|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_hmin, > glob_disp_incr, > glob_clock_sec, > min_in_hour, > glob_html_log, > glob_log10relerr, > glob_max_sec, > glob_warned2, > glob_relerr, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > djd_debug, > glob_log10normmin, > MAX_UNCHANGED, > glob_start, > glob_small_float, > glob_max_iter, > glob_iter, > hours_in_day, > glob_warned, > glob_h, > glob_initial_pass, > sec_in_min, > glob_display_flag, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > glob_dump, > glob_max_minutes, > glob_current_iter, > glob_smallish_float, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_almost_1, > days_in_year, > glob_orig_start_sec, > glob_max_trunc_err, > glob_hmax, > djd_debug2, > glob_optimal_clock_start_sec, > glob_large_float, > glob_not_yet_start_msg, > years_in_century, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_subiter_method, > glob_percent_done, > glob_normmax, > glob_curr_iter_when_opt, > glob_look_poles, > glob_hmin_init, > glob_reached_optimal_h, > #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_last_rel_error, > array_type_pole, > array_y, > array_x, > array_norms, > array_m1, > array_tmp1_g, > array_tmp2_g, > array_pole, > array_1st_rel_error, > array_y_init, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_complex_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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel, glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour, glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float, glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h, glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt, glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes, glob_current_iter, glob_smallish_float, glob_optimal_start, glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year, glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2, glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg, years_in_century, glob_max_opt_iter, glob_optimal_expect_sec, glob_subiter_method, glob_percent_done, glob_normmax, glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init, glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error, array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g, array_tmp2_g, array_pole, array_1st_rel_error, array_y_init, array_y_higher_work, array_real_pole, array_y_higher, array_poles, array_y_set_initial, array_y_higher_work2, array_complex_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 > INFO, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_hmin, > glob_disp_incr, > glob_clock_sec, > min_in_hour, > glob_html_log, > glob_log10relerr, > glob_max_sec, > glob_warned2, > glob_relerr, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > djd_debug, > glob_log10normmin, > MAX_UNCHANGED, > glob_start, > glob_small_float, > glob_max_iter, > glob_iter, > hours_in_day, > glob_warned, > glob_h, > glob_initial_pass, > sec_in_min, > glob_display_flag, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > glob_dump, > glob_max_minutes, > glob_current_iter, > glob_smallish_float, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_almost_1, > days_in_year, > glob_orig_start_sec, > glob_max_trunc_err, > glob_hmax, > djd_debug2, > glob_optimal_clock_start_sec, > glob_large_float, > glob_not_yet_start_msg, > years_in_century, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_subiter_method, > glob_percent_done, > glob_normmax, > glob_curr_iter_when_opt, > glob_look_poles, > glob_hmin_init, > glob_reached_optimal_h, > #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_last_rel_error, > array_type_pole, > array_y, > array_x, > array_norms, > array_m1, > array_tmp1_g, > array_tmp2_g, > array_pole, > array_1st_rel_error, > array_y_init, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_complex_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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel, glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour, glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float, glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h, glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt, glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes, glob_current_iter, glob_smallish_float, glob_optimal_start, glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year, glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2, glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg, years_in_century, glob_max_opt_iter, glob_optimal_expect_sec, glob_subiter_method, glob_percent_done, glob_normmax, glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init, glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error, array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g, array_tmp2_g, array_pole, array_1st_rel_error, array_y_init, array_y_higher_work, array_real_pole, array_y_higher, array_poles, array_y_set_initial, array_y_higher_work2, array_complex_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 > INFO, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_hmin, > glob_disp_incr, > glob_clock_sec, > min_in_hour, > glob_html_log, > glob_log10relerr, > glob_max_sec, > glob_warned2, > glob_relerr, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > djd_debug, > glob_log10normmin, > MAX_UNCHANGED, > glob_start, > glob_small_float, > glob_max_iter, > glob_iter, > hours_in_day, > glob_warned, > glob_h, > glob_initial_pass, > sec_in_min, > glob_display_flag, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > glob_dump, > glob_max_minutes, > glob_current_iter, > glob_smallish_float, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_almost_1, > days_in_year, > glob_orig_start_sec, > glob_max_trunc_err, > glob_hmax, > djd_debug2, > glob_optimal_clock_start_sec, > glob_large_float, > glob_not_yet_start_msg, > years_in_century, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_subiter_method, > glob_percent_done, > glob_normmax, > glob_curr_iter_when_opt, > glob_look_poles, > glob_hmin_init, > glob_reached_optimal_h, > #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_last_rel_error, > array_type_pole, > array_y, > array_x, > array_norms, > array_m1, > array_tmp1_g, > array_tmp2_g, > array_pole, > array_1st_rel_error, > array_y_init, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_complex_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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel, glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour, glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float, glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h, glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt, glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes, glob_current_iter, glob_smallish_float, glob_optimal_start, glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year, glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2, glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg, years_in_century, glob_max_opt_iter, glob_optimal_expect_sec, glob_subiter_method, glob_percent_done, glob_normmax, glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init, glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error, array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g, array_tmp2_g, array_pole, array_1st_rel_error, array_y_init, array_y_higher_work, array_real_pole, array_y_higher, array_poles, array_y_set_initial, array_y_higher_work2, array_complex_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 > INFO, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_hmin, > glob_disp_incr, > glob_clock_sec, > min_in_hour, > glob_html_log, > glob_log10relerr, > glob_max_sec, > glob_warned2, > glob_relerr, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > djd_debug, > glob_log10normmin, > MAX_UNCHANGED, > glob_start, > glob_small_float, > glob_max_iter, > glob_iter, > hours_in_day, > glob_warned, > glob_h, > glob_initial_pass, > sec_in_min, > glob_display_flag, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > glob_dump, > glob_max_minutes, > glob_current_iter, > glob_smallish_float, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_almost_1, > days_in_year, > glob_orig_start_sec, > glob_max_trunc_err, > glob_hmax, > djd_debug2, > glob_optimal_clock_start_sec, > glob_large_float, > glob_not_yet_start_msg, > years_in_century, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_subiter_method, > glob_percent_done, > glob_normmax, > glob_curr_iter_when_opt, > glob_look_poles, > glob_hmin_init, > glob_reached_optimal_h, > #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_last_rel_error, > array_type_pole, > array_y, > array_x, > array_norms, > array_m1, > array_tmp1_g, > array_tmp2_g, > array_pole, > array_1st_rel_error, > array_y_init, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_complex_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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel, glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour, glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float, glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h, glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt, glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes, glob_current_iter, glob_smallish_float, glob_optimal_start, glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year, glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2, glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg, years_in_century, glob_max_opt_iter, glob_optimal_expect_sec, glob_subiter_method, glob_percent_done, glob_normmax, glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init, glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error, array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g, array_tmp2_g, array_pole, array_1st_rel_error, array_y_init, array_y_higher_work, array_real_pole, array_y_higher, array_poles, array_y_set_initial, array_y_higher_work2, array_complex_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 > INFO, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_hmin, > glob_disp_incr, > glob_clock_sec, > min_in_hour, > glob_html_log, > glob_log10relerr, > glob_max_sec, > glob_warned2, > glob_relerr, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > djd_debug, > glob_log10normmin, > MAX_UNCHANGED, > glob_start, > glob_small_float, > glob_max_iter, > glob_iter, > hours_in_day, > glob_warned, > glob_h, > glob_initial_pass, > sec_in_min, > glob_display_flag, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > glob_dump, > glob_max_minutes, > glob_current_iter, > glob_smallish_float, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_almost_1, > days_in_year, > glob_orig_start_sec, > glob_max_trunc_err, > glob_hmax, > djd_debug2, > glob_optimal_clock_start_sec, > glob_large_float, > glob_not_yet_start_msg, > years_in_century, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_subiter_method, > glob_percent_done, > glob_normmax, > glob_curr_iter_when_opt, > glob_look_poles, > glob_hmin_init, > glob_reached_optimal_h, > #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_last_rel_error, > array_type_pole, > array_y, > array_x, > array_norms, > array_m1, > array_tmp1_g, > array_tmp2_g, > array_pole, > array_1st_rel_error, > array_y_init, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_complex_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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel, glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour, glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float, glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h, glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt, glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes, glob_current_iter, glob_smallish_float, glob_optimal_start, glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year, glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2, glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg, years_in_century, glob_max_opt_iter, glob_optimal_expect_sec, glob_subiter_method, glob_percent_done, glob_normmax, glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init, glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error, array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g, array_tmp2_g, array_pole, array_1st_rel_error, array_y_init, array_y_higher_work, array_real_pole, array_y_higher, array_poles, array_y_set_initial, array_y_higher_work2, array_complex_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 > INFO, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_hmin, > glob_disp_incr, > glob_clock_sec, > min_in_hour, > glob_html_log, > glob_log10relerr, > glob_max_sec, > glob_warned2, > glob_relerr, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > djd_debug, > glob_log10normmin, > MAX_UNCHANGED, > glob_start, > glob_small_float, > glob_max_iter, > glob_iter, > hours_in_day, > glob_warned, > glob_h, > glob_initial_pass, > sec_in_min, > glob_display_flag, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > glob_dump, > glob_max_minutes, > glob_current_iter, > glob_smallish_float, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_almost_1, > days_in_year, > glob_orig_start_sec, > glob_max_trunc_err, > glob_hmax, > djd_debug2, > glob_optimal_clock_start_sec, > glob_large_float, > glob_not_yet_start_msg, > years_in_century, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_subiter_method, > glob_percent_done, > glob_normmax, > glob_curr_iter_when_opt, > glob_look_poles, > glob_hmin_init, > glob_reached_optimal_h, > #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_last_rel_error, > array_type_pole, > array_y, > array_x, > array_norms, > array_m1, > array_tmp1_g, > array_tmp2_g, > array_pole, > array_1st_rel_error, > array_y_init, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_complex_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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel, glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour, glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float, glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h, glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt, glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes, glob_current_iter, glob_smallish_float, glob_optimal_start, glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year, glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2, glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg, years_in_century, glob_max_opt_iter, glob_optimal_expect_sec, glob_subiter_method, glob_percent_done, glob_normmax, glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init, glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error, array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g, array_tmp2_g, array_pole, array_1st_rel_error, array_y_init, array_y_higher_work, array_real_pole, array_y_higher, array_poles, array_y_set_initial, array_y_higher_work2, array_complex_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) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 2.0 - log(abs(cos(x))); > end; exact_soln_y := proc(x) 2.0 - log(abs(cos(x))) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_hmin, > glob_disp_incr, > glob_clock_sec, > min_in_hour, > glob_html_log, > glob_log10relerr, > glob_max_sec, > glob_warned2, > glob_relerr, > glob_abserr, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > djd_debug, > glob_log10normmin, > MAX_UNCHANGED, > glob_start, > glob_small_float, > glob_max_iter, > glob_iter, > hours_in_day, > glob_warned, > glob_h, > glob_initial_pass, > sec_in_min, > glob_display_flag, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_start_sec, > centuries_in_millinium, > glob_dump, > glob_max_minutes, > glob_current_iter, > glob_smallish_float, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_almost_1, > days_in_year, > glob_orig_start_sec, > glob_max_trunc_err, > glob_hmax, > djd_debug2, > glob_optimal_clock_start_sec, > glob_large_float, > glob_not_yet_start_msg, > years_in_century, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_subiter_method, > glob_percent_done, > glob_normmax, > glob_curr_iter_when_opt, > glob_look_poles, > glob_hmin_init, > glob_reached_optimal_h, > #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_last_rel_error, > array_type_pole, > array_y, > array_x, > array_norms, > array_m1, > array_tmp1_g, > array_tmp2_g, > array_pole, > array_1st_rel_error, > array_y_init, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_complex_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > ALWAYS := 1; > glob_iolevel := 5; > glob_log10abserr := 0.0; > glob_hmin := 0.00000000001; > glob_disp_incr := 0.1; > glob_clock_sec := 0.0; > min_in_hour := 60.0; > glob_html_log := true; > glob_log10relerr := 0.0; > glob_max_sec := 10000.0; > glob_warned2 := false; > glob_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_last_good_h := 0.1; > djd_debug := true; > glob_log10normmin := 0.1; > MAX_UNCHANGED := 10; > glob_start := 0; > glob_small_float := 0.1e-50; > glob_max_iter := 1000; > glob_iter := 0; > hours_in_day := 24.0; > glob_warned := false; > glob_h := 0.1; > glob_initial_pass := true; > sec_in_min := 60.0; > glob_display_flag := true; > glob_unchanged_h_cnt := 0; > glob_no_eqs := 0; > glob_max_hours := 0.0; > glob_optimal_done := false; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > glob_dump := false; > glob_max_minutes := 0.0; > glob_current_iter := 0; > glob_smallish_float := 0.1e-100; > glob_optimal_start := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_dump_analytic := false; > glob_almost_1 := 0.9990; > days_in_year := 365.0; > glob_orig_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_hmax := 1.0; > djd_debug2 := true; > glob_optimal_clock_start_sec := 0.0; > glob_large_float := 9.0e100; > glob_not_yet_start_msg := true; > years_in_century := 100.0; > glob_max_opt_iter := 10; > glob_optimal_expect_sec := 0.1; > glob_subiter_method := 3; > glob_percent_done := 0.0; > glob_normmax := 0.0; > glob_curr_iter_when_opt := 0; > glob_look_poles := false; > glob_hmin_init := 0.001; > glob_reached_optimal_h := false; > #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 := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"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(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_tmp1_g:= Array(1..(max_terms + 1),[]); > array_tmp2_g:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..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_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_norms[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_tmp1_g[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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[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_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > 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_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > #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_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_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_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 > #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 := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = 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,"2012-06-13T13:26:46-05:00") > ; > 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," 090 ") > ; > logitem_str(html_log_file,"div diffeq.mxt") > ; > logitem_str(html_log_file,"div maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel, glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour, glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr, glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float, glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h, glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt, glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes, glob_current_iter, glob_smallish_float, glob_optimal_start, glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year, glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2, glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg, years_in_century, glob_max_opt_iter, glob_optimal_expect_sec, glob_subiter_method, glob_percent_done, glob_normmax, glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init, glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error, array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g, array_tmp2_g, array_pole, array_1st_rel_error, array_y_init, array_y_higher_work, array_real_pole, array_y_higher, array_poles, array_y_set_initial, array_y_higher_work2, array_complex_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; ALWAYS := 1; glob_iolevel := 5; glob_log10abserr := 0.; glob_hmin := 0.1*10^(-10); glob_disp_incr := 0.1; glob_clock_sec := 0.; min_in_hour := 60.0; glob_html_log := true; glob_log10relerr := 0.; glob_max_sec := 10000.0; glob_warned2 := false; glob_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; djd_debug := true; glob_log10normmin := 0.1; MAX_UNCHANGED := 10; glob_start := 0; glob_small_float := 0.1*10^(-50); glob_max_iter := 1000; glob_iter := 0; hours_in_day := 24.0; glob_warned := false; glob_h := 0.1; glob_initial_pass := true; sec_in_min := 60.0; glob_display_flag := true; glob_unchanged_h_cnt := 0; glob_no_eqs := 0; glob_max_hours := 0.; glob_optimal_done := false; glob_not_yet_finished := true; glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; glob_dump := false; glob_max_minutes := 0.; glob_current_iter := 0; glob_smallish_float := 0.1*10^(-100); glob_optimal_start := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_dump_analytic := false; glob_almost_1 := 0.9990; days_in_year := 365.0; glob_orig_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_hmax := 1.0; djd_debug2 := true; glob_optimal_clock_start_sec := 0.; glob_large_float := 0.90*10^101; glob_not_yet_start_msg := true; years_in_century := 100.0; glob_max_opt_iter := 10; glob_optimal_expect_sec := 0.1; glob_subiter_method := 3; glob_percent_done := 0.; glob_normmax := 0.; glob_curr_iter_when_opt := 0; glob_look_poles := false; glob_hmin_init := 0.001; glob_reached_optimal_h := false; 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 := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "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(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_tmp1_g := Array(1 .. max_terms + 1, []); array_tmp2_g := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); 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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_norms[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_tmp1_g[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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; 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_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_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_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_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_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; 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 := 0.0001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = 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, "2012-06-13T13:26:46-05:00"); 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, " 090 "); logitem_str(html_log_file, "div diffeq.mxt"); logitem_str(html_log_file, "div maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/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 := 0.0001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 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 = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 2.0050183941408128764996479973735 y[1] (numeric) = 2.0050183941408128764996488429212 absolute error = 8.455477e-25 relative error = 4.2171568224556497595801630406164e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002 y[1] (analytic) = 2.0050284427592637190410951908048 y[1] (numeric) = 2.005028442759263719041096882039 absolute error = 1.6912342e-24 relative error = 8.4349636340947417548906943320370e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003 y[1] (analytic) = 2.0050385014787908383875034755221 y[1] (numeric) = 2.0050385014787908383875060125819 absolute error = 2.5370598e-24 relative error = 1.2653421857629285264440372393537e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004 y[1] (analytic) = 2.0050485702995974443703038670178 y[1] (numeric) = 2.0050485702995974443703072500424 absolute error = 3.3830246e-24 relative error = 1.6872531918239283628545282485996e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005 y[1] (analytic) = 2.0050586492218869549848330096909 y[1] (numeric) = 2.0050586492218869549848372388197 absolute error = 4.2291288e-24 relative error = 2.1092294739813316526353744856184e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.18 NO POLE x[1] = 0.1006 y[1] (analytic) = 2.0050687382458629964068540899123 y[1] (numeric) = 2.0050687382458629964068591652848 absolute error = 5.0753725e-24 relative error = 2.5312710747463931128553927210262e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007 y[1] (analytic) = 2.0050788373717294030090951541011 y[1] (numeric) = 2.0050788373717294030091010758569 absolute error = 5.9217558e-24 relative error = 2.9533780366273660618085390784161e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008 y[1] (analytic) = 2.0050889465996902173778048346799 y[1] (numeric) = 2.0050889465996902173778116029589 absolute error = 6.7682790e-24 relative error = 3.3755505018756985286179938588279e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009 y[1] (analytic) = 2.0050990659299496903293254867837 y[1] (numeric) = 2.0050990659299496903293331017259 absolute error = 7.6149422e-24 relative error = 3.7977885129921237823761615316473e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 2.0051091953627122809266837385959 y[1] (numeric) = 2.0051091953627122809266922003413 absolute error = 8.4617454e-24 relative error = 4.2200920626017680709170152108229e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1011 y[1] (analytic) = 2.0051193348981826564961984581912 y[1] (numeric) = 2.0051193348981826564962077668802 absolute error = 9.3086890e-24 relative error = 4.6424613428171261842850520940584e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1012 y[1] (analytic) = 2.0051294845365656926441061397678 y[1] (numeric) = 2.0051294845365656926441162955408 absolute error = 1.01557730e-23 relative error = 5.0648963462562851546002172858984e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1013 y[1] (analytic) = 2.0051396442780664732732037121527 y[1] (numeric) = 2.0051396442780664732732147151502 absolute error = 1.10029975e-23 relative error = 5.4873971154071595607378953802243e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1014 y[1] (analytic) = 2.0051498141228902905995087724693 y[1] (numeric) = 2.005149814122890290599520622832 absolute error = 1.18503627e-23 relative error = 5.9099637426262269489635762946320e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.39 NO POLE x[1] = 0.1015 y[1] (analytic) = 2.0051599940712426451689372478581 y[1] (numeric) = 2.005159994071242645168949945727 absolute error = 1.26978689e-23 relative error = 6.3325963701372595227452015562111e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1016 y[1] (analytic) = 2.0051701841233292458739984881456 y[1] (numeric) = 2.0051701841233292458740120336618 absolute error = 1.35455162e-23 relative error = 6.7552950404168160905633294285734e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1017 y[1] (analytic) = 2.0051803842793560099705077923581 y[1] (numeric) = 2.0051803842793560099705221856626 absolute error = 1.43933045e-23 relative error = 7.1780596961967716336588471875686e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1018 y[1] (analytic) = 2.0051905945395290630943163719814 y[1] (numeric) = 2.0051905945395290630943316132156 absolute error = 1.52412342e-23 relative error = 7.6008905295608516373798487387212e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1019 y[1] (analytic) = 2.0052008149040547392780587538716 y[1] (numeric) = 2.0052008149040547392780748431771 absolute error = 1.60893055e-23 relative error = 8.0237876328460620520997061363609e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 2.0052110453731395809679176257221 y[1] (numeric) = 2.0052110453731395809679345632405 absolute error = 1.69375184e-23 relative error = 8.4467509986452238356911610953498e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1021 y[1] (analytic) = 2.0052212859469903390404061269981 y[1] (numeric) = 2.0052212859469903390404239128712 absolute error = 1.77858731e-23 relative error = 8.8697807192887459048823597493689e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1022 y[1] (analytic) = 2.0052315366258139728191675882519 y[1] (numeric) = 2.0052315366258139728191862226217 absolute error = 1.86343698e-23 relative error = 9.2928768871029703356723345556365e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1023 y[1] (analytic) = 2.0052417974098176500917927217353 y[1] (numeric) = 2.0052417974098176500918122047438 absolute error = 1.94830085e-23 relative error = 9.7160394946715722812627204659171e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=0.61 NO POLE x[1] = 0.1024 y[1] (analytic) = 2.0052520682992087471266542662285 y[1] (numeric) = 2.005252068299208747126674598018 absolute error = 2.03317895e-23 relative error = 1.0139268684183320398513105211256e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1025 y[1] (analytic) = 2.0052623492941948486897590890093 y[1] (numeric) = 2.0052623492941948486897802697222 absolute error = 2.11807129e-23 relative error = 1.0562564498084309234547077953318e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1026 y[1] (analytic) = 2.005272640394983748061617747887 y[1] (numeric) = 2.0052726403949837480616397776659 absolute error = 2.20297789e-23 relative error = 1.0985927028686102936246181199963e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1027 y[1] (analytic) = 2.0052829416017834470541315162315 y[1] (numeric) = 2.0052829416017834470541543952192 absolute error = 2.28789877e-23 relative error = 1.1409356368296177609590366011963e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1028 y[1] (analytic) = 2.005293252914802156027496873929 y[1] (numeric) = 2.0052932529148021560275206022683 absolute error = 2.37283393e-23 relative error = 1.1832852509481880514686237426463e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1029 y[1] (analytic) = 2.0053035743342482939071274672 y[1] (numeric) = 2.0053035743342482939071520450339 absolute error = 2.45778339e-23 relative error = 1.2256415544544037208612364897635e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 2.0053139058603304882005935402182 y[1] (numeric) = 2.00531390586033048820061896769 absolute error = 2.54274718e-23 relative error = 1.2680045615646878070735127981650e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1031 y[1] (analytic) = 2.0053242474932575750145788414723 y[1] (numeric) = 2.0053242474932575750146051187252 absolute error = 2.62772529e-23 relative error = 1.3103742665480511526079407789594e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1032 y[1] (analytic) = 2.0053345992332385990718550078141 y[1] (numeric) = 2.0053345992332385990718821349917 absolute error = 2.71271776e-23 relative error = 1.3527506886068973293049137152377e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1033 y[1] (analytic) = 2.0053449610804828137282734291436 y[1] (numeric) = 2.0053449610804828137283014063895 absolute error = 2.79772459e-23 relative error = 1.3951338269963198137638733889834e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.0MB, time=0.82 NO POLE x[1] = 0.1034 y[1] (analytic) = 2.0053553330351996809897745966794 y[1] (numeric) = 2.0053553330351996809898034241374 absolute error = 2.88274580e-23 relative error = 1.4375236909445013676603667638772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1035 y[1] (analytic) = 2.005365715097598871529414937771 y[1] (numeric) = 2.005365715097598871529444615585 absolute error = 2.96778140e-23 relative error = 1.4799202846925910719783661125790e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1036 y[1] (analytic) = 2.0053761072678902647044111402085 y[1] (numeric) = 2.0053761072678902647044416685227 absolute error = 3.05283142e-23 relative error = 1.5223236224546203401110202368679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1037 y[1] (analytic) = 2.0053865095462839485732019689931 y[1] (numeric) = 2.0053865095462839485732333479517 absolute error = 3.13789586e-23 relative error = 1.5647337034843945357343456412184e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1038 y[1] (analytic) = 2.0053969219329902199125275785286 y[1] (numeric) = 2.0053969219329902199125598082761 absolute error = 3.22297475e-23 relative error = 1.6071505419951446421869778620905e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1039 y[1] (analytic) = 2.0054073444282195842345263232045 y[1] (numeric) = 2.0054073444282195842345594038854 absolute error = 3.30806809e-23 relative error = 1.6495741372400299980087471390276e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 2.0054177770321827558038490693382 y[1] (numeric) = 2.0054177770321827558038830010972 absolute error = 3.39317590e-23 relative error = 1.6920044984449874218939522482512e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1041 y[1] (analytic) = 2.0054282197450906576547910114508 y[1] (numeric) = 2.0054282197450906576548257944328 absolute error = 3.47829820e-23 relative error = 1.7344416348355392029299739378821e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1042 y[1] (analytic) = 2.0054386725671544216084409958533 y[1] (numeric) = 2.0054386725671544216084766302033 absolute error = 3.56343500e-23 relative error = 1.7768855506503524248666244843780e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.1MB, time=1.04 NO POLE x[1] = 0.1043 y[1] (analytic) = 2.0054491354985853882898483545216 y[1] (numeric) = 2.0054491354985853882898848403848 absolute error = 3.64858632e-23 relative error = 1.8193362551141969137073573933375e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1044 y[1] (analytic) = 2.0054596085395951071452072522444 y[1] (numeric) = 2.0054596085395951071452445897661 absolute error = 3.73375217e-23 relative error = 1.8617937524650385282934853637427e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1045 y[1] (analytic) = 2.005470091690395336459058550029 y[1] (numeric) = 2.0054700916903953364590967393547 absolute error = 3.81893257e-23 relative error = 1.9042580519268931453413838118852e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1046 y[1] (analytic) = 2.0054805849511980433715091877551 y[1] (numeric) = 2.0054805849511980433715482290305 absolute error = 3.90412754e-23 relative error = 1.9467291627233599931193767439325e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1047 y[1] (analytic) = 2.0054910883222154038954690890679 y[1] (numeric) = 2.0054910883222154038955089824387 absolute error = 3.98933708e-23 relative error = 1.9892070841050014359193096610952e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1048 y[1] (analytic) = 2.0055016018036598029339055915065 y[1] (numeric) = 2.0055016018036598029339463371187 absolute error = 4.07456122e-23 relative error = 2.0316918302810225201380567118235e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1049 y[1] (analytic) = 2.0055121253957438342971154048667 y[1] (numeric) = 2.0055121253957438342971570028665 absolute error = 4.15979998e-23 relative error = 2.0741834104738482715997599288970e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 2.0055226590986803007200141007995 y[1] (numeric) = 2.005522659098680300720056551333 absolute error = 4.24505335e-23 relative error = 2.1166818189467911674079690400622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1051 y[1] (analytic) = 2.0055332029126822138794431366493 y[1] (numeric) = 2.005533202912682213879486439863 absolute error = 4.33032137e-23 relative error = 2.1591870748940851293399765863293e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=1.26 NO POLE x[1] = 0.1052 y[1] (analytic) = 2.0055437568379627944114944165428 y[1] (numeric) = 2.0055437568379627944115385725833 absolute error = 4.41560405e-23 relative error = 2.2016991825507984581395639998991e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1053 y[1] (analytic) = 2.005554320874735471928852392737 y[1] (numeric) = 2.005554320874735471928897401751 absolute error = 4.50090140e-23 relative error = 2.2442181461516847775106444306250e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1054 y[1] (analytic) = 2.0055648950232138850381537102422 y[1] (numeric) = 2.0055648950232138850381995723766 absolute error = 4.58621344e-23 relative error = 2.2867439749173091645357000195837e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1055 y[1] (analytic) = 2.0055754792836118813573643977379 y[1] (numeric) = 2.0055754792836118813574111131397 absolute error = 4.67154018e-23 relative error = 2.3292766730817162431738485740254e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1056 y[1] (analytic) = 2.0055860736561435175331746078019 y[1] (numeric) = 2.0055860736561435175332221766183 absolute error = 4.75688164e-23 relative error = 2.3718162498647088196405854190933e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1057 y[1] (analytic) = 2.005596678141023059258410909477 y[1] (numeric) = 2.0055966781410230592584593318553 absolute error = 4.84223783e-23 relative error = 2.4143627094996211319746399206285e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1058 y[1] (analytic) = 2.0056072927384649812894661362023 y[1] (numeric) = 2.00560729273846498128951541229 absolute error = 4.92760877e-23 relative error = 2.4569160612054922299475252127801e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1059 y[1] (analytic) = 2.0056179174486839674637467921395 y[1] (numeric) = 2.0056179174486839674637969220843 absolute error = 5.01299448e-23 relative error = 2.4994763142009391267133659510289e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 2.0056285522718949107171380199288 y[1] (numeric) = 2.0056285522718949107171890038784 absolute error = 5.09839496e-23 relative error = 2.5420434677322200977032481403428e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1061 y[1] (analytic) = 2.0056391972083129131014861329089 y[1] (numeric) = 2.0056391972083129131015379710114 absolute error = 5.18381025e-23 relative error = 2.5846175409891487031918785804247e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=1.48 NO POLE x[1] = 0.1062 y[1] (analytic) = 2.0056498522581532858020987148442 y[1] (numeric) = 2.0056498522581532858021514072476 absolute error = 5.26924034e-23 relative error = 2.6271985282313276223264941916942e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1063 y[1] (analytic) = 2.005660517421631549155262290199 y[1] (numeric) = 2.0056605174216315491553158370516 absolute error = 5.35468526e-23 relative error = 2.6697864436618082988593594462356e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1064 y[1] (analytic) = 2.0056711926989634326657775680081 y[1] (numeric) = 2.0056711926989634326658319694584 absolute error = 5.44014503e-23 relative error = 2.7123812964972499132858014340745e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1065 y[1] (analytic) = 2.0056818780903648750245122623911 y[1] (numeric) = 2.0056818780903648750245675185877 absolute error = 5.52561966e-23 relative error = 2.7549830909680514634883825440335e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1066 y[1] (analytic) = 2.0056925735960520241259714927643 y[1] (numeric) = 2.0056925735960520241260276038558 absolute error = 5.61110915e-23 relative error = 2.7975918263184842182913114843393e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1067 y[1] (analytic) = 2.0057032792162412370858857668053 y[1] (numeric) = 2.0057032792162412370859427329407 absolute error = 5.69661354e-23 relative error = 2.8402075217357362718452366854708e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1068 y[1] (analytic) = 2.0057139949511490802588165492306 y[1] (numeric) = 2.005713994951149080258874370559 absolute error = 5.78213284e-23 relative error = 2.8828301814490898568125266599077e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1069 y[1] (analytic) = 2.005724720800992329255779419447 y[1] (numeric) = 2.0057247208009923292558380961175 absolute error = 5.86766705e-23 relative error = 2.9254598047017783860627519062753e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 2.0057354567659879689618848211429 y[1] (numeric) = 2.0057354567659879689619443533049 absolute error = 5.95321620e-23 relative error = 2.9680964056939290913743695345216e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=1.70 NO POLE x[1] = 0.1071 y[1] (analytic) = 2.0057462028463531935539964068893 y[1] (numeric) = 2.0057462028463531935540567946922 absolute error = 6.03878029e-23 relative error = 3.0107399836681084738066922227149e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1072 y[1] (analytic) = 2.0057569590423054065184069808196 y[1] (numeric) = 2.0057569590423054065184682244131 absolute error = 6.12435935e-23 relative error = 3.0533905528236160896716766655805e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1073 y[1] (analytic) = 2.0057677253540622206685320424664 y[1] (numeric) = 2.0057677253540622206685941420004 absolute error = 6.20995340e-23 relative error = 3.0960481223735945429552497520204e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1074 y[1] (analytic) = 2.0057785017818414581626209348313 y[1] (numeric) = 2.0057785017818414581626838904558 absolute error = 6.29556245e-23 relative error = 3.1387126965451626847303604890140e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1075 y[1] (analytic) = 2.00578928832586115052148559977 y[1] (numeric) = 2.0057892883258611505215494116351 absolute error = 6.38118651e-23 relative error = 3.1813842795651177385338310495096e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1076 y[1] (analytic) = 2.0058000849863395386462469437773 y[1] (numeric) = 2.0058000849863395386463116120333 absolute error = 6.46682560e-23 relative error = 3.2240628806454767830878456104484e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1077 y[1] (analytic) = 2.0058108917634950728360988172598 y[1] (numeric) = 2.0058108917634950728361643420571 absolute error = 6.55247973e-23 relative error = 3.2667485040123125011947612450789e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1078 y[1] (analytic) = 2.0058217086575464128060896103868 y[1] (numeric) = 2.005821708657546412806155991876 absolute error = 6.63814892e-23 relative error = 3.3094411588768630664294767950018e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1079 y[1] (analytic) = 2.0058325356687124277049214686148 y[1] (numeric) = 2.0058325356687124277049887069467 absolute error = 6.72383319e-23 relative error = 3.3521408544499362960088456713451e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=34.3MB, alloc=4.1MB, time=1.91 x[1] = 0.108 y[1] (analytic) = 2.0058433727972121961327671309818 y[1] (numeric) = 2.0058433727972121961328352263073 absolute error = 6.80953255e-23 relative error = 3.3948475949564750429021562862716e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1081 y[1] (analytic) = 2.0058542200432650061591043942728 y[1] (numeric) = 2.005854220043265006159173346743 absolute error = 6.89524702e-23 relative error = 3.4375613896065058433341058376517e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1082 y[1] (analytic) = 2.0058650774070903553405682061597 y[1] (numeric) = 2.0058650774070903553406380159257 absolute error = 6.98097660e-23 relative error = 3.4802822376388632181137113102745e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1083 y[1] (analytic) = 2.005875944888907950738820390423 y[1] (numeric) = 2.0058759448889079507388910576363 absolute error = 7.06672133e-23 relative error = 3.5230101582335783073793832511571e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1084 y[1] (analytic) = 2.0058868224889377089384370073665 y[1] (numeric) = 2.0058868224889377089385085321786 absolute error = 7.15248121e-23 relative error = 3.5657451506287291095196432882547e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1085 y[1] (analytic) = 2.0058977102073997560648133525357 y[1] (numeric) = 2.0058977102073997560648857350982 absolute error = 7.23825625e-23 relative error = 3.6084872190474760704555352208478e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1086 y[1] (analytic) = 2.0059086080445144278020865968595 y[1] (numeric) = 2.0059086080445144278021598373244 absolute error = 7.32404649e-23 relative error = 3.6512363826684706572909589573984e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1087 y[1] (analytic) = 2.005919516000502269411076071334 y[1] (numeric) = 2.0059195160005022694111501698532 absolute error = 7.40985192e-23 relative error = 3.6939926357434894314544999785867e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1088 y[1] (analytic) = 2.0059304340755840357472411993701 y[1] (numeric) = 2.0059304340755840357473161560957 absolute error = 7.49567256e-23 relative error = 3.7367559874798534024653046232187e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1089 y[1] (analytic) = 2.0059413622699806912786570799332 y[1] (numeric) = 2.0059413622699806912787328950176 absolute error = 7.58150844e-23 relative error = 3.7795264520696397284639412512021e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=2.14 NO POLE x[1] = 0.109 y[1] (analytic) = 2.0059523005839134101040077246038 y[1] (numeric) = 2.0059523005839134101040843981995 absolute error = 7.66735957e-23 relative error = 3.8223040337340551005166193173371e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1091 y[1] (analytic) = 2.0059632490176035759705969516906 y[1] (numeric) = 2.0059632490176035759706744839502 absolute error = 7.75322596e-23 relative error = 3.8650887366939794901449408030246e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1092 y[1] (analytic) = 2.0059742075712727822923769405337 y[1] (numeric) = 2.00597420757127278229245533161 absolute error = 7.83910763e-23 relative error = 3.9078805701550748772021424293465e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1093 y[1] (analytic) = 2.0059851762451428321679944491357 y[1] (numeric) = 2.0059851762451428321680736991816 absolute error = 7.92500459e-23 relative error = 3.9506795383374853159851087778558e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1094 y[1] (analytic) = 2.0059961550394357383988546982636 y[1] (numeric) = 2.0059961550394357383989348074322 absolute error = 8.01091686e-23 relative error = 3.9934856504460817097575285354616e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1095 y[1] (analytic) = 2.006007143954373723507202925167 y[1] (numeric) = 2.0060071439543737235072838936116 absolute error = 8.09684446e-23 relative error = 4.0362989156852979235125966385899e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1096 y[1] (analytic) = 2.0060181429901792197542236100613 y[1] (numeric) = 2.0060181429901792197543054379352 absolute error = 8.18278739e-23 relative error = 4.0791193332891307427066129248265e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1097 y[1] (analytic) = 2.0060291521470748691581573785274 y[1] (numeric) = 2.0060291521470748691582400659842 absolute error = 8.26874568e-23 relative error = 4.1219469174462750760860921724802e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1098 y[1] (analytic) = 2.006040171425283523512435582984 y[1] (numeric) = 2.0060401714252835235125191301775 absolute error = 8.35471935e-23 relative error = 4.1647816773599330746364879231201e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=2.35 NO POLE x[1] = 0.1099 y[1] (analytic) = 2.0060512008250282444038325663905 y[1] (numeric) = 2.0060512008250282444039169734745 absolute error = 8.44070840e-23 relative error = 4.2076236122630328069704889563164e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 2.0060622403465323032306356113409 y[1] (numeric) = 2.0060622403465323032307208784695 absolute error = 8.52671286e-23 relative error = 4.2504727363429530944443948500456e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1101 y[1] (analytic) = 2.0060732899900191812208325777162 y[1] (numeric) = 2.0060732899900191812209187050435 absolute error = 8.61273273e-23 relative error = 4.2933290488319352176787752285910e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1102 y[1] (analytic) = 2.0060843497557125694503172320603 y[1] (numeric) = 2.0060843497557125694504042197408 absolute error = 8.69876805e-23 relative error = 4.3361925689013412327480332055301e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1103 y[1] (analytic) = 2.0060954196438363688611122718535 y[1] (numeric) = 2.0060954196438363688612001200416 absolute error = 8.78481881e-23 relative error = 4.3790632907978340744317952845702e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1104 y[1] (analytic) = 2.0061064996546146902796100478556 y[1] (numeric) = 2.0061064996546146902796987567059 absolute error = 8.87088503e-23 relative error = 4.4219412237223066368214693659055e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1105 y[1] (analytic) = 2.0061175897882718544348309876978 y[1] (numeric) = 2.0061175897882718544349205573652 absolute error = 8.95696674e-23 relative error = 4.4648263818599633584298780850553e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1106 y[1] (analytic) = 2.0061286900450323919766997239048 y[1] (numeric) = 2.0061286900450323919767901545442 absolute error = 9.04306394e-23 relative error = 4.5077187644412815020750017997037e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1107 y[1] (analytic) = 2.006139800425121043494338929529 y[1] (numeric) = 2.0061398004251210434944302212956 absolute error = 9.12917666e-23 relative error = 4.5506183856506093759506136546679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1108 y[1] (analytic) = 2.006150920928762759534380864587 y[1] (numeric) = 2.0061509209287627595344730176361 absolute error = 9.21530491e-23 relative error = 4.5935252497024026552775703367907e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=2.57 NO POLE x[1] = 0.1109 y[1] (analytic) = 2.006162051556182700619296636487 y[1] (numeric) = 2.006162051556182700619389650974 absolute error = 9.30144870e-23 relative error = 4.6364393608107845895279834183504e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 2.0061731923076062372657431776415 y[1] (numeric) = 2.006173192307606237265837053722 absolute error = 9.38760805e-23 relative error = 4.6793607281741602763861767760628e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1111 y[1] (analytic) = 2.0061843431832589500029279434632 y[1] (numeric) = 2.006184343183258950003022681293 absolute error = 9.47378298e-23 relative error = 4.7222893609904910967072007726098e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1112 y[1] (analytic) = 2.0061955041833666293909913339431 y[1] (numeric) = 2.0061955041833666293910869336781 absolute error = 9.55997350e-23 relative error = 4.7652252634727351602858571344620e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1113 y[1] (analytic) = 2.0062066753081552760394068420149 y[1] (numeric) = 2.0062066753081552760395033038112 absolute error = 9.64617963e-23 relative error = 4.8081684448180482330630909911977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1114 y[1] (analytic) = 2.0062178565578511006253989319133 y[1] (numeric) = 2.0062178565578511006254962559271 absolute error = 9.73240138e-23 relative error = 4.8511189092386375297103034592508e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1115 y[1] (analytic) = 2.0062290479326805239123786507344 y[1] (numeric) = 2.006229047932680523912476837122 absolute error = 9.81863876e-23 relative error = 4.8940766609463759876472316415333e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1116 y[1] (analytic) = 2.006240249432870176768396976413 y[1] (numeric) = 2.0062402494328701767684960253311 absolute error = 9.90489181e-23 relative error = 4.9370417191061457357580768001503e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1117 y[1] (analytic) = 2.0062514610586469001846159053331 y[1] (numeric) = 2.0062514610586469001847158169383 absolute error = 9.99116052e-23 relative error = 4.9800140779600596694353731209562e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=2.79 NO POLE x[1] = 0.1118 y[1] (analytic) = 2.0062626828102377452937972827898 y[1] (numeric) = 2.006262682810237745293898057239 absolute error = 1.007744492e-22 relative error = 5.0229937516876869606288857129020e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1119 y[1] (analytic) = 2.0062739146878699733888093795282 y[1] (numeric) = 2.0062739146878699733889110169784 absolute error = 1.016374502e-22 relative error = 5.0659807444993096591161874301749e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 2.0062851566917710559411512175826 y[1] (numeric) = 2.0062851566917710559412537181909 absolute error = 1.025006083e-22 relative error = 5.1089750606048739202994727889643e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1121 y[1] (analytic) = 2.0062964088221686746194946486475 y[1] (numeric) = 2.0062964088221686746195980125713 absolute error = 1.033639238e-22 relative error = 5.1519767141826065280130768158197e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1122 y[1] (analytic) = 2.0063076710792907213082441882121 y[1] (numeric) = 2.006307671079290721308348415609 absolute error = 1.042273969e-22 relative error = 5.1949857144258936721760391631116e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1123 y[1] (analytic) = 2.006318943463365298126114608695 y[1] (numeric) = 2.0063189434633652981262196997225 absolute error = 1.050910275e-22 relative error = 5.2380020555749154464985421628579e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1124 y[1] (analytic) = 2.0063302259746207174447262948164 y[1] (numeric) = 2.0063302259746207174448322496324 absolute error = 1.059548160e-22 relative error = 5.2810257567908607308512299752664e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1125 y[1] (analytic) = 2.0063415186132855019072183644532 y[1] (numeric) = 2.0063415186132855019073251832155 absolute error = 1.068187623e-22 relative error = 5.3240568123132629834149279807451e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1126 y[1] (analytic) = 2.0063528213795883844468795582191 y[1] (numeric) = 2.0063528213795883844469872410859 absolute error = 1.076828668e-22 relative error = 5.3670952413023835692463648771417e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1127 y[1] (analytic) = 2.006364134273758308305796901022 y[1] (numeric) = 2.0063641342737583083059054481516 absolute error = 1.085471296e-22 relative error = 5.4101410479653883899687194394592e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=3.00 NO POLE x[1] = 0.1128 y[1] (analytic) = 2.006375457296024427053522138848 y[1] (numeric) = 2.0063754572960244270536315503988 absolute error = 1.094115508e-22 relative error = 5.4531942365091048362668558806387e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1129 y[1] (analytic) = 2.0063867904466161046057559540291 y[1] (numeric) = 2.0063867904466161046058662301598 absolute error = 1.102761307e-22 relative error = 5.4962548211081892549123364541933e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 2.0063981337257629152430499622528 y[1] (numeric) = 2.0063981337257629152431611031221 absolute error = 1.111408693e-22 relative error = 5.5393228009845665737993107949640e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1131 y[1] (analytic) = 2.0064094871336946436295264945746 y[1] (numeric) = 2.0064094871336946436296385003414 absolute error = 1.120057668e-22 relative error = 5.5823981853279899608122511750028e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1132 y[1] (analytic) = 2.0064208506706412848316161677002 y[1] (numeric) = 2.0064208506706412848317290385235 absolute error = 1.128708233e-22 relative error = 5.6254809783437608360617480160426e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1133 y[1] (analytic) = 2.0064322243368330443368132458039 y[1] (numeric) = 2.006432224336833044336926981843 absolute error = 1.137360391e-22 relative error = 5.6685711942047826219601415487914e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1134 y[1] (analytic) = 2.0064436081325003380724487971565 y[1] (numeric) = 2.0064436081325003380725633985708 absolute error = 1.146014143e-22 relative error = 5.7116688371155068855163782184017e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1135 y[1] (analytic) = 2.0064550020578737924244816488361 y[1] (numeric) = 2.0064550020578737924245971157851 absolute error = 1.154669490e-22 relative error = 5.7547739112800444498624028126691e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1136 y[1] (analytic) = 2.006466406113184244256307142801 y[1] (numeric) = 2.0064664061131842442564234754444 absolute error = 1.163326434e-22 relative error = 5.7978864258860512447583862291753e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=3.22 NO POLE x[1] = 0.1137 y[1] (analytic) = 2.0064778202986627409275836966056 y[1] (numeric) = 2.0064778202986627409277008951032 absolute error = 1.171984976e-22 relative error = 5.8410063851368708492573840574587e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1138 y[1] (analytic) = 2.0064892446145405403130771720435 y[1] (numeric) = 2.0064892446145405403131952365554 absolute error = 1.180645119e-22 relative error = 5.8841338032031639603970316219829e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1139 y[1] (analytic) = 2.0065006790610491108215230550071 y[1] (numeric) = 2.0065006790610491108216419856935 absolute error = 1.189306864e-22 relative error = 5.9272686842874203269701430923258e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 2.0065121236384201314145064498531 y[1] (numeric) = 2.0065121236384201314146262468744 absolute error = 1.197970213e-22 relative error = 5.9704110375755598665736998710545e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1141 y[1] (analytic) = 2.0065235783468854916253598915696 y[1] (numeric) = 2.0065235783468854916254805550861 absolute error = 1.206635165e-22 relative error = 6.0135608573018138666476410555330e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1142 y[1] (analytic) = 2.0065350431866772915780789790412 y[1] (numeric) = 2.0065350431866772915782005092136 absolute error = 1.215301724e-22 relative error = 6.0567181626188764536571062648421e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1143 y[1] (analytic) = 2.006546518158027842006255832715 y[1] (numeric) = 2.0065465181580278420063782297042 absolute error = 1.223969892e-22 relative error = 6.0998829627113826318538376823497e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1144 y[1] (analytic) = 2.0065580032611696642720303799694 y[1] (numeric) = 2.0065580032611696642721536439364 absolute error = 1.232639670e-22 relative error = 6.1430552617798511352958016534296e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1145 y[1] (analytic) = 2.0065694984963354903850594714949 y[1] (numeric) = 2.0065694984963354903851836026007 absolute error = 1.241311058e-22 relative error = 6.1862350590408266977123779385828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=61.0MB, alloc=4.1MB, time=3.45 x[1] = 0.1146 y[1] (analytic) = 2.0065810038637582630215038319959 y[1] (numeric) = 2.0065810038637582630216288304019 absolute error = 1.249984060e-22 relative error = 6.2294223736450299439583977287705e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1147 y[1] (analytic) = 2.0065925193636711355430328485301 y[1] (numeric) = 2.0065925193636711355431587143977 absolute error = 1.258658676e-22 relative error = 6.2726172048082026056335737353725e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1148 y[1] (analytic) = 2.0066040449963074720158471997996 y[1] (numeric) = 2.0066040449963074720159739332904 absolute error = 1.267334908e-22 relative error = 6.3158195617129443893224508677931e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1149 y[1] (analytic) = 2.0066155807619008472297193297164 y[1] (numeric) = 2.0066155807619008472298469309921 absolute error = 1.276012757e-22 relative error = 6.3590294485578797686724910673497e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 2.0066271266606850467170517685652 y[1] (numeric) = 2.0066271266606850467171802377878 absolute error = 1.284692226e-22 relative error = 6.4022468795082615769034437417154e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1151 y[1] (analytic) = 2.006638682692894066771953305091 y[1] (numeric) = 2.0066386826928940667720826424226 absolute error = 1.293373316e-22 relative error = 6.4454718587618509745833356003713e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1152 y[1] (analytic) = 2.0066502488587621144693330128412 y[1] (numeric) = 2.006650248858762114469463218444 absolute error = 1.302056028e-22 relative error = 6.4887043905160629155310482779582e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1153 y[1] (analytic) = 2.0066618251585236076840121340961 y[1] (numeric) = 2.0066618251585236076841432081325 absolute error = 1.310740364e-22 relative error = 6.5319444839513666410693523116250e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1154 y[1] (analytic) = 2.006673411592413175109853824725 y[1] (numeric) = 2.0066734115924131751099857673575 absolute error = 1.319426325e-22 relative error = 6.5751921432643976690691165525015e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1155 y[1] (analytic) = 2.0066850081606656562789107633069 y[1] (numeric) = 2.0066850081606656562790435746983 absolute error = 1.328113914e-22 relative error = 6.6184473826181307712865609901167e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.1MB, time=3.67 NO POLE x[1] = 0.1156 y[1] (analytic) = 2.0066966148635161015805906278612 y[1] (numeric) = 2.0066966148635161015807243081743 absolute error = 1.336803131e-22 relative error = 6.6617102012250198460635459718382e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1157 y[1] (analytic) = 2.0067082317011997722808394435325 y[1] (numeric) = 2.0067082317011997722809739929303 absolute error = 1.345493978e-22 relative error = 6.7049806082638573302079304130271e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1158 y[1] (analytic) = 2.0067198586739521405413428045815 y[1] (numeric) = 2.0067198586739521405414782232272 absolute error = 1.354186457e-22 relative error = 6.7482586129129722614728565002640e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1159 y[1] (analytic) = 2.0067314957820088894387449740344 y[1] (numeric) = 2.0067314957820088894388812620914 absolute error = 1.362880570e-22 relative error = 6.7915442243502297967081810092463e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 2.0067431430256059129838858643474 y[1] (numeric) = 2.0067431430256059129840230219792 absolute error = 1.371576318e-22 relative error = 6.8348374467698319411070772250159e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1161 y[1] (analytic) = 2.0067548004049793161410559024457 y[1] (numeric) = 2.006754800404979316141193929816 absolute error = 1.380273703e-22 relative error = 6.8781382893488014874841262543030e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1162 y[1] (analytic) = 2.0067664679203654148472687825009 y[1] (numeric) = 2.0067664679203654148474076797735 absolute error = 1.388972726e-22 relative error = 6.9214467562805551827135269560857e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1163 y[1] (analytic) = 2.0067781455720007360315521098124 y[1] (numeric) = 2.0067781455720007360316918771513 absolute error = 1.397673389e-22 relative error = 6.9647628567412719753626661635998e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1164 y[1] (analytic) = 2.0067898333601220176342559391624 y[1] (numeric) = 2.0067898333601220176343965767318 absolute error = 1.406375694e-22 relative error = 7.0080865999066648220785655656523e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=3.88 NO POLE x[1] = 0.1165 y[1] (analytic) = 2.0068015312849662086263792110185 y[1] (numeric) = 2.0068015312849662086265207189826 absolute error = 1.415079641e-22 relative error = 7.0514179849858726021565474463430e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1166 y[1] (analytic) = 2.0068132393467704690289140889579 y[1] (numeric) = 2.0068132393467704690290564674812 absolute error = 1.423785233e-22 relative error = 7.0947570261368740045472325626116e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1167 y[1] (analytic) = 2.0068249575457721699322082016954 y[1] (numeric) = 2.0068249575457721699323514509426 absolute error = 1.432492472e-22 relative error = 7.1381037325340685588721660950566e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1168 y[1] (analytic) = 2.0068366858822088935153447930956 y[1] (numeric) = 2.0068366858822088935154889132315 absolute error = 1.441201359e-22 relative error = 7.1814581083684215132779944062223e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1169 y[1] (analytic) = 2.0068484243563184330655407835567 y[1] (numeric) = 2.0068484243563184330656857747462 absolute error = 1.449911895e-22 relative error = 7.2248201578305464499701979660884e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 2.0068601729683387929975627461547 y[1] (numeric) = 2.006860172968338792997708608563 absolute error = 1.458624083e-22 relative error = 7.2681898950765214397430968649323e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1171 y[1] (analytic) = 2.0068719317185081888731608009409 y[1] (numeric) = 2.0068719317185081888733075347331 absolute error = 1.467337922e-22 relative error = 7.3115673143303228606251901958776e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1172 y[1] (analytic) = 2.0068837006070650474205204307878 y[1] (numeric) = 2.0068837006070650474206680361295 absolute error = 1.476053417e-22 relative error = 7.3549524397129068557435648935409e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1173 y[1] (analytic) = 2.0068954796342480065537322221844 y[1] (numeric) = 2.0068954796342480065538806992411 absolute error = 1.484770567e-22 relative error = 7.3983452654474858496572901183051e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1174 y[1] (analytic) = 2.006907268800295915392279534381 y[1] (numeric) = 2.0069072688002959153924288833185 absolute error = 1.493489375e-22 relative error = 7.4417458056883180455550628487157e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.1MB, time=4.10 NO POLE x[1] = 0.1175 y[1] (analytic) = 2.0069190681054478342805441002912 y[1] (numeric) = 2.0069190681054478342806943212754 absolute error = 1.502209842e-22 relative error = 7.4851540646235499889272240527021e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1176 y[1] (analytic) = 2.0069308775499430348073295625594 y[1] (numeric) = 2.0069308775499430348074806557563 absolute error = 1.510931969e-22 relative error = 7.5285700464409743300295501471506e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1177 y[1] (analytic) = 2.0069426971340209998254029482057 y[1] (numeric) = 2.0069426971340209998255549137816 absolute error = 1.519655759e-22 relative error = 7.5719937652934361906714948802124e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1178 y[1] (analytic) = 2.0069545268579214234710540852655 y[1] (numeric) = 2.0069545268579214234712069233867 absolute error = 1.528381212e-22 relative error = 7.6154252203851695813609030140856e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1179 y[1] (analytic) = 2.00696636672188421118367296484 y[1] (numeric) = 2.0069663667218842111838266756732 absolute error = 1.537108332e-22 relative error = 7.6588644308507493402470982996209e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 2.0069782167261494797253450519834 y[1] (numeric) = 2.0069782167261494797254996356953 absolute error = 1.545837119e-22 relative error = 7.7023113958935818300826436846561e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1181 y[1] (analytic) = 2.006990076870957557200464548849 y[1] (numeric) = 2.0069900768709575572006200056063 absolute error = 1.554567573e-22 relative error = 7.7457661147168355336103274619278e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1182 y[1] (analytic) = 2.0070019471565489830753656135249 y[1] (numeric) = 2.0070019471565489830755219434948 absolute error = 1.563299699e-22 relative error = 7.7892286114362220805250256544694e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1183 y[1] (analytic) = 2.0070138275831645081979715379917 y[1] (numeric) = 2.0070138275831645081981287413414 absolute error = 1.572033497e-22 relative error = 7.8326988852539918284868178715168e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.1MB, time=4.33 NO POLE x[1] = 0.1184 y[1] (analytic) = 2.0070257181510450948174618886362 y[1] (numeric) = 2.007025718151045094817619965533 absolute error = 1.580768968e-22 relative error = 7.8761769403546537450224264913233e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1185 y[1] (analytic) = 2.0070376188604319166039576127611 y[1] (numeric) = 2.0070376188604319166041165633725 absolute error = 1.589506114e-22 relative error = 7.9196627859048277042642210579244e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1186 y[1] (analytic) = 2.0070495297115663586682241145325 y[1] (numeric) = 2.0070495297115663586683839390261 absolute error = 1.598244936e-22 relative error = 7.9631564260882202565629538949106e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1187 y[1] (analytic) = 2.0070614507046900175813923038097 y[1] (numeric) = 2.0070614507046900175815530023535 absolute error = 1.606985438e-22 relative error = 8.0066578800354060498494734575465e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1188 y[1] (analytic) = 2.007073381840044701394697621308 y[1] (numeric) = 2.0070733818400447013948591940699 absolute error = 1.615727619e-22 relative error = 8.0501671419643523970642253343125e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1189 y[1] (analytic) = 2.0070853231178724296592370435438 y[1] (numeric) = 2.007085323117872429659399490692 absolute error = 1.624471482e-22 relative error = 8.0936842260223023789129216555409e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 2.0070972745384154334457440710196 y[1] (numeric) = 2.0070972745384154334459073927224 absolute error = 1.633217028e-22 relative error = 8.1372091363912644204962577127331e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1191 y[1] (analytic) = 2.0071092361019161553643817031061 y[1] (numeric) = 2.0071092361019161553645458995321 absolute error = 1.641964260e-22 relative error = 8.1807418872174679379665010705929e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1192 y[1] (analytic) = 2.0071212078086172495845534030846 y[1] (numeric) = 2.0071212078086172495847184744022 absolute error = 1.650713176e-22 relative error = 8.2242824677352449154474320153432e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1193 y[1] (analytic) = 2.0071331896587615818547320568124 y[1] (numeric) = 2.0071331896587615818548980031905 absolute error = 1.659463781e-22 relative error = 8.2678309020545375658451715097467e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.1MB, time=4.55 NO POLE x[1] = 0.1194 y[1] (analytic) = 2.0071451816525922295223069284837 y[1] (numeric) = 2.0071451816525922295224737500913 absolute error = 1.668216076e-22 relative error = 8.3113871943556500013898571246035e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1195 y[1] (analytic) = 2.0071571837903524815534486169537 y[1] (numeric) = 2.0071571837903524815536163139599 absolute error = 1.676970062e-22 relative error = 8.3549513488185262211240309791184e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1196 y[1] (analytic) = 2.0071691960722858385529920161042 y[1] (numeric) = 2.0071691960722858385531605886783 absolute error = 1.685725741e-22 relative error = 8.3985233746048909049019608254388e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1197 y[1] (analytic) = 2.0071812184986360127843372827272 y[1] (numeric) = 2.0071812184986360127845067310386 absolute error = 1.694483114e-22 relative error = 8.4421032758938776015363675018390e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1198 y[1] (analytic) = 2.0071932510696469281893688154094 y[1] (numeric) = 2.0071932510696469281895391396277 absolute error = 1.703242183e-22 relative error = 8.4856910618463402176806238830282e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1199 y[1] (analytic) = 2.0072052937855627204083922479023 y[1] (numeric) = 2.0072052937855627204085634481973 absolute error = 1.712002950e-22 relative error = 8.5292867416226519008624783323201e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 2.0072173466466277368000894604662 y[1] (numeric) = 2.0072173466466277368002615370079 absolute error = 1.720765417e-22 relative error = 8.5728903243827045582481863225547e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1201 y[1] (analytic) = 2.0072294096530865364614916126805 y[1] (numeric) = 2.0072294096530865364616645656389 absolute error = 1.729529584e-22 relative error = 8.6165018093219252333781285409782e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1202 y[1] (analytic) = 2.0072414828051838902479702012141 y[1] (numeric) = 2.0072414828051838902481440307595 absolute error = 1.738295454e-22 relative error = 8.6601212105813833084409724385130e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.1MB, time=4.77 NO POLE x[1] = 0.1203 y[1] (analytic) = 2.0072535661031647807932461460562 y[1] (numeric) = 2.007253566103164780793420852359 absolute error = 1.747063028e-22 relative error = 8.7037485323376825878220136690983e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1204 y[1] (analytic) = 2.0072656595472744025294169087069 y[1] (numeric) = 2.0072656595472744025295924919377 absolute error = 1.755832308e-22 relative error = 8.7473837837489655204893208879385e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1205 y[1] (analytic) = 2.007277763137758161707001645835 y[1] (numeric) = 2.0072777631377581617071781061645 absolute error = 1.764603295e-22 relative error = 8.7910269689910196475559334795367e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1206 y[1] (analytic) = 2.0072898768748616764150044019092 y[1] (numeric) = 2.0072898768748616764151817395083 absolute error = 1.773375991e-22 relative error = 8.8346780972211104348130623873185e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1207 y[1] (analytic) = 2.0073020007588307766009953443162 y[1] (numeric) = 2.007302000758830776601173559356 absolute error = 1.782150398e-22 relative error = 8.8783371775960191862506606566336e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1208 y[1] (analytic) = 2.0073141347899115040912100444795 y[1] (numeric) = 2.0073141347899115040913891371313 absolute error = 1.790926518e-22 relative error = 8.9220042192720425629438120980555e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1209 y[1] (analytic) = 2.0073262789683501126106668084981 y[1] (numeric) = 2.0073262789683501126108467789332 absolute error = 1.799704351e-22 relative error = 8.9656792214414898006361962417012e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 2.0073384332943930678033020608256 y[1] (numeric) = 2.0073384332943930678034829092155 absolute error = 1.808483899e-22 relative error = 9.0093621932598678167066916158902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1211 y[1] (analytic) = 2.0073505977682870472521237845162 y[1] (numeric) = 2.0073505977682870472523055110327 absolute error = 1.817265165e-22 relative error = 9.0530531488638885375750938884003e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1212 y[1] (analytic) = 2.007362772390278940499383021565 y[1] (numeric) = 2.0073627723902789404995656263799 absolute error = 1.826048149e-22 relative error = 9.0967520874446750142911096006528e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.1MB, time=4.99 NO POLE x[1] = 0.1213 y[1] (analytic) = 2.0073749571606158490667634368742 y[1] (numeric) = 2.0073749571606158490669469201596 absolute error = 1.834832854e-22 relative error = 9.1404590231379963425232327506287e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1214 y[1] (analytic) = 2.007387152079545086475588949381 y[1] (numeric) = 2.0073871520795450864757733113091 absolute error = 1.843619281e-22 relative error = 9.1841739601158133187731667891907e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1215 y[1] (analytic) = 2.0073993571473141782670494338844 y[1] (numeric) = 2.0073993571473141782672346746275 absolute error = 1.852407431e-22 relative error = 9.2278969025497201804014711676151e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1216 y[1] (analytic) = 2.0074115723641708620224444971134 y[1] (numeric) = 2.0074115723641708620226306168441 absolute error = 1.861197307e-22 relative error = 9.2716278645740233324742244912006e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1217 y[1] (analytic) = 2.0074237977303630873834453315821 y[1] (numeric) = 2.007423797730363087383632330473 absolute error = 1.869988909e-22 relative error = 9.3153668453778920260057160065135e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1218 y[1] (analytic) = 2.007436033246139016072374650778 y[1] (numeric) = 2.0074360332461390160725625290019 absolute error = 1.878782239e-22 relative error = 9.3591138541132069659522969656753e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1219 y[1] (analytic) = 2.0074482789117470219125047092377 y[1] (numeric) = 2.0074482789117470219126934669677 absolute error = 1.887577300e-22 relative error = 9.4028689049128080591633817582399e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 2.0074605347274356908483734110635 y[1] (numeric) = 2.0074605347274356908485630484727 absolute error = 1.896374092e-22 relative error = 9.4466319969646699550496149356925e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1221 y[1] (analytic) = 2.0074728006934538209661185104394 y[1] (numeric) = 2.0074728006934538209663090277011 absolute error = 1.905172617e-22 relative error = 9.4904031394192955842095806981273e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.1MB, time=5.21 NO POLE x[1] = 0.1222 y[1] (analytic) = 2.0074850768100504225138299077085 y[1] (numeric) = 2.0074850768100504225140213049963 absolute error = 1.913972878e-22 relative error = 9.5341823464080544736105710677382e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1223 y[1] (analytic) = 2.0074973630774747179219200445774 y[1] (numeric) = 2.007497363077474717922112322065 absolute error = 1.922774876e-22 relative error = 9.5779696220990500525320774581982e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1224 y[1] (analytic) = 2.0075096594959761418235124020146 y[1] (numeric) = 2.0075096594959761418237055598757 absolute error = 1.931578611e-22 relative error = 9.6217649656787201215603357501870e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1225 y[1] (analytic) = 2.0075219660658043410748481044157 y[1] (numeric) = 2.0075219660658043410750421428244 absolute error = 1.940384087e-22 relative error = 9.6655683962583170263404953994672e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1226 y[1] (analytic) = 2.0075342827872091747757106336107 y[1] (numeric) = 2.007534282787209174775905552741 absolute error = 1.949191303e-22 relative error = 9.7093799080421815954853263266094e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1227 y[1] (analytic) = 2.0075466096604407142898686562905 y[1] (numeric) = 2.0075466096604407142900644563168 absolute error = 1.958000263e-22 relative error = 9.7531995201405507902241538524174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1228 y[1] (analytic) = 2.0075589466857492432655369684361 y[1] (numeric) = 2.0075589466857492432657336495329 absolute error = 1.966810968e-22 relative error = 9.7970272367194024031251608820856e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1229 y[1] (analytic) = 2.0075712938633852576558555603345 y[1] (numeric) = 2.0075712938633852576560531226764 absolute error = 1.975623419e-22 relative error = 9.8408630619443430693184312641662e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 2.0075836511935994657393868057698 y[1] (numeric) = 2.0075836511935994657395852495315 absolute error = 1.984437617e-22 relative error = 9.8847069999806080338583995270762e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=95.3MB, alloc=4.1MB, time=5.42 x[1] = 0.1231 y[1] (analytic) = 2.0075960186766427881406307789818 y[1] (numeric) = 2.0075960186766427881408301043383 absolute error = 1.993253565e-22 relative error = 9.9285590649552245286779418110392e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1232 y[1] (analytic) = 2.0076083963127663578505587029874 y[1] (numeric) = 2.0076083963127663578507589101139 absolute error = 2.002071265e-22 relative error = 9.9724192660135511543308965601077e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1233 y[1] (analytic) = 2.0076207841022215202471645328628 y[1] (numeric) = 2.0076207841022215202473656219346 absolute error = 2.010890718e-22 relative error = 1.0016287607319430826109127194580e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1234 y[1] (analytic) = 2.0076331820452598331160346775888 y[1] (numeric) = 2.0076331820452598331162366487812 absolute error = 2.019711924e-22 relative error = 1.0060164088055344092362530963176e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1235 y[1] (analytic) = 2.0076455901421330666709358640636 y[1] (numeric) = 2.0076455901421330666711387175524 absolute error = 2.028534888e-22 relative error = 1.0104048732308315716164045250244e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1236 y[1] (analytic) = 2.007658008393093203574421146894 y[1] (numeric) = 2.0076580083930932035746248828549 absolute error = 2.037359609e-22 relative error = 1.0147941534278936391742455761720e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1237 y[1] (analytic) = 2.0076704367983924389584540675737 y[1] (numeric) = 2.0076704367983924389586586861827 absolute error = 2.046186090e-22 relative error = 1.0191842508091258261913546791816e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1238 y[1] (analytic) = 2.0076828753582831804450509666669 y[1] (numeric) = 2.0076828753582831804452564681001 absolute error = 2.055014332e-22 relative error = 1.0235751657906980125912257854158e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1239 y[1] (analytic) = 2.0076953240730180481669414526143 y[1] (numeric) = 2.0076953240730180481671478370478 absolute error = 2.063844335e-22 relative error = 1.0279668982906590977877832865870e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 2.0077077829428498747882470307837 y[1] (numeric) = 2.0077077829428498747884542983941 absolute error = 2.072676104e-22 relative error = 1.0323594507174351437337820675927e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.1MB, time=5.65 NO POLE x[1] = 0.1241 y[1] (analytic) = 2.0077202519680317055251778963918 y[1] (numeric) = 2.0077202519680317055253860473557 absolute error = 2.081509639e-22 relative error = 1.0367528229889784563187813968341e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1242 y[1] (analytic) = 2.0077327311488167981667478949241 y[1] (numeric) = 2.0077327311488167981669569294183 absolute error = 2.090344942e-22 relative error = 1.0411470160193646983260414687004e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1243 y[1] (analytic) = 2.0077452204854586230955076536869 y[1] (numeric) = 2.0077452204854586230957175718881 absolute error = 2.099182012e-22 relative error = 1.0455420292284060853609179372237e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1244 y[1] (analytic) = 2.0077577199782108633082958881249 y[1] (numeric) = 2.0077577199782108633085066902103 absolute error = 2.108020854e-22 relative error = 1.0499378650243104231016532620110e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1245 y[1] (analytic) = 2.0077702296273274144370088865459 y[1] (numeric) = 2.0077702296273274144372205726928 absolute error = 2.116861469e-22 relative error = 1.0543345238229384310780519516548e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1246 y[1] (analytic) = 2.0077827494330623847693881768925 y[1] (numeric) = 2.0077827494330623847696007472783 absolute error = 2.125703858e-22 relative error = 1.0587320060401131540116596100652e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1247 y[1] (analytic) = 2.007795279395670095269826379207 y[1] (numeric) = 2.0077952793956700952700398340093 absolute error = 2.134548023e-22 relative error = 1.0631303125896786850316134924047e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1248 y[1] (analytic) = 2.0078078195154050796001912474399 y[1] (numeric) = 2.0078078195154050796004055868363 absolute error = 2.143393964e-22 relative error = 1.0675294433893176816313518222413e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1249 y[1] (analytic) = 2.0078203697925220841406679042518 y[1] (numeric) = 2.0078203697925220841408831284204 absolute error = 2.152241686e-22 relative error = 1.0719294008469501074122819965806e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.1MB, time=5.87 NO POLE x[1] = 0.125 y[1] (analytic) = 2.0078329302272760680106192724675 y[1] (numeric) = 2.0078329302272760680108353815863 absolute error = 2.161091188e-22 relative error = 1.0763301843821118661563583191311e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1251 y[1] (analytic) = 2.0078455008199222030894647068384 y[1] (numeric) = 2.0078455008199222030896817010856 absolute error = 2.169942472e-22 relative error = 1.0807317949084648225024385522608e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1252 y[1] (analytic) = 2.0078580815707158740375768297778 y[1] (numeric) = 2.0078580815707158740377947093318 absolute error = 2.178795540e-22 relative error = 1.0851342333396205145295239792646e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1253 y[1] (analytic) = 2.007870672479912678317196574734 y[1] (numeric) = 2.0078706724799126783174153397733 absolute error = 2.187650393e-22 relative error = 1.0895375000911000607534434681980e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1254 y[1] (analytic) = 2.0078832735477684262133664408707 y[1] (numeric) = 2.0078832735477684262135860915742 absolute error = 2.196507035e-22 relative error = 1.0939415970724974175340228837200e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1255 y[1] (analytic) = 2.0078958847745391408548819627277 y[1] (numeric) = 2.0078958847745391408551024992741 absolute error = 2.205365464e-22 relative error = 1.0983465232051283130952188561152e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1256 y[1] (analytic) = 2.0079085061604810582352613985364 y[1] (numeric) = 2.0079085061604810582354828211048 absolute error = 2.214225684e-22 relative error = 1.1027522803984919953669952226664e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1257 y[1] (analytic) = 2.0079211377058506272337336408716 y[1] (numeric) = 2.0079211377058506272339559496413 absolute error = 2.223087697e-22 relative error = 1.1071588695659570704890078112332e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1258 y[1] (analytic) = 2.0079337794109045096362443533212 y[1] (numeric) = 2.0079337794109045096364675484715 absolute error = 2.231951503e-22 relative error = 1.1115662906247927603705303529440e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1259 y[1] (analytic) = 2.0079464312758995801564803368592 y[1] (numeric) = 2.0079464312758995801567044185697 absolute error = 2.240817105e-22 relative error = 1.1159745449863065054911113097608e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.2MB, time=6.09 NO POLE x[1] = 0.126 y[1] (analytic) = 2.0079590933010929264569121296132 y[1] (numeric) = 2.0079590933010929264571370980636 absolute error = 2.249684504e-22 relative error = 1.1203836330657062908431567688643e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1261 y[1] (analytic) = 2.0079717654867418491698548437183 y[1] (numeric) = 2.0079717654867418491700806990885 absolute error = 2.258553702e-22 relative error = 1.1247935557761769148816529223795e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1262 y[1] (analytic) = 2.0079844478331038619185472429535 y[1] (numeric) = 2.0079844478331038619187739854235 absolute error = 2.267424700e-22 relative error = 1.1292043135328405885310666684016e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1263 y[1] (analytic) = 2.0079971403404366913382490648612 y[1] (numeric) = 2.0079971403404366913384766946112 absolute error = 2.276297500e-22 relative error = 1.1336159072487899814876302584822e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1264 y[1] (analytic) = 2.0080098430089982770973565910516 y[1] (numeric) = 2.008009843008998277097585108262 absolute error = 2.285172104e-22 relative error = 1.1380283378370669200307789185942e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1265 y[1] (analytic) = 2.0080225558390467719185364694001 y[1] (numeric) = 2.0080225558390467719187658742515 absolute error = 2.294048514e-22 relative error = 1.1424416062106623390012249833644e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1266 y[1] (analytic) = 2.0080352788308405415998777918457 y[1] (numeric) = 2.0080352788308405416001080845187 absolute error = 2.302926730e-22 relative error = 1.1468557122865177963606254604923e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1267 y[1] (analytic) = 2.0080480119846381650360624315051 y[1] (numeric) = 2.0080480119846381650362936121806 absolute error = 2.311806755e-22 relative error = 1.1512706574755373079391107215378e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1268 y[1] (analytic) = 2.0080607553006984342395536428183 y[1] (numeric) = 2.0080607553006984342397857116774 absolute error = 2.320688591e-22 relative error = 1.1556864426905683419977332586678e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.2MB, time=6.32 NO POLE x[1] = 0.1269 y[1] (analytic) = 2.0080735087792803543618029284466 y[1] (numeric) = 2.0080735087792803543620358856704 absolute error = 2.329572238e-22 relative error = 1.1601030678484278226884822090609e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 2.0080862724206431437144751766449 y[1] (numeric) = 2.0080862724206431437147090224148 absolute error = 2.338457699e-22 relative error = 1.1645205343598665971592306204546e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1271 y[1] (analytic) = 2.0080990462250462337906920728367 y[1] (numeric) = 2.0080990462250462337909268073343 absolute error = 2.347344976e-22 relative error = 1.1689388431375883019169748537637e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1272 y[1] (analytic) = 2.0081118301927492692862937891218 y[1] (numeric) = 2.0081118301927492692865294125287 absolute error = 2.356234069e-22 relative error = 1.1733579940982849067854573437459e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1273 y[1] (analytic) = 2.0081246243240121081211189554484 y[1] (numeric) = 2.0081246243240121081213554679465 absolute error = 2.365124981e-22 relative error = 1.1777779886525537027616443168765e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1274 y[1] (analytic) = 2.0081374286190948214603029161898 y[1] (numeric) = 2.0081374286190948214605403179612 absolute error = 2.374017714e-22 relative error = 1.1821988277129541294653212628260e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1275 y[1] (analytic) = 2.0081502430782576937355942758636 y[1] (numeric) = 2.0081502430782576937358325670904 absolute error = 2.382912268e-22 relative error = 1.1866205111960528819130018525697e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1276 y[1] (analytic) = 2.0081630677017612226666897377377 y[1] (numeric) = 2.0081630677017612226669289186023 absolute error = 2.391808646e-22 relative error = 1.1910430405122933075242347190204e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1277 y[1] (analytic) = 2.0081759024898661192825872390716 y[1] (numeric) = 2.0081759024898661192828273097565 absolute error = 2.400706849e-22 relative error = 1.1954664160761259379080654978998e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1278 y[1] (analytic) = 2.0081887474428333079429573867419 y[1] (numeric) = 2.0081887474428333079431983474297 absolute error = 2.409606878e-22 relative error = 1.1998906383019625891126235363790e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.2MB, time=6.53 NO POLE x[1] = 0.1279 y[1] (analytic) = 2.008201602560923926359533197007 y[1] (numeric) = 2.0082016025609239263597750478806 absolute error = 2.418508736e-22 relative error = 1.2043157086000922850352216752175e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 2.0082144678443993256175181431687 y[1] (numeric) = 2.0082144678443993256177608844112 absolute error = 2.427412425e-22 relative error = 1.2087416278827849837265191332776e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1281 y[1] (analytic) = 2.0082273432935210701970125148905 y[1] (numeric) = 2.0082273432935210701972561466851 absolute error = 2.436317946e-22 relative error = 1.2131683965643074674097049138545e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1282 y[1] (analytic) = 2.0082402289085509379944580929379 y[1] (numeric) = 2.0082402289085509379947026154678 absolute error = 2.445225299e-22 relative error = 1.2175960145609392696979401272639e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1283 y[1] (analytic) = 2.0082531246897509203441011431073 y[1] (numeric) = 2.008253124689750920344346556556 absolute error = 2.454134487e-22 relative error = 1.2220244832827694323918727001353e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1284 y[1] (analytic) = 2.008266030637383222039473733116 y[1] (numeric) = 2.0082660306373832220397200376673 absolute error = 2.463045513e-22 relative error = 1.2264538041398225127747593669927e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1285 y[1] (analytic) = 2.0082789467517102613548933762267 y[1] (numeric) = 2.0082789467517102613551405720644 absolute error = 2.471958377e-22 relative error = 1.2308839770482421239880464957221e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1286 y[1] (analytic) = 2.008291873032994670066981005384 y[1] (numeric) = 2.0082918730329946700672290926922 absolute error = 2.480873082e-22 relative error = 1.2353150034179524805722465545888e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1287 y[1] (analytic) = 2.0083048094814992934761972816462 y[1] (numeric) = 2.0083048094814992934764462606089 absolute error = 2.489789627e-22 relative error = 1.2397468826670836059858686490306e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.2MB, time=6.75 NO POLE x[1] = 0.1288 y[1] (analytic) = 2.0083177560974871904283972406943 y[1] (numeric) = 2.0083177560974871904286471114959 absolute error = 2.498708016e-22 relative error = 1.2441796167033980178479811981828e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1289 y[1] (analytic) = 2.0083307128812216333364032812091 y[1] (numeric) = 2.0083307128812216333366540440342 absolute error = 2.507628251e-22 relative error = 1.2486132064387287181099781861903e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 2.0083436798329661082015964989065 y[1] (numeric) = 2.0083436798329661082018481539397 absolute error = 2.516550332e-22 relative error = 1.2530476517890112442742714690143e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1291 y[1] (analytic) = 2.0083566569529843146355263700252 y[1] (numeric) = 2.0083566569529843146357789174514 absolute error = 2.525474262e-22 relative error = 1.2574829541639134382714172314049e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1292 y[1] (analytic) = 2.0083696442415401658815387880679 y[1] (numeric) = 2.0083696442415401658817922280721 absolute error = 2.534400042e-22 relative error = 1.2619191139772056064201602248531e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1293 y[1] (analytic) = 2.0083826416988977888364224575948 y[1] (numeric) = 2.0083826416988977888366767903621 absolute error = 2.543327673e-22 relative error = 1.2663561316426188428281322594849e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1294 y[1] (analytic) = 2.0083956493253215240720736488762 y[1] (numeric) = 2.008395649325321524072328874592 absolute error = 2.552257158e-22 relative error = 1.2707940085696647296164585789861e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1295 y[1] (analytic) = 2.0084086671210759258571793172136 y[1] (numeric) = 2.0084086671210759258574354360634 absolute error = 2.561188498e-22 relative error = 1.2752327451719765032735295037407e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1296 y[1] (analytic) = 2.0084216950864257621789185907393 y[1] (numeric) = 2.0084216950864257621791756029088 absolute error = 2.570121695e-22 relative error = 1.2796723423610514934574853183178e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1297 memory used=122.0MB, alloc=4.2MB, time=6.97 y[1] (analytic) = 2.0084347332216360147646826305118 y[1] (numeric) = 2.0084347332216360147649405361868 absolute error = 2.579056750e-22 relative error = 1.2841128005504345937726251801829e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1298 y[1] (analytic) = 2.0084477815269718791038128667251 y[1] (numeric) = 2.0084477815269718791040716660917 absolute error = 2.587993666e-22 relative error = 1.2885541211494252005404392762026e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1299 y[1] (analytic) = 2.0084608400026987644693576148551 y[1] (numeric) = 2.0084608400026987644696173080993 absolute error = 2.596932442e-22 relative error = 1.2929963035756826145123642119016e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 2.008473908649082293939847075567 y[1] (numeric) = 2.0084739086490822939401076628753 absolute error = 2.605873083e-22 relative error = 1.2974393502341953701407824328559e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1301 y[1] (analytic) = 2.0084869874663883044210867222161 y[1] (numeric) = 2.008486987466388304421348203775 absolute error = 2.614815589e-22 relative error = 1.3018832610404245916725779334862e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1302 y[1] (analytic) = 2.0085000764548828466679690797711 y[1] (numeric) = 2.0085000764548828466682314557672 absolute error = 2.623759961e-22 relative error = 1.3063280364076888310342748286250e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1303 y[1] (analytic) = 2.0085131756148321853063038989989 y[1] (numeric) = 2.008513175614832185306567169619 absolute error = 2.632706201e-22 relative error = 1.3107736772471478339076148824439e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1304 y[1] (analytic) = 2.0085262849465027988546667297486 y[1] (numeric) = 2.0085262849465027988549308951798 absolute error = 2.641654312e-22 relative error = 1.3152201849677862686201411056562e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1305 y[1] (analytic) = 2.0085394044501613797462658971789 y[1] (numeric) = 2.0085394044501613797465309576084 absolute error = 2.650604295e-22 relative error = 1.3196675599827747419147799852200e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1306 y[1] (analytic) = 2.0085525341260748343508278847745 y[1] (numeric) = 2.0085525341260748343510938403895 absolute error = 2.659556150e-22 relative error = 1.3241158022073732424343907346359e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.2MB, time=7.20 NO POLE x[1] = 0.1307 y[1] (analytic) = 2.0085656739745102829965011280011 y[1] (numeric) = 2.0085656739745102829967679789893 absolute error = 2.668509882e-22 relative error = 1.3285649140461536851295479527093e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1308 y[1] (analytic) = 2.008578823995735059991778222454 y[1] (numeric) = 2.008578823995735059992045969003 absolute error = 2.677465490e-22 relative error = 1.3330148949164094286781570406322e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1309 y[1] (analytic) = 2.0085919841900167136474365503546 y[1] (numeric) = 2.0085919841900167136477051926522 absolute error = 2.686422976e-22 relative error = 1.3374657457290037429426267746019e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 2.0086051545576230062984973292569 y[1] (numeric) = 2.0086051545576230062987668674912 absolute error = 2.695382343e-22 relative error = 1.3419174678926050128761435645008e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1311 y[1] (analytic) = 2.0086183350988219143262030868267 y[1] (numeric) = 2.0086183350988219143264735211859 absolute error = 2.704343592e-22 relative error = 1.3463700618201063733192740642429e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1312 y[1] (analytic) = 2.0086315258138816281800135655609 y[1] (numeric) = 2.0086315258138816281802848962333 absolute error = 2.713306724e-22 relative error = 1.3508235279243611133251784229175e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1313 y[1] (analytic) = 2.0086447267030705523996200613169 y[1] (numeric) = 2.008644726703070552399892288491 absolute error = 2.722271741e-22 relative error = 1.3552778671160307725377978924604e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1314 y[1] (analytic) = 2.0086579377666573056369781995266 y[1] (numeric) = 2.0086579377666573056372513233911 absolute error = 2.731238645e-22 relative error = 1.3597330803057239009965611724053e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1315 y[1] (analytic) = 2.0086711590049107206783591529726 y[1] (numeric) = 2.0086711590049107206786331737164 absolute error = 2.740207438e-22 relative error = 1.3641891684039960111965369837497e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.2MB, time=7.41 x[1] = 0.1316 y[1] (analytic) = 2.0086843904180998444664193050063 y[1] (numeric) = 2.0086843904180998444666942228183 absolute error = 2.749178120e-22 relative error = 1.3686461313256729522168336500642e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1317 y[1] (analytic) = 2.0086976320064939381222883620933 y[1] (numeric) = 2.0086976320064939381225641771628 absolute error = 2.758150695e-22 relative error = 1.3731039709768937228363335956463e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1318 y[1] (analytic) = 2.0087108837703624769676759195738 y[1] (numeric) = 2.0087108837703624769679526320901 absolute error = 2.767125163e-22 relative error = 1.3775626872723910044423216973235e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1319 y[1] (analytic) = 2.0087241457099751505469964845279 y[1] (numeric) = 2.0087241457099751505472740946806 absolute error = 2.776101527e-22 relative error = 1.3820222816203558515732802532925e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 2.0087374178256018626495129596427 y[1] (numeric) = 2.0087374178256018626497914676214 absolute error = 2.785079787e-22 relative error = 1.3864827539354374737668743673685e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1321 y[1] (analytic) = 2.0087507001175127313314985919768 y[1] (numeric) = 2.0087507001175127313317779979714 absolute error = 2.794059946e-22 relative error = 1.3909441056257236694520991256994e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1322 y[1] (analytic) = 2.0087639925859780889384173905258 y[1] (numeric) = 2.0087639925859780889386976947263 absolute error = 2.803042005e-22 relative error = 1.3954063371035986099513258574148e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1323 y[1] (analytic) = 2.0087772952312684821271230164923 y[1] (numeric) = 2.0087772952312684821274042190889 absolute error = 2.812025966e-22 relative error = 1.3998694492792215262912272295397e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1324 y[1] (analytic) = 2.0087906080536546718880761501703 y[1] (numeric) = 2.0087906080536546718883582513534 absolute error = 2.821011831e-22 relative error = 1.4043334430626982251855583430151e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1325 y[1] (analytic) = 2.0088039310534076335675803383544 y[1] (numeric) = 2.0088039310534076335678633383145 absolute error = 2.829999601e-22 relative error = 1.4087983188662723776875001158484e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.2MB, time=7.63 NO POLE x[1] = 0.1326 y[1] (analytic) = 2.0088172642307985568900363261906 y[1] (numeric) = 2.0088172642307985568903202251184 absolute error = 2.838989278e-22 relative error = 1.4132640775999527104748152946927e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1327 y[1] (analytic) = 2.0088306075860988459802148773865 y[1] (numeric) = 2.0088306075860988459804996754729 absolute error = 2.847980864e-22 relative error = 1.4177307201736943970186624951609e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1328 y[1] (analytic) = 2.0088439611195801193855480867037 y[1] (numeric) = 2.0088439611195801193858337841398 absolute error = 2.856974361e-22 relative error = 1.4221982474973990096657107958410e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1329 y[1] (analytic) = 2.0088573248315142100984391886583 y[1] (numeric) = 2.0088573248315142100987257856353 absolute error = 2.865969770e-22 relative error = 1.4266666599831190396428364018155e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 2.0088706987221731655785908663584 y[1] (numeric) = 2.0088706987221731655788783630675 absolute error = 2.874967091e-22 relative error = 1.4311359575450744193025835965969e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1331 y[1] (analytic) = 2.0088840827918292477753520644111 y[1] (numeric) = 2.008884082791829247775640461044 absolute error = 2.883966329e-22 relative error = 1.4356061425864018907658080452946e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1332 y[1] (analytic) = 2.0088974770407549331500833098364 y[1] (numeric) = 2.0088974770407549331503726065848 absolute error = 2.892967484e-22 relative error = 1.4400772150212172073781006318047e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1333 y[1] (analytic) = 2.0089108814692229126985405449261 y[1] (numeric) = 2.0089108814692229126988307419818 absolute error = 2.901970557e-22 relative error = 1.4445491752613910146109540530155e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1334 y[1] (analytic) = 2.0089242960775060919732774759912 y[1] (numeric) = 2.0089242960775060919735685735463 absolute error = 2.910975551e-22 relative error = 1.4490220247143110691320883195710e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.2MB, time=7.85 NO POLE x[1] = 0.1335 y[1] (analytic) = 2.0089377208658775911060664419457 y[1] (numeric) = 2.0089377208658775911063584401924 absolute error = 2.919982467e-22 relative error = 1.4534957637917469085926317502056e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1336 y[1] (analytic) = 2.0089511558346107448303378066749 y[1] (numeric) = 2.0089511558346107448306307058056 absolute error = 2.928991307e-22 relative error = 1.4579703934031996133928776083311e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1337 y[1] (analytic) = 2.0089646009839791025036378791431 y[1] (numeric) = 2.0089646009839791025039316793504 absolute error = 2.938002073e-22 relative error = 1.4624459144581162762307463114003e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1338 y[1] (analytic) = 2.0089780563142564281301053651971 y[1] (numeric) = 2.0089780563142564281304000666737 absolute error = 2.947014766e-22 relative error = 1.4669223273681244376205332269970e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1339 y[1] (analytic) = 2.0089915218257167003829663550263 y[1] (numeric) = 2.008991521825716700383261957965 absolute error = 2.956029387e-22 relative error = 1.4713996325448108999114036517322e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 2.0090049975186341126270478502428 y[1] (numeric) = 2.0090049975186341126273443548367 absolute error = 2.965045939e-22 relative error = 1.4758778313952393870369244671815e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1341 y[1] (analytic) = 2.0090184833932830729413098345499 y[1] (numeric) = 2.0090184833932830729416072409924 absolute error = 2.974064425e-22 relative error = 1.4803569253264061082098475997893e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1342 y[1] (analytic) = 2.0090319794499382041413958919693 y[1] (numeric) = 2.0090319794499382041416942004537 absolute error = 2.983084844e-22 relative error = 1.4848369137542310597449024178665e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1343 y[1] (analytic) = 2.0090454856888743438022023766007 y[1] (numeric) = 2.0090454856888743438025015873205 absolute error = 2.992107198e-22 relative error = 1.4893177975878665482149186732266e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1344 y[1] (analytic) = 2.0090590021103665442804661378932 y[1] (numeric) = 2.0090590021103665442807662510422 absolute error = 3.001131490e-22 relative error = 1.4937995782341560632287883270692e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.2MB, time=8.07 NO POLE x[1] = 0.1345 y[1] (analytic) = 2.0090725287146900727373708054091 y[1] (numeric) = 2.0090725287146900727376718211812 absolute error = 3.010157721e-22 relative error = 1.4982822561043911429182812760246e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1346 y[1] (analytic) = 2.0090860655021204111611716370645 y[1] (numeric) = 2.0090860655021204111614735556537 absolute error = 3.019185892e-22 relative error = 1.5027658316098223511162106339209e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1347 y[1] (analytic) = 2.0090996124729332563898389348353 y[1] (numeric) = 2.009099612472933256390141756436 absolute error = 3.028216007e-22 relative error = 1.5072503066548654553615687811289e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1348 y[1] (analytic) = 2.0091131696274045201337200319217 y[1] (numeric) = 2.0091131696274045201340237567282 absolute error = 3.037248065e-22 relative error = 1.5117356806551946903840661383364e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1349 y[1] (analytic) = 2.009126736965810328998219855364 y[1] (numeric) = 2.0091267369658103289985244835709 absolute error = 3.046282069e-22 relative error = 1.5162219550173848140908595555933e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 2.0091403144884270245065000681108 y[1] (numeric) = 2.0091403144884270245068055999129 absolute error = 3.055318021e-22 relative error = 1.5207091306502172770481016350593e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1351 y[1] (analytic) = 2.0091539021955311631221967945406 y[1] (numeric) = 2.0091539021955311631225032301328 absolute error = 3.064355922e-22 relative error = 1.5251972079646969801599279011684e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1352 y[1] (analytic) = 2.0091675000873995162721569334432 y[1] (numeric) = 2.0091675000873995162724642730205 absolute error = 3.073395773e-22 relative error = 1.5296861873717876519381812344069e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1353 y[1] (analytic) = 2.0091811081643090703691930624693 y[1] (numeric) = 2.0091811081643090703695013062271 absolute error = 3.082437578e-22 relative error = 1.5341760707755574596156350147914e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.2MB, time=8.30 NO POLE x[1] = 0.1354 y[1] (analytic) = 2.0091947264265370268348569380627 y[1] (numeric) = 2.0091947264265370268351660861965 absolute error = 3.091481338e-22 relative error = 1.5386668585868573561291702287556e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1355 y[1] (analytic) = 2.0092083548743608021222315948896 y[1] (numeric) = 2.0092083548743608021225416475949 absolute error = 3.100527053e-22 relative error = 1.5431585507187885462035758783487e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1356 y[1] (analytic) = 2.0092219935080580277387420487853 y[1] (numeric) = 2.009221993508058027739053006258 absolute error = 3.109574727e-22 relative error = 1.5476511490752447729021216648929e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1357 y[1] (analytic) = 2.0092356423279065502689846072427 y[1] (numeric) = 2.0092356423279065502692964696787 absolute error = 3.118624360e-22 relative error = 1.5521446535692310803282401807367e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1358 y[1] (analytic) = 2.0092493013341844313975747914674 y[1] (numeric) = 2.0092493013341844313978875590628 absolute error = 3.127675954e-22 relative error = 1.5566390651091212991967371071477e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1359 y[1] (analytic) = 2.0092629705271699479320138740312 y[1] (numeric) = 2.0092629705271699479323275469823 absolute error = 3.136729511e-22 relative error = 1.5611343846032343231577280499799e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 2.0092766499071415918255740361572 y[1] (numeric) = 2.0092766499071415918258886146604 absolute error = 3.145785032e-22 relative error = 1.5656306124621425160454565292985e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1361 y[1] (analytic) = 2.0092903394743780702002021486734 y[1] (numeric) = 2.0092903394743780702005176329254 absolute error = 3.154842520e-22 relative error = 1.5701277500917530803614185404001e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1362 y[1] (analytic) = 2.0093040392291583053694421806765 y[1] (numeric) = 2.009304039229158305369758570874 absolute error = 3.163901975e-22 relative error = 1.5746257974048502973599496749608e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1363 y[1] (analytic) = 2.009317749171761434861376239949 y[1] (numeric) = 2.009317749171761434861693536289 absolute error = 3.172963400e-22 relative error = 1.5791247558072345809539897794599e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.2MB, time=8.52 NO POLE x[1] = 0.1364 y[1] (analytic) = 2.0093314693024668114415842491783 y[1] (numeric) = 2.009331469302466811441902451858 absolute error = 3.182026797e-22 relative error = 1.5836246262069596386691588716377e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1365 y[1] (analytic) = 2.009345199621554003136122262029 y[1] (numeric) = 2.0093451996215540031364413712456 absolute error = 3.191092166e-22 relative error = 1.5881254085166748368428411786888e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1366 y[1] (analytic) = 2.0093589401293027932545194231219 y[1] (numeric) = 2.009358940129302793254839439073 absolute error = 3.200159511e-22 relative error = 1.5926271046396861611779679288137e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1367 y[1] (analytic) = 2.0093726908259931804127935759804 y[1] (numeric) = 2.0093726908259931804131144988637 absolute error = 3.209228833e-22 relative error = 1.5971297149862138054572438308180e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1368 y[1] (analytic) = 2.009386451711905378556485523004 y[1] (numeric) = 2.0093864517119053785568073530172 absolute error = 3.218300132e-22 relative error = 1.6016332394687718944648809689564e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1369 y[1] (analytic) = 2.0094002227873198169837119415345 y[1] (numeric) = 2.0094002227873198169840346788757 absolute error = 3.227373412e-22 relative error = 1.6061376799904902049618881521774e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 2.0094140040525171403682369600856 y[1] (numeric) = 2.0094140040525171403685606049529 absolute error = 3.236448673e-22 relative error = 1.6106430364637857045465818131592e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1371 y[1] (analytic) = 2.0094277955077782087825623988053 y[1] (numeric) = 2.009427795507778208782886951397 absolute error = 3.245525917e-22 relative error = 1.6151493097963554229402976284128e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1372 y[1] (analytic) = 2.0094415971533840977210366782494 y[1] (numeric) = 2.0094415971533840977213621387641 absolute error = 3.254605147e-22 relative error = 1.6196565013934915814902125311315e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.2MB, time=8.74 NO POLE x[1] = 0.1373 y[1] (analytic) = 2.0094554089896160981229824005448 y[1] (numeric) = 2.0094554089896160981233087691811 absolute error = 3.263686363e-22 relative error = 1.6241646111674753594666541351248e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1374 y[1] (analytic) = 2.0094692310167557163958426070243 y[1] (numeric) = 2.0094692310167557163961698839811 absolute error = 3.272769568e-22 relative error = 1.6286736405234912533866032952326e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1375 y[1] (analytic) = 2.0094830632350846744383457164216 y[1] (numeric) = 2.0094830632350846744386739018979 absolute error = 3.281854763e-22 relative error = 1.6331835898713735849372717047392e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1376 y[1] (analytic) = 2.0094969056448849096636891477141 y[1] (numeric) = 2.0094969056448849096640182419091 absolute error = 3.290941950e-22 relative error = 1.6376944601185516909416307974473e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1377 y[1] (analytic) = 2.0095107582464385750227416317086 y[1] (numeric) = 2.0095107582464385750230716348217 absolute error = 3.300031131e-22 relative error = 1.6422062521723991842004345422559e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1378 y[1] (analytic) = 2.0095246210400280390272642154664 y[1] (numeric) = 2.0095246210400280390275951276971 absolute error = 3.309122307e-22 relative error = 1.6467189664426037748677572754777e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1379 y[1] (analytic) = 2.009538494025935885773149963668 y[1] (numeric) = 2.009538494025935885773481785216 absolute error = 3.318215480e-22 relative error = 1.6512326038364377904780743966146e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 2.0095523772044449149636823610216 y[1] (numeric) = 2.0095523772044449149640150920868 absolute error = 3.327310652e-22 relative error = 1.6557471652611177059142821563774e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1381 y[1] (analytic) = 2.0095662705758381419328124198236 y[1] (numeric) = 2.009566270575838141933146060606 absolute error = 3.336407824e-22 relative error = 1.6602626511261842784886376837485e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1382 memory used=156.4MB, alloc=4.2MB, time=8.96 y[1] (analytic) = 2.0095801741403987976684544967811 y[1] (numeric) = 2.0095801741403987976687890474809 absolute error = 3.345506998e-22 relative error = 1.6647790623387524628634309453363e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1383 y[1] (analytic) = 2.0095940878984103288358008232119 y[1] (numeric) = 2.0095940878984103288361362840295 absolute error = 3.354608176e-22 relative error = 1.6692963998058812324351648037549e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1384 y[1] (analytic) = 2.0096080118501563978006547527396 y[1] (numeric) = 2.0096080118501563978009911238757 absolute error = 3.363711361e-22 relative error = 1.6738146649321830126180490101384e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1385 y[1] (analytic) = 2.0096219459959208826527827306065 y[1] (numeric) = 2.0096219459959208826531200122617 absolute error = 3.372816552e-22 relative error = 1.6783338571317762275029655247673e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1386 y[1] (analytic) = 2.0096358903359878772292849887275 y[1] (numeric) = 2.0096358903359878772296231811027 absolute error = 3.381923752e-22 relative error = 1.6828539778091749069574175730698e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1387 y[1] (analytic) = 2.0096498448706416911379849706161 y[1] (numeric) = 2.0096498448706416911383240739125 absolute error = 3.391032964e-22 relative error = 1.6873750283688231170867408461590e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1388 y[1] (analytic) = 2.0096638096001668497808374903138 y[1] (numeric) = 2.0096638096001668497811775047326 absolute error = 3.400144188e-22 relative error = 1.6918970087223078923055385240841e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1389 y[1] (analytic) = 2.0096777845248480943773556294575 y[1] (numeric) = 2.0096777845248480943776965552001 absolute error = 3.409257426e-22 relative error = 1.6964199197763720902243822562749e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 2.0096917696449703819880563766269 y[1] (numeric) = 2.0096917696449703819883982138949 absolute error = 3.418372680e-22 relative error = 1.7009437624377022821952719753253e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1391 y[1] (analytic) = 2.0097057649608188855379250131123 y[1] (numeric) = 2.0097057649608188855382677621075 absolute error = 3.427489952e-22 relative error = 1.7054685376129287055031559804672e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.2MB, time=9.19 NO POLE x[1] = 0.1392 y[1] (analytic) = 2.0097197704726789938398982492511 y[1] (numeric) = 2.0097197704726789938402419101754 absolute error = 3.436609243e-22 relative error = 1.7099942457110434060492365364188e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1393 y[1] (analytic) = 2.0097337861808363116183661154816 y[1] (numeric) = 2.0097337861808363116187106885371 absolute error = 3.445730555e-22 relative error = 1.7145208876385742198428628674021e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1394 y[1] (analytic) = 2.0097478120855766595326926122686 y[1] (numeric) = 2.0097478120855766595330380976576 absolute error = 3.454853890e-22 relative error = 1.7190484643019925202686227857961e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1395 y[1] (analytic) = 2.0097618481871860742007551230576 y[1] (numeric) = 2.0097618481871860742011015209826 absolute error = 3.463979250e-22 relative error = 1.7235769766077131702850373869263e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1396 y[1] (analytic) = 2.0097758944859508082225025944182 y[1] (numeric) = 2.0097758944859508082228499050818 absolute error = 3.473106636e-22 relative error = 1.7281064249645265603399603636006e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1397 y[1] (analytic) = 2.0097899509821573302035324875403 y[1] (numeric) = 2.0097899509821573302038807111453 absolute error = 3.482236050e-22 relative error = 1.7326368102787448291321506224411e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1398 y[1] (analytic) = 2.0098040176760923247786865052525 y[1] (numeric) = 2.0098040176760923247790356420019 absolute error = 3.491367494e-22 relative error = 1.7371681334566234763973306844934e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1399 y[1] (analytic) = 2.0098180945680426926356650987319 y[1] (numeric) = 2.0098180945680426926360151488289 absolute error = 3.500500970e-22 relative error = 1.7417003954043613151140752025769e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 2.0098321816582955505386607580818 y[1] (numeric) = 2.0098321816582955505390117217296 absolute error = 3.509636478e-22 relative error = 1.7462335960329924648222934861032e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=164.0MB, alloc=4.2MB, time=9.41 x[1] = 0.1401 y[1] (analytic) = 2.0098462789471382313520100909542 y[1] (numeric) = 2.0098462789471382313523619683564 absolute error = 3.518774022e-22 relative error = 1.7507677372437241401000412190065e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1402 y[1] (analytic) = 2.0098603864348582840638646934013 y[1] (numeric) = 2.0098603864348582840642174847615 absolute error = 3.527913602e-22 relative error = 1.7553028189474908274250794534152e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1403 y[1] (analytic) = 2.0098745041217434738098808171383 y[1] (numeric) = 2.0098745041217434738102345226604 absolute error = 3.537055221e-22 relative error = 1.7598388425478286011247732398997e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1404 y[1] (analytic) = 2.0098886320080817818969278374097 y[1] (numeric) = 2.0098886320080817818972824572977 absolute error = 3.546198880e-22 relative error = 1.7643758084531226402458034977341e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1405 y[1] (analytic) = 2.0099027700941614058268155256495 y[1] (numeric) = 2.0099027700941614058271710601075 absolute error = 3.555344580e-22 relative error = 1.7689137170717151644177242909862e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1406 y[1] (analytic) = 2.0099169183802707593200401311326 y[1] (numeric) = 2.0099169183802707593203965803651 absolute error = 3.564492325e-22 relative error = 1.7734525703045044195564252920522e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1407 y[1] (analytic) = 2.0099310768666984723395492758173 y[1] (numeric) = 2.0099310768666984723399066400287 absolute error = 3.573642114e-22 relative error = 1.7779923675646560982871903103974e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1408 y[1] (analytic) = 2.0099452455537333911145256665804 y[1] (numeric) = 2.0099452455537333911148839459755 absolute error = 3.582793951e-22 relative error = 1.7825331107529508326525801350715e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1409 y[1] (analytic) = 2.0099594244416645781641896290547 y[1] (numeric) = 2.0099594244416645781645488238384 absolute error = 3.591947837e-22 relative error = 1.7870748002775166282100912634956e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 2.0099736135307813123216204672764 y[1] (numeric) = 2.0099736135307813123219805776537 absolute error = 3.601103773e-22 relative error = 1.7916174365464383565773626218476e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.2MB, time=9.63 NO POLE x[1] = 0.1411 y[1] (analytic) = 2.0099878128213730887575966533585 y[1] (numeric) = 2.0099878128213730887579576795346 absolute error = 3.610261761e-22 relative error = 1.7961610204652731867980310856724e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1412 y[1] (analytic) = 2.0100020223137296190044548514065 y[1] (numeric) = 2.0100020223137296190048167935868 absolute error = 3.619421803e-22 relative error = 1.8007055529395210394156896318766e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1413 y[1] (analytic) = 2.010016242008140830979967779898 y[1] (numeric) = 2.0100162420081408309803306382881 absolute error = 3.628583901e-22 relative error = 1.8052510348746245387049333910367e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1414 y[1] (analytic) = 2.0100304719048968690112409167512 y[1] (numeric) = 2.0100304719048968690116046915569 absolute error = 3.637748057e-22 relative error = 1.8097974671759689649043094675314e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1415 y[1] (analytic) = 2.01004471200428809385862805131 y[1] (numeric) = 2.0100447120042880938589927427372 absolute error = 3.646914272e-22 relative error = 1.8143448502513808354479050127834e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1416 y[1] (analytic) = 2.0100589623066050827396656874776 y[1] (numeric) = 2.0100589623066050827400312957323 absolute error = 3.656082547e-22 relative error = 1.8188931845086433363386647771307e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1417 y[1] (analytic) = 2.010073222812138629353026302234 y[1] (numeric) = 2.0100732228121386293533928275226 absolute error = 3.665252886e-22 relative error = 1.8234424718479792425239760188115e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1418 y[1] (analytic) = 2.0100874935211797439024904637777 y[1] (numeric) = 2.0100874935211797439028579063066 absolute error = 3.674425289e-22 relative error = 1.8279927121795624377881926795432e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1419 y[1] (analytic) = 2.0101017744340196531209378135313 y[1] (numeric) = 2.0101017744340196531213061735071 absolute error = 3.683599758e-22 relative error = 1.8325439064085119947820558933237e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.2MB, time=9.86 NO POLE x[1] = 0.142 y[1] (analytic) = 2.0101160655509498002943569162601 y[1] (numeric) = 2.0101160655509498002947261938897 absolute error = 3.692776296e-22 relative error = 1.8370960559373730963439434777835e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 733.2 Order of pole = 1.413e+04 x[1] = 0.1421 y[1] (analytic) = 2.0101303668722618452858739825521 y[1] (numeric) = 2.0101303668722618452862441780423 absolute error = 3.701954902e-22 relative error = 1.8416491601786984323251342773046e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 271.4 Order of pole = 5214 x[1] = 0.1422 y[1] (analytic) = 2.0101446783982476645598004679116 y[1] (numeric) = 2.0101446783982476645601715814696 absolute error = 3.711135580e-22 relative error = 1.8462032210324086328879966154680e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 166.8 Order of pole = 3194 x[1] = 0.1423 y[1] (analytic) = 2.010159000129199351205699552726 y[1] (numeric) = 2.0101590001291993512060715845592 absolute error = 3.720318332e-22 relative error = 1.8507582394033920880042220406356e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 120.4 Order of pole = 2300 x[1] = 0.1424 y[1] (analytic) = 2.0101733320654092149624715073639 y[1] (numeric) = 2.0101733320654092149628444576797 absolute error = 3.729503158e-22 relative error = 1.8553142152015403185514717229547e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 94.33 Order of pole = 1796 x[1] = 0.1425 y[1] (analytic) = 2.0101876742071697822424579466691 y[1] (numeric) = 2.0101876742071697822428318156751 absolute error = 3.738690060e-22 relative error = 1.8598711493316473788078419124241e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 77.57 Order of pole = 1472 x[1] = 0.1426 y[1] (analytic) = 2.0102020265547737961555649781188 y[1] (numeric) = 2.0102020265547737961559397660229 absolute error = 3.747879041e-22 relative error = 1.8644290431959119028584225089528e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 65.9 Order of pole = 1247 x[1] = 0.1427 y[1] (analytic) = 2.0102163891085142165334052479169 y[1] (numeric) = 2.0102163891085142165337809549271 absolute error = 3.757070102e-22 relative error = 1.8689878972015426358285242565605e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 57.3 Order of pole = 1081 x[1] = 0.1428 y[1] (analytic) = 2.0102307618686842199534588892967 y[1] (numeric) = 2.0102307618686842199538355156212 absolute error = 3.766263245e-22 relative error = 1.8735477122531599082597942266997e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 50.71 Order of pole = 953.9 x[1] = 0.1429 y[1] (analytic) = 2.010245144835577199763253377312 y[1] (numeric) = 2.0102451448355771997636309231592 absolute error = 3.775458472e-22 relative error = 1.8781084892553260497747733477997e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.2MB, time=10.09 Real estimate of pole used Radius of convergence = 45.49 Order of pole = 853.1 x[1] = 0.143 y[1] (analytic) = 2.0102595380094867661045622943983 y[1] (numeric) = 2.0102595380094867661049407599767 absolute error = 3.784655784e-22 relative error = 1.8826702286150971357257182931504e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 41.26 Order of pole = 771.5 x[1] = 0.1431 y[1] (analytic) = 2.0102739413907067459376230109899 y[1] (numeric) = 2.0102739413907067459380023965082 absolute error = 3.793855183e-22 relative error = 1.8872329312369300431627577943207e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 37.76 Order of pole = 703.9 x[1] = 0.1432 y[1] (analytic) = 2.0102883549795311830653732854818 y[1] (numeric) = 2.0102883549795311830657535911489 absolute error = 3.803056671e-22 relative error = 1.8917965980252235198579399334658e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 34.81 Order of pole = 647 x[1] = 0.1433 y[1] (analytic) = 2.010302778776254338157706787829 y[1] (numeric) = 2.010302778776254338158088013854 absolute error = 3.812260250e-22 relative error = 1.8963612298843181365728649309884e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 32.3 Order of pole = 598.6 x[1] = 0.1434 y[1] (analytic) = 2.0103172127811706887757475510807 y[1] (numeric) = 2.0103172127811706887761296976728 absolute error = 3.821465921e-22 relative error = 1.9009268272210623051997359608519e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 30.14 Order of pole = 556.7 x[1] = 0.1435 y[1] (analytic) = 2.0103316569945749293961433551473 y[1] (numeric) = 2.0103316569945749293965264225159 absolute error = 3.830673686e-22 relative error = 1.9054933909396908214638088616274e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 28.25 Order of pole = 520.3 x[1] = 0.1436 y[1] (analytic) = 2.0103461114167619714353780471061 y[1] (numeric) = 2.0103461114167619714357620354607 absolute error = 3.839883546e-22 relative error = 1.9100609214469533922042605620195e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 26.59 Order of pole = 488.2 x[1] = 0.1437 y[1] (analytic) = 2.0103605760480269432741028023507 y[1] (numeric) = 2.0103605760480269432744877119012 absolute error = 3.849095505e-22 relative error = 1.9146294206418253008080808799153e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 25.11 Order of pole = 459.8 x[1] = 0.1438 y[1] (analytic) = 2.0103750508886651902814863308969 y[1] (numeric) = 2.0103750508886651902818721618531 absolute error = 3.858309562e-22 relative error = 1.9191988879360966776145832514698e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.2MB, time=10.31 Real estimate of pole used Radius of convergence = 23.8 Order of pole = 434.4 x[1] = 0.1439 y[1] (analytic) = 2.0103895359389722748395840331573 y[1] (numeric) = 2.0103895359389722748399707857294 absolute error = 3.867525721e-22 relative error = 1.9237693252286223925372098861688e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 22.62 Order of pole = 411.7 x[1] = 0.144 y[1] (analytic) = 2.0104040311992439763677261095047 y[1] (numeric) = 2.010404031199243976368113783903 absolute error = 3.876743983e-22 relative error = 1.9283407329259327995149557079243e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 21.56 Order of pole = 391.1 x[1] = 0.1441 y[1] (analytic) = 2.0104185366697762913469246279442 y[1] (numeric) = 2.0104185366697762913473132243792 absolute error = 3.885964350e-22 relative error = 1.9329131119319229279103670454026e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 20.59 Order of pole = 372.5 x[1] = 0.1442 y[1] (analytic) = 2.01043305235086543334429955422 y[1] (numeric) = 2.0104330523508654333446890729023 absolute error = 3.895186823e-22 relative error = 1.9374864626530239578863294050431e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 19.71 Order of pole = 355.5 x[1] = 0.1443 y[1] (analytic) = 2.0104475782428078330375237486858 y[1] (numeric) = 2.0104475782428078330379141898261 absolute error = 3.904411403e-22 relative error = 1.9420607854956228204855270248310e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 18.9 Order of pole = 339.9 x[1] = 0.1444 y[1] (analytic) = 2.01046211434590013823928693427 y[1] (numeric) = 2.0104621143459001382396782980794 absolute error = 3.913638094e-22 relative error = 1.9466360823582564212451979376942e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 18.16 Order of pole = 325.6 x[1] = 0.1445 y[1] (analytic) = 2.010476660660439213921778639874 y[1] (numeric) = 2.0104766606604392139221709265636 absolute error = 3.922866896e-22 relative error = 1.9512123531497962514477957797290e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 17.48 Order of pole = 312.5 x[1] = 0.1446 y[1] (analytic) = 2.0104912171867221422411901235405 y[1] (numeric) = 2.0104912171867221422415833333217 absolute error = 3.932097812e-22 relative error = 1.9557895992712564912692340370723e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 16.85 Order of pole = 300.3 x[1] = 0.1447 y[1] (analytic) = 2.0105057839250462225622352797371 y[1] (numeric) = 2.0105057839250462225626294128214 absolute error = 3.941330843e-22 relative error = 1.9603678211288035634723864596463e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 16.26 Order of pole = 289 memory used=183.1MB, alloc=4.2MB, time=10.52 x[1] = 0.1448 y[1] (analytic) = 2.0105203608757089714826905351009 y[1] (numeric) = 2.0105203608757089714830855917 absolute error = 3.950565991e-22 relative error = 1.9649470196259431396284826481157e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 15.72 Order of pole = 278.5 x[1] = 0.1449 y[1] (analytic) = 2.0105349480390081228579537369952 y[1] (numeric) = 2.0105349480390081228583497173209 absolute error = 3.959803257e-22 relative error = 1.9695271951687419467820047494866e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 15.21 Order of pole = 268.7 x[1] = 0.145 y[1] (analytic) = 2.0105495454152416278256220392318 y[1] (numeric) = 2.0105495454152416278260189434962 absolute error = 3.969042644e-22 relative error = 1.9741083491579751324116168274259e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 14.74 Order of pole = 259.5 x[1] = 0.1451 y[1] (analytic) = 2.0105641530047076548300887893172 y[1] (numeric) = 2.0105641530047076548304866177325 absolute error = 3.978284153e-22 relative error = 1.9786904819995987505279886855255e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 14.29 Order of pole = 251 x[1] = 0.1452 y[1] (analytic) = 2.0105787708077045896471594215834 y[1] (numeric) = 2.010578770807704589647558174362 absolute error = 3.987527786e-22 relative error = 1.9832735945968935179386527134650e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 13.88 Order of pole = 242.9 x[1] = 0.1453 y[1] (analytic) = 2.0105933988245310354086863605688 y[1] (numeric) = 2.0105933988245310354090860379234 absolute error = 3.996773546e-22 relative error = 1.9878576883504466983131357209136e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 13.48 Order of pole = 235.4 x[1] = 0.1454 y[1] (analytic) = 2.0106080370554858126272229390177 y[1] (numeric) = 2.0106080370554858126276235411609 absolute error = 4.006021432e-22 relative error = 1.9924427626713240349988477099556e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 13.11 Order of pole = 228.2 x[1] = 0.1455 y[1] (analytic) = 2.0106226855008679592206963348692 y[1] (numeric) = 2.010622685500867959221097862014 absolute error = 4.015271448e-22 relative error = 1.9970288194573673830271501041319e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 12.77 Order of pole = 221.5 x[1] = 0.1456 y[1] (analytic) = 2.0106373441609767305370995316141 y[1] (numeric) = 2.0106373441609767305375019839736 absolute error = 4.024523595e-22 relative error = 2.0016158591142662190644051756476e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 12.44 Order of pole = 215.1 x[1] = 0.1457 y[1] (analytic) = 2.0106520130361115993792023063967 y[1] (numeric) = 2.0106520130361115993796056841841 absolute error = 4.033777874e-22 relative error = 2.0062038820476652859464718687416e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.2MB, time=10.75 Real estimate of pole used Radius of convergence = 12.12 Order of pole = 209.1 x[1] = 0.1458 y[1] (analytic) = 2.0106666921265722560292812502451 y[1] (numeric) = 2.0106666921265722560296855536738 absolute error = 4.043034287e-22 relative error = 2.0107928891605120435402913188335e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 11.83 Order of pole = 203.4 x[1] = 0.1459 y[1] (analytic) = 2.0106813814326586082738688248179 y[1] (numeric) = 2.0106813814326586082742740541016 absolute error = 4.052292837e-22 relative error = 2.0153828818530384786004468252780e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 11.55 Order of pole = 198 x[1] = 0.146 y[1] (analytic) = 2.0106960809546707814285214600564 y[1] (numeric) = 2.010696080954670781428927615409 absolute error = 4.061553526e-22 relative error = 2.0199738610280624686089565519881e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 11.28 Order of pole = 192.8 x[1] = 0.1461 y[1] (analytic) = 2.0107107906929091183626066971365 y[1] (numeric) = 2.0107107906929091183630137787719 absolute error = 4.070816354e-22 relative error = 2.0245658265936693352244449382148e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 11.03 Order of pole = 187.9 x[1] = 0.1462 y[1] (analytic) = 2.0107255106476741795241093811179 y[1] (numeric) = 2.0107255106476741795245173892502 absolute error = 4.080081323e-22 relative error = 2.0291587794525799060429223319661e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 10.78 Order of pole = 183.3 x[1] = 0.1463 y[1] (analytic) = 2.0107402408192667429644569076922 y[1] (numeric) = 2.0107402408192667429648658425358 absolute error = 4.089348436e-22 relative error = 2.0337527210047848011771565924486e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 10.55 Order of pole = 178.8 x[1] = 0.1464 y[1] (analytic) = 2.0107549812079878043633635284345 y[1] (numeric) = 2.0107549812079878043637733902039 absolute error = 4.098617694e-22 relative error = 2.0383476516555492483462082009588e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 10.33 Order of pole = 174.5 x[1] = 0.1465 y[1] (analytic) = 2.0107697318141385770536937189665 y[1] (numeric) = 2.0107697318141385770541045078764 absolute error = 4.107889099e-22 relative error = 2.0429435723074154566337317395955e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 10.12 Order of pole = 170.5 x[1] = 0.1466 y[1] (analytic) = 2.010784492638020492046344614444 y[1] (numeric) = 2.0107844926380204920467563307094 absolute error = 4.117162654e-22 relative error = 2.0475404843601843397764301078661e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.2MB, time=10.98 Real estimate of pole used Radius of convergence = 9.92 Order of pole = 166.6 x[1] = 0.1467 y[1] (analytic) = 2.0107992636799351980551475167846 y[1] (numeric) = 2.0107992636799351980555601606204 absolute error = 4.126438358e-22 relative error = 2.0521383872243237833562197808473e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.727 Order of pole = 162.8 x[1] = 0.1468 y[1] (analytic) = 2.0108140449401845615217884780537 y[1] (numeric) = 2.0108140449401845615222020496751 absolute error = 4.135716214e-22 relative error = 2.0567372822995299112182357443429e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.541 Order of pole = 159.3 x[1] = 0.1469 y[1] (analytic) = 2.0108288364190706666407479644335 y[1] (numeric) = 2.010828836419070666641162464056 absolute error = 4.144996225e-22 relative error = 2.0613371709854244688103252838189e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.363 Order of pole = 155.8 x[1] = 0.147 y[1] (analytic) = 2.0108436381168958153842596052013 y[1] (numeric) = 2.0108436381168958153846750330403 absolute error = 4.154278390e-22 relative error = 2.0659380526923399137000225778038e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.192 Order of pole = 152.5 x[1] = 0.1471 y[1] (analytic) = 2.010858450033962527527288031146 y[1] (numeric) = 2.0108584500339625275277043874174 absolute error = 4.163562714e-22 relative error = 2.0705399298143930671188365583208e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 9.028 Order of pole = 149.4 x[1] = 0.1472 y[1] (analytic) = 2.0108732721705735406725258068593 y[1] (numeric) = 2.010873272170573540672943091779 absolute error = 4.172849197e-22 relative error = 2.0751428022591149865447889209601e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.87 Order of pole = 146.3 x[1] = 0.1473 y[1] (analytic) = 2.0108881045270318102754094613368 y[1] (numeric) = 2.010888104527031810275827675121 absolute error = 4.182137842e-22 relative error = 2.0797466714258842454439021509965e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.718 Order of pole = 143.4 x[1] = 0.1474 y[1] (analytic) = 2.0109029471036405096691546213321 y[1] (numeric) = 2.010902947103640509669573764197 absolute error = 4.191428649e-22 relative error = 2.0843515372221376252986374219248e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.572 Order of pole = 140.5 x[1] = 0.1475 y[1] (analytic) = 2.0109177999007030300898102519074 y[1] (numeric) = 2.0109177999007030300902303240694 absolute error = 4.200721620e-22 relative error = 2.0889574005498519830825839054691e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.43 Order of pole = 137.8 x[1] = 0.1476 y[1] (analytic) = 2.0109326629185229807013320086304 y[1] (numeric) = 2.0109326629185229807017530103062 absolute error = 4.210016758e-22 relative error = 2.0935642628082258047463160830989e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.2MB, time=11.20 Real estimate of pole used Radius of convergence = 8.294 Order of pole = 135.2 x[1] = 0.1477 y[1] (analytic) = 2.0109475361574041886206747058693 y[1] (numeric) = 2.0109475361574041886210966372757 absolute error = 4.219314064e-22 relative error = 2.0981721244018267213372060408815e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.163 Order of pole = 132.7 x[1] = 0.1478 y[1] (analytic) = 2.010962419617650698942903905641 y[1] (numeric) = 2.0109624196176506989433267669951 absolute error = 4.228613541e-22 relative error = 2.1027809867297255811236201189175e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 8.036 Order of pole = 130.2 x[1] = 0.1479 y[1] (analytic) = 2.010977313299566774766326631474 y[1] (numeric) = 2.0109773132995667747667504229928 absolute error = 4.237915188e-22 relative error = 2.1073908492018356848228331446878e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.913 Order of pole = 127.8 x[1] = 0.148 y[1] (analytic) = 2.0109922172034568972176412117464 y[1] (numeric) = 2.0109922172034568972180659336473 absolute error = 4.247219009e-22 relative error = 2.1120017137143891215812345597403e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.794 Order of pole = 125.6 x[1] = 0.1481 y[1] (analytic) = 2.0110071313296257654771062569691 y[1] (numeric) = 2.0110071313296257654775319094696 absolute error = 4.256525005e-22 relative error = 2.1166135806717383680186658888768e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.68 Order of pole = 123.3 x[1] = 0.1482 y[1] (analytic) = 2.0110220556783782968037287754818 y[1] (numeric) = 2.0110220556783782968041553587997 absolute error = 4.265833179e-22 relative error = 2.1212264514727094888648179982686e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.568 Order of pole = 121.2 x[1] = 0.1483 y[1] (analytic) = 2.0110369902500196265604714320383 y[1] (numeric) = 2.0110369902500196265608989463914 absolute error = 4.275143531e-22 relative error = 2.1258403260242857072262093243499e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.461 Order of pole = 119.1 x[1] = 0.1484 y[1] (analytic) = 2.0110519350448551082394789537568 y[1] (numeric) = 2.0110519350448551082399073993632 absolute error = 4.284456064e-22 relative error = 2.1304552057251759642636160115433e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.357 Order of pole = 117.1 x[1] = 0.1485 y[1] (analytic) = 2.0110668900631903134873236879191 y[1] (numeric) = 2.0110668900631903134877530649971 absolute error = 4.293770780e-22 relative error = 2.1350710914767654438445162016008e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.2MB, time=11.42 Real estimate of pole used Radius of convergence = 7.256 Order of pole = 115.2 x[1] = 0.1486 y[1] (analytic) = 2.0110818553053310321302703161019 y[1] (numeric) = 2.0110818553053310321307006248699 absolute error = 4.303087680e-22 relative error = 2.1396879836831340012787752512448e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.158 Order of pole = 113.3 x[1] = 0.1487 y[1] (analytic) = 2.0110968307715832721995597291298 y[1] (numeric) = 2.0110968307715832721999909698065 absolute error = 4.312406767e-22 relative error = 2.1443058837427979286432286139358e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 7.062 Order of pole = 111.4 x[1] = 0.1488 y[1] (analytic) = 2.0111118164622532599567120673432 y[1] (numeric) = 2.0111118164622532599571442401472 absolute error = 4.321728040e-22 relative error = 2.1489247910652485122330425978415e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.97 Order of pole = 109.7 x[1] = 0.1489 y[1] (analytic) = 2.0111268123776474399188489306754 y[1] (numeric) = 2.0111268123776474399192820358257 absolute error = 4.331051503e-22 relative error = 2.1535447075461292962188492991111e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.881 Order of pole = 107.9 x[1] = 0.149 y[1] (analytic) = 2.0111418185180724748840347630414 y[1] (numeric) = 2.0111418185180724748844688007571 absolute error = 4.340377157e-22 relative error = 2.1581656335893035410975272008552e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.793 Order of pole = 106.2 x[1] = 0.1491 y[1] (analytic) = 2.0111568348838352459566374155395 y[1] (numeric) = 2.01115683488383524595707238604 absolute error = 4.349705005e-22 relative error = 2.1627875705930411370359300280506e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.709 Order of pole = 104.6 x[1] = 0.1492 y[1] (analytic) = 2.0111718614752428525727078929745 y[1] (numeric) = 2.0111718614752428525731437964793 absolute error = 4.359035048e-22 relative error = 2.1674105189610912333030289019780e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.626 Order of pole = 103 x[1] = 0.1493 y[1] (analytic) = 2.0111868982926026125253792882126 y[1] (numeric) = 2.0111868982926026125258161249413 absolute error = 4.368367287e-22 relative error = 2.1720344790971570047096490830692e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.546 Order of pole = 101.5 x[1] = 0.1494 y[1] (analytic) = 2.0112019453362220619902849088826 y[1] (numeric) = 2.0112019453362220619907226790551 absolute error = 4.377701725e-22 relative error = 2.1766594523993258522150316732465e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.468 Order of pole = 99.98 x[1] = 0.1495 memory used=202.1MB, alloc=4.2MB, time=11.64 y[1] (analytic) = 2.0112170026064089555509956009425 y[1] (numeric) = 2.0112170026064089555514343047788 absolute error = 4.387038363e-22 relative error = 2.1812854392711865981992952006367e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.393 Order of pole = 98.51 x[1] = 0.1496 y[1] (analytic) = 2.011232070103471266224476273632 y[1] (numeric) = 2.0112320701034712662249159113523 absolute error = 4.396377203e-22 relative error = 2.1859124406134896565734887716869e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.319 Order of pole = 97.09 x[1] = 0.1497 y[1] (analytic) = 2.0112471478277171854865616303376 y[1] (numeric) = 2.0112471478277171854870022021623 absolute error = 4.405718247e-22 relative error = 2.1905404573269244358892868301384e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.247 Order of pole = 95.7 x[1] = 0.1498 y[1] (analytic) = 2.0112622357794551232974511098996 y[1] (numeric) = 2.0112622357794551232978926160493 absolute error = 4.415061497e-22 relative error = 2.1951694903121192917292379567617e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.177 Order of pole = 94.35 x[1] = 0.1499 y[1] (analytic) = 2.011277333958993708127223042893 y[1] (numeric) = 2.0112773339589937081276654835884 absolute error = 4.424406954e-22 relative error = 2.1997995399724450044429877518702e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.108 Order of pole = 93.03 x[1] = 0.15 y[1] (analytic) = 2.0112924423666417869813680274198 y[1] (numeric) = 2.0112924423666417869818114028819 absolute error = 4.433754621e-22 relative error = 2.2044306077056116251812532165093e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 6.042 Order of pole = 91.75 x[1] = 0.1501 y[1] (analytic) = 2.0113075610027084254263415289534 y[1] (numeric) = 2.0113075610027084254267858394033 absolute error = 4.443104499e-22 relative error = 2.2090626939148750698856535736014e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.977 Order of pole = 90.49 x[1] = 0.1502 y[1] (analytic) = 2.0113226898675029076151357087776 y[1] (numeric) = 2.0113226898675029076155809544365 absolute error = 4.452456589e-22 relative error = 2.2136957990034449702312787120217e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.913 Order of pole = 89.27 x[1] = 0.1503 y[1] (analytic) = 2.0113378289613347363128704855695 y[1] (numeric) = 2.0113378289613347363133166666589 absolute error = 4.461810894e-22 relative error = 2.2183299243688476917075731929591e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.852 Order of pole = 88.08 x[1] = 0.1504 y[1] (analytic) = 2.0113529782845136329224038346771 y[1] (numeric) = 2.0113529782845136329228509514186 absolute error = 4.471167415e-22 relative error = 2.2229650704141777604770349939889e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.2MB, time=11.87 Real estimate of pole used Radius of convergence = 5.791 Order of pole = 86.91 x[1] = 0.1505 y[1] (analytic) = 2.0113681378373495375099613296463 y[1] (numeric) = 2.0113681378373495375104093822618 absolute error = 4.480526155e-22 relative error = 2.2276012385368313772560110905653e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.732 Order of pole = 85.77 x[1] = 0.1506 y[1] (analytic) = 2.0113833076201526088307849305573 y[1] (numeric) = 2.0113833076201526088312339192687 absolute error = 4.489887114e-22 relative error = 2.2322384286426175033105953918749e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.674 Order of pole = 84.66 x[1] = 0.1507 y[1] (analytic) = 2.0113984876332332243548010237308 y[1] (numeric) = 2.0113984876332332243552509487604 absolute error = 4.499250296e-22 relative error = 2.2368766426259797574890036641672e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.618 Order of pole = 83.58 x[1] = 0.1508 y[1] (analytic) = 2.0114136778769019802923077173731 y[1] (numeric) = 2.0114136778769019802927585789433 absolute error = 4.508615702e-22 relative error = 2.2415158808897819208729053905205e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.563 Order of pole = 82.52 x[1] = 0.1509 y[1] (analytic) = 2.0114288783514696916196813977271 y[1] (numeric) = 2.0114288783514696916201331960603 absolute error = 4.517983332e-22 relative error = 2.2461561433396822261248001240677e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.509 Order of pole = 81.48 x[1] = 0.151 y[1] (analytic) = 2.0114440890572473921051025503044 y[1] (numeric) = 2.0114440890572473921055552856234 absolute error = 4.527353190e-22 relative error = 2.2507974318699284098612518605287e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.457 Order of pole = 80.46 x[1] = 0.1511 y[1] (analytic) = 2.0114593099945463343343008507761 y[1] (numeric) = 2.0114593099945463343347545233038 absolute error = 4.536725277e-22 relative error = 2.2554397468832220196930706033730e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.405 Order of pole = 79.47 x[1] = 0.1512 y[1] (analytic) = 2.0114745411636779897363195301017 y[1] (numeric) = 2.0114745411636779897367741400611 absolute error = 4.546099594e-22 relative error = 2.2600830887822179716024925743892e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.355 Order of pole = 78.5 x[1] = 0.1513 y[1] (analytic) = 2.0114897825649540486092990184822 y[1] (numeric) = 2.0114897825649540486097545660967 absolute error = 4.555476145e-22 relative error = 2.2647274594609564130417643644392e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.2MB, time=12.09 Real estimate of pole used Radius of convergence = 5.306 Order of pole = 77.55 x[1] = 0.1514 y[1] (analytic) = 2.0115050341986864201462798727259 y[1] (numeric) = 2.0115050341986864201467363582189 absolute error = 4.564854930e-22 relative error = 2.2693728588248248106064479171952e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.258 Order of pole = 76.62 x[1] = 0.1515 y[1] (analytic) = 2.0115202960651872324610249916173 y[1] (numeric) = 2.0115202960651872324614824152124 absolute error = 4.574235951e-22 relative error = 2.2740192877734518151076401120262e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.21 Order of pole = 75.72 x[1] = 0.1516 y[1] (analytic) = 2.011535568164768832613861123887 y[1] (numeric) = 2.011535568164768832614319485808 absolute error = 4.583619210e-22 relative error = 2.2786667472064042270749331250110e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.164 Order of pole = 74.83 x[1] = 0.1517 y[1] (analytic) = 2.0115508504977437866375396733809 y[1] (numeric) = 2.0115508504977437866379989738517 absolute error = 4.593004708e-22 relative error = 2.2833152375260580798077197635559e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.119 Order of pole = 73.95 x[1] = 0.1518 y[1] (analytic) = 2.011566143064424879563116806032 y[1] (numeric) = 2.0115661430644248795635770452769 absolute error = 4.602392449e-22 relative error = 2.2879647606261178486398928146227e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.075 Order of pole = 73.1 x[1] = 0.1519 y[1] (analytic) = 2.0115814458651251154458528632428 y[1] (numeric) = 2.011581445865125115446314041486 absolute error = 4.611782432e-22 relative error = 2.2926153159145892351112139806409e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 5.031 Order of pole = 72.26 x[1] = 0.152 y[1] (analytic) = 2.0115967589001577173911310862869 y[1] (numeric) = 2.011596758900157717391593203753 absolute error = 4.621174661e-22 relative error = 2.2972669052850489164988118522987e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.989 Order of pole = 71.44 x[1] = 0.1521 y[1] (analytic) = 2.0116120821698361275803956563467 y[1] (numeric) = 2.0116120821698361275808587132604 absolute error = 4.630569137e-22 relative error = 2.3019195291396400059846308893053e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.947 Order of pole = 70.64 x[1] = 0.1522 y[1] (analytic) = 2.011627415674474007297109054803 y[1] (numeric) = 2.0116274156744740072975730513893 absolute error = 4.639965863e-22 relative error = 2.3065731888746785339349851564831e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.906 Order of pole = 69.85 x[1] = 0.1523 y[1] (analytic) = 2.0116427594143852369527287484003 y[1] (numeric) = 2.0116427594143852369531936848842 absolute error = 4.649364839e-22 relative error = 2.3112278843950847266083534510696e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.2MB, time=12.31 Real estimate of pole used Radius of convergence = 4.866 Order of pole = 69.08 x[1] = 0.1524 y[1] (analytic) = 2.0116581133898839161127032039115 y[1] (numeric) = 2.0116581133898839161131690805182 absolute error = 4.658766067e-22 relative error = 2.3158836165999516570432068936081e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.827 Order of pole = 68.32 x[1] = 0.1525 y[1] (analytic) = 2.0116734776012843635224872369323 y[1] (numeric) = 2.0116734776012843635229540538873 absolute error = 4.668169550e-22 relative error = 2.3205403868854087150861117267796e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.788 Order of pole = 67.58 x[1] = 0.1526 y[1] (analytic) = 2.011688852048901117133576699439 y[1] (numeric) = 2.0116888520489011171340444569678 absolute error = 4.677575288e-22 relative error = 2.3251981951562234986724897260418e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.75 Order of pole = 66.85 x[1] = 0.1527 y[1] (analytic) = 2.011704236733048934129562510744 y[1] (numeric) = 2.0117042367330489341300312090725 absolute error = 4.686983285e-22 relative error = 2.3298570433054955190394362450510e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.713 Order of pole = 66.13 x[1] = 0.1528 y[1] (analytic) = 2.0117196316540427909522040364923 y[1] (numeric) = 2.0117196316540427909526736758464 absolute error = 4.696393541e-22 relative error = 2.3345169312378828353581844186343e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.677 Order of pole = 65.43 x[1] = 0.1529 y[1] (analytic) = 2.0117350368121978833275218203408 y[1] (numeric) = 2.0117350368121978833279924009467 absolute error = 4.705806059e-22 relative error = 2.3391778603492615680118464283310e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.641 Order of pole = 64.74 x[1] = 0.153 y[1] (analytic) = 2.0117504522078296262919096729698 y[1] (numeric) = 2.0117504522078296262923811950538 absolute error = 4.715220840e-22 relative error = 2.3438398310412710392305655268118e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.606 Order of pole = 64.07 x[1] = 0.1531 y[1] (analytic) = 2.0117658778412536542182661230776 y[1] (numeric) = 2.0117658778412536542187385868663 absolute error = 4.724637887e-22 relative error = 2.3485028447096547507182963124333e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.572 Order of pole = 63.4 x[1] = 0.1532 y[1] (analytic) = 2.0117813137127858208421452350137 y[1] (numeric) = 2.0117813137127858208426186407338 absolute error = 4.734057201e-22 relative error = 2.3531669017559345419535311411562e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.2MB, time=12.53 Real estimate of pole used Radius of convergence = 4.538 Order of pole = 62.75 x[1] = 0.1533 y[1] (analytic) = 2.0117967598227421992879267977096 y[1] (numeric) = 2.0117967598227421992884011455879 absolute error = 4.743478783e-22 relative error = 2.3578320025815848889358759293693e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.505 Order of pole = 62.11 x[1] = 0.1534 y[1] (analytic) = 2.0118122161714390820950058895701 y[1] (numeric) = 2.0118122161714390820954811798337 absolute error = 4.752902636e-22 relative error = 2.3624981485821614505774148262372e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.472 Order of pole = 61.48 x[1] = 0.1535 y[1] (analytic) = 2.0118276827591929812440018239918 y[1] (numeric) = 2.0118276827591929812444780568679 absolute error = 4.762328761e-22 relative error = 2.3671653401590209793659659902943e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.44 Order of pole = 60.86 x[1] = 0.1536 y[1] (analytic) = 2.0118431595863206281829864801786 y[1] (numeric) = 2.0118431595863206281834636558947 absolute error = 4.771757161e-22 relative error = 2.3718335787075860450743353615225e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.408 Order of pole = 60.25 x[1] = 0.1537 y[1] (analytic) = 2.0118586466531389738537320239288 y[1] (numeric) = 2.0118586466531389738542101427124 absolute error = 4.781187836e-22 relative error = 2.3765028641320426832613281447182e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.377 Order of pole = 59.66 x[1] = 0.1538 y[1] (analytic) = 2.0118741439599651887179780230708 y[1] (numeric) = 2.0118741439599651887184570851498 absolute error = 4.790620790e-22 relative error = 2.3811731983247406452203700477388e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.347 Order of pole = 59.07 x[1] = 0.1539 y[1] (analytic) = 2.01188965150711666278371796223 y[1] (numeric) = 2.0118896515071166627841979678324 absolute error = 4.800056024e-22 relative error = 2.3858445816868007030741339820336e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.317 Order of pole = 58.49 x[1] = 0.154 y[1] (analytic) = 2.0119051692949110056315051616113 y[1] (numeric) = 2.0119051692949110056319861109651 absolute error = 4.809493538e-22 relative error = 2.3905170141222546972769285832190e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.287 Order of pole = 57.92 x[1] = 0.1541 y[1] (analytic) = 2.0119206973236660464407781044855 y[1] (numeric) = 2.0119206973236660464412599978192 absolute error = 4.818933337e-22 relative error = 2.3951904980202895944627058586227e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.258 Order of pole = 57.37 x[1] = 0.1542 y[1] (analytic) = 2.0119362355936998340162051780749 y[1] (numeric) = 2.0119362355936998340166880156169 absolute error = 4.828375420e-22 relative error = 2.3998650327877814320355929999740e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.2MB, time=12.75 Real estimate of pole used Radius of convergence = 4.23 Order of pole = 56.82 x[1] = 0.1543 y[1] (analytic) = 2.0119517841053306368140488325312 y[1] (numeric) = 2.0119517841053306368145326145102 absolute error = 4.837819790e-22 relative error = 2.4045406198197084653740103831780e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.202 Order of pole = 56.28 x[1] = 0.1544 y[1] (analytic) = 2.0119673428588769429685491627085 y[1] (numeric) = 2.0119673428588769429690338893535 absolute error = 4.847266450e-22 relative error = 2.4092172605109704829121798706280e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.174 Order of pole = 55.75 x[1] = 0.1545 y[1] (analytic) = 2.0119829118546574603183269174348 y[1] (numeric) = 2.0119829118546574603188125889747 absolute error = 4.856715399e-22 relative error = 2.4138949542683002782769811437265e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.147 Order of pole = 55.22 x[1] = 0.1546 y[1] (analytic) = 2.011998491092991116432805940988 y[1] (numeric) = 2.0119984910929911164332925576522 absolute error = 4.866166642e-22 relative error = 2.4185737034805232024094594589635e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.121 Order of pole = 54.71 x[1] = 0.1547 y[1] (analytic) = 2.012014080574197058638655051491 y[1] (numeric) = 2.0120140805741970586391426135088 absolute error = 4.875620178e-22 relative error = 2.4232535075542686876358912212857e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.094 Order of pole = 54.21 x[1] = 0.1548 y[1] (analytic) = 2.012029680298594654046249360938 y[1] (numeric) = 2.0120296802985946540467378685391 absolute error = 4.885076011e-22 relative error = 2.4279343683812019001758542973262e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.068 Order of pole = 53.71 x[1] = 0.1549 y[1] (analytic) = 2.0120452902665034895761510415733 y[1] (numeric) = 2.0120452902665034895766404949875 absolute error = 4.894534142e-22 relative error = 2.4326162863618737284411640294923e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.043 Order of pole = 53.22 x[1] = 0.155 y[1] (analytic) = 2.0120609104782433719856095433441 y[1] (numeric) = 2.0120609104782433719860999428013 absolute error = 4.903994572e-22 relative error = 2.4372992618967871019632518330555e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 4.018 Order of pole = 52.73 x[1] = 0.1551 y[1] (analytic) = 2.0120765409341343278950812671537 y[1] (numeric) = 2.0120765409341343278955726128841 absolute error = 4.913457304e-22 relative error = 2.4419832963803949399980006393984e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.2MB, time=12.98 Real estimate of pole used Radius of convergence = 3.993 Order of pole = 52.26 x[1] = 0.1552 y[1] (analytic) = 2.0120921816344966038147686986468 y[1] (numeric) = 2.0120921816344966038152609908807 absolute error = 4.922922339e-22 relative error = 2.4466683902130810058293511331543e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.969 Order of pole = 51.79 x[1] = 0.1553 y[1] (analytic) = 2.0121078325796506661711790072588 y[1] (numeric) = 2.0121078325796506661716722462268 absolute error = 4.932389680e-22 relative error = 2.4513545447891635188919706462705e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.945 Order of pole = 51.33 x[1] = 0.1554 y[1] (analytic) = 2.0121234937699172013337021152689 y[1] (numeric) = 2.0121234937699172013341963012018 absolute error = 4.941859329e-22 relative error = 2.4560417610058942843463160127507e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.922 Order of pole = 50.88 x[1] = 0.1555 y[1] (analytic) = 2.0121391652056171156412082415974 y[1] (numeric) = 2.0121391652056171156417033747259 absolute error = 4.951331285e-22 relative error = 2.4607300382695109396965309739070e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.898 Order of pole = 50.43 x[1] = 0.1556 y[1] (analytic) = 2.0121548468870715354286649250919 y[1] (numeric) = 2.0121548468870715354291610056472 absolute error = 4.960805553e-22 relative error = 2.4654193789681118040669776229087e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.875 Order of pole = 49.99 x[1] = 0.1557 y[1] (analytic) = 2.0121705388146018070537735320539 y[1] (numeric) = 2.0121705388146018070542705602673 absolute error = 4.970282134e-22 relative error = 2.4701097835017819482347689108388e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.853 Order of pole = 49.56 x[1] = 0.1558 y[1] (analytic) = 2.0121862409885294969236252527561 y[1] (numeric) = 2.012186240988529496924123228859 absolute error = 4.979761029e-22 relative error = 2.4748012522705581979861999835346e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.831 Order of pole = 49.13 x[1] = 0.1559 y[1] (analytic) = 2.012201953409176391521376591708 y[1] (numeric) = 2.012201953409176391521875515932 absolute error = 4.989242240e-22 relative error = 2.4794937861713971210794824226938e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.809 Order of pole = 48.71 x[1] = 0.156 y[1] (analytic) = 2.0122176760768644974329443564304 y[1] (numeric) = 2.0122176760768644974334442290074 absolute error = 4.998725770e-22 relative error = 2.4841873865981555889085000365475e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.2MB, time=13.20 Real estimate of pole used Radius of convergence = 3.787 Order of pole = 48.29 x[1] = 0.1561 y[1] (analytic) = 2.0122334089919160413737201495033 y[1] (numeric) = 2.0122334089919160413742209706652 absolute error = 5.008211619e-22 relative error = 2.4888820534537303368795276727898e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.766 Order of pole = 47.89 x[1] = 0.1562 y[1] (analytic) = 2.0122491521546534702153043686534 y[1] (numeric) = 2.0122491521546534702158061386324 absolute error = 5.017699790e-22 relative error = 2.4935777881318543310354471049164e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.745 Order of pole = 47.48 x[1] = 0.1563 y[1] (analytic) = 2.0122649055653994510122597196556 y[1] (numeric) = 2.0122649055653994510127624386841 absolute error = 5.027190285e-22 relative error = 2.4982745915292285622163135496092e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.725 Order of pole = 47.09 x[1] = 0.1564 y[1] (analytic) = 2.0122806692244768710288842468214 y[1] (numeric) = 2.0122806692244768710293879151319 absolute error = 5.036683105e-22 relative error = 2.5029724640455414388317618837452e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.704 Order of pole = 46.69 x[1] = 0.1565 y[1] (analytic) = 2.012296443132208837766003885855 y[1] (numeric) = 2.0122964431322088377665085036802 absolute error = 5.046178252e-22 relative error = 2.5076714065773775647613986861116e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.684 Order of pole = 46.31 x[1] = 0.1566 y[1] (analytic) = 2.0123122272889186789877845438599 y[1] (numeric) = 2.0123122272889186789882901114328 absolute error = 5.055675729e-22 relative error = 2.5123714205181982269281408265830e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.664 Order of pole = 45.93 x[1] = 0.1567 y[1] (analytic) = 2.0123280216949299427485637112828 y[1] (numeric) = 2.0123280216949299427490702288364 absolute error = 5.065175536e-22 relative error = 2.5170725057705743429941887044015e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.645 Order of pole = 45.55 x[1] = 0.1568 y[1] (analytic) = 2.0123438263505663974197016105846 y[1] (numeric) = 2.0123438263505663974202090783522 absolute error = 5.074677676e-22 relative error = 2.5217746637278427692667319982612e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.626 Order of pole = 45.18 x[1] = 0.1569 y[1] (analytic) = 2.0123596412561520317164518864344 y[1] (numeric) = 2.0123596412561520317169603046495 absolute error = 5.084182151e-22 relative error = 2.5264778952863314525376634791001e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.607 Order of pole = 44.81 x[1] = 0.157 y[1] (analytic) = 2.0123754664120110547248518422239 y[1] (numeric) = 2.0123754664120110547253612111201 absolute error = 5.093688962e-22 relative error = 2.5311822008453788969662004756047e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.2MB, time=13.41 Real estimate of pole used Radius of convergence = 3.588 Order of pole = 44.45 x[1] = 0.1571 y[1] (analytic) = 2.0123913018184678959286322277035 y[1] (numeric) = 2.0123913018184678959291425475146 absolute error = 5.103198111e-22 relative error = 2.5358875813011961668288197785865e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.569 Order of pole = 44.1 x[1] = 0.1572 y[1] (analytic) = 2.0124071474758472052361465825471 y[1] (numeric) = 2.0124071474758472052366578535073 absolute error = 5.112709602e-22 relative error = 2.5405940385437646366693880200284e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.551 Order of pole = 43.75 x[1] = 0.1573 y[1] (analytic) = 2.012423003384473853007320140655 y[1] (numeric) = 2.0124230033844738530078323629983 absolute error = 5.122223433e-22 relative error = 2.5453015714814894201181643315552e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.533 Order of pole = 43.4 x[1] = 0.1574 y[1] (analytic) = 2.0124388695446729300806183000065 y[1] (numeric) = 2.0124388695446729300811314739674 absolute error = 5.131739609e-22 relative error = 2.5500101825011403524832692296599e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.515 Order of pole = 43.06 x[1] = 0.1575 y[1] (analytic) = 2.0124547459567697478000346628826 y[1] (numeric) = 2.0124547459567697478005487886957 absolute error = 5.141258131e-22 relative error = 2.5547198720017534170017550124350e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.498 Order of pole = 42.72 x[1] = 0.1576 y[1] (analytic) = 2.0124706326210898380420986512764 y[1] (numeric) = 2.0124706326210898380426137291764 absolute error = 5.150779000e-22 relative error = 2.5594306403823157197182704992535e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.481 Order of pole = 42.39 x[1] = 0.1577 y[1] (analytic) = 2.0124865295379589532429027023178 y[1] (numeric) = 2.0124865295379589532434187325397 absolute error = 5.160302219e-22 relative error = 2.5641424890355609384716425687227e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.463 Order of pole = 42.06 x[1] = 0.1578 y[1] (analytic) = 2.0125024367077030664251490485412 y[1] (numeric) = 2.01250243670770306642566603132 absolute error = 5.169827788e-22 relative error = 2.5688554178634609829486790525561e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.447 Order of pole = 41.74 x[1] = 0.1579 y[1] (analytic) = 2.012518354130648371225216087827 y[1] (numeric) = 2.0125183541306483712257340233981 absolute error = 5.179355711e-22 relative error = 2.5735694287555140209658342809815e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.2MB, time=13.63 Real estimate of pole used Radius of convergence = 3.43 Order of pole = 41.42 x[1] = 0.158 y[1] (analytic) = 2.0125342818071212819202443478551 y[1] (numeric) = 2.012534281807121281920763236454 absolute error = 5.188885989e-22 relative error = 2.5782845221104642099555259922162e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.414 Order of pole = 41.1 x[1] = 0.1581 y[1] (analytic) = 2.0125502197374484334552420499082 y[1] (numeric) = 2.0125502197374484334557618917706 absolute error = 5.198418624e-22 relative error = 2.5830006988238886679123050622543e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.397 Order of pole = 40.79 x[1] = 0.1582 y[1] (analytic) = 2.0125661679219566814702102768707 y[1] (numeric) = 2.0125661679219566814707310722324 absolute error = 5.207953617e-22 relative error = 2.5877179592944216167318936979428e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.381 Order of pole = 40.48 x[1] = 0.1583 y[1] (analytic) = 2.0125821263609731023272877502688 y[1] (numeric) = 2.0125821263609731023278094993659 absolute error = 5.217490971e-22 relative error = 2.5924363049143964346373012698517e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.365 Order of pole = 40.18 x[1] = 0.1584 y[1] (analytic) = 2.0125980950548249931379152212051 y[1] (numeric) = 2.0125980950548249931384379242738 absolute error = 5.227030687e-22 relative error = 2.5971557360823254454045328668494e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.35 Order of pole = 39.88 x[1] = 0.1585 y[1] (analytic) = 2.012614074003839871790019480041 y[1] (numeric) = 2.0126140740038398717905431373178 absolute error = 5.236572768e-22 relative error = 2.6018762541904042795491316397612e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.334 Order of pole = 39.58 x[1] = 0.1586 y[1] (analytic) = 2.0126300632083454769752169896874 y[1] (numeric) = 2.0126300632083454769757416014088 absolute error = 5.246117214e-22 relative error = 2.6065978591401608839800301206145e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.319 Order of pole = 39.29 x[1] = 0.1587 y[1] (analytic) = 2.0126460626686697682160371473654 y[1] (numeric) = 2.0126460626686697682165627137683 absolute error = 5.255664029e-22 relative error = 2.6113205528205231403512053790085e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.304 Order of pole = 39 x[1] = 0.1588 y[1] (analytic) = 2.0126620723851409258931651797046 y[1] (numeric) = 2.0126620723851409258936917010259 absolute error = 5.265213213e-22 relative error = 2.6160443351329046471887524084772e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.289 Order of pole = 38.71 x[1] = 0.1589 y[1] (analytic) = 2.012678092358087351272704676048 y[1] (numeric) = 2.012678092358087351273232152525 absolute error = 5.274764770e-22 relative error = 2.6207692079660872544651118005804e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.2MB, time=13.86 Real estimate of pole used Radius of convergence = 3.275 Order of pole = 38.43 x[1] = 0.159 y[1] (analytic) = 2.01269412258783766653345976484 y[1] (numeric) = 2.0126941225878376665339881967099 absolute error = 5.284318699e-22 relative error = 2.6254951707245235574580907464182e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.26 Order of pole = 38.15 x[1] = 0.1591 y[1] (analytic) = 2.0127101630747207147942369379727 y[1] (numeric) = 2.012710163074720714794766325473 absolute error = 5.293875003e-22 relative error = 2.6302222248000185187594019532221e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.246 Order of pole = 37.87 x[1] = 0.1592 y[1] (analytic) = 2.0127262138190655601411665279745 y[1] (numeric) = 2.0127262138190655601416968713431 absolute error = 5.303433686e-22 relative error = 2.6349503720811345629089744251191e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.232 Order of pole = 37.6 x[1] = 0.1593 y[1] (analytic) = 2.0127422748212014876550438429267 y[1] (numeric) = 2.0127422748212014876555751424013 absolute error = 5.312994746e-22 relative error = 2.6396796114753294917498072486771e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.218 Order of pole = 37.33 x[1] = 0.1594 y[1] (analytic) = 2.0127583460814580034386899639954 y[1] (numeric) = 2.0127583460814580034392222198142 absolute error = 5.322558188e-22 relative error = 2.6444099453678736083983515683213e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.204 Order of pole = 37.07 x[1] = 0.1595 y[1] (analytic) = 2.0127744276001648346443322104752 y[1] (numeric) = 2.0127744276001648346448654228765 absolute error = 5.332124013e-22 relative error = 2.6491413741566175538605621494783e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.19 Order of pole = 36.8 x[1] = 0.1596 y[1] (analytic) = 2.0127905193776519295010042772393 y[1] (numeric) = 2.0127905193776519295015384464615 absolute error = 5.341692222e-22 relative error = 2.6538738982393623852704330614948e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.176 Order of pole = 36.54 x[1] = 0.1597 y[1] (analytic) = 2.0128066214142494573419660494982 y[1] (numeric) = 2.01280662141424945734250117578 absolute error = 5.351262818e-22 relative error = 2.6586075190074969839667840028540e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.163 Order of pole = 36.29 x[1] = 0.1598 y[1] (analytic) = 2.0128227337102878086321430997717 y[1] (numeric) = 2.012822733710287808632679183352 absolute error = 5.360835803e-22 relative error = 2.6633422373555140479384295549397e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.2MB, time=14.08 Real estimate of pole used Radius of convergence = 3.15 Order of pole = 36.03 x[1] = 0.1599 y[1] (analytic) = 2.0128388562660975949955858719827 y[1] (numeric) = 2.0128388562660975949961229131004 absolute error = 5.370411177e-22 relative error = 2.6680780531842191577740361487985e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.137 Order of pole = 35.78 x[1] = 0.16 y[1] (analytic) = 2.0128549890820096492429485575849 y[1] (numeric) = 2.0128549890820096492434865564793 absolute error = 5.379988944e-22 relative error = 2.6728149683816112110159175630860e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.124 Order of pole = 35.53 x[1] = 0.1601 y[1] (analytic) = 2.0128711321583550253989876686422 y[1] (numeric) = 2.0128711321583550253995266255527 absolute error = 5.389569105e-22 relative error = 2.6775529833451831874725491916029e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.111 Order of pole = 35.29 x[1] = 0.1602 y[1] (analytic) = 2.0128872854954649987300803127776 y[1] (numeric) = 2.0128872854954649987306202279438 absolute error = 5.399151662e-22 relative error = 2.6822920989691770786810510465683e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.099 Order of pole = 35.05 x[1] = 0.1603 y[1] (analytic) = 2.0129034490936710657717621749178 y[1] (numeric) = 2.0129034490936710657723030485794 absolute error = 5.408736616e-22 relative error = 2.6870323156509742853691176552804e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.086 Order of pole = 34.81 x[1] = 0.1604 y[1] (analytic) = 2.0129196229533049443562852107599 y[1] (numeric) = 2.0129196229533049443568270431569 absolute error = 5.418323970e-22 relative error = 2.6917736347814880036352082366813e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.074 Order of pole = 34.57 x[1] = 0.1605 y[1] (analytic) = 2.0129358070746985736401950568927 y[1] (numeric) = 2.0129358070746985736407378482653 absolute error = 5.427913726e-22 relative error = 2.6965160572547627678646518672121e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.062 Order of pole = 34.34 x[1] = 0.1606 y[1] (analytic) = 2.0129520014581841141319281625079 y[1] (numeric) = 2.0129520014581841141324719130963 absolute error = 5.437505884e-22 relative error = 2.7012595829712115281262256711111e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.049 Order of pole = 34.1 x[1] = 0.1607 y[1] (analytic) = 2.0129682061040939477194286476396 y[1] (numeric) = 2.0129682061040939477199733576844 absolute error = 5.447100448e-22 relative error = 2.7060042138183286034663983573458e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.037 Order of pole = 33.87 memory used=247.9MB, alloc=4.2MB, time=14.30 x[1] = 0.1608 y[1] (analytic) = 2.0129844210127606776977848928773 y[1] (numeric) = 2.0129844210127606776983305626192 absolute error = 5.456697419e-22 relative error = 2.7107499501931858187820015446373e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.026 Order of pole = 33.65 x[1] = 0.1609 y[1] (analytic) = 2.0130006461845171287968858654974 y[1] (numeric) = 2.0130006461845171287974324951772 absolute error = 5.466296798e-22 relative error = 2.7154967924928049569001850469091e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.014 Order of pole = 33.42 x[1] = 0.161 y[1] (analytic) = 2.0130168816196963472090971869651 y[1] (numeric) = 2.013016881619696347209644776824 absolute error = 5.475898589e-22 relative error = 2.7202447426044582034944526934869e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 3.002 Order of pole = 33.2 x[1] = 0.1611 y[1] (analytic) = 2.0130331273186316006169569467619 y[1] (numeric) = 2.0130331273186316006175054970411 absolute error = 5.485502792e-22 relative error = 2.7249938004282682943141930386603e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.991 Order of pole = 32.98 x[1] = 0.1612 y[1] (analytic) = 2.0130493832816563782208912674958 y[1] (numeric) = 2.0130493832816563782214407784367 absolute error = 5.495109409e-22 relative error = 2.7297439668578414605264016658014e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.98 Order of pole = 32.76 x[1] = 0.1613 y[1] (analytic) = 2.0130656495091043907669496262579 y[1] (numeric) = 2.0130656495091043907675000981022 absolute error = 5.504718443e-22 relative error = 2.7344952432834725029442127396147e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.968 Order of pole = 32.55 x[1] = 0.1614 y[1] (analytic) = 2.0130819260013095705745599371914 y[1] (numeric) = 2.013081926001309570575111370181 absolute error = 5.514329896e-22 relative error = 2.7392476305986231192791182083929e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.957 Order of pole = 32.34 x[1] = 0.1615 y[1] (analytic) = 2.0130982127586060715643034002433 y[1] (numeric) = 2.0130982127586060715648557946201 absolute error = 5.523943768e-22 relative error = 2.7440011287031951739602730404378e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.946 Order of pole = 32.13 x[1] = 0.1616 y[1] (analytic) = 2.0131145097813282692857091210714 y[1] (numeric) = 2.0131145097813282692862624770777 absolute error = 5.533560063e-22 relative error = 2.7487557394840272523115501759243e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.936 Order of pole = 31.92 x[1] = 0.1617 y[1] (analytic) = 2.0131308170698107609450685070872 y[1] (numeric) = 2.0131308170698107609456228249653 absolute error = 5.543178781e-22 relative error = 2.7535114628409045260311604124213e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.2MB, time=14.53 Real estimate of pole used Radius of convergence = 2.925 Order of pole = 31.71 x[1] = 0.1618 y[1] (analytic) = 2.0131471346243883654332694446133 y[1] (numeric) = 2.0131471346243883654338247246058 absolute error = 5.552799925e-22 relative error = 2.7582683001637819506909094013022e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.914 Order of pole = 31.51 x[1] = 0.1619 y[1] (analytic) = 2.0131634624453961233536502621437 y[1] (numeric) = 2.0131634624453961233542065044935 absolute error = 5.562423498e-22 relative error = 2.7630262528425318789436551044393e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.904 Order of pole = 31.31 x[1] = 0.162 y[1] (analytic) = 2.0131798005331692970498734846944 y[1] (numeric) = 2.0131798005331692970504306896443 absolute error = 5.572049499e-22 relative error = 2.7677853202800375040527097788395e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.893 Order of pole = 31.11 x[1] = 0.1621 y[1] (analytic) = 2.0131961488880433706338193842382 y[1] (numeric) = 2.0131961488880433706343775520314 absolute error = 5.581677932e-22 relative error = 2.7725455043627767487016058751061e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.883 Order of pole = 30.91 x[1] = 0.1622 y[1] (analytic) = 2.0132125075103540500134993312217 y[1] (numeric) = 2.0132125075103540500140584621015 absolute error = 5.591308798e-22 relative error = 2.7773068054869729774084248396076e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.873 Order of pole = 30.71 x[1] = 0.1623 y[1] (analytic) = 2.0132288764004372629209889521643 y[1] (numeric) = 2.0132288764004372629215490463742 absolute error = 5.600942099e-22 relative error = 2.7820692245455135298120353146452e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.863 Order of pole = 30.52 x[1] = 0.1624 y[1] (analytic) = 2.0132452555586291589403810983448 y[1] (numeric) = 2.0132452555586291589409421561285 absolute error = 5.610577837e-22 relative error = 2.7868327624312190209610349889381e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.853 Order of pole = 30.33 x[1] = 0.1625 y[1] (analytic) = 2.0132616449852661095357586305844 y[1] (numeric) = 2.0132616449852661095363206521859 absolute error = 5.620216015e-22 relative error = 2.7915974205335497218069736148359e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.843 Order of pole = 30.14 x[1] = 0.1626 y[1] (analytic) = 2.0132780446806847080791870251385 y[1] (numeric) = 2.0132780446806847080797500108019 absolute error = 5.629856634e-22 relative error = 2.7963631992484781362052981080727e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.2MB, time=14.76 Real estimate of pole used Radius of convergence = 2.833 Order of pole = 29.95 x[1] = 0.1627 y[1] (analytic) = 2.0132944546452217698787268057139 y[1] (numeric) = 2.0132944546452217698792907556833 absolute error = 5.639499694e-22 relative error = 2.8011300984752277473870403093709e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.823 Order of pole = 29.77 x[1] = 0.1628 y[1] (analytic) = 2.0133108748792143322064658066315 y[1] (numeric) = 2.0133108748792143322070307211515 absolute error = 5.649145200e-22 relative error = 2.8058981205964589439059508547976e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.814 Order of pole = 29.58 x[1] = 0.1629 y[1] (analytic) = 2.0133273053829996543265712721599 y[1] (numeric) = 2.0133273053829996543271371514751 absolute error = 5.658793152e-22 relative error = 2.8106672655112653970002041150138e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.804 Order of pole = 29.4 x[1] = 0.163 y[1] (analytic) = 2.0133437461569152175233617970464 y[1] (numeric) = 2.0133437461569152175239286414017 absolute error = 5.668443553e-22 relative error = 2.8154375346087647205145604709837e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.795 Order of pole = 29.22 x[1] = 0.1631 y[1] (analytic) = 2.0133601972012987251293991132787 y[1] (numeric) = 2.0133601972012987251299669229191 absolute error = 5.678096404e-22 relative error = 2.8202089282846270245093931437669e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.786 Order of pole = 29.04 x[1] = 0.1632 y[1] (analytic) = 2.0133766585164881025535997281127 y[1] (numeric) = 2.0133766585164881025541685032834 absolute error = 5.687751707e-22 relative error = 2.8249814474311496127751192989138e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.776 Order of pole = 28.86 x[1] = 0.1633 y[1] (analytic) = 2.0133931301028214973093664184062 y[1] (numeric) = 2.0133931301028214973099361593526 absolute error = 5.697409464e-22 relative error = 2.8297550929405626532186717146015e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.767 Order of pole = 28.69 x[1] = 0.1634 y[1] (analytic) = 2.0134096119606372790427395863025 y[1] (numeric) = 2.0134096119606372790433102932702 absolute error = 5.707069677e-22 relative error = 2.8345298657050291305298327423201e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.758 Order of pole = 28.52 x[1] = 0.1635 y[1] (analytic) = 2.013426104090274039560568481311 y[1] (numeric) = 2.0134261040902740395611401545458 absolute error = 5.716732348e-22 relative error = 2.8393057666166447988497415387685e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.749 Order of pole = 28.34 x[1] = 0.1636 y[1] (analytic) = 2.0134426064920705928587022938365 y[1] (numeric) = 2.0134426064920705928592749335843 absolute error = 5.726397478e-22 relative error = 2.8440827960707763489128318303025e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.2MB, time=14.98 Real estimate of pole used Radius of convergence = 2.74 Order of pole = 28.17 x[1] = 0.1637 y[1] (analytic) = 2.0134591191663659751502011252126 y[1] (numeric) = 2.0134591191663659751507747317196 absolute error = 5.736065070e-22 relative error = 2.8488609554560548636985858474058e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.732 Order of pole = 28 x[1] = 0.1638 y[1] (analytic) = 2.0134756421134994448935668392985 y[1] (numeric) = 2.013475642113499444894141412811 absolute error = 5.745735125e-22 relative error = 2.8536402451677204924674831218981e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.723 Order of pole = 27.84 x[1] = 0.1639 y[1] (analytic) = 2.0134921753338104828209938007017 y[1] (numeric) = 2.0134921753338104828215693414663 absolute error = 5.755407646e-22 relative error = 2.8584206665942613942260106665117e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.714 Order of pole = 27.67 x[1] = 0.164 y[1] (analytic) = 2.0135087188276387919666395046947 y[1] (numeric) = 2.0135087188276387919672160129582 absolute error = 5.765082635e-22 relative error = 2.8632022206274364752781312952743e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.706 Order of pole = 27.51 x[1] = 0.1641 y[1] (analytic) = 2.0135252725953242976949151038959 y[1] (numeric) = 2.0135252725953242976954925799051 absolute error = 5.774760092e-22 relative error = 2.8679849071656543376834212087002e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.697 Order of pole = 27.35 x[1] = 0.1642 y[1] (analytic) = 2.013541836637207147728795836789 y[1] (numeric) = 2.0135418366372071477293742807911 absolute error = 5.784440021e-22 relative error = 2.8727687280938379433238877519711e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.689 Order of pole = 27.19 x[1] = 0.1643 y[1] (analytic) = 2.0135584109536277121781513631614 y[1] (numeric) = 2.0135584109536277121787307754036 absolute error = 5.794122422e-22 relative error = 2.8775536833102770851901970730078e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.681 Order of pole = 27.03 x[1] = 0.1644 y[1] (analytic) = 2.0135749955449265835680960115416 y[1] (numeric) = 2.0135749955449265835686763922715 absolute error = 5.803807299e-22 relative error = 2.8823397746997431470837436506642e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.672 Order of pole = 26.87 x[1] = 0.1645 y[1] (analytic) = 2.0135915904114445768673589437253 y[1] (numeric) = 2.0135915904114445768679402931905 absolute error = 5.813494652e-22 relative error = 2.8871270021604069434128818814670e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.2MB, time=15.20 Real estimate of pole used Radius of convergence = 2.664 Order of pole = 26.71 x[1] = 0.1646 y[1] (analytic) = 2.0136081955535227295166742414772 y[1] (numeric) = 2.0136081955535227295172565599255 absolute error = 5.823184483e-22 relative error = 2.8919153665836461858248479059284e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.656 Order of pole = 26.56 x[1] = 0.1647 y[1] (analytic) = 2.0136248109715023014571909205055 y[1] (numeric) = 2.0136248109715023014577742081851 absolute error = 5.832876796e-22 relative error = 2.8967048698540045065766655516700e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.648 Order of pole = 26.41 x[1] = 0.1648 y[1] (analytic) = 2.0136414366657247751589028768064 y[1] (numeric) = 2.0136414366657247751594871339655 absolute error = 5.842571591e-22 relative error = 2.9014955118694739418026798326413e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.64 Order of pole = 26.25 x[1] = 0.1649 y[1] (analytic) = 2.0136580726365318556490987704801 y[1] (numeric) = 2.0136580726365318556496839973671 absolute error = 5.852268870e-22 relative error = 2.9062872935212287401718990945214e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.632 Order of pole = 26.1 x[1] = 0.165 y[1] (analytic) = 2.0136747188842654705408318521251 y[1] (numeric) = 2.0136747188842654705414180489887 absolute error = 5.861968636e-22 relative error = 2.9110802161969797759771402964024e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.625 Order of pole = 25.95 x[1] = 0.1651 y[1] (analytic) = 2.013691375409267770061409736921 y[1] (numeric) = 2.0136913754092677700619969040099 absolute error = 5.871670889e-22 relative error = 2.9158742797945522489656909170108e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.617 Order of pole = 25.81 x[1] = 0.1652 y[1] (analytic) = 2.0137080422118811270809041315125 y[1] (numeric) = 2.0137080422118811270814922690758 absolute error = 5.881375633e-22 relative error = 2.9206694861981214938374551341176e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.609 Order of pole = 25.66 x[1] = 0.1653 y[1] (analytic) = 2.0137247192924481371406805188141 y[1] (numeric) = 2.013724719292448137141269627101 absolute error = 5.891082869e-22 relative error = 2.9254658358019852891575918772495e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.602 Order of pole = 25.51 x[1] = 0.1654 y[1] (analytic) = 2.0137414066513116184819478058553 y[1] (numeric) = 2.0137414066513116184825378851151 absolute error = 5.900792598e-22 relative error = 2.9302633290003897593842572263198e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.594 Order of pole = 25.37 memory used=267.0MB, alloc=4.2MB, time=15.42 x[1] = 0.1655 y[1] (analytic) = 2.013758104288814612074327939793 y[1] (numeric) = 2.0137581042888146120749189902754 absolute error = 5.910504824e-22 relative error = 2.9350619676772812711129739340562e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.587 Order of pole = 25.23 x[1] = 0.1656 y[1] (analytic) = 2.0137748122053003816444454972214 y[1] (numeric) = 2.0137748122053003816450375191761 absolute error = 5.920219547e-22 relative error = 2.9398617517301856392411192849437e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.579 Order of pole = 25.09 x[1] = 0.1657 y[1] (analytic) = 2.0137915304011124137045372519107 y[1] (numeric) = 2.0137915304011124137051302455877 absolute error = 5.929936770e-22 relative error = 2.9446626825463205935016360945285e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.572 Order of pole = 24.95 x[1] = 0.1658 y[1] (analytic) = 2.013808258876594417581081726114 y[1] (numeric) = 2.0138082588765944175816756917634 absolute error = 5.939656494e-22 relative error = 2.9494647605196758787332026284191e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.565 Order of pole = 24.81 x[1] = 0.1659 y[1] (analytic) = 2.0138249976320903254434487305825 y[1] (numeric) = 2.0138249976320903254440436684548 absolute error = 5.949378723e-22 relative error = 2.9542679875338918470642759456232e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.557 Order of pole = 24.67 x[1] = 0.166 y[1] (analytic) = 2.0138417466679442923325688984354 y[1] (numeric) = 2.013841746667944292333164808781 absolute error = 5.959103456e-22 relative error = 2.9590723629896907026089569424373e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.55 Order of pole = 24.53 x[1] = 0.1661 y[1] (analytic) = 2.0138585059845006961896232180317 y[1] (numeric) = 2.0138585059845006961902201011013 absolute error = 5.968830696e-22 relative error = 2.9638778882740126549125179176867e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.543 Order of pole = 24.4 x[1] = 0.1662 y[1] (analytic) = 2.0138752755821041378847525699994 y[1] (numeric) = 2.0138752755821041378853504260439 absolute error = 5.978560445e-22 relative error = 2.9686845642771578448718343325092e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.536 Order of pole = 24.26 x[1] = 0.1663 y[1] (analytic) = 2.0138920554610994412457872735772 y[1] (numeric) = 2.0138920554610994412463861028477 absolute error = 5.988292705e-22 relative error = 2.9734923918893579028252423137710e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.529 Order of pole = 24.13 x[1] = 0.1664 y[1] (analytic) = 2.0139088456218316530869966474306 y[1] (numeric) = 2.0139088456218316530875964501784 absolute error = 5.998027478e-22 relative error = 2.9783013720007759012834006246297e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.2MB, time=15.65 Real estimate of pole used Radius of convergence = 2.522 Order of pole = 24 x[1] = 0.1665 y[1] (analytic) = 2.0139256460646460432378585901071 y[1] (numeric) = 2.0139256460646460432384593665838 absolute error = 6.007764767e-22 relative error = 2.9831115059980489689835831563198e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.516 Order of pole = 23.87 x[1] = 0.1666 y[1] (analytic) = 2.0139424567898881045718491852993 y[1] (numeric) = 2.0139424567898881045724509357565 absolute error = 6.017504572e-22 relative error = 2.9879227937781134536127887022755e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.509 Order of pole = 23.74 x[1] = 0.1667 y[1] (analytic) = 2.0139592777979035530352523370883 y[1] (numeric) = 2.0139592777979035530358550617779 absolute error = 6.027246896e-22 relative error = 2.9927352367274732741884294170022e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.502 Order of pole = 23.61 x[1] = 0.1668 y[1] (analytic) = 2.0139761090890383276759894403449 y[1] (numeric) = 2.013976109089038327676593139519 absolute error = 6.036991741e-22 relative error = 2.9975488357360167992633103726028e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.495 Order of pole = 23.48 x[1] = 0.1669 y[1] (analytic) = 2.0139929506636385906724690914686 y[1] (numeric) = 2.0139929506636385906730737653794 absolute error = 6.046739108e-22 relative error = 3.0023635911970375356337095823718e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.489 Order of pole = 23.36 x[1] = 0.167 y[1] (analytic) = 2.0140098025220507273624568446486 y[1] (numeric) = 2.0140098025220507273630624935486 absolute error = 6.056489000e-22 relative error = 3.0071795044968205931144530972269e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.482 Order of pole = 23.23 x[1] = 0.1671 y[1] (analytic) = 2.0140266646646213462719650188369 y[1] (numeric) = 2.0140266646646213462725716429787 absolute error = 6.066241418e-22 relative error = 3.0119965760285300675013155171413e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.476 Order of pole = 23.11 x[1] = 0.1672 y[1] (analytic) = 2.014043537091697279144162560624 y[1] (numeric) = 2.0140435370916972791447701602604 absolute error = 6.075996364e-22 relative error = 3.0168148066817913532250802414525e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.469 Order of pole = 22.98 x[1] = 0.1673 y[1] (analytic) = 2.0140604198036255809683049682149 y[1] (numeric) = 2.014060419803625580968913543599 absolute error = 6.085753841e-22 relative error = 3.0216341978426703108180122161574e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.2MB, time=15.87 Real estimate of pole used Radius of convergence = 2.463 Order of pole = 22.86 x[1] = 0.1674 y[1] (analytic) = 2.0140773128007535300086842817055 y[1] (numeric) = 2.0140773128007535300092938330905 absolute error = 6.095513850e-22 relative error = 3.0264547499041365873857343170507e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.457 Order of pole = 22.74 x[1] = 0.1675 y[1] (analytic) = 2.0140942160834286278335991448633 y[1] (numeric) = 2.0140942160834286278342096725026 absolute error = 6.105276393e-22 relative error = 3.0312764637556085231539063460241e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.45 Order of pole = 22.62 x[1] = 0.1676 y[1] (analytic) = 2.0141111296519985993443449436211 y[1] (numeric) = 2.0141111296519985993449564477683 absolute error = 6.115041472e-22 relative error = 3.0360993402864353482567716044200e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.444 Order of pole = 22.5 x[1] = 0.1677 y[1] (analytic) = 2.014128053506811392804224026496 y[1] (numeric) = 2.0141280535068113928048365074049 absolute error = 6.124809089e-22 relative error = 3.0409233803858971354964263190025e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.438 Order of pole = 22.38 x[1] = 0.1678 y[1] (analytic) = 2.0141449876482151798675760121493 y[1] (numeric) = 2.0141449876482151798681894700739 absolute error = 6.134579246e-22 relative error = 3.0457485849432047531043133464346e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.432 Order of pole = 22.27 x[1] = 0.1679 y[1] (analytic) = 2.014161932076558355608828189308 y[1] (numeric) = 2.0141619320765583556094426245024 absolute error = 6.144351944e-22 relative error = 3.0505749543510154067559897374097e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.426 Order of pole = 22.15 x[1] = 0.168 y[1] (analytic) = 2.0141788867921895385515660142714 y[1] (numeric) = 2.0141788867921895385521814269901 absolute error = 6.154127187e-22 relative error = 3.0554024904913744145803405745031e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.42 Order of pole = 22.04 x[1] = 0.1681 y[1] (analytic) = 2.0141958517954575706976237112318 y[1] (numeric) = 2.0141958517954575706982401017294 absolute error = 6.163904976e-22 relative error = 3.0602311937567961601570839065541e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.414 Order of pole = 21.92 x[1] = 0.1682 y[1] (analytic) = 2.0142128270867115175561949806404 y[1] (numeric) = 2.0142128270867115175568123491715 absolute error = 6.173685311e-22 relative error = 3.0650610640432704898738102828120e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.408 Order of pole = 21.81 x[1] = 0.1683 y[1] (analytic) = 2.014229812666300668172963820854 y[1] (numeric) = 2.0142298126663006681735821676737 absolute error = 6.183468197e-22 relative error = 3.0698921037290896973708390210935e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.2MB, time=16.09 Real estimate of pole used Radius of convergence = 2.402 Order of pole = 21.7 x[1] = 0.1684 y[1] (analytic) = 2.0142468085345745351592554683048 y[1] (numeric) = 2.0142468085345745351598747936681 absolute error = 6.193253633e-22 relative error = 3.0747243122136454094634112108924e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.396 Order of pole = 21.58 x[1] = 0.1685 y[1] (analytic) = 2.0142638146918828547212074614335 y[1] (numeric) = 2.0142638146918828547218277655958 absolute error = 6.203041623e-22 relative error = 3.0795576913786064933053096886602e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.39 Order of pole = 21.47 x[1] = 0.1686 y[1] (analytic) = 2.014280831138575586688960833637 y[1] (numeric) = 2.0142808311385755866895821168539 absolute error = 6.212832169e-22 relative error = 3.0843922421126285024306837465436e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.385 Order of pole = 21.36 x[1] = 0.1687 y[1] (analytic) = 2.0142978578750029145458714404807 y[1] (numeric) = 2.0142978578750029145464937030078 absolute error = 6.222625271e-22 relative error = 3.0892279643113955452770556046042e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.379 Order of pole = 21.26 x[1] = 0.1688 y[1] (analytic) = 2.0143148949015152454577414264311 y[1] (numeric) = 2.0143148949015152454583646685243 absolute error = 6.232420932e-22 relative error = 3.0940648593598957715158468952738e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.373 Order of pole = 21.15 x[1] = 0.1689 y[1] (analytic) = 2.0143319422184632103020708363699 y[1] (numeric) = 2.0143319422184632103026950582854 absolute error = 6.242219155e-22 relative error = 3.0989029286430308306127999340096e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.368 Order of pole = 21.04 x[1] = 0.169 y[1] (analytic) = 2.0143489998261976636973293771518 y[1] (numeric) = 2.0143489998261976636979545791459 absolute error = 6.252019941e-22 relative error = 3.1037421725527391930945395914439e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.362 Order of pole = 20.93 x[1] = 0.1691 y[1] (analytic) = 2.0143660677250696840322483344746 y[1] (numeric) = 2.0143660677250696840328745168038 absolute error = 6.261823292e-22 relative error = 3.1085825919773404335483388707812e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.356 Order of pole = 20.83 x[1] = 0.1692 y[1] (analytic) = 2.0143831459154305734951326503331 y[1] (numeric) = 2.014383145915430573495759813254 absolute error = 6.271629209e-22 relative error = 3.1134241873086543874345320819186e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.2MB, time=16.31 Real estimate of pole used Radius of convergence = 2.351 Order of pole = 20.72 x[1] = 0.1693 y[1] (analytic) = 2.0144002343976318581031931663323 y[1] (numeric) = 2.0144002343976318581038213101019 absolute error = 6.281437696e-22 relative error = 3.1182669604277248681372658363451e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.346 Order of pole = 20.62 x[1] = 0.1694 y[1] (analytic) = 2.0144173331720252877318990381402 y[1] (numeric) = 2.0144173331720252877325281630155 absolute error = 6.291248753e-22 relative error = 3.1231109112298061957139936872722e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.34 Order of pole = 20.52 x[1] = 0.1695 y[1] (analytic) = 2.0144344422389628361443503263627 y[1] (numeric) = 2.014434442238962836144980432601 absolute error = 6.301062383e-22 relative error = 3.1279560410993681536170046048204e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.335 Order of pole = 20.42 x[1] = 0.1696 y[1] (analytic) = 2.0144515615987967010206707691298 y[1] (numeric) = 2.0144515615987967010213018569885 absolute error = 6.310878587e-22 relative error = 3.1328023504279675690915904070120e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.329 Order of pole = 20.31 x[1] = 0.1697 y[1] (analytic) = 2.0144686912518793039874207416829 y[1] (numeric) = 2.0144686912518793039880528114198 absolute error = 6.320697369e-22 relative error = 3.1376498410963344884611135313768e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.324 Order of pole = 20.21 x[1] = 0.1698 y[1] (analytic) = 2.0144858311985632906470304082609 y[1] (numeric) = 2.0144858311985632906476634601337 absolute error = 6.330518728e-22 relative error = 3.1424985125030721323072893664833e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.319 Order of pole = 20.11 x[1] = 0.1699 y[1] (analytic) = 2.0145029814392015306072530715823 y[1] (numeric) = 2.0145029814392015306078871058491 absolute error = 6.340342668e-22 relative error = 3.1473483665287660252245256964429e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.314 Order of pole = 20.01 x[1] = 0.17 y[1] (analytic) = 2.0145201419741471175106387252292 y[1] (numeric) = 2.0145201419741471175112737421482 absolute error = 6.350169190e-22 relative error = 3.1521994035647092779295691583047e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.309 Order of pole = 19.92 x[1] = 0.1701 y[1] (analytic) = 2.0145373128037533690640278142393 y[1] (numeric) = 2.014537312803753369064663814069 absolute error = 6.359998297e-22 relative error = 3.1570516249949254452435105607479e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.303 Order of pole = 19.82 memory used=286.1MB, alloc=4.3MB, time=16.53 x[1] = 0.1702 y[1] (analytic) = 2.0145544939283738270680652092181 y[1] (numeric) = 2.014554493928373827068702192217 absolute error = 6.369829989e-22 relative error = 3.1619050307141878468958849642480e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.298 Order of pole = 19.72 x[1] = 0.1703 y[1] (analytic) = 2.0145716853483622574467343992862 y[1] (numeric) = 2.0145716853483622574473723657132 absolute error = 6.379664270e-22 relative error = 3.1667596226027670338665220562503e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.293 Order of pole = 19.63 x[1] = 0.1704 y[1] (analytic) = 2.0145888870640726502769119091827 y[1] (numeric) = 2.0145888870640726502775508592968 absolute error = 6.389501141e-22 relative error = 3.1716154010516916921698214700820e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.288 Order of pole = 19.53 x[1] = 0.1705 y[1] (analytic) = 2.0146060990758592198179419458464 y[1] (numeric) = 2.0146060990758592198185818799069 absolute error = 6.399340605e-22 relative error = 3.1764723674446869052352625864429e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.283 Order of pole = 19.44 x[1] = 0.1706 y[1] (analytic) = 2.014623321384076404541231279804 y[1] (numeric) = 2.0146233213840764045418721980702 absolute error = 6.409182662e-22 relative error = 3.1813305216762781689139869929330e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.278 Order of pole = 19.34 x[1] = 0.1707 y[1] (analytic) = 2.0146405539890788671598643666956 y[1] (numeric) = 2.0146405539890788671605062694272 absolute error = 6.419027316e-22 relative error = 3.1861898656264202268095512776869e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.273 Order of pole = 19.25 x[1] = 0.1708 y[1] (analytic) = 2.0146577968912214946582387142745 y[1] (numeric) = 2.0146577968912214946588816017313 absolute error = 6.428874568e-22 relative error = 3.1910503996858766248072945642155e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.269 Order of pole = 19.16 x[1] = 0.1709 y[1] (analytic) = 2.0146750500908593983217205002191 y[1] (numeric) = 2.014675050090859398322364372661 absolute error = 6.438724419e-22 relative error = 3.1959121242453572586318449657265e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.264 Order of pole = 19.06 x[1] = 0.171 y[1] (analytic) = 2.0146923135883479137663204461019 y[1] (numeric) = 2.0146923135883479137669653037891 absolute error = 6.448576872e-22 relative error = 3.2007750406882257669961998456600e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.259 Order of pole = 18.97 x[1] = 0.1711 y[1] (analytic) = 2.0147095873840426009683899528632 y[1] (numeric) = 2.0147095873840426009690357960561 absolute error = 6.458431929e-22 relative error = 3.2056391499014085959703950889433e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.3MB, time=16.75 Real estimate of pole used Radius of convergence = 2.254 Order of pole = 18.88 x[1] = 0.1712 y[1] (analytic) = 2.0147268714782992442943375031397 y[1] (numeric) = 2.0147268714782992442949843320989 absolute error = 6.468289592e-22 relative error = 3.2105044527717614118403550829102e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.25 Order of pole = 18.79 x[1] = 0.1713 y[1] (analytic) = 2.0147441658714738525303653358056 y[1] (numeric) = 2.0147441658714738525310131507919 absolute error = 6.478149863e-22 relative error = 3.2153709501860690539471670295586e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.245 Order of pole = 18.7 x[1] = 0.1714 y[1] (analytic) = 2.014761470563922658912226398084 y[1] (numeric) = 2.0147614705639226589128751993583 absolute error = 6.488012743e-22 relative error = 3.2202386425347088171037579196670e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.24 Order of pole = 18.61 x[1] = 0.1715 y[1] (analytic) = 2.0147787855560021211550015805935 y[1] (numeric) = 2.014778785556002121155651368417 absolute error = 6.497878235e-22 relative error = 3.2251075312006689467397075178523e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.236 Order of pole = 18.53 x[1] = 0.1716 y[1] (analytic) = 2.0147961108480689214828972406974 y[1] (numeric) = 2.0147961108480689214835480153314 absolute error = 6.507746340e-22 relative error = 3.2299776165741933888774605673084e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.231 Order of pole = 18.44 x[1] = 0.1717 y[1] (analytic) = 2.0148134464404799666590630195267 y[1] (numeric) = 2.0148134464404799666597147812328 absolute error = 6.517617061e-22 relative error = 3.2348489000381198887254707495825e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.226 Order of pole = 18.35 x[1] = 0.1718 y[1] (analytic) = 2.0148307923335923880154299580533 y[1] (numeric) = 2.0148307923335923880160827070932 absolute error = 6.527490399e-22 relative error = 3.2397213819825588647643564745184e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.222 Order of pole = 18.27 x[1] = 0.1719 y[1] (analytic) = 2.0148481485277635414825689175925 y[1] (numeric) = 2.0148481485277635414832226542282 absolute error = 6.537366357e-22 relative error = 3.2445950637901973635271812207938e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.217 Order of pole = 18.18 x[1] = 0.172 y[1] (analytic) = 2.0148655150233510076195693101194 y[1] (numeric) = 2.014865515023351007620224034613 absolute error = 6.547244936e-22 relative error = 3.2494699458510120972192387455478e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.3MB, time=16.97 Real estimate of pole used Radius of convergence = 2.213 Order of pole = 18.1 x[1] = 0.1721 y[1] (analytic) = 2.0148828918207125916439381437856 y[1] (numeric) = 2.0148828918207125916445938563995 absolute error = 6.557126139e-22 relative error = 3.2543460295475392152624511969539e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.209 Order of pole = 18.01 x[1] = 0.1722 y[1] (analytic) = 2.0149002789202063234615193890298 y[1] (numeric) = 2.0149002789202063234621760900266 absolute error = 6.567009968e-22 relative error = 3.2592233157659240222006542268338e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.204 Order of pole = 17.93 x[1] = 0.1723 y[1] (analytic) = 2.014917676322190457696433670677 y[1] (numeric) = 2.0149176763221904576970913603193 absolute error = 6.576896423e-22 relative error = 3.2641018043996441399389081754297e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.2 Order of pole = 17.85 x[1] = 0.1724 y[1] (analytic) = 2.0149350840270234737210382914257 y[1] (numeric) = 2.0149350840270234737216969699764 absolute error = 6.586785507e-22 relative error = 3.2689814968310218595736290539662e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.195 Order of pole = 17.76 x[1] = 0.1725 y[1] (analytic) = 2.0149525020350640756859075921287 y[1] (numeric) = 2.014952502035064075686567259851 absolute error = 6.596677223e-22 relative error = 3.2738623944422909484622823407272e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.191 Order of pole = 17.68 x[1] = 0.1726 y[1] (analytic) = 2.014969930346671192549833654274 y[1] (numeric) = 2.0149699303466711925504943114312 absolute error = 6.606571572e-22 relative error = 3.2787444976230259351526999531228e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.187 Order of pole = 17.6 x[1] = 0.1727 y[1] (analytic) = 2.0149873689622039781098473500784 y[1] (numeric) = 2.014987368962203978110508996934 absolute error = 6.616468556e-22 relative error = 3.2836278072590280681219874045226e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.183 Order of pole = 17.52 x[1] = 0.1728 y[1] (analytic) = 2.0150048178820218110312597456092 y[1] (numeric) = 2.0150048178820218110319223824269 absolute error = 6.626368177e-22 relative error = 3.2885123242360270765440667171434e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.178 Order of pole = 17.44 x[1] = 0.1729 y[1] (analytic) = 2.0150222771064842948777238623554 y[1] (numeric) = 2.0150222771064842948783874893991 absolute error = 6.636270437e-22 relative error = 3.2933980494396811231649447435795e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.174 Order of pole = 17.36 x[1] = 0.173 y[1] (analytic) = 2.0150397466359512581413168026708 y[1] (numeric) = 2.0150397466359512581419814202046 absolute error = 6.646175338e-22 relative error = 3.2982849837555767571802667105080e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.3MB, time=17.19 Real estimate of pole used Radius of convergence = 2.17 Order of pole = 17.28 x[1] = 0.1731 y[1] (analytic) = 2.0150572264707827542726422445185 y[1] (numeric) = 2.0150572264707827542733078528067 absolute error = 6.656082882e-22 relative error = 3.3031731280692288671151561606386e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.166 Order of pole = 17.2 x[1] = 0.1732 y[1] (analytic) = 2.0150747166113390617109533109483 y[1] (numeric) = 2.0150747166113390617116199102554 absolute error = 6.665993071e-22 relative error = 3.3080624832660806337063424684139e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.162 Order of pole = 17.12 x[1] = 0.1733 y[1] (analytic) = 2.0150922170579806839142958197434 y[1] (numeric) = 2.0150922170579806839149634103341 absolute error = 6.675905907e-22 relative error = 3.3129530502315034827865771043859e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.158 Order of pole = 17.05 x[1] = 0.1734 y[1] (analytic) = 2.0151097278110683493896719186767 y[1] (numeric) = 2.0151097278110683493903405008159 absolute error = 6.685821392e-22 relative error = 3.3178448298507970381713398226263e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.154 Order of pole = 16.97 x[1] = 0.1735 y[1] (analytic) = 2.015127248870963011723224111821 y[1] (numeric) = 2.0151272488709630117238936857738 absolute error = 6.695739528e-22 relative error = 3.3227378230091890745478359449505e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.15 Order of pole = 16.89 x[1] = 0.1736 y[1] (analytic) = 2.0151447802380258496104396823616 y[1] (numeric) = 2.0151447802380258496111102483933 absolute error = 6.705660317e-22 relative error = 3.3276320305918354703662859151624e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.146 Order of pole = 16.82 x[1] = 0.1737 y[1] (analytic) = 2.0151623219126182668863755173636 y[1] (numeric) = 2.0151623219126182668870470757397 absolute error = 6.715583761e-22 relative error = 3.3325274534838201607335082959530e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.142 Order of pole = 16.74 x[1] = 0.1738 y[1] (analytic) = 2.0151798738951018925559033399505 y[1] (numeric) = 2.0151798738951018925565758909366 absolute error = 6.725509861e-22 relative error = 3.3374240920739214721816375975564e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.138 Order of pole = 16.67 x[1] = 0.1739 y[1] (analytic) = 2.0151974361858385808239753543545 y[1] (numeric) = 2.0151974361858385808246488982165 absolute error = 6.735438620e-22 relative error = 3.3423219477433215792234443880938e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.3MB, time=17.42 Real estimate of pole used Radius of convergence = 2.134 Order of pole = 16.59 x[1] = 0.174 y[1] (analytic) = 2.0152150087851904111259103093034 y[1] (numeric) = 2.0152150087851904111265848463074 absolute error = 6.745370040e-22 relative error = 3.3472210213768883117090162354129e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.13 Order of pole = 16.52 x[1] = 0.1741 y[1] (analytic) = 2.0152325916935196881576999852122 y[1] (numeric) = 2.0152325916935196881583755156245 absolute error = 6.755304123e-22 relative error = 3.3521213138594173677421621798476e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.126 Order of pole = 16.45 x[1] = 0.1742 y[1] (analytic) = 2.0152501849111889419063361106532 y[1] (numeric) = 2.0152501849111889419070126347403 absolute error = 6.765240871e-22 relative error = 3.3570228260756322665854804048216e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.122 Order of pole = 16.37 x[1] = 0.1743 y[1] (analytic) = 2.01526778843856092768015771358 y[1] (numeric) = 2.0152677884385609276808352316085 absolute error = 6.775180285e-22 relative error = 3.3619255584139723312594008690688e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.119 Order of pole = 16.3 x[1] = 0.1744 y[1] (analytic) = 2.0152854022759986261392189127874 y[1] (numeric) = 2.0152854022759986261398974250241 absolute error = 6.785122367e-22 relative error = 3.3668295117590295929258810981510e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.115 Order of pole = 16.23 x[1] = 0.1745 y[1] (analytic) = 2.0153030264238652433256771550914 y[1] (numeric) = 2.0153030264238652433263566618035 absolute error = 6.795067121e-22 relative error = 3.3717346879877303652926954553136e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.111 Order of pole = 16.16 x[1] = 0.1746 y[1] (analytic) = 2.0153206608825242106942019037193 y[1] (numeric) = 2.015320660882524210694882405174 absolute error = 6.805014547e-22 relative error = 3.3766410869920980663715751849466e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.107 Order of pole = 16.09 x[1] = 0.1747 y[1] (analytic) = 2.0153383056523391851424037834014 y[1] (numeric) = 2.0153383056523391851430852798661 absolute error = 6.814964647e-22 relative error = 3.3815487096565076552858587363541e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.104 Order of pole = 16.02 x[1] = 0.1748 y[1] (analytic) = 2.0153559607336740490412841876626 y[1] (numeric) = 2.0153559607336740490419666794051 absolute error = 6.824917425e-22 relative error = 3.3864575578576421664092157480941e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.1 Order of pole = 15.95 memory used=305.1MB, alloc=4.3MB, time=17.64 x[1] = 0.1749 y[1] (analytic) = 2.0153736261268929102657053538156 y[1] (numeric) = 2.0153736261268929102663888411036 absolute error = 6.834872880e-22 relative error = 3.3913676309911477880591370488748e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.096 Order of pole = 15.88 x[1] = 0.175 y[1] (analytic) = 2.0153913018323601022248809111587 y[1] (numeric) = 2.0153913018323601022255653942603 absolute error = 6.844831016e-22 relative error = 3.3962789309335581586217902780008e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.093 Order of pole = 15.81 x[1] = 0.1751 y[1] (analytic) = 2.0154089878504401838928869078908 y[1] (numeric) = 2.0154089878504401838935723870743 absolute error = 6.854791835e-22 relative error = 3.4011914585689450984470131708178e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.089 Order of pole = 15.74 x[1] = 0.1752 y[1] (analytic) = 2.015426684181497939839193322254 y[1] (numeric) = 2.0154266841814979398398797977878 absolute error = 6.864755338e-22 relative error = 3.4061052142851349291412447634842e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.085 Order of pole = 15.67 x[1] = 0.1753 y[1] (analytic) = 2.0154443908258983802592160634235 y[1] (numeric) = 2.0154443908258983802599035355763 absolute error = 6.874721528e-22 relative error = 3.4110201994622356919670065629862e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.082 Order of pole = 15.61 x[1] = 0.1754 y[1] (analytic) = 2.0154621077840067410048894676653 y[1] (numeric) = 2.0154621077840067410055779367059 absolute error = 6.884690406e-22 relative error = 3.4159364144879369960773890259236e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.078 Order of pole = 15.54 x[1] = 0.1755 y[1] (analytic) = 2.0154798350561884836152592952874 y[1] (numeric) = 2.0154798350561884836159487614849 absolute error = 6.894661975e-22 relative error = 3.4208538607421926446093621202438e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.075 Order of pole = 15.47 x[1] = 0.1756 y[1] (analytic) = 2.0154975726428092953470962339154 y[1] (numeric) = 2.015497572642809295347786697539 absolute error = 6.904636236e-22 relative error = 3.4257725386125553558518651825760e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.071 Order of pole = 15.41 x[1] = 0.1757 y[1] (analytic) = 2.0155153205442350892055299136246 y[1] (numeric) = 2.0155153205442350892062213749438 absolute error = 6.914613192e-22 relative error = 3.4306924494788244967153879155832e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.068 Order of pole = 15.34 x[1] = 0.1758 y[1] (analytic) = 2.0155330787608320039747034394682 y[1] (numeric) = 2.0155330787608320039753958987526 absolute error = 6.924592844e-22 relative error = 3.4356135937284157162321088168773e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=309.0MB, alloc=4.3MB, time=17.85 Real estimate of pole used Radius of convergence = 2.064 Order of pole = 15.28 x[1] = 0.1759 y[1] (analytic) = 2.0155508472929664042484484469425 y[1] (numeric) = 2.0155508472929664042491419044619 absolute error = 6.934575194e-22 relative error = 3.4405359722448314634475664506090e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.061 Order of pole = 15.21 x[1] = 0.176 y[1] (analytic) = 2.0155686261410048804609806859361 y[1] (numeric) = 2.0155686261410048804616751419605 absolute error = 6.944560244e-22 relative error = 3.4454595859115011760236680538489e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.057 Order of pole = 15.15 x[1] = 0.1761 y[1] (analytic) = 2.0155864153053142489176161387125 y[1] (numeric) = 2.0155864153053142489183115935123 absolute error = 6.954547998e-22 relative error = 3.4503844366040482899668694575929e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.054 Order of pole = 15.08 x[1] = 0.1762 y[1] (analytic) = 2.0156042147862615518255076774816 y[1] (numeric) = 2.0156042147862615518262041313272 absolute error = 6.964538456e-22 relative error = 3.4553105242134714971343612599471e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.051 Order of pole = 15.02 x[1] = 0.1763 y[1] (analytic) = 2.015622024584214057324402267117 y[1] (numeric) = 2.0156220245842140573250997202789 absolute error = 6.974531619e-22 relative error = 3.4602378491268561405906410474057e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.047 Order of pole = 14.96 x[1] = 0.1764 y[1] (analytic) = 2.0156398446995392595174187185828 y[1] (numeric) = 2.0156398446995392595181171713319 absolute error = 6.984527491e-22 relative error = 3.4651664132195930401501510084296e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.044 Order of pole = 14.89 x[1] = 0.1765 y[1] (analytic) = 2.0156576751326048785018459986365 y[1] (numeric) = 2.0156576751326048785025454512439 absolute error = 6.994526074e-22 relative error = 3.4700962173747326974583162732718e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.041 Order of pole = 14.83 x[1] = 0.1766 y[1] (analytic) = 2.0156755158837788603999621013782 y[1] (numeric) = 2.0156755158837788604006625541151 absolute error = 7.004527369e-22 relative error = 3.4750272619791407083442567267342e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.037 Order of pole = 14.77 x[1] = 0.1767 y[1] (analytic) = 2.0156933669534293773898734872208 y[1] (numeric) = 2.0156933669534293773905749403587 absolute error = 7.014531379e-22 relative error = 3.4799595484118412951187699895647e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.3MB, time=18.08 Real estimate of pole used Radius of convergence = 2.034 Order of pole = 14.71 x[1] = 0.1768 y[1] (analytic) = 2.0157112283419248277363750948614 y[1] (numeric) = 2.0157112283419248277370775486719 absolute error = 7.024538105e-22 relative error = 3.4848930770595620926643581173565e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.031 Order of pole = 14.65 x[1] = 0.1769 y[1] (analytic) = 2.0157291000496338358218309318353 y[1] (numeric) = 2.0157291000496338358225343865903 absolute error = 7.034547550e-22 relative error = 3.4898278493011716988564248565228e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.028 Order of pole = 14.58 x[1] = 0.177 y[1] (analytic) = 2.0157469820769252521770752492412 y[1] (numeric) = 2.0157469820769252521777797052126 absolute error = 7.044559714e-22 relative error = 3.4947638650271656010761449409193e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.025 Order of pole = 14.52 x[1] = 0.1771 y[1] (analytic) = 2.0157648744241681535123343062277 y[1] (numeric) = 2.0157648744241681535130397636878 absolute error = 7.054574601e-22 relative error = 3.4997011261123593899334330292773e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.021 Order of pole = 14.46 x[1] = 0.1772 y[1] (analytic) = 2.0157827770917318427481687298376 y[1] (numeric) = 2.0157827770917318427488751890588 absolute error = 7.064592212e-22 relative error = 3.5046396329432042509716582472609e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.018 Order of pole = 14.4 x[1] = 0.1773 y[1] (analytic) = 2.0158006900799858490464364758087 y[1] (numeric) = 2.0158006900799858490471439370637 absolute error = 7.074612550e-22 relative error = 3.5095793868982569466940062130845e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.015 Order of pole = 14.34 x[1] = 0.1774 y[1] (analytic) = 2.0158186133892999278412763959354 y[1] (numeric) = 2.015818613389299927841984859497 absolute error = 7.084635616e-22 relative error = 3.5145203883638301669026538653258e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.012 Order of pole = 14.29 x[1] = 0.1775 y[1] (analytic) = 2.0158365470200440608701124175976 y[1] (numeric) = 2.0158365470200440608708218837389 absolute error = 7.094661413e-22 relative error = 3.5194626387183244558168254284996e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.009 Order of pole = 14.23 x[1] = 0.1776 y[1] (analytic) = 2.0158544909725884562046783410708 y[1] (numeric) = 2.0158544909725884562053888100651 absolute error = 7.104689943e-22 relative error = 3.5244061388439813800168884823419e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2.006 Order of pole = 14.17 x[1] = 0.1777 y[1] (analytic) = 2.0158724452473035482820632602317 y[1] (numeric) = 2.0158724452473035482827747323523 absolute error = 7.114721206e-22 relative error = 3.5293508886308424152844351172836e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.3MB, time=18.30 Real estimate of pole used Radius of convergence = 2.003 Order of pole = 14.11 x[1] = 0.1778 y[1] (analytic) = 2.0158904098445599979357776122798 y[1] (numeric) = 2.0158904098445599979364900878003 absolute error = 7.124755205e-22 relative error = 3.5342968894570866656351544007660e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 2 Order of pole = 14.05 x[1] = 0.1779 y[1] (analytic) = 2.0159083847647286924268398620996 y[1] (numeric) = 2.015908384764728692427553341294 absolute error = 7.134791944e-22 relative error = 3.5392441431968559411446533155532e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.997 Order of pole = 14 x[1] = 0.178 y[1] (analytic) = 2.0159263700081807454748838268924 y[1] (numeric) = 2.0159263700081807454755983100346 absolute error = 7.144831422e-22 relative error = 3.5441926492439333793835839201356e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.994 Order of pole = 13.94 x[1] = 0.1781 y[1] (analytic) = 2.0159443655752874972892866467076 y[1] (numeric) = 2.015944365575287497290002134072 absolute error = 7.154873644e-22 relative error = 3.5491424099683538367121745274950e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.991 Order of pole = 13.88 x[1] = 0.1782 y[1] (analytic) = 2.0159623714664205146003174065143 y[1] (numeric) = 2.0159623714664205146010338983753 absolute error = 7.164918610e-22 relative error = 3.5540934252598199491158607782488e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.988 Order of pole = 13.83 x[1] = 0.1783 y[1] (analytic) = 2.0159803876819515906903064154497 y[1] (numeric) = 2.0159803876819515906910239120819 absolute error = 7.174966322e-22 relative error = 3.5590456960000688371147652140292e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.985 Order of pole = 13.77 x[1] = 0.1784 y[1] (analytic) = 2.0159984142222527454248351488922 y[1] (numeric) = 2.0159984142222527454255536505704 absolute error = 7.185016782e-22 relative error = 3.5639992230707634812556669731885e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.982 Order of pole = 13.72 x[1] = 0.1785 y[1] (analytic) = 2.0160164510876962252839468590068 y[1] (numeric) = 2.0160164510876962252846663660062 absolute error = 7.195069994e-22 relative error = 3.5689540083455480717483905382785e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.979 Order of pole = 13.66 x[1] = 0.1786 y[1] (analytic) = 2.0160344982786545033933778594171 y[1] (numeric) = 2.0160344982786545033940983720128 absolute error = 7.205125957e-22 relative error = 3.5739100512178407521999114891958e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.3MB, time=18.52 Real estimate of pole used Radius of convergence = 1.976 Order of pole = 13.61 x[1] = 0.1787 y[1] (analytic) = 2.0160525557955002795558094896591 y[1] (numeric) = 2.0160525557955002795565310081266 absolute error = 7.215184675e-22 relative error = 3.5788673535611327452467918527351e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.973 Order of pole = 13.55 x[1] = 0.1788 y[1] (analytic) = 2.0160706236386064802821407650815 y[1] (numeric) = 2.0160706236386064802828632896964 absolute error = 7.225246149e-22 relative error = 3.5838259157607622885302563565073e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.97 Order of pole = 13.5 x[1] = 0.1789 y[1] (analytic) = 2.0160887018083462588227817178548 y[1] (numeric) = 2.0160887018083462588235052488931 absolute error = 7.235310383e-22 relative error = 3.5887857396900407873497655963320e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.967 Order of pole = 13.44 x[1] = 0.179 y[1] (analytic) = 2.0161067903050929951989674347616 y[1] (numeric) = 2.0161067903050929951996919724993 absolute error = 7.245377377e-22 relative error = 3.5937468252381477357661760228695e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.964 Order of pole = 13.39 x[1] = 0.1791 y[1] (analytic) = 2.01612488912922029623409279744 y[1] (numeric) = 2.0161248891292202962348183421533 absolute error = 7.255447133e-22 relative error = 3.5987091732862257892435584694791e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.962 Order of pole = 13.34 x[1] = 0.1792 y[1] (analytic) = 2.0161429982811019955850679307598 y[1] (numeric) = 2.0161429982811019955857944827251 absolute error = 7.265519653e-22 relative error = 3.6036727847153430873760464146107e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.959 Order of pole = 13.28 x[1] = 0.1793 y[1] (analytic) = 2.0161611177611121537736943650124 y[1] (numeric) = 2.0161611177611121537744219245064 absolute error = 7.275594940e-22 relative error = 3.6086376609024853134897764504339e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.956 Order of pole = 13.23 x[1] = 0.1794 y[1] (analytic) = 2.0161792475696250582180619176017 y[1] (numeric) = 2.0161792475696250582187904849013 absolute error = 7.285672996e-22 relative error = 3.6136038027285580543889683164349e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.953 Order of pole = 13.18 x[1] = 0.1795 y[1] (analytic) = 2.0161973877070152232639662999262 y[1] (numeric) = 2.0161973877070152232646958753085 absolute error = 7.295753823e-22 relative error = 3.6185712110743922253211796557190e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.951 Order of pole = 13.13 x[1] = 0.1796 y[1] (analytic) = 2.0162155381736573902163474551466 y[1] (numeric) = 2.0162155381736573902170780388889 absolute error = 7.305837423e-22 memory used=324.2MB, alloc=4.3MB, time=18.74 relative error = 3.6235398868207440230082536750941e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.948 Order of pole = 13.08 x[1] = 0.1797 y[1] (analytic) = 2.0162336989699265273707486325384 y[1] (numeric) = 2.016233698969926527371480224918 absolute error = 7.315923796e-22 relative error = 3.6285098298563463753777653574608e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.945 Order of pole = 13.03 x[1] = 0.1798 y[1] (analytic) = 2.0162518700961978300447962041316 y[1] (numeric) = 2.0162518700961978300455288054264 absolute error = 7.326012948e-22 relative error = 3.6334810430457118475729422489987e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.942 Order of pole = 12.97 x[1] = 0.1799 y[1] (analytic) = 2.0162700515528467206097002293467 y[1] (numeric) = 2.0162700515528467206104338398344 absolute error = 7.336104877e-22 relative error = 3.6384535252854841419529258681011e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.94 Order of pole = 12.92 x[1] = 0.18 y[1] (analytic) = 2.0162882433402488485217757733345 y[1] (numeric) = 2.0162882433402488485225103932932 absolute error = 7.346199587e-22 relative error = 3.6434272784480686295581486139567e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.937 Order of pole = 12.87 x[1] = 0.1801 y[1] (analytic) = 2.0163064454587800903539849847399 y[1] (numeric) = 2.016306445458780090354720614448 absolute error = 7.356297081e-22 relative error = 3.6484023039098035821457552930781e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.934 Order of pole = 12.82 x[1] = 0.1802 y[1] (analytic) = 2.0163246579088165498274999386058 y[1] (numeric) = 2.0163246579088165498282365783417 absolute error = 7.366397359e-22 relative error = 3.6533786015590787193936802063952e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.932 Order of pole = 12.77 x[1] = 0.1803 y[1] (analytic) = 2.0163428806907345578432862501419 y[1] (numeric) = 2.0163428806907345578440239001843 absolute error = 7.376500424e-22 relative error = 3.6583561727720867427900039219187e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.929 Order of pole = 12.72 x[1] = 0.1804 y[1] (analytic) = 2.0163611138049106725137074650875 y[1] (numeric) = 2.0163611138049106725144461257153 absolute error = 7.386606278e-22 relative error = 3.6633350184289844250102393321171e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.926 Order of pole = 12.68 x[1] = 0.1805 y[1] (analytic) = 2.016379357251721679194150232399 y[1] (numeric) = 2.0163793572517216791948899038913 absolute error = 7.396714923e-22 relative error = 3.6683151394098533975888290135803e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.3MB, time=18.96 Real estimate of pole used Radius of convergence = 1.924 Order of pole = 12.63 x[1] = 0.1806 y[1] (analytic) = 2.0163976110315445905146702649994 y[1] (numeric) = 2.0163976110315445905154109476355 absolute error = 7.406826361e-22 relative error = 3.6732965365947001039737711170779e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.921 Order of pole = 12.58 x[1] = 0.1807 y[1] (analytic) = 2.0164158751447566464116590943297 y[1] (numeric) = 2.016415875144756646412400788389 absolute error = 7.416940593e-22 relative error = 3.6782792103675263104846719060600e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.919 Order of pole = 12.53 x[1] = 0.1808 y[1] (analytic) = 2.0164341495917353141595316244471 y[1] (numeric) = 2.0164341495917353141602743302094 absolute error = 7.427057623e-22 relative error = 3.6832631626000513222545253665082e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.916 Order of pole = 12.48 x[1] = 0.1809 y[1] (analytic) = 2.0164524343728582884024344914196 y[1] (numeric) = 2.0164524343728582884031782091648 absolute error = 7.437177452e-22 relative error = 3.6882483936761218026980213070716e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.914 Order of pole = 12.43 x[1] = 0.181 y[1] (analytic) = 2.0164707294885034911859752337688 y[1] (numeric) = 2.0164707294885034911867199637771 absolute error = 7.447300083e-22 relative error = 3.6932349049713589247699849380857e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.911 Order of pole = 12.39 x[1] = 0.1811 y[1] (analytic) = 2.0164890349390490719889722797192 y[1] (numeric) = 2.0164890349390490719897180222708 absolute error = 7.457425516e-22 relative error = 3.6982226963735560830041475744255e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.909 Order of pole = 12.34 x[1] = 0.1812 y[1] (analytic) = 2.0165073507248734077552257570144 y[1] (numeric) = 2.0165073507248734077559725123898 absolute error = 7.467553754e-22 relative error = 3.7032117692581880572756446677237e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.906 Order of pole = 12.29 x[1] = 0.1813 y[1] (analytic) = 2.0165256768463551029253091310674 y[1] (numeric) = 2.0165256768463551029260568995473 absolute error = 7.477684799e-22 relative error = 3.7082021245047336601564532510955e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.904 Order of pole = 12.25 x[1] = 0.1814 y[1] (analytic) = 2.0165440133038729894683816772131 y[1] (numeric) = 2.0165440133038729894691304590784 absolute error = 7.487818653e-22 relative error = 3.7131937629925961406546747677367e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.3MB, time=19.18 Real estimate of pole used Radius of convergence = 1.901 Order of pole = 12.2 x[1] = 0.1815 y[1] (analytic) = 2.0165623600978061269140217928379 y[1] (numeric) = 2.0165623600978061269147715883699 absolute error = 7.497955320e-22 relative error = 3.7181866865928899719426825120917e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.899 Order of pole = 12.15 x[1] = 0.1816 y[1] (analytic) = 2.0165807172285338023840811551652 y[1] (numeric) = 2.0165807172285338023848319646451 absolute error = 7.508094799e-22 relative error = 3.7231808946971733406548733347244e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.896 Order of pole = 12.11 x[1] = 0.1817 y[1] (analytic) = 2.016599084696435530624559730477 y[1] (numeric) = 2.0165990846964355306253115541864 absolute error = 7.518237094e-22 relative error = 3.7281763891764048317607861199958e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.894 Order of pole = 12.06 x[1] = 0.1818 y[1] (analytic) = 2.0166174625018910540375016405613 y[1] (numeric) = 2.0166174625018910540382544787819 absolute error = 7.528382206e-22 relative error = 3.7331731704137915387130077474798e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.891 Order of pole = 12.02 x[1] = 0.1819 y[1] (analytic) = 2.0166358506452803427129118921734 y[1] (numeric) = 2.0166358506452803427136657451871 absolute error = 7.538530137e-22 relative error = 3.7381712392883581741306729568004e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.889 Order of pole = 11.97 x[1] = 0.182 y[1] (analytic) = 2.0166542491269835944606939753071 y[1] (numeric) = 2.0166542491269835944614488433961 absolute error = 7.548680890e-22 relative error = 3.7431705971749244274600220312022e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.887 Order of pole = 11.93 x[1] = 0.1821 y[1] (analytic) = 2.016672657947381234842608336076 y[1] (numeric) = 2.0166726579473812348433642195227 absolute error = 7.558834467e-22 relative error = 3.7481712449523496948743954427668e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.884 Order of pole = 11.88 x[1] = 0.1822 y[1] (analytic) = 2.0166910771068539172042517300062 y[1] (numeric) = 2.0166910771068539172050086290931 absolute error = 7.568990869e-22 relative error = 3.7531731830035556523911372162893e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.882 Order of pole = 11.84 x[1] = 0.1823 y[1] (analytic) = 2.0167095066057825227070574615498 y[1] (numeric) = 2.0167095066057825227078153765596 absolute error = 7.579150098e-22 relative error = 3.7581764122072633361380733013932e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.879 Order of pole = 11.79 x[1] = 0.1824 y[1] (analytic) = 2.01672794644454816036031651563 y[1] (numeric) = 2.0167279464445481603610754468457 absolute error = 7.589312157e-22 relative error = 3.7631809339379704508318731058763e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.3MB, time=19.40 Real estimate of pole used Radius of convergence = 1.877 Order of pole = 11.75 x[1] = 0.1825 y[1] (analytic) = 2.0167463966235321670532195870346 y[1] (numeric) = 2.0167463966235321670539795347395 absolute error = 7.599477049e-22 relative error = 3.7681867495700804763849643986243e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.875 Order of pole = 11.71 x[1] = 0.1826 y[1] (analytic) = 2.0167648571431161075869200134774 y[1] (numeric) = 2.0167648571431161075876809779548 absolute error = 7.609644774e-22 relative error = 3.7731938589903717177527295928585e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.872 Order of pole = 11.66 x[1] = 0.1827 y[1] (analytic) = 2.0167833280036817747066176181521 y[1] (numeric) = 2.0167833280036817747073795996855 absolute error = 7.619815334e-22 relative error = 3.7782022630772607767567368036317e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.87 Order of pole = 11.62 x[1] = 0.1828 y[1] (analytic) = 2.0168018092056111891336634676077 y[1] (numeric) = 2.016801809205611189134426466481 absolute error = 7.629988733e-22 relative error = 3.7832119637007571175769335394778e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.868 Order of pole = 11.58 x[1] = 0.1829 y[1] (analytic) = 2.0168203007492865995976855507784 y[1] (numeric) = 2.0168203007492865995984495672755 absolute error = 7.640164971e-22 relative error = 3.7882229607474375873862811998753e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.866 Order of pole = 11.54 x[1] = 0.183 y[1] (analytic) = 2.0168388026350904828687353850041 y[1] (numeric) = 2.0168388026350904828695004194092 absolute error = 7.650344051e-22 relative error = 3.7932352555913154183215682726571e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.863 Order of pole = 11.49 x[1] = 0.1831 y[1] (analytic) = 2.0168573148634055437894555548841 y[1] (numeric) = 2.0168573148634055437902216074817 absolute error = 7.660525976e-22 relative error = 3.7982488496063092773443419453592e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.861 Order of pole = 11.45 x[1] = 0.1832 y[1] (analytic) = 2.0168758374346147153072681898088 y[1] (numeric) = 2.0168758374346147153080352608834 absolute error = 7.670710746e-22 relative error = 3.8032637426787941687444592902965e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.859 Order of pole = 11.41 x[1] = 0.1833 y[1] (analytic) = 2.016894370349101158506584386019 y[1] (numeric) = 2.0168943703491011585073524758555 absolute error = 7.680898365e-22 relative error = 3.8082799366783522045273027453376e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.3MB, time=19.62 Real estimate of pole used Radius of convergence = 1.857 Order of pole = 11.37 x[1] = 0.1834 y[1] (analytic) = 2.0169129136072482626410345790476 y[1] (numeric) = 2.016912913607248262641803687931 absolute error = 7.691088834e-22 relative error = 3.8132974319870308448426086301882e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.854 Order of pole = 11.33 x[1] = 0.1835 y[1] (analytic) = 2.0169314672094396451657198724011 y[1] (numeric) = 2.0169314672094396451664900006166 absolute error = 7.701282155e-22 relative error = 3.8183162294826218821477935030882e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.852 Order of pole = 11.29 x[1] = 0.1836 y[1] (analytic) = 2.0169500311560591517694843283438 y[1] (numeric) = 2.0169500311560591517702554761769 absolute error = 7.711478331e-22 relative error = 3.8233363305386386021611297413019e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.85 Order of pole = 11.24 x[1] = 0.1837 y[1] (analytic) = 2.0169686054474908564072082266513 y[1] (numeric) = 2.0169686054474908564079803943876 absolute error = 7.721677363e-22 relative error = 3.8283577355369122953162807077492e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.848 Order of pole = 11.2 x[1] = 0.1838 y[1] (analytic) = 2.0169871900841190613321222972039 y[1] (numeric) = 2.0169871900841190613328954851293 absolute error = 7.731879254e-22 relative error = 3.8333804458507937450837844757588e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.846 Order of pole = 11.16 x[1] = 0.1839 y[1] (analytic) = 2.017005785066328297128142932296 y[1] (numeric) = 2.0170057850663282971289171406965 absolute error = 7.742084005e-22 relative error = 3.8384044618619699042437945630906e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.844 Order of pole = 11.12 x[1] = 0.184 y[1] (analytic) = 2.0170243903945033227422283845393 y[1] (numeric) = 2.0170243903945033227430036137012 absolute error = 7.752291619e-22 relative error = 3.8434297849436288567206121651904e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.841 Order of pole = 11.08 x[1] = 0.1841 y[1] (analytic) = 2.0170430060690291255167559562454 y[1] (numeric) = 2.0170430060690291255175322064551 absolute error = 7.762502097e-22 relative error = 3.8484564154773130400226339291287e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.839 Order of pole = 11.04 x[1] = 0.1842 y[1] (analytic) = 2.0170616320902909212219201861736 y[1] (numeric) = 2.0170616320902909212226974577178 absolute error = 7.772715442e-22 relative error = 3.8534843548360476412490684315537e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.837 Order of pole = 11 x[1] = 0.1843 y[1] (analytic) = 2.0170802684586741540881520395378 y[1] (numeric) = 2.0170802684586741540889303327033 absolute error = 7.782931655e-22 relative error = 3.8585136034012304050372641281950e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.3MB, time=19.84 Real estimate of pole used Radius of convergence = 1.835 Order of pole = 10.96 x[1] = 0.1844 y[1] (analytic) = 2.0170989151745644968385591071677 y[1] (numeric) = 2.0170989151745644968393384222417 absolute error = 7.793150740e-22 relative error = 3.8635441630414849324159748565519e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.833 Order of pole = 10.93 x[1] = 0.1845 y[1] (analytic) = 2.0171175722383478507213868197259 y[1] (numeric) = 2.0171175722383478507221671569956 absolute error = 7.803372697e-22 relative error = 3.8685760336422934185955779938204e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.831 Order of pole = 10.89 x[1] = 0.1846 y[1] (analytic) = 2.017136239650410345542500682884 y[1] (numeric) = 2.0171362396504103455432820426369 absolute error = 7.813597529e-22 relative error = 3.8736092165763546578917805079897e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.829 Order of pole = 10.85 x[1] = 0.1847 y[1] (analytic) = 2.0171549174111383396978895393694 y[1] (numeric) = 2.0171549174111383396986719218932 absolute error = 7.823825238e-22 relative error = 3.8786437127205242132984006352779e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.827 Order of pole = 10.81 x[1] = 0.1848 y[1] (analytic) = 2.0171736055209184202061898637934 y[1] (numeric) = 2.0171736055209184202069732693761 absolute error = 7.834055827e-22 relative error = 3.8836795234473236120193491619882e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.825 Order of pole = 10.77 x[1] = 0.1849 y[1] (analytic) = 2.0171923039801374027412310961809 y[1] (numeric) = 2.0171923039801374027420155251106 absolute error = 7.844289297e-22 relative error = 3.8887166491377016539793875348930e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.823 Order of pole = 10.73 x[1] = 0.185 y[1] (analytic) = 2.017211012789182331664602020121 y[1] (numeric) = 2.0172110127891823316653874726859 absolute error = 7.854525649e-22 relative error = 3.8937550901725482346349176549091e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.821 Order of pole = 10.69 x[1] = 0.1851 y[1] (analytic) = 2.0172297319484404800582381914664 y[1] (numeric) = 2.0172297319484404800590246679551 absolute error = 7.864764887e-22 relative error = 3.8987948484198823967839192715033e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.819 Order of pole = 10.66 x[1] = 0.1852 y[1] (analytic) = 2.0172484614582993497570304235115 y[1] (numeric) = 2.0172484614582993497578179242128 absolute error = 7.875007013e-22 relative error = 3.9038359247561594913151933037725e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.3MB, time=20.06 Real estimate of pole used Radius of convergence = 1.817 Order of pole = 10.62 x[1] = 0.1853 y[1] (analytic) = 2.0172672013191466713814543345839 y[1] (numeric) = 2.0172672013191466713822428597867 absolute error = 7.885252028e-22 relative error = 3.9088783195620372828719000447554e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.815 Order of pole = 10.58 x[1] = 0.1854 y[1] (analytic) = 2.0172859515313704043702209639874 y[1] (numeric) = 2.0172859515313704043710105139808 absolute error = 7.895499934e-22 relative error = 3.9139220337138300262082995740316e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.813 Order of pole = 10.55 x[1] = 0.1855 y[1] (analytic) = 2.0173047120953587370129484622411 y[1] (numeric) = 2.0173047120953587370137390373145 absolute error = 7.905750734e-22 relative error = 3.9189670685834853936258202011746e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.811 Order of pole = 10.51 x[1] = 0.1856 y[1] (analytic) = 2.0173234830115000864828548615613 y[1] (numeric) = 2.0173234830115000864836464620042 absolute error = 7.916004429e-22 relative error = 3.9240134245514424055597904037463e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.809 Order of pole = 10.47 x[1] = 0.1857 y[1] (analytic) = 2.0173422642801830988694719325372 y[1] (numeric) = 2.0173422642801830988702645586395 absolute error = 7.926261023e-22 relative error = 3.9290611034851860340432612029842e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.807 Order of pole = 10.44 x[1] = 0.1858 y[1] (analytic) = 2.0173610559017966492113801329582 y[1] (numeric) = 2.0173610559017966492121737850098 absolute error = 7.936520516e-22 relative error = 3.9341101052692983058699508938726e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.805 Order of pole = 10.4 x[1] = 0.1859 y[1] (analytic) = 2.0173798578767298415289646547511 y[1] (numeric) = 2.0173798578767298415297593330422 absolute error = 7.946782911e-22 relative error = 3.9391604312753978782939500487998e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.803 Order of pole = 10.36 x[1] = 0.186 y[1] (analytic) = 2.0173986702053720088571925749931 y[1] (numeric) = 2.0173986702053720088579882798141 absolute error = 7.957048210e-22 relative error = 3.9442120823793193247633837596346e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.801 Order of pole = 10.33 x[1] = 0.1861 y[1] (analytic) = 2.0174174928881127132784111169689 y[1] (numeric) = 2.0174174928881127132792078486104 absolute error = 7.967316415e-22 relative error = 3.9492650594568194081020580903686e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.3MB, time=20.29 Real estimate of pole used Radius of convergence = 1.799 Order of pole = 10.29 x[1] = 0.1862 y[1] (analytic) = 2.0174363259253417459551670272446 y[1] (numeric) = 2.0174363259253417459559647859975 absolute error = 7.977587529e-22 relative error = 3.9543193638792556269470582459585e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.797 Order of pole = 10.26 x[1] = 0.1863 y[1] (analytic) = 2.0174551693174491271630470747371 y[1] (numeric) = 2.0174551693174491271638458608924 absolute error = 7.987861553e-22 relative error = 3.9593749960265411297474940513252e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.795 Order of pole = 10.22 x[1] = 0.1864 y[1] (analytic) = 2.0174740230648251063235396777589 y[1] (numeric) = 2.0174740230648251063243394916078 absolute error = 7.998138489e-22 relative error = 3.9644319567741989592347153094475e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.793 Order of pole = 10.19 x[1] = 0.1865 y[1] (analytic) = 2.0174928871678601620369176650255 y[1] (numeric) = 2.0174928871678601620377185068594 absolute error = 8.008418339e-22 relative error = 3.9694902469976741602930895937128e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.791 Order of pole = 10.15 x[1] = 0.1866 y[1] (analytic) = 2.0175117616269450021151421766151 y[1] (numeric) = 2.0175117616269450021159440467257 absolute error = 8.018701106e-22 relative error = 3.9745498680679937927545858666203e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.789 Order of pole = 10.12 x[1] = 0.1867 y[1] (analytic) = 2.0175306464424705636147877108755 y[1] (numeric) = 2.0175306464424705636155906095547 absolute error = 8.028986792e-22 relative error = 3.9796108208604328467416877627674e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.788 Order of pole = 10.08 x[1] = 0.1868 y[1] (analytic) = 2.0175495416148280128699883232765 y[1] (numeric) = 2.0175495416148280128707922508163 absolute error = 8.039275398e-22 relative error = 3.9846731057545373813710247562895e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.786 Order of pole = 10.05 x[1] = 0.1869 y[1] (analytic) = 2.0175684471444087455254049832113 y[1] (numeric) = 2.017568447144408745526209939904 absolute error = 8.049566927e-22 relative error = 3.9897367241210861009728286911335e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.784 Order of pole = 10.01 x[1] = 0.187 y[1] (analytic) = 2.0175873630316043865692140947539 y[1] (numeric) = 2.017587363031604386570020080892 absolute error = 8.059861381e-22 relative error = 3.9948016768351194037182112385226e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.782 Order of pole = 9.978 x[1] = 0.1871 y[1] (analytic) = 2.0176062892768067903661171873849 y[1] (numeric) = 2.0176062892768067903669242032611 absolute error = 8.070158762e-22 relative error = 3.9998679647715993944264118415869e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.3MB, time=20.52 Real estimate of pole used Radius of convergence = 1.78 Order of pole = 9.945 x[1] = 0.1872 y[1] (analytic) = 2.0176252258804080406903717827008 y[1] (numeric) = 2.017625225880408040691179828608 absolute error = 8.080459072e-22 relative error = 4.0049355888054098377802986980784e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.778 Order of pole = 9.911 x[1] = 0.1873 y[1] (analytic) = 2.0176441728428004507588434431277 y[1] (numeric) = 2.017644172842800450759652519359 absolute error = 8.090762313e-22 relative error = 4.0100045498113561115443184272948e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.777 Order of pole = 9.877 x[1] = 0.1874 y[1] (analytic) = 2.0176631301643765632640790086638 y[1] (numeric) = 2.0176631301643765632648891155125 absolute error = 8.101068487e-22 relative error = 4.0150748486641651597848955112859e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.775 Order of pole = 9.844 x[1] = 0.1875 y[1] (analytic) = 2.0176820978455291504074010276796 y[1] (numeric) = 2.0176820978455291504082121654393 absolute error = 8.111377597e-22 relative error = 4.0201464867341036612064537960809e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.773 Order of pole = 9.811 x[1] = 0.1876 y[1] (analytic) = 2.0177010758866512139320233878089 y[1] (numeric) = 2.0177010758866512139328355567733 absolute error = 8.121689644e-22 relative error = 4.0252194644001140136909675337007e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.771 Order of pole = 9.778 x[1] = 0.1877 y[1] (analytic) = 2.0177200642881359851561881529683 y[1] (numeric) = 2.0177200642881359851570013534313 absolute error = 8.132004630e-22 relative error = 4.0302937825366875721863920494458e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.769 Order of pole = 9.745 x[1] = 0.1878 y[1] (analytic) = 2.0177390630503769250063236125469 y[1] (numeric) = 2.0177390630503769250071378448027 absolute error = 8.142322558e-22 relative error = 4.0353694425138412935715019622702e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.768 Order of pole = 9.712 x[1] = 0.1879 y[1] (analytic) = 2.0177580721737677240502235488123 y[1] (numeric) = 2.0177580721737677240510388131552 absolute error = 8.152643429e-22 relative error = 4.0404464447102956836323212689141e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.766 Order of pole = 9.68 x[1] = 0.188 y[1] (analytic) = 2.0177770916587023025302477285834 y[1] (numeric) = 2.017777091658702302531064025308 absolute error = 8.162967246e-22 relative error = 4.0455247904959009694481420687178e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.3MB, time=20.73 Real estimate of pole used Radius of convergence = 1.764 Order of pole = 9.648 x[1] = 0.1881 y[1] (analytic) = 2.0177961215055748103965436252249 y[1] (numeric) = 2.017796121505574810397360954626 absolute error = 8.173294011e-22 relative error = 4.0506044807448197129605086251372e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.762 Order of pole = 9.615 x[1] = 0.1882 y[1] (analytic) = 2.0178151617147796273402893770218 y[1] (numeric) = 2.0178151617147796273411077393945 absolute error = 8.183623727e-22 relative error = 4.0556855168267211853272358823363e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.761 Order of pole = 9.583 x[1] = 0.1883 y[1] (analytic) = 2.0178342122867113628269579879992 y[1] (numeric) = 2.0178342122867113628277773836386 absolute error = 8.193956394e-22 relative error = 4.0607678986244345140786154947057e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.759 Order of pole = 9.552 x[1] = 0.1884 y[1] (analytic) = 2.017853273221764856129602777252 y[1] (numeric) = 2.0178532732217648561304232064536 absolute error = 8.204292016e-22 relative error = 4.0658516280030520329470912603214e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.757 Order of pole = 9.52 x[1] = 0.1885 y[1] (analytic) = 2.0178723445203351763621640828602 y[1] (numeric) = 2.0178723445203351763629855459196 absolute error = 8.214630594e-22 relative error = 4.0709367053408351938180234661891e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.756 Order of pole = 9.488 x[1] = 0.1886 y[1] (analytic) = 2.0178914261828176225127972264629 y[1] (numeric) = 2.0178914261828176225136197236759 absolute error = 8.224972130e-22 relative error = 4.0760231315115519707797655543113e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.754 Order of pole = 9.457 x[1] = 0.1887 y[1] (analytic) = 2.0179105182096077234772217445737 y[1] (numeric) = 2.0179105182096077234780452762364 absolute error = 8.235316627e-22 relative error = 4.0811109078844533944494173599577e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.752 Order of pole = 9.426 x[1] = 0.1888 y[1] (analytic) = 2.0179296206011012380920918927223 y[1] (numeric) = 2.0179296206011012380929164591309 absolute error = 8.245664086e-22 relative error = 4.0862000348375777842872354337579e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.75 Order of pole = 9.395 x[1] = 0.1889 y[1] (analytic) = 2.0179487333576941551683884285103 y[1] (numeric) = 2.0179487333576941551692140299614 absolute error = 8.256014511e-22 relative error = 4.0912905142355612539548443850603e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.749 Order of pole = 9.364 x[1] = 0.189 y[1] (analytic) = 2.0179678564797826935248316796769 y[1] (numeric) = 2.017967856479782693525658316467 absolute error = 8.266367901e-22 relative error = 4.0963823454651829917875297115204e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.3MB, time=20.95 Real estimate of pole used Radius of convergence = 1.747 Order of pole = 9.333 x[1] = 0.1891 y[1] (analytic) = 2.0179869899677633020213159032704 y[1] (numeric) = 2.0179869899677633020221435756965 absolute error = 8.276724261e-22 relative error = 4.1014755308864592967252726465573e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.745 Order of pole = 9.303 x[1] = 0.1892 y[1] (analytic) = 2.0180061338220326595923649420299 y[1] (numeric) = 2.0180061338220326595931936503891 absolute error = 8.287083592e-22 relative error = 4.1065700708771162504858836939839e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.744 Order of pole = 9.272 x[1] = 0.1893 y[1] (analytic) = 2.0180252880429876752806091840824 y[1] (numeric) = 2.018025288042987675281438928672 absolute error = 8.297445896e-22 relative error = 4.1116659663103533113792766063145e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.742 Order of pole = 9.242 x[1] = 0.1894 y[1] (analytic) = 2.0180444526310254882702838320669 y[1] (numeric) = 2.0180444526310254882711146131844 absolute error = 8.307811175e-22 relative error = 4.1167632180592905394687466656997e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.741 Order of pole = 9.212 x[1] = 0.1895 y[1] (analytic) = 2.0180636275865434679207484878004 y[1] (numeric) = 2.0180636275865434679215803057437 absolute error = 8.318179433e-22 relative error = 4.1218618279880175795476801829267e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.739 Order of pole = 9.182 x[1] = 0.1896 y[1] (analytic) = 2.0180828129099392138000280586072 y[1] (numeric) = 2.0180828129099392138008609136741 absolute error = 8.328550669e-22 relative error = 4.1269617954829078780318805952577e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.737 Order of pole = 9.152 x[1] = 0.1897 y[1] (analytic) = 2.0181020086016105557183749914327 y[1] (numeric) = 2.0181020086016105557192088839213 absolute error = 8.338924886e-22 relative error = 4.1320631219123722357263985577952e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.736 Order of pole = 9.123 x[1] = 0.1898 y[1] (analytic) = 2.0181212146619555537618528408725 y[1] (numeric) = 2.0181212146619555537626877710813 absolute error = 8.349302088e-22 relative error = 4.1371658091402333952206167252864e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.734 Order of pole = 9.093 x[1] = 0.1899 y[1] (analytic) = 2.0181404310913724983259411772493 y[1] (numeric) = 2.0181404310913724983267771454768 absolute error = 8.359682275e-22 relative error = 4.1422698570481740942938718187619e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.3MB, time=21.17 Real estimate of pole used Radius of convergence = 1.732 Order of pole = 9.064 x[1] = 0.19 y[1] (analytic) = 2.0181596578902599101491618408727 y[1] (numeric) = 2.0181596578902599101499988474178 absolute error = 8.370065451e-22 relative error = 4.1473752674998388727580918987886e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.731 Order of pole = 9.035 x[1] = 0.1901 y[1] (analytic) = 2.0181788950590165403467265486265 y[1] (numeric) = 2.0181788950590165403475645937881 absolute error = 8.380451616e-22 relative error = 4.1524820403767699077663018458897e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.729 Order of pole = 9.006 x[1] = 0.1902 y[1] (analytic) = 2.0181981425980413704442058590264 y[1] (numeric) = 2.0181981425980413704450449431037 absolute error = 8.390840773e-22 relative error = 4.1575901770469418422314048638574e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.728 Order of pole = 8.977 x[1] = 0.1903 y[1] (analytic) = 2.0182174005077336124112195019001 y[1] (numeric) = 2.0182174005077336124120596251927 absolute error = 8.401232926e-22 relative error = 4.1626996793737173479965821840218e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.726 Order of pole = 8.948 x[1] = 0.1904 y[1] (analytic) = 2.0182366687884927086951480788442 y[1] (numeric) = 2.0182366687884927086959892416516 absolute error = 8.411628074e-22 relative error = 4.1678105467429312272659888479443e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.725 Order of pole = 8.919 x[1] = 0.1905 y[1] (analytic) = 2.0182559474407183322548661406152 y[1] (numeric) = 2.0182559474407183322557083432373 absolute error = 8.422026221e-22 relative error = 4.1729227810177816021673812541821e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.723 Order of pole = 8.891 x[1] = 0.1906 y[1] (analytic) = 2.0182752364648103865944966476205 y[1] (numeric) = 2.0182752364648103865953398903573 absolute error = 8.432427368e-22 relative error = 4.1780363825749310704070264835591e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.722 Order of pole = 8.863 x[1] = 0.1907 y[1] (analytic) = 2.0182945358611690057971868196743 y[1] (numeric) = 2.0182945358611690057980311028262 absolute error = 8.442831519e-22 relative error = 4.1831513532773846152236437970487e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.72 Order of pole = 8.834 x[1] = 0.1908 y[1] (analytic) = 2.0183138456301945545589053811929 y[1] (numeric) = 2.0183138456301945545597507050604 absolute error = 8.453238675e-22 relative error = 4.1882676935016399823191422151194e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.718 Order of pole = 8.806 memory used=370.0MB, alloc=4.3MB, time=21.39 x[1] = 0.1909 y[1] (analytic) = 2.0183331657722876282222612080037 y[1] (numeric) = 2.0183331657722876282231075728874 absolute error = 8.463648837e-22 relative error = 4.1933854036241337452398589709045e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.717 Order of pole = 8.779 x[1] = 0.191 y[1] (analytic) = 2.0183524962878490528103433819497 y[1] (numeric) = 2.0183524962878490528111907881506 absolute error = 8.474062009e-22 relative error = 4.1985044855076020678533937721342e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.715 Order of pole = 8.751 x[1] = 0.1911 y[1] (analytic) = 2.0183718371772798850605826594749 y[1] (numeric) = 2.0183718371772798850614311072941 absolute error = 8.484478192e-22 relative error = 4.2036249395283163841938908994472e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.714 Order of pole = 8.723 x[1] = 0.1912 y[1] (analytic) = 2.0183911884409814124586343603789 y[1] (numeric) = 2.0183911884409814124594838501178 absolute error = 8.494897389e-22 relative error = 4.2087467670533750397963448273243e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.712 Order of pole = 8.696 x[1] = 0.1913 y[1] (analytic) = 2.0184105500793551532722826829362 y[1] (numeric) = 2.0184105500793551532731332148963 absolute error = 8.505319601e-22 relative error = 4.2138699684588983657380680681733e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.711 Order of pole = 8.668 x[1] = 0.1914 y[1] (analytic) = 2.0184299220928028565853664515764 y[1] (numeric) = 2.0184299220928028565862180260595 absolute error = 8.515744831e-22 relative error = 4.2189945451118145157459397332023e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.709 Order of pole = 8.641 x[1] = 0.1915 y[1] (analytic) = 2.0184493044817265023317263033305 y[1] (numeric) = 2.0184493044817265023325789206385 absolute error = 8.526173080e-22 relative error = 4.2241204973880925410477796009721e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.708 Order of pole = 8.614 x[1] = 0.1916 y[1] (analytic) = 2.0184686972465283013291733192474 y[1] (numeric) = 2.0184686972465283013300269796826 absolute error = 8.536604352e-22 relative error = 4.2292478271499152792026846917911e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.706 Order of pole = 8.587 x[1] = 0.1917 y[1] (analytic) = 2.0184881003876106953134791069949 y[1] (numeric) = 2.0184881003876106953143338108597 absolute error = 8.547038648e-22 relative error = 4.2343765347730860375830424161910e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.705 Order of pole = 8.56 x[1] = 0.1918 y[1] (analytic) = 2.0185075139053763569723873408586 y[1] (numeric) = 2.0185075139053763569732430884556 absolute error = 8.557475970e-22 relative error = 4.2395066211287621499192934378954e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.3MB, time=21.61 Real estimate of pole used Radius of convergence = 1.704 Order of pole = 8.533 x[1] = 0.1919 y[1] (analytic) = 2.0185269378002281899796467653602 y[1] (numeric) = 2.0185269378002281899805035569922 absolute error = 8.567916320e-22 relative error = 4.2446380870880203400777718863426e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.702 Order of pole = 8.507 x[1] = 0.192 y[1] (analytic) = 2.0185463720725693290290656687196 y[1] (numeric) = 2.0185463720725693290299235046897 absolute error = 8.578359701e-22 relative error = 4.2497709340172626833222643143480e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.701 Order of pole = 8.48 x[1] = 0.1921 y[1] (analytic) = 2.0185658167228031398685878323895 y[1] (numeric) = 2.018565816722803139869446713001 absolute error = 8.588806115e-22 relative error = 4.2549051627873902272078353187508e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.699 Order of pole = 8.454 x[1] = 0.1922 y[1] (analytic) = 2.018585271751333219334389962896 y[1] (numeric) = 2.0185852717513332193352498884523 absolute error = 8.599255563e-22 relative error = 4.2600407737738267936389520306319e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.698 Order of pole = 8.428 x[1] = 0.1923 y[1] (analytic) = 2.0186047371585633953850006122226 y[1] (numeric) = 2.0186047371585633953858615830274 absolute error = 8.609708048e-22 relative error = 4.2651777683427178696504560313092e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.696 Order of pole = 8.402 x[1] = 0.1924 y[1] (analytic) = 2.0186242129448977271354405929807 y[1] (numeric) = 2.018624212944897727136302609338 absolute error = 8.620163573e-22 relative error = 4.2703161478601089808672189644404e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.695 Order of pole = 8.376 x[1] = 0.1925 y[1] (analytic) = 2.0186436991107405048913848946121 y[1] (numeric) = 2.018643699110740504892247956826 absolute error = 8.630622139e-22 relative error = 4.2754559127011813755383358293759e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.694 Order of pole = 8.35 x[1] = 0.1926 y[1] (analytic) = 2.018663195656496250183346106875 y[1] (numeric) = 2.0186631956564962501842102152498 absolute error = 8.641083748e-22 relative error = 4.2805970637364318118016664589929e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.692 Order of pole = 8.325 x[1] = 0.1927 y[1] (analytic) = 2.0186827025825697158008793568687 y[1] (numeric) = 2.018682702582569715801744511709 absolute error = 8.651548403e-22 relative error = 4.2857396023316486009464392599944e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.3MB, time=21.83 Real estimate of pole used Radius of convergence = 1.691 Order of pole = 8.299 x[1] = 0.1928 y[1] (analytic) = 2.0187022198893658858268087658574 y[1] (numeric) = 2.0187022198893658858276749674679 absolute error = 8.662016105e-22 relative error = 4.2908835288617843290606577683510e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.689 Order of pole = 8.274 x[1] = 0.1929 y[1] (analytic) = 2.0187217475772899756714754321555 y[1] (numeric) = 2.0187217475772899756723426808412 absolute error = 8.672486857e-22 relative error = 4.2960288446924555832624790208927e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.688 Order of pole = 8.248 x[1] = 0.193 y[1] (analytic) = 2.0187412856467474321070069463458 y[1] (numeric) = 2.0187412856467474321078752424119 absolute error = 8.682960661e-22 relative error = 4.3011755506938204602811846381133e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.687 Order of pole = 8.223 x[1] = 0.1931 y[1] (analytic) = 2.0187608340981439333016084451008 y[1] (numeric) = 2.0187608340981439333024777888527 absolute error = 8.693437519e-22 relative error = 4.3063236477359558577316163481272e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.685 Order of pole = 8.198 x[1] = 0.1932 y[1] (analytic) = 2.0187803929318853888538752098863 y[1] (numeric) = 2.0187803929318853888547456016297 absolute error = 8.703917434e-22 relative error = 4.3114731371842060070009135138072e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.684 Order of pole = 8.173 x[1] = 0.1933 y[1] (analytic) = 2.0187999621483779398271268168287 y[1] (numeric) = 2.0187999621483779398279982568694 absolute error = 8.714400407e-22 relative error = 4.3166240194131270847483742567043e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.682 Order of pole = 8.148 x[1] = 0.1934 y[1] (analytic) = 2.0188195417480279587837628440318 y[1] (numeric) = 2.0188195417480279587846353326759 absolute error = 8.724886441e-22 relative error = 4.3217762957878910778493064700596e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.681 Order of pole = 8.124 x[1] = 0.1935 y[1] (analytic) = 2.0188391317312420498196401426346 y[1] (numeric) = 2.0188391317312420498205136801883 absolute error = 8.735375537e-22 relative error = 4.3269299666829010269153378247810e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.68 Order of pole = 8.099 x[1] = 0.1936 y[1] (analytic) = 2.0188587320984270485984716779042 y[1] (numeric) = 2.018858732098427048599346264674 absolute error = 8.745867698e-22 relative error = 4.3320850334631564779930377477787e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.678 Order of pole = 8.075 x[1] = 0.1937 y[1] (analytic) = 2.0188783428499900223862469466646 y[1] (numeric) = 2.0188783428499900223871225829572 absolute error = 8.756362926e-22 relative error = 4.3372414969982317056685299828607e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.3MB, time=22.06 Real estimate of pole used Radius of convergence = 1.677 Order of pole = 8.05 x[1] = 0.1938 y[1] (analytic) = 2.018897963986338270085673977364 y[1] (numeric) = 2.0188979639863382700865506634863 absolute error = 8.766861223e-22 relative error = 4.3423993581576194443134779792045e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.676 Order of pole = 8.026 x[1] = 0.1939 y[1] (analytic) = 2.0189175955078793222706429190902 y[1] (numeric) = 2.0189175955078793222715206553494 absolute error = 8.777362592e-22 relative error = 4.3475586183060457578521587636305e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.674 Order of pole = 8.002 x[1] = 0.194 y[1] (analytic) = 2.0189372374150209412207112258461 y[1] (numeric) = 2.0189372374150209412215900125494 absolute error = 8.787867033e-22 relative error = 4.3527192773222055087868015295248e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.673 Order of pole = 7.978 x[1] = 0.1941 y[1] (analytic) = 2.0189568897081711209556104424024 y[1] (numeric) = 2.0189568897081711209564902798574 absolute error = 8.798374550e-22 relative error = 4.3578813370659715401869863839608e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.672 Order of pole = 7.954 x[1] = 0.1942 y[1] (analytic) = 2.0189765523877380872697745980507 y[1] (numeric) = 2.0189765523877380872706554865652 absolute error = 8.808885145e-22 relative error = 4.3630447984064954882118542475571e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.67 Order of pole = 7.93 x[1] = 0.1943 y[1] (analytic) = 2.0189962254541302977668902145811 y[1] (numeric) = 2.0189962254541302977677721544632 absolute error = 8.819398821e-22 relative error = 4.3682096627081428273429010635871e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.669 Order of pole = 7.906 x[1] = 0.1944 y[1] (analytic) = 2.0190159089077564418944679348163 y[1] (numeric) = 2.0190159089077564418953509263741 absolute error = 8.829915578e-22 relative error = 4.3733759298493054898966572412078e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.668 Order of pole = 7.883 x[1] = 0.1945 y[1] (analytic) = 2.0190356027490254409784357780363 y[1] (numeric) = 2.0190356027490254409793198215783 absolute error = 8.840435420e-22 relative error = 4.3785436016894760273282351757540e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.667 Order of pole = 7.859 x[1] = 0.1946 y[1] (analytic) = 2.0190553069783464482577540286343 y[1] (numeric) = 2.019055306978346448258639124469 absolute error = 8.850958347e-22 relative error = 4.3837126781069018776009821598256e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.3MB, time=22.29 Real estimate of pole used Radius of convergence = 1.665 Order of pole = 7.836 x[1] = 0.1947 y[1] (analytic) = 2.0190750215961288489190517643461 y[1] (numeric) = 2.0190750215961288489199379127824 absolute error = 8.861484363e-22 relative error = 4.3888831609608923655819789612778e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.664 Order of pole = 7.813 x[1] = 0.1948 y[1] (analytic) = 2.019094746602782260131285030403 y[1] (numeric) = 2.0190947466027822601321722317501 absolute error = 8.872013471e-22 relative error = 4.3940550516153646436391649143241e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.663 Order of pole = 7.79 x[1] = 0.1949 y[1] (analytic) = 2.01911448199871653108041666596 y[1] (numeric) = 2.0191144819987165310813049205271 absolute error = 8.882545671e-22 relative error = 4.3992283499483345654381317850985e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.662 Order of pole = 7.767 x[1] = 0.195 y[1] (analytic) = 2.0191342277843417430041177891565 y[1] (numeric) = 2.0191342277843417430050070972531 absolute error = 8.893080966e-22 relative error = 4.4044030573235599106736224434013e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.66 Order of pole = 7.744 x[1] = 0.1951 y[1] (analytic) = 2.0191539839600682092264909471717 y[1] (numeric) = 2.0191539839600682092273813091076 absolute error = 8.903619359e-22 relative error = 4.4095791751046969149924443782935e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.659 Order of pole = 7.721 x[1] = 0.1952 y[1] (analytic) = 2.019173750526306475192814937641 y[1] (numeric) = 2.0191737505263064751937063537261 absolute error = 8.914160851e-22 relative error = 4.4147567036647960387065900479129e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.658 Order of pole = 7.698 x[1] = 0.1953 y[1] (analytic) = 2.019193527483467318504311307803 y[1] (numeric) = 2.0191935274834673185052037783474 absolute error = 8.924705444e-22 relative error = 4.4199356438720920910992663739363e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.656 Order of pole = 7.676 x[1] = 0.1954 y[1] (analytic) = 2.0192133148319617489529325377533 y[1] (numeric) = 2.0192133148319617489538260630674 absolute error = 8.935253141e-22 relative error = 4.4251159970899799424269348675926e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.655 Order of pole = 7.653 x[1] = 0.1955 y[1] (analytic) = 2.019233112572201008556171914184 y[1] (numeric) = 2.0192331125722010085570664945785 absolute error = 8.945803945e-22 relative error = 4.4302977646817526786104660163201e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.654 Order of pole = 7.631 memory used=389.1MB, alloc=4.3MB, time=22.52 x[1] = 0.1956 y[1] (analytic) = 2.0192529207045965715918951009936 y[1] (numeric) = 2.0192529207045965715927907367792 absolute error = 8.956357856e-22 relative error = 4.4354809465249035428991129822256e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.653 Order of pole = 7.609 x[1] = 0.1957 y[1] (analytic) = 2.0192727392295601446331934131542 y[1] (numeric) = 2.019272739229560144634090104642 absolute error = 8.966914878e-22 relative error = 4.4406655444777933860583056050013e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.652 Order of pole = 7.587 x[1] = 0.1958 y[1] (analytic) = 2.0192925681475036665832588002312 y[1] (numeric) = 2.0192925681475036665841565477323 absolute error = 8.977475011e-22 relative error = 4.4458515584177698979420419154142e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.65 Order of pole = 7.565 x[1] = 0.1959 y[1] (analytic) = 2.0193124074588393087102805459507 y[1] (numeric) = 2.0193124074588393087111793497767 absolute error = 8.988038260e-22 relative error = 4.4510389906982274815813185171816e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.649 Order of pole = 7.543 x[1] = 0.196 y[1] (analytic) = 2.0193322571639794746823636902184 y[1] (numeric) = 2.019332257163979474683263550681 absolute error = 8.998604626e-22 relative error = 4.4562278416915667085560222130322e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.648 Order of pole = 7.521 x[1] = 0.1961 y[1] (analytic) = 2.0193521172633368006024691799948 y[1] (numeric) = 2.0193521172633368006033700974059 absolute error = 9.009174111e-22 relative error = 4.4614181122653332817270815137121e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.647 Order of pole = 7.499 x[1] = 0.1962 y[1] (analytic) = 2.0193719877573241550433757554385 y[1] (numeric) = 2.0193719877573241550442777301102 absolute error = 9.019746717e-22 relative error = 4.4666098032869901868244651250593e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.646 Order of pole = 7.477 x[1] = 0.1963 y[1] (analytic) = 2.0193918686463546390826635777324 y[1] (numeric) = 2.019391868646354639083566609977 absolute error = 9.030322446e-22 relative error = 4.4718029156239176458955117582467e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.644 Order of pole = 7.456 x[1] = 0.1964 y[1] (analytic) = 2.0194117599308415863377196050131 y[1] (numeric) = 2.0194117599308415863386236951431 absolute error = 9.040901300e-22 relative error = 4.4769974501434130707558089639001e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.643 Order of pole = 7.434 x[1] = 0.1965 y[1] (analytic) = 2.0194316616111985630007647228271 y[1] (numeric) = 2.0194316616111985630016698711553 absolute error = 9.051483282e-22 relative error = 4.4821934082078798455620746046633e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.3MB, time=22.75 Real estimate of pole used Radius of convergence = 1.642 Order of pole = 7.413 x[1] = 0.1966 y[1] (analytic) = 2.019451573687839367873902635543 y[1] (numeric) = 2.0194515736878393678748088423825 absolute error = 9.062068395e-22 relative error = 4.4873907911796189206225838519845e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.641 Order of pole = 7.392 x[1] = 0.1967 y[1] (analytic) = 2.0194714961611780324041905251536 y[1] (numeric) = 2.0194714961611780324050977908174 absolute error = 9.072656638e-22 relative error = 4.4925895984401124957120416068449e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.64 Order of pole = 7.371 x[1] = 0.1968 y[1] (analytic) = 2.0194914290316288207187314839033 y[1] (numeric) = 2.019491429031628820719639808705 absolute error = 9.083248017e-22 relative error = 4.4977898328370376122783059789792e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.638 Order of pole = 7.35 x[1] = 0.1969 y[1] (analytic) = 2.0195113722996062296597887271867 y[1] (numeric) = 2.0195113722996062296606981114398 absolute error = 9.093842531e-22 relative error = 4.5029914937517250565732122885814e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.637 Order of pole = 7.329 x[1] = 0.197 y[1] (analytic) = 2.019531325965524988819921593161 y[1] (numeric) = 2.0195313259655249888208320371795 absolute error = 9.104440185e-22 relative error = 4.5081945835364675391370426484963e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.636 Order of pole = 7.308 x[1] = 0.1971 y[1] (analytic) = 2.0195512900298000605771433355272 y[1] (numeric) = 2.0195512900298000605780548396252 absolute error = 9.115040980e-22 relative error = 4.5133991025627779096092205966744e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.635 Order of pole = 7.287 x[1] = 0.1972 y[1] (analytic) = 2.019571264492846640130100715933 y[1] (numeric) = 2.0195712644928466401310132804247 absolute error = 9.125644917e-22 relative error = 4.5186050512021053803428154987812e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.634 Order of pole = 7.266 x[1] = 0.1973 y[1] (analytic) = 2.019591249355080155533275402459 y[1] (numeric) = 2.0195912493550801555341890276589 absolute error = 9.136251999e-22 relative error = 4.5238124308161349031783421771927e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.633 Order of pole = 7.246 x[1] = 0.1974 y[1] (analytic) = 2.0196112446169162677322071806526 y[1] (numeric) = 2.0196112446169162677331218668755 absolute error = 9.146862229e-22 relative error = 4.5290212427664485306423853245029e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.3MB, time=22.98 Real estimate of pole used Radius of convergence = 1.632 Order of pole = 7.225 x[1] = 0.1975 y[1] (analytic) = 2.019631250278770870598738983579 y[1] (numeric) = 2.0196312502787708705996547311399 absolute error = 9.157475609e-22 relative error = 4.5342314879193854524762860919087e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.63 Order of pole = 7.205 x[1] = 0.1976 y[1] (analytic) = 2.0196512663410600909662837473629 y[1] (numeric) = 2.0196512663410600909672005565768 absolute error = 9.168092139e-22 relative error = 4.5394431661509314751254131632746e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.629 Order of pole = 7.185 x[1] = 0.1977 y[1] (analytic) = 2.019671292804200288665113098698 y[1] (numeric) = 2.0196712928042002886660309698804 absolute error = 9.178711824e-22 relative error = 4.5446562798126786009150863656031e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.628 Order of pole = 7.165 x[1] = 0.1978 y[1] (analytic) = 2.0196913296686080565576678808099 y[1] (numeric) = 2.0196913296686080565585868142765 absolute error = 9.189334666e-22 relative error = 4.5498708297707009202684891599814e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.627 Order of pole = 7.144 x[1] = 0.1979 y[1] (analytic) = 2.0197113769347002205738905243565 y[1] (numeric) = 2.0197113769347002205748105204231 absolute error = 9.199960666e-22 relative error = 4.5550868163958687075204951216944e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.626 Order of pole = 7.124 x[1] = 0.198 y[1] (analytic) = 2.0197314346028938397465792697594 y[1] (numeric) = 2.0197314346028938397475003287419 absolute error = 9.210589825e-22 relative error = 4.5603042400589882913602414889889e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.625 Order of pole = 7.104 x[1] = 0.1981 y[1] (analytic) = 2.0197515026736062062467642474619 y[1] (numeric) = 2.0197515026736062062476863696768 absolute error = 9.221222149e-22 relative error = 4.5655231036063540962514759039898e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.624 Order of pole = 7.085 x[1] = 0.1982 y[1] (analytic) = 2.019771581147254845419105422616 y[1] (numeric) = 2.0197715811472548454200286083796 absolute error = 9.231857636e-22 relative error = 4.5707434059232541931237202485855e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.623 Order of pole = 7.065 x[1] = 0.1983 y[1] (analytic) = 2.0197916700242575158173124107001 y[1] (numeric) = 2.0197916700242575158182366603292 absolute error = 9.242496291e-22 relative error = 4.5759651493606756250311266325363e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.621 Order of pole = 7.045 x[1] = 0.1984 y[1] (analytic) = 2.019811769305032209239586170582 y[1] (numeric) = 2.0198117693050322092405114843935 absolute error = 9.253138115e-22 relative error = 4.5811883342890799847840584188300e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.3MB, time=23.21 Real estimate of pole used Radius of convergence = 1.62 Order of pole = 7.026 x[1] = 0.1985 y[1] (analytic) = 2.0198318789899971507640825815373 y[1] (numeric) = 2.0198318789899971507650089598483 absolute error = 9.263783110e-22 relative error = 4.5864129615739554318561588483652e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.619 Order of pole = 7.006 x[1] = 0.1986 y[1] (analytic) = 2.0198519990795707987843979107446 y[1] (numeric) = 2.0198519990795707987853253538726 absolute error = 9.274431280e-22 relative error = 4.5916390330708777907885367789228e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.618 Order of pole = 6.987 x[1] = 0.1987 y[1] (analytic) = 2.0198721295741718450450761777806 y[1] (numeric) = 2.0198721295741718450460046860432 absolute error = 9.285082626e-22 relative error = 4.5968665491500569400888641357410e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.617 Order of pole = 6.968 x[1] = 0.1988 y[1] (analytic) = 2.0198922704742192146771384226419 y[1] (numeric) = 2.0198922704742192146780679963568 absolute error = 9.295737149e-22 relative error = 4.6020955101816384897064231567001e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.616 Order of pole = 6.948 x[1] = 0.1989 y[1] (analytic) = 2.0199124217801320662336338838268 y[1] (numeric) = 2.0199124217801320662345645233122 absolute error = 9.306394854e-22 relative error = 4.6073259185159876351769547654760e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.615 Order of pole = 6.929 x[1] = 0.199 y[1] (analytic) = 2.0199325834923297917252130930153 y[1] (numeric) = 2.0199325834923297917261447985893 absolute error = 9.317055740e-22 relative error = 4.6125577735329300304850916585358e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.614 Order of pole = 6.91 x[1] = 0.1991 y[1] (analytic) = 2.0199527556112320166557228928855 y[1] (numeric) = 2.0199527556112320166566556648666 absolute error = 9.327719811e-22 relative error = 4.6177910770875719058374514762556e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.613 Order of pole = 6.891 x[1] = 0.1992 y[1] (analytic) = 2.0199729381372586000578233846165 y[1] (numeric) = 2.0199729381372586000587572233235 absolute error = 9.338387070e-22 relative error = 4.6230258305398396116873845811809e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.612 Order of pole = 6.872 x[1] = 0.1993 y[1] (analytic) = 2.0199931310708296345286268116257 y[1] (numeric) = 2.0199931310708296345295617173774 absolute error = 9.349057517e-22 relative error = 4.6282620337644018907536316615187e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.3MB, time=23.43 Real estimate of pole used Radius of convergence = 1.611 Order of pole = 6.854 x[1] = 0.1994 y[1] (analytic) = 2.0200133344123654462653583860963 y[1] (numeric) = 2.0200133344123654462662943592119 absolute error = 9.359731156e-22 relative error = 4.6334996886160677358842801113792e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.61 Order of pole = 6.835 x[1] = 0.1995 y[1] (analytic) = 2.0200335481622865951010390648555 y[1] (numeric) = 2.0200335481622865951019761056543 absolute error = 9.370407988e-22 relative error = 4.6387387954643983344978523696122e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.609 Order of pole = 6.816 x[1] = 0.1996 y[1] (analytic) = 2.0200537723210138745401902811666 y[1] (numeric) = 2.0200537723210138745411283899682 absolute error = 9.381088016e-22 relative error = 4.6439793556689629516218887204289e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.608 Order of pole = 6.798 x[1] = 0.1997 y[1] (analytic) = 2.0200740068889683117945606390047 y[1] (numeric) = 2.0200740068889683117954998161289 absolute error = 9.391771242e-22 relative error = 4.6492213700941952160678261136793e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.607 Order of pole = 6.779 x[1] = 0.1998 y[1] (analytic) = 2.0200942518665711678188745763887 y[1] (numeric) = 2.0200942518665711678198148221555 absolute error = 9.402457668e-22 relative error = 4.6544648396044442623247116965156e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.606 Order of pole = 6.761 x[1] = 0.1999 y[1] (analytic) = 2.0201145072542439373466030043479 y[1] (numeric) = 2.0201145072542439373475443190776 absolute error = 9.413147297e-22 relative error = 4.6597097655589961278922019119706e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.605 Order of pole = 6.743 x[1] = 0.2 y[1] (analytic) = 2.0201347730524083489257559281057 y[1] (numeric) = 2.0201347730524083489266983121188 absolute error = 9.423840131e-22 relative error = 4.6649561488220159212264523454217e-20 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 1000 Total Elapsed Time = 23 Seconds Elapsed Time(since restart) = 23 Seconds Expected Time Remaining = 3 Minutes 8 Seconds Optimized Time Remaining = 3 Minutes 8 Seconds Time to Timeout = 14 Minutes 36 Seconds Percent Done = 11.12 % > quit memory used=407.1MB, alloc=4.3MB, time=23.59