|\^/| 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_max_terms, > glob_iolevel, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_relerr, > glob_large_float, > glob_clock_sec, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_start, > glob_last_good_h, > glob_display_flag, > glob_optimal_expect_sec, > glob_max_hours, > glob_abserr, > glob_log10_abserr, > hours_in_day, > glob_smallish_float, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump_analytic, > glob_hmax, > glob_reached_optimal_h, > djd_debug, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_iter, > glob_look_poles, > glob_hmin, > glob_initial_pass, > glob_not_yet_finished, > centuries_in_millinium, > djd_debug2, > glob_max_minutes, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_disp_incr, > days_in_year, > glob_log10abserr, > glob_dump, > glob_subiter_method, > glob_normmax, > glob_h, > years_in_century, > min_in_hour, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_no_eqs, > glob_optimal_done, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_log10_relerr, > glob_clock_start_sec, > sec_in_min, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_tmp1_g, > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_y_init, > array_m1, > array_tmp2_g, > array_type_pole, > array_norms, > array_1st_rel_error, > array_y_higher, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_real_pole, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_max_terms, glob_iolevel, ALWAYS, glob_max_sec, glob_relerr, glob_large_float, glob_clock_sec, glob_max_opt_iter, MAX_UNCHANGED, glob_current_iter, glob_start, glob_last_good_h, glob_display_flag, glob_optimal_expect_sec, glob_max_hours, glob_abserr, glob_log10_abserr, hours_in_day, glob_smallish_float, glob_not_yet_start_msg, glob_almost_1, glob_dump_analytic, glob_hmax, glob_reached_optimal_h, djd_debug, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_iter, glob_look_poles, glob_hmin, glob_initial_pass, glob_not_yet_finished, centuries_in_millinium, djd_debug2, glob_max_minutes, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_disp_incr, days_in_year, glob_log10abserr, glob_dump, glob_subiter_method, glob_normmax, glob_h, years_in_century, min_in_hour, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_no_eqs, glob_optimal_done, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_max_trunc_err, glob_log10_relerr, glob_clock_start_sec, sec_in_min, glob_log10normmin, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_tmp1_g, array_y, array_x, array_last_rel_error, array_fact_1, array_y_init, array_m1, array_tmp2_g, array_type_pole, array_norms, array_1st_rel_error, array_y_higher, array_y_set_initial, array_poles, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher_work2, array_real_pole, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_max_terms, > glob_iolevel, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_relerr, > glob_large_float, > glob_clock_sec, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_start, > glob_last_good_h, > glob_display_flag, > glob_optimal_expect_sec, > glob_max_hours, > glob_abserr, > glob_log10_abserr, > hours_in_day, > glob_smallish_float, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump_analytic, > glob_hmax, > glob_reached_optimal_h, > djd_debug, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_iter, > glob_look_poles, > glob_hmin, > glob_initial_pass, > glob_not_yet_finished, > centuries_in_millinium, > djd_debug2, > glob_max_minutes, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_disp_incr, > days_in_year, > glob_log10abserr, > glob_dump, > glob_subiter_method, > glob_normmax, > glob_h, > years_in_century, > min_in_hour, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_no_eqs, > glob_optimal_done, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_log10_relerr, > glob_clock_start_sec, > sec_in_min, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_tmp1_g, > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_y_init, > array_m1, > array_tmp2_g, > array_type_pole, > array_norms, > array_1st_rel_error, > array_y_higher, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_real_pole, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_max_terms, glob_iolevel, ALWAYS, glob_max_sec, glob_relerr, glob_large_float, glob_clock_sec, glob_max_opt_iter, MAX_UNCHANGED, glob_current_iter, glob_start, glob_last_good_h, glob_display_flag, glob_optimal_expect_sec, glob_max_hours, glob_abserr, glob_log10_abserr, hours_in_day, glob_smallish_float, glob_not_yet_start_msg, glob_almost_1, glob_dump_analytic, glob_hmax, glob_reached_optimal_h, djd_debug, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_iter, glob_look_poles, glob_hmin, glob_initial_pass, glob_not_yet_finished, centuries_in_millinium, djd_debug2, glob_max_minutes, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_disp_incr, days_in_year, glob_log10abserr, glob_dump, glob_subiter_method, glob_normmax, glob_h, years_in_century, min_in_hour, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_no_eqs, glob_optimal_done, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_max_trunc_err, glob_log10_relerr, glob_clock_start_sec, sec_in_min, glob_log10normmin, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_tmp1_g, array_y, array_x, array_last_rel_error, array_fact_1, array_y_init, array_m1, array_tmp2_g, array_type_pole, array_norms, array_1st_rel_error, array_y_higher, array_y_set_initial, array_poles, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher_work2, array_real_pole, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_max_terms, > glob_iolevel, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_relerr, > glob_large_float, > glob_clock_sec, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_start, > glob_last_good_h, > glob_display_flag, > glob_optimal_expect_sec, > glob_max_hours, > glob_abserr, > glob_log10_abserr, > hours_in_day, > glob_smallish_float, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump_analytic, > glob_hmax, > glob_reached_optimal_h, > djd_debug, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_iter, > glob_look_poles, > glob_hmin, > glob_initial_pass, > glob_not_yet_finished, > centuries_in_millinium, > djd_debug2, > glob_max_minutes, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_disp_incr, > days_in_year, > glob_log10abserr, > glob_dump, > glob_subiter_method, > glob_normmax, > glob_h, > years_in_century, > min_in_hour, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_no_eqs, > glob_optimal_done, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_log10_relerr, > glob_clock_start_sec, > sec_in_min, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_tmp1_g, > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_y_init, > array_m1, > array_tmp2_g, > array_type_pole, > array_norms, > array_1st_rel_error, > array_y_higher, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_real_pole, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_max_terms, glob_iolevel, ALWAYS, glob_max_sec, glob_relerr, glob_large_float, glob_clock_sec, glob_max_opt_iter, MAX_UNCHANGED, glob_current_iter, glob_start, glob_last_good_h, glob_display_flag, glob_optimal_expect_sec, glob_max_hours, glob_abserr, glob_log10_abserr, hours_in_day, glob_smallish_float, glob_not_yet_start_msg, glob_almost_1, glob_dump_analytic, glob_hmax, glob_reached_optimal_h, djd_debug, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_iter, glob_look_poles, glob_hmin, glob_initial_pass, glob_not_yet_finished, centuries_in_millinium, djd_debug2, glob_max_minutes, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_disp_incr, days_in_year, glob_log10abserr, glob_dump, glob_subiter_method, glob_normmax, glob_h, years_in_century, min_in_hour, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_no_eqs, glob_optimal_done, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_max_trunc_err, glob_log10_relerr, glob_clock_start_sec, sec_in_min, glob_log10normmin, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_tmp1_g, array_y, array_x, array_last_rel_error, array_fact_1, array_y_init, array_m1, array_tmp2_g, array_type_pole, array_norms, array_1st_rel_error, array_y_higher, array_y_set_initial, array_poles, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher_work2, array_real_pole, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_max_terms, > glob_iolevel, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_relerr, > glob_large_float, > glob_clock_sec, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_start, > glob_last_good_h, > glob_display_flag, > glob_optimal_expect_sec, > glob_max_hours, > glob_abserr, > glob_log10_abserr, > hours_in_day, > glob_smallish_float, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump_analytic, > glob_hmax, > glob_reached_optimal_h, > djd_debug, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_iter, > glob_look_poles, > glob_hmin, > glob_initial_pass, > glob_not_yet_finished, > centuries_in_millinium, > djd_debug2, > glob_max_minutes, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_disp_incr, > days_in_year, > glob_log10abserr, > glob_dump, > glob_subiter_method, > glob_normmax, > glob_h, > years_in_century, > min_in_hour, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_no_eqs, > glob_optimal_done, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_log10_relerr, > glob_clock_start_sec, > sec_in_min, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_tmp1_g, > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_y_init, > array_m1, > array_tmp2_g, > array_type_pole, > array_norms, > array_1st_rel_error, > array_y_higher, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_real_pole, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_max_terms, glob_iolevel, ALWAYS, glob_max_sec, glob_relerr, glob_large_float, glob_clock_sec, glob_max_opt_iter, MAX_UNCHANGED, glob_current_iter, glob_start, glob_last_good_h, glob_display_flag, glob_optimal_expect_sec, glob_max_hours, glob_abserr, glob_log10_abserr, hours_in_day, glob_smallish_float, glob_not_yet_start_msg, glob_almost_1, glob_dump_analytic, glob_hmax, glob_reached_optimal_h, djd_debug, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_iter, glob_look_poles, glob_hmin, glob_initial_pass, glob_not_yet_finished, centuries_in_millinium, djd_debug2, glob_max_minutes, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_disp_incr, days_in_year, glob_log10abserr, glob_dump, glob_subiter_method, glob_normmax, glob_h, years_in_century, min_in_hour, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_no_eqs, glob_optimal_done, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_max_trunc_err, glob_log10_relerr, glob_clock_start_sec, sec_in_min, glob_log10normmin, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_tmp1_g, array_y, array_x, array_last_rel_error, array_fact_1, array_y_init, array_m1, array_tmp2_g, array_type_pole, array_norms, array_1st_rel_error, array_y_higher, array_y_set_initial, array_poles, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher_work2, array_real_pole, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_max_terms, > glob_iolevel, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_relerr, > glob_large_float, > glob_clock_sec, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_start, > glob_last_good_h, > glob_display_flag, > glob_optimal_expect_sec, > glob_max_hours, > glob_abserr, > glob_log10_abserr, > hours_in_day, > glob_smallish_float, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump_analytic, > glob_hmax, > glob_reached_optimal_h, > djd_debug, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_iter, > glob_look_poles, > glob_hmin, > glob_initial_pass, > glob_not_yet_finished, > centuries_in_millinium, > djd_debug2, > glob_max_minutes, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_disp_incr, > days_in_year, > glob_log10abserr, > glob_dump, > glob_subiter_method, > glob_normmax, > glob_h, > years_in_century, > min_in_hour, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_no_eqs, > glob_optimal_done, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_log10_relerr, > glob_clock_start_sec, > sec_in_min, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_tmp1_g, > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_y_init, > array_m1, > array_tmp2_g, > array_type_pole, > array_norms, > array_1st_rel_error, > array_y_higher, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_real_pole, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_max_terms, glob_iolevel, ALWAYS, glob_max_sec, glob_relerr, glob_large_float, glob_clock_sec, glob_max_opt_iter, MAX_UNCHANGED, glob_current_iter, glob_start, glob_last_good_h, glob_display_flag, glob_optimal_expect_sec, glob_max_hours, glob_abserr, glob_log10_abserr, hours_in_day, glob_smallish_float, glob_not_yet_start_msg, glob_almost_1, glob_dump_analytic, glob_hmax, glob_reached_optimal_h, djd_debug, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_iter, glob_look_poles, glob_hmin, glob_initial_pass, glob_not_yet_finished, centuries_in_millinium, djd_debug2, glob_max_minutes, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_disp_incr, days_in_year, glob_log10abserr, glob_dump, glob_subiter_method, glob_normmax, glob_h, years_in_century, min_in_hour, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_no_eqs, glob_optimal_done, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_max_trunc_err, glob_log10_relerr, glob_clock_start_sec, sec_in_min, glob_log10normmin, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_tmp1_g, array_y, array_x, array_last_rel_error, array_fact_1, array_y_init, array_m1, array_tmp2_g, array_type_pole, array_norms, array_1st_rel_error, array_y_higher, array_y_set_initial, array_poles, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher_work2, array_real_pole, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_max_terms, > glob_iolevel, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_relerr, > glob_large_float, > glob_clock_sec, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_start, > glob_last_good_h, > glob_display_flag, > glob_optimal_expect_sec, > glob_max_hours, > glob_abserr, > glob_log10_abserr, > hours_in_day, > glob_smallish_float, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump_analytic, > glob_hmax, > glob_reached_optimal_h, > djd_debug, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_iter, > glob_look_poles, > glob_hmin, > glob_initial_pass, > glob_not_yet_finished, > centuries_in_millinium, > djd_debug2, > glob_max_minutes, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_disp_incr, > days_in_year, > glob_log10abserr, > glob_dump, > glob_subiter_method, > glob_normmax, > glob_h, > years_in_century, > min_in_hour, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_no_eqs, > glob_optimal_done, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_log10_relerr, > glob_clock_start_sec, > sec_in_min, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_tmp1_g, > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_y_init, > array_m1, > array_tmp2_g, > array_type_pole, > array_norms, > array_1st_rel_error, > array_y_higher, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_real_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin $eq_no = 1 iii = 1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre cos $eq_no = 1 > array_tmp2_g[1] := sin(array_x[1]); > array_tmp2[1] := cos(array_x[1]); > #emit pre div $eq_no = 1 i = 1 > array_tmp3[1] := (array_tmp1[1] / (array_tmp2[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 2 > #emit pre sin 2 $eq_no = 1 > array_tmp1[2] := att(1,array_tmp1_g,array_x,1); > array_tmp1_g[2] := -att(1,array_tmp1,array_x,1); > #emit pre cos $eq_no = 1 > array_tmp2_g[2] := (att(1,array_tmp2,array_x,1)); > array_tmp2[2] := (-att(1,array_tmp2_g,array_x,1)); > #emit pre div $eq_no = 1 i = 2 > array_tmp3[2] := ((array_tmp1[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 2 > array_tmp4[2] := array_const_0D0[2] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 3 > #emit pre sin 3 $eq_no = 1 > array_tmp1[3] := att(2,array_tmp1_g,array_x,1); > array_tmp1_g[3] := -att(2,array_tmp1,array_x,1); > #emit pre cos $eq_no = 1 > array_tmp2_g[3] := (att(2,array_tmp2,array_x,1)); > array_tmp2[3] := (-att(2,array_tmp2_g,array_x,1)); > #emit pre div $eq_no = 1 i = 3 > array_tmp3[3] := ((array_tmp1[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 3 > array_tmp4[3] := array_const_0D0[3] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 4 > #emit pre sin 4 $eq_no = 1 > array_tmp1[4] := att(3,array_tmp1_g,array_x,1); > array_tmp1_g[4] := -att(3,array_tmp1,array_x,1); > #emit pre cos $eq_no = 1 > array_tmp2_g[4] := (att(3,array_tmp2,array_x,1)); > array_tmp2[4] := (-att(3,array_tmp2_g,array_x,1)); > #emit pre div $eq_no = 1 i = 4 > array_tmp3[4] := ((array_tmp1[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 4 > array_tmp4[4] := array_const_0D0[4] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 5 > #emit pre sin 5 $eq_no = 1 > array_tmp1[5] := att(4,array_tmp1_g,array_x,1); > array_tmp1_g[5] := -att(4,array_tmp1,array_x,1); > #emit pre cos $eq_no = 1 > array_tmp2_g[5] := (att(4,array_tmp2,array_x,1)); > array_tmp2[5] := (-att(4,array_tmp2_g,array_x,1)); > #emit pre div $eq_no = 1 i = 5 > array_tmp3[5] := ((array_tmp1[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit pre add $eq_no = 1 i = 5 > array_tmp4[5] := array_const_0D0[5] + array_tmp3[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_tmp4[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 sin $eq_no = 1 > array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1); > array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1); > #emit cos $eq_no = 1 > array_tmp2_g[kkk] := (att(kkk-1,array_tmp2,array_x,1)); > array_tmp2[kkk] := (-att(kkk-1,array_tmp2_g,array_x,1)); > #emit div $eq_no = 1 > array_tmp3[kkk] := ((array_tmp1[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]); > #emit add $eq_no = 1 > array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[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_tmp4[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 DEBUGMASSIVE, DEBUGL, INFO, glob_max_terms, glob_iolevel, ALWAYS, glob_max_sec, glob_relerr, glob_large_float, glob_clock_sec, glob_max_opt_iter, MAX_UNCHANGED, glob_current_iter, glob_start, glob_last_good_h, glob_display_flag, glob_optimal_expect_sec, glob_max_hours, glob_abserr, glob_log10_abserr, hours_in_day, glob_smallish_float, glob_not_yet_start_msg, glob_almost_1, glob_dump_analytic, glob_hmax, glob_reached_optimal_h, djd_debug, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_iter, glob_look_poles, glob_hmin, glob_initial_pass, glob_not_yet_finished, centuries_in_millinium, djd_debug2, glob_max_minutes, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_disp_incr, days_in_year, glob_log10abserr, glob_dump, glob_subiter_method, glob_normmax, glob_h, years_in_century, min_in_hour, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_no_eqs, glob_optimal_done, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_max_trunc_err, glob_log10_relerr, glob_clock_start_sec, sec_in_min, glob_log10normmin, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_tmp1_g, array_y, array_x, array_last_rel_error, array_fact_1, array_y_init, array_m1, array_tmp2_g, array_type_pole, array_norms, array_1st_rel_error, array_y_higher, array_y_set_initial, array_poles, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher_work2, array_real_pole, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2_g[1] := sin(array_x[1]); array_tmp2[1] := cos(array_x[1]); array_tmp3[1] := array_tmp1[1]/array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := att(1, array_tmp1_g, array_x, 1); array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1); array_tmp2_g[2] := att(1, array_tmp2, array_x, 1); array_tmp2[2] := -att(1, array_tmp2_g, array_x, 1); array_tmp3[2] := (array_tmp1[2] - ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[2] := array_const_0D0[2] + array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := att(2, array_tmp1_g, array_x, 1); array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1); array_tmp2_g[3] := att(2, array_tmp2, array_x, 1); array_tmp2[3] := -att(2, array_tmp2_g, array_x, 1); array_tmp3[3] := (array_tmp1[3] - ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[3] := array_const_0D0[3] + array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := att(3, array_tmp1_g, array_x, 1); array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1); array_tmp2_g[4] := att(3, array_tmp2, array_x, 1); array_tmp2[4] := -att(3, array_tmp2_g, array_x, 1); array_tmp3[4] := (array_tmp1[4] - ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[4] := array_const_0D0[4] + array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := att(4, array_tmp1_g, array_x, 1); array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1); array_tmp2_g[5] := att(4, array_tmp2, array_x, 1); array_tmp2[5] := -att(4, array_tmp2_g, array_x, 1); array_tmp3[5] := (array_tmp1[5] - ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[5] := array_const_0D0[5] + array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1); array_tmp2_g[kkk] := att(kkk - 1, array_tmp2, array_x, 1); array_tmp2[kkk] := -att(kkk - 1, array_tmp2_g, array_x, 1); array_tmp3[kkk] := ( array_tmp1[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/ array_tmp2[1]; array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[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_tmp4[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 13 > if array_fact_1[nnn] = 0 then # if number 14 > ret := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > if array_fact_2[mmm,nnn] = 0 then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 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,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_max_terms, > glob_iolevel, > ALWAYS, > #Top Generate Globals Decl > glob_max_sec, > glob_relerr, > glob_large_float, > glob_clock_sec, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_start, > glob_last_good_h, > glob_display_flag, > glob_optimal_expect_sec, > glob_max_hours, > glob_abserr, > glob_log10_abserr, > hours_in_day, > glob_smallish_float, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump_analytic, > glob_hmax, > glob_reached_optimal_h, > djd_debug, > glob_log10relerr, > glob_iter, > glob_orig_start_sec, > glob_max_iter, > glob_look_poles, > glob_hmin, > glob_initial_pass, > glob_not_yet_finished, > centuries_in_millinium, > djd_debug2, > glob_max_minutes, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_disp_incr, > days_in_year, > glob_log10abserr, > glob_dump, > glob_subiter_method, > glob_normmax, > glob_h, > years_in_century, > min_in_hour, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_no_eqs, > glob_optimal_done, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_log10_relerr, > glob_clock_start_sec, > sec_in_min, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_tmp1_g, > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_y_init, > array_m1, > array_tmp2_g, > array_type_pole, > array_norms, > array_1st_rel_error, > array_y_higher, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_y_higher_work2, > array_real_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > DEBUGL := 3; > INFO := 2; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > glob_max_sec := 10000.0; > glob_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_clock_sec := 0.0; > glob_max_opt_iter := 10; > MAX_UNCHANGED := 10; > glob_current_iter := 0; > glob_start := 0; > glob_last_good_h := 0.1; > glob_display_flag := true; > glob_optimal_expect_sec := 0.1; > glob_max_hours := 0.0; > glob_abserr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > hours_in_day := 24.0; > glob_smallish_float := 0.1e-100; > glob_not_yet_start_msg := true; > glob_almost_1 := 0.9990; > glob_dump_analytic := false; > glob_hmax := 1.0; > glob_reached_optimal_h := false; > djd_debug := true; > glob_log10relerr := 0.0; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_max_iter := 1000; > glob_look_poles := false; > glob_hmin := 0.00000000001; > glob_initial_pass := true; > glob_not_yet_finished := true; > centuries_in_millinium := 10.0; > djd_debug2 := true; > glob_max_minutes := 0.0; > glob_small_float := 0.1e-50; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_hmin_init := 0.001; > glob_disp_incr := 0.1; > days_in_year := 365.0; > glob_log10abserr := 0.0; > glob_dump := false; > glob_subiter_method := 3; > glob_normmax := 0.0; > glob_h := 0.1; > years_in_century := 100.0; > min_in_hour := 60.0; > glob_html_log := true; > glob_curr_iter_when_opt := 0; > glob_warned2 := false; > glob_no_eqs := 0; > glob_optimal_done := false; > glob_percent_done := 0.0; > glob_warned := false; > glob_unchanged_h_cnt := 0; > glob_max_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_clock_start_sec := 0.0; > sec_in_min := 60.0; > glob_log10normmin := 0.1; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/divpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 1.0 ;"); > 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 := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"2.0 - log(abs(cos(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_tmp2_g:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2_g[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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_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 <=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_real_pole[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_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2_g[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 > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 1.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := 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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) / cos ( 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,"2012-06-17T20:26:41-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"div") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 092 ") > ; > logitem_str(html_log_file,"div diffeq.mxt") > ; > logitem_str(html_log_file,"div maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global DEBUGMASSIVE, DEBUGL, INFO, glob_max_terms, glob_iolevel, ALWAYS, glob_max_sec, glob_relerr, glob_large_float, glob_clock_sec, glob_max_opt_iter, MAX_UNCHANGED, glob_current_iter, glob_start, glob_last_good_h, glob_display_flag, glob_optimal_expect_sec, glob_max_hours, glob_abserr, glob_log10_abserr, hours_in_day, glob_smallish_float, glob_not_yet_start_msg, glob_almost_1, glob_dump_analytic, glob_hmax, glob_reached_optimal_h, djd_debug, glob_log10relerr, glob_iter, glob_orig_start_sec, glob_max_iter, glob_look_poles, glob_hmin, glob_initial_pass, glob_not_yet_finished, centuries_in_millinium, djd_debug2, glob_max_minutes, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_disp_incr, days_in_year, glob_log10abserr, glob_dump, glob_subiter_method, glob_normmax, glob_h, years_in_century, min_in_hour, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_no_eqs, glob_optimal_done, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_max_trunc_err, glob_log10_relerr, glob_clock_start_sec, sec_in_min, glob_log10normmin, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_tmp1_g, array_y, array_x, array_last_rel_error, array_fact_1, array_y_init, array_m1, array_tmp2_g, array_type_pole, array_norms, array_1st_rel_error, array_y_higher, array_y_set_initial, array_poles, array_y_higher_work, array_fact_2, array_complex_pole, array_y_higher_work2, array_real_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; DEBUGL := 3; INFO := 2; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; glob_max_sec := 10000.0; glob_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_clock_sec := 0.; glob_max_opt_iter := 10; MAX_UNCHANGED := 10; glob_current_iter := 0; glob_start := 0; glob_last_good_h := 0.1; glob_display_flag := true; glob_optimal_expect_sec := 0.1; glob_max_hours := 0.; glob_abserr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); hours_in_day := 24.0; glob_smallish_float := 0.1*10^(-100); glob_not_yet_start_msg := true; glob_almost_1 := 0.9990; glob_dump_analytic := false; glob_hmax := 1.0; glob_reached_optimal_h := false; djd_debug := true; glob_log10relerr := 0.; glob_iter := 0; glob_orig_start_sec := 0.; glob_max_iter := 1000; glob_look_poles := false; glob_hmin := 0.1*10^(-10); glob_initial_pass := true; glob_not_yet_finished := true; centuries_in_millinium := 10.0; djd_debug2 := true; glob_max_minutes := 0.; glob_small_float := 0.1*10^(-50); glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_hmin_init := 0.001; glob_disp_incr := 0.1; days_in_year := 365.0; glob_log10abserr := 0.; glob_dump := false; glob_subiter_method := 3; glob_normmax := 0.; glob_h := 0.1; years_in_century := 100.0; min_in_hour := 60.0; glob_html_log := true; glob_curr_iter_when_opt := 0; glob_warned2 := false; glob_no_eqs := 0; glob_optimal_done := false; glob_percent_done := 0.; glob_warned := false; glob_unchanged_h_cnt := 0; glob_max_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_clock_start_sec := 0.; sec_in_min := 60.0; glob_log10normmin := 0.1; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/divpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 1.0 ;"); 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 := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "2.0 - log(abs(cos(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_tmp2_g := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_g[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_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[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 <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_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_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_tmp2_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_g[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; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 1.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) / cos ( 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, "2012-06-17T20:26:41-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "div"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 092 "); logitem_str(html_log_file, "div diffeq.mxt"); logitem_str(html_log_file, "div maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 1.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 2.0 - log(abs(cos(x))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 2.0050083556232353090791329977213 y[1] (numeric) = 2.0050083556232353090791329977213 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 2.0051091953627122809266837385959 y[1] (numeric) = 2.005109195362712281772476612613 absolute error = 8.457928740171e-19 relative error = 4.2181885952804735869893087833584e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 2.0052110453731395809679176257221 y[1] (numeric) = 2.0052110453731395826609019545366 absolute error = 1.6929843288145e-18 relative error = 8.4429234155722551860216533236185e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 2.0053139058603304882005935402182 y[1] (numeric) = 2.005313905860330490742183178976 absolute error = 2.5415896387578e-18 relative error = 1.2674273246349397008933871484136e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 2.0054177770321827558038490693382 y[1] (numeric) = 2.0054177770321827591954731898984 absolute error = 3.3916241205602e-18 relative error = 1.6912307048456824042694121695966e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 2.0055226590986803007200141007995 y[1] (numeric) = 2.0055226590986803049631172345627 absolute error = 4.2431031337632e-18 relative error = 2.1157093960085848925657605556408e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.17 NO POLE x[1] = 0.106 y[1] (analytic) = 2.0056285522718949107171380199288 y[1] (numeric) = 2.0056285522718949158131801011482 absolute error = 5.0960420812194e-18 relative error = 2.5408703298757936153047925229802e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 2.0057354567659879689618848211429 y[1] (numeric) = 2.0057354567659879749123412307198 absolute error = 5.9504564095769e-18 relative error = 2.9667204563314195225439639682232e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 2.0058433727972121961327671309818 y[1] (numeric) = 2.0058433727972122029391287407479 absolute error = 6.8063616097661e-18 relative error = 3.3932667435914564356509346622573e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 2.0059523005839134101040077246038 y[1] (numeric) = 2.0059523005839134177677809420923 absolute error = 7.6637732174885e-18 relative error = 3.8205161784044662327764805615078e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 2.0060622403465323032306356113409 y[1] (numeric) = 2.0060622403465323117533424250483 absolute error = 8.5227068137074e-18 relative error = 4.2484757662529782263888362551422e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 2.0061731923076062372657431776415 y[1] (numeric) = 2.0061731923076062466489212027821 absolute error = 9.3831780251406e-18 relative error = 4.6771525315556498118384892809599e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 2.0062851566917710559411512175826 y[1] (numeric) = 2.0062851566917710661863537423383 absolute error = 1.02452025247557e-17 relative error = 5.1065535178704846484557923033260e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 2.0063981337257629152430499622528 y[1] (numeric) = 2.0063981337257629263518459945197 absolute error = 1.11087960322669e-17 relative error = 5.5366857880985571977926215250485e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 2.0065121236384201314145064498531 y[1] (numeric) = 2.0065121236384201433884807644876 absolute error = 1.19739743146345e-17 relative error = 5.9675564246888389435993799771792e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=0.38 NO POLE x[1] = 0.115 y[1] (analytic) = 2.0066271266606850467170517685652 y[1] (numeric) = 2.0066271266606850595578049551315 absolute error = 1.28407531865663e-17 relative error = 6.3991725298437246373443694966209e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 2.0067431430256059129838858643474 y[1] (numeric) = 2.0067431430256059266930343753687 absolute error = 1.37091485110213e-17 relative error = 6.8315412257254550637964955626504e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 2.0068601729683387929975627461547 y[1] (numeric) = 2.0068601729683388075767389458704 absolute error = 1.45791761997157e-17 relative error = 7.2646696546634333999215915100311e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 2.0069782167261494797253450519834 y[1] (numeric) = 2.0069782167261494951761972656141 absolute error = 1.54508522136307e-17 relative error = 7.6985649793621830948684243108923e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 2.0070972745384154334457440710196 y[1] (numeric) = 2.007097274538415449769936634543 absolute error = 1.63241925635234e-17 relative error = 8.1332343831105921198623887186913e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 2.0072173466466277368000894604662 y[1] (numeric) = 2.0072173466466277539993027709058 absolute error = 1.71992133104396e-17 relative error = 8.5686850699918426102712937893759e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 2.0073384332943930678033020608256 y[1] (numeric) = 2.007338433294393085879232627054 absolute error = 1.80759305662284e-17 relative error = 9.0049242650939731796898196352558e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 2.0074605347274356908483734110635 y[1] (numeric) = 2.0074605347274357098027339051238 absolute error = 1.89543604940603e-17 relative error = 9.4419592147219178534927035243051e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 2.0075836511935994657393868057698 y[1] (numeric) = 2.0075836511935994855739061147164 absolute error = 1.98345193089466e-17 relative error = 9.8797971866099225088074908591405e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.0MB, time=0.60 NO POLE x[1] = 0.124 y[1] (analytic) = 2.0077077829428498747882470307837 y[1] (numeric) = 2.0077077829428498955046703090457 absolute error = 2.07164232782620e-17 relative error = 1.0318445470135282356779545651439e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 2.0078329302272760680106192724675 y[1] (numeric) = 2.0078329302272760896107079947367 absolute error = 2.16000887222692e-17 relative error = 1.0757911376532799570298369719707e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 2.0079590933010929264569121296132 y[1] (numeric) = 2.0079590933010929489424441442592 absolute error = 2.24855320146460e-17 relative error = 1.1198202239110207070722412213852e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 2.0080862724206431437144751766449 y[1] (numeric) = 2.00808627242064316708724475966 absolute error = 2.33727695830151e-17 relative error = 1.1639325413464654952516125731749e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 2.0082144678443993256175181431687 y[1] (numeric) = 2.0082144678443993498793360526452 absolute error = 2.42618179094765e-17 relative error = 1.2081288277700206571472288031454e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 2.0083436798329661082015964989065 y[1] (numeric) = 2.0083436798329661333542900300482 absolute error = 2.51526935311417e-17 relative error = 1.2524098232645942784585733317146e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 2.008473908649082293939847075567 y[1] (numeric) = 2.0084739086490823199852601162387 absolute error = 2.60454130406717e-17 relative error = 1.2967762702075667112957653756398e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 2.0086051545576230062984973292569 y[1] (numeric) = 2.0086051545576230332384904160731 absolute error = 2.69399930868162e-17 relative error = 1.3412289132927913921081211450788e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 2.0087374178256018626495129596427 y[1] (numeric) = 2.0087374178256018904859633345997 absolute error = 2.78364503749570e-17 relative error = 1.3857684995527750183627948909006e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 2.0088706987221731655785908663584 y[1] (numeric) = 2.0088706987221731943133925340108 absolute error = 2.87348016676524e-17 relative error = 1.4303957783808774300198534919527e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.81 NO POLE x[1] = 0.134 y[1] (analytic) = 2.0090049975186341126270478502428 y[1] (numeric) = 2.0090049975186341422621116354284 absolute error = 2.96350637851856e-17 relative error = 1.4751115015536802347564070967801e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 2.0091403144884270245065000681108 y[1] (numeric) = 2.0091403144884270550437536742261 absolute error = 3.05372536061153e-17 relative error = 1.5199164232534342267405037749657e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 2.0092766499071415918255740361572 y[1] (numeric) = 2.0092766499071416232669621039857 absolute error = 3.14413880678285e-17 relative error = 1.5648113000905852792445309729097e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 2.0094140040525171403682369600856 y[1] (numeric) = 2.0094140040525171727157211271831 absolute error = 3.23474841670975e-17 relative error = 1.6097968911264779215226168433456e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 2.0095523772044449149636823610216 y[1] (numeric) = 2.0095523772044449482192413216596 absolute error = 3.32555589606380e-17 relative error = 1.6548739578960819663185733717856e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 2.0096917696449703819880563766269 y[1] (numeric) = 2.0096917696449704161536859422982 absolute error = 3.41656295656713e-17 relative error = 1.7000432644308911663477016451415e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 2.0098321816582955505386607580818 y[1] (numeric) = 2.0098321816582955856163739185705 absolute error = 3.50777131604887e-17 relative error = 1.7453055772818989926129644215655e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 2.0099736135307813123216204672764 y[1] (numeric) = 2.0099736135307813483134474522956 absolute error = 3.59918269850192e-17 relative error = 1.7906616655427059336421367790889e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 2.0101160655509498002943569162601 y[1] (numeric) = 2.0101160655509498372023452576593 absolute error = 3.69079883413992e-17 relative error = 1.8361123008726932862536857809179e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.1MB, time=1.03 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) = 2.0102595380094868039307768889449 absolute error = 3.78262145945466e-17 relative error = 1.8816582575203824990990719957080e-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) = 2.0104040311992440151142492822417 absolute error = 3.87465231727370e-17 relative error = 1.9273003123468652765117988491861e-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) = 2.0105495454152416674945536074142 absolute error = 3.96689315681824e-17 relative error = 1.9730392448493240051962662006498e-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) = 2.0106960809546708220219787976703 absolute error = 4.05934573376139e-17 relative error = 2.0188758371847167608282729567232e-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) = 2.0108436381168958569043777080685 absolute error = 4.15201181028672e-17 relative error = 2.0648108741935668342835402131931e-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) = 2.0109922172034569396665727632174 absolute error = 4.24489315514710e-17 relative error = 2.1108451434238613945923860878246e-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) = 2.0111418185180725182639502002795 absolute error = 4.33799154372381e-17 relative error = 2.1569794351550489840966831287754e-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) = 2.0112924423666418312944556082807 absolute error = 4.43130875808609e-17 relative error = 2.2032145424222200120329295103192e-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) = 2.0114440890572474373535684208131 absolute error = 4.52484658705087e-17 relative error = 2.2495512610403405833363413564096e-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) = 2.011596758900157763577199348716 absolute error = 4.61860682624291e-17 relative error = 2.2959903896286536626640842031188e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=1.25 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) = 2.0117504522078296734178224545222 absolute error = 4.71259127815524e-17 relative error = 2.3425327296351924956462496990472e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0119051692949110536995226837105 absolute error = 4.80680175220992e-17 relative error = 2.3891790853614158557302782780137e-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) = 2.0120609104782434209980101915352 absolute error = 4.90124006481911e-17 relative error = 2.4359302639869597668537183329864e-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) = 2.0122176760768645473920247508959 absolute error = 4.99590803944655e-17 relative error = 2.4827870755945550193056821651264e-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) = 2.0123754664120111056329269089166 absolute error = 5.09080750666927e-17 relative error = 2.5297503331950206239643025819844e-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) = 2.0125342818071213337796473902525 absolute error = 5.18594030423974e-17 relative error = 2.5768208527524371894401711781855e-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) = 2.0126941225878377193465425363231 absolute error = 5.28130827714831e-17 relative error = 2.6239994532094252742296711026744e-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) = 2.0128549890820097030120813344447 absolute error = 5.37691327768598e-17 relative error = 2.6712869565125482040719140670835e-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) = 2.013016881619696401936668842041 absolute error = 5.47275716550759e-17 relative error = 2.7186841876378836684508020854339e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=1.47 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) = 2.0131798005331693527382915616474 absolute error = 5.56884180769530e-17 relative error = 2.7661919746166990992998305783010e-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) = 2.0133437461569152741750525852708 absolute error = 5.66516907882244e-17 relative error = 2.8138111485612701784277664986951e-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) = 2.013508718827638849584048114872 absolute error = 5.76174086101773e-17 relative error = 2.8615425436908420606990223779180e-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) = 2.0136747188842655291264222924241 absolute error = 5.85855904402990e-17 relative error = 2.9093869973577477957867836869209e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0138417466679443518888241513613 absolute error = 5.95562552529259e-17 relative error = 2.9573453500736239345800412401301e-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) = 2.0140098025220507878918789445456 absolute error = 6.05294220998970e-17 relative error = 3.0054184455358073349036696444360e-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) = 2.014178886792189600056676125482 absolute error = 6.15051101112106e-17 relative error = 3.0536071306538481787310109153649e-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) = 2.0143489998261977261806678728373 absolute error = 6.24833384956855e-17 relative error = 3.1019122555762033277376615863425e-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) = 2.0145201419741471809747652668543 absolute error = 6.34641265416251e-17 relative error = 3.1503346737170301433113031011681e-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) = 2.0146923135883479782138140635877 absolute error = 6.44474936174858e-17 relative error = 3.1988752417831498546538356113441e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=1.69 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) = 2.014865515023351073053028482669 absolute error = 6.54334591725496e-17 relative error = 3.2475348198011750623852461510897e-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) = 2.0150397466359513245633595402708 absolute error = 6.64220427376000e-17 relative error = 3.2963142711447562642947066515194e-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) = 2.0152150087851904785391742349057 absolute error = 6.74132639256023e-17 relative error = 3.3452144625620015632776593989518e-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) = 2.0153913018323601706320233435464 absolute error = 6.84071424323877e-17 relative error = 3.3942362642030393263826835847796e-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) = 2.0155686261410049498646787232775 absolute error = 6.94036980373414e-17 relative error = 3.4433805496477332730695399303378e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0157469820769253225800258533364 absolute error = 7.04029506040952e-17 relative error = 3.4926481959335743441842359501576e-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) = 2.0159263700081808168798039081157 absolute error = 7.14049200812233e-17 relative error = 3.5420400835836843939961783633565e-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) = 2.016106790305093067608593937705 absolute error = 7.24096265029434e-17 relative error = 3.5915570966350354328004171423670e-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) = 2.0162882433402489219388657631551 absolute error = 7.34170899898206e-17 relative error = 3.6412001226667599286424476941796e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=1.91 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) = 2.0164707294885035656133059832463 absolute error = 7.44273307494775e-17 relative error = 3.6909700528287203534856204024031e-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) = 2.016654249126983669901063052613 absolute error = 7.54403690773059e-17 relative error = 3.7408677818701093380414811133817e-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) = 2.0168388026350905593249607421896 absolute error = 7.64562253571855e-17 relative error = 3.7908942081683477878813994212354e-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) = 2.0170243903945034002171484467447 absolute error = 7.74749200622054e-17 relative error = 3.8410502337580721668728197559953e-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) = 2.0172110127891824101610757755105 absolute error = 7.84964737553895e-17 relative error = 3.8913367643602650425199929631364e-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) = 2.0173986702053720883780996654214 absolute error = 7.95209070904283e-17 relative error = 3.9417547094116523418278200761425e-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) = 2.0175873630316044671174549071669 absolute error = 8.05482408124130e-17 relative error = 3.9923049820941635477738153837380e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0177770916587023841087434871592 absolute error = 8.15784957585758e-17 relative error = 4.0429884993646476910888842874586e-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) = 2.0179678564797827761365245387101 absolute error = 8.26116928590332e-17 relative error = 4.0938061819846860054438746663495e-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) = 2.0181596578902599937970149784083 absolute error = 8.36478531375356e-17 relative error = 4.1447589545506643063035877684258e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=2.14 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) = 2.0183524962878491374973410941696 absolute error = 8.46869977122199e-17 relative error = 4.1958477455239410275510759343900e-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) = 2.0185463720725694147582134650873 absolute error = 8.57291477963677e-17 relative error = 4.2470734872612392610875910994954e-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) = 2.018741285646747518881331645514 absolute error = 8.67743246991682e-17 relative error = 4.2984371160452176679610071220779e-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) = 2.0189372374150210290432610523313 absolute error = 8.78225498264852e-17 relative error = 4.3499395721151900199102306131892e-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) = 2.0191342277843418318779624707863 absolute error = 8.88738446816298e-17 relative error = 4.4015817996980721080360411637146e-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) = 2.0193322571639795646105945563555 absolute error = 8.99282308661371e-17 relative error = 4.4533647470394712702355994906440e-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) = 2.0195313259655250798056516737093 absolute error = 9.09857300805483e-17 relative error = 4.5052893664349873527425216830863e-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) = 2.0197314346028939317929433949569 absolute error = 9.20463641251975e-17 relative error = 4.5573566142616898894753249945201e-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) = 2.0199325834923298848353679940192 absolute error = 9.31101549010039e-17 relative error = 4.6095674510098056163199289277256e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.614 Order of pole = 6.91 memory used=41.9MB, alloc=4.1MB, time=2.36 x[1] = 0.2 y[1] (analytic) = 2.0201347730524083489257559281057 y[1] (numeric) = 2.0201347730524084431028803383737 absolute error = 9.41771244102680e-17 relative error = 4.6619228413145464533159816883634e-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) = 2.0203380037040404025175047098103 absolute error = 9.52472947574739e-17 relative error = 4.7144237539881813784008616156889e-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) = 2.0205422758704754245346952986012 absolute error = 9.63206881500966e-17 relative error = 4.7670711620522971565111144103249e-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) = 2.0207475899773056319268014270984 absolute error = 9.73973268994134e-17 relative error = 4.8198660427702028255197407496778e-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) = 2.0209539464524692266348509858136 absolute error = 9.84772334213220e-17 relative error = 4.8728093776796060592679362504572e-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) = 2.0211613457262541297553241241865 absolute error = 9.95604302371630e-17 relative error = 4.9259021526254469849412570420064e-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) = 2.0213697882313016437290499463099 absolute error = 1.006469399745472e-16 relative error = 4.9791453577929086944047942106649e-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) = 2.0215792744026101367998218357518 absolute error = 1.017367853681895e-16 relative error = 5.0325399877406929227745864334303e-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) = 2.0217898046775387498107920903038 absolute error = 1.028299892607473e-16 relative error = 5.0860870414344563919464221201726e-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) = 2.0220013794958111254071738041147 absolute error = 1.039265746036645e-16 relative error = 5.1397875222804616585698610856492e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=2.59 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) = 2.0222139992995191597142474084658 absolute error = 1.050265644580210e-16 relative error = 5.1936424381594369165162982328675e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0224276645331267765601409907537 absolute error = 1.061299819953880e-16 relative error = 5.2476528014606589827500414785745e-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) = 2.0226423756434737243133274715178 absolute error = 1.072368504986882e-16 relative error = 5.3018196291162143511235019598617e-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) = 2.0228581330797793954052579491574 absolute error = 1.083471933630628e-16 relative error = 5.3561439426355316509366730281377e-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) = 2.0230749372936466686090290390018 absolute error = 1.094610340967426e-16 relative error = 5.4106267681400513868862375630432e-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) = 2.0232927887390657741454628554322 absolute error = 1.105783963219263e-16 relative error = 5.4652691363981856090791671901984e-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) = 2.0235116878724181816884614307145 absolute error = 1.116993037756638e-16 relative error = 5.5200720828604581058047773883133e-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) = 2.0237316351524805113419828501225 absolute error = 1.128237803107454e-16 relative error = 5.5750366476948689840517823633261e-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) = 2.0239526310404284676614742279643 absolute error = 1.139518498965971e-16 relative error = 5.6301638758224928750247509210803e-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) = 2.0241746759998407967930868715376 absolute error = 1.150835366201815e-16 relative error = 5.6854548169532854075395350346903e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=2.81 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) = 2.0243977704967032668044915982267 absolute error = 1.162188646869053e-16 relative error = 5.7409105256221467062242872960504e-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) = 2.0246219149994126712816072034288 absolute error = 1.173578584215320e-16 relative error = 5.7965320612251720835567618129247e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0248471099787808562660525423946 absolute error = 1.185005422691018e-16 relative error = 5.8523204880561880660295093376910e-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) = 2.02507335590803877060863260615 absolute error = 1.196469407958562e-16 relative error = 5.9082768753434495890668485264993e-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) = 2.0253006532628405398146713593181 absolute error = 1.207970786901700e-16 relative error = 5.9644022972866310535829810817207e-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) = 2.0255290025212675634575089848958 absolute error = 1.219509807634894e-16 relative error = 6.0206978330940463346963066538975e-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) = 2.0257584041638326362369885669934 absolute error = 1.231086719512756e-16 relative error = 6.0771645670200674415125093264712e-15 % 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) = 2.0259888586734840927602671564943 absolute error = 1.242701773139559e-16 relative error = 6.1338035884028398824213582021172e-15 % 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) = 2.0262203665356099761227986259235 absolute error = 1.254355220378804e-16 relative error = 6.1906159917022002201226112139315e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.2MB, time=3.03 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) = 2.0264529282380422303678507480646 absolute error = 1.266047314362855e-16 relative error = 6.2476028765378543585851372817884e-15 % 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) = 2.026686544271060916903436547692 absolute error = 1.277778309502637e-16 relative error = 6.3047653477277911653185238453702e-15 % 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) = 2.0269212151273984549560601969822 absolute error = 1.289548461497406e-16 relative error = 6.3621045153269751211827826921630e-15 % 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) = 2.0271569413022438861412005726642 absolute error = 1.301358027344579e-16 relative error = 6.4196214946662580513637124072658e-15 % 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) = 2.0273937232932471632309810868278 absolute error = 1.313207265349635e-16 relative error = 6.4773174063915634880532013616393e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0276315616005234632000025637294 absolute error = 1.325096435136081e-16 relative error = 6.5351933765033133190792035801377e-15 % 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) = 2.0278704567266575246308467822565 absolute error = 1.337025797655485e-16 relative error = 6.5932505363961058504054702352012e-15 % 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) = 2.0281104091767080095612918584126 absolute error = 1.348995615197589e-16 relative error = 6.6514900228987086347131238131769e-15 % 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) = 2.0283514194582118898558169248782 absolute error = 1.361006151400475e-16 relative error = 6.7099129783142321486757351907494e-15 % 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) = 2.0285934880811888581845125961562 absolute error = 1.373057671260817e-16 relative error = 6.7685205504606462949794295820565e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.2MB, time=3.26 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) = 2.0288366155581457636930555089158 absolute error = 1.385150441144185e-16 relative error = 6.8273138927114713074448497350903e-15 % 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) = 2.0290808024040810724479498189623 absolute error = 1.397284728795447e-16 relative error = 6.8862941640368690606808526782994e-15 % 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) = 2.0293260491364893527417859399637 absolute error = 1.409460803349212e-16 relative error = 6.9454625290448530057054720070105e-15 % 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) = 2.0295723562753657853438170460073 absolute error = 1.421678935340374e-16 relative error = 7.0048201580229116955189484012238e-15 % 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) = 2.0298197243432106987817069517163 absolute error = 1.433939396714710e-16 relative error = 7.0643682269798134335966090965187e-15 % 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) = 2.0300681538650341297408589516714 absolute error = 1.446242460839559e-16 relative error = 7.1241079176877243182691183241226e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.030317645368360408668294067037 absolute error = 1.458588402514577e-16 relative error = 7.1840404177246142111389780774588e-15 % 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) = 2.0305681993832327706686089335256 absolute error = 1.470977497982566e-16 relative error = 7.2441669205169399510846282699130e-15 % 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) = 2.0308198164422179917801082932372 absolute error = 1.483410024940375e-16 relative error = 7.3044886253825951404138900778138e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.2MB, time=3.49 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) = 2.0310724970804110507197747457312 absolute error = 1.495886262549887e-16 relative error = 7.3650067375741946110329703996953e-15 % 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) = 2.0313262418354398161863090933238 absolute error = 1.508406491449070e-16 relative error = 7.4257224683225843810259881083393e-15 % 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) = 2.0315810512474697598110483046194 absolute error = 1.520970993763119e-16 relative error = 7.4866370348807092067533509954180e-15 % 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) = 2.0318369258592086948471448413895 absolute error = 1.533580053115671e-16 relative error = 7.5477516605677482232986557811168e-15 % 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) = 2.0320938662159115406879708699942 absolute error = 1.546233954640094e-16 relative error = 7.6090675748135227495750902403380e-15 % 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) = 2.0323518728653851133062937326302 absolute error = 1.558932984990865e-16 relative error = 7.6705860132032492105930902932200e-15 % 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) = 2.0326109463579929417063550089935 absolute error = 1.571677432355026e-16 relative error = 7.7323082175225821352525083746716e-15 % 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) = 2.0328710872466601104815745788286 absolute error = 1.584467586463720e-16 relative error = 7.7942354358029561867917796653793e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0331322960868781285711933238303 absolute error = 1.597303738603806e-16 relative error = 7.8563689223672214125118585750443e-15 % 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) = 2.0333945734367098243097635071733 absolute error = 1.610186181629566e-16 relative error = 7.9187099378756347498769905893002e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.2MB, time=3.70 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) = 2.0336579198567942668639944644301 absolute error = 1.623115209974485e-16 relative error = 7.9812597493721134030290279560282e-15 % 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) = 2.0339223359103517141520630548455 absolute error = 1.636091119663125e-16 relative error = 8.0440196303308524594821228688755e-15 % 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) = 2.0341878221631885873411033810683 absolute error = 1.649114208323077e-16 relative error = 8.1069908607032271137006079575290e-15 % 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) = 2.0344543791837024720191986128905 absolute error = 1.662184775196999e-16 relative error = 8.1701747269650179085494004665020e-15 % 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) = 2.0347220075428871461388093708596 absolute error = 1.675303121154752e-16 relative error = 8.2335725221640170181185996770653e-15 % 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) = 2.0349907078143376348291880635532 absolute error = 1.688469548705603e-16 relative error = 8.2971855459678622245974310745988e-15 % 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) = 2.0352604805742552921759468527453 absolute error = 1.701684362010535e-16 relative error = 8.3610151047122942469441562684300e-15 % 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) = 2.0355313264014529100665685687435 absolute error = 1.714947866894636e-16 relative error = 8.4250625114496988007248501521348e-15 % 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) = 2.0358032458773598542012749391057 absolute error = 1.728260370859581e-16 relative error = 8.4893290859980012154952894114490e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.2MB, time=3.92 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) = 2.0360762395860272273692949532164 absolute error = 1.741622183096202e-16 relative error = 8.5538161549898880407376480008970e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0363503081141330600912080884456 absolute error = 1.755033614497153e-16 relative error = 8.6185250519223890209618476971214e-15 % 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) = 2.0366254520509875287286724966636 absolute error = 1.768494977669662e-16 relative error = 8.6834571172067791267283316604779e-15 % 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) = 2.0369016719885382011634871187457 absolute error = 1.782006586948382e-16 relative error = 8.7486136982188585533823791065612e-15 % 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) = 2.0371789685213753101485790855814 absolute error = 1.795568758408332e-16 relative error = 8.8139961493495654460330658486175e-15 % 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) = 2.037457342246737054434153703393 absolute error = 1.809181809877930e-16 relative error = 8.8796058320559301402759490517266e-15 % 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) = 2.0377367937645149277728938354501 absolute error = 1.822846060952128e-16 relative error = 8.9454441149124189510612770468863e-15 % 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) = 2.0380173236772590759087486083271 absolute error = 1.836561833005638e-16 relative error = 9.0115123736626124410488996222742e-15 % 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) = 2.0382989325901836816545081156558 absolute error = 1.850329449206257e-16 relative error = 9.0778119912712563680617061752981e-15 % 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) = 2.0385816211111723781640211930544 absolute error = 1.864149234528291e-16 relative error = 9.1443443579766842191182670306450e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.2MB, time=4.15 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) = 2.0388653898507836905055774219368 absolute error = 1.878021515766074e-16 relative error = 9.2111108713435906136168634924015e-15 % 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) = 2.0391502394222565056436423147951 absolute error = 1.891946621547590e-16 relative error = 9.2781129363161937220622284892856e-15 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0394361704415155709368061680803 absolute error = 1.905924882348195e-16 relative error = 9.3453519652717708603753531600017e-15 % 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) = 2.0397231835271770212604823689608 absolute error = 1.919956630504440e-16 relative error = 9.4128293780745710404841275229678e-15 % 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) = 2.0400112793005539348635700372058 absolute error = 1.934042200227996e-16 relative error = 9.4805466021301082461564508730423e-15 % 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) = 2.0403004583856619180689788016094 absolute error = 1.948181927619682e-16 relative error = 9.5485050724398391912207177635500e-15 % 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) = 2.0405907214092247189286002803578 absolute error = 1.962376150683600e-16 relative error = 9.6167062316562440070465509500371e-15 % 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) = 2.0408820690006798699440014853494 absolute error = 1.976625209341371e-16 relative error = 9.6851515301382792789694631121618e-15 % 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) = 2.0411745017921843599648099307522 absolute error = 1.990929445446476e-16 relative error = 9.7538424260072218697959666489033e-15 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.298 Order of pole = 2.31 memory used=76.2MB, alloc=4.2MB, time=4.37 x[1] = 0.286 y[1] (analytic) = 2.0414680204186201348485384453887 y[1] (numeric) = 2.04146802041862033537745872526 absolute error = 2.005289202798713e-16 relative error = 9.8227803852029562288018403780080e-15 % 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) = 2.0417626255176008306976623950586 absolute error = 2.019704827158751e-16 relative error = 9.8919668815406108840718645711757e-15 % 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) = 2.0420583177294755286807006501196 absolute error = 2.034176666262797e-16 relative error = 9.9614033967676213122892158202731e-15 % 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) = 2.0423550976973365500642978000077 absolute error = 2.048705069837375e-16 relative error = 1.0031091420621213045813067183137e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.042652966067024273059600077044 absolute error = 2.063290389614215e-16 relative error = 1.0101032450886293979984965168837e-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) = 2.0429519234871331827064717647743 absolute error = 2.077932979345247e-16 relative error = 1.0171227993453730163491827149053e-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) = 2.0432519706090177502100537888207 absolute error = 2.092633194817723e-16 relative error = 1.0241679562379116413016572092805e-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) = 2.0435531080867983423762553361677 absolute error = 2.107391393869431e-16 relative error = 1.0312388679941864241418726903277e-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) = 2.0438553365773671612645801587874 absolute error = 2.122207936404045e-16 relative error = 1.0383356876704821206222648802877e-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) = 2.0441586567403942141774245195193 absolute error = 2.137083184406581e-16 relative error = 1.0454585691574273516941851128900e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.2MB, time=4.59 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) = 2.0444630692383333141057232838068 absolute error = 2.152017501958963e-16 relative error = 1.0526076671860350208896193702144e-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) = 2.0447685747364281107515644819963 absolute error = 2.167011255255724e-16 relative error = 1.0597831373337949862403872350263e-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) = 2.0450751739027181522491407954218 absolute error = 2.182064812619806e-16 relative error = 1.0669851360308012415287626470006e-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) = 2.0453828674080449777061588876579 absolute error = 2.197178544518500e-16 relative error = 1.0742138205659335277689513213821e-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) = 2.045691655926058240688584342603 absolute error = 2.212352823579489e-16 relative error = 1.0814693490930751420987808570805e-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) = 2.0460015401332218637723612161735 absolute error = 2.227588024607024e-16 relative error = 1.0887518806373814790994193449596e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0463125207088202242865108913221 absolute error = 2.242884524598221e-16 relative error = 1.0960615751015932963839837711032e-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) = 2.0466245983349643713727850800576 absolute error = 2.258242702759480e-16 relative error = 1.1033985932723950545448682109549e-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) = 2.0469377736965982744878224746149 absolute error = 2.273662940523032e-16 relative error = 1.1107630968268211228792323536181e-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) = 2.0472520474815051034745377466335 absolute error = 2.289145621563611e-16 relative error = 1.1181552483387082418240668797793e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.2MB, time=4.82 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) = 2.0475674203803135403302553621333 absolute error = 2.304691131815250e-16 relative error = 1.1255752112851936108157423130322e-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) = 2.0478838930865041227998890554794 absolute error = 2.320299859488214e-16 relative error = 1.1330231500532648064477065760587e-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) = 2.0482014662964156199232608219076 absolute error = 2.335972195086062e-16 relative error = 1.1404992299463574742656188603766e-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) = 2.0485201407092514396664509803126 absolute error = 2.351708531422824e-16 relative error = 1.1480036171909938126075657863539e-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) = 2.0488399170270860687678732609268 absolute error = 2.367509263640336e-16 relative error = 1.1555364789434826952572900953766e-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) = 2.0491607959548715449305760215363 absolute error = 2.383374789225687e-16 relative error = 1.1630979832966588202726780975436e-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) = 2.0494827782004439614930826265866 absolute error = 2.399305508028812e-16 relative error = 1.1706882992866773338171799585110e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0498058644745300047119007717656 absolute error = 2.415301822280217e-16 relative error = 1.1783075968998569393730112830014e-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) = 2.0501300554907535237896521385541 absolute error = 2.431364136608839e-16 relative error = 1.1859560470795728026069805134113e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.2MB, time=5.04 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) = 2.0504553519656421337836002552104 absolute error = 2.447492858060050e-16 relative error = 1.1936338217332034856711694596316e-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) = 2.0507817546186338515301858593968 absolute error = 2.463688396113797e-16 relative error = 1.2013410937391278487801918152280e-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) = 2.0511092641720837647220154401372 absolute error = 2.479951162702880e-16 relative error = 1.2090780369537727364112470981014e-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) = 2.0514378813512707342745900202784 absolute error = 2.496281572231378e-16 relative error = 1.2168448262187161630923628629403e-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) = 2.0517676068844041301209076626592 absolute error = 2.512680041593212e-16 relative error = 1.2246416373678404715524644225371e-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) = 2.0520984415026306005729246816198 absolute error = 2.529146990190860e-16 relative error = 1.2324686472345426119655819984531e-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) = 2.0524303859400408753897171544378 absolute error = 2.545682839954208e-16 relative error = 1.2403260336589935766801727005041e-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) = 2.0527634409336766026930460931924 absolute error = 2.562288015359559e-16 relative error = 1.2482139754954575456360383711832e-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) = 2.0530976072235372198718965951696 absolute error = 2.578962943448782e-16 relative error = 1.2561326526196618001294306071397e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0534328855525868586184334782566 absolute error = 2.595708053848612e-16 relative error = 1.2640822459362225957541414155527e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.2MB, time=5.27 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) = 2.0537692766667612842386933661785 absolute error = 2.612523778790109e-16 relative error = 1.2720629373861307167424224817761e-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) = 2.0541067813149748693822159565485 absolute error = 2.629410553128258e-16 relative error = 1.2800749099542877703113643828854e-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) = 2.0544454002491276023357053224902 absolute error = 2.646368814361734e-16 relative error = 1.2881183476771047336678769326610e-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) = 2.0547851342241121300267056063226 absolute error = 2.663399002652810e-16 relative error = 1.2961934356501518632448122797582e-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) = 2.0551259839978208358841744020562 absolute error = 2.680501560847432e-16 relative error = 1.3043003600358714719840570454886e-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) = 2.0554679503311529527037415331392 absolute error = 2.697676934495449e-16 relative error = 1.3124393080713475498080340840989e-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) = 2.0558110339880217106663508542467 absolute error = 2.714925571871003e-16 relative error = 1.3206104680761344784277360743921e-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) = 2.0561552357353615206598981824676 absolute error = 2.732247923993075e-16 relative error = 1.3288140294601427103274719677346e-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) = 2.0565005563431351930543995359015 absolute error = 2.749644444646201e-16 relative error = 1.3370501827315880361309452904996e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.2MB, time=5.49 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) = 2.0568469965843411920821505686339 absolute error = 2.767115590401346e-16 relative error = 1.3453191195049984137190975633645e-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) = 2.0571945572350209259752704828582 absolute error = 2.784661820636947e-16 relative error = 1.3536210325092835195838734479669e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.057543239074266073013961814441 absolute error = 2.802283597560121e-16 relative error = 1.3619561155958648844395313407701e-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) = 2.0578930428842259436397613706951 absolute error = 2.819981386228044e-16 relative error = 1.3703245637468693360581158972352e-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) = 2.0582439694501148787890072921004 absolute error = 2.837755654569491e-16 relative error = 1.3787265730833806936918582475943e-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) = 2.0585960195602196846027027571045 absolute error = 2.855606873406562e-16 relative error = 1.3871623408737616659220722515226e-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) = 2.0589491940059071036699182951918 absolute error = 2.873535516476571e-16 relative error = 1.3956320655420345732647601326595e-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) = 2.0593034935816313229628420627528 absolute error = 2.891542060454108e-16 relative error = 1.4041359466763255559275550408317e-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) = 2.0596589190849415186225608138664 absolute error = 2.909626984973284e-16 relative error = 1.4126741850373769194158160045096e-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) = 2.0600154713164894377556337092579 absolute error = 2.927790772650152e-16 relative error = 1.4212469825671240105394432252184e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.2MB, time=5.72 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) = 2.0603731510800370174025065970954 absolute error = 2.946033909105302e-16 relative error = 1.4298545423973354467125300134405e-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) = 2.0607319591824640408398060149857 absolute error = 2.964356882986646e-16 relative error = 1.4384970688583242564744259397377e-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) = 2.0610918964337758313795499499471 absolute error = 2.982760185992376e-16 relative error = 1.4471747674877214663207984354718e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0614529636471109838293163990601 absolute error = 3.001244312894112e-16 relative error = 1.4558878450393201725451999546795e-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) = 2.0618151616387491337784210450896 absolute error = 3.019809761560237e-16 relative error = 1.4646365094919884239584874657429e-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) = 2.0621784912281187648761719461802 absolute error = 3.038457032979418e-16 relative error = 1.4734209700586502120878732842129e-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) = 2.0625429532378050542692920846714 absolute error = 3.057186631284312e-16 relative error = 1.4822414371953338649992423929894e-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) = 2.0629085484935577563666299754751 absolute error = 3.075999063775470e-16 relative error = 1.4910981226102939269722838500944e-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) = 2.0632752778242991251003143479999 absolute error = 3.094894840945433e-16 relative error = 1.4999912392732033875092455525769e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.2MB, time=5.94 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) = 2.0636431420621318748535512363887 absolute error = 3.113874476503014e-16 relative error = 1.5089210014244131260920607833618e-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) = 2.0640121420423471802263106903468 absolute error = 3.132938487397793e-16 relative error = 1.5178876245842914303666427994934e-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) = 2.0643822786034327148112058029613 absolute error = 3.152087393844791e-16 relative error = 1.5268913255626268767472694273436e-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) = 2.0647535525870807291529288929441 absolute error = 3.171321719349360e-16 relative error = 1.5359323224681122714878964441524e-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) = 2.0651259648381961680656785273645 absolute error = 3.190641990732263e-16 relative error = 1.5450108347178968167179307371024e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.065499516204904827484086678285 absolute error = 3.210048738154969e-16 relative error = 1.5541270830472183741931368507560e-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) = 2.0658742075385615510242377242948 absolute error = 3.229542495145143e-16 relative error = 1.5632812895191058982507329107378e-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) = 2.0662500396937584664324602876976 absolute error = 3.249123798622348e-16 relative error = 1.5724736775341600290634791344337e-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) = 2.0666270135283332621006690924108 absolute error = 3.268793188923960e-16 relative error = 1.5817044718404120820130882668833e-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) = 2.0670051299033775038281371892648 absolute error = 3.288551209831289e-16 relative error = 1.5909738985432577966661570233929e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.2MB, time=6.16 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) = 2.0673843896832449920106890775774 absolute error = 3.308398408595914e-16 relative error = 1.6002821851154694680501606795506e-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) = 2.0677647937355601594394225082654 absolute error = 3.328335335966237e-16 relative error = 1.6096295604072886251367282987012e-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) = 2.0681463429312265098921911384433 absolute error = 3.348362546214249e-16 relative error = 1.6190162546565956142685527605286e-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) = 2.068529038144435097702211774976 absolute error = 3.368480597162520e-16 relative error = 1.6284424994991616342105713072908e-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) = 2.0689128802526730484892987497806 absolute error = 3.388690050211405e-16 relative error = 1.6379085279789790926940165163470e-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) = 2.0692978701367321212403740682437 absolute error = 3.408991470366483e-16 relative error = 1.6474145745586782401030098313974e-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) = 2.069684008680717311927055419814 absolute error = 3.429385426266205e-16 relative error = 1.6569608751300182125912915560649e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0700712967720554988492849929971 absolute error = 3.449872490209788e-16 relative error = 1.6665476670244701004332005595849e-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) = 2.070459735301504129895130352417 absolute error = 3.470453238185326e-16 relative error = 1.6761751890238777523438828631919e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.202 Order of pole = 2.093 memory used=110.6MB, alloc=4.2MB, time=6.38 x[1] = 0.372 y[1] (analytic) = 2.0708493251631596027952394807824 y[1] (numeric) = 2.0708493251631599519080644705961 absolute error = 3.491128249898137e-16 relative error = 1.6858436813712052249733861672331e-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) = 2.0712400672544677823542154193853 absolute error = 3.511898108799342e-16 relative error = 1.6955533857813686671589993503636e-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) = 2.0716319624762293234832672737664 absolute error = 3.532763402114684e-16 relative error = 1.7053045454521562225395554106377e-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) = 2.0720250117326120191778925227528 absolute error = 3.553724720873579e-16 relative error = 1.7150974050752318049501938606303e-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) = 2.0724192159311579546878027775151 absolute error = 3.574782659938416e-16 relative error = 1.7249322108472306686261633648198e-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) = 2.0728145759827927994457188753312 absolute error = 3.595937818034089e-16 relative error = 1.7348092104809382785017449171216e-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) = 2.0732110928018347931637836596713 absolute error = 3.617190797777784e-16 relative error = 1.7447286532165632906631260918994e-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) = 2.0736087673060037754101708323442 absolute error = 3.638542205709006e-16 relative error = 1.7546907898330971090484723826288e-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) = 2.0740076004164302588668813843226 absolute error = 3.659992652319859e-16 relative error = 1.7646958726597659944950873136075e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0744075930576645464709652793045 absolute error = 3.681542752085575e-16 relative error = 1.7747441555875734959989102851051e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.2MB, time=6.61 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) = 2.0748087461576858926426603504489 absolute error = 3.703193123495305e-16 relative error = 1.7848358940809391690217924686558e-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) = 2.075211060647911708805202838747 absolute error = 3.724944389083154e-16 relative error = 1.7949713451894245962137414526659e-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) = 2.0756145374632068134023347143895 absolute error = 3.746797175459486e-16 relative error = 1.8051507675595589363524186070866e-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) = 2.0760191775418927266208119440144 absolute error = 3.768752113342482e-16 relative error = 1.8153744214467554935761354055992e-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) = 2.0764249818257570100265052611587 absolute error = 3.790809837589971e-16 relative error = 1.8256425687273286292335323325743e-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) = 2.0768319512600626513239808294134 absolute error = 3.812970987231518e-16 relative error = 1.8359554729106029879480560484555e-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) = 2.0772400867935574944507525230563 absolute error = 3.835236205500786e-16 relative error = 1.8463133991511229064080281130517e-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) = 2.0776493893784837152187104542294 absolute error = 3.857606139868168e-16 relative error = 1.8567166142609597513636829301374e-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) = 2.0780598599705873427165519154913 absolute error = 3.880081442073695e-16 relative error = 1.8671653867221197468712721033166e-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) = 2.0784714995291278266883711488396 absolute error = 3.902662768160216e-16 relative error = 1.8776599866990500333849359715731e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.2MB, time=6.84 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) = 2.0788843090168876511049033646404 absolute error = 3.925350778506859e-16 relative error = 1.8882006860512469560339207240865e-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) = 2.0792982894001819941452662844743 absolute error = 3.948146137862778e-16 relative error = 1.8987877583459686471543312830264e-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) = 2.0797134416488684348083992394359 absolute error = 3.971049515381175e-16 relative error = 1.9094214788710462692326894861796e-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) = 2.0801297667363567063747655892039 absolute error = 3.994061584653618e-16 relative error = 1.9201021246478036748077413640391e-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) = 2.0805472656396184969402590071224 absolute error = 4.017183023744646e-16 relative error = 1.9308299744440808027250550511154e-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) = 2.0809659393391972972456380730712 absolute error = 4.040414515226661e-16 relative error = 1.9416053087873604602187446201988e-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) = 2.0813857888192182960262067001258 absolute error = 4.063756746215124e-16 relative error = 1.9524284099780063061928016900273e-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) = 2.0818068150673983231078602645874 absolute error = 4.087210408404042e-16 relative error = 1.9632995621026054255652576169707e-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) = 2.0822290190750558404770289841703 absolute error = 4.110776198101760e-16 relative error = 1.9742190510474218596965685898520e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.2MB, time=7.06 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) = 2.0826524018371209815534711688662 absolute error = 4.134454816267052e-16 relative error = 1.9851871645119578420917014828518e-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) = 2.0830769643521456388962995267571 absolute error = 4.158246968545528e-16 relative error = 1.9962041920226305327735948193106e-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) = 2.083502707622313600575063816958 absolute error = 4.182153365306339e-16 relative error = 2.0072704249465552309430942781148e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0839296326534507354391628786919 absolute error = 4.206174721679197e-16 relative error = 2.0183861565054428529762256720297e-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) = 2.0843577404550352275203185046293 absolute error = 4.230311757591719e-16 relative error = 2.0295516817896156094952545958928e-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) = 2.0847870320402078598043128440928 absolute error = 4.254565197807078e-16 relative error = 2.0407672977721323349327625383828e-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) = 2.0852175084257823476096700942255 absolute error = 4.278935771961986e-16 relative error = 2.0520333033230350762956295748147e-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) = 2.0856491706322557218124522420776 absolute error = 4.303424214604987e-16 relative error = 2.0633499992237059911836121420362e-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) = 2.0860820196838187621578376357811 absolute error = 4.328031265235096e-16 relative error = 2.0747176881813514239322724354975e-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) = 2.0865160566083664809006602672182 absolute error = 4.352757668340751e-16 relative error = 2.0861366748435969286844236170945e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.2MB, time=7.28 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) = 2.086951282437508657018606921178 absolute error = 4.377604173439110e-16 relative error = 2.0976072658132081783934155919421e-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) = 2.0873876982065804212432988669579 absolute error = 4.402571535115685e-16 relative error = 2.1091297696629335085243556239456e-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) = 2.0878253049546528921560246183902 absolute error = 4.427660513064304e-16 relative error = 2.1207044969504633695894266047141e-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) = 2.0882641037245438635964405487654 absolute error = 4.452871872127434e-16 relative error = 2.1323317602335220802629564347924e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0887040955628285436341169001548 absolute error = 4.478206382336839e-16 relative error = 2.1440118740850789970358186136200e-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) = 2.0891452815198503453543780550186 absolute error = 4.503664818954587e-16 relative error = 2.1557451551086853817975735054069e-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) = 2.0895876626497317297114679252126 absolute error = 4.529247962514423e-16 relative error = 2.1675319219539446710577845815430e-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) = 2.090031240010385100703664043814 absolute error = 4.554956598863482e-16 relative error = 2.1793724953321032607435539627810e-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) = 2.0904760146635237531265675035194 absolute error = 4.580791519204373e-16 relative error = 2.1912671980317762059874264241222e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.2MB, time=7.50 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) = 2.0909219876746728731624103574133 absolute error = 4.606753520137628e-16 relative error = 2.2032163549348045124292781317970e-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) = 2.0913691601131805920648475700833 absolute error = 4.632843403704507e-16 relative error = 2.2152202930322392637545722748048e-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) = 2.0918175330522290932003371665435 absolute error = 4.659061977430190e-16 relative error = 2.2272793414404669574953646528460e-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) = 2.0922671075688457727088599611395 absolute error = 4.685410054367326e-16 relative error = 2.2393938314174612385261367703230e-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) = 2.0927178847439144540483892472381 absolute error = 4.711888453139974e-16 relative error = 2.2515640963791773021417999082452e-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) = 2.0931698656621866566891911804999 absolute error = 4.738497997987916e-16 relative error = 2.2637904719160789316321001285446e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.0936230514122929192257183841293 absolute error = 4.765239518811361e-16 relative error = 2.2760732958098067774389986876510e-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) = 2.0940774430867541771755526347039 absolute error = 4.792113851216038e-16 relative error = 2.2884129080499864387096257132747e-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) = 2.0945330417819931957365574438081 absolute error = 4.819121836558675e-16 relative error = 2.3008096508511744299275440177228e-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) = 2.0949898485983460577751180263418 absolute error = 4.846264321992881e-16 relative error = 2.3132638686699496620455855641337e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.2MB, time=7.73 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) = 2.0954478646400737073200746344444 absolute error = 4.873542160515429e-16 relative error = 2.3257759082221489837578845674428e-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) = 2.0959070910153735488386956307025 absolute error = 4.900956211012938e-16 relative error = 2.3383461185002453277918965798100e-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) = 2.0963675288363911025727890707315 absolute error = 4.928507338308969e-16 relative error = 2.3509748507908751156280083921735e-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) = 2.09682917921923171621481605922 absolute error = 4.956196413211526e-16 relative error = 2.3636624586925101131978520689449e-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) = 2.0972920432839723332056458318116 absolute error = 4.984024312560981e-16 relative error = 2.3764092981332822857449197249234e-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) = 2.0977561221546733179373814953317 absolute error = 5.011991919278413e-16 relative error = 2.3892157273889563572679053625843e-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) = 2.0982214169593903381464867292655 absolute error = 5.040100122414375e-16 relative error = 2.4020821071010562241283140742766e-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 y[1] (analytic) = 2.0986879288301857979492758915178 y[1] (numeric) = 2.0986879288301863047842576113267 absolute error = 5.068349817198089e-16 relative error = 2.4150088002951446872154742964196e-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) = 2.0991556589031433696535101795853 absolute error = 5.096741905087071e-16 relative error = 2.4279961723992569172497706246003e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.2MB, time=7.95 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) = 2.099624608318374981102193483961 absolute error = 5.125277293817195e-16 relative error = 2.4410445912624913974575755988324e-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) = 2.1000947782200379980664898128664 absolute error = 5.153956897453200e-16 relative error = 2.4541544271737596967441659837020e-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) = 2.1005661697563448627578286092038 absolute error = 5.182781636439637e-16 relative error = 2.4673260528806930879959121205400e-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) = 2.1010387840795758322901184175074 absolute error = 5.211752437652269e-16 relative error = 2.4805598436087116413295928759668e-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) = 2.1015126223460912695453921354087 absolute error = 5.240870234449929e-16 relative error = 2.4938561770802576015212418419269e-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) = 2.1019876857163439935779649833443 absolute error = 5.270135966726828e-16 relative error = 2.5072154335341886671987965152863e-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) = 2.1024639753548916898591220630152 absolute error = 5.299550580965334e-16 relative error = 2.5206379957453405868662653426816e-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) = 2.1029414924304093806662832549709 absolute error = 5.329115030289213e-16 relative error = 2.5341242490442542002501964159087e-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) = 2.1034202381157019559225376172156 absolute error = 5.358830274517346e-16 relative error = 2.5476745813370729929911115135743e-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) = 2.1039002135877167647943974992624 absolute error = 5.388697280217923e-16 relative error = 2.5612893831256110387819477177477e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.2MB, time=8.18 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) = 2.104381420027556268357594389899 absolute error = 5.418717020763115e-16 relative error = 2.5749690475275911993257814695741e-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) = 2.1048638586204907536427241833763 absolute error = 5.448890476384235e-16 relative error = 2.5887139702970581996504685743463e-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) = 2.1053475305559711093745491900605 absolute error = 5.479218634227391e-16 relative error = 2.6025245498449673839968336237929e-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) = 2.1058324370276416637207779470857 absolute error = 5.509702488409632e-16 relative error = 2.6164011872599490021923000382504e-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) = 2.1063185792333530843681718164909 absolute error = 5.540343040075601e-16 relative error = 2.6303442863292540444974334872889e-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) = 2.1068059583751753412458696080283 absolute error = 5.571141297454681e-16 relative error = 2.6443542535598743373939262651718e-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) = 2.1072945756594107322178781476274 absolute error = 5.602098275918671e-16 relative error = 2.6584314981998538237115780781243e-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) = 2.1077844322966069720687479477574 absolute error = 5.633214998039959e-16 relative error = 2.6725764322597747046671872960738e-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) = 2.1082755295015703451085390410776 absolute error = 5.664492493650227e-16 relative error = 2.6867894705344344012257107768030e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.2MB, time=8.40 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) = 2.1087678684933789217252827332775 absolute error = 5.695931799899682e-16 relative error = 2.7010710306247098155796730148642e-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) = 2.1092614504953958392152606354395 absolute error = 5.727533961316813e-16 relative error = 2.7154215329596082202721669708835e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1097562767352826472235529722357 absolute error = 5.759300029868687e-16 relative error = 2.7298414008185102611839699424870e-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) = 2.1102523484450127181294539525228 absolute error = 5.791231065021792e-16 relative error = 2.7443310603536081764807415458374e-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) = 2.1107496668608847227135130572445 absolute error = 5.823328133803420e-16 relative error = 2.7588909406125352167587066466462e-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) = 2.1112482332235361714451375709303 absolute error = 5.855592310863604e-16 relative error = 2.7735214735611922013342692561797e-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) = 2.1117480487779570217318836835558 absolute error = 5.888024678537622e-16 relative error = 2.7882230941067766562923197383209e-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) = 2.1122491147735033514737711462907 absolute error = 5.920626326909051e-16 relative error = 2.8029962401210057620350153474350e-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) = 2.112751432463911099268179906064 absolute error = 5.953398353873406e-16 relative error = 2.8178413524635489624358740642802e-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) = 2.1132550031073098716131264994056 absolute error = 5.986341865202339e-16 relative error = 2.8327588750056576606143271799280e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.2MB, time=8.63 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) = 2.1137598279662368174589733863664 absolute error = 6.019457974608430e-16 relative error = 2.8477492546540064116057426380678e-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) = 2.1142659083076505704608959823144 absolute error = 6.052747803810565e-16 relative error = 2.8628129413747424896999754627302e-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) = 2.1147732454029452592867200321036 absolute error = 6.086212482599894e-16 relative error = 2.8779503882177397634832683833714e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.103 Order of pole = 2.082 x[1] = 0.471 y[1] (analytic) = 2.1152818405279639743517314111258 y[1] (numeric) = 2.1152818405279645863370463017665 absolute error = 6.119853148906407e-16 relative error = 2.8931620513410740882313623625753e-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) = 2.115791694963015975236900472951 absolute error = 6.153670948866097e-16 relative error = 2.9084483900357047752958090049871e-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) = 2.1163028099928847874604837515112 absolute error = 6.187667036888749e-16 relative error = 2.9238098667503797992798852334828e-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) = 2.1168151869068486084529541819024 absolute error = 6.221842575726332e-16 relative error = 2.9392469471167530753252817406266e-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) = 2.1173288269986916036155401325202 absolute error = 6.256198736542022e-16 relative error = 2.9547600999747262431185865269734e-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) = 2.1178437315667189445226760243152 absolute error = 6.290736698979857e-16 relative error = 2.9703497973980146160860914416792e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.096 Order of pole = 2.082 memory used=152.5MB, alloc=4.2MB, time=8.86 x[1] = 0.477 y[1] (analytic) = 2.1183599019137706731964911341508 y[1] (numeric) = 2.1183599019137713057422562576528 absolute error = 6.325457651235020e-16 relative error = 2.9860165147199345892303713845236e-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) = 2.1188773393472394326325265934981 absolute error = 6.360362790124769e-16 relative error = 3.0017607305594206537741795120144e-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) = 2.119396045179078780491573108929 absolute error = 6.395453321160018e-16 relative error = 3.0175829268472730679787003235510e-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) = 2.1199160207258242254378274193683 absolute error = 6.430730458617566e-16 relative error = 3.0334835888526339239109137477442e-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) = 2.1204372673086048474024832877667 absolute error = 6.466195425612996e-16 relative error = 3.0494632052097011388449981484815e-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) = 2.1209597862531587856172141725937 absolute error = 6.501849454174237e-16 relative error = 3.0655222679446762026071841772575e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.121483578889848166983093851597 absolute error = 6.537693785315804e-16 relative error = 3.0816612725029518847853342917224e-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) = 2.1220086465536741077091531479324 absolute error = 6.573729669113715e-16 relative error = 3.0978807177765385477410174102516e-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) = 2.1225349905842917886115551319026 absolute error = 6.609958364781114e-16 relative error = 3.1141811061317418422858218936444e-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) = 2.1230626123260256044669391290178 absolute error = 6.646381140744563e-16 relative error = 3.1305629434370734445092185898816e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.2MB, time=9.08 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) = 2.1235915131278843878160705886824 absolute error = 6.682999274721062e-16 relative error = 3.1470267390914217291789629219581e-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) = 2.1241216943435767076165395142026 absolute error = 6.719814053795768e-16 relative error = 3.1635730060524677867812261571525e-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) = 2.1246531573315262431458748821522 absolute error = 6.756826774500432e-16 relative error = 3.1802022608653548061533649261011e-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) = 2.125185903454887233559086447018 absolute error = 6.794038742892564e-16 relative error = 3.1969150236916145876325686329983e-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) = 2.1257199340815600035073086965502 absolute error = 6.831451274635328e-16 relative error = 3.2137118183383511744668121644292e-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) = 2.1262552505842065652269046569243 absolute error = 6.869065695078179e-16 relative error = 3.2305931722876862870946441724306e-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) = 2.1267918543402662975110899087475 absolute error = 6.906883339338244e-16 relative error = 3.2475596167264665272323786379764e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1273297467319717019788597306949 absolute error = 6.944905552382466e-16 relative error = 3.2646116865762403036123843350971e-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) = 2.1278689291463642370587449042606 absolute error = 6.983133689110501e-16 relative error = 3.2817499205234987800110052266947e-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) = 2.1284094029753102301076845594239 absolute error = 7.021569114438391e-16 relative error = 3.2989748610501906557297153028756e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.2MB, time=9.30 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) = 2.1289511696155168680880876871968 absolute error = 7.060213203383018e-16 relative error = 3.3162870544645121073344349908335e-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) = 2.1294942304685482672289587628555 absolute error = 7.099067341147335e-16 relative error = 3.3336870509319689846772185065250e-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) = 2.1300385869408416220997874865781 absolute error = 7.138132923206410e-16 relative error = 3.3511754045067271324053507071261e-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) = 2.1305842404437234345287481312507 absolute error = 7.177411355394247e-16 relative error = 3.3687526731632328753537001536615e-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) = 2.1311311923934258227996205670241 absolute error = 7.216904053991446e-16 relative error = 3.3864194188281317210195160104807e-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) = 2.1316794442111029115647328871142 absolute error = 7.256612445813661e-16 relative error = 3.4041762074124649491223325128153e-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) = 2.1322289973228473029141348693259 absolute error = 7.296537968300895e-16 relative error = 3.4220236088441613123173782223505e-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) = 2.1327798531597066290441424544911 absolute error = 7.336682069607639e-16 relative error = 3.4399621971008260256913831074893e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.068 Order of pole = 2.082 x[1] = 0.505 y[1] (analytic) = 2.1333320131576994492667253204352 y[1] (numeric) = 2.1333320131577001869713461898187 absolute error = 7.377046208693835e-16 relative error = 3.4579925502428165546204967778272e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.2MB, time=9.53 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) = 2.133885478757835655741151357129 absolute error = 7.417631855416718e-16 relative error = 3.4761152504466298721398783305171e-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) = 2.134440251406125896582914469901 absolute error = 7.458440490623503e-16 relative error = 3.4943308840385841013585520194053e-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) = 2.1349963325536058364667601675682 absolute error = 7.499473606244953e-16 relative error = 3.5126400415288102733367767606085e-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) = 2.1355537236563494355202044508918 absolute error = 7.540732705389823e-16 relative error = 3.5310433176455506918340053273475e-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) = 2.1361124261754867387657748806523 absolute error = 7.582219302440198e-16 relative error = 3.5495413113697711632025268506891e-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) = 2.1366724415772210126439059972608 absolute error = 7.623934923147725e-16 relative error = 3.5681346259700859024981362557553e-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) = 2.1372337713328459667884990069753 absolute error = 7.665881104730763e-16 relative error = 3.5868238690380051510174798709177e-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) = 2.137796416918763061525668918812 absolute error = 7.708059395972440e-16 relative error = 3.6056096525234991395019452884743e-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) = 2.1383603798164989015693600044578 absolute error = 7.750471357319644e-16 relative error = 3.6244925927708898072549301184028e-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) = 2.138925661512722716390691892865 absolute error = 7.793118560982953e-16 relative error = 3.6434733105550713697838819601127e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.2MB, time=9.75 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) = 2.1394922634992639277411040050194 absolute error = 7.836002591037508e-16 relative error = 3.6625524311180603496575027899955e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.140060187273129804812595587804 absolute error = 7.879125043524844e-16 relative error = 3.6817305842058808157458840673859e-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) = 2.1406294343365232075216125260673 absolute error = 7.922487526555692e-16 relative error = 3.7010084041057896211779208336078e-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) = 2.1412000061968604184064106080504 absolute error = 7.966091660413751e-16 relative error = 3.7203865296838398733064808734144e-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) = 2.141771904366789063631028202315 absolute error = 8.009939077660457e-16 relative error = 3.7398656044227939374712420791063e-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) = 2.1423451303642061235923295873378 absolute error = 8.054031423240741e-16 relative error = 3.7594462764603809063512524264336e-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) = 2.1429196857122760336299336731155 absolute error = 8.098370354589801e-16 relative error = 3.7791291986279088683181470350887e-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) = 2.1434955719394488753422217846265 absolute error = 8.142957541740893e-16 relative error = 3.7989150284892329466844995150457e-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) = 2.1440727905794786590150227590615 absolute error = 8.187794667434146e-16 relative error = 3.8188044283800800706772339319380e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.2MB, time=9.97 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) = 2.1446513431714416976730040636946 absolute error = 8.232883427226425e-16 relative error = 3.8387980654477402871136490328670e-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) = 2.1452312312597550732672541925643 absolute error = 8.278225529602243e-16 relative error = 3.8588966116911236700063956505042e-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) = 2.1458124563941951955160244733532 absolute error = 8.323822696085735e-16 relative error = 3.8791007440011874703586757622949e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1463950201299164539191078387356 absolute error = 8.369676661353703e-16 relative error = 3.8994111442017362654213129061618e-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) = 2.1469789240274699634698683189274 absolute error = 8.415789173349754e-16 relative error = 3.9198284990906039062574685773432e-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) = 2.1475641696528224045924982263461 absolute error = 8.462161993399526e-16 relative error = 3.9403535004812134613623970572937e-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) = 2.1481507585773749578356704635314 absolute error = 8.508796896327032e-16 relative error = 3.9609868452445276457466180331876e-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) = 2.1487386923779823338573713283914 absolute error = 8.555695670572114e-16 relative error = 3.9817292353513845030534383636320e-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) = 2.1493279726369718992393448553104 absolute error = 8.602860118309039e-16 relative error = 4.0025813779152317202588714853868e-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) = 2.1499186009421628986732533578638 absolute error = 8.650292055566232e-16 relative error = 4.0235439852352557052227348721979e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.2MB, time=10.20 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) = 2.1505105788868857740643606723412 absolute error = 8.697993312347163e-16 relative error = 4.0446177748399117858105548208094e-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) = 2.1511039080700015811022748868361 absolute error = 8.745965732752420e-16 relative error = 4.0658034695308688382613948212685e-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) = 2.151698590095921503852046326546 absolute error = 8.794211175102937e-16 relative error = 4.0871017974273523335245559788337e-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) = 2.1522946265746264679227045027765 absolute error = 8.842731512064439e-16 relative error = 4.1085134920109130248421503882783e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1528920191216868527741348740012 absolute error = 8.891528630773078e-16 relative error = 4.1300392921706075537913470838412e-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) = 2.153490769358282303727042867709 absolute error = 8.940604432962294e-16 relative error = 4.1516799422486051333552863045096e-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) = 2.1540908789112216442446289296471 absolute error = 8.989960835090918e-16 relative error = 4.1734361920862265323607842238031e-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) = 2.1546923494129628890585046629269 absolute error = 9.039599768472498e-16 relative error = 4.1953087970704048529855752577749e-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) = 2.155295182501633358715316656321 absolute error = 9.089523179405907e-16 relative error = 4.2172985181805937953157844329828e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.2MB, time=10.42 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) = 2.1558993798210498961245116445057 absolute error = 9.139733029307209e-16 relative error = 4.2394061220361105352758898544345e-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) = 2.1565049430207391856916744611585 absolute error = 9.190231294842821e-16 relative error = 4.2616323809439291098535073218521e-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) = 2.1571118737559581756258991094705 absolute error = 9.241019968063965e-16 relative error = 4.2839780729469197587539230476988e-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) = 2.1577201736877146040137134571884 absolute error = 9.292101056542439e-16 relative error = 4.3064439818725458910053718438248e-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) = 2.1583298444827876292561698408387 absolute error = 9.343476583507725e-16 relative error = 4.3290308973820252104599562227497e-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) = 2.1589408878137485654698375150834 absolute error = 9.395148587985421e-16 relative error = 4.3517396150199471485127721183403e-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) = 2.1595533053589817234565886897166 absolute error = 9.447119124937046e-16 relative error = 4.3745709362643674677092493017957e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1601670988027053578512581428896 absolute error = 9.499390265401207e-16 relative error = 4.3975256685773730648339683819733e-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) = 2.1607822698349927210604773717971 absolute error = 9.551964096636160e-16 relative error = 4.4206046254561299057029241350532e-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) = 2.1613988201517932246102382311274 absolute error = 9.604842722263769e-16 relative error = 4.4438086264844140274137059145389e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.2MB, time=10.65 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) = 2.1620167514549537085240283077818 absolute error = 9.658028262414877e-16 relative error = 4.4671384973846301565955781842438e-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) = 2.1626360654522398193577011832881 absolute error = 9.711522853876118e-16 relative error = 4.4905950700703294050330543209122e-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) = 2.1632567638573574975215995414627 absolute error = 9.765328650238174e-16 relative error = 4.5141791826992259082105191097337e-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) = 2.1638788483899745745248380896465 absolute error = 9.819447822045489e-16 relative error = 4.5378916797267159565662653149116e-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) = 2.1645023207757424807810767816584 absolute error = 9.873882556947472e-16 relative error = 4.5617334119599123878722793103763e-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) = 2.1651271827463180646195731668839 absolute error = 9.928635059851187e-16 relative error = 4.5857052366121912628941934456457e-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) = 2.1657534360393855231497961530926 absolute error = 9.983707553075564e-16 relative error = 4.6098080173582644621572389744044e-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) = 2.1663810823986784456324123741686 absolute error = 1.0039102276507126e-15 relative error = 4.6340426243897737940442031639027e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1670101235740019700140210145707 absolute error = 1.0094821487757276e-15 relative error = 4.6584099344714248125652092967742e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.2MB, time=10.87 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) = 2.1676405613212550532876136797577 absolute error = 1.0150867462321131e-15 relative error = 4.6829108309976521910116740609137e-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) = 2.1682723974024528563453730389607 absolute error = 1.0207242493737945e-15 relative error = 4.7075462040498338682254098612172e-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) = 2.1689056335857492439950978296827 absolute error = 1.0263948893753128e-15 relative error = 4.7323169504540549926047812082202e-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) = 2.1695402716454594008162527315376 absolute error = 1.0320988992481870e-15 relative error = 4.7572239738394235938211445001377e-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) = 2.1701763133620825635363899231582 absolute error = 1.0378365138574405e-15 relative error = 4.7822681846969518735959731030592e-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) = 2.1708137605223248706134751658687 absolute error = 1.0436079699382926e-15 relative error = 4.8074505004390059036990658964860e-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) = 2.1714526149191223297144753509511 absolute error = 1.0494135061130159e-15 relative error = 4.8327718454593251160851476227172e-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) = 2.1720928783516639037854269463355 absolute error = 1.0552533629079631e-15 relative error = 4.8582331511936253819890034872376e-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) = 2.1727345526254147164131060295331 absolute error = 1.0611277827707633e-15 relative error = 4.8838353561807837803829785811890e-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) = 2.1733776395521393771833609462012 absolute error = 1.0670370100876923e-15 relative error = 4.9095794061246233900233044732463e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.3MB, time=11.10 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) = 2.1740221409499254277461484409558 absolute error = 1.0729812912012152e-15 relative error = 4.9354662539562878615609895366727e-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) = 2.1746680586432069093023337255616 absolute error = 1.0789608744277065e-15 relative error = 4.9614968598972272634048414340816e-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) = 2.1753153944627880522323747396221 absolute error = 1.0849760100753478e-15 relative error = 4.9876721915227931829807390792501e-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) = 2.1759641502458670885921111841873 absolute error = 1.0910269504622059e-15 relative error = 5.0139932238264534616707507953587e-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) = 2.1766143278360601882060201367576 absolute error = 1.0971139499344924e-15 relative error = 5.0404609392846290901110155903425e-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) = 2.1772659290834255190934825581655 absolute error = 1.1032372648850081e-15 relative error = 5.0670763279221658721157643409673e-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) = 2.1779189558444874329688291526617 absolute error = 1.1093971537717731e-15 relative error = 5.0938403873784423986529197665457e-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) = 2.1785734099822607765612002209135 absolute error = 1.1155938771368454e-15 relative error = 5.1207541229741245736789466782988e-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) = 2.1792292933662753295055627340386 absolute error = 1.1218276976253298e-15 relative error = 5.1478185477785723028746866421042e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.3MB, time=11.32 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) = 2.1798866078726003695615792416257 absolute error = 1.1280988800045789e-15 relative error = 5.1750346826779039251889401548323e-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) = 2.1805453553838693659224177982117 absolute error = 1.1344076911835890e-15 relative error = 5.2024035564437285218321091563678e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9893 Order of pole = 2.082 x[1] = 0.584 y[1] (analytic) = 2.1812055377893036606266300125238 y[1] (numeric) = 2.1812055377893048013810302451167 absolute error = 1.1407544002325929e-15 relative error = 5.2299262058025525271499910598006e-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) = 2.181867156984743124126908316114 absolute error = 1.1471392784028514e-15 relative error = 5.2576036755058661153268324554186e-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) = 2.1825302148726598299518535483894 absolute error = 1.1535625991466461e-15 relative error = 5.2854370184009184705763194652083e-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) = 2.183194713362194675648868280971 absolute error = 1.1600246381374755e-15 relative error = 5.3134272955021882593888075529688e-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) = 2.1838606543691770243938915217642 absolute error = 1.1665256732904573e-15 relative error = 5.3415755760635597102244479369906e-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) = 2.1845280398161513239057655761581 absolute error = 1.1730659847829382e-15 relative error = 5.3698829376512073372586278491510e-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) = 2.1851968716324027181855274737579 absolute error = 1.1796458550753138e-15 relative error = 5.3983504662171982670699540966480e-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) = 2.1858671517539827936418738282863 absolute error = 1.1862655689320628e-15 relative error = 5.4269792561738284053806128686214e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.3MB, time=11.54 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) = 2.1865388821237354604154492465503 absolute error = 1.1929254134429943e-15 relative error = 5.4557704104686839246734444446137e-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) = 2.1872120646913229697204571974263 absolute error = 1.1996256780447143e-15 relative error = 5.4847250406604529300947821212974e-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) = 2.1878867014132520680279887973119 absolute error = 1.2063666545423109e-15 relative error = 5.5138442669954819134840150598995e-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) = 2.1885627942529002889214097051564 absolute error = 1.2131486371312635e-15 relative error = 5.5431292184850980993858874655581e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1892403451805423834601386932285 absolute error = 1.2199719224195752e-15 relative error = 5.5725810329836908503861682428863e-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) = 2.1899193561733768898941939190223 absolute error = 1.2268368094501347e-15 relative error = 5.6022008572675777161314729364243e-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) = 2.1905998292155528435779749235437 absolute error = 1.2337435997233067e-15 relative error = 5.6319898471146473014189124682400e-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) = 2.1912817662981966279378903807568 absolute error = 1.2406925972197561e-15 relative error = 5.6619491673847998767441596162780e-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) = 2.1919651694194389673546340860137 absolute error = 1.2476841084235072e-15 relative error = 5.6920799921011878760975211610744e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.3MB, time=11.77 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) = 2.1926500405844420628271550664252 absolute error = 1.2547184423452410e-15 relative error = 5.7223835045322670645166860701149e-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) = 2.1933363818054268712916624967858 absolute error = 1.2617959105458334e-15 relative error = 5.7528608972746677407473652265353e-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) = 2.1940241951017005294753527891441 absolute error = 1.2689168271601365e-15 relative error = 5.7835133723368925594747113132194e-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) = 2.1947134824996839231709452756665 absolute error = 1.2760815089210071e-15 relative error = 5.8143421412238561752224212021148e-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) = 2.1954042460329394028245648113223 absolute error = 1.2832902751835833e-15 relative error = 5.8453484250222672726201172469240e-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) = 2.1960964877421986463360148784329 absolute error = 1.2905434479498135e-15 relative error = 5.8765334544868690047011066829904e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.1967902096753906699770438776924 absolute error = 1.2978413518932409e-15 relative error = 5.9078984701275483341427892823215e-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) = 2.1974854138876699883398207434715 absolute error = 1.3051843143840440e-15 relative error = 5.9394447222973128899142422233615e-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) = 2.1981821024414449242345043338862 absolute error = 1.3125726655143399e-15 relative error = 5.9711734712811625908590372045865e-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) = 2.1988802774064060694615147323559 absolute error = 1.3200067381237500e-15 relative error = 6.0030859873858504499838092800401e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.3MB, time=11.98 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) = 2.1995799408595548973908941766598 absolute error = 1.3274868678252324e-15 relative error = 6.0351835510305483299168629393666e-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) = 2.2002810948852325282879813286977 absolute error = 1.3350133930311851e-15 relative error = 6.0674674528384324455632974919686e-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) = 2.2009837415751486483315155436289 absolute error = 1.3425866549798208e-15 relative error = 6.0999389937291883532131196332849e-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) = 2.2016878830284105832772382266838 absolute error = 1.3502069977618186e-15 relative error = 6.1325994850124555787927931758075e-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) = 2.2023935213515525277270668212136 absolute error = 1.3578747683472552e-15 relative error = 6.1654502484822197006816981779809e-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) = 2.2031006586585649309709839996159 absolute error = 1.3655903166128172e-15 relative error = 6.1984926165121551166474270437665e-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) = 2.2038092970709240403759107825427 absolute error = 1.3733539953693006e-15 relative error = 6.2317279321519421083088471622886e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.2045194387176216033030181499388 absolute error = 1.3811661603893985e-15 relative error = 6.2651575492245585941633511249564e-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) = 2.2052310857351947285421777945353 absolute error = 1.3890271704357812e-15 relative error = 6.2987828324245614443395122449186e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.3MB, time=12.21 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) = 2.2059442402677559082595595749052 absolute error = 1.3969373872894725e-15 relative error = 6.3326051574173703505213912852948e-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) = 2.2066589044670232014617515275692 absolute error = 1.4048971757785249e-15 relative error = 6.3666259109395621975195977196243e-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) = 2.2073750804923505799872085784677 absolute error = 1.4129069038069970e-15 relative error = 6.4008464909001865517102791413456e-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) = 2.2080927705107584380433289420907 absolute error = 1.4209669423842380e-15 relative error = 6.4352683064831200709445155408578e-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) = 2.2088119766969642663150132065805 absolute error = 1.4290776656544815e-15 relative error = 6.4698927782504653409435926411081e-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) = 2.2095327012334134916781808763934 absolute error = 1.4372394509267522e-15 relative error = 6.5047213382470059350745592428256e-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) = 2.2102549463103104835594032881705 absolute error = 1.4454526787050906e-15 relative error = 6.5397554301057362199114654005145e-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) = 2.2109787141256497279905609443055 absolute error = 1.4537177327190973e-15 relative error = 6.5749965091544685198063246495625e-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) = 2.2117040068852471704152480428024 absolute error = 1.4620349999548029e-15 relative error = 6.6104460425235401099042188741453e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9442 Order of pole = 2.082 x[1] = 0.629 y[1] (analytic) = 2.2124308268027702579066572625857 y[1] (numeric) = 2.2124308268027717283115279484507 absolute error = 1.4704048706858650e-15 relative error = 6.6461055092546220770568902428078e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.3MB, time=12.43 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) = 2.2131591760997769747035911828511 absolute error = 1.4788277385050981e-15 relative error = 6.6819764004106514800534537432310e-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) = 2.2138890570057329936428828498595 absolute error = 1.4873040003563398e-15 relative error = 6.7180602191868973112995228036151e-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) = 2.2146204717580584087473499058713 absolute error = 1.4958340565666554e-15 relative error = 6.7543584810231648315535951062427e-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) = 2.2153534226021525858956109852238 absolute error = 1.5044183108788885e-15 relative error = 6.7908727137171676308993553058592e-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) = 2.2160879117914280111810732610037 absolute error = 1.5130571704845575e-15 relative error = 6.8276044575390619120590976338611e-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) = 2.2168239415873428452393127289368 absolute error = 1.5217510460571063e-15 relative error = 6.8645552653471753647452332408521e-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) = 2.2175615142594336550703970221585 absolute error = 1.5305003517855092e-15 relative error = 6.9017267027049254509723820060219e-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) = 2.2183006320853483244862640801114 absolute error = 1.5393055054082379e-15 relative error = 6.9391203479989575129489940184282e-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) = 2.2190412973508791443217763954822 absolute error = 1.5481669282475921e-15 relative error = 6.9767377925585041576377613698460e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.3MB, time=12.66 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) = 2.219783512349996083556649846277 absolute error = 1.5570850452443997e-15 relative error = 7.0145806407759876046122841170614e-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) = 2.220527279384880242504108990615 absolute error = 1.5660602849930897e-15 relative error = 7.0526505102288735297280944398198e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.2212726007659574892308478719624 absolute error = 1.5750930797771444e-15 relative error = 7.0909490318028006343035808544297e-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) = 2.2220194788119322803816775723373 absolute error = 1.5841838656049316e-15 relative error = 7.1294778498159835149167981293284e-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) = 2.2227679158498216675911196882787 absolute error = 1.5933330822459261e-15 relative error = 7.1682386221449250682698772802499e-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) = 2.2235179142149894906731593246958 absolute error = 1.6025411732673204e-15 relative error = 7.2072330203514322546085546360319e-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) = 2.2242694762511807587894028486686 absolute error = 1.6118085860710332e-15 relative error = 7.2464627298109681350938073379764e-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) = 2.22502260431055622080499527044 absolute error = 1.6211357719311179e-15 relative error = 7.2859294498423442068033957578381e-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) = 2.2257773007537271260508404819543 absolute error = 1.6305231860315766e-15 relative error = 7.3256348938387718347144143284738e-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) = 2.2265335679497901767199354522997 absolute error = 1.6399712875045849e-15 relative error = 7.3655807894002905906926965903584e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.3MB, time=12.88 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) = 2.2272914082763626731349776305831 absolute error = 1.6494805394691319e-15 relative error = 7.4057688784675871796828289860329e-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) = 2.2280508241196178531338340247945 absolute error = 1.6590514090700807e-15 relative error = 7.4462009174572225942547467229828e-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) = 2.2288118178743204268289715033348 absolute error = 1.6686843675176534e-15 relative error = 7.4868786773982792161397721750066e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.2295743919438623080065416059297 absolute error = 1.6783798901273483e-15 relative error = 7.5278039440704561042133305562970e-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) = 2.2303385487402985434404903632111 absolute error = 1.6881384563602905e-15 relative error = 7.5689785181436114447543661112615e-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) = 2.2311042906843834414068251287356 absolute error = 1.6979605498640254e-15 relative error = 7.6104042153187883004739528363914e-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) = 2.2318716202056069006930170519735 absolute error = 1.7078466585137567e-15 relative error = 7.6520828664707242554403602783843e-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) = 2.232640539742230941407450403251 absolute error = 1.7177972744540374e-15 relative error = 7.6940163177918764118621563670971e-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) = 2.2334110517413264389038493483161 absolute error = 1.7278128941409166e-15 relative error = 7.7362064309379675414908303384076e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.3MB, time=13.11 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) = 2.2341831586588100621457198169593 absolute error = 1.7378940183845497e-15 relative error = 7.7786550831750806169676827872298e-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) = 2.2349568629594814178460396821496 absolute error = 1.7480411523922756e-15 relative error = 7.8213641675283109294823423188433e-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) = 2.2357321671170604017277154381559 absolute error = 1.7582548058121692e-15 relative error = 7.8643355929320059488483707039997e-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) = 2.2365090736142247582606988224044 absolute error = 1.7685354927770720e-15 relative error = 7.9075712843815983590431636670497e-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) = 2.2372875849426478502421232604174 absolute error = 1.7788837319491087e-15 relative error = 7.9510731830870604343728049251092e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.2380677036030366395963785299449 absolute error = 1.7893000465646947e-15 relative error = 7.9948432466279943898672339610474e-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) = 2.2388494321051698807826935531784 absolute error = 1.7997849644800412e-15 relative error = 8.0388834491103812890498371661037e-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) = 2.239632772967936528208542658629 absolute error = 1.8103390182171629e-15 relative error = 8.0831957813250033885104502583606e-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) = 2.2404177287193743590580309409829 absolute error = 1.8209627450103961e-15 relative error = 8.1277822509075672039490339552004e-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) = 2.2412043018967088129553504324505 absolute error = 1.8316566868534308e-15 relative error = 8.1726448825005357145202861708613e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.3MB, time=13.32 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) = 2.2419924950463920498944316377084 absolute error = 1.8424213905468660e-15 relative error = 8.2177857179167030242787901114869e-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) = 2.2427823107241422278770455419635 absolute error = 1.8532574077462927e-15 relative error = 8.2632068163045236969439524674048e-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) = 2.2435737514949830017128404541429 absolute error = 1.8641652950109119e-15 relative error = 8.3089102543152213722519107065406e-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) = 2.2443668199332832444461269817544 absolute error = 1.8751456138526930e-15 relative error = 8.3548981262716926828469848306424e-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) = 2.2451615186227969928856540485803 absolute error = 1.8861989307860815e-15 relative error = 8.4011725443392379794720292209068e-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) = 2.2459578501567036187251501701672 absolute error = 1.8973258173782598e-15 relative error = 8.4477356386981275198417064506649e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8992 Order of pole = 2.082 x[1] = 0.674 y[1] (analytic) = 2.2467558171376463182271879154443 y[1] (numeric) = 2.2467558171376482267540382154151 absolute error = 1.9085268502999708e-15 relative error = 8.4945895577180379555812653311836e-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) = 2.2475554221777822816694696371918 absolute error = 1.9198026113769087e-15 relative error = 8.5417364681343702143082155560874e-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) = 2.2483566678988044650126666940544 absolute error = 1.9311536876416856e-15 relative error = 8.5891785552264784645910613929123e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.3MB, time=13.76 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) = 2.2491595569320017637645095637863 absolute error = 1.9425806713863810e-15 relative error = 8.6369180229978330390120844127903e-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) = 2.249964091918290792147360534273 absolute error = 1.9540841602156802e-15 relative error = 8.6849570943581351766529680306156e-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) = 2.2507702755082593481922807269408 absolute error = 1.9656647571006097e-15 relative error = 8.7332980113074106649733802893175e-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) = 2.2515781103622082066430671533471 absolute error = 1.9773230704328775e-15 relative error = 8.7819430351221084340464713342701e-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) = 2.2523875991501931497809204295774 absolute error = 1.9890597140798243e-15 relative error = 8.8308944465432215838030896614545e-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) = 2.2531987445520672377660472913128 absolute error = 2.0008753074399950e-15 relative error = 8.8801545459664633014524013286265e-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) = 2.2540115492575233201051082927712 absolute error = 2.0127704754993363e-15 relative error = 8.9297256536345139975750992103509e-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) = 2.2548260159661367898661408759033 absolute error = 2.0247458488880299e-15 relative error = 8.9796101098313722869062550688740e-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) = 2.2556421473874085822754225158129 absolute error = 2.0368020639379683e-15 relative error = 9.0298102750788311968227610234412e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.2564599462408084193436890509684 absolute error = 2.0489397627408808e-15 relative error = 9.0803285303351035172927395897082e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.3MB, time=14.31 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) = 2.2572794152558183021821907721765 absolute error = 2.0611595932071191e-15 relative error = 9.1311672771956280436816313525079e-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) = 2.2581005571719762526822545656421 absolute error = 2.0734622091251098e-15 relative error = 9.1823289380960790035988000395950e-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) = 2.2589233747389203062453255894113 absolute error = 2.0858482702214817e-15 relative error = 9.2338159565176034811068712439935e-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) = 2.2597478707164327572638878294472 absolute error = 2.0983184422218782e-15 relative error = 9.2856307971943221299471557381591e-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) = 2.260574047874484659067210665737 absolute error = 2.1108733969124609e-15 relative error = 9.3377759463231097140860285133294e-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) = 2.261401908993280580059539528437 absolute error = 2.1235138122021151e-15 relative error = 9.3902539117756922348625532502502e-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) = 2.2622314568633036177921441015849 absolute error = 2.1362403721853651e-15 relative error = 9.4430672233130848463106318103913e-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) = 2.26306269428536067272455861421 absolute error = 2.1490537672060083e-15 relative error = 9.4962184328023994758848474038674e-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) = 2.2638956240706279834443968371701 absolute error = 2.1619546939214769e-15 relative error = 9.5497101144360500244420407643151e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.3MB, time=14.84 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) = 2.2647302490406969251293007849189 absolute error = 2.1749438553679375e-15 relative error = 9.6035448649533894845884599968935e-14 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.2655665720276200730488881257685 absolute error = 2.1880219610261360e-15 relative error = 9.6577253038648003378716065189367e-14 % 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) = 2.2664045958739575329190002683097 absolute error = 2.2011897268879996e-15 relative error = 9.7122540736782788640611245535827e-14 % 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) = 2.2672443234328235399351223670314 absolute error = 2.2144478755240026e-15 relative error = 9.7671338401285313021397852155793e-14 % 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) = 2.268085757567933328326549443923 absolute error = 2.2277971361513088e-15 relative error = 9.8223672924086265640343930154395e-14 % 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) = 2.2689289011536502732877108377138 absolute error = 2.2412382447026975e-15 relative error = 9.8779571434042244253853659096268e-14 % 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) = 2.269773757075033307158039667086 absolute error = 2.2547719438962854e-15 relative error = 9.9339061299304213291098654008173e-14 % 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) = 2.2706203282278846117368863434808 absolute error = 2.2683989833060525e-15 relative error = 9.9902170129712372312690439345343e-14 % 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) = 2.2714686175187975886352268240939 absolute error = 2.2821201194331838e-15 relative error = 1.0046892577921783052973921450573e-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) = 2.2723186278652051095813087039481 absolute error = 2.2959361157782360e-15 relative error = 1.0103935634833136655818313452715e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.3MB, time=15.37 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) = 2.2731703621954280486129128718774 absolute error = 2.3098477429141409e-15 relative error = 1.0161349018659966085365334953086e-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) = 2.2740238234487240981045867801446 absolute error = 2.3238557785600549e-15 relative error = 1.0219135589510928508414977775031e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.2748790145753368705940288996891 absolute error = 2.3379610076560667e-15 relative error = 1.0277298232901884963471388770811e-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) = 2.2757359385365452883877741684729 absolute error = 2.3521642224387726e-15 relative error = 1.0335839860011958967962107940138e-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) = 2.2765945983047132629424487224863 absolute error = 2.3664662225177320e-15 relative error = 1.0394763407942480905117027076358e-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) = 2.277454996863339666034130478921 absolute error = 2.3808678149528143e-15 relative error = 1.0454071839978853746245015807672e-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) = 2.2783171372071085947447717881094 absolute error = 2.3953698143324471e-15 relative error = 1.0513768145855369755840273527616e-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) = 2.2791810223419399323112129726377 absolute error = 2.4099730428527789e-15 relative error = 1.0573855342023022119910589278759e-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) = 2.2800466552850402068990427346533 absolute error = 2.4246783303977675e-15 relative error = 1.0634336471920346435478966072917e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.3MB, time=15.90 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) = 2.2809140390649537503804447606462 absolute error = 2.4394865146202057e-15 relative error = 1.0695214606247328547848149367199e-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) = 2.2817831767216141592122110307317 absolute error = 2.4543984410236975e-15 relative error = 1.0756492843242422022998875727616e-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) = 2.2826540713063960595273030097739 absolute error = 2.4694149630455950e-15 relative error = 1.0818174308962705166294921379542e-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) = 2.2835267258821671785707037431363 absolute error = 2.4845369421409107e-15 relative error = 1.0880262157567227010563054529929e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8541 Order of pole = 2.082 x[1] = 0.719 y[1] (analytic) = 2.2844011435233382248625807355185 y[1] (numeric) = 2.2844011435233407246278286027349 absolute error = 2.4997652478672164e-15 relative error = 1.0942759571603576119686335685570e-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) = 2.2852773273159280776114517517018 absolute error = 2.5151007579705424e-15 relative error = 1.1005669762297716783648447017875e-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) = 2.2861552803575917924909610609054 absolute error = 2.5305443584722884e-15 relative error = 1.1068995969847126876111603136139e-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) = 2.287035005757698917765777980884 absolute error = 2.5460969437571611e-15 relative error = 1.1132741463717287172093032675268e-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) = 2.2879165066373746312029725322937 absolute error = 2.5617594166621514e-15 relative error = 1.1196909542941562480795807948202e-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) = 2.2887997861295561950774689316526 absolute error = 2.5775326885665633e-15 relative error = 1.1261503536424511216667366167080e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.3MB, time=16.42 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) = 2.2896848473790472331717762432186 absolute error = 2.5934176794831100e-15 relative error = 1.1326526803248674654043987269710e-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) = 2.2905716935425723318108926900993 absolute error = 2.6094153181500904e-15 relative error = 1.1391982732984886795695336226120e-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) = 2.2914603277888319672269237378855 absolute error = 2.6255265421246601e-15 relative error = 1.1457874746006149469251772009178e-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) = 2.2923507532985577615670246741116 absolute error = 2.6417522978772108e-15 relative error = 1.1524206293805116135813001784848e-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) = 2.2932429732645680698775300610316 absolute error = 2.6580935408868736e-15 relative error = 1.1590980859315234616430209492488e-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) = 2.2941369908918239004165670746594 absolute error = 2.6745512357381602e-15 relative error = 1.1658201957235592125260379126888e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.295032809397485170667069319914 absolute error = 2.6911263562187570e-15 relative error = 1.1725873134359510096125579450709e-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) = 2.2959304320109673014419142135421 absolute error = 2.7078198854184877e-15 relative error = 1.1793997969906938628478851847009e-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) = 2.2968298619739981514929024604316 absolute error = 2.7246328158294588e-15 relative error = 1.1862580075860694870750856913652e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.3MB, time=16.95 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) = 2.2977311025406752950554845461189 absolute error = 2.7415661494474050e-15 relative error = 1.1931623097306600706276600161653e-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) = 2.2986341569775236447815185841542 absolute error = 2.7586208978742490e-15 relative error = 1.2001130712777563925973539764720e-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) = 2.2995390285635534225329183715554 absolute error = 2.7757980824218925e-15 relative error = 1.2071106634601656801827964995661e-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) = 2.3004457205903184805298222238125 absolute error = 2.7930987342172547e-15 relative error = 1.2141554609254243496932405829348e-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) = 2.3013542363619749753678842130193 absolute error = 2.8105238943085739e-15 relative error = 1.2212478417714204406830607108898e-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) = 2.3022645791953403974404619745267 absolute error = 2.8280746137729902e-15 relative error = 1.2283881875824315660463141849710e-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) = 2.3031767524199529583228514607684 absolute error = 2.8457519538254256e-15 relative error = 1.2355768834655834302632060299907e-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) = 2.3040907593781313386973011136342 absolute error = 2.8635569859287788e-15 relative error = 1.2428143180877343716732186091159e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.3050066034250347994193281335979 absolute error = 2.8814907919054519e-15 relative error = 1.2501008837127913094274959319795e-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) = 2.3059242879287236583478601063702 absolute error = 2.8995544640502277e-15 relative error = 1.2574369762394630944324722781453e-13 % h = 0.001 memory used=259.4MB, alloc=4.3MB, time=17.48 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) = 2.3068438162702201355839384950973 absolute error = 2.9177491052445143e-15 relative error = 1.2648229952394563625597761580701e-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) = 2.3077651918435695697851487347247 absolute error = 2.9360758290719767e-15 relative error = 1.2722593439961202569243386689907e-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) = 2.3086884180559020082455872198178 absolute error = 2.9545357599355723e-15 relative error = 1.2797464295435451374971924305575e-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) = 2.3096134983274941734540407310481 absolute error = 2.9731300331760105e-15 relative error = 1.2872846627061217931328902245704e-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) = 2.3105404360918318088661412007116 absolute error = 2.9918597951916547e-15 relative error = 1.2948744581385668120535771062934e-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) = 2.3114692347956724066495706052491 absolute error = 3.0107262035598863e-15 relative error = 1.3025162343664202950067435717781e-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) = 2.3123998978991083201849296535913 absolute error = 3.0297304271599504e-15 relative error = 1.3102104138270221023624018015342e-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) = 2.3133324288756302641286523050572 absolute error = 3.0488736462973032e-15 relative error = 1.3179574229109729196048776992546e-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) = 2.3142668312121912048683485206992 absolute error = 3.0681570528294802e-15 relative error = 1.3257576920040859997111478946028e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.3MB, time=18.00 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) = 2.3152031084092706442251925794202 absolute error = 3.0875818502935080e-15 relative error = 1.3336116555298370030653141960491e-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) = 2.3161412639809392992824463581252 absolute error = 3.1071492540348780e-15 relative error = 1.3415197519923173713645771061194e-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) = 2.3170813014549241812439187984974 absolute error = 3.1268604913381052e-15 relative error = 1.3494824240196987515169866318435e-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) = 2.3180232243726740762511170086492 absolute error = 3.1467168015588920e-15 relative error = 1.3575001184082145196962303633075e-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) = 2.31896703628942543111304375536 absolute error = 3.1667194362579192e-15 relative error = 1.3655732861666654097804191176225e-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) = 2.3199127407742686469280432042683 absolute error = 3.1868696593362873e-15 relative error = 1.3737023825614565971919942863698e-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) = 2.3208603414102147836027944070308 absolute error = 3.2071687471726290e-15 relative error = 1.3818878671621725986295880798702e-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) = 2.3218098417942626782995029957311 absolute error = 3.2276179887619157e-15 relative error = 1.3901302038876971268227027458262e-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) = 2.3227612455374664808685486396533 absolute error = 3.2482186858559832e-15 relative error = 1.3984298610528860301543465045347e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.811 Order of pole = 2.082 memory used=267.0MB, alloc=4.3MB, time=18.54 x[1] = 0.762 y[1] (analytic) = 2.3237145562650003403781587908365 y[1] (numeric) = 2.3237145562650036093503118966336 absolute error = 3.2689721531057971e-15 relative error = 1.4067873114157993782585481616876e-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) = 2.3246697776162431286566320345236 absolute error = 3.2898797182054830e-15 relative error = 1.4152030322255006938066102221897e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.3256269132448145555693401275043 absolute error = 3.3109427220381468e-15 relative error = 1.4236775052704313703424307859289e-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) = 2.3265859668186770932205722029654 absolute error = 3.3321625188235068e-15 relative error = 1.4322112169273667218572662535994e-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) = 2.3275469420201892982470984199961 absolute error = 3.3535404762673653e-15 relative error = 1.4408046582109626456832636799050e-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) = 2.3285098425461791838387092300093 absolute error = 3.3750779757129429e-15 relative error = 1.4494583248238998970803270011330e-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) = 2.3294746721080147619287812711503 absolute error = 3.3967764122941020e-15 relative error = 1.4581727172076343460610350609472e-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) = 2.3304414344316750278035074866637 absolute error = 3.4186371950904854e-15 relative error = 1.4669483405937612801867302189521e-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) = 2.3314101332578213904349207778047 absolute error = 3.4406617472845960e-15 relative error = 1.4757857050560018112514158374713e-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) = 2.3323807723418695518717715879718 absolute error = 3.4628515063208447e-15 relative error = 1.4846853255628198663284382039849e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.3MB, time=19.06 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) = 2.333353355454061839051540390129 absolute error = 3.4852079240665939e-15 relative error = 1.4936477220306783213777249721384e-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) = 2.3343278863795399914263793782706 absolute error = 3.5077324669752232e-15 relative error = 1.5026734193779424414025904990528e-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) = 2.3353043689184184078255870506031 absolute error = 3.5304266162512463e-15 relative error = 1.5117629475794397682737182744216e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.798 Order of pole = 2.082 x[1] = 0.775 y[1] (analytic) = 2.3362828068858543027154601462071 y[1] (numeric) = 2.3362828068858578560073281637141 absolute error = 3.5532918680175070e-15 relative error = 1.5209168417216850722687879962485e-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) = 2.337263204112139648382723121779 absolute error = 3.5763297334844835e-15 relative error = 1.5301356420587794866903013729055e-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) = 2.3382455644427402874261486740047 absolute error = 3.5995417391217297e-15 relative error = 1.5394198940689926760988075476062e-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) = 2.3392298917384065843166193014481 absolute error = 3.6229294268314836e-15 relative error = 1.5487701485120374326777229422631e-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) = 2.3402161898752312543864593993531 absolute error = 3.6464943541244731e-15 relative error = 1.5581869614870461239463823963180e-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) = 2.3412044627447289929851338659635 absolute error = 3.6702380942979496e-15 relative error = 1.5676708944912584004544142090088e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.3MB, time=19.59 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) = 2.3421947142539130353980826012092 absolute error = 3.6941622366159805e-15 relative error = 1.5772225144794298132662353110432e-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) = 2.3431869483253722044927063522553 absolute error = 3.7182683864920322e-15 relative error = 1.5868423939239711454778817098836e-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) = 2.3441811688973484497962810175211 absolute error = 3.7425581656738756e-15 relative error = 1.5965311108758283727132930885308e-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) = 2.3451773799238148817435386832869 absolute error = 3.7670332124308469e-15 relative error = 1.6062892490261134479030693814342e-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) = 2.3461755853745543048649501119238 absolute error = 3.7916951817434966e-15 relative error = 1.6161173977684960860775554963058e-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) = 2.347175789235238253720378970947 absolute error = 3.8165457454956598e-15 relative error = 1.6260161522623667475064003526666e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.3481779955075065354167566793318 absolute error = 3.8415865926689824e-15 relative error = 1.6359861134967815931396814327921e-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) = 2.3491822082090472825827522933674 absolute error = 3.8668194295399382e-15 relative error = 1.6460278883552002909501601581218e-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) = 2.3501884313736775207080883506454 absolute error = 3.8922459798793706e-15 relative error = 1.6561420896810269321337119688287e-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) = 2.3511966690514242537901850805897 absolute error = 3.9178679851545960e-15 relative error = 1.6663293363439656973111239202586e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.3MB, time=20.13 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) = 2.3522069253086060722662059680272 absolute error = 3.9436872047341040e-15 relative error = 1.6765902533072019924754666734721e-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) = 2.3532192042279152872443314700257 absolute error = 3.9697054160948926e-15 relative error = 1.6869254716954210242608322255095e-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) = 2.3542335099085005950842089362197 absolute error = 3.9959244150324735e-15 relative error = 1.6973356288636743949873842745507e-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) = 2.3552498464660502764130197237785 absolute error = 4.0223460158735882e-15 relative error = 1.7078213684671076074917277248339e-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) = 2.3562682180328759337004734395297 absolute error = 4.0489720516916704e-15 relative error = 1.7183833405315590862460999739103e-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) = 2.3572886287579967715532885485923 absolute error = 4.0758043745250968e-15 relative error = 1.7290222015250440517784187840835e-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) = 2.3583110828072244239273526826392 absolute error = 4.1028448555982634e-15 relative error = 1.7397386144301343859181713863733e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.3593355843632483324937793402138 absolute error = 4.1300953855455293e-15 relative error = 1.7505332488172476299418666577902e-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) = 2.3603621376257216804334948329675 absolute error = 4.1575578746380683e-15 relative error = 1.7614067809188574576203398401411e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.3MB, time=20.70 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) = 2.3613907468113478859738048906872 absolute error = 4.1852342530136700e-15 relative error = 1.7723598937046384803607254510866e-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) = 2.3624214161539676600196089496237 absolute error = 4.2131264709095327e-15 relative error = 1.7833932769575584155276577185015e-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) = 2.3634541499046466322715565284923 absolute error = 4.2412364988980906e-15 relative error = 1.7945076273509306523308423672100e-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) = 2.3644889523317635502634790215675 absolute error = 4.2695663281259195e-15 relative error = 1.8057036485264408866701471458728e-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) = 2.3655258277210990557918865477451 absolute error = 4.2981179705557654e-15 relative error = 1.8169820511731614960344435439003e-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) = 2.3665647803759250432511980906718 absolute error = 4.3268934592117393e-15 relative error = 1.8283435531075667752343334966068e-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) = 2.3676058146170946044296790144656 absolute error = 4.3558948484277264e-15 relative error = 1.8397888793545641391077757209987e-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) = 2.3686489347831325643627981735793 absolute error = 4.3851242140990536e-15 relative error = 1.8513187622295544910603201436250e-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) = 2.3696941452303266128828923513119 absolute error = 4.4145836539374650e-15 relative error = 1.8629339414215373179839320076686e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.3707414503328190365466438235364 absolute error = 4.4442752877294497e-15 relative error = 1.8746351640772736994201014291514e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.3MB, time=21.22 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) = 2.3717908544826990556649426844146 absolute error = 4.4742012575979749e-15 relative error = 1.8864231848865239996864443039458e-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) = 2.3728423620900957712032244900338 absolute error = 4.5043637282676697e-15 relative error = 1.8982987661683737081376493902784e-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) = 2.3738959775832717263643511446875 absolute error = 4.5347648873335125e-15 relative error = 1.9102626779586639623888537013474e-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) = 2.3749517054087170877105442143928 absolute error = 4.5654069455330708e-15 relative error = 1.9223156980985414616531505442376e-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) = 2.3760095500312444507257905165214 absolute error = 4.5962921370223480e-15 relative error = 1.9344586123241448227946164519805e-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) = 2.3770695159340842747655254893381 absolute error = 4.6274227196552862e-15 relative error = 1.9466922143574419711188020614573e-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) = 2.3781316076189809523862661509755 absolute error = 4.6588009752669812e-15 relative error = 1.9590173059982360887329017323260e-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) = 2.3791958296062895180942181491426 absolute error = 4.6904292099606634e-15 relative error = 1.9714346972173564845068318357799e-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) = 2.3802621864350730015987262920259 absolute error = 4.7223097543984987e-15 relative error = 1.9839452062510508129849989886570e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.3MB, time=21.75 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) = 2.3813306826632004307037809259929 absolute error = 4.7544449640962665e-15 relative error = 1.9965496596965962236122590131178e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.3824013228674454890186395538331 absolute error = 4.7868372197219713e-15 relative error = 2.0092488926091466590186359937783e-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) = 2.3834741116435858337169802148729 absolute error = 4.8194889273984462e-15 relative error = 2.0220437485998341659615470752778e-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) = 2.3845490536065030786228765025853 absolute error = 4.8524025190100058e-15 relative error = 2.0349350799351416334842557807749e-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) = 2.3856261533902834479512798853621 absolute error = 4.8855804525132100e-15 relative error = 2.0479237476375659367307974374509e-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) = 2.3867054156483191060806195140976 absolute error = 4.9190252122517980e-15 relative error = 2.0610106215875894237047609653865e-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) = 2.3877868450534101687855893226269 absolute error = 4.9527393092758547e-15 relative error = 2.0741965806269787802140106304376e-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) = 2.3888704462978674014091934159068 absolute error = 4.9867252816652722e-15 relative error = 2.0874825126634303960775071822579e-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) = 2.3899562240936156095046700449769 absolute error = 5.0209856948575699e-15 relative error = 2.1008693147765815676472859380996e-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) = 2.3910441831722977275300185241552 absolute error = 5.0555231419801379e-15 relative error = 2.1143578933254072490638434783155e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.3MB, time=22.27 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) = 2.392134328285379611230518980974 absolute error = 5.0903402441869694e-15 relative error = 2.1279491640570223558233083008098e-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) = 2.3932266642042555393978686601598 absolute error = 5.1254396509999489e-15 relative error = 2.1416440522169099549124618241365e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7419 Order of pole = 2.082 x[1] = 0.831 y[1] (analytic) = 2.3943211957203492699243268839312 y[1] (numeric) = 2.3943211957203544307483675386963 absolute error = 5.1608240406547651e-15 relative error = 2.1554434926605964216504369771907e-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) = 2.395417927645246781716977252328 absolute error = 5.1964961204515148e-15 relative error = 2.1693484299667934229966416045305e-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) = 2.3965168648107523310190578822688 absolute error = 5.2324586271100720e-15 relative error = 2.1833598185520297519573445770237e-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) = 2.3976180120690484568871641981222 absolute error = 5.2687143271302886e-15 relative error = 2.1974786227867926402369488997790e-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) = 2.398721374292779312946463790571 absolute error = 5.3052660171571042e-15 relative error = 2.2117058171132026708299180328163e-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) = 2.3998269563751657087491315458656 absolute error = 5.3421165243506346e-15 relative error = 2.2260423861642429698030689346749e-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) = 2.4009347632301157410454856048128 absolute error = 5.3792687067613157e-15 relative error = 2.2404893248845661746511192014305e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.3MB, time=22.80 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) = 2.4020447997923361819276669052654 absolute error = 5.4167254537101791e-15 relative error = 2.2550476386529023595028720011566e-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) = 2.4031570710174446300403353261575 absolute error = 5.4544896861743350e-15 relative error = 2.2697183434060906555528315728304e-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) = 2.4042715818820824311121681353035 absolute error = 5.4925643571777437e-15 relative error = 2.2845024657647595256807619380012e-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) = 2.40538833738402837412190880168 absolute error = 5.5309524521873522e-15 relative error = 2.2994010431606784970532688759756e-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) = 2.406507342542313169473334283415 absolute error = 5.5696569895146805e-15 relative error = 2.3144151239658073684545006340510e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.4076286023973347156147947729504 absolute error = 5.6086810207229375e-15 relative error = 2.3295457676230667908425909873339e-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) = 2.4087521220109741606009398103369 absolute error = 5.6480276310397516e-15 relative error = 2.3447940447788561188605456631648e-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) = 2.4098779064667127651568870172987 absolute error = 5.6876999397756018e-15 relative error = 2.3601610374173445531805271542561e-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) = 2.4110059608697495738684229266839 absolute error = 5.7277011007480343e-15 relative error = 2.3756478389965610916084353450895e-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) = 2.4121362903471199011858580692222 absolute error = 5.7680343027117545e-15 relative error = 2.3912555545863106686338735064662e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.3MB, time=23.33 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) = 2.4132689000478146389938993358518 absolute error = 5.8087027697946827e-15 relative error = 2.4069853010079430221103284002554e-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) = 2.4144037951429003925653604834814 absolute error = 5.8497097619400663e-15 relative error = 2.4228382069760025132834444020804e-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) = 2.415540980825640451782715441462 absolute error = 5.8910585753547384e-15 relative error = 2.4388154132417857417599497942030e-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) = 2.4166804623116166045784178760277 absolute error = 5.9327525429636199e-15 relative error = 2.4549180727388365959638271252266e-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) = 2.4178222448388517996125734773812 absolute error = 5.9747950348705591e-15 relative error = 2.4711473507304069051036807548970e-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) = 2.4189663336679336652749679738564 absolute error = 6.0171894588256064e-15 relative error = 2.4875044249589121585492099201760e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.4201127340821388921676334045843 absolute error = 6.0599392606988239e-15 relative error = 2.5039904857974124727400238756406e-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) = 2.4212614513875584862940872832189 absolute error = 6.1030479249607290e-15 relative error = 2.5206067364031484975228429153087e-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) = 2.4224124909132239002521136814734 absolute error = 6.1465189751694762e-15 relative error = 2.5373543928731638602620719898658e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.3MB, time=23.87 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) = 2.4235658580112340497984818094817 absolute error = 6.1903559744648800e-15 relative error = 2.5542346844020450018983378217415e-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) = 2.424721558056883223226326365547 absolute error = 6.2345625260693845e-15 relative error = 2.5712488534418101660277236063847e-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) = 2.4258795964487898910690549061871 absolute error = 6.2791422737960888e-15 relative error = 2.5883981558639805330663012325649e-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) = 2.4270399786090264237186110265604 absolute error = 6.3240989025639356e-15 relative error = 2.6056838611238655728978176715751e-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) = 2.4282027099832497246207186640712 absolute error = 6.3694361389201760e-15 relative error = 2.6231072524270967791406812919034e-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) = 2.429367796040832786785372913873 absolute error = 6.4151577515702226e-15 relative error = 2.6406696268984433514185235182239e-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) = 2.4305352422749971804273370930045 absolute error = 6.4612675519150073e-15 relative error = 2.6583722957529449353264915693033e-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) = 2.4317050542029464796287652804349 absolute error = 6.5077693945959584e-15 relative error = 2.6762165844693955559209853653127e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.4328772373660006359943052177119 absolute error = 6.5546671780477195e-15 relative error = 2.6942038329662158959340475073297e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7069 Order of pole = 2.082 memory used=308.9MB, alloc=4.3MB, time=24.40 x[1] = 0.866 y[1] (analytic) = 2.4340517973297247053833144011125 y[1] (numeric) = 2.4340517973297313073481594598408 absolute error = 6.6019648450587283e-15 relative error = 2.7123353957797490168717994593228e-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) = 2.4352287396840981496026043578798 absolute error = 6.6496663833397794e-15 relative error = 2.7306126422450168455497185034195e-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) = 2.4364080700435860800083983341411 absolute error = 6.6977758261006976e-15 relative error = 2.7490369566789754836485251878171e-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) = 2.4375897940473435200793646422268 absolute error = 6.7462972526352473e-15 relative error = 2.7676097385663067737181035242052e-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) = 2.4387739173593216265662212181174 absolute error = 6.7952347889144082e-15 relative error = 2.7863324027477851866304731611984e-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) = 2.4399604456684145189384633248166 absolute error = 6.8445926081881505e-15 relative error = 2.8052063796112600619408326523064e-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) = 2.4411493846886005119177956428843 absolute error = 6.8943749315958411e-15 relative error = 2.8242331152852922672106935640372e-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) = 2.4423407401590843616922716081072 absolute error = 6.9445860287854193e-15 relative error = 2.8434140718354869409781314753934e-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) = 2.4435345178444405345269416681527 absolute error = 6.9952302185414803e-15 relative error = 2.8627507274635636223687828225079e-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) = 2.4447307235347575065744514247668 absolute error = 7.0463118694224072e-15 relative error = 2.8822445767092057712956640318389e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.3MB, time=24.92 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) = 2.4459293630457831037776782320343 absolute error = 7.0978354004066951e-15 relative error = 2.9018971306547325830125659235462e-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) = 2.4471304422190708908461638051398 absolute error = 7.1498052815486140e-15 relative error = 2.9217099171326369758415511781497e-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) = 2.4483339669221276183788040171849 absolute error = 7.2022260346433589e-15 relative error = 2.9416844809360340272504804752014e-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) = 2.4495399430485617372970087747022 absolute error = 7.2551022339018381e-15 relative error = 2.9618223840320648928444231698906e-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) = 2.4507483765182329898453583109028 absolute error = 7.3084385066352531e-15 relative error = 2.9821252057783019145801493406049e-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) = 2.4519592732774030865106712624061 absolute error = 7.3622395339496285e-15 relative error = 3.0025945431422023509329733178322e-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) = 2.4531726392988874783053785440769 absolute error = 7.4165100514504488e-15 relative error = 3.0232320109236572280853350625991e-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) = 2.4543884805822082339571795555093 absolute error = 7.4712548499575652e-15 relative error = 3.0440392419806840160947237332218e-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) = 2.4556068031537480316441580968324 absolute error = 7.5264787762305382e-15 relative error = 3.0650178874583126008880125568860e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6879 Order of pole = 2.082 memory used=316.6MB, alloc=4.3MB, time=25.45 x[1] = 0.885 y[1] (analytic) = 2.4568276130668976928261355020896 y[1] (numeric) = 2.4568276130669052750128692066721 absolute error = 7.5821867337045825e-15 relative error = 3.0861696170207139693814553496575e-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) = 2.4580509164022503433163898411028 absolute error = 7.6383836832372845e-15 relative error = 3.1074961190866222298752044696932e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6859 Order of pole = 2.082 x[1] = 0.887 y[1] (analytic) = 2.4592767192676752905353271202512 y[1] (numeric) = 2.4592767192676829856099709865201 absolute error = 7.6950746438662689e-15 relative error = 3.1289991010681027621832328683706e-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) = 2.460505027798590869043751759765 absolute error = 7.7522646935779873e-15 relative error = 3.1506802896127174684885252189319e-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) = 2.4617358481580092913950128382487 absolute error = 7.8099589700878117e-15 relative error = 3.1725414308491418019958950592992e-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) = 2.4629691865367820680866729521143 absolute error = 7.8681626716316153e-15 relative error = 3.1945842906362876735169691971620e-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) = 2.4642050491537236040441841622973 absolute error = 7.9268810577690258e-15 relative error = 3.2168106548159870976262253867769e-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) = 2.4654434422557821608496754809606 absolute error = 7.9861194501985425e-15 relative error = 3.2392223294692935332451538540785e-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) = 2.4666843721182043297601465418315 absolute error = 8.0458832335847086e-15 relative error = 3.2618211411764575214334682829637e-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) = 2.4679278450447007212657402183797 absolute error = 8.1061778563975367e-15 relative error = 3.2846089372806355029605387134516e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.3MB, time=25.98 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) = 2.4691738673676128819746422857316 absolute error = 8.1670088317643863e-15 relative error = 3.3075875861553906151748909556924e-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) = 2.4704224454480814497229846471514 absolute error = 8.2283817383344968e-15 relative error = 3.3307589774760457600404583866831e-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) = 2.4716735856762155579212837726513 absolute error = 8.2903022211563845e-15 relative error = 3.3541250224949508384562690386629e-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) = 2.4729272944712635002634455601698 absolute error = 8.3527759925683122e-15 relative error = 3.3776876543207256566826251758190e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.474183578281784667040229826923 absolute error = 8.4158088331020483e-15 relative error = 3.4014488282015429335429620417180e-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) = 2.4754424435858227644163103362373 absolute error = 8.4794065924001321e-15 relative error = 3.4254105218125153089247716835990e-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) = 2.4767038968910803281487082021719 absolute error = 8.5435751901468687e-15 relative error = 3.4495747355472525103082359326926e-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) = 2.4779679447350945433444365062857 absolute error = 8.6083206170132795e-15 relative error = 3.4739434928136554212685007805565e-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) = 2.4792345936854143819766911052929 absolute error = 8.6736489356162390e-15 relative error = 3.4985188403340152232793835439708e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.3MB, time=26.52 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) = 2.480503850339779070001876288568 absolute error = 8.7395662814920320e-15 relative error = 3.5233028484494866746357380323451e-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) = 2.4817757213262978960441838349017 absolute error = 8.8060788640845705e-15 relative error = 3.5482976114290061996463184090343e-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) = 2.4830502133036313737403700887032 absolute error = 8.8731929677485138e-15 relative error = 3.5735052477827266560190758174440e-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) = 2.4843273329611737699648181977248 absolute error = 8.9409149527675385e-15 relative error = 3.5989279005800414305775521651726e-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) = 2.4856070870192370112839522037083 absolute error = 9.0092512563880112e-15 relative error = 3.6245677377722724541662328592206e-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) = 2.4868894822292359811196071411482 absolute error = 9.0782083938683200e-15 relative error = 3.6504269525200975277477969808513e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.4881745253738752202330758805099 absolute error = 9.1477929595441273e-15 relative error = 3.6765077635257943902287221002234e-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) = 2.4894622232673370432752706747314 absolute error = 9.2180116279098081e-15 relative error = 3.7028124153703790947784228674302e-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) = 2.4907525827554710842837770821272 absolute error = 9.2888711547163466e-15 relative error = 3.7293431788557191612666737169908e-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) = 2.4920456107159852841445623272956 absolute error = 9.3603783780859657e-15 relative error = 3.7561023513517021260419982209949e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.3MB, time=27.04 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) = 2.4933413140586383331747517441624 absolute error = 9.4325402196437720e-15 relative error = 3.7830922571485427445832513592172e-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) = 2.4946396997254335821232285848795 absolute error = 9.5053636856666996e-15 relative error = 3.8103152478143117930039378746670e-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) = 2.4959407746908144350278673868328 absolute error = 9.5788558682500478e-15 relative error = 3.8377737025577735481089971762294e-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) = 2.4972445459618612375120028341473 absolute error = 9.6530239464919059e-15 relative error = 3.8654700285966176485143752129143e-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) = 2.4985510205784896742482885572131 absolute error = 9.7278751876957698e-15 relative error = 3.8934066615311750260872288348253e-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) = 2.4998602056136506894654378780883 absolute error = 9.8034169485916570e-15 relative error = 3.9215860657237077190537919915682e-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) = 2.5011721081735319445224857983987 absolute error = 9.8796566765760342e-15 relative error = 3.9500107346833647727034506158214e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.5024867353977608267261935860817 absolute error = 9.9566019109708754e-15 relative error = 3.9786831914568972525039823630491e-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) = 2.5038040944596090237200595803196 absolute error = 1.00342602843021778e-14 relative error = 4.0076059890252284799127985357673e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.3MB, time=27.57 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) = 2.505124192566198677928128124851 absolute error = 1.01126395235982655e-14 relative error = 4.0367817107059759913220720843215e-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) = 2.5064470369587101356934290820972 absolute error = 1.01917474517082173e-14 relative error = 4.0662129705620235388248522670300e-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) = 2.5077726349125913059094598034884 absolute error = 1.02715919886407653e-14 relative error = 4.0959024138162448895820211948901e-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) = 2.509100993737768643103666776991 absolute error = 1.03521811529240115e-14 relative error = 4.1258527172724806500871863966843e-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) = 2.5104321207788597700944229028065 absolute error = 1.04335230629863209e-14 relative error = 4.1560665897428731089659452766743e-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) = 2.5117660234153877555075563511005 absolute error = 1.05156259385587531e-14 relative error = 4.1865467724816647290921933151699e-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) = 2.5131027090619970616050965542087 absolute error = 1.05984981020994039e-14 relative error = 4.2172960396255689343688005418825e-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) = 2.514442185168671178047590844468 absolute error = 1.06821479802400323e-14 relative error = 4.2483171986408226023850273295390e-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) = 2.5157844592209519573821407813007 absolute error = 1.07665841052553595e-14 relative error = 4.2796130907770333307273446940060e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.5171295387401606682212399880584 absolute error = 1.08518151165554286e-14 relative error = 4.3111865915279345610651120087522e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.3MB, time=28.10 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) = 2.5184774312836207822525954758756 absolute error = 1.09378497622014258e-14 relative error = 4.3430406110991656244272215192579e-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) = 2.5198281444448825113974125767253 absolute error = 1.10246969004453683e-14 relative error = 4.3751780948831946677192914388813e-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) = 2.5211816858539491116141508303708 absolute error = 1.11123655012940739e-14 relative error = 4.4076020239415054477484404482606e-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) = 2.5225380631775049700265460487183 absolute error = 1.12008646480978330e-14 relative error = 4.4403154154941703571972070332721e-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) = 2.5238972841191454922387743927763 absolute error = 1.12902035391642141e-14 relative error = 4.4733213234169352724290664927752e-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) = 2.5252593564196088068870402251218 absolute error = 1.13803914893974399e-14 relative error = 4.5066228387459432720050987338403e-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) = 2.5266242878570093046656338428667 absolute error = 1.14714379319637810e-14 relative error = 4.5402230901902272616508709867725e-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) = 2.5279920862470730292566615753142 absolute error = 1.15633524199834216e-14 relative error = 4.5741252446521035160497941516312e-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) = 2.5293627594433749377862333029386 absolute error = 1.16561446282492615e-14 relative error = 4.6083325077556010922772463131692e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.3MB, time=28.63 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) = 2.5307363153375780486259359189281 absolute error = 1.17498243549731263e-14 relative error = 4.6428481243830640817884446144903e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6298 Order of pole = 2.082 x[1] = 0.943 y[1] (analytic) = 2.5321127618596626501554373026144 y[1] (numeric) = 2.5321127618596744945569608624819 absolute error = 1.18444015235598675e-14 relative error = 4.6776753792200665296251541739749e-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) = 2.5334921069782284995153254174899 absolute error = 1.19398861844098433e-14 relative error = 4.7128175973087824114187030338419e-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) = 2.5348743587006212973402673761068 absolute error = 1.20362885167502803e-14 relative error = 4.7482781446099557167229987919118e-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) = 2.5362595250732980111541378809136 absolute error = 1.21336188304960259e-14 relative error = 4.7840604285736184010230749707103e-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) = 2.5376476141820165122110053408208 absolute error = 1.22318875681402115e-14 relative error = 4.8201678987187069349162862965382e-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) = 2.5390386341520982772627524261796 absolute error = 1.23311053066753554e-14 relative error = 4.8566040472217305293536556600562e-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) = 2.5404325931486812637057370625437 absolute error = 1.24312827595454459e-14 relative error = 4.8933724095146475461971232670309e-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) = 2.5418294993769748219881364590684 absolute error = 1.25324307786295554e-14 relative error = 4.9304765648921094945123121534113e-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 memory used=343.3MB, alloc=4.3MB, time=29.16 y[1] (analytic) = 2.5432293610825040304175843031698 y[1] (numeric) = 2.5432293610825166649779405607157 absolute error = 1.26345603562575459e-14 relative error = 4.9679201371282346035695372540779e-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) = 2.5446321865514319142142485837707 absolute error = 1.27376826272584378e-14 relative error = 5.0057067951030762766141952602983e-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) = 2.5460379841106942431900908201246 absolute error = 1.28418088710420267e-14 relative error = 5.0438402534389555251844858856272e-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) = 2.5474467621283891380434896854756 absolute error = 1.29469505137143405e-14 relative error = 5.0823242731468282075580555649952e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.5488585290139792962649317297987 absolute error = 1.30531191302275450e-14 relative error = 5.1211626622828628544371272922825e-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) = 2.550273293218572184263889408695 absolute error = 1.31603264465649150e-14 relative error = 5.1603592766154070034941968956156e-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) = 2.5516910632351897748745519213574 absolute error = 1.32685843419615007e-14 relative error = 5.1999180203025236472326616545944e-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) = 2.5531118475990404861215431635716 absolute error = 1.33779048511611332e-14 relative error = 5.2398428465802835202241310324279e-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) = 2.5545356548877933428101673629222 absolute error = 1.34883001667104235e-14 relative error = 5.2801377584620017086674191929023e-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) = 2.5559624937218543827526755436906 absolute error = 1.35997826412904220e-14 relative error = 5.3208068094486105773365607410938e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.3MB, time=29.69 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) = 2.5573923727646453296922356547204 absolute error = 1.37123647900866227e-14 relative error = 5.3618541042503662884911586374144e-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) = 2.558825300722884555239763800793 absolute error = 1.38260592931980033e-14 relative error = 5.4032837995200874400733378154840e-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) = 2.5602612863468703523955821488831 absolute error = 1.39408789980858125e-14 relative error = 5.4451001045981306992939922353200e-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) = 2.5617003384307665434880601374247 absolute error = 1.40568369220628251e-14 relative error = 5.4873072822693103939246137257597e-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) = 2.5631424658128904456250198166195 absolute error = 1.41739462548238034e-14 relative error = 5.5299096495319744395745176180650e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.5645876773760032170207945376924 absolute error = 1.42922203610179147e-14 relative error = 5.5729115783794517810268738303111e-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) = 2.5660359820476026078324746804153 absolute error = 1.44116727828638733e-14 relative error = 5.6163174965940921405508845539897e-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) = 2.5674873888002181394131074128778 absolute error = 1.45323172428085867e-14 relative error = 5.6601318885541215932705736752062e-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) = 2.5689419066517087361674932429359 absolute error = 1.46541676462301059e-14 relative error = 5.7043592960535436511194863669378e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.6027 Order of pole = 2.082 memory used=350.9MB, alloc=4.3MB, time=30.22 x[1] = 0.97 y[1] (analytic) = 2.5703995446655480572397106807342 y[1] (numeric) = 2.5703995446655628344777948664249 absolute error = 1.47772380841856907e-14 relative error = 5.7490043191353180711336071567542e-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) = 2.571860311951200993451498970713 absolute error = 1.49015428362058222e-14 relative error = 5.7940716169380561129728417358591e-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) = 2.5733242176642810325334055659942 absolute error = 1.50270963731350064e-14 relative error = 5.8395659085564736984857420375683e-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) = 2.5747912710070057213163193852691 absolute error = 1.51539133600202351e-14 relative error = 5.8854919739158507391323080512045e-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) = 2.5762614812284330471820421708558 absolute error = 1.52820086590479819e-14 relative error = 5.9318546546607475036999405176125e-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) = 2.5777348576247890867051724810585 absolute error = 1.54113973325306355e-14 relative error = 5.9786588550582364389827945890482e-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) = 2.5792114095397835070571712308193 absolute error = 1.55420946459432835e-14 relative error = 6.0259095429159101432045573908733e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.5806911463649277239572077637113 absolute error = 1.56741160710117848e-14 relative error = 6.0736117505149338340002894051254e-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) = 2.582174077539855743029525110593 absolute error = 1.58074772888530841e-14 relative error = 6.1217705755584145565043441589547e-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) = 2.5836602125526477117445175450937 absolute error = 1.59421941931687421e-14 relative error = 6.1703911821353650594510975619656e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.3MB, time=30.74 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) = 2.5851495609401562094424629911965 absolute error = 1.60782828934926750e-14 relative error = 6.2194788017005458607296541397279e-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) = 2.5866421322883353032649627577668 absolute error = 1.62157597184941186e-14 relative error = 6.2690387340704752243855312454454e-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) = 2.5881379362325723981496780643914 absolute error = 1.63546412193368491e-14 relative error = 6.3190763484359010244730125153733e-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) = 2.5896369824580229093789846098286 absolute error = 1.64949441730957191e-14 relative error = 6.3695970843910363873478355731776e-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) = 2.5911392806999477865127618993876 absolute error = 1.66366855862315848e-14 relative error = 6.4206064529798654215060252921708e-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) = 2.5926448407440539178797632461938 absolute error = 1.67798826981257240e-14 relative error = 6.4721100377598320681297394671054e-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) = 2.5941536724268374451509465459979 absolute error = 1.69245529846748681e-14 relative error = 6.5241134958832317707225364569220e-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) = 2.5956657856359300178718575678711 absolute error = 1.70707141619479926e-14 relative error = 6.5766225591966313822014199004793e-13 % h = 0.001 TOP MAIN SOLVE Loop 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) = 2.5971811903104480181897203181584 absolute error = 1.72183841899060354e-14 relative error = 6.6296430353586497406091448024698e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.3MB, time=31.27 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) = 2.5986998964413447863743780027393 absolute error = 1.73675812761857369e-14 relative error = 6.6831808089764382567423762418008e-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) = 2.6002219140717658781007195031483 absolute error = 1.75183238799488183e-14 relative error = 6.7372418427612068222735513147045e-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) = 2.6017472532974073848337976799545 absolute error = 1.76706307157977427e-14 relative error = 6.7918321787031484835241894724766e-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) = 2.6032759242668773490365761457938 absolute error = 1.78245207577593276e-14 relative error = 6.8469579392661227792108735260520e-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) = 2.604807937182060306304210699168 absolute error = 1.79800132433375047e-14 relative error = 6.9026253286024652986406552888538e-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) = 2.6063433022984849869180620579134 absolute error = 1.81371276776365481e-14 relative error = 6.9588406337882978003178971066933e-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) = 2.6078820299256952097073309747705 absolute error = 1.82958838375561241e-14 relative error = 7.0156102260797225952025537145996e-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) = 2.6094241304276240015063897978265 absolute error = 1.84563017760595371e-14 relative error = 7.0729405621902900448401976809111e-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) = 2.6109696142229709759016420689368 absolute error = 1.86184018265165827e-14 relative error = 7.1308381855901389726295647551018e-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) = 2.6125184917855830053731613470437 absolute error = 1.87822046071224426e-14 relative error = 7.1893097278272156308122694730954e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.3MB, time=31.81 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) = 2.6140707736448382213535311432771 absolute error = 1.89477310253940898e-14 relative error = 7.2483619098709866254734151833481e-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) = 2.6156264703860333771493202621097 absolute error = 1.91150022827457008e-14 relative error = 7.3080015434790686976128193057238e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.5717 Order of pole = 2.082 x[1] = 1.001 y[1] (analytic) = 2.6171855926507553250596950030027 y[1] (numeric) = 2.6171855926507746090995741476093 absolute error = 1.92840398791446066e-14 relative error = 7.3682355325872083170457925700501e-13 % h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 901 Total Elapsed Time = 31 Seconds Elapsed Time(since restart) = 31 Seconds Time to Timeout = 14 Minutes 28 Seconds Percent Done = 100.2 % > quit memory used=363.6MB, alloc=4.3MB, time=31.98