570979295483760584190366e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=7.6MB, alloc=3.8MB, time=0.85 x[1] = 0.018 y[1] (analytic) = 2.0001620087487559015488131694577 y[1] (numeric) = 2.000162008748755915561023565867 absolute error = 1.40122103964093e-17 relative error = 7.0055377190045409008551365282039e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 2.0001805108611289119406209541629 y[1] (numeric) = 2.000180510861128926732799945687 absolute error = 1.47921789915241e-17 relative error = 7.3954220187635406384598966859107e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 2.0002000133347557282763656359674 y[1] (numeric) = 2.0002000133347557438487608450876 absolute error = 1.55723952091202e-17 relative error = 7.7854190107506945552247074910310e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 2.0002205162086561689906934554522 y[1] (numeric) = 2.0002205162086561853435657980831 absolute error = 1.63528723426309e-17 relative error = 8.1755347523517873161960899998461e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 2.0002420195238532570080352096754 y[1] (numeric) = 2.0002420195238532741416589027855 absolute error = 1.71336236931101e-17 relative error = 8.5657753041247808663973677917849e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 2.0002645233233735481345621745959 y[1] (numeric) = 2.0002645233233735660492247442166 absolute error = 1.79146625696207e-17 relative error = 8.9561467299615347196349700165146e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 2.0002880276522474755102508164671 y[1] (numeric) = 2.0002880276522474942062531060922 absolute error = 1.86960022896251e-17 relative error = 9.3466550972505360141083922249527e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 2.0003125325575097101269175008517 y[1] (numeric) = 2.0003125325575097296045736802265 absolute error = 1.94776561793748e-17 relative error = 9.7373064770391375464166487383454e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 2.0003380380881995374183583345463 y[1] (numeric) = 2.0003380380881995576779959088471 absolute error = 2.02596375743008e-17 relative error = 1.0128106944196151736928694362178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 2.0003645442953612499290033815852 y[1] (numeric) = 2.0003645442953612709709632009899 absolute error = 2.10419598194047e-17 relative error = 1.0519062577574748559933542877675e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 2.0003920512320445560677687876376 y[1] (numeric) = 2.0003920512320445778924050572873 absolute error = 2.18246362696497e-17 relative error = 1.0910179460175255540716974940100e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=3.9MB, time=1.31 x[1] = 0.029 y[1] (analytic) = 2.0004205589533050049540648355588 y[1] (numeric) = 2.0004205589533050275617451259114 absolute error = 2.26076802903526e-17 relative error = 1.1301463679308407762928376450706e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 2.000450067516204427363192646657 y[1] (numeric) = 2.0004500675162044507542979042327 absolute error = 2.33911052575757e-17 relative error = 1.1692921326758496013146309517125e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 2.0004805769798113927786371454431 y[1] (numeric) = 2.0004805769798114169535617039625 absolute error = 2.41749245585194e-17 relative error = 1.2084558498946811021689224552270e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 2.0005120874052016825590390283112 y[1] (numeric) = 2.0005120874052017075181906202267 absolute error = 2.49591515919155e-17 relative error = 1.2476381297095381811691510913776e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 2.0005445988554587792279038268238 y[1] (numeric) = 2.0005445988554588049717035952449 absolute error = 2.57437997684211e-17 relative error = 1.2868395827390956177463173564621e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 2.0005781113956743718943817421411 y[1] (numeric) = 2.0005781113956743984232642531532 absolute error = 2.65288825110121e-17 relative error = 1.3260608201148721445284768638503e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 2.0006126250929488778137277567206 y[1] (numeric) = 2.0006126250929489051281410120991 absolute error = 2.73144132553785e-17 relative error = 1.3653024534976863244932590742350e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 2.0006481400163919800963276108466 y[1] (numeric) = 2.0006481400163920081967330611665 absolute error = 2.81004054503199e-17 relative error = 1.4045650950941160482708472423992e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 2.0006846562371231815744515729312 y[1] (numeric) = 2.0006846562371232104613241310719 absolute error = 2.88868725581407e-17 relative error = 1.4438493576729364623039149323374e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 2.000722173828272374836174541998 y[1] (numeric) = 2.000722173828272404510002597045 absolute error = 2.96738280550470e-17 relative error = 1.4831558545816360970941727678045e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 2.0007606928649804284361779064556 y[1] (numeric) = 2.0007606928649804588974633379996 absolute error = 3.04612854315440e-17 relative error = 1.5224851997629510104456324101950e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 2.0008002134243997892934257533484 y[1] (numeric) = 2.0008002134243998205426839461815 absolute error = 3.12492581928331e-17 relative error = 1.5618380077713767609396810117089e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.0MB, time=1.77 NO POLE x[1] = 0.041 y[1] (analytic) = 2.0008407355856951012859854848946 y[1] (numeric) = 2.0008407355856951333237453441055 absolute error = 3.20377598592109e-17 relative error = 1.6012148937897679700134520493034e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 2.0008822594300438400535406624792 y[1] (numeric) = 2.0008822594300438728803446289472 absolute error = 3.28268039664680e-17 relative error = 1.6406164736459203078066823609252e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 2.0009247850406369640184219705438 y[1] (numeric) = 2.0009247850406369976348260368329 absolute error = 3.36164040662891e-17 relative error = 1.6800433638292096713044032762471e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 2.0009683125026795816362605822236 y[1] (numeric) = 2.0009683125026796160428343088766 absolute error = 3.44065737266530e-17 relative error = 1.7194961815072183806051216838984e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 2.0010128419033916348876469233352 y[1] (numeric) = 2.0010128419033916700849734555695 absolute error = 3.51973265322343e-17 relative error = 1.7589755445424381497451958566531e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 2.0010583733320085990224568796665 y[1] (numeric) = 2.0010583733320086350111329644716 absolute error = 3.59886760848051e-17 relative error = 1.7984820715089646648060588736434e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 2.0011049068797821985687868826991 y[1] (numeric) = 2.001104906879782235349422886337 absolute error = 3.67806360036379e-17 relative error = 1.8380163817092435366276569991709e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 2.0011524426399811396187190491822 y[1] (numeric) = 2.0011524426399811771919389750913 absolute error = 3.75732199259091e-17 relative error = 1.8775790951908374359295734666720e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 2.001200980707891858403417648649 y[1] (numeric) = 2.0012009807078918967698591557525 absolute error = 3.83664415071035e-17 relative error = 1.9171708327632341936582533170408e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 2.0012505211808192861703386383269 y[1] (numeric) = 2.001250521180819325330653059746 absolute error = 3.91603144214191e-17 relative error = 1.9567922160146606794145359119941e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 2.0013010641580876303756148452488 y[1] (numeric) = 2.0013010641580876703304672074221 absolute error = 3.99548523621733e-17 relative error = 1.9964438673289572187206096287002e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.0MB, time=2.24 NO POLE x[1] = 0.052 y[1] (analytic) = 2.0013526097410411722049605990636 y[1] (numeric) = 2.0013526097410412129550296412735 absolute error = 4.07500690422099e-17 relative error = 2.0361264099024823558457640987200e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 2.0014051580330450804367212344132 y[1] (numeric) = 2.0014051580330451219826994287198 absolute error = 4.15459781943066e-17 relative error = 2.0758404677610327637463976396497e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 2.0014587091394862416609748971576 y[1] (numeric) = 2.0014587091394862840035684687412 absolute error = 4.23425935715836e-17 relative error = 2.1155866657768080725779889262446e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 2.0015132631677741068688765125758 y[1] (numeric) = 2.0015132631677741500088054604895 absolute error = 4.31399289479137e-17 relative error = 2.1553656296854403889621647767611e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 2.0015688202273415544267166143509 y[1] (numeric) = 2.0015688202273415983647147326827 absolute error = 4.39379981183318e-17 relative error = 2.1951779861029833710119637246700e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 2.0016253804296457694494509990761 y[1] (numeric) = 2.0016253804296458141862658985236 absolute error = 4.47368148994475e-17 relative error = 2.2350243625430455113518417132425e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 2.001682943888169139588740870654 y[1] (numeric) = 2.0016829438881691851251340005103 absolute error = 4.55363931298563e-17 relative error = 2.2749053874338425830294407594979e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 2.0017415107184201672508272807356 y[1] (numeric) = 2.0017415107184202135875739512895 absolute error = 4.63367466705539e-17 relative error = 2.3148216901353938622260411929832e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 2.0018010810379343982598482637709 y[1] (numeric) = 2.0018010810379344453977376691214 absolute error = 4.71378894053505e-17 relative error = 2.3547739009567070310864777602629e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.061 y[1] (analytic) = 2.0018616549662753669824921167912 y[1] (numeric) = 2.0018616549662754149223273580767 absolute error = 4.79398352412855e-17 relative error = 2.3947626511729715366244140928918e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 2.0019232326250355579301657932514 y[1] (numeric) = 2.0019232326250356066727639022963 absolute error = 4.87425981090449e-17 relative error = 2.4347885730428750855348255140222e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=2.71 NO POLE x[1] = 0.063 y[1] (analytic) = 2.0019858141378373838551433756696 y[1] (numeric) = 2.0019858141378374334013353390478 absolute error = 4.95461919633782e-17 relative error = 2.4748522998258831985730121433759e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 2.0020493996303341803574460719639 y[1] (numeric) = 2.0020493996303342307080768554815 absolute error = 5.03506307835176e-17 relative error = 2.5149544657996214798513555335202e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 2.0021139892302112170194921539039 y[1] (numeric) = 2.0021139892302112681754207275008 absolute error = 5.11559285735969e-17 relative error = 2.5550957062772305058084482057542e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 2.0021795830671867250858427315552 y[1] (numeric) = 2.0021795830671867770479420946285 absolute error = 5.19620993630733e-17 relative error = 2.5952766576248529554016804764750e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 2.0022461812730129417056572436521 y[1] (numeric) = 2.0022461812730129944748144508007 absolute error = 5.27691572071486e-17 relative error = 2.6354979572790779366326024974286e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 2.0023137839814771707557610491142 y[1] (numeric) = 2.0023137839814772243328772363072 absolute error = 5.35771161871930e-17 relative error = 2.6757602437645021226572013968851e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 2.0023823913284028602625165381279 y[1] (numeric) = 2.0023823913284029146485069492969 absolute error = 5.43859904111690e-17 relative error = 2.7160641567112826064996667452237e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 2.0024520034516506964409787510246 y[1] (numeric) = 2.0024520034516507516367727650816 absolute error = 5.51957940140570e-17 relative error = 2.7564103368727611653393045488977e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 2.0025226204911197143701066083408 y[1] (numeric) = 2.0025226204911197703766477666233 absolute error = 5.60065411582825e-17 relative error = 2.7967994261431547098739367977824e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 2.0025942425887484253230915246866 y[1] (numeric) = 2.0025942425887484821413375588299 absolute error = 5.68182460341433e-17 relative error = 2.8372320675752317917325276515026e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 2.0026668698885159607721564111478 y[1] (numeric) = 2.0026668698885160184030792713874 absolute error = 5.76309228602396e-17 relative error = 2.8777089053981197644197903064233e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 2.0027405025364432330874698747138 y[1] (numeric) = 2.0027405025364432915320557586179 absolute error = 5.84445858839041e-17 relative error = 2.9182305850350975475848411185945e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=3.18 NO POLE x[1] = 0.075 y[1] (analytic) = 2.0028151406805941129501128074729 y[1] (numeric) = 2.0028151406805941722093621891067 absolute error = 5.92592493816338e-17 relative error = 2.9587977531214586623384093120039e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 2.0028907844710766234993275319063 y[1] (numeric) = 2.0028907844710766835742551914298 absolute error = 6.00749276595235e-17 relative error = 2.9994110575224443024526791525593e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 2.0029674340600441512345732404228 y[1] (numeric) = 2.0029674340600442121262082941227 absolute error = 6.08916350536999e-17 relative error = 3.0400711473511912866500367075886e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 2.0030450896016966736932056462047 y[1] (numeric) = 2.0030450896016967354025915769626 absolute error = 6.17093859307579e-17 relative error = 3.0807786729867745478788319031788e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 2.0031237512522820039248935574283 y[1] (numeric) = 2.0031237512522820664530882456259 absolute error = 6.25281946881976e-17 relative error = 3.1215342860922690317520878795453e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 2.0032034191700970517841805069258 y[1] (numeric) = 2.0032034191700971151322562617889 absolute error = 6.33480757548631e-17 relative error = 3.1623386396328856908042498223570e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 2.0032840935154891020628956233724 y[1] (numeric) = 2.0032840935154891662319392147547 absolute error = 6.41690435913823e-17 relative error = 3.2031923878941413988603695248441e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 2.0033657744508571094844146271212 y[1] (numeric) = 2.00336577445085717447552731773 absolute error = 6.49911126906088e-17 relative error = 3.2440961865001174620572032236225e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 2.0034484621406530105820691829242 y[1] (numeric) = 2.003448462140653076396366760989 absolute error = 6.58142975780648e-17 relative error = 3.2850506924317515736497958135075e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 2.0035321567513830524843008520412 y[1] (numeric) = 2.0035321567513831191229136644264 absolute error = 6.66386128123852e-17 relative error = 3.3260565640451729621115661524508e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 2.0036168584516091386294545667602 y[1] (numeric) = 2.0036168584516092060935275525246 absolute error = 6.74640729857644e-17 relative error = 3.3671144610901553607113315788071e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=3.65 NO POLE x[1] = 0.086 y[1] (analytic) = 2.0037025674119501914334059102733 y[1] (numeric) = 2.003702567411950259724098634676 absolute error = 6.82906927244027e-17 relative error = 3.4082250447285328253891249726109e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 2.0037892838050835319335165333294 y[1] (numeric) = 2.0037892838050836010520032222859 absolute error = 6.91184866889565e-17 relative error = 3.4493889775527877892833606033815e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 2.0038770078057462764327127853365 y[1] (numeric) = 2.0038770078057463463801823603246 absolute error = 6.99474695749881e-17 relative error = 3.4906069236046014818190613707323e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 2.003965739590736750167784090823 y[1] (numeric) = 2.0039657395907368209454402042414 absolute error = 7.07776561134184e-17 relative error = 3.5318795483935311698449872933574e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 2.0040554793389159180262997716708 y[1] (numeric) = 2.0040554793389159896353608426513 absolute error = 7.16090610709805e-17 relative error = 3.5732075189157141559493742090814e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 2.0041462272312088323368459105899 y[1] (numeric) = 2.0041462272312089047785451612652 absolute error = 7.24416992506753e-17 relative error = 3.6145915036726531826368384949370e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 2.0042379834506060977575874812476 y[1] (numeric) = 2.004237983450606171033172973476 absolute error = 7.32755854922284e-17 relative error = 3.6560321726900480607187171781829e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 2.0043307481821653532884653446555 y[1] (numeric) = 2.0043307481821654273992000172048 absolute error = 7.41107346725493e-17 relative error = 3.6975301975367231682417685340960e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 2.0044245216130127714326428392592 y[1] (numeric) = 2.0044245216130128463798045454508 absolute error = 7.49471617061916e-17 relative error = 3.7390862513435857006451864118635e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 2.0045193039323445745331225830883 y[1] (numeric) = 2.0045193039323446503180041289036 absolute error = 7.57848815458153e-17 relative error = 3.7807010088226693053163784161792e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 2.0046150953314285683107607697867 y[1] (numeric) = 2.0046150953314286449346699524376 absolute error = 7.66239091826509e-17 relative error = 3.8223751462862478732954538119884e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=4.12 NO POLE x[1] = 0.097 y[1] (analytic) = 2.0047118960036056926302136858497 y[1] (numeric) = 2.0047118960036057700944733328146 absolute error = 7.74642596469649e-17 relative error = 3.8641093416659992770474461478415e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 2.0048097061442915895206594134848 y[1] (numeric) = 2.0048097061442916678266074220122 absolute error = 7.83059480085274e-17 relative error = 3.9059042745322537179058345254173e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 2.0049085259509781884784467217598 y[1] (numeric) = 2.0049085259509782676274360988414 absolute error = 7.91489893770816e-17 relative error = 3.9477606261133164423210877998309e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 2.0050083556232353090791329977213 y[1] (numeric) = 2.0050083556232353890725319005363 absolute error = 7.99933989028150e-17 relative error = 3.9896790793148545886616297051058e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 2.0051091953627122809266837385959 y[1] (numeric) = 2.005109195362712361765875515428 absolute error = 8.08391917768321e-17 relative error = 4.0316603187393379291088702813137e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 2.0052110453731395809679176257221 y[1] (numeric) = 2.0052110453731396626543008573516 absolute error = 8.16863832316295e-17 relative error = 4.0737050307055781312313799723971e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 2.0053139058603304882005935402182 y[1] (numeric) = 2.005313905860330570735582081791 absolute error = 8.25349885415728e-17 relative error = 4.1158139032683363432112448834593e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 2.0054177770321827558038490693382 y[1] (numeric) = 2.0054177770321828391888720927134 absolute error = 8.33850230233752e-17 relative error = 4.1579876262379938499913659579388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 2.0055226590986803007200141007995 y[1] (numeric) = 2.0055226590986803849565161373777 absolute error = 8.42365020365782e-17 relative error = 4.2002268912003054797118918549945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 2.0056285522718949107171380199288 y[1] (numeric) = 2.0056285522718949958065790039632 absolute error = 8.50894409840344e-17 relative error = 4.2425323915362354864345236006228e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 2.0057354567659879689618848211429 y[1] (numeric) = 2.0057354567659880549057401335348 absolute error = 8.59438553123919e-17 relative error = 4.2849048224418507052920049050303e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 2.0058433727972121961327671309818 y[1] (numeric) = 2.0058433727972122829325276435629 absolute error = 8.67997605125811e-17 relative error = 4.3273448809483105962250125193130e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=4.59 NO POLE x[1] = 0.109 y[1] (analytic) = 2.0059523005839134101040077246038 y[1] (numeric) = 2.0059523005839134977611798449073 absolute error = 8.76571721203035e-17 relative error = 4.3698532659419339521830653644869e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 2.0060622403465323032306356113409 y[1] (numeric) = 2.0060622403465323917467413278633 absolute error = 8.85161057165224e-17 relative error = 4.4124306781843370095253207052034e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 2.0061731923076062372657431776415 y[1] (numeric) = 2.0061731923076063266423201055971 absolute error = 8.93765769279556e-17 relative error = 4.4550778203326476685176469180060e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 2.0062851566917710559411512175826 y[1] (numeric) = 2.0062851566917711461797526451533 absolute error = 9.02386014275707e-17 relative error = 4.4977953969598254500756781462720e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 2.0063981337257629152430499622528 y[1] (numeric) = 2.0063981337257630063452448973347 absolute error = 9.11021949350819e-17 relative error = 4.5405841145750320712144232941847e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 2.0065121236384201314145064498531 y[1] (numeric) = 2.0065121236384202233818796673026 absolute error = 9.19673732174495e-17 relative error = 4.5834446816441121716629893638085e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 2.0066271266606850467170517685652 y[1] (numeric) = 2.0066271266606851395512038579465 absolute error = 9.28341520893813e-17 relative error = 4.6263778086101440260245317785984e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 2.0067431430256059129838858643474 y[1] (numeric) = 2.0067431430256060066864332781837 absolute error = 9.37025474138363e-17 relative error = 4.6693842079140798909329180896462e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 2.0068601729683387929975627461547 y[1] (numeric) = 2.0068601729683388875701378486854 absolute error = 9.45725751025307e-17 relative error = 4.7124645940154756945305030026228e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 2.0069782167261494797253450519834 y[1] (numeric) = 2.0069782167261495751695961684291 absolute error = 9.54442511164457e-17 relative error = 4.7556196834132848610439691239756e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 2.0070972745384154334457440710196 y[1] (numeric) = 2.007097274538415529763335537358 absolute error = 9.63175914663384e-17 relative error = 4.7988501946667807553393607603066e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=5.07 NO POLE x[1] = 0.12 y[1] (analytic) = 2.0072173466466277368000894604662 y[1] (numeric) = 2.0072173466466278339927016737208 absolute error = 9.71926122132546e-17 relative error = 4.8421568484165476496820558803639e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 2.0073384332943930678033020608256 y[1] (numeric) = 2.007338433294393165872631529869 absolute error = 9.80693294690434e-17 relative error = 4.8855403674055349406856163604637e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 2.0074605347274356908483734110635 y[1] (numeric) = 2.0074605347274357897961328079388 absolute error = 9.89477593968753e-17 relative error = 4.9290014765002590111937819571889e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 2.0075836511935994657393868057698 y[1] (numeric) = 2.0075836511935995655673050175314 absolute error = 9.98279182117616e-17 relative error = 4.9725409027120428257899278565374e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 2.0077077829428498747882470307837 y[1] (numeric) = 2.0077077829428499754980692118607 absolute error = 1.007098221810770e-16 relative error = 5.0161593752183876135204678818421e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 2.0078329302272760680106192724675 y[1] (numeric) = 2.0078329302272761696041068975517 absolute error = 1.015934876250842e-16 relative error = 5.0598576253844165481482967866714e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 2.0079590933010929264569121296132 y[1] (numeric) = 2.0079590933010930289358430470742 absolute error = 1.024789309174610e-16 relative error = 5.1036363867844150272891537327638e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 2.0080862724206431437144751766449 y[1] (numeric) = 2.008086272420643247080643662475 absolute error = 1.033661684858301e-16 relative error = 5.1474963952234771983214215049686e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 2.0082144678443993256175181431687 y[1] (numeric) = 2.0082144678443994298727349554602 absolute error = 1.042552168122915e-16 relative error = 5.1914383887592534336357768201123e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 2.0083436798329661082015964989065 y[1] (numeric) = 2.0083436798329662133476889328632 absolute error = 1.051460924339567e-16 relative error = 5.2354631077237586040303936564425e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 2.008473908649082293939847075567 y[1] (numeric) = 2.0084739086490823999786590190537 absolute error = 1.060388119434867e-16 relative error = 5.2795712947453404273886768076009e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=45.7MB, alloc=4.1MB, time=5.56 x[1] = 0.131 y[1] (analytic) = 2.0086051545576230062984973292569 y[1] (numeric) = 2.0086051545576231132318893188881 absolute error = 1.069333919896312e-16 relative error = 5.3237636947706781019736339637189e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 2.0087374178256018626495129596427 y[1] (numeric) = 2.0087374178256019704793622374147 absolute error = 1.078298492777720e-16 relative error = 5.3680410550869602814498420758704e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 2.0088706987221731655785908663584 y[1] (numeric) = 2.0088706987221732743067914368258 absolute error = 1.087282005704674e-16 relative error = 5.4124041253440827376783408403045e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 2.0090049975186341126270478502428 y[1] (numeric) = 2.0090049975186342222555105382434 absolute error = 1.096284626880006e-16 relative error = 5.4568536575770147502360266793937e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 2.0091403144884270245065000681108 y[1] (numeric) = 2.0091403144884271350371525770411 absolute error = 1.105306525089303e-16 relative error = 5.5013904062282442724591772686908e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 2.0092766499071415918255740361572 y[1] (numeric) = 2.0092766499071417032603610068007 absolute error = 1.114347869706435e-16 relative error = 5.5460151281703015542997422427768e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 2.0094140040525171403682369600856 y[1] (numeric) = 2.0094140040525172527091200299981 absolute error = 1.123408830699125e-16 relative error = 5.5907285827284604324177562383101e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 2.0095523772044449149636823610216 y[1] (numeric) = 2.0095523772044450282126402244746 absolute error = 1.132489578634530e-16 relative error = 5.6355315317034626538752490411662e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 2.0096917696449703819880563766269 y[1] (numeric) = 2.0096917696449704961470848451132 absolute error = 1.141590284684863e-16 relative error = 5.6804247393944142117737752802891e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 2.0098321816582955505386607580818 y[1] (numeric) = 2.0098321816582956656097728213855 absolute error = 1.150711120633037e-16 relative error = 5.7254089726217587856948396731254e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 2.0099736135307813123216204672764 y[1] (numeric) = 2.0099736135307814283068463551106 absolute error = 1.159852258878342e-16 relative error = 5.7704850007503826860285676850101e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 2.0101160655509498002943569162601 y[1] (numeric) = 2.0101160655509499171957441604743 absolute error = 1.169013872442142e-16 relative error = 5.8156535957127862727970793502855e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=6.04 Real estimate of pole used Radius of convergence = 733.2 Order of pole = 1.413e+04 x[1] = 0.143 y[1] (analytic) = 2.0102595380094867661045622943983 y[1] (numeric) = 2.0102595380094868839241757917599 absolute error = 1.178196134973616e-16 relative error = 5.8609155320324409102189331104032e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 41.26 Order of pole = 771.5 x[1] = 0.144 y[1] (analytic) = 2.0104040311992439763677261095047 y[1] (numeric) = 2.0104040311992440951076481850567 absolute error = 1.187399220755520e-16 relative error = 5.9062715868472166645436063468147e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 21.56 Order of pole = 391.1 x[1] = 0.145 y[1] (analytic) = 2.0105495454152416278256220392318 y[1] (numeric) = 2.0105495454152417474879525102292 absolute error = 1.196623304709974e-16 relative error = 5.9517225399329003076876758613007e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 14.74 Order of pole = 259.5 x[1] = 0.146 y[1] (analytic) = 2.0106960809546707814285214600564 y[1] (numeric) = 2.0106960809546709020153777004853 absolute error = 1.205868562404289e-16 relative error = 5.9972691737268778837431156017167e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 11.28 Order of pole = 192.8 x[1] = 0.147 y[1] (analytic) = 2.0108436381168958153842596052013 y[1] (numeric) = 2.0108436381168959368977766108835 absolute error = 1.215135170056822e-16 relative error = 6.0429122733519217780726207004623e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.192 Order of pole = 152.5 x[1] = 0.148 y[1] (analytic) = 2.0109922172034568972176412117464 y[1] (numeric) = 2.0109922172034570196599716660324 absolute error = 1.224423304542860e-16 relative error = 6.0886526266400869060885911159705e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.794 Order of pole = 125.6 x[1] = 0.149 y[1] (analytic) = 2.0111418185180724748840347630414 y[1] (numeric) = 2.0111418185180725982573491030945 absolute error = 1.233733143400531e-16 relative error = 6.1344910241567057171903718957353e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.793 Order of pole = 106.2 x[1] = 0.15 y[1] (analytic) = 2.0112924423666417869813680274198 y[1] (numeric) = 2.0112924423666419112878545110957 absolute error = 1.243064864836759e-16 relative error = 6.1804282592245661800820108641838e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.042 Order of pole = 91.75 x[1] = 0.151 y[1] (analytic) = 2.0114440890572473921051025503044 y[1] (numeric) = 2.0114440890572475173469673236281 absolute error = 1.252418647733237e-16 relative error = 6.2264651279481430862638335719307e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.457 Order of pole = 80.46 x[1] = 0.152 y[1] (analytic) = 2.0115967589001577173911310862869 y[1] (numeric) = 2.011596758900157843570598251531 absolute error = 1.261794671652441e-16 relative error = 6.2726024292379966716943083601651e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.989 Order of pole = 71.44 x[1] = 0.153 y[1] (analytic) = 2.0117504522078296262919096729698 y[1] (numeric) = 2.0117504522078297534112213573372 absolute error = 1.271193116843674e-16 relative error = 6.3188409648352834786291242664720e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=6.52 Real estimate of pole used Radius of convergence = 4.606 Order of pole = 64.07 x[1] = 0.154 y[1] (analytic) = 2.0119051692949110056315051616113 y[1] (numeric) = 2.0119051692949111336929215865255 absolute error = 1.280614164249142e-16 relative error = 6.3651815393363890260014603514282e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.287 Order of pole = 57.92 x[1] = 0.155 y[1] (analytic) = 2.0120609104782433719856095433441 y[1] (numeric) = 2.0120609104782435009914090943502 absolute error = 1.290057995510061e-16 relative error = 6.4116249602176769385765754665809e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.018 Order of pole = 52.73 x[1] = 0.156 y[1] (analytic) = 2.0122176760768644974329443564304 y[1] (numeric) = 2.0122176760768646273854236537109 absolute error = 1.299524792972805e-16 relative error = 6.4581720378604038522392773002519e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.787 Order of pole = 48.29 x[1] = 0.157 y[1] (analytic) = 2.0123754664120110547248518422239 y[1] (numeric) = 2.0123754664120111856263258117316 absolute error = 1.309014739695077e-16 relative error = 6.5048235855757102405997326284368e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.588 Order of pole = 44.45 x[1] = 0.158 y[1] (analytic) = 2.0125342818071212819202443478551 y[1] (numeric) = 2.0125342818071214137730462930675 absolute error = 1.318528019452124e-16 relative error = 6.5515804196297911474457167632359e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.414 Order of pole = 41.1 x[1] = 0.159 y[1] (analytic) = 2.01269412258783766653345976484 y[1] (numeric) = 2.0126941225878377993399414391381 absolute error = 1.328064816742981e-16 relative error = 6.5984433592691718771432902784825e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.26 Order of pole = 38.15 x[1] = 0.16 y[1] (analytic) = 2.0128549890820096492429485575849 y[1] (numeric) = 2.0128549890820097830054802372597 absolute error = 1.337625316796748e-16 relative error = 6.6454132267461081331776457652650e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.124 Order of pole = 35.53 x[1] = 0.161 y[1] (analytic) = 2.0130168816196963472090971869651 y[1] (numeric) = 2.013016881619696481930067744856 absolute error = 1.347209705578909e-16 relative error = 6.6924908473441549187736352296713e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.002 Order of pole = 33.2 x[1] = 0.162 y[1] (analytic) = 2.0131798005331692970498734846944 y[1] (numeric) = 2.0131798005331694327316904644624 absolute error = 1.356818169797680e-16 relative error = 6.7396770494038392026515414087965e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.893 Order of pole = 31.11 x[1] = 0.163 y[1] (analytic) = 2.0133437461569152175233617970464 y[1] (numeric) = 2.0133437461569153541684514880858 absolute error = 1.366450896910394e-16 relative error = 6.7869726643484756964341292181691e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.795 Order of pole = 29.22 x[1] = 0.164 y[1] (analytic) = 2.0135087188276387919666395046947 y[1] (numeric) = 2.013508718827638929577447017687 absolute error = 1.376108075129923e-16 relative error = 6.8343785267101253307366560852683e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.706 Order of pole = 27.51 x[1] = 0.165 y[1] (analytic) = 2.0136747188842654705408318521251 y[1] (numeric) = 2.0136747188842656091198211952391 absolute error = 1.385789893431140e-16 relative error = 6.8818954741557109127557111044431e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=7.00 Real estimate of pole used Radius of convergence = 2.625 Order of pole = 25.95 x[1] = 0.166 y[1] (analytic) = 2.0138417466679442923325688984354 y[1] (numeric) = 2.0138417466679444318822230541763 absolute error = 1.395496541557409e-16 relative error = 6.9295243475132299514358013415227e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.55 Order of pole = 24.53 x[1] = 0.167 y[1] (analytic) = 2.0140098025220507273624568446486 y[1] (numeric) = 2.0140098025220508678852778473606 absolute error = 1.405228210027120e-16 relative error = 6.9772659907981486648705463271383e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.482 Order of pole = 23.23 x[1] = 0.168 y[1] (analytic) = 2.0141788867921895385515660142714 y[1] (numeric) = 2.014178886792189680050075028297 absolute error = 1.414985090140256e-16 relative error = 7.0251212512399121821156127008322e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.42 Order of pole = 22.04 x[1] = 0.169 y[1] (analytic) = 2.0143489998261976636973293771518 y[1] (numeric) = 2.0143489998261978061740667756523 absolute error = 1.424767373985005e-16 relative error = 7.0730909793086350662597123396476e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.362 Order of pole = 20.93 x[1] = 0.17 y[1] (analytic) = 2.0145201419741471175106387252292 y[1] (numeric) = 2.0145201419741472609681641696693 absolute error = 1.434575254444401e-16 relative error = 7.1211760287418922848660802960538e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.309 Order of pole = 19.92 x[1] = 0.171 y[1] (analytic) = 2.0146923135883479137663204461019 y[1] (numeric) = 2.0146923135883480582072129664027 absolute error = 1.444408925203008e-16 relative error = 7.1693772565716797114182200829958e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.259 Order of pole = 18.97 x[1] = 0.172 y[1] (analytic) = 2.0148655150233510076195693101194 y[1] (numeric) = 2.014865515023351153046427385484 absolute error = 1.454268580753646e-16 relative error = 7.2176955231515387451768249260893e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.213 Order of pole = 18.1 x[1] = 0.173 y[1] (analytic) = 2.0150397466359512581413168026708 y[1] (numeric) = 2.0150397466359514045567584430858 absolute error = 1.464154416404150e-16 relative error = 7.2661316921837999360907976675207e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.17 Order of pole = 17.28 x[1] = 0.174 y[1] (analytic) = 2.0152150087851904111259103093034 y[1] (numeric) = 2.0152150087851905585325731377207 absolute error = 1.474066628284173e-16 relative error = 7.3146866307469997747985030655718e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.13 Order of pole = 16.52 x[1] = 0.175 y[1] (analytic) = 2.0153913018323601022248809111587 y[1] (numeric) = 2.0153913018323602506254222463614 absolute error = 1.484005413352027e-16 relative error = 7.3633612093234404166403705271679e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.093 Order of pole = 15.81 x[1] = 0.176 y[1] (analytic) = 2.0155686261410048804609806859361 y[1] (numeric) = 2.0155686261410050298580776260925 absolute error = 1.493970969401564e-16 relative error = 7.4121563018269018177815162281307e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.1MB, time=7.48 Real estimate of pole used Radius of convergence = 2.057 Order of pole = 15.15 x[1] = 0.177 y[1] (analytic) = 2.0157469820769252521770752492412 y[1] (numeric) = 2.0157469820769254025734247561514 absolute error = 1.503963495069102e-16 relative error = 7.4610727856305306349474460624001e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.025 Order of pole = 14.52 x[1] = 0.178 y[1] (analytic) = 2.0159263700081807454748838268924 y[1] (numeric) = 2.0159263700081808968732028109307 absolute error = 1.513983189840383e-16 relative error = 7.5101115415948409311150710349434e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.994 Order of pole = 13.94 x[1] = 0.179 y[1] (analytic) = 2.0161067903050929951989674347616 y[1] (numeric) = 2.01610679030509314760199284052 absolute error = 1.524030254057584e-16 relative error = 7.5592734540959304146591502351208e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.964 Order of pole = 13.39 x[1] = 0.18 y[1] (analytic) = 2.0162882433402488485217757733345 y[1] (numeric) = 2.0162882433402490019322646659701 absolute error = 1.534104888926356e-16 relative error = 7.6085594110537877205086833863943e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.937 Order of pole = 12.87 x[1] = 0.181 y[1] (analytic) = 2.0164707294885034911859752337688 y[1] (numeric) = 2.0164707294885036456067048860613 absolute error = 1.544207296522925e-16 relative error = 7.6579703039608589186303018601452e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.911 Order of pole = 12.39 x[1] = 0.182 y[1] (analytic) = 2.0166542491269835944606939753071 y[1] (numeric) = 2.016654249126983749894461955428 absolute error = 1.554337679801209e-16 relative error = 7.7075070279106446140559248555923e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.887 Order of pole = 11.93 x[1] = 0.183 y[1] (analytic) = 2.0168388026350904828687353850041 y[1] (numeric) = 2.0168388026350906393183596450046 absolute error = 1.564496242600005e-16 relative error = 7.7571704816265949910699234743324e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.863 Order of pole = 11.49 x[1] = 0.184 y[1] (analytic) = 2.0170243903945033227422283845393 y[1] (numeric) = 2.0170243903945034802105473495597 absolute error = 1.574683189650204e-16 relative error = 7.8069615674910940075959556127082e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.841 Order of pole = 11.08 x[1] = 0.185 y[1] (analytic) = 2.017211012789182331664602020121 y[1] (numeric) = 2.0172110127891824901544746783255 absolute error = 1.584898726582045e-16 relative error = 7.8568811915745868343600986102125e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.821 Order of pole = 10.69 x[1] = 0.186 y[1] (analytic) = 2.0173986702053720088571925749931 y[1] (numeric) = 2.0173986702053721683714985682364 absolute error = 1.595143059932433e-16 relative error = 7.9069302636649739874456212167170e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.801 Order of pole = 10.33 x[1] = 0.187 y[1] (analytic) = 2.0175873630316043865692140947539 y[1] (numeric) = 2.0175873630316045471108538099819 absolute error = 1.605416397152280e-16 relative error = 7.9571096972970683843210517278151e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.1MB, time=7.95 Real estimate of pole used Radius of convergence = 1.782 Order of pole = 9.978 x[1] = 0.188 y[1] (analytic) = 2.0177770916587023025302477285834 y[1] (numeric) = 2.0177770916587024641021423899742 absolute error = 1.615718946613908e-16 relative error = 8.0074204097823081780388266882910e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.764 Order of pole = 9.648 x[1] = 0.189 y[1] (analytic) = 2.0179678564797826935248316796769 y[1] (numeric) = 2.0179678564797828561299234415251 absolute error = 1.626050917618482e-16 relative error = 8.0578633222385662376980062064978e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.747 Order of pole = 9.333 x[1] = 0.19 y[1] (analytic) = 2.0181596578902599101491618408727 y[1] (numeric) = 2.0181596578902600737904138812233 absolute error = 1.636412520403506e-16 relative error = 8.1084393596202193354292069067829e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.731 Order of pole = 9.035 x[1] = 0.191 y[1] (analytic) = 2.0183524962878490528103433819497 y[1] (numeric) = 2.0183524962878492174907399969846 absolute error = 1.646803966150349e-16 relative error = 8.1591494507483129740009817690844e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.715 Order of pole = 8.751 x[1] = 0.192 y[1] (analytic) = 2.0185463720725693290290656687196 y[1] (numeric) = 2.0185463720725694947516123679023 absolute error = 1.657225466991827e-16 relative error = 8.2099945283409502002493489307834e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.701 Order of pole = 8.48 x[1] = 0.193 y[1] (analytic) = 2.0187412856467474321070069463458 y[1] (numeric) = 2.018741285646747598874730548329 absolute error = 1.667677236019832e-16 relative error = 8.2609755290438592728795660582606e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.687 Order of pole = 8.223 x[1] = 0.194 y[1] (analytic) = 2.0189372374150209412207112258461 y[1] (numeric) = 2.0189372374150211090366599551463 absolute error = 1.678159487293002e-16 relative error = 8.3120933934611099435238731901779e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.673 Order of pole = 7.978 x[1] = 0.195 y[1] (analytic) = 2.0191342277843417430041177891565 y[1] (numeric) = 2.0191342277843419118713613736013 absolute error = 1.688672435844448e-16 relative error = 8.3633490661860570877617870787501e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.66 Order of pole = 7.744 x[1] = 0.196 y[1] (analytic) = 2.0193322571639794746823636902184 y[1] (numeric) = 2.0193322571639796446039934591705 absolute error = 1.699216297689521e-16 relative error = 8.4147434958324269377362608111643e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.648 Order of pole = 7.521 x[1] = 0.197 y[1] (analytic) = 2.019531325965524988819921593161 y[1] (numeric) = 2.0195313259655251597990505765243 absolute error = 1.709791289833633e-16 relative error = 8.4662776350656147317036145058423e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.636 Order of pole = 7.308 x[1] = 0.198 y[1] (analytic) = 2.0197314346028938397465792697594 y[1] (numeric) = 2.0197314346028940117863422977719 absolute error = 1.720397630280125e-16 relative error = 8.5179524406341585642159817153745e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.625 Order of pole = 7.104 x[1] = 0.199 y[1] (analytic) = 2.0199325834923297917252130930153 y[1] (numeric) = 2.0199325834923299648287668968342 absolute error = 1.731035538038189e-16 relative error = 8.5697688734014235540578252513998e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=8.43 Real estimate of pole used Radius of convergence = 1.614 Order of pole = 6.91 x[1] = 0.2 y[1] (analytic) = 2.0201347730524083489257559281057 y[1] (numeric) = 2.0201347730524085230962792411887 absolute error = 1.741705233130830e-16 relative error = 8.6217278983774264629020924665558e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.604 Order of pole = 6.724 x[1] = 0.201 y[1] (analytic) = 2.0203380037040403072702099523364 y[1] (numeric) = 2.0203380037040404825109036126253 absolute error = 1.752406936602889e-16 relative error = 8.6738304847509041883355887528974e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.594 Order of pole = 6.547 x[1] = 0.202 y[1] (analytic) = 2.0205422758704753282140071485046 y[1] (numeric) = 2.0205422758704755045280942014162 absolute error = 1.763140870529116e-16 relative error = 8.7260776059215710950489876153117e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.584 Order of pole = 6.377 x[1] = 0.203 y[1] (analytic) = 2.020747589977305534529474527685 y[1] (numeric) = 2.0207475899773057119202003299134 absolute error = 1.773907258022284e-16 relative error = 8.7784702395325200856654770272942e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.575 Order of pole = 6.214 x[1] = 0.204 y[1] (analytic) = 2.0209539464524691281576175644916 y[1] (numeric) = 2.0209539464524693066282498886286 absolute error = 1.784706323241370e-16 relative error = 8.8310093675028955314621559084731e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.566 Order of pole = 6.058 x[1] = 0.205 y[1] (analytic) = 2.0211613457262540301948938870235 y[1] (numeric) = 2.0211613457262542097487230270015 absolute error = 1.795538291399780e-16 relative error = 8.8836959760607236402295918100776e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.557 Order of pole = 5.909 x[1] = 0.206 y[1] (analytic) = 2.0213697882313015430821099717627 y[1] (numeric) = 2.0213697882313017237224488491249 absolute error = 1.806403388773622e-16 relative error = 8.9365310557759195008794860075135e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.549 Order of pole = 5.766 x[1] = 0.207 y[1] (analytic) = 2.0215792744026100350630364675623 y[1] (numeric) = 2.0215792744026102167932207385668 absolute error = 1.817301842710045e-16 relative error = 8.9895156015935592780729625419873e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.541 Order of pole = 5.629 x[1] = 0.208 y[1] (analytic) = 2.0217898046775386469808028295565 y[1] (numeric) = 2.0217898046775388298041909931188 absolute error = 1.828233881635623e-16 relative error = 9.0426506128673130545858432015056e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.534 Order of pole = 5.498 x[1] = 0.209 y[1] (analytic) = 2.0220013794958110214805992004502 y[1] (numeric) = 2.0220013794958112054005727069297 absolute error = 1.839199735064795e-16 relative error = 9.0959370933930921608938717380222e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.526 Order of pole = 5.371 x[1] = 0.21 y[1] (analytic) = 2.0222139992995190546876829504448 y[1] (numeric) = 2.0222139992995192397076463112808 absolute error = 1.850199633608360e-16 relative error = 9.1493760514429054420217648336085e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.1MB, time=8.92 Real estimate of pole used Radius of convergence = 1.519 Order of pole = 5.251 x[1] = 0.211 y[1] (analytic) = 2.0224276645331266704301589953657 y[1] (numeric) = 2.0224276645331268565535398935687 absolute error = 1.861233808982030e-16 relative error = 9.2029684997989386905600379792431e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.512 Order of pole = 5.134 x[1] = 0.212 y[1] (analytic) = 2.0226423756434736170764769728296 y[1] (numeric) = 2.0226423756434738043067263743328 absolute error = 1.872302494015032e-16 relative error = 9.2567154557878121303656002794629e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.506 Order of pole = 5.023 x[1] = 0.213 y[1] (analytic) = 2.0228581330797792870580645860946 y[1] (numeric) = 2.0228581330797794753986568519724 absolute error = 1.883405922658778e-16 relative error = 9.3106179413151092877811098390291e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.499 Order of pole = 4.916 x[1] = 0.214 y[1] (analytic) = 2.0230749372936465591479949422592 y[1] (numeric) = 2.0230749372936467486024279418168 absolute error = 1.894544329995576e-16 relative error = 9.3646769829000431269931627181473e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.493 Order of pole = 4.813 x[1] = 0.215 y[1] (analytic) = 2.0232927887390656635670665335059 y[1] (numeric) = 2.0232927887390658541388617582472 absolute error = 1.905717952247413e-16 relative error = 9.4188936117104120981988299207974e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.487 Order of pole = 4.714 x[1] = 0.216 y[1] (analytic) = 2.0235116878724180699891576550507 y[1] (numeric) = 2.0235116878724182616818603335295 absolute error = 1.916927026784788e-16 relative error = 9.4732688635977366912690738258392e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.481 Order of pole = 4.62 x[1] = 0.217 y[1] (analytic) = 2.0237316351524803985182025393771 y[1] (numeric) = 2.0237316351524805913353817529375 absolute error = 1.928171792135604e-16 relative error = 9.5278037791326203598900710171029e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.476 Order of pole = 4.528 x[1] = 0.218 y[1] (analytic) = 2.0239526310404283537096243313672 y[1] (numeric) = 2.0239526310404285476548731307793 absolute error = 1.939452487994121e-16 relative error = 9.5824994036403440534312405819499e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.471 Order of pole = 4.441 x[1] = 0.219 y[1] (analytic) = 2.0241746759998406817095502513561 y[1] (numeric) = 2.0241746759998408767864857743526 absolute error = 1.950769355229965e-16 relative error = 9.6373567872366689994138612709707e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.465 Order of pole = 4.356 x[1] = 0.22 y[1] (analytic) = 2.0243977704967031505856269113214 y[1] (numeric) = 2.0243977704967033467978905010417 absolute error = 1.962122635897203e-16 relative error = 9.6923769848638964935011183564955e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.46 Order of pole = 4.275 x[1] = 0.221 y[1] (analytic) = 2.0246219149994125539237487818968 y[1] (numeric) = 2.0246219149994127512750061062438 absolute error = 1.973512573243470e-16 relative error = 9.7475610563271148660344114384437e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.1MB, time=9.39 Real estimate of pole used Radius of convergence = 1.455 Order of pole = 4.197 x[1] = 0.222 y[1] (analytic) = 2.0248471099787807377655102732928 y[1] (numeric) = 2.0248471099787809362594514452096 absolute error = 1.984939411719168e-16 relative error = 9.8029100663307317654015817907214e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.451 Order of pole = 4.122 x[1] = 0.223 y[1] (analytic) = 2.0250733559080386509616918102938 y[1] (numeric) = 2.025073355908038850602031508965 absolute error = 1.996403396986712e-16 relative error = 9.8584250845151675928548991492148e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.446 Order of pole = 4.05 x[1] = 0.224 y[1] (analytic) = 2.0253006532628404190175926691481 y[1] (numeric) = 2.0253006532628406198080702621331 absolute error = 2.007904775929850e-16 relative error = 9.9141071854938427816620429607567e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.442 Order of pole = 3.98 x[1] = 0.225 y[1] (analytic) = 2.0255290025212674415065282214064 y[1] (numeric) = 2.0255290025212676434509078877108 absolute error = 2.019443796663044e-16 relative error = 9.9699574488903940110989095629196e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.437 Order of pole = 3.913 x[1] = 0.226 y[1] (analytic) = 2.0257584041638325131283166157178 y[1] (numeric) = 2.0257584041638327162303874698084 absolute error = 2.031020708540906e-16 relative error = 1.0025976959376089054190500095513e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.433 Order of pole = 3.849 x[1] = 0.227 y[1] (analytic) = 2.0259888586734839684900898425384 y[1] (numeric) = 2.0259888586734841727536660593093 absolute error = 2.042635762167709e-16 relative error = 1.0082166806707538313638421074808e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.429 Order of pole = 3.787 x[1] = 0.228 y[1] (analytic) = 2.0262203665356098506872765880431 y[1] (numeric) = 2.0262203665356100561161975287385 absolute error = 2.054289209406954e-16 relative error = 1.0138528085764608530143881644953e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.425 Order of pole = 3.727 x[1] = 0.229 y[1] (analytic) = 2.0264529282380421037631193117791 y[1] (numeric) = 2.0264529282380423103612496508796 absolute error = 2.065981303391005e-16 relative error = 1.0195061896588597205323702035360e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.421 Order of pole = 3.67 x[1] = 0.23 y[1] (analytic) = 2.0266865442710607891256055974283 y[1] (numeric) = 2.026686544271060996896835450507 absolute error = 2.077712298530787e-16 relative error = 1.0251769344420642342591903213192e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.417 Order of pole = 3.614 x[1] = 0.231 y[1] (analytic) = 2.0269212151273983260012140472416 y[1] (numeric) = 2.0269212151273985349494590997972 absolute error = 2.089482450525556e-16 relative error = 1.0308651539740411198225696181698e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.414 Order of pole = 3.561 x[1] = 0.232 y[1] (analytic) = 2.0271569413022437560053978382063 y[1] (numeric) = 2.0271569413022439661345994754792 absolute error = 2.101292016372729e-16 relative error = 1.0365709598305008096236536377811e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.41 Order of pole = 3.509 x[1] = 0.233 y[1] (analytic) = 2.0273937232932470319102545518643 y[1] (numeric) = 2.0273937232932472432243799896428 absolute error = 2.113141254377785e-16 relative error = 1.0422944641188154857578534819295e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.1MB, time=9.87 Real estimate of pole used Radius of convergence = 1.407 Order of pole = 3.46 x[1] = 0.234 y[1] (analytic) = 2.0276315616005233306903590501213 y[1] (numeric) = 2.0276315616005235431934014665444 absolute error = 2.125030424164231e-16 relative error = 1.0480357794819613497931865690044e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.403 Order of pole = 3.412 x[1] = 0.235 y[1] (analytic) = 2.027870456726657390928267016708 y[1] (numeric) = 2.0278704567266576046242456850715 absolute error = 2.136959786683635e-16 relative error = 1.0537950191024860321974059070408e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.4 Order of pole = 3.366 x[1] = 0.236 y[1] (analytic) = 2.0281104091767078746617303386537 y[1] (numeric) = 2.0281104091767080895546907612276 absolute error = 2.148929604225739e-16 relative error = 1.0595722967065074766343969427905e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.397 Order of pole = 3.321 x[1] = 0.237 y[1] (analytic) = 2.0283514194582117537552017848307 y[1] (numeric) = 2.0283514194582119698492158276932 absolute error = 2.160940140428625e-16 relative error = 1.0653677265677309073902680268677e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.394 Order of pole = 3.279 x[1] = 0.238 y[1] (analytic) = 2.0285934880811887208787454700745 y[1] (numeric) = 2.0285934880811889381779114989712 absolute error = 2.172991660288967e-16 relative error = 1.0711814235115000775335366648315e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.391 Order of pole = 3.237 x[1] = 0.239 y[1] (analytic) = 2.0288366155581456251780113944973 y[1] (numeric) = 2.0288366155581458436864544117308 absolute error = 2.185084430172335e-16 relative error = 1.0770135029188659556443334207810e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.388 Order of pole = 3.197 x[1] = 0.24 y[1] (analytic) = 2.0290808024040809327194769394176 y[1] (numeric) = 2.0290808024040811524413487217773 absolute error = 2.197218717823597e-16 relative error = 1.0828640807306954512548394839327e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.385 Order of pole = 3.159 x[1] = 0.241 y[1] (analytic) = 2.0293260491364892117957056050425 y[1] (numeric) = 2.0293260491364894327351848427787 absolute error = 2.209394792377362e-16 relative error = 1.0887332734517920011437287252532e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.382 Order of pole = 3.122 x[1] = 0.242 y[1] (analytic) = 2.0295723562753656431759235119699 y[1] (numeric) = 2.0295723562753658653372159488223 absolute error = 2.221612924368524e-16 relative error = 1.0946211981550575128823012845604e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.379 Order of pole = 3.086 x[1] = 0.243 y[1] (analytic) = 2.0298197243432105553877672802453 y[1] (numeric) = 2.0298197243432107787751058545313 absolute error = 2.233873385742860e-16 relative error = 1.1005279724856724189282825694065e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.376 Order of pole = 3.052 x[1] = 0.244 y[1] (analytic) = 2.0300681538650339851166128677155 y[1] (numeric) = 2.0300681538650342097342578544864 absolute error = 2.246176449867709e-16 relative error = 1.1064537146653070685632246084353e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.1MB, time=10.35 Real estimate of pole used Radius of convergence = 1.374 Order of pole = 3.019 x[1] = 0.245 y[1] (analytic) = 2.0303176453683602628094538155793 y[1] (numeric) = 2.030317645368360488661692969852 absolute error = 2.258522391542727e-16 relative error = 1.1123985434963619104875712613570e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.371 Order of pole = 2.986 x[1] = 0.246 y[1] (analytic) = 2.030568199383232623570859135269 y[1] (numeric) = 2.0305681993832328506620078363406 absolute error = 2.270911487010716e-16 relative error = 1.1183625783662353982276844764564e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.369 Order of pole = 2.955 x[1] = 0.247 y[1] (analytic) = 2.0308198164422178434391057991997 y[1] (numeric) = 2.0308198164422180717735071960522 absolute error = 2.283344013968525e-16 relative error = 1.1243459392516185510101568695159e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.366 Order of pole = 2.926 x[1] = 0.248 y[1] (analytic) = 2.0310724970804109011311484907425 y[1] (numeric) = 2.0310724970804111307131736485462 absolute error = 2.295820251578037e-16 relative error = 1.1303487467228229808891718131014e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.364 Order of pole = 2.897 x[1] = 0.249 y[1] (analytic) = 2.0313262418354396653456599484168 y[1] (numeric) = 2.0313262418354398961797079961388 absolute error = 2.308340480477220e-16 relative error = 1.1363711219481314671655348916946e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.362 Order of pole = 2.869 x[1] = 0.25 y[1] (analytic) = 2.0315810512474696077139489283075 y[1] (numeric) = 2.0315810512474698398044472074344 absolute error = 2.320904982791269e-16 relative error = 1.1424131866981842886073256824038e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.359 Order of pole = 2.842 x[1] = 0.251 y[1] (analytic) = 2.0318369258592085414891395298224 y[1] (numeric) = 2.0318369258592087748405437442045 absolute error = 2.333514042143821e-16 relative error = 1.1484750633503923627542413393833e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.357 Order of pole = 2.816 x[1] = 0.252 y[1] (analytic) = 2.0320938662159113860645754059848 y[1] (numeric) = 2.0320938662159116206813697728092 absolute error = 2.346167943668244e-16 relative error = 1.1545568748933775999358221876783e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.355 Order of pole = 2.791 x[1] = 0.253 y[1] (analytic) = 2.0323518728653849574129952335437 y[1] (numeric) = 2.0323518728653851932996926354452 absolute error = 2.358866974019015e-16 relative error = 1.1606587449314477672528148592965e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.353 Order of pole = 2.767 x[1] = 0.254 y[1] (analytic) = 2.0326109463579927845386117734909 y[1] (numeric) = 2.0326109463579930216997539118085 absolute error = 2.371611421383176e-16 relative error = 1.1667807976891003583570666855682e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.35 Order of pole = 2.744 x[1] = 0.255 y[1] (analytic) = 2.0328710872466599520348159324566 y[1] (numeric) = 2.0328710872466601904749734816436 absolute error = 2.384401575491870e-16 relative error = 1.1729231580155563647422558075731e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.1MB, time=10.82 Real estimate of pole used Radius of convergence = 1.348 Order of pole = 2.721 x[1] = 0.256 y[1] (analytic) = 2.0331322960868779688408194634497 y[1] (numeric) = 2.0331322960868782085645922266453 absolute error = 2.397237727631956e-16 relative error = 1.1790859513893233672062776538345e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.346 Order of pole = 2.699 x[1] = 0.257 y[1] (analytic) = 2.0333945734367096632911453442167 y[1] (numeric) = 2.0333945734367099043031624099883 absolute error = 2.410120170657716e-16 relative error = 1.1852693039227942511945251980676e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.344 Order of pole = 2.678 x[1] = 0.258 y[1] (analytic) = 2.0336579198567941045524734669816 y[1] (numeric) = 2.0336579198567943468573933672451 absolute error = 2.423049199002635e-16 relative error = 1.1914733423668721074267521219045e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.342 Order of pole = 2.658 x[1] = 0.259 y[1] (analytic) = 2.033922335910351550542951088533 y[1] (numeric) = 2.0339223359103517941454619576605 absolute error = 2.436025108691275e-16 relative error = 1.1976981941156315547832077848956e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.34 Order of pole = 2.639 x[1] = 0.26 y[1] (analytic) = 2.0341878221631884224296825487606 y[1] (numeric) = 2.0341878221631886673345022838833 absolute error = 2.449048197351227e-16 relative error = 1.2039439872110085221193176611481e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.338 Order of pole = 2.62 x[1] = 0.261 y[1] (analytic) = 2.0344543791837023058007210931906 y[1] (numeric) = 2.0344543791837025520125975157055 absolute error = 2.462118764225149e-16 relative error = 1.2102108503475223301068225830386e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.336 Order of pole = 2.602 x[1] = 0.262 y[1] (analytic) = 2.0347220075428869786084972553844 y[1] (numeric) = 2.0347220075428872261322082736746 absolute error = 2.475237110182902e-16 relative error = 1.2164989128770358754505103548110e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.335 Order of pole = 2.584 x[1] = 0.263 y[1] (analytic) = 2.0349907078143374659822331929929 y[1] (numeric) = 2.0349907078143377148225869663682 absolute error = 2.488403537733753e-16 relative error = 1.2228083048135385827470084791846e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.333 Order of pole = 2.567 x[1] = 0.264 y[1] (analytic) = 2.0352604805742551220075106516918 y[1] (numeric) = 2.0352604805742553721693457555603 absolute error = 2.501618351038685e-16 relative error = 1.2291391568379716897592399558493e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.331 Order of pole = 2.551 x[1] = 0.265 y[1] (analytic) = 2.0355313264014527385717818792799 y[1] (numeric) = 2.0355313264014529900599674715585 absolute error = 2.514881855922786e-16 relative error = 1.2354916003030820040427589030299e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.329 Order of pole = 2.535 x[1] = 0.266 y[1] (analytic) = 2.0358032458773596813752378531476 y[1] (numeric) = 2.0358032458773599341946738419207 absolute error = 2.528194359887731e-16 relative error = 1.2418657672383109135603034376261e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.327 Order of pole = 2.519 x[1] = 0.267 y[1] (analytic) = 2.0360762395860270532070766435962 y[1] (numeric) = 2.0360762395860273073626938560314 absolute error = 2.541556172124352e-16 relative error = 1.2482617903547160943846347006459e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.1MB, time=11.31 Real estimate of pole used Radius of convergence = 1.326 Order of pole = 2.505 x[1] = 0.268 y[1] (analytic) = 2.0363503081141328845878466387303 y[1] (numeric) = 2.0363503081141331400846069912606 absolute error = 2.554967603525303e-16 relative error = 1.2546798030499292535495323397917e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.324 Order of pole = 2.49 x[1] = 0.269 y[1] (analytic) = 2.0366254520509873518791747296974 y[1] (numeric) = 2.0366254520509876087220713994786 absolute error = 2.568428966697812e-16 relative error = 1.2611199394131458757234947957288e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.322 Order of pole = 2.476 x[1] = 0.27 y[1] (analytic) = 2.0369016719885380229628284239075 y[1] (numeric) = 2.0369016719885382811568860215607 absolute error = 2.581940575976532e-16 relative error = 1.2675823342301527648840136829580e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.321 Order of pole = 2.463 x[1] = 0.271 y[1] (analytic) = 2.0371789685213751305917032447482 y[1] (numeric) = 2.0371789685213753901419779883964 absolute error = 2.595502747436482e-16 relative error = 1.2740671229883888568445760238051e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.319 Order of pole = 2.45 x[1] = 0.272 y[1] (analytic) = 2.0374573422467368735159727156 y[1] (numeric) = 2.037457342246737134427552606208 absolute error = 2.609115798906080e-16 relative error = 1.2805744418820401815831311271841e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.318 Order of pole = 2.438 x[1] = 0.273 y[1] (analytic) = 2.0377367937645147454882877402373 y[1] (numeric) = 2.0377367937645150077662927382651 absolute error = 2.622780049980278e-16 relative error = 1.2871044278171737786110167023501e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.316 Order of pole = 2.426 x[1] = 0.274 y[1] (analytic) = 2.0380173236772588922525653077633 y[1] (numeric) = 2.0380173236772591559021475111421 absolute error = 2.636495822033788e-16 relative error = 1.2936572184169050585152616744912e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.314 Order of pole = 2.414 x[1] = 0.275 y[1] (analytic) = 2.0382989325901834966215631950301 y[1] (numeric) = 2.0382989325901837616479070184708 absolute error = 2.650263438234407e-16 relative error = 1.3002329520266024306342336564307e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.313 Order of pole = 2.403 x[1] = 0.276 y[1] (analytic) = 2.0385816211111721917490977402253 y[1] (numeric) = 2.0385816211111724581574200958694 absolute error = 2.664083223556441e-16 relative error = 1.3068317677191290876134689839162e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.311 Order of pole = 2.392 x[1] = 0.277 y[1] (analytic) = 2.0388653898507835027034258453294 y[1] (numeric) = 2.0388653898507837704989763247518 absolute error = 2.677955504794224e-16 relative error = 1.3134538053001198750976592787462e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.31 Order of pole = 2.382 x[1] = 0.278 y[1] (analytic) = 2.0391502394222563164489801600361 y[1] (numeric) = 2.0391502394222565856370412176101 absolute error = 2.691880610575740e-16 relative error = 1.3200992053132970611966670321737e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.1MB, time=11.79 Real estimate of pole used Radius of convergence = 1.308 Order of pole = 2.372 x[1] = 0.279 y[1] (analytic) = 2.0394361704415153803443179332608 y[1] (numeric) = 2.0394361704415156509302050708953 absolute error = 2.705858871376345e-16 relative error = 1.3267681090458234217283308167079e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.307 Order of pole = 2.362 x[1] = 0.28 y[1] (analytic) = 2.0397231835271768292648193185168 y[1] (numeric) = 2.0397231835271771012538812717758 absolute error = 2.719890619532590e-16 relative error = 1.3334606585336930193065466479824e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.305 Order of pole = 2.352 x[1] = 0.281 y[1] (analytic) = 2.0400112793005537414593500144062 y[1] (numeric) = 2.0400112793005540148569689400208 absolute error = 2.733976189256146e-16 relative error = 1.3401769965671600531694832681335e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.304 Order of pole = 2.343 x[1] = 0.282 y[1] (analytic) = 2.0403004583856617232507860396412 y[1] (numeric) = 2.0403004583856619980623777044244 absolute error = 2.748115916647832e-16 relative error = 1.3469172666962061554611005088950e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.303 Order of pole = 2.334 x[1] = 0.283 y[1] (analytic) = 2.0405907214092245226909852119978 y[1] (numeric) = 2.0405907214092247989219991831728 absolute error = 2.762310139711750e-16 relative error = 1.3536816132360479786519206740369e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.301 Order of pole = 2.326 x[1] = 0.284 y[1] (analytic) = 2.0408820690006796722814805512123 y[1] (numeric) = 2.0408820690006799499374003881644 absolute error = 2.776559198369521e-16 relative error = 1.3604701812726820160660680179342e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.3 Order of pole = 2.318 x[1] = 0.285 y[1] (analytic) = 2.0411745017921841608718653861046 y[1] (numeric) = 2.0411745017921844399582088335672 absolute error = 2.790863434474626e-16 relative error = 1.3672831166684684993268591007868e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.298 Order of pole = 2.31 x[1] = 0.286 y[1] (analytic) = 2.0414680204186201348485384453887 y[1] (numeric) = 2.041468020418620415370857628075 absolute error = 2.805223191826863e-16 relative error = 1.3741205660677596425608295722622e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.297 Order of pole = 2.302 x[1] = 0.287 y[1] (analytic) = 2.0417626255176006287271796791835 y[1] (numeric) = 2.0417626255176009106910612978736 absolute error = 2.819638816186901e-16 relative error = 1.3809826769025628031436268740277e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.296 Order of pole = 2.295 x[1] = 0.288 y[1] (analytic) = 2.0420583177294753252630340238399 y[1] (numeric) = 2.0420583177294756086740995529346 absolute error = 2.834110655290947e-16 relative error = 1.3878695973982462783971698967241e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.294 Order of pole = 2.287 x[1] = 0.289 y[1] (analytic) = 2.0423550976973363451937908162702 y[1] (numeric) = 2.0423550976973366300576967028227 absolute error = 2.848639058865525e-16 relative error = 1.3947814765792871242204954201584e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.1MB, time=12.27 Real estimate of pole used Radius of convergence = 1.293 Order of pole = 2.28 x[1] = 0.29 y[1] (analytic) = 2.0426529660670240667305611156225 y[1] (numeric) = 2.042652966067024353052998979859 absolute error = 2.863224378642365e-16 relative error = 1.4017184642750598919468970328261e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.292 Order of pole = 2.274 x[1] = 0.291 y[1] (analytic) = 2.0429519234871329749131738302496 y[1] (numeric) = 2.0429519234871332626998706675893 absolute error = 2.877866968373397e-16 relative error = 1.4086807111256637117086725431542e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.29 Order of pole = 2.267 x[1] = 0.292 y[1] (analytic) = 2.0432519706090175409467343070484 y[1] (numeric) = 2.0432519706090178302034526916357 absolute error = 2.892567183845873e-16 relative error = 1.4156683685877988564310957960296e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.289 Order of pole = 2.261 x[1] = 0.293 y[1] (analytic) = 2.0435531080867981316371159492246 y[1] (numeric) = 2.0435531080867984223696542389827 absolute error = 2.907325382897581e-16 relative error = 1.4226815889406750353783445720308e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.288 Order of pole = 2.255 x[1] = 0.294 y[1] (analytic) = 2.0438553365773669490437865183829 y[1] (numeric) = 2.0438553365773672412579790616024 absolute error = 2.922141925432195e-16 relative error = 1.4297205252919728279276287439188e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.287 Order of pole = 2.249 x[1] = 0.295 y[1] (analytic) = 2.0441586567403940004691060788612 y[1] (numeric) = 2.0441586567403942941708234223343 absolute error = 2.937017173434731e-16 relative error = 1.4367853315838434414228300907220e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.285 Order of pole = 2.244 x[1] = 0.296 y[1] (analytic) = 2.0444630692383330989039730879105 y[1] (numeric) = 2.0444630692383333940991221866218 absolute error = 2.951951490987113e-16 relative error = 1.4438761625989486238717749367498e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.284 Order of pole = 2.238 x[1] = 0.297 y[1] (analytic) = 2.0447685747364278940504389564239 y[1] (numeric) = 2.0447685747364281907449633848113 absolute error = 2.966945244283874e-16 relative error = 1.4509931739665528293737603637249e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.283 Order of pole = 2.233 x[1] = 0.298 y[1] (analytic) = 2.0450751739027179340426595334412 y[1] (numeric) = 2.0450751739027182322425396982368 absolute error = 2.981998801647956e-16 relative error = 1.4581365221686498910696852643445e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.281 Order of pole = 2.228 x[1] = 0.299 y[1] (analytic) = 2.0453828674080447579883044358079 y[1] (numeric) = 2.0453828674080450576995577904729 absolute error = 2.997112533546650e-16 relative error = 1.4653063645461441225126124156314e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.28 Order of pole = 2.223 x[1] = 0.3 y[1] (analytic) = 2.0456916559260580194533019846541 y[1] (numeric) = 2.045691655926058320681983245418 absolute error = 3.012286812607639e-16 relative error = 1.4725028593050676146364907078808e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.279 Order of pole = 2.218 x[1] = 0.301 y[1] (analytic) = 2.0460015401332216410135587554711 y[1] (numeric) = 2.0460015401332219437657601189885 absolute error = 3.027522013635174e-16 relative error = 1.4797261655228482633392080858949e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.2MB, time=12.75 Real estimate of pole used Radius of convergence = 1.278 Order of pole = 2.213 x[1] = 0.302 y[1] (analytic) = 2.0463125207088199999980584315 y[1] (numeric) = 2.0463125207088203042799097941371 absolute error = 3.042818513626371e-16 relative error = 1.4869764431546225195191727275053e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.277 Order of pole = 2.209 x[1] = 0.303 y[1] (analytic) = 2.0466245983349641455485148041096 y[1] (numeric) = 2.0466245983349644513661839828726 absolute error = 3.058176691787630e-16 relative error = 1.4942538530395932116535700159803e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.275 Order of pole = 2.205 x[1] = 0.304 y[1] (analytic) = 2.0469377736965980471215284223117 y[1] (numeric) = 2.0469377736965983544812213774299 absolute error = 3.073596929551182e-16 relative error = 1.5015585569074352323360345820078e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.274 Order of pole = 2.201 x[1] = 0.305 y[1] (analytic) = 2.0472520474815048745599755902724 y[1] (numeric) = 2.0472520474815051834679366494485 absolute error = 3.089079610591761e-16 relative error = 1.5088907173847474797034336950596e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.273 Order of pole = 2.197 x[1] = 0.306 y[1] (analytic) = 2.0475674203803133098611421806083 y[1] (numeric) = 2.0475674203803136203236542649483 absolute error = 3.104625120843400e-16 relative error = 1.5162504980015504224649292434554e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.272 Order of pole = 2.193 x[1] = 0.307 y[1] (analytic) = 2.047883893086503890769903106658 y[1] (numeric) = 2.0478838930865042027932879582944 absolute error = 3.120233848516364e-16 relative error = 1.5236380631978354934052248595726e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.271 Order of pole = 2.189 x[1] = 0.308 y[1] (analytic) = 2.0482014662964153863260413133014 y[1] (numeric) = 2.0482014662964156999166597247226 absolute error = 3.135906184114212e-16 relative error = 1.5310535783301622546995076706078e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.269 Order of pole = 2.185 x[1] = 0.309 y[1] (analytic) = 2.0485201407092512044955978380302 y[1] (numeric) = 2.0485201407092515196598498831276 absolute error = 3.151642520450974e-16 relative error = 1.5384972096782963534459329102411e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.268 Order of pole = 2.182 x[1] = 0.31 y[1] (analytic) = 2.0488399170270858320169468968932 y[1] (numeric) = 2.0488399170270861487612721637418 absolute error = 3.167443252668486e-16 relative error = 1.5459691244519091141817641179342e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.267 Order of pole = 2.178 x[1] = 0.311 y[1] (analytic) = 2.0491607959548713065930970989676 y[1] (numeric) = 2.0491607959548716249239749243513 absolute error = 3.183308778253837e-16 relative error = 1.5534694907973161557435776984713e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.266 Order of pole = 2.175 x[1] = 0.312 y[1] (analytic) = 2.0494827782004437215625318237054 y[1] (numeric) = 2.0494827782004440414864815294016 absolute error = 3.199239497056962e-16 relative error = 1.5609984778042714812973483761931e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.2MB, time=13.23 Real estimate of pole used Radius of convergence = 1.265 Order of pole = 2.172 x[1] = 0.313 y[1] (analytic) = 2.0498058644745297631817185437439 y[1] (numeric) = 2.0498058644745300847052996745806 absolute error = 3.215235811308367e-16 relative error = 1.5685562555128100519153861899911e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.264 Order of pole = 2.169 x[1] = 0.314 y[1] (analytic) = 2.0501300554907532806532384776702 y[1] (numeric) = 2.0501300554907536037830510413691 absolute error = 3.231298125636989e-16 relative error = 1.5761429949201401539690713088872e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.263 Order of pole = 2.166 x[1] = 0.315 y[1] (analytic) = 2.0504553519656418890343144492054 y[1] (numeric) = 2.0504553519656422137769991580254 absolute error = 3.247426847088200e-16 relative error = 1.5837588679875897941176951525934e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.261 Order of pole = 2.163 x[1] = 0.316 y[1] (analytic) = 2.0507817546186336051613462480171 y[1] (numeric) = 2.0507817546186339315235847622118 absolute error = 3.263622385141947e-16 relative error = 1.5914040476476030597331930803696e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.26 Order of pole = 2.16 x[1] = 0.317 y[1] (analytic) = 2.0511092641720835167268991698492 y[1] (numeric) = 2.0511092641720838447154143429522 absolute error = 3.279885151731030e-16 relative error = 1.5990787078107872621050255662917e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.259 Order of pole = 2.158 x[1] = 0.318 y[1] (analytic) = 2.0514378813512704846464327971406 y[1] (numeric) = 2.0514378813512708142679889230934 absolute error = 3.296215561259528e-16 relative error = 1.6067830233730155773886190909205e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.258 Order of pole = 2.155 x[1] = 0.319 y[1] (analytic) = 2.051767606884403878852903503338 y[1] (numeric) = 2.0517676068844042101143065654742 absolute error = 3.312614030621362e-16 relative error = 1.6145171702225796580690031015909e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.257 Order of pole = 2.153 x[1] = 0.32 y[1] (analytic) = 2.0520984415026303476582256625338 y[1] (numeric) = 2.0520984415026306805663235844348 absolute error = 3.329080979219010e-16 relative error = 1.6222813252473993636699286381183e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.256 Order of pole = 2.15 x[1] = 0.321 y[1] (analytic) = 2.052430385940040620821433159017 y[1] (numeric) = 2.0524303859400409553831160572528 absolute error = 3.345616828982358e-16 relative error = 1.6300756663422816450974000884750e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.255 Order of pole = 2.148 x[1] = 0.322 y[1] (analytic) = 2.0527634409336763464642445572365 y[1] (numeric) = 2.0527634409336766826864449960074 absolute error = 3.362222004387709e-16 relative error = 1.6379003724162391378180333909055e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.254 Order of pole = 2.146 x[1] = 0.323 y[1] (analytic) = 2.0530976072235369619756022502914 y[1] (numeric) = 2.0530976072235372998652954979846 absolute error = 3.378896932476932e-16 relative error = 1.6457556233998595215307423156095e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.2MB, time=13.70 Real estimate of pole used Radius of convergence = 1.253 Order of pole = 2.144 x[1] = 0.324 y[1] (analytic) = 2.0534328855525865990476280933954 y[1] (numeric) = 2.0534328855525869386118323810716 absolute error = 3.395642042876762e-16 relative error = 1.6536416002527308371574394697850e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.251 Order of pole = 2.142 x[1] = 0.325 y[1] (analytic) = 2.0537692766667610229863154871676 y[1] (numeric) = 2.0537692766667613642320922689935 absolute error = 3.412457767818259e-16 relative error = 1.6615584849709264833744608764402e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.25 Order of pole = 2.139 x[1] = 0.326 y[1] (analytic) = 2.0541067813149746064411606437227 y[1] (numeric) = 2.0541067813149749493756148593635 absolute error = 3.429344542156408e-16 relative error = 1.6695064605945409512881888457492e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.249 Order of pole = 2.138 x[1] = 0.327 y[1] (analytic) = 2.0544454002491273376988238863168 y[1] (numeric) = 2.0544454002491276823291042253052 absolute error = 3.446302803389884e-16 relative error = 1.6774857112152878099058350396059e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.248 Order of pole = 2.136 x[1] = 0.328 y[1] (analytic) = 2.0547851342241118636868053410416 y[1] (numeric) = 2.0547851342241122100201045091376 absolute error = 3.463332991680960e-16 relative error = 1.6854964219841490519717232169579e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.247 Order of pole = 2.134 x[1] = 0.329 y[1] (analytic) = 2.055125983997820567834018317313 y[1] (numeric) = 2.0551259839978209158775733048712 absolute error = 3.480435549875582e-16 relative error = 1.6935387791190873059826727814558e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.246 Order of pole = 2.132 x[1] = 0.33 y[1] (analytic) = 2.0554679503311526829360480835943 y[1] (numeric) = 2.0554679503311530326971404359542 absolute error = 3.497610923523599e-16 relative error = 1.7016129699128148895216753361001e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.245 Order of pole = 2.13 x[1] = 0.331 y[1] (analytic) = 2.0558110339880214391737936671464 y[1] (numeric) = 2.0558110339880217906597497570617 absolute error = 3.514859560899153e-16 relative error = 1.7097191827406219550557146784472e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.244 Order of pole = 2.129 x[1] = 0.332 y[1] (analytic) = 2.0561552357353612474351057831601 y[1] (numeric) = 2.0561552357353616006532970852826 absolute error = 3.532181913021225e-16 relative error = 1.7178576070682615980356159041004e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.243 Order of pole = 2.127 x[1] = 0.333 y[1] (analytic) = 2.0565005563431349180899550712814 y[1] (numeric) = 2.0565005563431352730477984387165 absolute error = 3.549578433674351e-16 relative error = 1.7260284334598985515002234910541e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.242 Order of pole = 2.126 x[1] = 0.334 y[1] (analytic) = 2.0568469965843409153705915284993 y[1] (numeric) = 2.0568469965843412720755494714489 absolute error = 3.567049579429496e-16 relative error = 1.7342318535861154405529985463143e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.241 Order of pole = 2.124 x[1] = 0.335 y[1] (analytic) = 2.0571945572350206475090884191635 y[1] (numeric) = 2.0571945572350210059686693856732 absolute error = 3.584595809665097e-16 relative error = 1.7424680602319817571928246002578e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.2MB, time=14.20 Real estimate of pole used Radius of convergence = 1.24 Order of pole = 2.123 x[1] = 0.336 y[1] (analytic) = 2.0575432390742657927856020584289 y[1] (numeric) = 2.057543239074266153007360717256 absolute error = 3.602217586588271e-16 relative error = 1.7507372473051834175182541097216e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.238 Order of pole = 2.121 x[1] = 0.337 y[1] (analytic) = 2.0578930428842256616416227478907 y[1] (numeric) = 2.0578930428842260236331602735101 absolute error = 3.619915375256194e-16 relative error = 1.7590396098442156242693960692672e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.237 Order of pole = 2.12 x[1] = 0.338 y[1] (analytic) = 2.0582439694501145950134418351513 y[1] (numeric) = 2.0582439694501149587824061949154 absolute error = 3.637689643597641e-16 relative error = 1.7673753440266339790677696912391e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.236 Order of pole = 2.119 x[1] = 0.339 y[1] (analytic) = 2.0585960195602193990420154164483 y[1] (numeric) = 2.0585960195602197645961016599195 absolute error = 3.655540862434712e-16 relative error = 1.7757446471773757961912267907692e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.235 Order of pole = 2.117 x[1] = 0.34 y[1] (analytic) = 2.0589491940059068163163666475347 y[1] (numeric) = 2.0589491940059071836633171980068 absolute error = 3.673469505504721e-16 relative error = 1.7841477177771402392116654003367e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.234 Order of pole = 2.116 x[1] = 0.341 y[1] (analytic) = 2.059303493581631033808636017342 y[1] (numeric) = 2.0593034935816314029562409655678 absolute error = 3.691476049482258e-16 relative error = 1.7925847554708319408876460442347e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.233 Order of pole = 2.115 x[1] = 0.342 y[1] (analytic) = 2.059658919084941227659862316538 y[1] (numeric) = 2.0596589190849415986159597166814 absolute error = 3.709560974001434e-16 relative error = 1.8010559610760727590071845195736e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.232 Order of pole = 2.114 x[1] = 0.343 y[1] (analytic) = 2.0600154713164891449765564442427 y[1] (numeric) = 2.0600154713164895177490326120729 absolute error = 3.727724761678302e-16 relative error = 1.8095615365917780607297218227102e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.231 Order of pole = 2.113 x[1] = 0.344 y[1] (analytic) = 2.0603731510800367227991156865652 y[1] (numeric) = 2.0603731510800370973959054999104 absolute error = 3.745967898133452e-16 relative error = 1.8181016852067963583167943110803e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.23 Order of pole = 2.112 x[1] = 0.345 y[1] (analytic) = 2.0607319591824637444041177163211 y[1] (numeric) = 2.0607319591824641208332049178007 absolute error = 3.764290872014796e-16 relative error = 1.8266766113086198541773593667622e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.229 Order of pole = 2.111 x[1] = 0.346 y[1] (analytic) = 2.0610918964337755331035313507095 y[1] (numeric) = 2.0610918964337759113729488527621 absolute error = 3.782694175020526e-16 relative error = 1.8352865204921574303137181884976e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.2MB, time=14.68 Real estimate of pole used Radius of convergence = 1.228 Order of pole = 2.11 x[1] = 0.347 y[1] (analytic) = 2.0614529636471106837048851096489 y[1] (numeric) = 2.0614529636471110638227153018751 absolute error = 3.801178301922262e-16 relative error = 1.8439316195685781208658707120949e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.227 Order of pole = 2.109 x[1] = 0.348 y[1] (analytic) = 2.0618151616387488317974448890659 y[1] (numeric) = 2.0618151616387492137718199479046 absolute error = 3.819743750588387e-16 relative error = 1.8526121165742233936189506071875e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.226 Order of pole = 2.108 x[1] = 0.349 y[1] (analytic) = 2.0621784912281184610304686482384 y[1] (numeric) = 2.0621784912281188448695708489952 absolute error = 3.838391022007568e-16 relative error = 1.8613282207795875370727936256091e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.225 Order of pole = 2.107 x[1] = 0.35 y[1] (analytic) = 2.0625429532378047485506289562402 y[1] (numeric) = 2.0625429532378051342626909874864 absolute error = 3.857120620312462e-16 relative error = 1.8700801426983654492145215883308e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.224 Order of pole = 2.106 x[1] = 0.351 y[1] (analytic) = 2.0629085484935574487667235979281 y[1] (numeric) = 2.0629085484935578363600288782901 absolute error = 3.875933052803620e-16 relative error = 1.8788680940965739102209094196792e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.223 Order of pole = 2.105 x[1] = 0.352 y[1] (analytic) = 2.0632752778242988156108302534566 y[1] (numeric) = 2.0632752778242992050937132508149 absolute error = 3.894828829973583e-16 relative error = 1.8876922880017432025685367631438e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.222 Order of pole = 2.104 x[1] = 0.353 y[1] (analytic) = 2.0636431420621315634661035860873 y[1] (numeric) = 2.0636431420621319548469501392037 absolute error = 3.913808465531164e-16 relative error = 1.8965529387121759449636371168045e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.221 Order of pole = 2.104 x[1] = 0.354 y[1] (analytic) = 2.0640121420423468669324619505675 y[1] (numeric) = 2.0640121420423472602197095931618 absolute error = 3.932872476425943e-16 relative error = 1.9054502618062859977675772902801e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.22 Order of pole = 2.103 x[1] = 0.355 y[1] (analytic) = 2.0643822786034323996024664184822 y[1] (numeric) = 2.0643822786034327948046047057763 absolute error = 3.952021382872941e-16 relative error = 1.9143844741520007289079975098319e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.219 Order of pole = 2.102 x[1] = 0.356 y[1] (analytic) = 2.0647535525870804120207569580081 y[1] (numeric) = 2.0647535525870808091463277957591 absolute error = 3.971255708377510e-16 relative error = 1.9233557939162443383195309136428e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.218 Order of pole = 2.102 x[1] = 0.357 y[1] (analytic) = 2.0651259648381958490014794541382 y[1] (numeric) = 2.0651259648381962480590774301795 absolute error = 3.990575979760413e-16 relative error = 1.9323644405744894054086847752808e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.2MB, time=15.16 Real estimate of pole used Radius of convergence = 1.217 Order of pole = 2.101 x[1] = 0.358 y[1] (analytic) = 2.0654995162049045064792128627881 y[1] (numeric) = 2.0654995162049049074774855811 absolute error = 4.009982727183119e-16 relative error = 1.9414106349203885322905795782600e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.215 Order of pole = 2.1 x[1] = 0.359 y[1] (analytic) = 2.0658742075385612280699882097805 y[1] (numeric) = 2.0658742075385616310176366271098 absolute error = 4.029476484173293e-16 relative error = 1.9504945990754761542835953866423e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.214 Order of pole = 2.1 x[1] = 0.36 y[1] (analytic) = 2.0662500396937581415200804254628 y[1] (numeric) = 2.0662500396937585464258591905126 absolute error = 4.049057787650498e-16 relative error = 1.9596165564989485087536929027322e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.213 Order of pole = 2.099 x[1] = 0.361 y[1] (analytic) = 2.0666270135283329352213502000148 y[1] (numeric) = 2.0666270135283333420940679952258 absolute error = 4.068727177952110e-16 relative error = 1.9687767319975219981256732303204e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.212 Order of pole = 2.098 x[1] = 0.362 y[1] (analytic) = 2.0670051299033771749730162061359 y[1] (numeric) = 2.0670051299033775838215360920798 absolute error = 4.088485198859439e-16 relative error = 1.9779753517353663105414803805997e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.211 Order of pole = 2.098 x[1] = 0.363 y[1] (analytic) = 2.067384389683244661170848217986 y[1] (numeric) = 2.0673843896832450720040879803924 absolute error = 4.108332397624064e-16 relative error = 1.9872126432441159208599636661713e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.21 Order of pole = 2.097 x[1] = 0.364 y[1] (analytic) = 2.0677647937355598266058889116417 y[1] (numeric) = 2.0677647937355602394328214110804 absolute error = 4.128269324994387e-16 relative error = 1.9964888354329621369021622994189e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.209 Order of pole = 2.097 x[1] = 0.365 y[1] (analytic) = 2.0681463429312261750559365170184 y[1] (numeric) = 2.0681463429312265898855900412583 absolute error = 4.148296535242399e-16 relative error = 2.0058041585988220486752807774245e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.208 Order of pole = 2.096 x[1] = 0.366 y[1] (analytic) = 2.068529038144434760854152058724 y[1] (numeric) = 2.068529038144435177695610677791 absolute error = 4.168414586190670e-16 relative error = 2.0151588444365899272527745501281e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.207 Order of pole = 2.096 x[1] = 0.367 y[1] (analytic) = 2.0689128802526727096202937286401 y[1] (numeric) = 2.0689128802526731284826976525956 absolute error = 4.188624039239555e-16 relative error = 2.0245531260494669431758987899358e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.206 Order of pole = 2.095 x[1] = 0.368 y[1] (analytic) = 2.0692978701367317803412270315954 y[1] (numeric) = 2.0692978701367322012337729710587 absolute error = 4.208925459394633e-16 relative error = 2.0339872379593771600231142004253e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.205 Order of pole = 2.095 x[1] = 0.369 y[1] (analytic) = 2.0696840086807169689885127931935 y[1] (numeric) = 2.069684008680717391920454322629 absolute error = 4.229319415294355e-16 relative error = 2.0434614161174579354316342333627e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.2MB, time=15.64 Real estimate of pole used Radius of convergence = 1.204 Order of pole = 2.094 x[1] = 0.37 y[1] (analytic) = 2.0700712967720551538620359720183 y[1] (numeric) = 2.0700712967720555788426838958121 absolute error = 4.249806479237938e-16 relative error = 2.0529758979146423453718858528700e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.203 Order of pole = 2.094 x[1] = 0.371 y[1] (analytic) = 2.0704597353015037828498065338844 y[1] (numeric) = 2.070459735301504209888529255232 absolute error = 4.270387227213476e-16 relative error = 2.0625309221923193424064900894559e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.202 Order of pole = 2.093 x[1] = 0.372 y[1] (analytic) = 2.0708493251631596027952394807824 y[1] (numeric) = 2.0708493251631600319014633734111 absolute error = 4.291062238926287e-16 relative error = 2.0721267292530805571350144630814e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.201 Order of pole = 2.093 x[1] = 0.373 y[1] (analytic) = 2.0712400672544674311644045394511 y[1] (numeric) = 2.0712400672544678623476143222003 absolute error = 4.311832097827492e-16 relative error = 2.0817635608715515324054190291470e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.2 Order of pole = 2.093 x[1] = 0.374 y[1] (analytic) = 2.071631962476228970206927062298 y[1] (numeric) = 2.0716319624762294034766661765814 absolute error = 4.332697391142834e-16 relative error = 2.0914416603053109738924446999041e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.199 Order of pole = 2.092 x[1] = 0.375 y[1] (analytic) = 2.0720250117326116638054204353949 y[1] (numeric) = 2.0720250117326120991712914255678 absolute error = 4.353658709901729e-16 relative error = 2.1011612723058938714579372513927e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.198 Order of pole = 2.092 x[1] = 0.376 y[1] (analytic) = 2.0724192159311575972095367836735 y[1] (numeric) = 2.0724192159311580346812016803301 absolute error = 4.374716648966566e-16 relative error = 2.1109226431298864133181521708998e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.197 Order of pole = 2.092 x[1] = 0.377 y[1] (analytic) = 2.0728145759827924398519370719223 y[1] (numeric) = 2.0728145759827928794391177781462 absolute error = 4.395871807062239e-16 relative error = 2.1207260205501041983005517302247e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.196 Order of pole = 2.091 x[1] = 0.378 y[1] (analytic) = 2.0732110928018344314447038818929 y[1] (numeric) = 2.0732110928018348731571825624863 absolute error = 4.417124786805934e-16 relative error = 2.1305716538668645562453223763012e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.195 Order of pole = 2.091 x[1] = 0.379 y[1] (analytic) = 2.0736087673060034115559502614436 y[1] (numeric) = 2.0736087673060038554035697351592 absolute error = 4.438476194737156e-16 relative error = 2.1404597939193454426412222309173e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.194 Order of pole = 2.091 x[1] = 0.38 y[1] (analytic) = 2.0740076004164298928676161523367 y[1] (numeric) = 2.0740076004164303388602802871376 absolute error = 4.459926641348009e-16 relative error = 2.1503906930970368835919801286554e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.2MB, time=16.12 Real estimate of pole used Radius of convergence = 1.193 Order of pole = 2.09 x[1] = 0.381 y[1] (analytic) = 2.074407593057664178316690070747 y[1] (numeric) = 2.0744075930576646264643641821195 absolute error = 4.481476741113725e-16 relative error = 2.1603646053512827409747906084665e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.192 Order of pole = 2.09 x[1] = 0.382 y[1] (analytic) = 2.0748087461576855223233480009184 y[1] (numeric) = 2.0748087461576859726360592532639 absolute error = 4.503127112523455e-16 relative error = 2.1703817862069187626226060853054e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.191 Order of pole = 2.09 x[1] = 0.383 y[1] (analytic) = 2.0752110606479113363107639304316 y[1] (numeric) = 2.075211060647911788798601741562 absolute error = 4.524878378111304e-16 relative error = 2.1804424927739979328936430081011e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.19 Order of pole = 2.089 x[1] = 0.384 y[1] (analytic) = 2.0756145374632064387226171684409 y[1] (numeric) = 2.0756145374632068933957336172045 absolute error = 4.546731164487636e-16 relative error = 2.1905469837596153494265770152490e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.189 Order of pole = 2.089 x[1] = 0.385 y[1] (analytic) = 2.0760191775418923497456006097662 y[1] (numeric) = 2.0760191775418928066142108468294 absolute error = 4.568686102370632e-16 relative error = 2.2006955194798241181538290430122e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.188 Order of pole = 2.089 x[1] = 0.386 y[1] (analytic) = 2.0764249818257566309455215021616 y[1] (numeric) = 2.0764249818257570900199041639737 absolute error = 4.590743826618121e-16 relative error = 2.2108883618716515888922461419730e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.187 Order of pole = 2.089 x[1] = 0.387 y[1] (analytic) = 2.0768319512600622700268821062616 y[1] (numeric) = 2.0768319512600627313173797322284 absolute error = 4.612904976259668e-16 relative error = 2.2211257745052079031053769486262e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.186 Order of pole = 2.088 x[1] = 0.388 y[1] (analytic) = 2.0772400867935571109271319729777 y[1] (numeric) = 2.0772400867935575744441514258713 absolute error = 4.635170194528936e-16 relative error = 2.2314080225958947223441832634481e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.185 Order of pole = 2.088 x[1] = 0.389 y[1] (analytic) = 2.0776493893784833294580964674126 y[1] (numeric) = 2.0776493893784837952121093570444 absolute error = 4.657540128896318e-16 relative error = 2.2417353730167118838435771601289e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.184 Order of pole = 2.088 x[1] = 0.39 y[1] (analytic) = 2.0780598599705869547084077081218 y[1] (numeric) = 2.0780598599705874227099508183063 absolute error = 4.680015431101845e-16 relative error = 2.2521080943106645433108559158492e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.183 Order of pole = 2.088 x[1] = 0.391 y[1] (analytic) = 2.078471499529127436422094332818 y[1] (numeric) = 2.0784714995291279066817700516546 absolute error = 4.702596757188366e-16 relative error = 2.2625264567032685475026736969537e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.2MB, time=16.61 Real estimate of pole used Radius of convergence = 1.182 Order of pole = 2.088 x[1] = 0.392 y[1] (analytic) = 2.0788843090168872585698255139545 y[1] (numeric) = 2.0788843090168877310983022674554 absolute error = 4.725284767535009e-16 relative error = 2.2729907321151580339240293570512e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.181 Order of pole = 2.087 x[1] = 0.393 y[1] (analytic) = 2.0792982894001815993306524981965 y[1] (numeric) = 2.0792982894001820741386651872893 absolute error = 4.748080126890928e-16 relative error = 2.2835011941747973227143240088564e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.18 Order of pole = 2.087 x[1] = 0.394 y[1] (analytic) = 2.0797134416488680377034477013184 y[1] (numeric) = 2.0797134416488685148017981422509 absolute error = 4.770983504409325e-16 relative error = 2.2940581182312914668735836111540e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.179 Order of pole = 2.087 x[1] = 0.395 y[1] (analytic) = 2.0801297667363563069686071238421 y[1] (numeric) = 2.0801297667363567863681644920189 absolute error = 4.793995573681768e-16 relative error = 2.3046617813673052173710780318131e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.178 Order of pole = 2.087 x[1] = 0.396 y[1] (analytic) = 2.0805472656396180952219566326578 y[1] (numeric) = 2.0805472656396185769336579099374 absolute error = 4.817117012772796e-16 relative error = 2.3153124624120857225266274676404e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.177 Order of pole = 2.087 x[1] = 0.397 y[1] (analytic) = 2.0809659393391968932041865504051 y[1] (numeric) = 2.0809659393391973772390369758862 absolute error = 4.840348504254811e-16 relative error = 2.3260104419545886111346422415715e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.176 Order of pole = 2.086 x[1] = 0.398 y[1] (analytic) = 2.0813857888192178896505320786134 y[1] (numeric) = 2.0813857888192183760196056029408 absolute error = 4.863690735243274e-16 relative error = 2.3367560023567152746990496642430e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.175 Order of pole = 2.086 x[1] = 0.399 y[1] (analytic) = 2.0818068150673979143868194241832 y[1] (numeric) = 2.0818068150673984031012591674024 absolute error = 4.887144397432192e-16 relative error = 2.3475494277666547386379634240785e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.174 Order of pole = 2.086 x[1] = 0.4 y[1] (analytic) = 2.0822290190750554293994091739943 y[1] (numeric) = 2.0822290190750559204704278869853 absolute error = 4.910710187129910e-16 relative error = 2.3583910041323364874750810056039e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.173 Order of pole = 2.086 x[1] = 0.401 y[1] (analytic) = 2.082652401837120568107989542161 y[1] (numeric) = 2.0826524018371210615468700716812 absolute error = 4.934388805295202e-16 relative error = 2.3692810192149909932028404067508e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.172 Order of pole = 2.086 x[1] = 0.402 y[1] (analytic) = 2.0830769643521452230716026722043 y[1] (numeric) = 2.0830769643521457188896984295721 absolute error = 4.958180957573678e-16 relative error = 2.3802197626028257402105238651411e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.171 Order of pole = 2.086 x[1] = 0.403 y[1] (analytic) = 2.0835027076223131823597272863241 y[1] (numeric) = 2.083502707622313680568462719773 absolute error = 4.982087354334489e-16 relative error = 2.3912075257248077263878810276903e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.2MB, time=17.09 Real estimate of pole used Radius of convergence = 1.17 Order of pole = 2.086 x[1] = 0.404 y[1] (analytic) = 2.0839296326534503148216907107722 y[1] (numeric) = 2.0839296326534508154325617815069 absolute error = 5.006108710707347e-16 relative error = 2.4022446018645602274505668431062e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.169 Order of pole = 2.085 x[1] = 0.405 y[1] (analytic) = 2.0843577404550348044891427454574 y[1] (numeric) = 2.0843577404550353075137174074443 absolute error = 5.030245746619869e-16 relative error = 2.4133312861743777582192347729854e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.168 Order of pole = 2.085 x[1] = 0.406 y[1] (analytic) = 2.084787032040207434347793063385 y[1] (numeric) = 2.0847870320402079397977117469078 absolute error = 5.054499186835228e-16 relative error = 2.4244678756893506842668652585397e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.167 Order of pole = 2.085 x[1] = 0.407 y[1] (analytic) = 2.0852175084257819197160928980269 y[1] (numeric) = 2.0852175084257824276030689970405 absolute error = 5.078869760990136e-16 relative error = 2.4356546693416110906365281451087e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.166 Order of pole = 2.085 x[1] = 0.408 y[1] (analytic) = 2.0856491706322552914700307815789 y[1] (numeric) = 2.0856491706322558018058511448926 absolute error = 5.103358203633137e-16 relative error = 2.4468919679746889576795342853763e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.165 Order of pole = 2.085 x[1] = 0.409 y[1] (analytic) = 2.0860820196838183293547111122715 y[1] (numeric) = 2.0860820196838188421512365385961 absolute error = 5.127965254263246e-16 relative error = 2.4581800743579955128789574079803e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.164 Order of pole = 2.085 x[1] = 0.41 y[1] (analytic) = 2.0865160566083660456248934331431 y[1] (numeric) = 2.0865160566083665608940591700332 absolute error = 5.152691657368901e-16 relative error = 2.4695192932014175274578725029878e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.163 Order of pole = 2.085 x[1] = 0.411 y[1] (analytic) = 2.086951282437508219258189577267 y[1] (numeric) = 2.086951282437508737012005823993 absolute error = 5.177538162467260e-16 relative error = 2.4809099311700374967707747488560e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.162 Order of pole = 2.085 x[1] = 0.412 y[1] (analytic) = 2.0873876982065799809861453553894 y[1] (numeric) = 2.0873876982065805012366977697729 absolute error = 5.202505524143835e-16 relative error = 2.4923522968989754532393694059551e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.161 Order of pole = 2.084 x[1] = 0.413 y[1] (analytic) = 2.0878253049546524493899733119598 y[1] (numeric) = 2.0878253049546529721494235212052 absolute error = 5.227594502092454e-16 relative error = 2.5038467010083476859639482181116e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.16 Order of pole = 2.084 x[1] = 0.414 y[1] (analytic) = 2.088264103724543418309253336022 y[1] (numeric) = 2.0882641037245439435898394515804 absolute error = 5.252805861155584e-16 relative error = 2.5153934561183577587510147605191e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.2MB, time=17.57 Real estimate of pole used Radius of convergence = 1.159 Order of pole = 2.084 x[1] = 0.415 y[1] (analytic) = 2.0887040955628280958134786664709 y[1] (numeric) = 2.0887040955628286236275158029698 absolute error = 5.278140371364989e-16 relative error = 2.5269928768645069425117037407727e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.158 Order of pole = 2.084 x[1] = 0.416 y[1] (analytic) = 2.0891452815198498949878961595599 y[1] (numeric) = 2.0891452815198504253477769578336 absolute error = 5.303598807982737e-16 relative error = 2.5386452799129303434143242378153e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.157 Order of pole = 2.084 x[1] = 0.417 y[1] (analytic) = 2.0895876626497312767866716737703 y[1] (numeric) = 2.0895876626497318097048668280276 absolute error = 5.329181951542573e-16 relative error = 2.5503509839758664304973369782662e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.156 Order of pole = 2.084 x[1] = 0.418 y[1] (analytic) = 2.0900312400103846452080041574658 y[1] (numeric) = 2.090031240010385180697062946629 absolute error = 5.354890587891632e-16 relative error = 2.5621103098272470766746407252034e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.155 Order of pole = 2.084 x[1] = 0.419 y[1] (analytic) = 2.0904760146635232950474155830821 y[1] (numeric) = 2.0904760146635238331199664063344 absolute error = 5.380725508232523e-16 relative error = 2.5739235803184225125421023165618e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.154 Order of pole = 2.084 x[1] = 0.42 y[1] (analytic) = 2.0909219876746724124870583436505 y[1] (numeric) = 2.0909219876746729531558092602283 absolute error = 5.406687509165778e-16 relative error = 2.5857911203940178695036862862572e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.153 Order of pole = 2.084 x[1] = 0.421 y[1] (analytic) = 2.0913691601131801287805071996326 y[1] (numeric) = 2.0913691601131806720582464728983 absolute error = 5.432777392732657e-16 relative error = 2.5977132571079165569342598484713e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.152 Order of pole = 2.084 x[1] = 0.422 y[1] (analytic) = 2.0918175330522286272941394235245 y[1] (numeric) = 2.0918175330522291731937360693585 absolute error = 5.458995966458340e-16 relative error = 2.6096903196393848454001035415377e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.151 Order of pole = 2.084 x[1] = 0.423 y[1] (analytic) = 2.0922671075688453041678545244069 y[1] (numeric) = 2.0922671075688458527022588639545 absolute error = 5.485344043395476e-16 relative error = 2.6217226393093228453638055923645e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.15 Order of pole = 2.084 x[1] = 0.424 y[1] (analytic) = 2.0927178847439139828595439332407 y[1] (numeric) = 2.0927178847439145340417881500531 absolute error = 5.511822442168124e-16 relative error = 2.6338105495966581532554369187528e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.149 Order of pole = 2.084 x[1] = 0.425 y[1] (analytic) = 2.0931698656621861828393913817083 y[1] (numeric) = 2.0931698656621867366825900833149 absolute error = 5.538431987016066e-16 relative error = 2.6459543861548721298187427590954e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.2MB, time=18.05 Real estimate of pole used Radius of convergence = 1.148 Order of pole = 2.083 x[1] = 0.426 y[1] (analytic) = 2.0936230514122924427017665029932 y[1] (numeric) = 2.0936230514122929992191172869443 absolute error = 5.565173507839511e-16 relative error = 2.6581544868286674178133836834921e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.147 Order of pole = 2.083 x[1] = 0.427 y[1] (analytic) = 2.0940774430867536979641675131001 y[1] (numeric) = 2.0940774430867542571689515375189 absolute error = 5.592047840244188e-16 relative error = 2.6704111916707752598802340099135e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.146 Order of pole = 2.083 x[1] = 0.428 y[1] (analytic) = 2.0945330417819927138243737879406 y[1] (numeric) = 2.0945330417819932757299563466231 absolute error = 5.619055825586825e-16 relative error = 2.6827248429589006992468362087328e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.145 Order of pole = 2.083 x[1] = 0.429 y[1] (analytic) = 2.0949898485983455731486858270537 y[1] (numeric) = 2.0949898485983461377685169291568 absolute error = 5.646198311021031e-16 relative error = 2.6950957852128132926905867076210e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.144 Order of pole = 2.083 x[1] = 0.43 y[1] (analytic) = 2.0954478646400732199658585829015 y[1] (numeric) = 2.0954478646400737873134735372594 absolute error = 5.673476149543579e-16 relative error = 2.7075243652115818813915408026306e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.143 Order of pole = 2.083 x[1] = 0.431 y[1] (analytic) = 2.0959070910153730587430745294087 y[1] (numeric) = 2.0959070910153736288320945335175 absolute error = 5.700890200041088e-16 relative error = 2.7200109320109519645498402178569e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.142 Order of pole = 2.083 x[1] = 0.432 y[1] (analytic) = 2.0963675288363906097220552398346 y[1] (numeric) = 2.0963675288363911825661879735465 absolute error = 5.728441327337119e-16 relative error = 2.7325558369608723291695324443207e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.141 Order of pole = 2.083 x[1] = 0.433 y[1] (analytic) = 2.0968291792192312205951747380674 y[1] (numeric) = 2.096829179219231796208214962035 absolute error = 5.756130402239676e-16 relative error = 2.7451594337231661285540092154808e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.14 Order of pole = 2.083 x[1] = 0.434 y[1] (analytic) = 2.0972920432839718348032145757135 y[1] (numeric) = 2.0972920432839724131990447346266 absolute error = 5.783958301589131e-16 relative error = 2.7578220782893549576907241427421e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.139 Order of pole = 2.083 x[1] = 0.435 y[1] (analytic) = 2.0977561221546728167381895674904 y[1] (numeric) = 2.0977561221546733979307803981467 absolute error = 5.811925908306563e-16 relative error = 2.7705441289986306309396282471534e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.138 Order of pole = 2.083 x[1] = 0.436 y[1] (analytic) = 2.098221416959389834136474487828 y[1] (numeric) = 2.0982214169593904181398856320805 absolute error = 5.840034111442525e-16 relative error = 2.7833259465559808116008247408130e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.137 Order of pole = 2.083 x[1] = 0.437 memory used=148.7MB, alloc=4.2MB, time=18.53 y[1] (analytic) = 2.0986879288301857979492758915178 y[1] (numeric) = 2.0986879288301863847776565141417 absolute error = 5.868283806226239e-16 relative error = 2.7961678940504679577484880495369e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.136 Order of pole = 2.083 x[1] = 0.438 y[1] (analytic) = 2.0991556589031428599793196708782 y[1] (numeric) = 2.0991556589031434496469090824003 absolute error = 5.896675894115221e-16 relative error = 2.8090703369736619989057217674564e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.135 Order of pole = 2.083 x[1] = 0.439 y[1] (analytic) = 2.0996246083183744685744641022415 y[1] (numeric) = 2.099624608318375061095592386776 absolute error = 5.925211282845345e-16 relative error = 2.8220336432382304877876386309867e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.134 Order of pole = 2.083 x[1] = 0.44 y[1] (analytic) = 2.1000947782200374826708000675464 y[1] (numeric) = 2.1000947782200380780598887156814 absolute error = 5.953890886481350e-16 relative error = 2.8350581831966875802326998278544e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.133 Order of pole = 2.083 x[1] = 0.441 y[1] (analytic) = 2.1005661697563443444796649652401 y[1] (numeric) = 2.1005661697563449427512275120188 absolute error = 5.982715625467787e-16 relative error = 2.8481443296602998579473007356676e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.132 Order of pole = 2.083 x[1] = 0.442 y[1] (analytic) = 2.1010387840795753111148746522805 y[1] (numeric) = 2.1010387840795759122835173203224 absolute error = 6.011686426680419e-16 relative error = 2.8612924579181546238751004689130e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.131 Order of pole = 2.083 x[1] = 0.443 y[1] (analytic) = 2.1015126223460907454583686904158 y[1] (numeric) = 2.1015126223460913495387910382237 absolute error = 6.040804223478079e-16 relative error = 2.8745029457563924794170916892278e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.13 Order of pole = 2.083 x[1] = 0.444 y[1] (analytic) = 2.1019876857163434665643683106615 y[1] (numeric) = 2.1019876857163440735713638861593 absolute error = 6.070069955754978e-16 relative error = 2.8877761734775998010802187571043e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.129 Order of pole = 2.083 x[1] = 0.445 y[1] (analytic) = 2.1024639753548911599040639664818 y[1] (numeric) = 2.1024639753548917698525209658302 absolute error = 6.099484569993484e-16 relative error = 2.9011125239203705316157406134581e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.128 Order of pole = 2.083 x[1] = 0.446 y[1] (analytic) = 2.1029414924304088477547802260496 y[1] (numeric) = 2.1029414924304094606596821577859 absolute error = 6.129049019317363e-16 relative error = 2.9145123824790324141315484311563e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.127 Order of pole = 2.083 x[1] = 0.447 y[1] (analytic) = 2.103420238115701420039510165481 y[1] (numeric) = 2.1034202381157020359159365200306 absolute error = 6.158764263545496e-16 relative error = 2.9279761371235437371944723356191e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.126 Order of pole = 2.082 x[1] = 0.448 y[1] (analytic) = 2.1039002135877162259246694774701 y[1] (numeric) = 2.1039002135877168447877964020774 absolute error = 6.188631269246073e-16 relative error = 2.9415041784195604650179339687652e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.2MB, time=19.00 Real estimate of pole used Radius of convergence = 1.125 Order of pole = 2.082 x[1] = 0.449 y[1] (analytic) = 2.1043814200275557264858923135875 y[1] (numeric) = 2.104381420027556348350993292714 absolute error = 6.218651009791265e-16 relative error = 2.9550968995486736231004778385572e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.124 Order of pole = 2.082 x[1] = 0.45 y[1] (analytic) = 2.1048638586204902087536765449528 y[1] (numeric) = 2.1048638586204908336361230861913 absolute error = 6.248824465412385e-16 relative error = 2.9687546963288215568460161633201e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.123 Order of pole = 2.082 x[1] = 0.451 y[1] (analytic) = 2.1053475305559705614526857673214 y[1] (numeric) = 2.1053475305559711893679480928755 absolute error = 6.279152623255541e-16 relative error = 2.9824779672348778683755645822692e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.122 Order of pole = 2.082 x[1] = 0.452 y[1] (analytic) = 2.1058324370276411127505291061225 y[1] (numeric) = 2.1058324370276417437141768499007 absolute error = 6.309636477437782e-16 relative error = 2.9962671134194148814354461251700e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.121 Order of pole = 2.082 x[1] = 0.453 y[1] (analytic) = 2.1063185792333525303338678089308 y[1] (numeric) = 2.1063185792333531643615707193059 absolute error = 6.340277029103751e-16 relative error = 3.0101225387336486523824642550500e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.12 Order of pole = 2.082 x[1] = 0.454 y[1] (analytic) = 2.1068059583751747841317398625602 y[1] (numeric) = 2.1068059583751754212392685108433 absolute error = 6.371075286482831e-16 relative error = 3.0240446497485582397075420562165e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.119 Order of pole = 2.082 x[1] = 0.455 y[1] (analytic) = 2.1072945756594101720080505557603 y[1] (numeric) = 2.1072945756594108122112770504424 absolute error = 6.402032264946821e-16 relative error = 3.0380338557761961554882935332599e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.118 Order of pole = 2.082 x[1] = 0.456 y[1] (analytic) = 2.1077844322966064087472481437615 y[1] (numeric) = 2.1077844322966070520621468505724 absolute error = 6.433148987068109e-16 relative error = 3.0520905688911736763362921644170e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.117 Order of pole = 2.082 x[1] = 0.457 y[1] (analytic) = 2.1082755295015697786592896760549 y[1] (numeric) = 2.1082755295015704251019379438926 absolute error = 6.464426482678377e-16 relative error = 3.0662152039523369712421860559501e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.116 Order of pole = 2.082 x[1] = 0.458 y[1] (analytic) = 2.1087678684933783521321027433093 y[1] (numeric) = 2.1087678684933790017186816360925 absolute error = 6.495865788927832e-16 relative error = 3.0804081786246305271073713994101e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.115 Order of pole = 2.082 x[1] = 0.459 y[1] (analytic) = 2.1092614504953952664618645037582 y[1] (numeric) = 2.1092614504953959192086595382545 absolute error = 6.527467950344963e-16 relative error = 3.0946699134011471994802368073241e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.2MB, time=19.49 Real estimate of pole used Radius of convergence = 1.114 Order of pole = 2.082 x[1] = 0.46 y[1] (analytic) = 2.109756276735282071293549985367 y[1] (numeric) = 2.1097562767352827272169518750507 absolute error = 6.559234018896837e-16 relative error = 3.1090008316253703747101109351607e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.113 Order of pole = 2.082 x[1] = 0.461 y[1] (analytic) = 2.1102523484450121390063474503436 y[1] (numeric) = 2.1102523484450127981228528553378 absolute error = 6.591165054049942e-16 relative error = 3.1234013595136113456074278849441e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.112 Order of pole = 2.082 x[1] = 0.462 y[1] (analytic) = 2.1107496668608841403806996769025 y[1] (numeric) = 2.1107496668608848027069119600595 absolute error = 6.623262122831570e-16 relative error = 3.1378719261776378858409985852671e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.111 Order of pole = 2.082 x[1] = 0.463 y[1] (analytic) = 2.1112482332235355858859064845699 y[1] (numeric) = 2.1112482332235362514385364737453 absolute error = 6.655526299891754e-16 relative error = 3.1524129636474999580102569949960e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.11 Order of pole = 2.082 x[1] = 0.464 y[1] (analytic) = 2.1117480487779564329294158297936 y[1] (numeric) = 2.1117480487779571017252825863708 absolute error = 6.687958667565772e-16 relative error = 3.1670249068945580009996033274453e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.109 Order of pole = 2.082 x[1] = 0.465 y[1] (analytic) = 2.1122491147735027594111384553856 y[1] (numeric) = 2.1122491147735034314671700491057 absolute error = 6.720560315937201e-16 relative error = 3.1817081938547050243489207240476e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.108 Order of pole = 2.082 x[1] = 0.466 y[1] (analytic) = 2.1127514324639105039283445187234 y[1] (numeric) = 2.112751432463911179261578808879 absolute error = 6.753332342901556e-16 relative error = 3.1964632654517983617373378488232e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.107 Order of pole = 2.082 x[1] = 0.467 y[1] (analytic) = 2.1132550031073092729789399791717 y[1] (numeric) = 2.1132550031073099516065254022206 absolute error = 6.786275854230489e-16 relative error = 3.2112905656212885085875509852125e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.106 Order of pole = 2.082 x[1] = 0.468 y[1] (analytic) = 2.1137598279662362155131759255234 y[1] (numeric) = 2.1137598279662368974523722891814 absolute error = 6.819391963636580e-16 relative error = 3.2261905413340594540578209340537e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.105 Order of pole = 2.082 x[1] = 0.469 y[1] (analytic) = 2.1142659083076499651861156012579 y[1] (numeric) = 2.1142659083076506504542948851294 absolute error = 6.852681792838715e-16 relative error = 3.2411636426204773851867390107122e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.104 Order of pole = 2.082 x[1] = 0.47 y[1] (analytic) = 2.1147732454029446506654717721142 y[1] (numeric) = 2.1147732454029453392801189349186 absolute error = 6.886146471628044e-16 relative error = 3.2562103225946436962175574290469e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.103 Order of pole = 2.082 memory used=160.2MB, alloc=4.2MB, time=19.96 x[1] = 0.471 y[1] (analytic) = 2.1152818405279639743517314111258 y[1] (numeric) = 2.1152818405279646663304452045815 absolute error = 6.919787137934557e-16 relative error = 3.2713310374788695127418496766149e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.102 Order of pole = 2.082 x[1] = 0.472 y[1] (analytic) = 2.1157916949630153598698055863413 y[1] (numeric) = 2.115791694963016055230299375766 absolute error = 6.953604937894247e-16 relative error = 3.2865262466283562902963319972962e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.101 Order of pole = 2.082 x[1] = 0.473 y[1] (analytic) = 2.1163028099928841686937800626363 y[1] (numeric) = 2.1163028099928848674538826543262 absolute error = 6.987601025916899e-16 relative error = 3.3017964125561001482010182547148e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.1 Order of pole = 2.082 x[1] = 0.474 y[1] (analytic) = 2.1168151869068479862686966092692 y[1] (numeric) = 2.1168151869068486884463530847174 absolute error = 7.021776564754482e-16 relative error = 3.3171420009580082709515838293851e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.098 Order of pole = 2.082 x[1] = 0.475 y[1] (analytic) = 2.117328826998690977995666478318 y[1] (numeric) = 2.1173288269986916836089390353352 absolute error = 7.056132725570172e-16 relative error = 3.3325634807382398137665957675349e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.097 Order of pole = 2.082 x[1] = 0.476 y[1] (analytic) = 2.1178437315667183154490061263295 y[1] (numeric) = 2.1178437315667190245160749271302 absolute error = 7.090670688008007e-16 relative error = 3.3480613240347709707497042652328e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.096 Order of pole = 2.082 x[1] = 0.477 y[1] (analytic) = 2.1183599019137706731964911341508 y[1] (numeric) = 2.1183599019137713857356551604678 absolute error = 7.125391640263170e-16 relative error = 3.3636360062451814991117430733560e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.095 Order of pole = 2.082 x[1] = 0.478 y[1] (analytic) = 2.1188773393472387965962475810212 y[1] (numeric) = 2.1188773393472395126259254963131 absolute error = 7.160296779152919e-16 relative error = 3.3792880060526708476097103434588e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.094 Order of pole = 2.082 x[1] = 0.479 y[1] (analytic) = 2.1193960451790781409462409929272 y[1] (numeric) = 2.119396045179078860484972011744 absolute error = 7.195387310188168e-16 relative error = 3.3950178054523049385610297077123e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.093 Order of pole = 2.082 x[1] = 0.48 y[1] (analytic) = 2.1199160207258235823647815576117 y[1] (numeric) = 2.1199160207258243054312263221833 absolute error = 7.230664447645716e-16 relative error = 3.4108258897774913431991318549920e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.092 Order of pole = 2.082 x[1] = 0.481 y[1] (analytic) = 2.1204372673086042007829407264671 y[1] (numeric) = 2.1204372673086049273958821905817 absolute error = 7.266129414641146e-16 relative error = 3.4267127477266923790465003705385e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.091 Order of pole = 2.082 x[1] = 0.482 y[1] (analytic) = 2.12095978625315813543226875517 y[1] (numeric) = 2.1209597862531588656106130754087 absolute error = 7.301783443202387e-16 relative error = 3.4426788713903719606057377965349e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.2MB, time=20.43 Real estimate of pole used Radius of convergence = 1.09 Order of pole = 2.082 x[1] = 0.483 y[1] (analytic) = 2.1214835788898475132137153200166 y[1] (numeric) = 2.121483578889848246976492754412 absolute error = 7.337627774343954e-16 relative error = 3.4587247562781824072809984205229e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.089 Order of pole = 2.082 x[1] = 0.484 y[1] (analytic) = 2.1220086465536734503361862365609 y[1] (numeric) = 2.1220086465536741877025520507474 absolute error = 7.373663658141865e-16 relative error = 3.4748509013463898544585560737169e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.088 Order of pole = 2.082 x[1] = 0.485 y[1] (analytic) = 2.1225349905842911276157186537912 y[1] (numeric) = 2.1225349905842918686049540347176 absolute error = 7.409892353809264e-16 relative error = 3.4910578090255510445991755329671e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.087 Order of pole = 2.082 x[1] = 0.486 y[1] (analytic) = 2.1230626123260249398288250545615 y[1] (numeric) = 2.1230626123260256844603380318328 absolute error = 7.446315129772713e-16 relative error = 3.5073459852484231568204507163455e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.086 Order of pole = 2.082 x[1] = 0.487 y[1] (analytic) = 2.1235915131278837195161431165762 y[1] (numeric) = 2.1235915131278844678094694914974 absolute error = 7.482933263749212e-16 relative error = 3.5237159394781335703808756147113e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.085 Order of pole = 2.082 x[1] = 0.488 y[1] (analytic) = 2.1241216943435760356351341346258 y[1] (numeric) = 2.1241216943435767876099384170176 absolute error = 7.519748042823918e-16 relative error = 3.5401681847365949691235400209914e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.084 Order of pole = 2.082 x[1] = 0.489 y[1] (analytic) = 2.124653157331525567463197432109 y[1] (numeric) = 2.1246531573315263231392737849672 absolute error = 7.556760763528582e-16 relative error = 3.5567032376331738088229854585037e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.083 Order of pole = 2.082 x[1] = 0.49 y[1] (analytic) = 2.1251859034548865541552121577616 y[1] (numeric) = 2.125185903454887313552485349833 absolute error = 7.593972731920714e-16 relative error = 3.5733216183936159123490111364930e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.082 Order of pole = 2.082 x[1] = 0.491 y[1] (analytic) = 2.1257199340815593203621812330174 y[1] (numeric) = 2.1257199340815600835007075993652 absolute error = 7.631385263663478e-16 relative error = 3.5900238508892291803843308211865e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.081 Order of pole = 2.082 x[1] = 0.492 y[1] (analytic) = 2.1262552505842058783203351491064 y[1] (numeric) = 2.1262552505842066452203035597393 absolute error = 7.668999684106329e-16 relative error = 3.6068104626663281022930071084396e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.08 Order of pole = 2.082 x[1] = 0.493 y[1] (analytic) = 2.1267918543402656068227559749231 y[1] (numeric) = 2.1267918543402663775044888115625 absolute error = 7.706817328366394e-16 relative error = 3.6236819849759400340685491757238e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.2MB, time=20.92 Real estimate of pole used Radius of convergence = 1.079 Order of pole = 2.082 x[1] = 0.494 y[1] (analytic) = 2.1273297467319710074883044924483 y[1] (numeric) = 2.1273297467319717819722586335099 absolute error = 7.744839541410616e-16 relative error = 3.6406389528037811951956085933039e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.078 Order of pole = 2.082 x[1] = 0.495 y[1] (analytic) = 2.1278689291463635387453759932105 y[1] (numeric) = 2.1278689291463643170521438070756 absolute error = 7.783067678138651e-16 relative error = 3.6576819049004966850539671959771e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.077 Order of pole = 2.082 x[1] = 0.496 y[1] (analytic) = 2.1284094029753095279507731155848 y[1] (numeric) = 2.1284094029753103101010834622389 absolute error = 7.821503103466541e-16 relative error = 3.6748113838121743290185019252935e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.076 Order of pole = 2.082 x[1] = 0.497 y[1] (analytic) = 2.128951169615516162066767348895 y[1] (numeric) = 2.1289511696155169480814865900118 absolute error = 7.860147192411168e-16 relative error = 3.6920279359111336830500550127991e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.075 Order of pole = 2.082 x[1] = 0.498 y[1] (analytic) = 2.129494230468547557322224648122 y[1] (numeric) = 2.1294942304685483472223576656705 absolute error = 7.899001330175485e-16 relative error = 3.7093321114269872897913393675295e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.074 Order of pole = 2.082 x[1] = 0.499 y[1] (analytic) = 2.1300385869408409082864951659371 y[1] (numeric) = 2.1300385869408417020931863893931 absolute error = 7.938066912234560e-16 relative error = 3.7267244644779900573627568756932e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.073 Order of pole = 2.082 x[1] = 0.5 y[1] (analytic) = 2.130584240443722716787612591826 y[1] (numeric) = 2.1305842404437235145221470340657 absolute error = 7.977345344422397e-16 relative error = 3.7442055531026587992437335267109e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.072 Order of pole = 2.082 x[1] = 0.501 y[1] (analytic) = 2.1311311923934251011092151678795 y[1] (numeric) = 2.1311311923934259027930194698391 absolute error = 8.016838043019596e-16 relative error = 3.7617759392916899884284336480713e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.071 Order of pole = 2.082 x[1] = 0.502 y[1] (analytic) = 2.1316794442111021859034883057481 y[1] (numeric) = 2.1316794442111029915581317899292 absolute error = 8.056546434841811e-16 relative error = 3.7794361890201553958481084775127e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.07 Order of pole = 2.082 x[1] = 0.503 y[1] (analytic) = 2.1322289973228465732603380392364 y[1] (numeric) = 2.1322289973228473829075337721409 absolute error = 8.096471957329045e-16 relative error = 3.7971868722799928371179840169523e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.069 Order of pole = 2.082 x[1] = 0.504 y[1] (analytic) = 2.1327798531597058953759354937272 y[1] (numeric) = 2.1327798531597067090375413573061 absolute error = 8.136616058635789e-16 relative error = 3.8150285631127942052270045374656e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.068 Order of pole = 2.082 memory used=171.6MB, alloc=4.2MB, time=21.40 x[1] = 0.505 y[1] (analytic) = 2.1333320131576994492667253204352 y[1] (numeric) = 2.1333320131577002669647450926337 absolute error = 8.176980197721985e-16 relative error = 3.8329618396428802987394833816808e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.067 Order of pole = 2.082 x[1] = 0.506 y[1] (analytic) = 2.1338854787578349139779658154572 y[1] (numeric) = 2.133885478757835735734550259944 absolute error = 8.217565844444868e-16 relative error = 3.8509872841106871166474741935352e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.066 Order of pole = 2.082 x[1] = 0.507 y[1] (analytic) = 2.1344402514061251507388654075507 y[1] (numeric) = 2.134440251406125976576313372716 absolute error = 8.258374479651653e-16 relative error = 3.8691054829064465353966231802292e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.065 Order of pole = 2.082 x[1] = 0.508 y[1] (analytic) = 2.1349963325536050865193995430729 y[1] (numeric) = 2.1349963325536059164601590703832 absolute error = 8.299407595273103e-16 relative error = 3.8873170266041770984918298969857e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.064 Order of pole = 2.082 x[1] = 0.509 y[1] (analytic) = 2.1355537236563486814469339119095 y[1] (numeric) = 2.1355537236563495155136033537068 absolute error = 8.340666694417973e-16 relative error = 3.9056225099959814100797843236273e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.063 Order of pole = 2.082 x[1] = 0.51 y[1] (analytic) = 2.1361124261754859805438446366325 y[1] (numeric) = 2.1361124261754868187591737834673 absolute error = 8.382153291468348e-16 relative error = 3.9240225321266573907723775562803e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.062 Order of pole = 2.082 x[1] = 0.511 y[1] (analytic) = 2.1366724415772202502504136824883 y[1] (numeric) = 2.1366724415772210926373049000758 absolute error = 8.423868912175875e-16 relative error = 3.9425176963286222067711445869859e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.061 Order of pole = 2.082 x[1] = 0.512 y[1] (analytic) = 2.137233771332845200200388533899 y[1] (numeric) = 2.1372337713328460467818979097903 absolute error = 8.465815093758913e-16 relative error = 3.9611086102571589074911137294490e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.06 Order of pole = 2.082 x[1] = 0.513 y[1] (analytic) = 2.137796416918762290719729321568 y[1] (numeric) = 2.137796416918763141519067821627 absolute error = 8.507993385000590e-16 relative error = 3.9797958859259794059125659033635e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.059 Order of pole = 2.082 x[1] = 0.514 y[1] (analytic) = 2.1383603798164981265222242724934 y[1] (numeric) = 2.1383603798164989815627589072728 absolute error = 8.550405346347794e-16 relative error = 3.9985801397431152118960826965457e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.058 Order of pole = 2.082 x[1] = 0.515 y[1] (analytic) = 2.1389256615127219370788357945697 y[1] (numeric) = 2.13892566151272279638409079568 absolute error = 8.593052550011103e-16 relative error = 4.0174619925471370110607282763104e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.057 Order of pole = 2.082 x[1] = 0.516 y[1] (analytic) = 2.1394922634992631441408449012686 y[1] (numeric) = 2.1394922634992640077345029078344 absolute error = 8.635936580065658e-16 relative error = 4.0364420696437037039041188830927e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.2MB, time=21.88 Real estimate of pole used Radius of convergence = 1.056 Order of pole = 2.082 x[1] = 0.517 y[1] (analytic) = 2.1400601872731290169000912353196 y[1] (numeric) = 2.140060187273129884805994490619 absolute error = 8.679059032552994e-16 relative error = 4.0555210008424466503204138472450e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.055 Order of pole = 2.082 x[1] = 0.518 y[1] (analytic) = 2.1406294343365224152728598704981 y[1] (numeric) = 2.1406294343365232875150114288823 absolute error = 8.722421515583842e-16 relative error = 4.0746994204941939098387504540816e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.054 Order of pole = 2.082 x[1] = 0.519 y[1] (analytic) = 2.1412000061968596217972445666753 y[1] (numeric) = 2.1412000061968604983998095108654 absolute error = 8.766025649441901e-16 relative error = 4.0939779675285327108606784924291e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.053 Order of pole = 2.082 x[1] = 0.52 y[1] (analytic) = 2.1417719043667882626371204362693 y[1] (numeric) = 2.14177190436678914362442710513 absolute error = 8.809873066688607e-16 relative error = 4.1133572854917214506744924063842e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.052 Order of pole = 2.082 x[1] = 0.521 y[1] (analytic) = 2.1423451303642053181891872632637 y[1] (numeric) = 2.1423451303642062035857284901528 absolute error = 8.853965412268891e-16 relative error = 4.1328380225849461580264045445834e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.051 Order of pole = 2.082 x[1] = 0.522 y[1] (analytic) = 2.1429196857122752237928982141354 y[1] (numeric) = 2.1429196857122761136233325759305 absolute error = 8.898304343617951e-16 relative error = 4.1524208317029317516472866574305e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.05 Order of pole = 2.082 x[1] = 0.523 y[1] (analytic) = 2.1434955719394480610464676105372 y[1] (numeric) = 2.1434955719394489553356206874415 absolute error = 8.942891530769043e-16 relative error = 4.1721063704729090666171523945707e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.049 Order of pole = 2.082 x[1] = 0.524 y[1] (analytic) = 2.1440727905794778402355560156469 y[1] (numeric) = 2.1440727905794787390084216618765 absolute error = 8.987728656462296e-16 relative error = 4.1918953012939386093849048354181e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.048 Order of pole = 2.082 x[1] = 0.525 y[1] (analytic) = 2.1446513431714408743846613410521 y[1] (numeric) = 2.1446513431714417776664029665096 absolute error = 9.032817416254575e-16 relative error = 4.2117882913766008504083998117117e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.047 Order of pole = 2.082 x[1] = 0.526 y[1] (analytic) = 2.14523123125975424544470123234 y[1] (numeric) = 2.1452312312597551532606530953793 absolute error = 9.078159518630393e-16 relative error = 4.2317860127830521116285657390117e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.046 Order of pole = 2.082 x[1] = 0.527 y[1] (analytic) = 2.1458124563941943631337548647797 y[1] (numeric) = 2.1458124563941952755094233761682 absolute error = 9.123756685113885e-16 relative error = 4.2518891424674506910261481720600e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.2MB, time=22.37 Real estimate of pole used Radius of convergence = 1.045 Order of pole = 2.082 x[1] = 0.528 y[1] (analytic) = 2.1463950201299156169514417033653 y[1] (numeric) = 2.1463950201299165339125067415506 absolute error = 9.169610650381853e-16 relative error = 4.2720983623167559835199277141877e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.044 Order of pole = 2.082 x[1] = 0.529 y[1] (analytic) = 2.146978924027469121890950983952 y[1] (numeric) = 2.1469789240274700434632672217424 absolute error = 9.215723162377904e-16 relative error = 4.2924143591919093970392832704398e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.043 Order of pole = 2.082 x[1] = 0.53 y[1] (analytic) = 2.1475641696528215583762988863935 y[1] (numeric) = 2.1475641696528224845858971291611 absolute error = 9.262095982427676e-16 relative error = 4.3128378249693932615054881361161e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.042 Order of pole = 2.082 x[1] = 0.531 y[1] (analytic) = 2.1481507585773741069559808308282 y[1] (numeric) = 2.1481507585773750378290693663464 absolute error = 9.308730885355182e-16 relative error = 4.3333694565831802201170102291224e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.041 Order of pole = 2.082 x[1] = 0.532 y[1] (analytic) = 2.14873869237798147828780427118 y[1] (numeric) = 2.1487386923779824138507702312064 absolute error = 9.355629659600264e-16 relative error = 4.3540099560670678704965359078046e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.04 Order of pole = 2.082 x[1] = 0.533 y[1] (analytic) = 2.1493279726369710389533330244065 y[1] (numeric) = 2.1493279726369719792327437581254 absolute error = 9.402794107337189e-16 relative error = 4.3747600305974120352344493122248e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.039 Order of pole = 2.082 x[1] = 0.534 y[1] (analytic) = 2.1499186009421620336440478012406 y[1] (numeric) = 2.1499186009421629786666522606788 absolute error = 9.450226044594382e-16 relative error = 4.3956203925362547920841256547958e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.038 Order of pole = 2.082 x[1] = 0.535 y[1] (analytic) = 2.1505105788868849042650294376249 y[1] (numeric) = 2.1505105788868858540577595751562 absolute error = 9.497927301375313e-16 relative error = 4.4165917594748536225151395299713e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.037 Order of pole = 2.082 x[1] = 0.536 y[1] (analytic) = 2.1511039080700007065057016115941 y[1] (numeric) = 2.1511039080700016610956737896511 absolute error = 9.545899721780570e-16 relative error = 4.4376748542776249862858692762962e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.036 Order of pole = 2.082 x[1] = 0.537 y[1] (analytic) = 2.1516985900959206244309288162523 y[1] (numeric) = 2.151698590095921583845445229361 absolute error = 9.594145164131087e-16 relative error = 4.4588704051264863107447028111137e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.035 Order of pole = 2.082 x[1] = 0.538 y[1] (analytic) = 2.1522946265746255836495532963326 y[1] (numeric) = 2.1522946265746265479161034055915 absolute error = 9.642665501092589e-16 relative error = 4.4801791455656236181229941571739e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.2MB, time=22.86 Real estimate of pole used Radius of convergence = 1.034 Order of pole = 2.082 x[1] = 0.539 y[1] (analytic) = 2.1528920191216859636212717966934 y[1] (numeric) = 2.1528920191216869327675337768162 absolute error = 9.691462619801228e-16 relative error = 4.5016018145466710680196091503659e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.033 Order of pole = 2.082 x[1] = 0.54 y[1] (analytic) = 2.1534907693582814096665995714796 y[1] (numeric) = 2.153490769358282383720441770524 absolute error = 9.740538421990444e-16 relative error = 4.5231391564743165736319846571112e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.032 Order of pole = 2.082 x[1] = 0.541 y[1] (analytic) = 2.1540908789112207452485454205553 y[1] (numeric) = 2.1540908789112217242380278324621 absolute error = 9.789894824119068e-16 relative error = 4.5447919212523397160576409309398e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.031 Order of pole = 2.082 x[1] = 0.542 y[1] (analytic) = 2.1546923494129619850985278156771 y[1] (numeric) = 2.1546923494129629690519035657419 absolute error = 9.839533757500648e-16 relative error = 4.5665608643300714483545997556130e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.03 Order of pole = 2.082 x[1] = 0.543 y[1] (analytic) = 2.1552951825016324497629987157303 y[1] (numeric) = 2.155295182501633438708715559136 absolute error = 9.889457168434057e-16 relative error = 4.5884467467493012833269935984292e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.029 Order of pole = 2.082 x[1] = 0.544 y[1] (analytic) = 2.1558993798210489821512087137848 y[1] (numeric) = 2.1558993798210499761179105473207 absolute error = 9.939667018335359e-16 relative error = 4.6104503351916190913436049117984e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.028 Order of pole = 2.082 x[1] = 0.545 y[1] (analytic) = 2.1565049430207382666685449768764 y[1] (numeric) = 2.1565049430207392656850733639735 absolute error = 9.990165283870971e-16 relative error = 4.6325724020262074020970322267113e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.027 Order of pole = 2.082 x[1] = 0.546 y[1] (analytic) = 2.157111873755957251523902303074 y[1] (numeric) = 2.1571118737559582556192980122855 absolute error = 1.0040953957092115e-15 relative error = 4.6548137253580796594236582179006e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.026 Order of pole = 2.082 x[1] = 0.547 y[1] (analytic) = 2.1577201736877136748036078029445 y[1] (numeric) = 2.1577201736877146840071123600034 absolute error = 1.0092035045570589e-15 relative error = 4.6771750890767760976905500917621e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.025 Order of pole = 2.082 x[1] = 0.548 y[1] (analytic) = 2.1583298444827866949085114900662 y[1] (numeric) = 2.1583298444827877092495687436537 absolute error = 1.0143410572535875e-15 relative error = 4.6996572829055237736792036046526e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.024 Order of pole = 2.082 x[1] = 0.549 y[1] (analytic) = 2.1589408878137476259549787165413 y[1] (numeric) = 2.1589408878137486454632364178984 absolute error = 1.0195082577013571e-15 relative error = 4.7222611024508529022735942675947e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.023 Order of pole = 2.082 x[1] = 0.55 y[1] (analytic) = 2.159553305358980778744676196012 y[1] (numeric) = 2.1595533053589818034499875925316 absolute error = 1.0247053113965196e-15 relative error = 4.7449873492526903596073227591613e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.2MB, time=23.34 Real estimate of pole used Radius of convergence = 1.022 Order of pole = 2.082 x[1] = 0.551 y[1] (analytic) = 2.1601670988027044079122316027689 y[1] (numeric) = 2.1601670988027054378446570457046 absolute error = 1.0299324254429357e-15 relative error = 4.7678368308349233822477755735308e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.021 Order of pole = 2.082 x[1] = 0.552 y[1] (analytic) = 2.1607822698349917658640677081811 y[1] (numeric) = 2.1607822698349928010538762746121 absolute error = 1.0351898085664310e-15 relative error = 4.7908103607564463946238090687869e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.02 Order of pole = 2.082 x[1] = 0.553 y[1] (analytic) = 2.1613988201517922641259660047505 y[1] (numeric) = 2.1613988201517933046036371339424 absolute error = 1.0404776711291919e-15 relative error = 4.8139087586626909004358444511080e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.019 Order of pole = 2.082 x[1] = 0.554 y[1] (analytic) = 2.1620167514549527427212020662941 y[1] (numeric) = 2.1620167514549537885174272105968 absolute error = 1.0457962251443027e-15 relative error = 4.8371328503376429865746509615448e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.018 Order of pole = 2.082 x[1] = 0.555 y[1] (analytic) = 2.1626360654522388482054157956763 y[1] (numeric) = 2.1626360654522398993511000861031 absolute error = 1.0511456842904268e-15 relative error = 4.8604834677563599009065811426020e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.017 Order of pole = 2.082 x[1] = 0.556 y[1] (analytic) = 2.1632567638573565209887345176453 y[1] (numeric) = 2.1632567638573575775149984442777 absolute error = 1.0565262639266324e-15 relative error = 4.8839614491379855694568599043130e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.016 Order of pole = 2.082 x[1] = 0.557 y[1] (analytic) = 2.1638788483899735925800558850976 y[1] (numeric) = 2.1638788483899746545182369924615 absolute error = 1.0619381811073639e-15 relative error = 4.9075676389992686027632136857468e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.015 Order of pole = 2.082 x[1] = 0.558 y[1] (analytic) = 2.1645023207757414933928210869112 y[1] (numeric) = 2.1645023207757425607744756844734 absolute error = 1.0673816545975622e-15 relative error = 4.9313028882085955597999692717230e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.014 Order of pole = 2.082 x[1] = 0.559 y[1] (analytic) = 2.1651271827463170717560671817652 y[1] (numeric) = 2.1651271827463181446129720696989 absolute error = 1.0728569048879337e-15 relative error = 4.9551680540405364916107072108806e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.013 Order of pole = 2.082 x[1] = 0.56 y[1] (analytic) = 2.1657534360393845247790408455362 y[1] (numeric) = 2.1657534360393856031431950559076 absolute error = 1.0783641542103714e-15 relative error = 4.9791640002309164024588426577484e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.012 Order of pole = 2.082 x[1] = 0.561 y[1] (analytic) = 2.166381082398677441722184723456 y[1] (numeric) = 2.1663810823986785256258112769836 absolute error = 1.0839036265535276e-15 relative error = 5.0032915970324082187055469952292e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.2MB, time=23.83 Real estimate of pole used Radius of convergence = 1.011 Order of pole = 2.082 x[1] = 0.562 y[1] (analytic) = 2.1670101235740009605318722388431 y[1] (numeric) = 2.1670101235740020500074199173857 absolute error = 1.0894755476785426e-15 relative error = 5.0275517212706654637381084417222e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.01 Order of pole = 2.082 x[1] = 0.563 y[1] (analytic) = 2.1676405613212540382008674476446 y[1] (numeric) = 2.1676405613212551332810125825727 absolute error = 1.0950801451349281e-15 relative error = 5.0519452564009864851442343882079e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.009 Order of pole = 2.082 x[1] = 0.564 y[1] (analytic) = 2.1682723974024518356211236651662 y[1] (numeric) = 2.1682723974024529363387719417757 absolute error = 1.1007176482766095e-15 relative error = 5.0764730925655274508462790001990e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 2.082 x[1] = 0.565 y[1] (analytic) = 2.1689056335857482176002084543699 y[1] (numeric) = 2.1689056335857493239884967324977 absolute error = 1.1063882882781278e-15 relative error = 5.1011361266510651393001879779785e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 2.082 x[1] = 0.566 y[1] (analytic) = 2.1695402716454583687173534833506 y[1] (numeric) = 2.1695402716454594808096516343526 absolute error = 1.1120922981510020e-15 relative error = 5.1259352623473114537151382446142e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 2.082 x[1] = 0.567 y[1] (analytic) = 2.1701763133620815256998760657177 y[1] (numeric) = 2.1701763133620826435297888259732 absolute error = 1.1178299127602555e-15 relative error = 5.1508714102057935516268876027490e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 2.082 x[1] = 0.568 y[1] (analytic) = 2.1708137605223238270055052275761 y[1] (numeric) = 2.1708137605223249506068740686837 absolute error = 1.1236013688411076e-15 relative error = 5.1759454876993023779677093067986e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 2.082 x[1] = 0.569 y[1] (analytic) = 2.1714526149191212803009692379352 y[1] (numeric) = 2.1714526149191224097078742537661 absolute error = 1.1294069050158309e-15 relative error = 5.2011584192819109865325592628293e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 2.082 x[1] = 0.57 y[1] (analytic) = 2.1720928783516628485320640383724 y[1] (numeric) = 2.1720928783516639837788258491505 absolute error = 1.1352467618107781e-15 relative error = 5.2265111364495764466438192135732e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 2.082 x[1] = 0.571 y[1] (analytic) = 2.1727345526254136552853232587698 y[1] (numeric) = 2.1727345526254147964065049323481 absolute error = 1.1411211816735783e-15 relative error = 5.2520045778013234354005078597456e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 2.082 x[1] = 0.572 y[1] (analytic) = 2.1733776395521383101463508585089 y[1] (numeric) = 2.1733776395521394571767598490162 absolute error = 1.1470304089905073e-15 relative error = 5.2776396891010278497203430390092e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.2MB, time=24.30 Real estimate of pole used Radius of convergence = 1 Order of pole = 2.082 x[1] = 0.573 y[1] (analytic) = 2.1740221409499243547648572397406 y[1] (numeric) = 2.1740221409499255077395473437708 absolute error = 1.1529746901040302e-15 relative error = 5.3034174233397901946321706113171e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9993 Order of pole = 2.082 x[1] = 0.574 y[1] (analytic) = 2.1746680586432058303414592978551 y[1] (numeric) = 2.1746680586432069892957326283766 absolute error = 1.1589542733305215e-15 relative error = 5.3293387407989202414879647708077e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9983 Order of pole = 2.082 x[1] = 0.575 y[1] (analytic) = 2.1753153944627869672563646642743 y[1] (numeric) = 2.1753153944627881322257736424371 absolute error = 1.1649694089781628e-15 relative error = 5.3554046091135309377200095123326e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9973 Order of pole = 2.082 x[1] = 0.576 y[1] (analytic) = 2.1759641502458659975651607219814 y[1] (numeric) = 2.1759641502458671685855100870023 absolute error = 1.1710203493650209e-15 relative error = 5.3816160033367519464082053787891e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9963 Order of pole = 2.082 x[1] = 0.577 y[1] (analytic) = 2.1766143278360590910920702022652 y[1] (numeric) = 2.1766143278360602681994190395726 absolute error = 1.1771073488373074e-15 relative error = 5.4079739060045653423176196922465e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9953 Order of pole = 2.082 x[1] = 0.578 y[1] (analytic) = 2.1772659290834244158562176731574 y[1] (numeric) = 2.1772659290834255990868814609805 absolute error = 1.1832306637878231e-15 relative error = 5.4344793072012760726547110861217e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9943 Order of pole = 2.082 x[1] = 0.579 y[1] (analytic) = 2.1779189558444863235716753808886 y[1] (numeric) = 2.1779189558444875129622280554767 absolute error = 1.1893905526745881e-15 relative error = 5.4611332046256187239485728464010e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9933 Order of pole = 2.082 x[1] = 0.58 y[1] (analytic) = 2.1785734099822596609673230840681 y[1] (numeric) = 2.1785734099822608565545991237285 absolute error = 1.1955872760396604e-15 relative error = 5.4879366036575108368456226247520e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9923 Order of pole = 2.082 x[1] = 0.581 y[1] (analytic) = 2.1792292933662742076778651087088 y[1] (numeric) = 2.1792292933662754094989616368536 absolute error = 1.2018210965281448e-15 relative error = 5.5148905174254583798400780262460e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9913 Order of pole = 2.082 x[1] = 0.582 y[1] (analytic) = 2.1798866078725992414626992370468 y[1] (numeric) = 2.1798866078726004495549781444407 absolute error = 1.2080922789073939e-15 relative error = 5.5419959668746189618274346534190e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9903 Order of pole = 2.082 x[1] = 0.583 y[1] (analytic) = 2.1805453553838682315147266146227 y[1] (numeric) = 2.1805453553838694459158167010267 absolute error = 1.2144010900864040e-15 relative error = 5.5692539808355329181035598451268e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9893 Order of pole = 2.082 memory used=198.3MB, alloc=4.2MB, time=24.78 x[1] = 0.584 y[1] (analytic) = 2.1812055377893036606266300125238 y[1] (numeric) = 2.1812055377893048813744291479317 absolute error = 1.2207477991354079e-15 relative error = 5.5966655960935286942196394519632e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9883 Order of pole = 2.082 x[1] = 0.585 y[1] (analytic) = 2.1818671569847419769876299132626 y[1] (numeric) = 2.181867156984743204120307218929 absolute error = 1.2271326773056664e-15 relative error = 5.6242318574588080016220765038764e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9873 Order of pole = 2.082 x[1] = 0.586 y[1] (analytic) = 2.1825302148726586763892544017433 y[1] (numeric) = 2.1825302148726599099452524512044 absolute error = 1.2335559980494611e-15 relative error = 5.6519538178372198527158527747947e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9863 Order of pole = 2.082 x[1] = 0.587 y[1] (analytic) = 2.1831947133621935156242301434955 y[1] (numeric) = 2.183194713362194755642267183786 absolute error = 1.2400180370402905e-15 relative error = 5.6798325383017297938993321824488e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9853 Order of pole = 2.082 x[1] = 0.588 y[1] (analytic) = 2.1838606543691758578682182313069 y[1] (numeric) = 2.1838606543691771043872904245792 absolute error = 1.2465190721932723e-15 relative error = 5.7078690881645947419396801746807e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9843 Order of pole = 2.082 x[1] = 0.589 y[1] (analytic) = 2.1845280398161501508397807932199 y[1] (numeric) = 2.1845280398161514038991644789731 absolute error = 1.2530593836857532e-15 relative error = 5.7360645450502464602746729772266e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9833 Order of pole = 2.082 x[1] = 0.59 y[1] (analytic) = 2.1851968716324015385396723984441 y[1] (numeric) = 2.1851968716324027981789263765729 absolute error = 1.2596392539781288e-15 relative error = 5.7644199949688926341103211618628e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9823 Order of pole = 2.082 x[1] = 0.591 y[1] (analytic) = 2.1858671517539816073763048962235 y[1] (numeric) = 2.1858671517539828736352727311013 absolute error = 1.2662589678348778e-15 relative error = 5.7929365323908517814031725851706e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9813 Order of pole = 2.082 x[1] = 0.592 y[1] (analytic) = 2.186538882123734267490035803556 y[1] (numeric) = 2.1865388821237355404088481493653 absolute error = 1.2729188123458093e-15 relative error = 5.8216152603216134805305012909639e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9803 Order of pole = 2.082 x[1] = 0.593 y[1] (analytic) = 2.187212064691321770094779152712 y[1] (numeric) = 2.1872120646913230497138561002413 absolute error = 1.2796190769475293e-15 relative error = 5.8504572903776487720361341686153e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9793 Order of pole = 2.082 x[1] = 0.594 y[1] (analytic) = 2.187886701413250861661334255001 y[1] (numeric) = 2.1878867014132521480213877001269 absolute error = 1.2863600534451259e-15 relative error = 5.8794637428629653442714107855784e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9783 Order of pole = 2.082 x[1] = 0.595 y[1] (analytic) = 2.1885627942528990757727725738929 y[1] (numeric) = 2.1885627942529003689148086079714 absolute error = 1.2931420360340785e-15 relative error = 5.9086357468464286067656564502528e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.2MB, time=25.27 Real estimate of pole used Radius of convergence = 0.9773 Order of pole = 2.082 x[1] = 0.596 y[1] (analytic) = 2.1892403451805411634882162736533 y[1] (numeric) = 2.1892403451805424634535375960435 absolute error = 1.2999653213223902e-15 relative error = 5.9379744402398418186450009009236e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9763 Order of pole = 2.082 x[1] = 0.597 y[1] (analytic) = 2.1899193561733756630573844688876 y[1] (numeric) = 2.1899193561733769698875928218373 absolute error = 1.3068302083529497e-15 relative error = 5.9674809698768108564383519533521e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9753 Order of pole = 2.082 x[1] = 0.598 y[1] (analytic) = 2.190599829215551609834375200237 y[1] (numeric) = 2.1905998292155529235713738263587 absolute error = 1.3137369986261217e-15 relative error = 5.9971564915923857966340540697914e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9743 Order of pole = 2.082 x[1] = 0.599 y[1] (analytic) = 2.1912817662981953872452931610007 y[1] (numeric) = 2.1912817662981967079312892835718 absolute error = 1.3206859961225711e-15 relative error = 6.0270021703035002363535048125135e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9733 Order of pole = 2.082 x[1] = 0.6 y[1] (analytic) = 2.1919651694194377196705256625065 y[1] (numeric) = 2.1919651694194390473480329888287 absolute error = 1.3276775073263222e-15 relative error = 6.0570191800902104969088243283131e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9723 Order of pole = 2.082 x[1] = 0.601 y[1] (analytic) = 2.1926500405844408081087127211842 y[1] (numeric) = 2.1926500405844421428205539692402 absolute error = 1.3347118412480560e-15 relative error = 6.0872087042777454927305792698008e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9713 Order of pole = 2.082 x[1] = 0.602 y[1] (analytic) = 2.1933363818054256094957519509524 y[1] (numeric) = 2.1933363818054269512850613996008 absolute error = 1.3417893094486484e-15 relative error = 6.1175719355193766309939301205418e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9703 Order of pole = 2.082 x[1] = 0.603 y[1] (analytic) = 2.1940241951016992605585256290076 y[1] (numeric) = 2.1940241951017006094687516919591 absolute error = 1.3489102260629515e-15 relative error = 6.1481100758801143263830650130786e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9693 Order of pole = 2.082 x[1] = 0.604 y[1] (analytic) = 2.1947134824996826470894363546594 y[1] (numeric) = 2.1947134824996840031643441784815 absolute error = 1.3560749078238221e-15 relative error = 6.1788243369212463330676164666576e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9683 Order of pole = 2.082 x[1] = 0.605 y[1] (analytic) = 2.195404246032938119534289627739 y[1] (numeric) = 2.1954042460329394828179637141373 absolute error = 1.3632836740863983e-15 relative error = 6.2097159397857184585682696876219e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9673 Order of pole = 2.082 x[1] = 0.606 y[1] (analytic) = 2.1960964877421973557925669286194 y[1] (numeric) = 2.1960964877421987263294137812479 absolute error = 1.3705368468526285e-15 relative error = 6.2407861152843736811500906050387e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.2MB, time=25.74 Real estimate of pole used Radius of convergence = 0.9663 Order of pole = 2.082 x[1] = 0.607 y[1] (analytic) = 2.1967902096753893721356919844515 y[1] (numeric) = 2.1967902096753907499704427805074 absolute error = 1.3778347507960559e-15 relative error = 6.2720361039830601656320880254773e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9653 Order of pole = 2.082 x[1] = 0.608 y[1] (analytic) = 2.1974854138876686831555063594275 y[1] (numeric) = 2.1974854138876700683332196462865 absolute error = 1.3851777132868590e-15 relative error = 6.3034671562906067900535969001022e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9643 Order of pole = 2.082 x[1] = 0.609 y[1] (analytic) = 2.1981821024414436116618388195463 y[1] (numeric) = 2.1981821024414450042279032367012 absolute error = 1.3925660644171549e-15 relative error = 6.3350805325476934347014080815550e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9633 Order of pole = 2.082 x[1] = 0.61 y[1] (analytic) = 2.1988802774064047494547766086059 y[1] (numeric) = 2.1988802774064061494549136351709 absolute error = 1.4000001370265650e-15 relative error = 6.3668775031166104472438452160352e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9623 Order of pole = 2.082 x[1] = 0.611 y[1] (analytic) = 2.1995799408595535699040263514274 y[1] (numeric) = 2.1995799408595549773842930794748 absolute error = 1.4074802667280474e-15 relative error = 6.3988593484719230544115647700401e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9613 Order of pole = 2.082 x[1] = 0.612 y[1] (analytic) = 2.2002810948852311932745882975126 y[1] (numeric) = 2.2002810948852326082813802315127 absolute error = 1.4150067919340001e-15 relative error = 6.4310273592920555162268595151158e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9603 Order of pole = 2.082 x[1] = 0.613 y[1] (analytic) = 2.2009837415751473057448605638081 y[1] (numeric) = 2.2009837415751487283249144464439 absolute error = 1.4225800538826358e-15 relative error = 6.4633828365517947620130378627697e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9593 Order of pole = 2.082 x[1] = 0.614 y[1] (analytic) = 2.2016878830284092330702404648652 y[1] (numeric) = 2.2016878830284106632706371294988 absolute error = 1.4302003966646336e-15 relative error = 6.4959270916157336608492382465991e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9583 Order of pole = 2.082 x[1] = 0.615 y[1] (analytic) = 2.2023935213515511698522984739584 y[1] (numeric) = 2.2023935213515526077204657240286 absolute error = 1.4378681672500702e-15 relative error = 6.5286614463326617418668631354300e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9573 Order of pole = 2.082 x[1] = 0.616 y[1] (analytic) = 2.2031006586585635653806673867987 y[1] (numeric) = 2.2031006586585650109643829024309 absolute error = 1.4455837155156322e-15 relative error = 6.5615872331309065939160741590324e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9563 Order of pole = 2.082 x[1] = 0.617 y[1] (analytic) = 2.2038092970709226670219154132421 y[1] (numeric) = 2.2038092970709241203693096853577 absolute error = 1.4533473942721156e-15 relative error = 6.5947057951146495579855917904621e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.2MB, time=26.22 Real estimate of pole used Radius of convergence = 0.9553 Order of pole = 2.082 x[1] = 0.618 y[1] (analytic) = 2.2045194387176202221368577605403 y[1] (numeric) = 2.2045194387176216832964170527538 absolute error = 1.4611595592922135e-15 relative error = 6.6280184861612161033863328563049e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9543 Order of pole = 2.082 x[1] = 0.619 y[1] (analytic) = 2.2052310857351933395150073587541 y[1] (numeric) = 2.2052310857351948085355766973503 absolute error = 1.4690205693385962e-15 relative error = 6.6615266710193557608340125717264e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9533 Order of pole = 2.082 x[1] = 0.62 y[1] (analytic) = 2.2059442402677545113221722854327 y[1] (numeric) = 2.2059442402677559882529584777202 absolute error = 1.4769307861922875e-15 relative error = 6.6952317254085246058506610812849e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9523 Order of pole = 2.082 x[1] = 0.621 y[1] (analytic) = 2.2066589044670217965645757490443 y[1] (numeric) = 2.2066589044670232814551504303842 absolute error = 1.4848905746813399e-15 relative error = 6.7291350361191782389336553554504e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9513 Order of pole = 2.082 x[1] = 0.622 y[1] (analytic) = 2.2073750804923491670803047714707 y[1] (numeric) = 2.2073750804923506599806074812827 absolute error = 1.4929003027098120e-15 relative error = 6.7632380011140858776867293727322e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9503 Order of pole = 2.082 x[1] = 0.623 y[1] (analytic) = 2.2080927705107570170763865578527 y[1] (numeric) = 2.2080927705107585180367278449057 absolute error = 1.5009603412870530e-15 relative error = 6.7975420296306833654885187251752e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9493 Order of pole = 2.082 x[1] = 0.624 y[1] (analytic) = 2.208811976696962837237347552099 y[1] (numeric) = 2.2088119766969643463084121093955 absolute error = 1.5090710645572965e-15 relative error = 6.8320485422844706016869816677743e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9483 Order of pole = 2.082 x[1] = 0.625 y[1] (analytic) = 2.2095327012334120544387299496412 y[1] (numeric) = 2.2095327012334135716715797792084 absolute error = 1.5172328498295672e-15 relative error = 6.8667589711734651901867560918438e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9473 Order of pole = 2.082 x[1] = 0.626 y[1] (analytic) = 2.2102549463103090381067245830799 y[1] (numeric) = 2.2102549463103105635528021909855 absolute error = 1.5254460776079056e-15 relative error = 6.9016747599837308288072887450286e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9463 Order of pole = 2.082 x[1] = 0.627 y[1] (analytic) = 2.2109787141256482742728282252082 y[1] (numeric) = 2.2109787141256498079839598471205 absolute error = 1.5337111316219123e-15 relative error = 6.9367973640959830526080026501926e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9453 Order of pole = 2.082 x[1] = 0.628 y[1] (analytic) = 2.2117040068852457083802480879995 y[1] (numeric) = 2.2117040068852472504086469456174 absolute error = 1.5420283988576179e-15 relative error = 6.9721282506932948005869255168263e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9442 Order of pole = 2.082 memory used=213.6MB, alloc=4.2MB, time=26.69 x[1] = 0.629 y[1] (analytic) = 2.2124308268027702579066572625857 y[1] (numeric) = 2.2124308268027718083049268512657 absolute error = 1.5503982695886800e-15 relative error = 7.0076688988699038451789074736405e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9432 Order of pole = 2.082 x[1] = 0.63 y[1] (analytic) = 2.213159176099775495875852677753 y[1] (numeric) = 2.2131591760997770546969900856661 absolute error = 1.5588211374079131e-15 relative error = 7.0434207997411435159436234630040e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9422 Order of pole = 2.082 x[1] = 0.631 y[1] (analytic) = 2.2138890570057315063388824935197 y[1] (numeric) = 2.2138890570057330736362817526745 absolute error = 1.5672973992591548e-15 relative error = 7.0793854565545072195459906943475e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9412 Order of pole = 2.082 x[1] = 0.632 y[1] (analytic) = 2.2146204717580569129132933392159 y[1] (numeric) = 2.2146204717580584887407488086863 absolute error = 1.5758274554694704e-15 relative error = 7.1155643848018513276089604489654e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9402 Order of pole = 2.082 x[1] = 0.633 y[1] (analytic) = 2.2153534226021510814773001063353 y[1] (numeric) = 2.2153534226021526658890098880388 absolute error = 1.5844117097817035e-15 relative error = 7.1519591123327657855882255728251e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9392 Order of pole = 2.082 x[1] = 0.634 y[1] (analytic) = 2.2160879117914264981239027764462 y[1] (numeric) = 2.2160879117914280911744721638187 absolute error = 1.5930505693873725e-15 relative error = 7.1885711794691069387447018425003e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9382 Order of pole = 2.082 x[1] = 0.635 y[1] (analytic) = 2.2168239415873413234882666718305 y[1] (numeric) = 2.2168239415873429252327116317518 absolute error = 1.6017444449599213e-15 relative error = 7.2254021391207249438821719670501e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9372 Order of pole = 2.082 x[1] = 0.636 y[1] (analytic) = 2.2175615142594321245700452366493 y[1] (numeric) = 2.2175615142594337350637959249735 absolute error = 1.6104937506883242e-15 relative error = 7.2624535569023805867427826794554e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9362 Order of pole = 2.082 x[1] = 0.637 y[1] (analytic) = 2.2183006320853467851807586718735 y[1] (numeric) = 2.2183006320853484044796629829264 absolute error = 1.6192989043110529e-15 relative error = 7.2997270112518819166492957540758e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9352 Order of pole = 2.082 x[1] = 0.638 y[1] (analytic) = 2.2190412973508775961548481478901 y[1] (numeric) = 2.2190412973508792243151752982972 absolute error = 1.6281603271504071e-15 relative error = 7.3372240935494421524530722011459e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9342 Order of pole = 2.082 x[1] = 0.639 y[1] (analytic) = 2.2197835123499945264716046018773 y[1] (numeric) = 2.219783512349996163550048749092 absolute error = 1.6370784441472147e-15 relative error = 7.3749464082382805463847331434676e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9332 Order of pole = 2.082 x[1] = 0.64 y[1] (analytic) = 2.2205272793848786764438239975253 y[1] (numeric) = 2.22052727938488032249750789343 absolute error = 1.6460536838959047e-15 relative error = 7.4128955729464747382948401227162e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.2MB, time=27.18 Real estimate of pole used Radius of convergence = 0.9322 Order of pole = 2.082 x[1] = 0.641 y[1] (analytic) = 2.221272600765955914137768094818 y[1] (numeric) = 2.2212726007659575692242467747774 absolute error = 1.6550864786799594e-15 relative error = 7.4510732186100888299491325103266e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9312 Order of pole = 2.082 x[1] = 0.642 y[1] (analytic) = 2.2220194788119306961978119674057 y[1] (numeric) = 2.2220194788119323603750764751523 absolute error = 1.6641772645077466e-15 relative error = 7.4894809895975747544530585794914e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9302 Order of pole = 2.082 x[1] = 0.643 y[1] (analytic) = 2.2227679158498200742580374423526 y[1] (numeric) = 2.2227679158498217475845185910937 absolute error = 1.6733264811487411e-15 relative error = 7.5281205438354831752258186043460e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9292 Order of pole = 2.082 x[1] = 0.644 y[1] (analytic) = 2.2235179142149878881319860573754 y[1] (numeric) = 2.2235179142149895706665582275108 absolute error = 1.6825345721701354e-15 relative error = 7.5669935529354777379796940082596e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9282 Order of pole = 2.082 x[1] = 0.645 y[1] (analytic) = 2.2242694762511791469808167776354 y[1] (numeric) = 2.2242694762511808387828017514836 absolute error = 1.6918019849738482e-15 relative error = 7.6061017023226855910696539427624e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9272 Order of pole = 2.082 x[1] = 0.646 y[1] (analytic) = 2.2250226043105545996692233393221 y[1] (numeric) = 2.225022604310556300798394173255 absolute error = 1.7011291708339329e-15 relative error = 7.6454466913653881978587907147077e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9262 Order of pole = 2.082 x[1] = 0.647 y[1] (analytic) = 2.2257773007537254955276544503777 y[1] (numeric) = 2.2257773007537272060442393847693 absolute error = 1.7105165849343916e-15 relative error = 7.6850302335060712404181813089809e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9252 Order of pole = 2.082 x[1] = 0.648 y[1] (analytic) = 2.2265335679497885367486479477148 y[1] (numeric) = 2.2265335679497902567133343551147 absolute error = 1.7199646864073999e-15 relative error = 7.7248540563938514245542592712933e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9242 Order of pole = 2.082 x[1] = 0.649 y[1] (analytic) = 2.2272914082763610236544381614512 y[1] (numeric) = 2.2272914082763627531283765333981 absolute error = 1.7294739383719469e-15 relative error = 7.7649199020182938663244305200926e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9232 Order of pole = 2.082 x[1] = 0.65 y[1] (analytic) = 2.2280508241196161940824249547138 y[1] (numeric) = 2.2280508241196179331272329276095 absolute error = 1.7390448079728957e-15 relative error = 7.8052295268446377011636238683023e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9222 Order of pole = 2.082 x[1] = 0.651 y[1] (analytic) = 2.2288118178743187581446039856814 y[1] (numeric) = 2.2288118178743205068223704061498 absolute error = 1.7486777664204684e-15 relative error = 7.8457847019504416342210904358805e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.2MB, time=27.68 Real estimate of pole used Radius of convergence = 0.9212 Order of pole = 2.082 x[1] = 0.652 y[1] (analytic) = 2.2295743919438606296266514785814 y[1] (numeric) = 2.2295743919438623879999405087447 absolute error = 1.7583732890301633e-15 relative error = 7.8865872131636776713308744561617e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9202 Order of pole = 2.082 x[1] = 0.653 y[1] (analytic) = 2.2303385487402968553020340029206 y[1] (numeric) = 2.2303385487402986234338892660261 absolute error = 1.7681318552631055e-15 relative error = 7.9276388612022720064118983320558e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9192 Order of pole = 2.082 x[1] = 0.654 y[1] (analytic) = 2.2311042906843817434462752647102 y[1] (numeric) = 2.2311042906843835214002240315506 absolute error = 1.7779539487668404e-15 relative error = 7.9689414618151292017558051814783e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9182 Order of pole = 2.082 x[1] = 0.655 y[1] (analytic) = 2.2318716202056051928463585382168 y[1] (numeric) = 2.2318716202056069806864159547885 absolute error = 1.7878400574165717e-15 relative error = 8.0104968459246402582951959939592e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9172 Order of pole = 2.082 x[1] = 0.656 y[1] (analytic) = 2.2326405397422292236101759492136 y[1] (numeric) = 2.232640539742231021400849306066 absolute error = 1.7977906733568524e-15 relative error = 8.0523068597707060317789450128548e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9162 Order of pole = 2.082 x[1] = 0.657 y[1] (analytic) = 2.2334110517413247110909552073995 y[1] (numeric) = 2.2334110517413265188972482511311 absolute error = 1.8078062930437316e-15 relative error = 8.0943733650562817975809008341323e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9152 Order of pole = 2.082 x[1] = 0.658 y[1] (analytic) = 2.2341831586588083242517014324096 y[1] (numeric) = 2.2341831586588101421391187197743 absolute error = 1.8178874172873647e-15 relative error = 8.1366982390944701894312651581487e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9142 Order of pole = 2.082 x[1] = 0.659 y[1] (analytic) = 2.234956862959479669804887289874 y[1] (numeric) = 2.2349568629594814978394385849646 absolute error = 1.8280345512950906e-15 relative error = 8.1792833749571717184022716773450e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9132 Order of pole = 2.082 x[1] = 0.66 y[1] (analytic) = 2.2357321671170586434729096259867 y[1] (numeric) = 2.2357321671170604817211143409709 absolute error = 1.8382482047149842e-15 relative error = 8.2221306816253230282176057747882e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9122 Order of pole = 2.082 x[1] = 0.661 y[1] (analytic) = 2.2365090736142229897252060453324 y[1] (numeric) = 2.2365090736142248382540977252194 absolute error = 1.8485288916798870e-15 relative error = 8.2652420841407283198964643007114e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9112 Order of pole = 2.082 x[1] = 0.662 y[1] (analytic) = 2.2372875849426460713583913113087 y[1] (numeric) = 2.2372875849426479302355221632324 absolute error = 1.8588771308519237e-15 relative error = 8.3086195237595121108563161424755e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.2MB, time=28.16 Real estimate of pole used Radius of convergence = 0.9102 Order of pole = 2.082 x[1] = 0.663 y[1] (analytic) = 2.2380677036030348502963319652502 y[1] (numeric) = 2.2380677036030367195897774327599 absolute error = 1.8692934454675097e-15 relative error = 8.3522649581072079620428356958263e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9092 Order of pole = 2.082 x[1] = 0.664 y[1] (analytic) = 2.2388494321051680809977290731372 y[1] (numeric) = 2.2388494321051699607760924559934 absolute error = 1.8797783633828562e-15 relative error = 8.3961803613355057561939365710700e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9082 Order of pole = 2.082 x[1] = 0.665 y[1] (analytic) = 2.2396327729679347178695244414661 y[1] (numeric) = 2.239632772967936608201941561444 absolute error = 1.8903324171199779e-15 relative error = 8.4403677242806724066294147325934e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9072 Order of pole = 2.082 x[1] = 0.666 y[1] (analytic) = 2.2404177287193725380952859305868 y[1] (numeric) = 2.2404177287193744390514298437979 absolute error = 1.9009561439132111e-15 relative error = 8.4848290546236732811956854344636e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9062 Order of pole = 2.082 x[1] = 0.667 y[1] (analytic) = 2.2412043018967069812986635790197 y[1] (numeric) = 2.2412043018967088929487493352655 absolute error = 1.9116500857562458e-15 relative error = 8.5295663770520027581577981743630e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9052 Order of pole = 2.082 x[1] = 0.668 y[1] (analytic) = 2.2419924950463902074730410908424 y[1] (numeric) = 2.2419924950463921298878305405234 absolute error = 1.9224147894496810e-15 relative error = 8.5745817334232572327999460059122e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9042 Order of pole = 2.082 x[1] = 0.669 y[1] (analytic) = 2.2427823107241403746196377956708 y[1] (numeric) = 2.2427823107241423078704444447785 absolute error = 1.9332508066491077e-15 relative error = 8.6198771829304627909150338188683e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9032 Order of pole = 2.082 x[1] = 0.67 y[1] (analytic) = 2.243573751494981137547545443231 y[1] (numeric) = 2.2435737514949830817062393569579 absolute error = 1.9441586939137269e-15 relative error = 8.6654548022691821574114858438445e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9022 Order of pole = 2.082 x[1] = 0.671 y[1] (analytic) = 2.2443668199332813693005131290614 y[1] (numeric) = 2.2443668199332833244395258845694 absolute error = 1.9551390127555080e-15 relative error = 8.7113166858064169389505572149233e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9012 Order of pole = 2.082 x[1] = 0.672 y[1] (analytic) = 2.2451615186227951066867232624988 y[1] (numeric) = 2.2451615186227970728790529513953 absolute error = 1.9661923296888965e-15 relative error = 8.7574649457513366683338802581588e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9002 Order of pole = 2.082 x[1] = 0.673 y[1] (analytic) = 2.2459578501567017213993327919074 y[1] (numeric) = 2.2459578501567036987185490729822 absolute error = 1.9773192162810748e-15 relative error = 8.8039017123278433059853253200061e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8992 Order of pole = 2.082 memory used=228.8MB, alloc=4.2MB, time=28.64 x[1] = 0.674 y[1] (analytic) = 2.2467558171376463182271879154443 y[1] (numeric) = 2.2467558171376483067474371182301 absolute error = 1.9885202492027858e-15 relative error = 8.8506291339490060328694965326102e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8982 Order of pole = 2.082 x[1] = 0.675 y[1] (analytic) = 2.2475554221777803618668582602831 y[1] (numeric) = 2.2475554221777823616628685400068 absolute error = 1.9997960102797237e-15 relative error = 8.8976493773933774318836704802976e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8972 Order of pole = 2.082 x[1] = 0.676 y[1] (analytic) = 2.2483566678988025338589790523688 y[1] (numeric) = 2.2483566678988045450060655968694 absolute error = 2.0111470865445006e-15 relative error = 8.9449646279832207454164305297493e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8962 Order of pole = 2.082 x[1] = 0.677 y[1] (analytic) = 2.2491595569319998211838381774053 y[1] (numeric) = 2.2491595569320018437579084666013 absolute error = 2.0225740702891960e-15 relative error = 8.9925770897646710842587490644830e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8952 Order of pole = 2.082 x[1] = 0.678 y[1] (analytic) = 2.2499640919182888380632003185928 y[1] (numeric) = 2.249964091918290872140759437088 absolute error = 2.0340775591184952e-15 relative error = 9.0404889856898484491447417749515e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8942 Order of pole = 2.082 x[1] = 0.679 y[1] (analytic) = 2.2507702755082573825275236263311 y[1] (numeric) = 2.2507702755082594281856796297558 absolute error = 2.0456581560034247e-15 relative error = 9.0887025578009496448503081126121e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8932 Order of pole = 2.082 x[1] = 0.68 y[1] (analytic) = 2.2515781103622062293199967204696 y[1] (numeric) = 2.2515781103622082866364660561621 absolute error = 2.0573164693356925e-15 relative error = 9.1372200674163451397713754634871e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8922 Order of pole = 2.082 x[1] = 0.681 y[1] (analytic) = 2.2523875991501911607212063497531 y[1] (numeric) = 2.2523875991501932297743193323924 absolute error = 2.0690531129826393e-15 relative error = 9.1860437953186983515909727802540e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8912 Order of pole = 2.082 x[1] = 0.682 y[1] (analytic) = 2.2531987445520652368907398513178 y[1] (numeric) = 2.2531987445520673177594461941278 absolute error = 2.0808687063428100e-15 relative error = 9.2351760419451398161598971465798e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8902 Order of pole = 2.082 x[1] = 0.683 y[1] (analytic) = 2.2540115492575213073346327934349 y[1] (numeric) = 2.2540115492575234000985071955862 absolute error = 2.0927638744021513e-15 relative error = 9.2846191275795125680438943227497e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8892 Order of pole = 2.082 x[1] = 0.684 y[1] (analytic) = 2.2548260159661347651202919878734 y[1] (numeric) = 2.2548260159661368698595397787183 absolute error = 2.1047392477908449e-15 relative error = 9.3343753925467213587107917224627e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8882 Order of pole = 2.082 x[1] = 0.685 y[1] (analytic) = 2.2556421473874065454733585778446 y[1] (numeric) = 2.2556421473874086622688214186279 absolute error = 2.1167954628407833e-15 relative error = 9.3844471974092070953285647879792e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.2MB, time=29.13 Real estimate of pole used Radius of convergence = 0.8872 Order of pole = 2.082 x[1] = 0.686 y[1] (analytic) = 2.2564599462408063704039263100876 y[1] (numeric) = 2.2564599462408084993370879537834 absolute error = 2.1289331616436958e-15 relative error = 9.4348369231655704138873959941321e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8862 Order of pole = 2.082 x[1] = 0.687 y[1] (analytic) = 2.2572794152558162410225975650574 y[1] (numeric) = 2.2572794152558183821755896749915 absolute error = 2.1411529921099341e-15 relative error = 9.4855469714513761379957582155634e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8852 Order of pole = 2.082 x[1] = 0.688 y[1] (analytic) = 2.2581005571719741792200454405323 y[1] (numeric) = 2.2581005571719763326756534684571 absolute error = 2.1534556080279248e-15 relative error = 9.5365797647421609144893244160963e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8842 Order of pole = 2.082 x[1] = 0.689 y[1] (analytic) = 2.2589233747389182203970553679296 y[1] (numeric) = 2.2589233747389203862387244922263 absolute error = 2.1658416691242967e-15 relative error = 9.5879377465586688391295184969718e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8832 Order of pole = 2.082 x[1] = 0.69 y[1] (analytic) = 2.259747870716430658945445607569 y[1] (numeric) = 2.2597478707164328372572867322622 absolute error = 2.1783118411246932e-15 relative error = 9.6396233816743503639992900810540e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8822 Order of pole = 2.082 x[1] = 0.691 y[1] (analytic) = 2.2605740478744825481938137532761 y[1] (numeric) = 2.260574047874484739060609568552 absolute error = 2.1908667958152759e-15 relative error = 9.6916391563251410248548462610217e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8812 Order of pole = 2.082 x[1] = 0.692 y[1] (analytic) = 2.2614019089932784565457273263219 y[1] (numeric) = 2.261401908993280660052938431252 absolute error = 2.2035072111049301e-15 relative error = 9.7439875784215567476671187577662e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8802 Order of pole = 2.082 x[1] = 0.693 y[1] (analytic) = 2.2622314568633014815517719162198 y[1] (numeric) = 2.2622314568633036977855430043999 absolute error = 2.2162337710881801e-15 relative error = 9.7966711777631299358793584164671e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8791 Order of pole = 2.082 x[1] = 0.694 y[1] (analytic) = 2.2630626942853585236707914082017 y[1] (numeric) = 2.263062694285360752717957517025 absolute error = 2.2290471661088233e-15 relative error = 9.8496925062552152555627583541443e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8781 Order of pole = 2.082 x[1] = 0.695 y[1] (analytic) = 2.2638956240706258214897029156932 y[1] (numeric) = 2.2638956240706280634377957399851 absolute error = 2.2419480928242919e-15 relative error = 9.9030541381281929922744947542534e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8771 Order of pole = 2.082 x[1] = 0.696 y[1] (analytic) = 2.2647302490406947501854454169814 y[1] (numeric) = 2.2647302490406970051226996877339 absolute error = 2.2549372542707525e-15 relative error = 9.9567586701591043186799893032897e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.2MB, time=29.61 Real estimate of pole used Radius of convergence = 0.8761 Order of pole = 2.082 x[1] = 0.697 y[1] (analytic) = 2.2655665720276178850269270996325 y[1] (numeric) = 2.2655665720276201530422870285835 absolute error = 2.2680153599289510e-15 relative error = 1.0010808721895739833370089303840e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8751 Order of pole = 2.082 x[1] = 0.698 y[1] (analytic) = 2.2664045958739553317292733803101 y[1] (numeric) = 2.2664045958739576129123991711247 absolute error = 2.2811831257908146e-15 relative error = 1.0065206935883222004068693414573e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8741 Order of pole = 2.082 x[1] = 0.699 y[1] (analytic) = 2.2672443234328213254872468430288 y[1] (numeric) = 2.2672443234328236199285212698464 absolute error = 2.2944412744268176e-15 relative error = 1.0119955977893099454802657977059e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8731 Order of pole = 2.082 x[1] = 0.7 y[1] (analytic) = 2.2680857575679311005294132926142 y[1] (numeric) = 2.268085757567933408319948346738 absolute error = 2.3077905350541238e-15 relative error = 1.0175058537154997798014195627868e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8721 Order of pole = 2.082 x[1] = 0.701 y[1] (analytic) = 2.2689289011536480320494661350163 y[1] (numeric) = 2.2689289011536503532811097405288 absolute error = 2.3212316436055125e-15 relative error = 1.0230517326590845935864497633888e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8711 Order of pole = 2.082 x[1] = 0.702 y[1] (analytic) = 2.2697737570750310523860957708006 y[1] (numeric) = 2.269773757075033387151438569901 absolute error = 2.3347653427991004e-15 relative error = 1.0286335083051719966433029654552e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8701 Order of pole = 2.082 x[1] = 0.703 y[1] (analytic) = 2.2706203282278823433379030374283 y[1] (numeric) = 2.2706203282278846917302852462958 absolute error = 2.3483923822088675e-15 relative error = 1.0342514567557328124272230682327e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8691 Order of pole = 2.082 x[1] = 0.704 y[1] (analytic) = 2.2714686175187953065151073909101 y[1] (numeric) = 2.2714686175187976686286257269089 absolute error = 2.3621135183359988e-15 relative error = 1.0399058565538176319000875210545e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8681 Order of pole = 2.082 x[1] = 0.705 y[1] (analytic) = 2.2723186278652028136451929257121 y[1] (numeric) = 2.2723186278652051895747076067631 absolute error = 2.3759295146810510e-15 relative error = 1.0455969887080442189372851212326e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8671 Order of pole = 2.082 x[1] = 0.706 y[1] (analytic) = 2.2731703621954257387651699577365 y[1] (numeric) = 2.2731703621954281286063117746924 absolute error = 2.3898411418169559e-15 relative error = 1.0513251367173596417295786844216e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8661 Order of pole = 2.082 x[1] = 0.707 y[1] (analytic) = 2.2740238234487217742488082200897 y[1] (numeric) = 2.2740238234487241780979856829596 absolute error = 2.4038491774628699e-15 relative error = 1.0570905865960799727474506523049e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.2MB, time=30.08 Real estimate of pole used Radius of convergence = 0.8651 Order of pole = 2.082 x[1] = 0.708 y[1] (analytic) = 2.2748790145753345326330212436224 y[1] (numeric) = 2.2748790145753369505874278025041 absolute error = 2.4179544065588817e-15 relative error = 1.0628936268992115692044997937304e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8641 Order of pole = 2.082 x[1] = 0.709 y[1] (analytic) = 2.2757359385365429362235517297003 y[1] (numeric) = 2.2757359385365453683811730712879 absolute error = 2.4321576213415876e-15 relative error = 1.0687345487480567383697770019297e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8631 Order of pole = 2.082 x[1] = 0.71 y[1] (analytic) = 2.2765945983047108964762262047543 y[1] (numeric) = 2.2765945983047133429358476253013 absolute error = 2.4464596214205470e-15 relative error = 1.0746136458561079800144546737582e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8621 Order of pole = 2.082 x[1] = 0.711 y[1] (analytic) = 2.2774549968633372851663155261067 y[1] (numeric) = 2.277454996863339746027529381736 absolute error = 2.4608612138556293e-15 relative error = 1.0805312145552343615611987119712e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8611 Order of pole = 2.082 x[1] = 0.712 y[1] (analytic) = 2.2783171372071061993749574556623 y[1] (numeric) = 2.2783171372071086747381706909244 absolute error = 2.4753632132352621e-15 relative error = 1.0864875538221629906739788931558e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8601 Order of pole = 2.082 x[1] = 0.713 y[1] (analytic) = 2.2791810223419375223381701198588 y[1] (numeric) = 2.2791810223419400123046118754527 absolute error = 2.4899664417555939e-15 relative error = 1.0924829653052599793220208437590e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8591 Order of pole = 2.082 x[1] = 0.714 y[1] (analytic) = 2.2800466552850377822207123368858 y[1] (numeric) = 2.2800466552850402868924416374683 absolute error = 2.5046717293005825e-15 relative error = 1.0985177533516143931074850513603e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8581 Order of pole = 2.082 x[1] = 0.715 y[1] (analytic) = 2.2809140390649513108939301404405 y[1] (numeric) = 2.2809140390649538303738436634612 absolute error = 2.5194799135230207e-15 relative error = 1.1045922250344288345102210005917e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8571 Order of pole = 2.082 x[1] = 0.716 y[1] (analytic) = 2.2817831767216117048137700070342 y[1] (numeric) = 2.2817831767216142392056099335467 absolute error = 2.5343918399265125e-15 relative error = 1.1107066901807209887810260847746e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8561 Order of pole = 2.082 x[1] = 0.717 y[1] (analytic) = 2.2826540713063935901123399641789 y[1] (numeric) = 2.2826540713063961395207019125889 absolute error = 2.5494083619484100e-15 relative error = 1.1168614613993391235950188291706e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8551 Order of pole = 2.082 x[1] = 0.718 y[1] (analytic) = 2.2835267258821646940337616022256 y[1] (numeric) = 2.2835267258821672585641026459513 absolute error = 2.5645303410437257e-15 relative error = 1.1230568541092964847661914818079e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8541 Order of pole = 2.082 memory used=244.1MB, alloc=4.2MB, time=30.57 x[1] = 0.719 y[1] (analytic) = 2.2844011435233382248625807355185 y[1] (numeric) = 2.2844011435233408046212275055499 absolute error = 2.5797586467700314e-15 relative error = 1.1292931865684279726311937425103e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8531 Order of pole = 2.082 x[1] = 0.72 y[1] (analytic) = 2.2852773273159255625106937811594 y[1] (numeric) = 2.2852773273159281576048506545168 absolute error = 2.5950941568733574e-15 relative error = 1.1355707799023735566902753390010e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8521 Order of pole = 2.082 x[1] = 0.721 y[1] (analytic) = 2.286155280357589261946602588617 y[1] (numeric) = 2.2861552803575918724843599637204 absolute error = 2.6105377573751034e-15 relative error = 1.1418899581338918556077541163407e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8511 Order of pole = 2.082 x[1] = 0.722 y[1] (analytic) = 2.2870350057576963716688342237229 y[1] (numeric) = 2.287035005757698997759176883699 absolute error = 2.6260903426599761e-15 relative error = 1.1482510482125088623225714027681e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8501 Order of pole = 2.082 x[1] = 0.723 y[1] (analytic) = 2.2879165066373720694435558701423 y[1] (numeric) = 2.2879165066373747111963714351087 absolute error = 2.6417528155649664e-15 relative error = 1.1546543800445058497685261536359e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8491 Order of pole = 2.082 x[1] = 0.724 y[1] (analytic) = 2.2887997861295536175447803650893 y[1] (numeric) = 2.2887997861295562750708678344676 absolute error = 2.6575260874693783e-15 relative error = 1.1611002865232501195054865119709e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8481 Order of pole = 2.082 x[1] = 0.725 y[1] (analytic) = 2.2896848473790446397540967601086 y[1] (numeric) = 2.2896848473790473131651751460336 absolute error = 2.6734110783859250e-15 relative error = 1.1675891035598737177913196416509e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8471 Order of pole = 2.082 x[1] = 0.726 y[1] (analytic) = 2.2905716935425697223955745400089 y[1] (numeric) = 2.2905716935425724118042915929143 absolute error = 2.6894087170529054e-15 relative error = 1.1741211701143042121198145853556e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8461 Order of pole = 2.082 x[1] = 0.727 y[1] (analytic) = 2.2914603277888293417003816132254 y[1] (numeric) = 2.2914603277888320472203226407005 absolute error = 2.7055199410274751e-15 relative error = 1.1806968282266519896166814862385e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8451 Order of pole = 2.082 x[1] = 0.728 y[1] (analytic) = 2.2923507532985551198147267969008 y[1] (numeric) = 2.2923507532985578415604235769266 absolute error = 2.7217456967800258e-15 relative error = 1.1873164230489584257172468440852e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8441 Order of pole = 2.082 x[1] = 0.729 y[1] (analytic) = 2.293242973264565411783989174158 y[1] (numeric) = 2.2932429732645681498709289638466 absolute error = 2.7380869397896886e-15 relative error = 1.1939803028773099436887677669382e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8431 Order of pole = 2.082 x[1] = 0.73 y[1] (analytic) = 2.2941369908918212258653313364992 y[1] (numeric) = 2.2941369908918239804099659774744 absolute error = 2.7545446346409752e-15 relative error = 1.2006888191843223038708950512770e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.2MB, time=31.05 Real estimate of pole used Radius of convergence = 0.8421 Order of pole = 2.082 x[1] = 0.731 y[1] (analytic) = 2.295032809397482479540713101157 y[1] (numeric) = 2.295032809397485250660468222729 absolute error = 2.7711197551215720e-15 relative error = 1.2074423266519998713011668479095e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8411 Order of pole = 2.082 x[1] = 0.732 y[1] (analytic) = 2.2959304320109645936220287950544 y[1] (numeric) = 2.2959304320109673814353131163571 absolute error = 2.7878132843213027e-15 relative error = 1.2142411832049748443192489706772e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8401 Order of pole = 2.082 x[1] = 0.733 y[1] (analytic) = 2.2968298619739954268600866309728 y[1] (numeric) = 2.2968298619739982314863013632466 absolute error = 2.8046262147322738e-15 relative error = 1.2210857500441308759408356106373e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8391 Order of pole = 2.082 x[1] = 0.734 y[1] (analytic) = 2.2977311025406725534893350987139 y[1] (numeric) = 2.2977311025406753750488834489339 absolute error = 2.8215595483502200e-15 relative error = 1.2279763916806166245145865202151e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8381 Order of pole = 2.082 x[1] = 0.735 y[1] (analytic) = 2.2986341569775208861606207099052 y[1] (numeric) = 2.2986341569775237247749174869692 absolute error = 2.8386142967770640e-15 relative error = 1.2349134759702536520726203205341e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8371 Order of pole = 2.082 x[1] = 0.736 y[1] (analytic) = 2.2995390285635506467348359496629 y[1] (numeric) = 2.2995390285635535025263172743704 absolute error = 2.8557914813247075e-15 relative error = 1.2418973741483440617735869833826e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8361 Order of pole = 2.082 x[1] = 0.737 y[1] (analytic) = 2.3004457205903156874310880065578 y[1] (numeric) = 2.3004457205903185605232211266275 absolute error = 2.8730921331200697e-15 relative error = 1.2489284608648830180058740471058e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8351 Order of pole = 2.082 x[1] = 0.738 y[1] (analytic) = 2.3013542363619721648439899044454 y[1] (numeric) = 2.3013542363619750553612831158343 absolute error = 2.8905172932113889e-15 relative error = 1.2560071142201809586198222295854e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8341 Order of pole = 2.082 x[1] = 0.739 y[1] (analytic) = 2.3022645791953375693658482015365 y[1] (numeric) = 2.3022645791953404774338608773417 absolute error = 2.9080680126758052e-15 relative error = 1.2631337158009013221114235148488e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8331 Order of pole = 2.082 x[1] = 0.74 y[1] (analytic) = 2.3031767524199501125708976353428 y[1] (numeric) = 2.3031767524199530383162503635834 absolute error = 2.9257453527282406e-15 relative error = 1.2703086507165188419424497678442e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8321 Order of pole = 2.082 x[1] = 0.741 y[1] (analytic) = 2.3040907593781284751403151848554 y[1] (numeric) = 2.3040907593781314186907000164492 absolute error = 2.9435503848315938e-15 relative error = 1.2775323076362038638648236496239e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.2MB, time=31.53 Real estimate of pole used Radius of convergence = 0.8311 Order of pole = 2.082 x[1] = 0.742 y[1] (analytic) = 2.305006603425031917928536228146 y[1] (numeric) = 2.3050066034250348794127270364129 absolute error = 2.9614841908082669e-15 relative error = 1.2848050788261380668948141689662e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8301 Order of pole = 2.082 x[1] = 0.743 y[1] (analytic) = 2.3059242879287207587933960561425 y[1] (numeric) = 2.3059242879287237383412590091852 absolute error = 2.9795478629530427e-15 relative error = 1.2921273601872675872419800194513e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8291 Order of pole = 2.082 x[1] = 0.744 y[1] (analytic) = 2.306843816270217217834833250583 y[1] (numeric) = 2.3068438162702202155773373979123 absolute error = 2.9977425041473293e-15 relative error = 1.2994995512934986434607658812708e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8281 Order of pole = 2.082 x[1] = 0.745 y[1] (analytic) = 2.307765191843566633709319662748 y[1] (numeric) = 2.3077651918435696497785476375397 absolute error = 3.0160692279747917e-15 relative error = 1.3069220554303420296194949828584e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8271 Order of pole = 2.082 x[1] = 0.746 y[1] (analytic) = 2.3086884180558990537098272842455 y[1] (numeric) = 2.3086884180559020882389861226328 absolute error = 3.0345291588383873e-15 relative error = 1.3143952796340115947459978696419e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8261 Order of pole = 2.082 x[1] = 0.747 y[1] (analytic) = 2.3096134983274912003240075550376 y[1] (numeric) = 2.3096134983274942534474396338631 absolute error = 3.0531234320788255e-15 relative error = 1.3219196347309832236224992300035e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8251 Order of pole = 2.082 x[1] = 0.748 y[1] (analytic) = 2.3105404360918288170063460090569 y[1] (numeric) = 2.3105404360918318888595401035266 absolute error = 3.0718531940944697e-15 relative error = 1.3294955353780199749644276674273e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8241 Order of pole = 2.082 x[1] = 0.749 y[1] (analytic) = 2.3114692347956693959233670453628 y[1] (numeric) = 2.3114692347956724866429695080641 absolute error = 3.0907196024627013e-15 relative error = 1.3371234001026695611927449470533e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8231 Order of pole = 2.082 x[1] = 0.75 y[1] (analytic) = 2.3123998978991052904545024936409 y[1] (numeric) = 2.3123998978991084001783285564063 absolute error = 3.1097238260627654e-15 relative error = 1.3448036513442403610580429235108e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8221 Order of pole = 2.082 x[1] = 0.751 y[1] (analytic) = 2.313332428875627215255006007754 y[1] (numeric) = 2.3133324288756303441220512078722 absolute error = 3.1288670452001182e-15 relative error = 1.3525367154952622495640437123378e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8211 Order of pole = 2.082 x[1] = 0.752 y[1] (analytic) = 2.314266831212188136711295691219 y[1] (numeric) = 2.3142668312121912848617474235142 absolute error = 3.1481504517322952e-15 relative error = 1.3603230229434381036748111827664e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.2MB, time=32.01 Real estimate of pole used Radius of convergence = 0.8201 Order of pole = 2.082 x[1] = 0.753 y[1] (analytic) = 2.3152031084092675566433422859122 y[1] (numeric) = 2.3152031084092707242185914822352 absolute error = 3.1675752491963230e-15 relative error = 1.3681630081140934044475806336320e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8191 Order of pole = 2.082 x[1] = 0.754 y[1] (analytic) = 2.3161412639809361921331923232472 y[1] (numeric) = 2.3161412639809393792758452609402 absolute error = 3.1871426529376930e-15 relative error = 1.3760571095131293720388175030117e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8181 Order of pole = 2.082 x[1] = 0.755 y[1] (analytic) = 2.3170813014549210543834274603922 y[1] (numeric) = 2.3170813014549242612373177013124 absolute error = 3.2068538902409202e-15 relative error = 1.3840057697704871495759668341263e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8171 Order of pole = 2.082 x[1] = 0.756 y[1] (analytic) = 2.3180232243726709295343154497572 y[1] (numeric) = 2.3180232243726741562445159114642 absolute error = 3.2267102004617070e-15 relative error = 1.3920094356841290860522705941842e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8161 Order of pole = 2.082 x[1] = 0.757 y[1] (analytic) = 2.3189670362894222643936074974408 y[1] (numeric) = 2.318967036289425511106442658175 absolute error = 3.2467128351607342e-15 relative error = 1.4000685582645441224636632772233e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8151 Order of pole = 2.082 x[1] = 0.758 y[1] (analytic) = 2.319912740774265460058383867981 y[1] (numeric) = 2.3199127407742687269214421070833 absolute error = 3.2668630582391023e-15 relative error = 1.4081835927797846321968524419920e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.814 Order of pole = 2.082 x[1] = 0.759 y[1] (analytic) = 2.3208603414102115764340472344018 y[1] (numeric) = 2.3208603414102148635961933098458 absolute error = 3.2871621460754440e-15 relative error = 1.4163549988010410761513296329581e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.813 Order of pole = 2.082 x[1] = 0.76 y[1] (analytic) = 2.3218098417942594506815142338154 y[1] (numeric) = 2.3218098417942627582929018985461 absolute error = 3.3076113876647307e-15 relative error = 1.4245832402487616117180231141984e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.812 Order of pole = 2.082 x[1] = 0.761 y[1] (analytic) = 2.3227612455374632326498627836701 y[1] (numeric) = 2.3227612455374665608619475424683 absolute error = 3.3282120847587982e-15 relative error = 1.4328687854393247854515059568139e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.811 Order of pole = 2.082 x[1] = 0.762 y[1] (analytic) = 2.3237145562650003403781587908365 y[1] (numeric) = 2.3237145562650036893437107994486 absolute error = 3.3489655520086121e-15 relative error = 1.4412121071322713705343870273815e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.81 Order of pole = 2.082 x[1] = 0.763 y[1] (analytic) = 2.3246697776162398387769138290406 y[1] (numeric) = 2.3246697776162432086500309373386 absolute error = 3.3698731171082980e-15 relative error = 1.4496136825781033492393794101260e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.2MB, time=32.49 Real estimate of pole used Radius of convergence = 0.809 Order of pole = 2.082 x[1] = 0.764 y[1] (analytic) = 2.3256269132448112446266180893575 y[1] (numeric) = 2.3256269132448146355627390303193 absolute error = 3.3909361209409618e-15 relative error = 1.4580739935666580802409397033250e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.808 Order of pole = 2.082 x[1] = 0.765 y[1] (analytic) = 2.3265859668186737610580533794586 y[1] (numeric) = 2.3265859668186771732139711057804 absolute error = 3.4121559177263218e-15 relative error = 1.4665935264760640964583411482554e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.807 Order of pole = 2.082 x[1] = 0.766 y[1] (analytic) = 2.3275469420201859447066221526308 y[1] (numeric) = 2.3275469420201893782404973228111 absolute error = 3.4335338751701803e-15 relative error = 1.4751727723222875150009274418275e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.806 Order of pole = 2.082 x[1] = 0.767 y[1] (analytic) = 2.3285098425461758087607335170664 y[1] (numeric) = 2.3285098425461792638321081328243 absolute error = 3.4550713746157579e-15 relative error = 1.4838122268092760575814558628731e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.805 Order of pole = 2.082 x[1] = 0.768 y[1] (analytic) = 2.3294746721080113651523689770483 y[1] (numeric) = 2.3294746721080148419221801739653 absolute error = 3.4767698111969170e-15 relative error = 1.4925123903797090519335177261132e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.804 Order of pole = 2.082 x[1] = 0.769 y[1] (analytic) = 2.3304414344316716091663123961783 y[1] (numeric) = 2.3304414344316751077969063894787 absolute error = 3.4986305939933004e-15 relative error = 1.5012737682663614779573500161663e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.803 Order of pole = 2.082 x[1] = 0.77 y[1] (analytic) = 2.3314101332578179497731734932087 y[1] (numeric) = 2.3314101332578214704283196806197 absolute error = 3.5206551461874110e-15 relative error = 1.5100968705440901165017958252180e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.802 Order of pole = 2.082 x[1] = 0.771 y[1] (analytic) = 2.3323807723418660890202652671271 y[1] (numeric) = 2.3323807723418696318651704907868 absolute error = 3.5428449052236597e-15 relative error = 1.5189822121824502812484320152942e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.801 Order of pole = 2.082 x[1] = 0.772 y[1] (analytic) = 2.3333533554540583538436163235351 y[1] (numeric) = 2.333353355454061919044939292944 absolute error = 3.5652013229694089e-15 relative error = 1.5279303130989516918866018539232e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8 Order of pole = 2.082 x[1] = 0.773 y[1] (analytic) = 2.3343278863795364836939124030474 y[1] (numeric) = 2.3343278863795400714197782810856 absolute error = 3.5877258658780382e-15 relative error = 1.5369416982129616525592507282514e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.799 Order of pole = 2.082 x[1] = 0.774 y[1] (analytic) = 2.3353043689184148773989707993568 y[1] (numeric) = 2.3353043689184184878189859534181 absolute error = 3.6104200151540613e-15 relative error = 1.5460168975002646766879841728953e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.798 Order of pole = 2.082 memory used=263.2MB, alloc=4.2MB, time=32.97 x[1] = 0.775 y[1] (analytic) = 2.3362828068858543027154601462071 y[1] (numeric) = 2.3362828068858579360007270665291 absolute error = 3.6332852669203220e-15 relative error = 1.5551564460482871742165453614712e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.797 Order of pole = 2.082 x[1] = 0.776 y[1] (analytic) = 2.3372632041121360720529896372955 y[1] (numeric) = 2.337263204112139728376122024594 absolute error = 3.6563231323872985e-15 relative error = 1.5643608841119963206259155264048e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.796 Order of pole = 2.082 x[1] = 0.777 y[1] (analytic) = 2.338245564442736687884409552275 y[1] (numeric) = 2.3382455644427403674195475768197 absolute error = 3.6795351380245447e-15 relative error = 1.5736307571704819582488066040511e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.795 Order of pole = 2.082 x[1] = 0.778 y[1] (analytic) = 2.3392298917384029613871924699645 y[1] (numeric) = 2.3392298917384066643100182042631 absolute error = 3.7029228257342986e-15 relative error = 1.5829666159842309243902275367292e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.794 Order of pole = 2.082 x[1] = 0.779 y[1] (analytic) = 2.34021618987522760789210527488 y[1] (numeric) = 2.3402161898752313343798583021681 absolute error = 3.7264877530272881e-15 relative error = 1.5923690166531032294611651847021e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.793 Order of pole = 2.082 x[1] = 0.78 y[1] (analytic) = 2.3412044627447253227470395680139 y[1] (numeric) = 2.3412044627447290729785327687785 absolute error = 3.7502314932007646e-15 relative error = 1.6018385206750194937487931772311e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.792 Order of pole = 2.082 x[1] = 0.781 y[1] (analytic) = 2.3421947142539093412358459852287 y[1] (numeric) = 2.3421947142539131153914815040242 absolute error = 3.7741556355187955e-15 relative error = 1.6113756950053692926222414841837e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.791 Order of pole = 2.082 x[1] = 0.782 y[1] (analytic) = 2.3431869483253684862243198602231 y[1] (numeric) = 2.3431869483253722844861052550703 absolute error = 3.7982617853948472e-15 relative error = 1.6209811121171502144062934254658e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.79 Order of pole = 2.082 x[1] = 0.783 y[1] (analytic) = 2.3441811688973447072381153436455 y[1] (numeric) = 2.3441811688973485297896799203361 absolute error = 3.8225515645766906e-15 relative error = 1.6306553500618475458601947624869e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.789 Order of pole = 2.082 x[1] = 0.784 y[1] (analytic) = 2.34517737992381111471032625244 y[1] (numeric) = 2.3451773799238149617369375861019 absolute error = 3.8470266113336619e-15 relative error = 1.6403989925310647805545718154391e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.788 Order of pole = 2.082 x[1] = 0.785 y[1] (analytic) = 2.3461755853745505131697683684272 y[1] (numeric) = 2.3461755853745543848583490147388 absolute error = 3.8716885806463116e-15 relative error = 1.6502126289189151258682064064839e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.787 Order of pole = 2.082 x[1] = 0.786 y[1] (analytic) = 2.3471757892352344371746334752872 y[1] (numeric) = 2.347175789235238333713777873762 absolute error = 3.8965391443984748e-15 relative error = 1.6600968543851842069266170881365e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.2MB, time=33.45 Real estimate of pole used Radius of convergence = 0.786 Order of pole = 2.082 x[1] = 0.787 y[1] (analytic) = 2.3481779955075026938301640103494 y[1] (numeric) = 2.3481779955075066154101555821468 absolute error = 3.9215799915717974e-15 relative error = 1.6700522699192747414272519346343e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.785 Order of pole = 2.082 x[1] = 0.788 y[1] (analytic) = 2.3491822082090434157633227534292 y[1] (numeric) = 2.3491822082090473625761511961824 absolute error = 3.9468128284427532e-15 relative error = 1.6800794824049440639404822120552e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.784 Order of pole = 2.082 x[1] = 0.789 y[1] (analytic) = 2.3501884313736736284621084712748 y[1] (numeric) = 2.3501884313736776007014872534604 absolute error = 3.9722393787821856e-15 relative error = 1.6901791046858447586329738453852e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.783 Order of pole = 2.082 x[1] = 0.79 y[1] (analytic) = 2.3511966690514203359221999259937 y[1] (numeric) = 2.3511966690514243337835839834047 absolute error = 3.9978613840574110e-15 relative error = 1.7003517556318800405460706819453e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.782 Order of pole = 2.082 x[1] = 0.791 y[1] (analytic) = 2.3522069253086021285790012339232 y[1] (numeric) = 2.3522069253086061522596048708422 absolute error = 4.0236806036369190e-15 relative error = 1.7105980602063846051627448567495e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.781 Order of pole = 2.082 x[1] = 0.792 y[1] (analytic) = 2.3532192042279113175389153751331 y[1] (numeric) = 2.3532192042279153672377303728407 absolute error = 4.0496988149977076e-15 relative error = 1.7209186495341429158281603637636e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.78 Order of pole = 2.082 x[1] = 0.793 y[1] (analytic) = 2.3542335099084965991597939037462 y[1] (numeric) = 2.3542335099085006750776078390347 absolute error = 4.0759178139352885e-15 relative error = 1.7313141609702555094679568937759e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.779 Order of pole = 2.082 x[1] = 0.794 y[1] (analytic) = 2.3552498464660462540670038501903 y[1] (numeric) = 2.3552498464660503564064186265935 absolute error = 4.1023394147764032e-15 relative error = 1.7417852381698662106023250833091e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.778 Order of pole = 2.082 x[1] = 0.795 y[1] (analytic) = 2.3562682180328718847284217478593 y[1] (numeric) = 2.3562682180328760136938723423447 absolute error = 4.1289654505944854e-15 relative error = 1.7523325311587608601483439871462e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.777 Order of pole = 2.082 x[1] = 0.796 y[1] (analytic) = 2.3572886287579926957489140234955 y[1] (numeric) = 2.3572886287579968515466874514073 absolute error = 4.1557977734279118e-15 relative error = 1.7629566964048508960114863225422e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.776 Order of pole = 2.082 x[1] = 0.797 y[1] (analytic) = 2.3583110828072203210824970843758 y[1] (numeric) = 2.3583110828072245039207515854542 absolute error = 4.1828382545010784e-15 relative error = 1.7736583968905529229800484909999e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.2MB, time=33.94 Real estimate of pole used Radius of convergence = 0.775 Order of pole = 2.082 x[1] = 0.798 y[1] (analytic) = 2.3593355843632442023983937946845 y[1] (numeric) = 2.3593355843632484124871782430288 absolute error = 4.2100887844483443e-15 relative error = 1.7844383021860774139849002114905e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.774 Order of pole = 2.082 x[1] = 0.799 y[1] (analytic) = 2.3603621376257175228756201948992 y[1] (numeric) = 2.3603621376257217604268937357825 absolute error = 4.2375512735408833e-15 relative error = 1.7952970885236388847154158752200e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.773 Order of pole = 2.082 x[1] = 0.8 y[1] (analytic) = 2.3613907468113437007395518770172 y[1] (numeric) = 2.3613907468113479659672037935022 absolute error = 4.2652276519164850e-15 relative error = 1.8062354388726003987728745654553e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.772 Order of pole = 2.082 x[1] = 0.801 y[1] (analytic) = 2.362421416153963446893138040091 y[1] (numeric) = 2.3624214161539677400130078524387 absolute error = 4.2931198698123477e-15 relative error = 1.8172540430155654344342570080010e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.771 Order of pole = 2.082 x[1] = 0.802 y[1] (analytic) = 2.3634541499046423910350576304017 y[1] (numeric) = 2.3634541499046467122649554313073 absolute error = 4.3212298978009056e-15 relative error = 1.8283535976254301474018488371283e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.77 Order of pole = 2.082 x[1] = 0.803 y[1] (analytic) = 2.364488952331759280697150895648 y[1] (numeric) = 2.3644889523317636302568779243825 absolute error = 4.3495597270287345e-15 relative error = 1.8395348063434097009179587095235e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.769 Order of pole = 2.082 x[1] = 0.804 y[1] (analytic) = 2.3655258277210947576739159919797 y[1] (numeric) = 2.3655258277210991357852854505601 absolute error = 4.3781113694585804e-15 relative error = 1.8507983798580523343290394061579e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.768 Order of pole = 2.082 x[1] = 0.805 y[1] (analytic) = 2.3665647803759207163577388789325 y[1] (numeric) = 2.3665647803759251232445969934868 absolute error = 4.4068868581145543e-15 relative error = 1.8621450359852542908672948998895e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.767 Order of pole = 2.082 x[1] = 0.806 y[1] (analytic) = 2.3676058146170902485348305867392 y[1] (numeric) = 2.3676058146170946844230779172806 absolute error = 4.4358882473305414e-15 relative error = 1.8735754997492907107766296326689e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.766 Order of pole = 2.082 x[1] = 0.807 y[1] (analytic) = 2.3686489347831281792385840745257 y[1] (numeric) = 2.3686489347831326443561970763943 absolute error = 4.4651176130018686e-15 relative error = 1.8850905034648756886323814073215e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.765 Order of pole = 2.082 x[1] = 0.808 y[1] (analytic) = 2.3696941452303221982992384138469 y[1] (numeric) = 2.3696941452303266928762912541269 absolute error = 4.4945770528402800e-15 relative error = 1.8966907868202670553864426745462e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.2MB, time=34.42 Real estimate of pole used Radius of convergence = 0.764 Order of pole = 2.082 x[1] = 0.809 y[1] (analytic) = 2.3707414503328145922713560940867 y[1] (numeric) = 2.3707414503328191165400427263514 absolute error = 4.5242686866322647e-15 relative error = 1.9083770969614290729909783237896e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.763 Order of pole = 2.082 x[1] = 0.81 y[1] (analytic) = 2.3717908544826945814636850864397 y[1] (numeric) = 2.3717908544826991356583415872296 absolute error = 4.5541946565007899e-15 relative error = 1.9201501885772698103073462465684e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.762 Order of pole = 2.082 x[1] = 0.811 y[1] (analytic) = 2.3728423620900912668394962223641 y[1] (numeric) = 2.3728423620900958511966233928488 absolute error = 4.5843571271704847e-15 relative error = 1.9320108239859666654583627618885e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.761 Order of pole = 2.082 x[1] = 0.812 y[1] (analytic) = 2.373895977583267191599463811175 y[1] (numeric) = 2.3738959775832718063577500475025 absolute error = 4.6147582862363275e-15 relative error = 1.9439597732223965694391680584698e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.76 Order of pole = 2.082 x[1] = 0.813 y[1] (analytic) = 2.374951705408712522303598681322 y[1] (numeric) = 2.3749517054087171677039431172078 absolute error = 4.6454003444358858e-15 relative error = 1.9559978141266855781254536090980e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.759 Order of pole = 2.082 x[1] = 0.814 y[1] (analytic) = 2.3760095500312398544336534941734 y[1] (numeric) = 2.3760095500312445307191894193364 absolute error = 4.6762855359251630e-15 relative error = 1.9681257324338949052673788527767e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.758 Order of pole = 2.082 x[1] = 0.815 y[1] (analytic) = 2.3770695159340796473428058340519 y[1] (numeric) = 2.3770695159340843547589243921531 absolute error = 4.7074161185581012e-15 relative error = 1.9803443218648579884779454930878e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.757 Order of pole = 2.082 x[1] = 0.816 y[1] (analytic) = 2.3781316076189762935852908839943 y[1] (numeric) = 2.3781316076189810323796650537905 absolute error = 4.7387943741697962e-15 relative error = 1.9926543842181861110347485540877e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.756 Order of pole = 2.082 x[1] = 0.817 y[1] (analytic) = 2.3791958296062848276650081884792 y[1] (numeric) = 2.3791958296062895980876170519576 absolute error = 4.7704226088634784e-15 relative error = 2.0050567294634589435129183088998e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.755 Order of pole = 2.082 x[1] = 0.818 y[1] (analytic) = 2.3802621864350682792889718935272 y[1] (numeric) = 2.3802621864350730815921251948409 absolute error = 4.8023031533013137e-15 relative error = 2.0175521758356164325854971588536e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.754 Order of pole = 2.082 x[1] = 0.819 y[1] (analytic) = 2.3813306826631956762588168297264 y[1] (numeric) = 2.3813306826632005106971798288079 absolute error = 4.8344383629990815e-15 relative error = 2.0301415499305696183410924233203e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.2MB, time=34.89 Real estimate of pole used Radius of convergence = 0.753 Order of pole = 2.082 x[1] = 0.82 y[1] (analytic) = 2.3824013228674407021814198318618 y[1] (numeric) = 2.3824013228674455690120384566481 absolute error = 4.8668306186247863e-15 relative error = 2.0428256868020475988495907169388e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.752 Order of pole = 2.082 x[1] = 0.821 y[1] (analytic) = 2.3834741116435810142280528164267 y[1] (numeric) = 2.3834741116435859137103791176879 absolute error = 4.8994823263012612e-15 relative error = 2.0556054300596985055607707196404e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.751 Order of pole = 2.082 x[1] = 0.822 y[1] (analytic) = 2.3845490536064982262203574925795 y[1] (numeric) = 2.3845490536065031586162754054003 absolute error = 4.9323959179128208e-15 relative error = 2.0684816319684619040805018580422e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.75 Order of pole = 2.082 x[1] = 0.823 y[1] (analytic) = 2.3856261533902785623708273721521 y[1] (numeric) = 2.3856261533902835279446787881771 absolute error = 4.9655738514160250e-15 relative error = 2.0814551535492315987506095011323e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7489 Order of pole = 2.082 x[1] = 0.824 y[1] (analytic) = 2.3867054156483141870554072622996 y[1] (numeric) = 2.3867054156483191860740184169126 absolute error = 4.9990186111546130e-15 relative error = 2.0945268646808267783054989102416e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7479 Order of pole = 2.082 x[1] = 0.825 y[1] (analytic) = 2.3877868450534052160462800467722 y[1] (numeric) = 2.3877868450534102487789882254419 absolute error = 5.0327327081786697e-15 relative error = 2.1076976442032905378331991670558e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7469 Order of pole = 2.082 x[1] = 0.826 y[1] (analytic) = 2.3888704462978624146839117506346 y[1] (numeric) = 2.3888704462978674814025923187218 absolute error = 5.0667186805680872e-15 relative error = 2.1209683800225349001024324206631e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7459 Order of pole = 2.082 x[1] = 0.827 y[1] (analytic) = 2.389956224093610588518975187407 y[1] (numeric) = 2.3899562240936156894980689477919 absolute error = 5.1009790937603849e-15 relative error = 2.1343399692163516712940788723505e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7449 Order of pole = 2.082 x[1] = 0.828 y[1] (analytic) = 2.3910441831722926720068765440173 y[1] (numeric) = 2.3910441831722978075234174269702 absolute error = 5.1355165408829529e-15 relative error = 2.1478133181418088435404675860020e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7439 Order of pole = 2.082 x[1] = 0.829 y[1] (analytic) = 2.3921343282853745208902747940046 y[1] (numeric) = 2.392134328285379691223917883789 absolute error = 5.1703336430897844e-15 relative error = 2.1613893425440525478359110666169e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7429 Order of pole = 2.082 x[1] = 0.83 y[1] (analytic) = 2.3932266642042504139582176602109 y[1] (numeric) = 2.3932266642042556193912675629748 absolute error = 5.2054330499027639e-15 relative error = 2.1750689676665348915594553584354e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7419 Order of pole = 2.082 memory used=282.2MB, alloc=4.3MB, time=35.36 x[1] = 0.831 y[1] (analytic) = 2.3943211957203492699243268839312 y[1] (numeric) = 2.3943211957203545107417664415113 absolute error = 5.2408174395575801e-15 relative error = 2.1888531283626887607334396055449e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7409 Order of pole = 2.082 x[1] = 0.832 y[1] (analytic) = 2.3954179276452415852208568008132 y[1] (numeric) = 2.395417927645246861710376155143 absolute error = 5.2764895193543298e-15 relative error = 2.2027427692090694467620389119574e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7399 Order of pole = 2.082 x[1] = 0.833 y[1] (analytic) = 2.3965168648107470985604307721968 y[1] (numeric) = 2.3965168648107524110124567850838 absolute error = 5.3124520260128870e-15 relative error = 2.2167388446199861222667134447183e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7389 Order of pole = 2.082 x[1] = 0.834 y[1] (analytic) = 2.3976180120690431881728370678336 y[1] (numeric) = 2.3976180120690485368805631009372 absolute error = 5.3487077260331036e-15 relative error = 2.2308423189636427931489300974850e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7379 Order of pole = 2.082 x[1] = 0.835 y[1] (analytic) = 2.3987213742927740076804466334668 y[1] (numeric) = 2.398721374292779392939862693386 absolute error = 5.3852594160599192e-15 relative error = 2.2450541666798128485603204353858e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7369 Order of pole = 2.082 x[1] = 0.836 y[1] (analytic) = 2.399826956375160366632607195231 y[1] (numeric) = 2.3998269563751657887425304486806 absolute error = 5.4221099232534496e-15 relative error = 2.2593753723990678880140399072034e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7359 Order of pole = 2.082 x[1] = 0.837 y[1] (analytic) = 2.4009347632301103617767788434971 y[1] (numeric) = 2.4009347632301158210388845076278 absolute error = 5.4592621056641307e-15 relative error = 2.2738069310635843230041196164031e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7349 Order of pole = 2.082 x[1] = 0.838 y[1] (analytic) = 2.4020447997923307652022131950863 y[1] (numeric) = 2.4020447997923362619210658080804 absolute error = 5.4967188526129941e-15 relative error = 2.2883498480495509333939491678848e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7339 Order of pole = 2.082 x[1] = 0.839 y[1] (analytic) = 2.4031570710174391755506491518225 y[1] (numeric) = 2.4031570710174447100337342289725 absolute error = 5.5344830850771500e-15 relative error = 2.3030051392912001169322875103103e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7329 Order of pole = 2.082 x[1] = 0.84 y[1] (analytic) = 2.4042715818820769385478109575598 y[1] (numeric) = 2.4042715818820825111055670381185 absolute error = 5.5725577560805587e-15 relative error = 2.3177738314064877908427663247953e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7319 Order of pole = 2.082 x[1] = 0.841 y[1] (analytic) = 2.4053883373840228431694566143278 y[1] (numeric) = 2.405388337384028454115307704495 absolute error = 5.6109458510901672e-15 relative error = 2.3326569618244447492642640635503e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7309 Order of pole = 2.082 x[1] = 0.842 y[1] (analytic) = 2.4065073425423075998163447687345 y[1] (numeric) = 2.40650734254231324946673318623 absolute error = 5.6496503884174955e-15 relative error = 2.3476555789142254932723886928253e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.3MB, time=35.85 Real estimate of pole used Radius of convergence = 0.7299 Order of pole = 2.082 x[1] = 0.843 y[1] (analytic) = 2.4076286023973291069337740500129 y[1] (numeric) = 2.4076286023973347956081936757654 absolute error = 5.6886744196257525e-15 relative error = 2.3627707421158784319616782277728e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7289 Order of pole = 2.082 x[1] = 0.844 y[1] (analytic) = 2.4087521220109685125733087705853 y[1] (numeric) = 2.4087521220109742405943387131519 absolute error = 5.7280210299425666e-15 relative error = 2.3780035220728633523000467782292e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7279 Order of pole = 2.082 x[1] = 0.845 y[1] (analytic) = 2.4098779064667070774569472416969 y[1] (numeric) = 2.4098779064667128451502859201137 absolute error = 5.7676933386784168e-15 relative error = 2.3933550007663421776170973851407e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7269 Order of pole = 2.082 x[1] = 0.846 y[1] (analytic) = 2.4110059608697438461673221786496 y[1] (numeric) = 2.4110059608697496538618218294989 absolute error = 5.8076944996508493e-15 relative error = 2.4088262716512685326357031800475e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7259 Order of pole = 2.082 x[1] = 0.847 y[1] (analytic) = 2.4121362903471141331515553574677 y[1] (numeric) = 2.4121362903471199811792569720372 absolute error = 5.8480277016145695e-15 relative error = 2.4244184397943034947142866627984e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7249 Order of pole = 2.082 x[1] = 0.848 y[1] (analytic) = 2.4132689000478088302911295411691 y[1] (numeric) = 2.4132689000478147189872982386668 absolute error = 5.8886961686974977e-15 relative error = 2.4401326220135840699668004717045e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7239 Order of pole = 2.082 x[1] = 0.849 y[1] (analytic) = 2.4144037951428945428555985434151 y[1] (numeric) = 2.4144037951429004725587593862964 absolute error = 5.9297031608428813e-15 relative error = 2.4559699470203726204602968164189e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7229 Order of pole = 2.082 x[1] = 0.85 y[1] (analytic) = 2.4155409808256345607241400867236 y[1] (numeric) = 2.415540980825640531776114344277 absolute error = 5.9710519742575534e-15 relative error = 2.4719315555626140840644818359628e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7219 Order of pole = 2.082 x[1] = 0.851 y[1] (analytic) = 2.4166804623116106718258749124078 y[1] (numeric) = 2.4166804623116166845718167788427 absolute error = 6.0127459418664349e-15 relative error = 2.4880186005704306274815139319798e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7209 Order of pole = 2.082 x[1] = 0.852 y[1] (analytic) = 2.4178222448388458248175386068221 y[1] (numeric) = 2.4178222448388518796059723801962 absolute error = 6.0547884337733741e-15 relative error = 2.5042322473035818984614935661143e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7199 Order of pole = 2.082 x[1] = 0.853 y[1] (analytic) = 2.41896633366792764808550914825 y[1] (numeric) = 2.4189663336679337452683668766714 absolute error = 6.0971828577284214e-15 relative error = 2.5205736735009203430828725971718e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.3MB, time=36.33 Real estimate of pole used Radius of convergence = 0.7189 Order of pole = 2.082 x[1] = 0.854 y[1] (analytic) = 2.4201127340821328322283727057604 y[1] (numeric) = 2.4201127340821389721610323073993 absolute error = 6.1399326596016389e-15 relative error = 2.5370440695318717682021629487547e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7179 Order of pole = 2.082 x[1] = 0.855 y[1] (analytic) = 2.4212614513875523832461623224899 y[1] (numeric) = 2.4212614513875585662874861860339 absolute error = 6.1830413238635440e-15 relative error = 2.5536446385499708409499532568117e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7169 Order of pole = 2.082 x[1] = 0.856 y[1] (analytic) = 2.4224124909132177537331385119972 y[1] (numeric) = 2.4224124909132239802455125842884 absolute error = 6.2265123740722912e-15 relative error = 2.5703765966484831235990047416199e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7159 Order of pole = 2.082 x[1] = 0.857 y[1] (analytic) = 2.4235658580112278594425073446017 y[1] (numeric) = 2.4235658580112341297918807122967 absolute error = 6.2703493733676950e-15 relative error = 2.5872411730181444979596194855369e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7149 Order of pole = 2.082 x[1] = 0.858 y[1] (analytic) = 2.4247215580568769886638002961625 y[1] (numeric) = 2.424721558056883303219725268362 absolute error = 6.3145559249721995e-15 relative error = 2.6042396101070497403554332685713e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7139 Order of pole = 2.082 x[1] = 0.859 y[1] (analytic) = 2.4258795964487836119267811100983 y[1] (numeric) = 2.4258795964487899710624538090021 absolute error = 6.3591356726989038e-15 relative error = 2.6213731637827232392244647555768e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7129 Order of pole = 2.082 x[1] = 0.86 y[1] (analytic) = 2.4270399786090200996197084626248 y[1] (numeric) = 2.4270399786090265037120099293754 absolute error = 6.4040923014667506e-15 relative error = 2.6386431034964039287233213313397e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7119 Order of pole = 2.082 x[1] = 0.861 y[1] (analytic) = 2.4282027099832433551845797438952 y[1] (numeric) = 2.4282027099832498046141175668862 absolute error = 6.4494295378229910e-15 relative error = 2.6560507124495786014505607354122e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7109 Order of pole = 2.082 x[1] = 0.862 y[1] (analytic) = 2.4293677960408263716276213436504 y[1] (numeric) = 2.429367796040832866778771816688 absolute error = 6.4951511504730376e-15 relative error = 2.6735972877627971666531449982021e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7099 Order of pole = 2.082 x[1] = 0.863 y[1] (analytic) = 2.4305352422749907191597851779972 y[1] (numeric) = 2.4305352422749972604207359958195 absolute error = 6.5412609508178223e-15 relative error = 2.6912841406468049635876090960857e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7089 Order of pole = 2.082 x[1] = 0.864 y[1] (analytic) = 2.4317050542029399718593706844765 y[1] (numeric) = 2.4317050542029465596221641832499 absolute error = 6.5877627934987734e-15 relative error = 2.7091125965760262658429275871675e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.3MB, time=36.80 Real estimate of pole used Radius of convergence = 0.7079 Order of pole = 2.082 x[1] = 0.865 y[1] (analytic) = 2.4328772373659940813271271699924 y[1] (numeric) = 2.4328772373660007159877041205269 absolute error = 6.6346605769505345e-15 relative error = 2.7270839954644361278053596509740e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7069 Order of pole = 2.082 x[1] = 0.866 y[1] (analytic) = 2.4340517973297247053833144011125 y[1] (numeric) = 2.4340517973297313873415583626558 absolute error = 6.6819582439615433e-15 relative error = 2.7451996918438556714035363672544e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7059 Order of pole = 2.082 x[1] = 0.867 y[1] (analytic) = 2.4352287396840914999362210181004 y[1] (numeric) = 2.4352287396840982295960032606948 absolute error = 6.7296597822425944e-15 relative error = 2.7634610550447081356652525021883e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7049 Order of pole = 2.082 x[1] = 0.868 y[1] (analytic) = 2.4364080700435793822325722334435 y[1] (numeric) = 2.4364080700435861600017972369561 absolute error = 6.7777692250035126e-15 relative error = 2.7818694693792737466481949925861e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7039 Order of pole = 2.082 x[1] = 0.869 y[1] (analytic) = 2.4375897940473367737821120069795 y[1] (numeric) = 2.4375897940473436000727635450418 absolute error = 6.8262906515380623e-15 relative error = 2.8004263343274808411502853835060e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7029 Order of pole = 2.082 x[1] = 0.87 y[1] (analytic) = 2.4387739173593148313314323037092 y[1] (numeric) = 2.4387739173593217065596201209324 absolute error = 6.8752281878172232e-15 relative error = 2.8191330647252723091787006973692e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7019 Order of pole = 2.082 x[1] = 0.871 y[1] (analytic) = 2.4399604456684076743458551366661 y[1] (numeric) = 2.4399604456684145989318622276316 absolute error = 6.9245860070909655e-15 relative error = 2.8379910909555873866144250551528e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7009 Order of pole = 2.082 x[1] = 0.872 y[1] (analytic) = 2.4411493846885936175428640470432 y[1] (numeric) = 2.4411493846886005919111945456993 absolute error = 6.9743683304986561e-15 relative error = 2.8570018591419978641039706165260e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6999 Order of pole = 2.082 x[1] = 0.873 y[1] (analytic) = 2.4423407401590774171062428226879 y[1] (numeric) = 2.4423407401590844416856705109222 absolute error = 7.0245794276882343e-15 relative error = 2.8761668313450403768406959703780e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6989 Order of pole = 2.082 x[1] = 0.874 y[1] (analytic) = 2.4435345178444335392967231266724 y[1] (numeric) = 2.4435345178444406145203405709677 absolute error = 7.0752236174442953e-15 relative error = 2.8954874857612860782065338787980e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6979 Order of pole = 2.082 x[1] = 0.875 y[1] (analytic) = 2.4447307235347504602625820023596 y[1] (numeric) = 2.4447307235347575865678503275818 absolute error = 7.1263052683252222e-15 relative error = 2.9149653169251897011991662167079e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.3MB, time=37.28 Real estimate of pole used Radius of convergence = 0.6969 Order of pole = 2.082 x[1] = 0.876 y[1] (analytic) = 2.4459293630457760059422778253392 y[1] (numeric) = 2.4459293630457831837710771348493 absolute error = 7.1778287993095101e-15 relative error = 2.9346018359137609113861364870374e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6959 Order of pole = 2.082 x[1] = 0.877 y[1] (analytic) = 2.4471304422190637410408822565258 y[1] (numeric) = 2.4471304422190709708395627079548 absolute error = 7.2297986804514290e-15 relative error = 2.9543985705541018301829386216039e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6949 Order of pole = 2.082 x[1] = 0.878 y[1] (analytic) = 2.448333966922120416152769373826 y[1] (numeric) = 2.4483339669221276983722029199999 absolute error = 7.2822194335461739e-15 relative error = 2.9743570656338550036072896004328e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6939 Order of pole = 2.082 x[1] = 0.879 y[1] (analytic) = 2.4495399430485544821947748728641 y[1] (numeric) = 2.4495399430485618172904076775172 absolute error = 7.3350956328046531e-15 relative error = 2.9944788831146068510494921429255e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6929 Order of pole = 2.082 x[1] = 0.88 y[1] (analytic) = 2.4507483765182256814068516756497 y[1] (numeric) = 2.4507483765182330698387572137178 absolute error = 7.3884319055380681e-15 relative error = 3.0147656023482923003439005793962e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6919 Order of pole = 2.082 x[1] = 0.881 y[1] (analytic) = 2.4519592732773957242711373127776 y[1] (numeric) = 2.4519592732774031665040701652211 absolute error = 7.4422329328524435e-15 relative error = 3.0352188202966480418463395688839e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6909 Order of pole = 2.082 x[1] = 0.882 y[1] (analytic) = 2.4531726392988800617953270936281 y[1] (numeric) = 2.4531726392988875582987774468919 absolute error = 7.4965034503532638e-15 relative error = 3.0558401517537609005622022260677e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6899 Order of pole = 2.082 x[1] = 0.883 y[1] (analytic) = 2.4543884805822007627023295979441 y[1] (numeric) = 2.4543884805822083139505784583243 absolute error = 7.5512482488603802e-15 relative error = 3.0766312295717600302579301554639e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6889 Order of pole = 2.082 x[1] = 0.884 y[1] (analytic) = 2.4556068031537405051653818662942 y[1] (numeric) = 2.4556068031537481116375569996474 absolute error = 7.6064721751333532e-15 relative error = 3.0975937048897024003777979253832e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6879 Order of pole = 2.082 x[1] = 0.885 y[1] (analytic) = 2.4568276130668976928261355020896 y[1] (numeric) = 2.4568276130669053550062681094871 absolute error = 7.6621801326073975e-15 relative error = 3.1187292473657009930398582551870e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6869 Order of pole = 2.082 x[1] = 0.886 y[1] (analytic) = 2.4580509164022427049327066038183 y[1] (numeric) = 2.4580509164022504233097887439178 absolute error = 7.7183770821400995e-15 relative error = 3.1400395454123463322342633670982e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6859 Order of pole = 2.082 memory used=301.3MB, alloc=4.3MB, time=37.76 x[1] = 0.887 y[1] (analytic) = 2.4592767192676752905353271202512 y[1] (numeric) = 2.4592767192676830656033698893351 absolute error = 7.7750680427690839e-15 relative error = 3.1615263064354741396589477575406e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6848 Order of pole = 2.082 x[1] = 0.888 y[1] (analytic) = 2.4605050277985831167790581817777 y[1] (numeric) = 2.46050502779859094903715066258 absolute error = 7.8322580924808023e-15 relative error = 3.1831912570763300881563840330114e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6838 Order of pole = 2.082 x[1] = 0.889 y[1] (analytic) = 2.461735848158001481436042750437 y[1] (numeric) = 2.4617358481580093713884117410637 absolute error = 7.8899523689906267e-15 relative error = 3.2050361434571863297973566027203e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6828 Order of pole = 2.082 x[1] = 0.89 y[1] (analytic) = 2.462969186536774199924001320499 y[1] (numeric) = 2.4629691865367821480800718549293 absolute error = 7.9481560705344303e-15 relative error = 3.2270627314304638987196205999922e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6818 Order of pole = 2.082 x[1] = 0.891 y[1] (analytic) = 2.4642050491537156771631263932715 y[1] (numeric) = 2.4642050491537236840375830651123 absolute error = 8.0068744566718408e-15 relative error = 3.2492728068314158503333934748236e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6808 Order of pole = 2.082 x[1] = 0.892 y[1] (analytic) = 2.4654434422557741747302252824181 y[1] (numeric) = 2.4654434422557822408430743837756 absolute error = 8.0661128491013575e-15 relative error = 3.2716681757344280917235435790107e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6798 Order of pole = 2.082 x[1] = 0.893 y[1] (analytic) = 2.4666843721181962838769129571229 y[1] (numeric) = 2.4666843721182044097535454446465 absolute error = 8.1258766324875236e-15 relative error = 3.2942506647129945059999243777160e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6788 Order of pole = 2.082 x[1] = 0.894 y[1] (analytic) = 2.467927845044692615087883820843 y[1] (numeric) = 2.4679278450447008012591391211947 absolute error = 8.1861712553003517e-15 relative error = 3.3170221211034252531412759606660e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6778 Order of pole = 2.082 x[1] = 0.895 y[1] (analytic) = 2.4691738673676047149658105213453 y[1] (numeric) = 2.4691738673676129619680411885466 absolute error = 8.2470022306672013e-15 relative error = 3.3399844132723470468225107666249e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6768 Order of pole = 2.082 x[1] = 0.896 y[1] (analytic) = 2.4704224454480732213412463126546 y[1] (numeric) = 2.4704224454480815297163835499664 absolute error = 8.3083751372373118e-15 relative error = 3.3631394308880556990657616303994e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6758 Order of pole = 2.082 x[1] = 0.897 y[1] (analytic) = 2.4716735856762072676190626162668 y[1] (numeric) = 2.4716735856762156379146826754663 absolute error = 8.3702956200591995e-15 relative error = 3.3864890851957828278032840412644e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6748 Order of pole = 2.082 x[1] = 0.898 y[1] (analytic) = 2.4729272944712551474874529918576 y[1] (numeric) = 2.4729272944712635802568444629848 absolute error = 8.4327693914711272e-15 relative error = 3.4100353092969382331463922903476e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.3MB, time=38.24 Real estimate of pole used Radius of convergence = 0.6738 Order of pole = 2.082 x[1] = 0.899 y[1] (analytic) = 2.4741835782817762512313967248747 y[1] (numeric) = 2.474183578281784747033628729738 absolute error = 8.4958022320048633e-15 relative error = 3.4337800584323923710004488928336e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6728 Order of pole = 2.082 x[1] = 0.9 y[1] (analytic) = 2.4754424435858142850097179361052 y[1] (numeric) = 2.4754424435858228444097092390523 absolute error = 8.5593999913029471e-15 relative error = 3.4577253102698628245198327961170e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6718 Order of pole = 2.082 x[1] = 0.901 y[1] (analytic) = 2.4767038968910717845735180553032 y[1] (numeric) = 2.4767038968910804081421071049869 absolute error = 8.6235685890496837e-15 relative error = 3.4818730651954709301017735954781e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6708 Order of pole = 2.082 x[1] = 0.902 y[1] (analytic) = 2.4779679447350859350238194930062 y[1] (numeric) = 2.4779679447350946233378354091007 absolute error = 8.6883140159160945e-15 relative error = 3.5062253466095353018349272691856e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6698 Order of pole = 2.082 x[1] = 0.903 y[1] (analytic) = 2.4792345936854057083277554890539 y[1] (numeric) = 2.4792345936854144619700900081079 absolute error = 8.7536423345190540e-15 relative error = 3.5307842012266704257001247746681e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6688 Order of pole = 2.082 x[1] = 0.904 y[1] (analytic) = 2.480503850339770330435594796536 y[1] (numeric) = 2.480503850339779149995275191383 absolute error = 8.8195596803948470e-15 relative error = 3.5555516993802593873098518486167e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6678 Order of pole = 2.082 x[1] = 0.905 y[1] (analytic) = 2.4817757213262890899653197503312 y[1] (numeric) = 2.4817757213262979760375827377167 absolute error = 8.8860722629873855e-15 relative error = 3.5805299353313714063073234680451e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6668 Order of pole = 2.082 x[1] = 0.906 y[1] (analytic) = 2.4830502133036225005474023401894 y[1] (numeric) = 2.4830502133036314537337689915182 absolute error = 8.9531863666513288e-15 relative error = 3.6057210275821960453157958560633e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6658 Order of pole = 2.082 x[1] = 0.907 y[1] (analytic) = 2.4843273329611648290498654301863 y[1] (numeric) = 2.4843273329611738499582171005398 absolute error = 9.0209083516703535e-15 relative error = 3.6311271191940667435451716492109e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6648 Order of pole = 2.082 x[1] = 0.908 y[1] (analytic) = 2.4856070870192280020326958156971 y[1] (numeric) = 2.4856070870192370912773511065233 absolute error = 9.0892446552908262e-15 relative error = 3.6567503781101482658818299694164e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6638 Order of pole = 2.082 x[1] = 0.909 y[1] (analytic) = 2.4868894822292269029112132728282 y[1] (numeric) = 2.4868894822292360611130060439632 absolute error = 9.1582017927711350e-15 relative error = 3.6825929974828634594323648329197e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=309.0MB, alloc=4.3MB, time=38.74 Real estimate of pole used Radius of convergence = 0.6628 Order of pole = 2.082 x[1] = 0.91 y[1] (analytic) = 2.4881745253738660724401163363826 y[1] (numeric) = 2.4881745253738753002264747833249 absolute error = 9.2277863584469423e-15 relative error = 3.7086571960061367480251052518576e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6618 Order of pole = 2.082 x[1] = 0.911 y[1] (analytic) = 2.4894622232673278252636427649233 y[1] (numeric) = 2.4894622232673371232686695775464 absolute error = 9.2980050268126231e-15 relative error = 3.7349452182525319314016797007882e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6608 Order of pole = 2.082 x[1] = 0.912 y[1] (analytic) = 2.4907525827554617954126223657806 y[1] (numeric) = 2.4907525827554711642771759849422 absolute error = 9.3688645536191616e-15 relative error = 3.7614593350153647566901223185120e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6598 Order of pole = 2.082 x[1] = 0.913 y[1] (analytic) = 2.4920456107159759237661842413299 y[1] (numeric) = 2.4920456107159853641379612301106 absolute error = 9.4403717769887807e-15 relative error = 3.7882018436558708833486099776238e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6588 Order of pole = 2.082 x[1] = 0.914 y[1] (analytic) = 2.4933413140586289006345321003904 y[1] (numeric) = 2.4933413140586384131681506469774 absolute error = 9.5125336185465870e-15 relative error = 3.8151750684555124970781186653918e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6578 Order of pole = 2.082 x[1] = 0.915 y[1] (analytic) = 2.4946396997254240767595429181799 y[1] (numeric) = 2.4946396997254336621166274876945 absolute error = 9.5853570845695146e-15 relative error = 3.8423813609735065186492560589829e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6568 Order of pole = 2.082 x[1] = 0.916 y[1] (analytic) = 2.495940774690804856171999136785 y[1] (numeric) = 2.4959407746908145150212662896478 absolute error = 9.6588492671528628e-15 relative error = 3.8698231004096614873083619180741e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6558 Order of pole = 2.082 x[1] = 0.917 y[1] (analytic) = 2.4972445459618515844880563422414 y[1] (numeric) = 2.4972445459618613175054017369623 absolute error = 9.7330173453947209e-15 relative error = 3.8975026939726088212382011806470e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6548 Order of pole = 2.082 x[1] = 0.918 y[1] (analytic) = 2.4985510205784799463731008614433 y[1] (numeric) = 2.4985510205784897542416874600281 absolute error = 9.8078685865985848e-15 relative error = 3.9254225772535181442957388360537e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6538 Order of pole = 2.082 x[1] = 0.919 y[1] (analytic) = 2.4998602056136408860484892864313 y[1] (numeric) = 2.4998602056136507694588367809033 absolute error = 9.8834103474944720e-15 relative error = 3.9535852146053864903383043244191e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6528 Order of pole = 2.082 x[1] = 0.92 y[1] (analytic) = 2.5011721081735220648658092223645 y[1] (numeric) = 2.5011721081735320245158847012137 absolute error = 9.9596500754788492e-15 relative error = 3.9819930995279935910306012325572e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.3MB, time=39.22 Real estimate of pole used Radius of convergence = 0.6518 Order of pole = 2.082 x[1] = 0.921 y[1] (analytic) = 2.5024867353977508701242826152063 y[1] (numeric) = 2.5024867353977609067195924888967 absolute error = 1.00365953098736904e-14 relative error = 4.0106487550586162719110535308786e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6508 Order of pole = 2.082 x[1] = 0.922 y[1] (analytic) = 2.5038040944595989894597752781418 y[1] (numeric) = 2.5038040944596091037134584831346 absolute error = 1.01142536832049928e-14 relative error = 4.0395547341685980669654824725292e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6498 Order of pole = 2.082 x[1] = 0.923 y[1] (analytic) = 2.5051241925661885652886045265855 y[1] (numeric) = 2.505124192566198757921527027666 absolute error = 1.01926329225010805e-14 relative error = 4.0687136201658705521087720676029e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6488 Order of pole = 2.082 x[1] = 0.924 y[1] (analytic) = 2.5064470369586999439459773738799 y[1] (numeric) = 2.5064470369587102156868279849122 absolute error = 1.02717408506110323e-14 relative error = 4.0981280271035247162240104125440e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6478 Order of pole = 2.082 x[1] = 0.925 y[1] (analytic) = 2.5077726349125810343174711627231 y[1] (numeric) = 2.5077726349125913859028587063034 absolute error = 1.03515853875435803e-14 relative error = 4.1278006001945341265009568605320e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6468 Order of pole = 2.082 x[1] = 0.926 y[1] (analytic) = 2.5091009937377582909225138529795 y[1] (numeric) = 2.509100993737768723097065679806 absolute error = 1.04321745518268265e-14 relative error = 4.1577340162327311143325273173177e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6458 Order of pole = 2.082 x[1] = 0.927 y[1] (analytic) = 2.5104321207788493365713599164856 y[1] (numeric) = 2.5104321207788598500878218056215 absolute error = 1.05135164618891359e-14 relative error = 4.1879309840201409753669303328671e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6448 Order of pole = 2.082 x[1] = 0.928 y[1] (analytic) = 2.5117660234153772398816177923474 y[1] (numeric) = 2.5117660234153878355009552539155 absolute error = 1.05956193374615681e-14 relative error = 4.2183942448007798144589164841453e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6438 Order of pole = 2.082 x[1] = 0.929 y[1] (analytic) = 2.5131027090619864631069944548048 y[1] (numeric) = 2.5131027090619971415984954570237 absolute error = 1.06784915010022189e-14 relative error = 4.2491265727010246808278452030896e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6428 Order of pole = 2.082 x[1] = 0.93 y[1] (analytic) = 2.5144421851686604958996106044357 y[1] (numeric) = 2.514442185168671258040989747283 absolute error = 1.07621413791428473e-14 relative error = 4.2801307751766654045949037665748e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6418 Order of pole = 2.082 x[1] = 0.931 y[1] (analytic) = 2.5157844592209411907980355259412 y[1] (numeric) = 2.5157844592209520373755396841157 absolute error = 1.08465775041581745e-14 relative error = 4.3114096934667512024356863481309e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.3MB, time=39.70 Real estimate of pole used Radius of convergence = 0.6408 Order of pole = 2.082 x[1] = 0.932 y[1] (analytic) = 2.5171295387401498164061234326298 y[1] (numeric) = 2.5171295387401607482146388908734 absolute error = 1.09318085154582436e-14 relative error = 4.3429662030543451364287027277704e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6398 Order of pole = 2.082 x[1] = 0.933 y[1] (analytic) = 2.5184774312836098444028332744498 y[1] (numeric) = 2.5184774312836208622459943786906 absolute error = 1.10178431611042408e-14 relative error = 4.3748032141343034894746115707710e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6388 Order of pole = 2.082 x[1] = 0.934 y[1] (analytic) = 2.519828144444871486700512131357 y[1] (numeric) = 2.5198281444448825913908114795403 absolute error = 1.11046902993481833e-14 relative error = 4.4069236720881980172940092103051e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6378 Order of pole = 2.082 x[1] = 0.935 y[1] (analytic) = 2.5211816858539379992486495362969 y[1] (numeric) = 2.5211816858539491916075497331858 absolute error = 1.11923589001968889e-14 relative error = 4.4393305579665020632286142576790e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6368 Order of pole = 2.082 x[1] = 0.936 y[1] (analytic) = 2.5225380631774937691618979508853 y[1] (numeric) = 2.5225380631775050500199449515333 absolute error = 1.12808580470006480e-14 relative error = 4.4720268889781629002447719729453e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6358 Order of pole = 2.082 x[1] = 0.937 y[1] (analytic) = 2.5238972841191342020352352285622 y[1] (numeric) = 2.5238972841191455722321732955913 absolute error = 1.13701969380670291e-14 relative error = 4.5050157189876858899786392951861e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6348 Order of pole = 2.082 x[1] = 0.938 y[1] (analytic) = 2.5252593564195974264955508276819 y[1] (numeric) = 2.5252593564196088868804391279368 absolute error = 1.14603848883002549e-14 relative error = 4.5383001390198575076590537881921e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6338 Order of pole = 2.082 x[1] = 0.939 y[1] (analytic) = 2.5266242878569978332277018790857 y[1] (numeric) = 2.5266242878570093846590327456817 absolute error = 1.15514313308665960e-14 relative error = 4.5718832777722372686031372657094e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6328 Order of pole = 2.082 x[1] = 0.94 y[1] (analytic) = 2.5279920862470614659042415918926 y[1] (numeric) = 2.5279920862470731092500604781292 absolute error = 1.16433458188862366e-14 relative error = 4.6057683021355505666164102805734e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6318 Order of pole = 2.082 x[1] = 0.941 y[1] (analytic) = 2.5293627594433632816416050536771 y[1] (numeric) = 2.5293627594433750177796322057536 absolute error = 1.17361380271520765e-14 relative error = 4.6399584177221173790667535968445e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6308 Order of pole = 2.082 x[1] = 0.942 y[1] (analytic) = 2.5307363153375662988015809458018 y[1] (numeric) = 2.5307363153375781286193348217431 absolute error = 1.18298177538759413e-14 relative error = 4.6744568694024538054997597164824e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6298 Order of pole = 2.082 memory used=320.4MB, alloc=4.3MB, time=40.18 x[1] = 0.943 y[1] (analytic) = 2.5321127618596626501554373026144 y[1] (numeric) = 2.5321127618596745745503597652969 absolute error = 1.19243949224626825e-14 relative error = 4.7092669418501862684146384343303e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6288 Order of pole = 2.082 x[1] = 0.944 y[1] (analytic) = 2.5334921069782165596291410076466 y[1] (numeric) = 2.5334921069782285795087243203049 absolute error = 1.20198795833126583e-14 relative error = 4.7443919600954207667317281340942e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6278 Order of pole = 2.082 x[1] = 0.945 y[1] (analytic) = 2.5348743587006092610517506258265 y[1] (numeric) = 2.5348743587006213773336662789218 absolute error = 1.21162819156530953e-14 relative error = 4.7798352900867122304383925803645e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6268 Order of pole = 2.082 x[1] = 0.946 y[1] (analytic) = 2.5362595250732858775353073848877 y[1] (numeric) = 2.5362595250732980911475367837286 absolute error = 1.22136122293988409e-14 relative error = 4.8156003392617817387114106031485e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6258 Order of pole = 2.082 x[1] = 0.947 y[1] (analytic) = 2.5376476141820042803234372006093 y[1] (numeric) = 2.5376476141820165922044042436358 absolute error = 1.23118809670430265e-14 relative error = 4.8516905571271323299650462027468e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6248 Order of pole = 2.082 x[1] = 0.948 y[1] (analytic) = 2.5390386341520859461574457508242 y[1] (numeric) = 2.5390386341520983572561513289946 absolute error = 1.24110987055781704e-14 relative error = 4.8881094358467164826638529016186e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6238 Order of pole = 2.082 x[1] = 0.949 y[1] (analytic) = 2.5404325931486688324229775170978 y[1] (numeric) = 2.5404325931486813436991359653587 absolute error = 1.25112761584482609e-14 relative error = 4.9248605108398117761069902055135e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6228 Order of pole = 2.082 x[1] = 0.95 y[1] (analytic) = 2.541829499376962289557357829513 y[1] (numeric) = 2.5418294993769749019815353618834 absolute error = 1.26124241775323704e-14 relative error = 4.9619473613882641315541635091125e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6218 Order of pole = 2.082 x[1] = 0.951 y[1] (analytic) = 2.5432293610825040304175843031698 y[1] (numeric) = 2.5432293610825167449713394635307 absolute error = 1.27145537551603609e-14 relative error = 4.9993736112532606246158750217764e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6208 Order of pole = 2.082 x[1] = 0.952 y[1] (analytic) = 2.5446321865514191765316213253329 y[1] (numeric) = 2.5446321865514319942076474865857 absolute error = 1.28176760261612528e-14 relative error = 5.0371429293017971729185398850502e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6197 Order of pole = 2.082 x[1] = 0.953 y[1] (analytic) = 2.5460379841106814013812197780979 y[1] (numeric) = 2.5460379841106943231834897229396 absolute error = 1.29218022699448417e-14 relative error = 5.0752590301430101987712848197563e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6187 Order of pole = 2.082 x[1] = 0.954 y[1] (analytic) = 2.5474467621283761910929759711351 y[1] (numeric) = 2.5474467621283892180368885882906 absolute error = 1.30269439126171555e-14 relative error = 5.1137256747745430903643299626149e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.3MB, time=40.66 Real estimate of pole used Radius of convergence = 0.6177 Order of pole = 2.082 x[1] = 0.955 y[1] (analytic) = 2.5488585290139662431458015022537 y[1] (numeric) = 2.5488585290139793762583306326137 absolute error = 1.31331125291303600e-14 relative error = 5.1525466712391232445562631885721e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6167 Order of pole = 2.082 x[1] = 0.956 y[1] (analytic) = 2.55027329321855902393744284378 y[1] (numeric) = 2.55027329321857226425728831151 absolute error = 1.32403198454677300e-14 relative error = 5.1917258752915276128194617046892e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6157 Order of pole = 2.082 x[1] = 0.957 y[1] (analytic) = 2.5516910632351765062902099598567 y[1] (numeric) = 2.5516910632351898548679508241724 absolute error = 1.33485777408643157e-14 relative error = 5.2312671910761183547446230420751e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6147 Order of pole = 2.082 x[1] = 0.958 y[1] (analytic) = 2.5531118475990271082166920024384 y[1] (numeric) = 2.5531118475990405661149420663866 absolute error = 1.34578982500639482e-14 relative error = 5.2711745718151343251121659150045e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6137 Order of pole = 2.082 x[1] = 0.959 y[1] (analytic) = 2.5545356548877798545100006524987 y[1] (numeric) = 2.5545356548877934228035662657372 absolute error = 1.35682935656132385e-14 relative error = 5.3114520205079268774209184221259e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6127 Order of pole = 2.082 x[1] = 0.96 y[1] (analytic) = 2.5559624937218407829700342532686 y[1] (numeric) = 2.5559624937218544627460744465056 absolute error = 1.36797760401932370e-14 relative error = 5.3521035906413319788862524724361e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6117 Order of pole = 2.082 x[1] = 0.961 y[1] (analytic) = 2.5573923727646316173274455680977 y[1] (numeric) = 2.5573923727646454096856345575354 absolute error = 1.37923581889894377e-14 relative error = 5.3931333869113759114251828915083e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6107 Order of pole = 2.082 x[1] = 0.962 y[1] (analytic) = 2.5588253007228707291804706027897 y[1] (numeric) = 2.558825300722884635233162703608 absolute error = 1.39060526921008183e-14 relative error = 5.4345455659565130858962986215291e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6097 Order of pole = 2.082 x[1] = 0.963 y[1] (analytic) = 2.5602612863468564115165840630706 y[1] (numeric) = 2.5602612863468704323889810516981 absolute error = 1.40208723969886275e-14 relative error = 5.4763443371026008456401842118397e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6087 Order of pole = 2.082 x[1] = 0.964 y[1] (analytic) = 2.5617003384307524866511380745996 y[1] (numeric) = 2.5617003384307666234814590402397 absolute error = 1.41368303209656401e-14 relative error = 5.5185339631198182215789590944062e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6077 Order of pole = 2.082 x[1] = 0.965 y[1] (analytic) = 2.5631424658128762716787649928161 y[1] (numeric) = 2.5631424658128905256184187194345 absolute error = 1.42539396537266184e-14 relative error = 5.5611187609917410170964494415533e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.3MB, time=41.14 Real estimate of pole used Radius of convergence = 0.6067 Order of pole = 2.082 x[1] = 0.966 y[1] (analytic) = 2.5645876773759889248004335197777 y[1] (numeric) = 2.5645876773760032970141934405074 absolute error = 1.43722137599207297e-14 relative error = 5.6041031026967884007134535799578e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6057 Order of pole = 2.082 x[1] = 0.967 y[1] (analytic) = 2.566035982047588196159691816542 y[1] (numeric) = 2.5660359820476026878258735832303 absolute error = 1.44916661817666883e-14 relative error = 5.6474914160022617994158386926000e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6047 Order of pole = 2.082 x[1] = 0.968 y[1] (analytic) = 2.5674873888002036070958646042911 y[1] (numeric) = 2.5674873888002182194065063156928 absolute error = 1.46123106417114017e-14 relative error = 5.6912881852711996126556664148834e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6037 Order of pole = 2.082 x[1] = 0.969 y[1] (analytic) = 2.56894190665169408199984701283 y[1] (numeric) = 2.5689419066517088161608921457509 absolute error = 1.47341610451329209e-14 relative error = 5.7354979522822774284937056353849e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6027 Order of pole = 2.082 x[1] = 0.97 y[1] (analytic) = 2.5703995446655480572397106807342 y[1] (numeric) = 2.5703995446655629144711937692399 absolute error = 1.48572314830885057e-14 relative error = 5.7801253170629859575740194633477e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6017 Order of pole = 2.082 x[1] = 0.971 y[1] (analytic) = 2.5718603119511860919086627648908 y[1] (numeric) = 2.571860311951201073444897873528 absolute error = 1.49815362351086372e-14 relative error = 5.8251749387363254097586603287269e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6007 Order of pole = 2.082 x[1] = 0.972 y[1] (analytic) = 2.5733242176642660054370324309878 y[1] (numeric) = 2.5733242176642811125268044688092 absolute error = 1.51070897720378214e-14 relative error = 5.8706515363812577661741426165428e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5997 Order of pole = 2.082 x[1] = 0.973 y[1] (analytic) = 2.574791271006990567402959365034 y[1] (numeric) = 2.5747912710070058013097182880841 absolute error = 1.52339067589230501e-14 relative error = 5.9165598899071652124208083511791e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5987 Order of pole = 2.082 x[1] = 0.974 y[1] (analytic) = 2.5762614812284177651733831228739 y[1] (numeric) = 2.5762614812284331271754410736708 absolute error = 1.53620020579507969e-14 relative error = 5.9629048409425656053157251736069e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5977 Order of pole = 2.082 x[1] = 0.975 y[1] (analytic) = 2.577734857624773675307839950423 y[1] (numeric) = 2.5777348576247891666985713838735 absolute error = 1.54913907314334505e-14 relative error = 6.0096912937383433857742055759212e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5967 Order of pole = 2.082 x[1] = 0.976 y[1] (analytic) = 2.5792114095397679649625252875358 y[1] (numeric) = 2.5792114095397835870505701336343 absolute error = 1.56220880448460985e-14 relative error = 6.0569242160857566375440735993126e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.3MB, time=41.64 Real estimate of pole used Radius of convergence = 0.5957 Order of pole = 2.082 x[1] = 0.977 y[1] (analytic) = 2.5806911463649120498411367519265 y[1] (numeric) = 2.5806911463649278039506066665263 absolute error = 1.57541094699145998e-14 relative error = 6.1046086402494886335416770357262e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5947 Order of pole = 2.082 x[1] = 0.978 y[1] (analytic) = 2.5821740775398399355522362575089 y[1] (numeric) = 2.582174077539855823022924013408 absolute error = 1.58874706877558991e-14 relative error = 6.1527496639160161152692629123176e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5937 Order of pole = 2.082 x[1] = 0.979 y[1] (analytic) = 2.5836602125526317695503243763516 y[1] (numeric) = 2.5836602125526477917379164479087 absolute error = 1.60221875920715571e-14 relative error = 6.2013524511575722331522862569159e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5927 Order of pole = 2.082 x[1] = 0.98 y[1] (analytic) = 2.5851495609401401311595694985215 y[1] (numeric) = 2.5851495609401562894358618940115 absolute error = 1.61582762923954900e-14 relative error = 6.2504222334119876691688834414687e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5917 Order of pole = 2.082 x[1] = 0.981 y[1] (analytic) = 2.5866421322883190875052442636482 y[1] (numeric) = 2.5866421322883353832583616605818 absolute error = 1.62957531173969336e-14 relative error = 6.2999643104786996636947905211646e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5907 Order of pole = 2.082 x[1] = 0.982 y[1] (analytic) = 2.5881379362325560435084587275423 y[1] (numeric) = 2.5881379362325724781430769672064 absolute error = 1.64346346182396641e-14 relative error = 6.3499840515312229218968821975404e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5897 Order of pole = 2.082 x[1] = 0.983 y[1] (analytic) = 2.5896369824580064144348115141095 y[1] (numeric) = 2.5896369824580229893723835126436 absolute error = 1.65749375719985341e-14 relative error = 6.4004868961463842911936753895852e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5887 Order of pole = 2.082 x[1] = 0.984 y[1] (analytic) = 2.5911392806999311498271756678028 y[1] (numeric) = 2.5911392806999478665061608022026 absolute error = 1.67166789851343998e-14 relative error = 6.4514783553506275188164717513685e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5877 Order of pole = 2.082 x[1] = 0.985 y[1] (analytic) = 2.5926448407440371379970651204698 y[1] (numeric) = 2.5926448407440539978731621490088 absolute error = 1.68598760970285390e-14 relative error = 6.5029640126837011225590423459197e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5867 Order of pole = 2.082 x[1] = 0.986 y[1] (analytic) = 2.5941536724268205205979618711298 y[1] (numeric) = 2.5941536724268375251443454488129 absolute error = 1.70045463835776831e-14 relative error = 6.5549495252800490730244628413549e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5857 Order of pole = 2.082 x[1] = 0.987 y[1] (analytic) = 2.5956657856359129471576956198785 y[1] (numeric) = 2.5956657856359300978652564706861 absolute error = 1.71507075608508076e-14 relative error = 6.6074406249682297056618045382660e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.3MB, time=42.12 Real estimate of pole used Radius of convergence = 0.5847 Order of pole = 2.082 x[1] = 0.988 y[1] (analytic) = 2.597181190310430799805530412123 y[1] (numeric) = 2.5971811903104480981831192209734 absolute error = 1.72983775888088504e-14 relative error = 6.6604431193886952936806559258702e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5837 Order of pole = 2.082 x[1] = 0.989 y[1] (analytic) = 2.5986998964413274187931018170024 y[1] (numeric) = 2.5986998964413448663677769055543 absolute error = 1.74475746750885519e-14 relative error = 6.7139628931302716250626852359885e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5827 Order of pole = 2.082 x[1] = 0.99 y[1] (analytic) = 2.60022191407174835977683955433 y[1] (numeric) = 2.6002219140717659580941184059633 absolute error = 1.75983172788516333e-14 relative error = 6.7680059088856828921708310931229e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5817 Order of pole = 2.082 x[1] = 0.991 y[1] (analytic) = 2.6017472532973897142030818822118 y[1] (numeric) = 2.6017472532974074648271965827695 absolute error = 1.77506241147005577e-14 relative error = 6.8225782086264753390357084550945e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5807 Order of pole = 2.082 x[1] = 0.992 y[1] (analytic) = 2.6032759242668595245158183864662 y[1] (numeric) = 2.6032759242668774290299750486088 absolute error = 1.79045141566621426e-14 relative error = 6.8776859147976995645613878026684e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5797 Order of pole = 2.082 x[1] = 0.993 y[1] (analytic) = 2.6048079371820423262909673616633 y[1] (numeric) = 2.604807937182060386297609601983 absolute error = 1.80600066422403197e-14 relative error = 6.9333352315327190380473188113459e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5787 Order of pole = 2.082 x[1] = 0.994 y[1] (analytic) = 2.6063433022984668497903844213653 y[1] (numeric) = 2.6063433022984850669114609607284 absolute error = 1.82171210765393631e-14 relative error = 6.9895324458885191669074963330059e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5777 Order of pole = 2.082 x[1] = 0.995 y[1] (analytic) = 2.6078820299256769138234934186464 y[1] (numeric) = 2.6078820299256952897007298775855 absolute error = 1.83758772364589391e-14 relative error = 7.0462839291019006207450165796693e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5767 Order of pole = 2.082 x[1] = 0.996 y[1] (analytic) = 2.6094241304276055452046137382894 y[1] (numeric) = 2.6094241304276240814997887006415 absolute error = 1.85362951749623521e-14 relative error = 7.1035961378669457619195144634927e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5757 Order of pole = 2.082 x[1] = 0.997 y[1] (analytic) = 2.6109696142229523574998155523541 y[1] (numeric) = 2.6109696142229710558950409717518 absolute error = 1.86983952254193977e-14 relative error = 7.1614756156341579807894775208878e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5747 Order of pole = 2.082 x[1] = 0.998 y[1] (analytic) = 2.6125184917855642231685542246011 y[1] (numeric) = 2.6125184917855830853665602498587 absolute error = 1.88621980060252576e-14 relative error = 7.2199289939316795781293242849911e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.3MB, time=42.60 Real estimate of pole used Radius of convergence = 0.5737 Order of pole = 2.082 x[1] = 0.999 y[1] (analytic) = 2.6140707736448192736225057491873 y[1] (numeric) = 2.6140707736448383013469300460921 absolute error = 1.90277244242969048e-14 relative error = 7.2789629937090035969242139625007e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5727 Order of pole = 2.082 x[1] = 1 y[1] (analytic) = 2.6156264703860142621470375164089 y[1] (numeric) = 2.6156264703860334571427191649247 absolute error = 1.91949956816485158e-14 relative error = 7.3385844267036025015155426835761e-13 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 1000 Total Elapsed Time = 42 Seconds Elapsed Time(since restart) = 42 Seconds Expected Time Remaining = 2 Minutes 50 Seconds Optimized Time Remaining = 2 Minutes 49 Seconds Time to Timeout = 14 Minutes 17 Seconds Percent Done = 20.02 % > quit memory used=340.0MB, alloc=4.3MB, time=42.66