|\^/| 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 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > 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 := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then 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 := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 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_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(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 (omniabs(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"); > 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 > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(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 < omniabs(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"); 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; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > 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)); > glob_total_exp_sec := glob_optimal_expect_sec + total_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)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_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; 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 glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, 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)); glob_total_exp_sec := glob_optimal_expect_sec + total_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)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_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 > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; > #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 ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * 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)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > 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 (omniabs(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 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := 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 ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(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 (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(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_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing 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_sing := 1; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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] > -1.0 * glob_smallish_float) 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_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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] > -1.0 * glob_smallish_float))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing 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_sing := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > 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 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float*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)*rm0 - convfloat(m - 1)*rm1; if glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; 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 < omniabs(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 rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) or omniabs(array_y_higher[1, m]) <= glob_small_float or omniabs(array_y_higher[1, m - 1]) <= glob_small_float or omniabs(array_y_higher[1, m - 2]) <= glob_small_float or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := 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 omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(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 < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(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_sing := 0; if 1 <> found_sing 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_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing 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 -1.0*glob_smallish_float < 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_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing 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_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < 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_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing 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_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") 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; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_y[1] * (array_y[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_y,array_y,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_y,array_y,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(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 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 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 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_y[1]*array_y[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_y, array_y, 1); array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_y, array_y, 1); array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_y, array_y, 1); array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_y, array_y, 1); array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_y, array_y, 1); array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(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 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > 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 > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > 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 > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > 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 > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_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, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > 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 if 0; > 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 > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > 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 2 > 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 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 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, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > 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 5 > 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 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 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 > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > 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 + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_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 + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_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 6 > 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 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_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 + arr_aa[iii_att]*arr_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 > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > 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 6 > 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 6 > 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 > # End Function number 16 > # Begin Function number 17 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > fprintf(file,""); > 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 > # End Function number 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > 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 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > 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 > # End Function number 26 > # Begin Function number 27 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 27 > # Begin Function number 28 > 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 (sub2 > glob_small_float) then # if number 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > rrr; > 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 < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(1.0/(1.0 - x)); > end; exact_soln_y := proc(x) return 1.0/(1.0 - x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-200; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/nonlinear1postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 0.5 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > 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,"return(1.0/(1.0 - x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_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_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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_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 <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > 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_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_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := 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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 0.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #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); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > 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; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > if (glob_max_h < glob_h) then # if number 2 > glob_h := glob_max_h; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > 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] * expt(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]* expt(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(); > 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 ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #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] / expt(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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = y * y;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T18:55:17-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"nonlinear1") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > 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 4 > 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 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"nonlinear1 diffeq.mxt") > ; > logitem_str(html_log_file,"nonlinear1 maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-200); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/nonlinear1postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 0.5 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); 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, "return(1.0/(1.0 - x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_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_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_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; 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_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 0.5; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; 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); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; 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; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_max_h < glob_h then glob_h := glob_max_h end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(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]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(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]* expt(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(); 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 glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; 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]/( expt(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* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(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* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(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* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = y * y;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T18:55:17-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "nonlinear1"); logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); 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_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 165 "); logitem_str(html_log_file, "nonlinear1 diffeq.mxt"); logitem_str(html_log_file, "nonlinear1 maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 0.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(1.0/(1.0 - x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.5 estimated_steps = 500 step_error = 2.0000000000000000000000000000000e-13 est_needed_step_err = 2.0000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.0005002500000000000000000000000e-78 max_value3 = 1.0005002500000000000000000000000e-78 value3 = 1.0005002500000000000000000000000e-78 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 1 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.001 y[1] (analytic) = 1.001001001001001001001001001001 y[1] (numeric) = 1.001001001001001001001001001001 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.999 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.002 y[1] (analytic) = 1.0020040080160320641282565130261 y[1] (numeric) = 1.0020040080160320641282565130261 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.998 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.003 y[1] (analytic) = 1.0030090270812437311935807422267 y[1] (numeric) = 1.0030090270812437311935807422267 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.997 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.004 y[1] (analytic) = 1.0040160642570281124497991967871 y[1] (numeric) = 1.0040160642570281124497991967872 absolute error = 1e-31 relative error = 9.9600000000000000000000000000005e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.996 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.005 y[1] (analytic) = 1.0050251256281407035175879396985 y[1] (numeric) = 1.0050251256281407035175879396985 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.995 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.006 y[1] (analytic) = 1.006036217303822937625754527163 y[1] (numeric) = 1.006036217303822937625754527163 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.994 Order of pole = 651 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.31 x[1] = 0.007 y[1] (analytic) = 1.0070493454179254783484390735146 y[1] (numeric) = 1.0070493454179254783484390735146 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.993 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.008 y[1] (analytic) = 1.0080645161290322580645161290323 y[1] (numeric) = 1.0080645161290322580645161290323 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.992 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.009 y[1] (analytic) = 1.0090817356205852674066599394551 y[1] (numeric) = 1.0090817356205852674066599394551 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.991 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 1.010101010101010101010101010101 y[1] (numeric) = 1.010101010101010101010101010101 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.99 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.011 y[1] (analytic) = 1.0111223458038422649140546006067 y[1] (numeric) = 1.0111223458038422649140546006067 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.989 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.012 y[1] (analytic) = 1.0121457489878542510121457489879 y[1] (numeric) = 1.0121457489878542510121457489879 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.988 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.013 y[1] (analytic) = 1.0131712259371833839918946301925 y[1] (numeric) = 1.0131712259371833839918946301925 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.987 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.014 y[1] (analytic) = 1.0141987829614604462474645030426 y[1] (numeric) = 1.0141987829614604462474645030426 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.986 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.015 y[1] (analytic) = 1.0152284263959390862944162436548 y[1] (numeric) = 1.0152284263959390862944162436548 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.985 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.016 y[1] (analytic) = 1.016260162601626016260162601626 y[1] (numeric) = 1.016260162601626016260162601626 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.984 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.017 y[1] (analytic) = 1.0172939979654120040691759918616 y[1] (numeric) = 1.0172939979654120040691759918616 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.983 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.018 y[1] (analytic) = 1.0183299389002036659877800407332 y[1] (numeric) = 1.0183299389002036659877800407331 absolute error = 1e-31 relative error = 9.8200000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.982 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.019 y[1] (analytic) = 1.0193679918450560652395514780836 y[1] (numeric) = 1.0193679918450560652395514780835 absolute error = 1e-31 relative error = 9.8099999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.981 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 1.0204081632653061224489795918367 y[1] (numeric) = 1.0204081632653061224489795918366 absolute error = 1e-31 relative error = 9.8000000000000000000000000000003e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.98 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.021 y[1] (analytic) = 1.0214504596527068437180796731359 y[1] (numeric) = 1.0214504596527068437180796731357 absolute error = 2e-31 relative error = 1.9579999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.979 Order of pole = 651 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.67 x[1] = 0.022 y[1] (analytic) = 1.0224948875255623721881390593047 y[1] (numeric) = 1.0224948875255623721881390593046 absolute error = 1e-31 relative error = 9.7800000000000000000000000000000e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.978 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.023 y[1] (analytic) = 1.0235414534288638689866939611054 y[1] (numeric) = 1.0235414534288638689866939611053 absolute error = 1e-31 relative error = 9.7700000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.977 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.024 y[1] (analytic) = 1.0245901639344262295081967213115 y[1] (numeric) = 1.0245901639344262295081967213114 absolute error = 1e-31 relative error = 9.7599999999999999999999999999998e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.976 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.025 y[1] (analytic) = 1.025641025641025641025641025641 y[1] (numeric) = 1.025641025641025641025641025641 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.975 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.026 y[1] (analytic) = 1.0266940451745379876796714579055 y[1] (numeric) = 1.0266940451745379876796714579055 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.974 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.027 y[1] (analytic) = 1.0277492291880781089414182939363 y[1] (numeric) = 1.0277492291880781089414182939362 absolute error = 1e-31 relative error = 9.7299999999999999999999999999998e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.973 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.028 y[1] (analytic) = 1.0288065843621399176954732510288 y[1] (numeric) = 1.0288065843621399176954732510287 absolute error = 1e-31 relative error = 9.7200000000000000000000000000001e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.972 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.029 y[1] (analytic) = 1.029866117404737384140061791967 y[1] (numeric) = 1.0298661174047373841400617919669 absolute error = 1e-31 relative error = 9.7100000000000000000000000000004e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.971 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 1.0309278350515463917525773195876 y[1] (numeric) = 1.0309278350515463917525773195875 absolute error = 1e-31 relative error = 9.7000000000000000000000000000003e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.97 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.031 y[1] (analytic) = 1.0319917440660474716202270381837 y[1] (numeric) = 1.0319917440660474716202270381836 absolute error = 1e-31 relative error = 9.6899999999999999999999999999999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.969 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.032 y[1] (analytic) = 1.0330578512396694214876033057851 y[1] (numeric) = 1.033057851239669421487603305785 absolute error = 1e-31 relative error = 9.6800000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.968 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.033 y[1] (analytic) = 1.0341261633919338159255429162358 y[1] (numeric) = 1.0341261633919338159255429162357 absolute error = 1e-31 relative error = 9.6699999999999999999999999999998e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.967 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.034 y[1] (analytic) = 1.0351966873706004140786749482402 y[1] (numeric) = 1.0351966873706004140786749482401 absolute error = 1e-31 relative error = 9.6599999999999999999999999999997e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.966 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.035 y[1] (analytic) = 1.0362694300518134715025906735751 y[1] (numeric) = 1.0362694300518134715025906735751 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.965 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.036 y[1] (analytic) = 1.037344398340248962655601659751 y[1] (numeric) = 1.037344398340248962655601659751 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.964 Order of pole = 651 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=1.05 x[1] = 0.037 y[1] (analytic) = 1.0384215991692627206645898234683 y[1] (numeric) = 1.0384215991692627206645898234683 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.963 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.038 y[1] (analytic) = 1.039501039501039501039501039501 y[1] (numeric) = 1.039501039501039501039501039501 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.962 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.039 y[1] (analytic) = 1.0405827263267429760665972944849 y[1] (numeric) = 1.0405827263267429760665972944849 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.961 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 1.0416666666666666666666666666667 y[1] (numeric) = 1.0416666666666666666666666666667 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.96 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.041 y[1] (analytic) = 1.0427528675703858185610010427529 y[1] (numeric) = 1.0427528675703858185610010427529 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.959 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.042 y[1] (analytic) = 1.0438413361169102296450939457202 y[1] (numeric) = 1.0438413361169102296450939457203 absolute error = 1e-31 relative error = 9.5800000000000000000000000000005e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.958 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.043 y[1] (analytic) = 1.0449320794148380355276907001045 y[1] (numeric) = 1.0449320794148380355276907001045 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.957 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.044 y[1] (analytic) = 1.0460251046025104602510460251046 y[1] (numeric) = 1.0460251046025104602510460251046 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.956 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.045 y[1] (analytic) = 1.0471204188481675392670157068063 y[1] (numeric) = 1.0471204188481675392670157068063 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.955 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.046 y[1] (analytic) = 1.0482180293501048218029350104822 y[1] (numeric) = 1.0482180293501048218029350104822 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.954 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.047 y[1] (analytic) = 1.0493179433368310598111227701994 y[1] (numeric) = 1.0493179433368310598111227701994 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.953 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.048 y[1] (analytic) = 1.0504201680672268907563025210084 y[1] (numeric) = 1.0504201680672268907563025210084 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.952 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.049 y[1] (analytic) = 1.0515247108307045215562565720294 y[1] (numeric) = 1.0515247108307045215562565720294 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.951 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 1.0526315789473684210526315789474 y[1] (numeric) = 1.0526315789473684210526315789473 absolute error = 1e-31 relative error = 9.4999999999999999999999999999997e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.95 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.051 y[1] (analytic) = 1.0537407797681770284510010537408 y[1] (numeric) = 1.0537407797681770284510010537407 absolute error = 1e-31 relative error = 9.4899999999999999999999999999998e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.949 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.052 y[1] (analytic) = 1.0548523206751054852320675105485 y[1] (numeric) = 1.0548523206751054852320675105484 absolute error = 1e-31 relative error = 9.4800000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.948 Order of pole = 651 memory used=15.2MB, alloc=3.9MB, time=1.43 TOP MAIN SOLVE Loop x[1] = 0.053 y[1] (analytic) = 1.0559662090813093980992608236536 y[1] (numeric) = 1.0559662090813093980992608236535 absolute error = 1e-31 relative error = 9.4700000000000000000000000000004e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.947 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.054 y[1] (analytic) = 1.0570824524312896405919661733615 y[1] (numeric) = 1.0570824524312896405919661733614 absolute error = 1e-31 relative error = 9.4600000000000000000000000000002e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.946 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.055 y[1] (analytic) = 1.0582010582010582010582010582011 y[1] (numeric) = 1.0582010582010582010582010582009 absolute error = 2e-31 relative error = 1.8899999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.945 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.056 y[1] (analytic) = 1.0593220338983050847457627118644 y[1] (numeric) = 1.0593220338983050847457627118642 absolute error = 2e-31 relative error = 1.8880000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.944 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.057 y[1] (analytic) = 1.0604453870625662778366914103924 y[1] (numeric) = 1.0604453870625662778366914103922 absolute error = 2e-31 relative error = 1.8859999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.943 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.058 y[1] (analytic) = 1.0615711252653927813163481953291 y[1] (numeric) = 1.0615711252653927813163481953289 absolute error = 2e-31 relative error = 1.8840000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.942 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.059 y[1] (analytic) = 1.0626992561105207226354941551541 y[1] (numeric) = 1.0626992561105207226354941551539 absolute error = 2e-31 relative error = 1.8820000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.941 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 1.0638297872340425531914893617021 y[1] (numeric) = 1.0638297872340425531914893617019 absolute error = 2e-31 relative error = 1.8800000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.94 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.061 y[1] (analytic) = 1.0649627263045793397231096911608 y[1] (numeric) = 1.0649627263045793397231096911606 absolute error = 2e-31 relative error = 1.8780000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.939 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.062 y[1] (analytic) = 1.0660980810234541577825159914712 y[1] (numeric) = 1.066098081023454157782515991471 absolute error = 2e-31 relative error = 1.8760000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.938 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.063 y[1] (analytic) = 1.0672358591248665955176093916756 y[1] (numeric) = 1.0672358591248665955176093916753 absolute error = 3e-31 relative error = 2.8109999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.937 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.064 y[1] (analytic) = 1.0683760683760683760683760683761 y[1] (numeric) = 1.0683760683760683760683760683758 absolute error = 3e-31 relative error = 2.8079999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.936 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.065 y[1] (analytic) = 1.069518716577540106951871657754 y[1] (numeric) = 1.0695187165775401069518716577537 absolute error = 3e-31 relative error = 2.8050000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.935 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.066 y[1] (analytic) = 1.0706638115631691648822269807281 y[1] (numeric) = 1.0706638115631691648822269807277 absolute error = 4e-31 relative error = 3.7359999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.934 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.067 y[1] (analytic) = 1.0718113612004287245444801714898 y[1] (numeric) = 1.0718113612004287245444801714895 absolute error = 3e-31 relative error = 2.7990000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.933 memory used=19.0MB, alloc=4.0MB, time=1.80 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.068 y[1] (analytic) = 1.0729613733905579399141630901288 y[1] (numeric) = 1.0729613733905579399141630901284 absolute error = 4e-31 relative error = 3.7279999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.932 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.069 y[1] (analytic) = 1.0741138560687432867883995703545 y[1] (numeric) = 1.0741138560687432867883995703541 absolute error = 4e-31 relative error = 3.7239999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.931 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 1.0752688172043010752688172043011 y[1] (numeric) = 1.0752688172043010752688172043007 absolute error = 4e-31 relative error = 3.7199999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.93 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.071 y[1] (analytic) = 1.0764262648008611410118406889128 y[1] (numeric) = 1.0764262648008611410118406889124 absolute error = 4e-31 relative error = 3.7160000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.929 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.072 y[1] (analytic) = 1.0775862068965517241379310344828 y[1] (numeric) = 1.0775862068965517241379310344823 absolute error = 5e-31 relative error = 4.6399999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.928 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.073 y[1] (analytic) = 1.0787486515641855447680690399137 y[1] (numeric) = 1.0787486515641855447680690399132 absolute error = 5e-31 relative error = 4.6350000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.927 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.074 y[1] (analytic) = 1.0799136069114470842332613390929 y[1] (numeric) = 1.0799136069114470842332613390924 absolute error = 5e-31 relative error = 4.6299999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.926 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.075 y[1] (analytic) = 1.0810810810810810810810810810811 y[1] (numeric) = 1.0810810810810810810810810810806 absolute error = 5e-31 relative error = 4.6249999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.925 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.076 y[1] (analytic) = 1.0822510822510822510822510822511 y[1] (numeric) = 1.0822510822510822510822510822506 absolute error = 5e-31 relative error = 4.6199999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.924 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.077 y[1] (analytic) = 1.0834236186348862405200433369447 y[1] (numeric) = 1.0834236186348862405200433369443 absolute error = 4e-31 relative error = 3.6920000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.923 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.078 y[1] (analytic) = 1.0845986984815618221258134490239 y[1] (numeric) = 1.0845986984815618221258134490234 absolute error = 5e-31 relative error = 4.6099999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.922 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.079 y[1] (analytic) = 1.0857763300760043431053203040174 y[1] (numeric) = 1.0857763300760043431053203040169 absolute error = 5e-31 relative error = 4.6049999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.921 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 1.0869565217391304347826086956522 y[1] (numeric) = 1.0869565217391304347826086956517 absolute error = 5e-31 relative error = 4.5999999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.92 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.081 y[1] (analytic) = 1.0881392818280739934711643090316 y[1] (numeric) = 1.0881392818280739934711643090311 absolute error = 5e-31 relative error = 4.5949999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.919 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.082 y[1] (analytic) = 1.0893246187363834422657952069717 y[1] (numeric) = 1.0893246187363834422657952069712 memory used=22.8MB, alloc=4.0MB, time=2.19 absolute error = 5e-31 relative error = 4.5899999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.918 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.083 y[1] (analytic) = 1.0905125408942202835332606324973 y[1] (numeric) = 1.0905125408942202835332606324968 absolute error = 5e-31 relative error = 4.5849999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.917 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.084 y[1] (analytic) = 1.0917030567685589519650655021834 y[1] (numeric) = 1.0917030567685589519650655021829 absolute error = 5e-31 relative error = 4.5800000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.916 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.085 y[1] (analytic) = 1.0928961748633879781420765027322 y[1] (numeric) = 1.0928961748633879781420765027317 absolute error = 5e-31 relative error = 4.5750000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.915 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.086 y[1] (analytic) = 1.0940919037199124726477024070022 y[1] (numeric) = 1.0940919037199124726477024070016 absolute error = 6e-31 relative error = 5.4839999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.914 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.087 y[1] (analytic) = 1.0952902519167579408543263964951 y[1] (numeric) = 1.0952902519167579408543263964945 absolute error = 6e-31 relative error = 5.4779999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.913 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.088 y[1] (analytic) = 1.0964912280701754385964912280702 y[1] (numeric) = 1.0964912280701754385964912280696 absolute error = 6e-31 relative error = 5.4719999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.912 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.089 y[1] (analytic) = 1.0976948408342480790340285400659 y[1] (numeric) = 1.0976948408342480790340285400653 absolute error = 6e-31 relative error = 5.4659999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.911 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 1.0989010989010989010989010989011 y[1] (numeric) = 1.0989010989010989010989010989005 absolute error = 6e-31 relative error = 5.4600000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.91 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.091 y[1] (analytic) = 1.10011001100110011001100110011 y[1] (numeric) = 1.1001100110011001100110011001094 absolute error = 6e-31 relative error = 5.4540000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.909 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.092 y[1] (analytic) = 1.1013215859030837004405286343612 y[1] (numeric) = 1.1013215859030837004405286343606 absolute error = 6e-31 relative error = 5.4480000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.908 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.093 y[1] (analytic) = 1.1025358324145534729878721058434 y[1] (numeric) = 1.1025358324145534729878721058428 absolute error = 6e-31 relative error = 5.4420000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.907 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.094 y[1] (analytic) = 1.1037527593818984547461368653422 y[1] (numeric) = 1.1037527593818984547461368653415 absolute error = 7e-31 relative error = 6.3419999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.906 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.095 y[1] (analytic) = 1.1049723756906077348066298342541 y[1] (numeric) = 1.1049723756906077348066298342535 absolute error = 6e-31 relative error = 5.4300000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.905 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.096 y[1] (analytic) = 1.1061946902654867256637168141593 y[1] (numeric) = 1.1061946902654867256637168141586 absolute error = 7e-31 relative error = 6.3280000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.904 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.097 y[1] (analytic) = 1.1074197120708748615725359911406 y[1] (numeric) = 1.1074197120708748615725359911399 absolute error = 7e-31 relative error = 6.3210000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 memory used=26.7MB, alloc=4.1MB, time=2.57 Real estimate of pole used for equation 1 Radius of convergence = 0.903 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.098 y[1] (analytic) = 1.1086474501108647450110864745011 y[1] (numeric) = 1.1086474501108647450110864745004 absolute error = 7e-31 relative error = 6.3140000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.902 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.099 y[1] (analytic) = 1.1098779134295227524972253052164 y[1] (numeric) = 1.1098779134295227524972253052157 absolute error = 7e-31 relative error = 6.3070000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.901 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.1111111111111111111111111111111 y[1] (numeric) = 1.1111111111111111111111111111104 absolute error = 7e-31 relative error = 6.3000000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = 1.112347052280311457174638487208 y[1] (numeric) = 1.1123470522803114571746384872073 absolute error = 7e-31 relative error = 6.2930000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.899 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 1.113585746102449888641425389755 y[1] (numeric) = 1.1135857461024498886414253897543 absolute error = 7e-31 relative error = 6.2860000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.898 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.103 y[1] (analytic) = 1.1148272017837235228539576365663 y[1] (numeric) = 1.1148272017837235228539576365656 absolute error = 7e-31 relative error = 6.2790000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.897 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = 1.1160714285714285714285714285714 y[1] (numeric) = 1.1160714285714285714285714285707 absolute error = 7e-31 relative error = 6.2720000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.896 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.105 y[1] (analytic) = 1.1173184357541899441340782122905 y[1] (numeric) = 1.1173184357541899441340782122898 absolute error = 7e-31 relative error = 6.2650000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.895 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 1.1185682326621923937360178970917 y[1] (numeric) = 1.118568232662192393736017897091 absolute error = 7e-31 relative error = 6.2580000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.894 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = 1.1198208286674132138857782754759 y[1] (numeric) = 1.1198208286674132138857782754752 absolute error = 7e-31 relative error = 6.2510000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.893 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 1.1210762331838565022421524663677 y[1] (numeric) = 1.121076233183856502242152466367 absolute error = 7e-31 relative error = 6.2440000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.892 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = 1.1223344556677890011223344556678 y[1] (numeric) = 1.1223344556677890011223344556671 absolute error = 7e-31 relative error = 6.2369999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.891 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.1235955056179775280898876404494 y[1] (numeric) = 1.1235955056179775280898876404487 absolute error = 7e-31 relative error = 6.2300000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.89 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.111 y[1] (analytic) = 1.1248593925759280089988751406074 y[1] (numeric) = 1.1248593925759280089988751406067 absolute error = 7e-31 relative error = 6.2230000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.889 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = 1.1261261261261261261261261261261 y[1] (numeric) = 1.1261261261261261261261261261254 absolute error = 7e-31 relative error = 6.2160000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.888 Order of pole = 651 memory used=30.5MB, alloc=4.1MB, time=2.95 TOP MAIN SOLVE Loop x[1] = 0.113 y[1] (analytic) = 1.1273957158962795941375422773393 y[1] (numeric) = 1.1273957158962795941375422773386 absolute error = 7e-31 relative error = 6.2090000000000000000000000000003e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.887 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.114 y[1] (analytic) = 1.1286681715575620767494356659142 y[1] (numeric) = 1.1286681715575620767494356659135 absolute error = 7e-31 relative error = 6.2020000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.886 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = 1.1299435028248587570621468926554 y[1] (numeric) = 1.1299435028248587570621468926546 absolute error = 8e-31 relative error = 7.0799999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.885 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.116 y[1] (analytic) = 1.1312217194570135746606334841629 y[1] (numeric) = 1.1312217194570135746606334841621 absolute error = 8e-31 relative error = 7.0720000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.884 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = 1.1325028312570781426953567383918 y[1] (numeric) = 1.132502831257078142695356738391 absolute error = 8e-31 relative error = 7.0640000000000000000000000000003e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.883 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.118 y[1] (analytic) = 1.1337868480725623582766439909297 y[1] (numeric) = 1.1337868480725623582766439909289 absolute error = 8e-31 relative error = 7.0560000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.882 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.119 y[1] (analytic) = 1.1350737797956867196367763904654 y[1] (numeric) = 1.1350737797956867196367763904646 absolute error = 8e-31 relative error = 7.0479999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.881 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.1363636363636363636363636363636 y[1] (numeric) = 1.1363636363636363636363636363629 absolute error = 7e-31 relative error = 6.1600000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.88 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.121 y[1] (analytic) = 1.1376564277588168373151308304892 y[1] (numeric) = 1.1376564277588168373151308304885 absolute error = 7e-31 relative error = 6.1530000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.879 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.122 y[1] (analytic) = 1.1389521640091116173120728929385 y[1] (numeric) = 1.1389521640091116173120728929378 absolute error = 7e-31 relative error = 6.1460000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.878 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = 1.1402508551881413911060433295325 y[1] (numeric) = 1.1402508551881413911060433295318 absolute error = 7e-31 relative error = 6.1390000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.877 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.124 y[1] (analytic) = 1.1415525114155251141552511415525 y[1] (numeric) = 1.1415525114155251141552511415518 absolute error = 7e-31 relative error = 6.1320000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.876 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = 1.1428571428571428571428571428571 y[1] (numeric) = 1.1428571428571428571428571428564 absolute error = 7e-31 relative error = 6.1250000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.875 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.126 y[1] (analytic) = 1.1441647597254004576659038901602 y[1] (numeric) = 1.1441647597254004576659038901594 absolute error = 8e-31 relative error = 6.9919999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.874 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.127 y[1] (analytic) = 1.145475372279495990836197021764 y[1] (numeric) = 1.1454753722794959908361970217632 absolute error = 8e-31 relative error = 6.9840000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.873 Order of pole = 651 memory used=34.3MB, alloc=4.1MB, time=3.33 TOP MAIN SOLVE Loop x[1] = 0.128 y[1] (analytic) = 1.146788990825688073394495412844 y[1] (numeric) = 1.1467889908256880733944954128432 absolute error = 8e-31 relative error = 6.9760000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.872 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = 1.1481056257175660160734787600459 y[1] (numeric) = 1.1481056257175660160734787600451 absolute error = 8e-31 relative error = 6.9680000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.871 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.1494252873563218390804597701149 y[1] (numeric) = 1.1494252873563218390804597701141 absolute error = 8e-31 relative error = 6.9600000000000000000000000000003e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.87 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = 1.1507479861910241657077100115075 y[1] (numeric) = 1.1507479861910241657077100115066 absolute error = 9e-31 relative error = 7.8209999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.869 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.132 y[1] (analytic) = 1.1520737327188940092165898617512 y[1] (numeric) = 1.1520737327188940092165898617503 absolute error = 9e-31 relative error = 7.8119999999999999999999999999997e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.868 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.133 y[1] (analytic) = 1.1534025374855824682814302191465 y[1] (numeric) = 1.1534025374855824682814302191456 absolute error = 9e-31 relative error = 7.8029999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.867 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = 1.1547344110854503464203233256351 y[1] (numeric) = 1.1547344110854503464203233256342 absolute error = 9e-31 relative error = 7.7940000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.866 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.135 y[1] (analytic) = 1.1560693641618497109826589595376 y[1] (numeric) = 1.1560693641618497109826589595367 absolute error = 9e-31 relative error = 7.7849999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.865 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = 1.1574074074074074074074074074074 y[1] (numeric) = 1.1574074074074074074074074074065 absolute error = 9e-31 relative error = 7.7760000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.864 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.137 y[1] (analytic) = 1.158748551564310544611819235226 y[1] (numeric) = 1.158748551564310544611819235225 absolute error = 1.0e-30 relative error = 8.6299999999999999999999999999997e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.863 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.138 y[1] (analytic) = 1.1600928074245939675174013921114 y[1] (numeric) = 1.1600928074245939675174013921104 absolute error = 1.0e-30 relative error = 8.6199999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.862 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.139 y[1] (analytic) = 1.1614401858304297328687572590012 y[1] (numeric) = 1.1614401858304297328687572590002 absolute error = 1.0e-30 relative error = 8.6099999999999999999999999999997e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.861 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.1627906976744186046511627906977 y[1] (numeric) = 1.1627906976744186046511627906967 absolute error = 1.0e-30 relative error = 8.5999999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.86 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.141 y[1] (analytic) = 1.1641443538998835855646100116414 y[1] (numeric) = 1.1641443538998835855646100116405 absolute error = 9e-31 relative error = 7.7310000000000000000000000000003e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.859 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.142 y[1] (analytic) = 1.1655011655011655011655011655012 y[1] (numeric) = 1.1655011655011655011655011655002 absolute error = 1.0e-30 relative error = 8.5799999999999999999999999999997e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.858 Order of pole = 651 memory used=38.1MB, alloc=4.1MB, time=3.72 TOP MAIN SOLVE Loop x[1] = 0.143 y[1] (analytic) = 1.1668611435239206534422403733956 y[1] (numeric) = 1.1668611435239206534422403733946 absolute error = 1.0e-30 relative error = 8.5699999999999999999999999999997e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.857 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.144 y[1] (analytic) = 1.1682242990654205607476635514019 y[1] (numeric) = 1.1682242990654205607476635514009 absolute error = 1.0e-30 relative error = 8.5599999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.856 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.145 y[1] (analytic) = 1.1695906432748538011695906432749 y[1] (numeric) = 1.1695906432748538011695906432739 absolute error = 1.0e-30 relative error = 8.5499999999999999999999999999997e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.855 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = 1.1709601873536299765807962529274 y[1] (numeric) = 1.1709601873536299765807962529264 absolute error = 1.0e-30 relative error = 8.5400000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.854 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.147 y[1] (analytic) = 1.1723329425556858147713950762016 y[1] (numeric) = 1.1723329425556858147713950762006 absolute error = 1.0e-30 relative error = 8.5300000000000000000000000000003e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.853 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = 1.1737089201877934272300469483568 y[1] (numeric) = 1.1737089201877934272300469483558 absolute error = 1.0e-30 relative error = 8.5200000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.852 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.149 y[1] (analytic) = 1.1750881316098707403055229142186 y[1] (numeric) = 1.1750881316098707403055229142176 absolute error = 1.0e-30 relative error = 8.5099999999999999999999999999998e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.851 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.1764705882352941176470588235294 y[1] (numeric) = 1.1764705882352941176470588235284 absolute error = 1.0e-30 relative error = 8.5000000000000000000000000000001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.85 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.151 y[1] (analytic) = 1.1778563015312131919905771495878 y[1] (numeric) = 1.1778563015312131919905771495867 absolute error = 1.1e-30 relative error = 9.3389999999999999999999999999996e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.849 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.152 y[1] (analytic) = 1.1792452830188679245283018867925 y[1] (numeric) = 1.1792452830188679245283018867914 absolute error = 1.1e-30 relative error = 9.3279999999999999999999999999996e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.848 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.153 y[1] (analytic) = 1.180637544273907910271546635183 y[1] (numeric) = 1.1806375442739079102715466351819 absolute error = 1.1e-30 relative error = 9.3170000000000000000000000000000e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.847 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.154 y[1] (analytic) = 1.1820330969267139479905437352246 y[1] (numeric) = 1.1820330969267139479905437352235 absolute error = 1.1e-30 relative error = 9.3059999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.846 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.155 y[1] (analytic) = 1.183431952662721893491124260355 y[1] (numeric) = 1.1834319526627218934911242603539 absolute error = 1.1e-30 relative error = 9.2950000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.845 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.156 y[1] (analytic) = 1.1848341232227488151658767772512 y[1] (numeric) = 1.1848341232227488151658767772501 absolute error = 1.1e-30 relative error = 9.2839999999999999999999999999999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.844 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.157 y[1] (analytic) = 1.1862396204033214709371293001186 y[1] (numeric) = 1.1862396204033214709371293001175 absolute error = 1.1e-30 relative error = 9.2730000000000000000000000000002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.843 Order of pole = 651 memory used=41.9MB, alloc=4.1MB, time=4.11 TOP MAIN SOLVE Loop x[1] = 0.158 y[1] (analytic) = 1.1876484560570071258907363420428 y[1] (numeric) = 1.1876484560570071258907363420416 absolute error = 1.2e-30 relative error = 1.0104000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.842 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = 1.1890606420927467300832342449465 y[1] (numeric) = 1.1890606420927467300832342449453 absolute error = 1.2e-30 relative error = 1.0092000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.841 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 1.1904761904761904761904761904762 y[1] (numeric) = 1.190476190476190476190476190475 absolute error = 1.2e-30 relative error = 1.0080000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.84 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.161 y[1] (analytic) = 1.1918951132300357568533969010727 y[1] (numeric) = 1.1918951132300357568533969010715 absolute error = 1.2e-30 relative error = 1.0068000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.839 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.162 y[1] (analytic) = 1.1933174224343675417661097852029 y[1] (numeric) = 1.1933174224343675417661097852017 absolute error = 1.2e-30 relative error = 1.0056000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.838 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = 1.1947431302270011947431302270012 y[1] (numeric) = 1.194743130227001194743130227 absolute error = 1.2e-30 relative error = 1.0044000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.837 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.164 y[1] (analytic) = 1.1961722488038277511961722488038 y[1] (numeric) = 1.1961722488038277511961722488026 absolute error = 1.2e-30 relative error = 1.0032000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.836 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.165 y[1] (analytic) = 1.1976047904191616766467065868263 y[1] (numeric) = 1.1976047904191616766467065868251 absolute error = 1.2e-30 relative error = 1.0020000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.835 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.166 y[1] (analytic) = 1.1990407673860911270983213429257 y[1] (numeric) = 1.1990407673860911270983213429244 absolute error = 1.3e-30 relative error = 1.0842000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.834 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = 1.2004801920768307322929171668667 y[1] (numeric) = 1.2004801920768307322929171668655 absolute error = 1.2e-30 relative error = 9.9960000000000000000000000000004e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.833 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.168 y[1] (analytic) = 1.2019230769230769230769230769231 y[1] (numeric) = 1.2019230769230769230769230769218 absolute error = 1.3e-30 relative error = 1.0816000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.832 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = 1.2033694344163658243080625752106 y[1] (numeric) = 1.2033694344163658243080625752093 absolute error = 1.3e-30 relative error = 1.0803000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.831 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 1.2048192771084337349397590361446 y[1] (numeric) = 1.2048192771084337349397590361433 absolute error = 1.3e-30 relative error = 1.0790000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.83 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.171 y[1] (analytic) = 1.2062726176115802171290711700844 y[1] (numeric) = 1.2062726176115802171290711700832 absolute error = 1.2e-30 relative error = 9.9480000000000000000000000000003e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.829 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.172 y[1] (analytic) = 1.2077294685990338164251207729469 y[1] (numeric) = 1.2077294685990338164251207729456 absolute error = 1.3e-30 relative error = 1.0764000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.828 Order of pole = 651 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=4.49 x[1] = 0.173 y[1] (analytic) = 1.2091898428053204353083434099154 y[1] (numeric) = 1.2091898428053204353083434099141 absolute error = 1.3e-30 relative error = 1.0751000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.827 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.174 y[1] (analytic) = 1.2106537530266343825665859564165 y[1] (numeric) = 1.2106537530266343825665859564152 absolute error = 1.3e-30 relative error = 1.0738000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.826 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = 1.2121212121212121212121212121212 y[1] (numeric) = 1.2121212121212121212121212121199 absolute error = 1.3e-30 relative error = 1.0725000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.825 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.176 y[1] (analytic) = 1.2135922330097087378640776699029 y[1] (numeric) = 1.2135922330097087378640776699016 absolute error = 1.3e-30 relative error = 1.0712000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.824 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.177 y[1] (analytic) = 1.2150668286755771567436208991495 y[1] (numeric) = 1.2150668286755771567436208991481 absolute error = 1.4e-30 relative error = 1.1522000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.823 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = 1.216545012165450121654501216545 y[1] (numeric) = 1.2165450121654501216545012165437 absolute error = 1.3e-30 relative error = 1.0686000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.822 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.179 y[1] (analytic) = 1.2180267965895249695493300852619 y[1] (numeric) = 1.2180267965895249695493300852606 absolute error = 1.3e-30 relative error = 1.0673000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.821 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 1.2195121951219512195121951219512 y[1] (numeric) = 1.2195121951219512195121951219499 absolute error = 1.3e-30 relative error = 1.0660000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.82 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.181 y[1] (analytic) = 1.2210012210012210012210012210012 y[1] (numeric) = 1.2210012210012210012210012209999 absolute error = 1.3e-30 relative error = 1.0647000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.819 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.182 y[1] (analytic) = 1.2224938875305623471882640586797 y[1] (numeric) = 1.2224938875305623471882640586784 absolute error = 1.3e-30 relative error = 1.0634000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.818 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.183 y[1] (analytic) = 1.2239902080783353733170134638923 y[1] (numeric) = 1.223990208078335373317013463891 absolute error = 1.3e-30 relative error = 1.0621000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.817 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = 1.2254901960784313725490196078431 y[1] (numeric) = 1.2254901960784313725490196078418 absolute error = 1.3e-30 relative error = 1.0608000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.816 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.185 y[1] (analytic) = 1.2269938650306748466257668711656 y[1] (numeric) = 1.2269938650306748466257668711643 absolute error = 1.3e-30 relative error = 1.0595000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.815 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = 1.2285012285012285012285012285012 y[1] (numeric) = 1.2285012285012285012285012284999 absolute error = 1.3e-30 relative error = 1.0582000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.814 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.187 y[1] (analytic) = 1.2300123001230012300123001230012 y[1] (numeric) = 1.2300123001230012300123001229999 absolute error = 1.3e-30 relative error = 1.0569000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.813 Order of pole = 651 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=4.88 x[1] = 0.188 y[1] (analytic) = 1.2315270935960591133004926108374 y[1] (numeric) = 1.2315270935960591133004926108361 absolute error = 1.3e-30 relative error = 1.0556000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.812 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.189 y[1] (analytic) = 1.2330456226880394574599260172626 y[1] (numeric) = 1.2330456226880394574599260172613 absolute error = 1.3e-30 relative error = 1.0543000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.811 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 1.2345679012345679012345679012346 y[1] (numeric) = 1.2345679012345679012345679012332 absolute error = 1.4e-30 relative error = 1.1340000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.81 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.191 y[1] (analytic) = 1.23609394313967861557478368356 y[1] (numeric) = 1.2360939431396786155747836835586 absolute error = 1.4e-30 relative error = 1.1326000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.809 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = 1.2376237623762376237623762376238 y[1] (numeric) = 1.2376237623762376237623762376224 absolute error = 1.4e-30 relative error = 1.1312000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.808 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.193 y[1] (analytic) = 1.2391573729863692688971499380421 y[1] (numeric) = 1.2391573729863692688971499380408 absolute error = 1.3e-30 relative error = 1.0491000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.807 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.194 y[1] (analytic) = 1.2406947890818858560794044665012 y[1] (numeric) = 1.2406947890818858560794044664999 absolute error = 1.3e-30 relative error = 1.0478000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.806 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.195 y[1] (analytic) = 1.2422360248447204968944099378882 y[1] (numeric) = 1.2422360248447204968944099378869 absolute error = 1.3e-30 relative error = 1.0465000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.805 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = 1.2437810945273631840796019900498 y[1] (numeric) = 1.2437810945273631840796019900484 absolute error = 1.4e-30 relative error = 1.1256000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.804 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.197 y[1] (analytic) = 1.24533001245330012453300124533 y[1] (numeric) = 1.2453300124533001245330012453287 absolute error = 1.3e-30 relative error = 1.0439000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.803 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.198 y[1] (analytic) = 1.2468827930174563591022443890274 y[1] (numeric) = 1.2468827930174563591022443890261 absolute error = 1.3e-30 relative error = 1.0426000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.802 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.199 y[1] (analytic) = 1.2484394506866416978776529338327 y[1] (numeric) = 1.2484394506866416978776529338314 absolute error = 1.3e-30 relative error = 1.0413000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.801 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 1.25 y[1] (numeric) = 1.2499999999999999999999999999987 absolute error = 1.3e-30 relative error = 1.0400000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.201 y[1] (analytic) = 1.2515644555694618272841051314143 y[1] (numeric) = 1.251564455569461827284105131413 absolute error = 1.3e-30 relative error = 1.0387000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.799 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.202 y[1] (analytic) = 1.2531328320802005012531328320802 y[1] (numeric) = 1.2531328320802005012531328320789 absolute error = 1.3e-30 relative error = 1.0374000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.798 Order of pole = 651 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=5.25 x[1] = 0.203 y[1] (analytic) = 1.2547051442910915934755332496863 y[1] (numeric) = 1.254705144291091593475533249685 absolute error = 1.3e-30 relative error = 1.0361000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.797 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.204 y[1] (analytic) = 1.2562814070351758793969849246231 y[1] (numeric) = 1.2562814070351758793969849246218 absolute error = 1.3e-30 relative error = 1.0348000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.796 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.205 y[1] (analytic) = 1.2578616352201257861635220125786 y[1] (numeric) = 1.2578616352201257861635220125773 absolute error = 1.3e-30 relative error = 1.0335000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.795 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.206 y[1] (analytic) = 1.2594458438287153652392947103275 y[1] (numeric) = 1.2594458438287153652392947103261 absolute error = 1.4e-30 relative error = 1.1116000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.794 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.207 y[1] (analytic) = 1.2610340479192938209331651954603 y[1] (numeric) = 1.2610340479192938209331651954589 absolute error = 1.4e-30 relative error = 1.1102000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.793 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.208 y[1] (analytic) = 1.2626262626262626262626262626263 y[1] (numeric) = 1.2626262626262626262626262626249 absolute error = 1.4e-30 relative error = 1.1088000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.792 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.209 y[1] (analytic) = 1.2642225031605562579013906447535 y[1] (numeric) = 1.2642225031605562579013906447521 absolute error = 1.4e-30 relative error = 1.1074000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.791 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 1.2658227848101265822784810126582 y[1] (numeric) = 1.2658227848101265822784810126568 absolute error = 1.4e-30 relative error = 1.1060000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.79 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.211 y[1] (analytic) = 1.2674271229404309252217997465146 y[1] (numeric) = 1.2674271229404309252217997465131 absolute error = 1.5e-30 relative error = 1.1835000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.789 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.212 y[1] (analytic) = 1.2690355329949238578680203045685 y[1] (numeric) = 1.269035532994923857868020304567 absolute error = 1.5e-30 relative error = 1.1820000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.788 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.213 y[1] (analytic) = 1.2706480304955527318932655654384 y[1] (numeric) = 1.2706480304955527318932655654368 absolute error = 1.6e-30 relative error = 1.2592000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.787 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.214 y[1] (analytic) = 1.2722646310432569974554707379135 y[1] (numeric) = 1.2722646310432569974554707379119 absolute error = 1.6e-30 relative error = 1.2576000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.786 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.215 y[1] (analytic) = 1.2738853503184713375796178343949 y[1] (numeric) = 1.2738853503184713375796178343933 absolute error = 1.6e-30 relative error = 1.2560000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.785 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.216 y[1] (analytic) = 1.2755102040816326530612244897959 y[1] (numeric) = 1.2755102040816326530612244897943 absolute error = 1.6e-30 relative error = 1.2544000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.784 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.217 y[1] (analytic) = 1.2771392081736909323116219667944 y[1] (numeric) = 1.2771392081736909323116219667928 absolute error = 1.6e-30 relative error = 1.2528000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.783 Order of pole = 651 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=5.64 x[1] = 0.218 y[1] (analytic) = 1.278772378516624040920716112532 y[1] (numeric) = 1.2787723785166240409207161125304 absolute error = 1.6e-30 relative error = 1.2512000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.782 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.219 y[1] (analytic) = 1.2804097311139564660691421254802 y[1] (numeric) = 1.2804097311139564660691421254786 absolute error = 1.6e-30 relative error = 1.2496000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.781 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 1.2820512820512820512820512820513 y[1] (numeric) = 1.2820512820512820512820512820497 absolute error = 1.6e-30 relative error = 1.2480000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.78 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.221 y[1] (analytic) = 1.2836970474967907573812580231065 y[1] (numeric) = 1.283697047496790757381258023105 absolute error = 1.5e-30 relative error = 1.1685000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.779 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.222 y[1] (analytic) = 1.2853470437017994858611825192802 y[1] (numeric) = 1.2853470437017994858611825192787 absolute error = 1.5e-30 relative error = 1.1670000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.778 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.223 y[1] (analytic) = 1.2870012870012870012870012870013 y[1] (numeric) = 1.2870012870012870012870012869998 absolute error = 1.5e-30 relative error = 1.1655000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.777 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.224 y[1] (analytic) = 1.2886597938144329896907216494845 y[1] (numeric) = 1.288659793814432989690721649483 absolute error = 1.5e-30 relative error = 1.1640000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.776 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.225 y[1] (analytic) = 1.2903225806451612903225806451613 y[1] (numeric) = 1.2903225806451612903225806451598 absolute error = 1.5e-30 relative error = 1.1625000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.775 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.226 y[1] (analytic) = 1.2919896640826873385012919896641 y[1] (numeric) = 1.2919896640826873385012919896626 absolute error = 1.5e-30 relative error = 1.1610000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.774 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.227 y[1] (analytic) = 1.2936610608020698576972833117723 y[1] (numeric) = 1.2936610608020698576972833117708 absolute error = 1.5e-30 relative error = 1.1595000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.773 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.228 y[1] (analytic) = 1.2953367875647668393782383419689 y[1] (numeric) = 1.2953367875647668393782383419674 absolute error = 1.5e-30 relative error = 1.1580000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.772 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.229 y[1] (analytic) = 1.2970168612191958495460440985733 y[1] (numeric) = 1.2970168612191958495460440985718 absolute error = 1.5e-30 relative error = 1.1565000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.771 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 1.2987012987012987012987012987013 y[1] (numeric) = 1.2987012987012987012987012986998 absolute error = 1.5e-30 relative error = 1.1550000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.77 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.231 y[1] (analytic) = 1.3003901170351105331599479843953 y[1] (numeric) = 1.3003901170351105331599479843938 absolute error = 1.5e-30 relative error = 1.1535000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.769 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.232 y[1] (analytic) = 1.3020833333333333333333333333333 y[1] (numeric) = 1.3020833333333333333333333333318 absolute error = 1.5e-30 relative error = 1.1520000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.768 Order of pole = 651 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.1MB, time=6.03 x[1] = 0.233 y[1] (analytic) = 1.3037809647979139504563233376793 y[1] (numeric) = 1.3037809647979139504563233376777 absolute error = 1.6e-30 relative error = 1.2272000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.767 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.234 y[1] (analytic) = 1.3054830287206266318537859007833 y[1] (numeric) = 1.3054830287206266318537859007817 absolute error = 1.6e-30 relative error = 1.2256000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.766 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.235 y[1] (analytic) = 1.307189542483660130718954248366 y[1] (numeric) = 1.3071895424836601307189542483644 absolute error = 1.6e-30 relative error = 1.2240000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.765 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.236 y[1] (analytic) = 1.3089005235602094240837696335079 y[1] (numeric) = 1.3089005235602094240837696335062 absolute error = 1.7e-30 relative error = 1.2988000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.764 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.237 y[1] (analytic) = 1.3106159895150720838794233289646 y[1] (numeric) = 1.310615989515072083879423328963 absolute error = 1.6e-30 relative error = 1.2208000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.763 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.238 y[1] (analytic) = 1.3123359580052493438320209973753 y[1] (numeric) = 1.3123359580052493438320209973737 absolute error = 1.6e-30 relative error = 1.2192000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.762 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.239 y[1] (analytic) = 1.3140604467805519053876478318003 y[1] (numeric) = 1.3140604467805519053876478317986 absolute error = 1.7e-30 relative error = 1.2937000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.761 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 1.3157894736842105263157894736842 y[1] (numeric) = 1.3157894736842105263157894736825 absolute error = 1.7e-30 relative error = 1.2920000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.76 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.241 y[1] (analytic) = 1.3175230566534914361001317523057 y[1] (numeric) = 1.317523056653491436100131752304 absolute error = 1.7e-30 relative error = 1.2903000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.759 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.242 y[1] (analytic) = 1.3192612137203166226912928759894 y[1] (numeric) = 1.3192612137203166226912928759878 absolute error = 1.6e-30 relative error = 1.2128000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.758 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.243 y[1] (analytic) = 1.321003963011889035667107001321 y[1] (numeric) = 1.3210039630118890356671070013194 absolute error = 1.6e-30 relative error = 1.2112000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.757 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.244 y[1] (analytic) = 1.3227513227513227513227513227513 y[1] (numeric) = 1.3227513227513227513227513227497 absolute error = 1.6e-30 relative error = 1.2096000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.756 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.245 y[1] (analytic) = 1.3245033112582781456953642384106 y[1] (numeric) = 1.324503311258278145695364238409 absolute error = 1.6e-30 relative error = 1.2080000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.755 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.246 y[1] (analytic) = 1.3262599469496021220159151193634 y[1] (numeric) = 1.3262599469496021220159151193618 absolute error = 1.6e-30 relative error = 1.2064000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.754 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.247 y[1] (analytic) = 1.3280212483399734395750332005312 y[1] (numeric) = 1.3280212483399734395750332005296 absolute error = 1.6e-30 relative error = 1.2048000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.753 Order of pole = 651 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.1MB, time=6.41 x[1] = 0.248 y[1] (analytic) = 1.3297872340425531914893617021277 y[1] (numeric) = 1.329787234042553191489361702126 absolute error = 1.7e-30 relative error = 1.2784000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.752 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.249 y[1] (analytic) = 1.3315579227696404793608521970706 y[1] (numeric) = 1.3315579227696404793608521970689 absolute error = 1.7e-30 relative error = 1.2767000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.751 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 1.3333333333333333333333333333333 y[1] (numeric) = 1.3333333333333333333333333333317 absolute error = 1.6e-30 relative error = 1.2000000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.75 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.251 y[1] (analytic) = 1.3351134846461949265687583444593 y[1] (numeric) = 1.3351134846461949265687583444576 absolute error = 1.7e-30 relative error = 1.2733000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.749 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.252 y[1] (analytic) = 1.3368983957219251336898395721925 y[1] (numeric) = 1.3368983957219251336898395721908 absolute error = 1.7e-30 relative error = 1.2716000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.748 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.253 y[1] (analytic) = 1.3386880856760374832663989290495 y[1] (numeric) = 1.3386880856760374832663989290478 absolute error = 1.7e-30 relative error = 1.2699000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.747 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.254 y[1] (analytic) = 1.3404825737265415549597855227882 y[1] (numeric) = 1.3404825737265415549597855227865 absolute error = 1.7e-30 relative error = 1.2682000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.746 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.255 y[1] (analytic) = 1.3422818791946308724832214765101 y[1] (numeric) = 1.3422818791946308724832214765084 absolute error = 1.7e-30 relative error = 1.2665000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.745 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.256 y[1] (analytic) = 1.3440860215053763440860215053763 y[1] (numeric) = 1.3440860215053763440860215053747 absolute error = 1.6e-30 relative error = 1.1904000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.744 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.257 y[1] (analytic) = 1.3458950201884253028263795423957 y[1] (numeric) = 1.345895020188425302826379542394 absolute error = 1.7e-30 relative error = 1.2631000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.743 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.258 y[1] (analytic) = 1.3477088948787061994609164420485 y[1] (numeric) = 1.3477088948787061994609164420468 absolute error = 1.7e-30 relative error = 1.2614000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.742 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.259 y[1] (analytic) = 1.3495276653171390013495276653171 y[1] (numeric) = 1.3495276653171390013495276653154 absolute error = 1.7e-30 relative error = 1.2597000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.741 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 1.3513513513513513513513513513514 y[1] (numeric) = 1.3513513513513513513513513513496 absolute error = 1.8e-30 relative error = 1.3320000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.74 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.261 y[1] (analytic) = 1.3531799729364005412719891745602 y[1] (numeric) = 1.3531799729364005412719891745585 absolute error = 1.7e-30 relative error = 1.2563000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.739 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.262 y[1] (analytic) = 1.3550135501355013550135501355014 y[1] (numeric) = 1.3550135501355013550135501354996 absolute error = 1.8e-30 relative error = 1.3284000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.738 Order of pole = 651 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=6.79 x[1] = 0.263 y[1] (analytic) = 1.3568521031207598371777476255088 y[1] (numeric) = 1.3568521031207598371777476255071 absolute error = 1.7e-30 relative error = 1.2529000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.737 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.264 y[1] (analytic) = 1.3586956521739130434782608695652 y[1] (numeric) = 1.3586956521739130434782608695635 absolute error = 1.7e-30 relative error = 1.2512000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.736 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.265 y[1] (analytic) = 1.3605442176870748299319727891156 y[1] (numeric) = 1.3605442176870748299319727891139 absolute error = 1.7e-30 relative error = 1.2495000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.735 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.266 y[1] (analytic) = 1.3623978201634877384196185286104 y[1] (numeric) = 1.3623978201634877384196185286086 absolute error = 1.8e-30 relative error = 1.3212000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.734 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.267 y[1] (analytic) = 1.3642564802182810368349249658936 y[1] (numeric) = 1.3642564802182810368349249658918 absolute error = 1.8e-30 relative error = 1.3194000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.733 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.268 y[1] (analytic) = 1.3661202185792349726775956284153 y[1] (numeric) = 1.3661202185792349726775956284135 absolute error = 1.8e-30 relative error = 1.3176000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.732 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.269 y[1] (analytic) = 1.3679890560875512995896032831737 y[1] (numeric) = 1.3679890560875512995896032831719 absolute error = 1.8e-30 relative error = 1.3158000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.731 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 1.369863013698630136986301369863 y[1] (numeric) = 1.3698630136986301369863013698612 absolute error = 1.8e-30 relative error = 1.3140000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.73 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.271 y[1] (analytic) = 1.3717421124828532235939643347051 y[1] (numeric) = 1.3717421124828532235939643347033 absolute error = 1.8e-30 relative error = 1.3122000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.729 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.272 y[1] (analytic) = 1.3736263736263736263736263736264 y[1] (numeric) = 1.3736263736263736263736263736246 absolute error = 1.8e-30 relative error = 1.3104000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.728 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.273 y[1] (analytic) = 1.3755158184319119669876203576341 y[1] (numeric) = 1.3755158184319119669876203576323 absolute error = 1.8e-30 relative error = 1.3086000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.727 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.274 y[1] (analytic) = 1.3774104683195592286501377410468 y[1] (numeric) = 1.377410468319559228650137741045 absolute error = 1.8e-30 relative error = 1.3068000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.726 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.275 y[1] (analytic) = 1.3793103448275862068965517241379 y[1] (numeric) = 1.3793103448275862068965517241361 absolute error = 1.8e-30 relative error = 1.3050000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.725 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.276 y[1] (analytic) = 1.3812154696132596685082872928177 y[1] (numeric) = 1.3812154696132596685082872928158 absolute error = 1.9e-30 relative error = 1.3756000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.724 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.277 y[1] (analytic) = 1.3831258644536652835408022130014 y[1] (numeric) = 1.3831258644536652835408022129995 absolute error = 1.9e-30 relative error = 1.3737000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.723 Order of pole = 651 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.1MB, time=7.18 x[1] = 0.278 y[1] (analytic) = 1.3850415512465373961218836565097 y[1] (numeric) = 1.3850415512465373961218836565078 absolute error = 1.9e-30 relative error = 1.3718000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.722 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.279 y[1] (analytic) = 1.3869625520110957004160887656033 y[1] (numeric) = 1.3869625520110957004160887656014 absolute error = 1.9e-30 relative error = 1.3699000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.721 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 1.3888888888888888888888888888889 y[1] (numeric) = 1.388888888888888888888888888887 absolute error = 1.9e-30 relative error = 1.3680000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.72 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.281 y[1] (analytic) = 1.3908205841446453407510431154381 y[1] (numeric) = 1.3908205841446453407510431154362 absolute error = 1.9e-30 relative error = 1.3661000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.719 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.282 y[1] (analytic) = 1.3927576601671309192200557103064 y[1] (numeric) = 1.3927576601671309192200557103045 absolute error = 1.9e-30 relative error = 1.3642000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.718 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.283 y[1] (analytic) = 1.3947001394700139470013947001395 y[1] (numeric) = 1.3947001394700139470013947001376 absolute error = 1.9e-30 relative error = 1.3623000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.717 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.284 y[1] (analytic) = 1.3966480446927374301675977653631 y[1] (numeric) = 1.3966480446927374301675977653613 absolute error = 1.8e-30 relative error = 1.2888000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.716 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.285 y[1] (analytic) = 1.3986013986013986013986013986014 y[1] (numeric) = 1.3986013986013986013986013985996 absolute error = 1.8e-30 relative error = 1.2870000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.715 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.286 y[1] (analytic) = 1.4005602240896358543417366946779 y[1] (numeric) = 1.4005602240896358543417366946761 absolute error = 1.8e-30 relative error = 1.2852000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.714 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.287 y[1] (analytic) = 1.4025245441795231416549789621318 y[1] (numeric) = 1.4025245441795231416549789621301 absolute error = 1.7e-30 relative error = 1.2121000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.713 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.288 y[1] (analytic) = 1.4044943820224719101123595505618 y[1] (numeric) = 1.4044943820224719101123595505601 absolute error = 1.7e-30 relative error = 1.2104000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.712 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.289 y[1] (analytic) = 1.4064697609001406469760900140647 y[1] (numeric) = 1.406469760900140646976090014063 absolute error = 1.7e-30 relative error = 1.2087000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.711 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 1.4084507042253521126760563380282 y[1] (numeric) = 1.4084507042253521126760563380265 absolute error = 1.7e-30 relative error = 1.2070000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.71 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.291 y[1] (analytic) = 1.4104372355430183356840620592384 y[1] (numeric) = 1.4104372355430183356840620592367 absolute error = 1.7e-30 relative error = 1.2053000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.709 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.292 y[1] (analytic) = 1.4124293785310734463276836158192 y[1] (numeric) = 1.4124293785310734463276836158175 absolute error = 1.7e-30 relative error = 1.2036000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.708 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.293 y[1] (analytic) = 1.4144271570014144271570014144272 y[1] (numeric) = 1.4144271570014144271570014144254 absolute error = 1.8e-30 memory used=76.2MB, alloc=4.1MB, time=7.57 relative error = 1.2726000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.707 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.294 y[1] (analytic) = 1.416430594900849858356940509915 y[1] (numeric) = 1.4164305949008498583569405099133 absolute error = 1.7e-30 relative error = 1.2002000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.706 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.295 y[1] (analytic) = 1.4184397163120567375886524822695 y[1] (numeric) = 1.4184397163120567375886524822678 absolute error = 1.7e-30 relative error = 1.1985000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.705 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.296 y[1] (analytic) = 1.4204545454545454545454545454545 y[1] (numeric) = 1.4204545454545454545454545454528 absolute error = 1.7e-30 relative error = 1.1968000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.704 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.297 y[1] (analytic) = 1.4224751066856330014224751066856 y[1] (numeric) = 1.4224751066856330014224751066839 absolute error = 1.7e-30 relative error = 1.1951000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.703 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.298 y[1] (analytic) = 1.4245014245014245014245014245014 y[1] (numeric) = 1.4245014245014245014245014244997 absolute error = 1.7e-30 relative error = 1.1934000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.702 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.299 y[1] (analytic) = 1.4265335235378031383737517831669 y[1] (numeric) = 1.4265335235378031383737517831652 absolute error = 1.7e-30 relative error = 1.1917000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.701 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 1.4285714285714285714285714285714 y[1] (numeric) = 1.4285714285714285714285714285697 absolute error = 1.7e-30 relative error = 1.1900000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.301 y[1] (analytic) = 1.4306151645207439198855507868383 y[1] (numeric) = 1.4306151645207439198855507868366 absolute error = 1.7e-30 relative error = 1.1883000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.699 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.302 y[1] (analytic) = 1.4326647564469914040114613180516 y[1] (numeric) = 1.4326647564469914040114613180498 absolute error = 1.8e-30 relative error = 1.2564000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.698 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.303 y[1] (analytic) = 1.4347202295552367288378766140603 y[1] (numeric) = 1.4347202295552367288378766140585 absolute error = 1.8e-30 relative error = 1.2546000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.697 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.304 y[1] (analytic) = 1.4367816091954022988505747126437 y[1] (numeric) = 1.4367816091954022988505747126419 absolute error = 1.8e-30 relative error = 1.2528000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.696 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.305 y[1] (analytic) = 1.4388489208633093525179856115108 y[1] (numeric) = 1.438848920863309352517985611509 absolute error = 1.8e-30 relative error = 1.2510000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.695 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.306 y[1] (analytic) = 1.440922190201729106628242074928 y[1] (numeric) = 1.4409221902017291066282420749262 absolute error = 1.8e-30 relative error = 1.2492000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.694 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.307 y[1] (analytic) = 1.4430014430014430014430014430014 y[1] (numeric) = 1.4430014430014430014430014429997 absolute error = 1.7e-30 relative error = 1.1781000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.693 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.308 y[1] (analytic) = 1.445086705202312138728323699422 y[1] (numeric) = 1.4450867052023121387283236994202 absolute error = 1.8e-30 relative error = 1.2456000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.692 Order of pole = 651 memory used=80.1MB, alloc=4.1MB, time=7.96 TOP MAIN SOLVE Loop x[1] = 0.309 y[1] (analytic) = 1.4471780028943560057887120115774 y[1] (numeric) = 1.4471780028943560057887120115757 absolute error = 1.7e-30 relative error = 1.1747000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.691 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 1.4492753623188405797101449275362 y[1] (numeric) = 1.4492753623188405797101449275345 absolute error = 1.7e-30 relative error = 1.1730000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.69 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.311 y[1] (analytic) = 1.4513788098693759071117561683599 y[1] (numeric) = 1.4513788098693759071117561683582 absolute error = 1.7e-30 relative error = 1.1713000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.689 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.312 y[1] (analytic) = 1.4534883720930232558139534883721 y[1] (numeric) = 1.4534883720930232558139534883703 absolute error = 1.8e-30 relative error = 1.2384000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.688 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.313 y[1] (analytic) = 1.4556040756914119359534206695779 y[1] (numeric) = 1.4556040756914119359534206695761 absolute error = 1.8e-30 relative error = 1.2366000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.687 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.314 y[1] (analytic) = 1.4577259475218658892128279883382 y[1] (numeric) = 1.4577259475218658892128279883364 absolute error = 1.8e-30 relative error = 1.2348000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.686 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.315 y[1] (analytic) = 1.459854014598540145985401459854 y[1] (numeric) = 1.4598540145985401459854014598522 absolute error = 1.8e-30 relative error = 1.2330000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.685 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.316 y[1] (analytic) = 1.4619883040935672514619883040936 y[1] (numeric) = 1.4619883040935672514619883040917 absolute error = 1.9e-30 relative error = 1.2996000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.684 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.317 y[1] (analytic) = 1.4641288433382137628111273792094 y[1] (numeric) = 1.4641288433382137628111273792075 absolute error = 1.9e-30 relative error = 1.2977000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.683 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.318 y[1] (analytic) = 1.4662756598240469208211143695015 y[1] (numeric) = 1.4662756598240469208211143694996 absolute error = 1.9e-30 relative error = 1.2958000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.682 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.319 y[1] (analytic) = 1.4684287812041116005873715124816 y[1] (numeric) = 1.4684287812041116005873715124798 absolute error = 1.8e-30 relative error = 1.2258000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.681 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 1.4705882352941176470588235294118 y[1] (numeric) = 1.4705882352941176470588235294099 absolute error = 1.9e-30 relative error = 1.2920000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.68 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.321 y[1] (analytic) = 1.4727540500736377025036818851252 y[1] (numeric) = 1.4727540500736377025036818851233 absolute error = 1.9e-30 relative error = 1.2901000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.679 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.322 y[1] (analytic) = 1.4749262536873156342182890855457 y[1] (numeric) = 1.4749262536873156342182890855438 absolute error = 1.9e-30 relative error = 1.2882000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.678 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.323 y[1] (analytic) = 1.477104874446085672082717872969 y[1] (numeric) = 1.4771048744460856720827178729671 absolute error = 1.9e-30 relative error = 1.2863000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.677 Order of pole = 651 memory used=83.9MB, alloc=4.1MB, time=8.35 TOP MAIN SOLVE Loop x[1] = 0.324 y[1] (analytic) = 1.4792899408284023668639053254438 y[1] (numeric) = 1.4792899408284023668639053254419 absolute error = 1.9e-30 relative error = 1.2844000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.676 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.325 y[1] (analytic) = 1.4814814814814814814814814814815 y[1] (numeric) = 1.4814814814814814814814814814796 absolute error = 1.9e-30 relative error = 1.2825000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.675 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.326 y[1] (analytic) = 1.4836795252225519287833827893175 y[1] (numeric) = 1.4836795252225519287833827893156 absolute error = 1.9e-30 relative error = 1.2806000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.674 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.327 y[1] (analytic) = 1.4858841010401188707280832095097 y[1] (numeric) = 1.4858841010401188707280832095077 absolute error = 2.0e-30 relative error = 1.3460000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.673 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.328 y[1] (analytic) = 1.4880952380952380952380952380952 y[1] (numeric) = 1.4880952380952380952380952380933 absolute error = 1.9e-30 relative error = 1.2768000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.672 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.329 y[1] (analytic) = 1.4903129657228017883755588673621 y[1] (numeric) = 1.4903129657228017883755588673602 absolute error = 1.9e-30 relative error = 1.2749000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.671 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 1.4925373134328358208955223880597 y[1] (numeric) = 1.4925373134328358208955223880577 absolute error = 2.0e-30 relative error = 1.3400000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.67 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.331 y[1] (analytic) = 1.4947683109118086696562032884903 y[1] (numeric) = 1.4947683109118086696562032884883 absolute error = 2.0e-30 relative error = 1.3380000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.669 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.332 y[1] (analytic) = 1.4970059880239520958083832335329 y[1] (numeric) = 1.4970059880239520958083832335309 absolute error = 2.0e-30 relative error = 1.3360000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.668 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.333 y[1] (analytic) = 1.4992503748125937031484257871064 y[1] (numeric) = 1.4992503748125937031484257871044 absolute error = 2.0e-30 relative error = 1.3340000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.667 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.334 y[1] (analytic) = 1.5015015015015015015015015015015 y[1] (numeric) = 1.5015015015015015015015015014994 absolute error = 2.1e-30 relative error = 1.3986000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.666 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.335 y[1] (analytic) = 1.5037593984962406015037593984962 y[1] (numeric) = 1.5037593984962406015037593984941 absolute error = 2.1e-30 relative error = 1.3965000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.665 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.336 y[1] (analytic) = 1.5060240963855421686746987951807 y[1] (numeric) = 1.5060240963855421686746987951786 absolute error = 2.1e-30 relative error = 1.3944000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.664 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.337 y[1] (analytic) = 1.5082956259426847662141779788839 y[1] (numeric) = 1.5082956259426847662141779788817 absolute error = 2.2e-30 relative error = 1.4586000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.663 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.338 y[1] (analytic) = 1.5105740181268882175226586102719 y[1] (numeric) = 1.5105740181268882175226586102697 absolute error = 2.2e-30 relative error = 1.4564000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.662 Order of pole = 651 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.1MB, time=8.73 x[1] = 0.339 y[1] (analytic) = 1.5128593040847201210287443267776 y[1] (numeric) = 1.5128593040847201210287443267754 absolute error = 2.2e-30 relative error = 1.4542000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.661 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 1.5151515151515151515151515151515 y[1] (numeric) = 1.5151515151515151515151515151493 absolute error = 2.2e-30 relative error = 1.4520000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.66 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.341 y[1] (analytic) = 1.517450682852807283763277693475 y[1] (numeric) = 1.5174506828528072837632776934727 absolute error = 2.3e-30 relative error = 1.5157000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.659 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.342 y[1] (analytic) = 1.5197568389057750759878419452888 y[1] (numeric) = 1.5197568389057750759878419452865 absolute error = 2.3e-30 relative error = 1.5134000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.658 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.343 y[1] (analytic) = 1.52207001522070015220700152207 y[1] (numeric) = 1.5220700152207001522070015220678 absolute error = 2.2e-30 relative error = 1.4454000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.657 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.344 y[1] (analytic) = 1.524390243902439024390243902439 y[1] (numeric) = 1.5243902439024390243902439024368 absolute error = 2.2e-30 relative error = 1.4432000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.656 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.345 y[1] (analytic) = 1.5267175572519083969465648854962 y[1] (numeric) = 1.526717557251908396946564885494 absolute error = 2.2e-30 relative error = 1.4410000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.655 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.346 y[1] (analytic) = 1.5290519877675840978593272171254 y[1] (numeric) = 1.5290519877675840978593272171232 absolute error = 2.2e-30 relative error = 1.4388000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.654 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.347 y[1] (analytic) = 1.531393568147013782542113323124 y[1] (numeric) = 1.5313935681470137825421133231219 absolute error = 2.1e-30 relative error = 1.3713000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.653 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.348 y[1] (analytic) = 1.5337423312883435582822085889571 y[1] (numeric) = 1.5337423312883435582822085889549 absolute error = 2.2e-30 relative error = 1.4344000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.652 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.349 y[1] (analytic) = 1.5360983102918586789554531490015 y[1] (numeric) = 1.5360983102918586789554531489994 absolute error = 2.1e-30 relative error = 1.3671000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.651 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 1.5384615384615384615384615384615 y[1] (numeric) = 1.5384615384615384615384615384594 absolute error = 2.1e-30 relative error = 1.3650000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.65 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.351 y[1] (analytic) = 1.5408320493066255778120184899846 y[1] (numeric) = 1.5408320493066255778120184899824 absolute error = 2.2e-30 relative error = 1.4278000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.649 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.352 y[1] (analytic) = 1.5432098765432098765432098765432 y[1] (numeric) = 1.543209876543209876543209876541 absolute error = 2.2e-30 relative error = 1.4256000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.648 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.353 y[1] (analytic) = 1.5455950540958268933539412673879 y[1] (numeric) = 1.5455950540958268933539412673857 absolute error = 2.2e-30 relative error = 1.4234000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.647 Order of pole = 651 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.1MB, time=9.12 x[1] = 0.354 y[1] (analytic) = 1.5479876160990712074303405572755 y[1] (numeric) = 1.5479876160990712074303405572733 absolute error = 2.2e-30 relative error = 1.4212000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.646 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.355 y[1] (analytic) = 1.5503875968992248062015503875969 y[1] (numeric) = 1.5503875968992248062015503875947 absolute error = 2.2e-30 relative error = 1.4190000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.645 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.356 y[1] (analytic) = 1.5527950310559006211180124223602 y[1] (numeric) = 1.552795031055900621118012422358 absolute error = 2.2e-30 relative error = 1.4168000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.644 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.357 y[1] (analytic) = 1.5552099533437013996889580093313 y[1] (numeric) = 1.555209953343701399688958009329 absolute error = 2.3e-30 relative error = 1.4789000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.643 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.358 y[1] (analytic) = 1.5576323987538940809968847352025 y[1] (numeric) = 1.5576323987538940809968847352002 absolute error = 2.3e-30 relative error = 1.4766000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.642 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.359 y[1] (analytic) = 1.56006240249609984399375975039 y[1] (numeric) = 1.5600624024960998439937597503877 absolute error = 2.3e-30 relative error = 1.4743000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.641 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 1.5625 y[1] (numeric) = 1.5624999999999999999999999999977 absolute error = 2.3e-30 relative error = 1.4720000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.64 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.361 y[1] (analytic) = 1.5649452269170579029733959311424 y[1] (numeric) = 1.5649452269170579029733959311401 absolute error = 2.3e-30 relative error = 1.4697000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.639 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.362 y[1] (analytic) = 1.5673981191222570532915360501567 y[1] (numeric) = 1.5673981191222570532915360501544 absolute error = 2.3e-30 relative error = 1.4674000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.638 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.363 y[1] (analytic) = 1.5698587127158555729984301412873 y[1] (numeric) = 1.5698587127158555729984301412849 absolute error = 2.4e-30 relative error = 1.5288000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.637 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.364 y[1] (analytic) = 1.5723270440251572327044025157233 y[1] (numeric) = 1.5723270440251572327044025157209 absolute error = 2.4e-30 relative error = 1.5264000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.636 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.365 y[1] (analytic) = 1.5748031496062992125984251968504 y[1] (numeric) = 1.574803149606299212598425196848 absolute error = 2.4e-30 relative error = 1.5240000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.635 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.366 y[1] (analytic) = 1.5772870662460567823343848580442 y[1] (numeric) = 1.5772870662460567823343848580418 absolute error = 2.4e-30 relative error = 1.5216000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.634 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.367 y[1] (analytic) = 1.5797788309636650868878357030016 y[1] (numeric) = 1.5797788309636650868878357029992 absolute error = 2.4e-30 relative error = 1.5192000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.633 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.368 y[1] (analytic) = 1.5822784810126582278481012658228 y[1] (numeric) = 1.5822784810126582278481012658204 absolute error = 2.4e-30 relative error = 1.5168000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.632 Order of pole = 651 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.1MB, time=9.51 x[1] = 0.369 y[1] (analytic) = 1.5847860538827258320126782884311 y[1] (numeric) = 1.5847860538827258320126782884287 absolute error = 2.4e-30 relative error = 1.5144000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.631 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 1.5873015873015873015873015873016 y[1] (numeric) = 1.5873015873015873015873015872992 absolute error = 2.4e-30 relative error = 1.5120000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.63 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.371 y[1] (analytic) = 1.5898251192368839427662957074722 y[1] (numeric) = 1.5898251192368839427662957074698 absolute error = 2.4e-30 relative error = 1.5096000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.629 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.372 y[1] (analytic) = 1.5923566878980891719745222929936 y[1] (numeric) = 1.5923566878980891719745222929912 absolute error = 2.4e-30 relative error = 1.5072000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.628 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.373 y[1] (analytic) = 1.5948963317384370015948963317384 y[1] (numeric) = 1.594896331738437001594896331736 absolute error = 2.4e-30 relative error = 1.5048000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.627 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.374 y[1] (analytic) = 1.5974440894568690095846645367412 y[1] (numeric) = 1.5974440894568690095846645367388 absolute error = 2.4e-30 relative error = 1.5024000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.626 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.375 y[1] (analytic) = 1.6 y[1] (numeric) = 1.5999999999999999999999999999976 absolute error = 2.4e-30 relative error = 1.5000000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.625 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.376 y[1] (analytic) = 1.6025641025641025641025641025641 y[1] (numeric) = 1.6025641025641025641025641025617 absolute error = 2.4e-30 relative error = 1.4976000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.624 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.377 y[1] (analytic) = 1.6051364365971107544141252006421 y[1] (numeric) = 1.6051364365971107544141252006396 absolute error = 2.5e-30 relative error = 1.5575000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.623 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.378 y[1] (analytic) = 1.6077170418006430868167202572347 y[1] (numeric) = 1.6077170418006430868167202572323 absolute error = 2.4e-30 relative error = 1.4928000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.622 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.379 y[1] (analytic) = 1.6103059581320450885668276972625 y[1] (numeric) = 1.61030595813204508856682769726 absolute error = 2.5e-30 relative error = 1.5525000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.621 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 1.6129032258064516129032258064516 y[1] (numeric) = 1.6129032258064516129032258064491 absolute error = 2.5e-30 relative error = 1.5500000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.62 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.381 y[1] (analytic) = 1.6155088852988691437802907915994 y[1] (numeric) = 1.6155088852988691437802907915968 absolute error = 2.6e-30 relative error = 1.6094000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.619 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.382 y[1] (analytic) = 1.6181229773462783171521035598706 y[1] (numeric) = 1.618122977346278317152103559868 absolute error = 2.6e-30 relative error = 1.6068000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.618 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.383 y[1] (analytic) = 1.6207455429497568881685575364668 y[1] (numeric) = 1.6207455429497568881685575364642 absolute error = 2.6e-30 relative error = 1.6042000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.617 Order of pole = 651 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.1MB, time=9.90 x[1] = 0.384 y[1] (analytic) = 1.6233766233766233766233766233766 y[1] (numeric) = 1.623376623376623376623376623374 absolute error = 2.6e-30 relative error = 1.6016000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.616 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.385 y[1] (analytic) = 1.6260162601626016260162601626016 y[1] (numeric) = 1.626016260162601626016260162599 absolute error = 2.6e-30 relative error = 1.5990000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.615 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.386 y[1] (analytic) = 1.6286644951140065146579804560261 y[1] (numeric) = 1.6286644951140065146579804560234 absolute error = 2.7e-30 relative error = 1.6578000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.614 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.387 y[1] (analytic) = 1.6313213703099510603588907014682 y[1] (numeric) = 1.6313213703099510603588907014655 absolute error = 2.7e-30 relative error = 1.6551000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.613 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.388 y[1] (analytic) = 1.6339869281045751633986928104575 y[1] (numeric) = 1.6339869281045751633986928104548 absolute error = 2.7e-30 relative error = 1.6524000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.612 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.389 y[1] (analytic) = 1.6366612111292962356792144026187 y[1] (numeric) = 1.6366612111292962356792144026159 absolute error = 2.8e-30 relative error = 1.7108000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.611 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 1.6393442622950819672131147540984 y[1] (numeric) = 1.6393442622950819672131147540956 absolute error = 2.8e-30 relative error = 1.7080000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.61 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.391 y[1] (analytic) = 1.6420361247947454844006568144499 y[1] (numeric) = 1.6420361247947454844006568144471 absolute error = 2.8e-30 relative error = 1.7052000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.609 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.392 y[1] (analytic) = 1.6447368421052631578947368421053 y[1] (numeric) = 1.6447368421052631578947368421024 absolute error = 2.9e-30 relative error = 1.7632000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.608 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.393 y[1] (analytic) = 1.6474464579901153212520593080725 y[1] (numeric) = 1.6474464579901153212520593080696 absolute error = 2.9e-30 relative error = 1.7603000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.607 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.394 y[1] (analytic) = 1.650165016501650165016501650165 y[1] (numeric) = 1.6501650165016501650165016501621 absolute error = 2.9e-30 relative error = 1.7574000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.606 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.395 y[1] (analytic) = 1.6528925619834710743801652892562 y[1] (numeric) = 1.6528925619834710743801652892533 absolute error = 2.9e-30 relative error = 1.7545000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.605 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.396 y[1] (analytic) = 1.6556291390728476821192052980132 y[1] (numeric) = 1.6556291390728476821192052980103 absolute error = 2.9e-30 relative error = 1.7516000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.604 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.397 y[1] (analytic) = 1.658374792703150912106135986733 y[1] (numeric) = 1.65837479270315091210613598673 absolute error = 3.0e-30 relative error = 1.8090000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.603 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.398 y[1] (analytic) = 1.661129568106312292358803986711 y[1] (numeric) = 1.661129568106312292358803986708 absolute error = 3.0e-30 relative error = 1.8060000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.602 Order of pole = 651 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.1MB, time=10.28 x[1] = 0.399 y[1] (analytic) = 1.6638935108153078202995008319468 y[1] (numeric) = 1.6638935108153078202995008319438 absolute error = 3.0e-30 relative error = 1.8030000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.601 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 1.6666666666666666666666666666667 y[1] (numeric) = 1.6666666666666666666666666666637 absolute error = 3.0e-30 relative error = 1.8000000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.6 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.401 y[1] (analytic) = 1.669449081803005008347245409015 y[1] (numeric) = 1.669449081803005008347245409012 absolute error = 3.0e-30 relative error = 1.7970000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.599 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.402 y[1] (analytic) = 1.6722408026755852842809364548495 y[1] (numeric) = 1.6722408026755852842809364548465 absolute error = 3.0e-30 relative error = 1.7940000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.598 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.403 y[1] (analytic) = 1.6750418760469011725293132328308 y[1] (numeric) = 1.6750418760469011725293132328278 absolute error = 3.0e-30 relative error = 1.7910000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.597 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.404 y[1] (analytic) = 1.6778523489932885906040268456376 y[1] (numeric) = 1.6778523489932885906040268456346 absolute error = 3.0e-30 relative error = 1.7880000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.596 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.405 y[1] (analytic) = 1.6806722689075630252100840336134 y[1] (numeric) = 1.6806722689075630252100840336105 absolute error = 2.9e-30 relative error = 1.7255000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.595 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.406 y[1] (analytic) = 1.6835016835016835016835016835017 y[1] (numeric) = 1.6835016835016835016835016834987 absolute error = 3.0e-30 relative error = 1.7820000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.594 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.407 y[1] (analytic) = 1.6863406408094435075885328836425 y[1] (numeric) = 1.6863406408094435075885328836395 absolute error = 3.0e-30 relative error = 1.7790000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.593 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.408 y[1] (analytic) = 1.6891891891891891891891891891892 y[1] (numeric) = 1.6891891891891891891891891891862 absolute error = 3.0e-30 relative error = 1.7760000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.592 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.409 y[1] (analytic) = 1.692047377326565143824027072758 y[1] (numeric) = 1.692047377326565143824027072755 absolute error = 3.0e-30 relative error = 1.7730000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.591 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 1.694915254237288135593220338983 y[1] (numeric) = 1.69491525423728813559322033898 absolute error = 3.0e-30 relative error = 1.7700000000000000000000000000001e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.59 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.411 y[1] (analytic) = 1.697792869269949066213921901528 y[1] (numeric) = 1.697792869269949066213921901525 absolute error = 3.0e-30 relative error = 1.7670000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.589 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.412 y[1] (analytic) = 1.7006802721088435374149659863946 y[1] (numeric) = 1.7006802721088435374149659863915 absolute error = 3.1e-30 relative error = 1.8228000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.588 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.413 y[1] (analytic) = 1.7035775127768313458262350936968 y[1] (numeric) = 1.7035775127768313458262350936937 absolute error = 3.1e-30 relative error = 1.8197000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.587 Order of pole = 651 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.1MB, time=10.66 x[1] = 0.414 y[1] (analytic) = 1.7064846416382252559726962457338 y[1] (numeric) = 1.7064846416382252559726962457307 absolute error = 3.1e-30 relative error = 1.8166000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.586 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.415 y[1] (analytic) = 1.7094017094017094017094017094017 y[1] (numeric) = 1.7094017094017094017094017093986 absolute error = 3.1e-30 relative error = 1.8135000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.585 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.416 y[1] (analytic) = 1.7123287671232876712328767123288 y[1] (numeric) = 1.7123287671232876712328767123256 absolute error = 3.2e-30 relative error = 1.8688000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.584 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.417 y[1] (analytic) = 1.7152658662092624356775300171527 y[1] (numeric) = 1.7152658662092624356775300171495 absolute error = 3.2e-30 relative error = 1.8656000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.583 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.418 y[1] (analytic) = 1.718213058419243986254295532646 y[1] (numeric) = 1.7182130584192439862542955326429 absolute error = 3.1e-30 relative error = 1.8042000000000000000000000000001e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.582 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.419 y[1] (analytic) = 1.7211703958691910499139414802065 y[1] (numeric) = 1.7211703958691910499139414802034 absolute error = 3.1e-30 relative error = 1.8011000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.581 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 1.7241379310344827586206896551724 y[1] (numeric) = 1.7241379310344827586206896551693 absolute error = 3.1e-30 relative error = 1.7980000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.58 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.421 y[1] (analytic) = 1.7271157167530224525043177892919 y[1] (numeric) = 1.7271157167530224525043177892888 absolute error = 3.1e-30 relative error = 1.7949000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.579 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.422 y[1] (analytic) = 1.7301038062283737024221453287197 y[1] (numeric) = 1.7301038062283737024221453287166 absolute error = 3.1e-30 relative error = 1.7918000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.578 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.423 y[1] (analytic) = 1.7331022530329289428076256499133 y[1] (numeric) = 1.7331022530329289428076256499102 absolute error = 3.1e-30 relative error = 1.7887000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.577 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.424 y[1] (analytic) = 1.7361111111111111111111111111111 y[1] (numeric) = 1.736111111111111111111111111108 absolute error = 3.1e-30 relative error = 1.7856000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.576 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.425 y[1] (analytic) = 1.7391304347826086956521739130435 y[1] (numeric) = 1.7391304347826086956521739130404 absolute error = 3.1e-30 relative error = 1.7825000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.575 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.426 y[1] (analytic) = 1.7421602787456445993031358885017 y[1] (numeric) = 1.7421602787456445993031358884987 absolute error = 3.0e-30 relative error = 1.7220000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.574 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.427 y[1] (analytic) = 1.7452006980802792321116928446771 y[1] (numeric) = 1.7452006980802792321116928446741 absolute error = 3.0e-30 relative error = 1.7190000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.573 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.428 y[1] (analytic) = 1.7482517482517482517482517482517 y[1] (numeric) = 1.7482517482517482517482517482487 absolute error = 3.0e-30 relative error = 1.7160000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.572 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.429 y[1] (analytic) = 1.7513134851138353765323992994746 y[1] (numeric) = 1.7513134851138353765323992994715 memory used=110.6MB, alloc=4.1MB, time=11.05 absolute error = 3.1e-30 relative error = 1.7701000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.571 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 1.7543859649122807017543859649123 y[1] (numeric) = 1.7543859649122807017543859649092 absolute error = 3.1e-30 relative error = 1.7670000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.57 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.431 y[1] (analytic) = 1.7574692442882249560632688927944 y[1] (numeric) = 1.7574692442882249560632688927913 absolute error = 3.1e-30 relative error = 1.7639000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.569 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.432 y[1] (analytic) = 1.7605633802816901408450704225352 y[1] (numeric) = 1.7605633802816901408450704225321 absolute error = 3.1e-30 relative error = 1.7608000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.568 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.433 y[1] (analytic) = 1.7636684303350970017636684303351 y[1] (numeric) = 1.763668430335097001763668430332 absolute error = 3.1e-30 relative error = 1.7577000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.567 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.434 y[1] (analytic) = 1.7667844522968197879858657243816 y[1] (numeric) = 1.7667844522968197879858657243785 absolute error = 3.1e-30 relative error = 1.7546000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.566 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.435 y[1] (analytic) = 1.7699115044247787610619469026549 y[1] (numeric) = 1.7699115044247787610619469026517 absolute error = 3.2e-30 relative error = 1.8080000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.565 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.436 y[1] (analytic) = 1.7730496453900709219858156028369 y[1] (numeric) = 1.7730496453900709219858156028337 absolute error = 3.2e-30 relative error = 1.8048000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.564 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.437 y[1] (analytic) = 1.7761989342806394316163410301954 y[1] (numeric) = 1.7761989342806394316163410301922 absolute error = 3.2e-30 relative error = 1.8016000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.563 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.438 y[1] (analytic) = 1.7793594306049822064056939501779 y[1] (numeric) = 1.7793594306049822064056939501747 absolute error = 3.2e-30 relative error = 1.7984000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.562 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.439 y[1] (analytic) = 1.78253119429590017825311942959 y[1] (numeric) = 1.7825311942959001782531194295868 absolute error = 3.2e-30 relative error = 1.7952000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.561 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 1.7857142857142857142857142857143 y[1] (numeric) = 1.7857142857142857142857142857111 absolute error = 3.2e-30 relative error = 1.7920000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.56 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.441 y[1] (analytic) = 1.7889087656529516994633273703041 y[1] (numeric) = 1.7889087656529516994633273703009 absolute error = 3.2e-30 relative error = 1.7888000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.559 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.442 y[1] (analytic) = 1.7921146953405017921146953405018 y[1] (numeric) = 1.7921146953405017921146953404986 absolute error = 3.2e-30 relative error = 1.7856000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.558 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.443 y[1] (analytic) = 1.7953321364452423698384201077199 y[1] (numeric) = 1.7953321364452423698384201077167 absolute error = 3.2e-30 relative error = 1.7824000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.557 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.444 y[1] (analytic) = 1.7985611510791366906474820143885 y[1] (numeric) = 1.7985611510791366906474820143852 absolute error = 3.3e-30 relative error = 1.8348000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.556 Order of pole = 651 memory used=114.4MB, alloc=4.1MB, time=11.44 TOP MAIN SOLVE Loop x[1] = 0.445 y[1] (analytic) = 1.8018018018018018018018018018018 y[1] (numeric) = 1.8018018018018018018018018017985 absolute error = 3.3e-30 relative error = 1.8315000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.555 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.446 y[1] (analytic) = 1.8050541516245487364620938628159 y[1] (numeric) = 1.8050541516245487364620938628126 absolute error = 3.3e-30 relative error = 1.8282000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.554 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.447 y[1] (analytic) = 1.8083182640144665461121157323689 y[1] (numeric) = 1.8083182640144665461121157323656 absolute error = 3.3e-30 relative error = 1.8249000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.553 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.448 y[1] (analytic) = 1.8115942028985507246376811594203 y[1] (numeric) = 1.811594202898550724637681159417 absolute error = 3.3e-30 relative error = 1.8216000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.552 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.449 y[1] (analytic) = 1.814882032667876588021778584392 y[1] (numeric) = 1.8148820326678765880217785843887 absolute error = 3.3e-30 relative error = 1.8183000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.551 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 1.8181818181818181818181818181818 y[1] (numeric) = 1.8181818181818181818181818181785 absolute error = 3.3e-30 relative error = 1.8150000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.55 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.451 y[1] (analytic) = 1.8214936247723132969034608378871 y[1] (numeric) = 1.8214936247723132969034608378837 absolute error = 3.4e-30 relative error = 1.8666000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.549 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.452 y[1] (analytic) = 1.8248175182481751824817518248175 y[1] (numeric) = 1.8248175182481751824817518248141 absolute error = 3.4e-30 relative error = 1.8632000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.548 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.453 y[1] (analytic) = 1.8281535648994515539305301645338 y[1] (numeric) = 1.8281535648994515539305301645304 absolute error = 3.4e-30 relative error = 1.8598000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.547 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.454 y[1] (analytic) = 1.8315018315018315018315018315018 y[1] (numeric) = 1.8315018315018315018315018314984 absolute error = 3.4e-30 relative error = 1.8564000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.546 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.455 y[1] (analytic) = 1.8348623853211009174311926605505 y[1] (numeric) = 1.834862385321100917431192660547 absolute error = 3.5e-30 relative error = 1.9075000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.545 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.456 y[1] (analytic) = 1.8382352941176470588235294117647 y[1] (numeric) = 1.8382352941176470588235294117612 absolute error = 3.5e-30 relative error = 1.9040000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.544 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.457 y[1] (analytic) = 1.8416206261510128913443830570902 y[1] (numeric) = 1.8416206261510128913443830570867 absolute error = 3.5e-30 relative error = 1.9005000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.543 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.458 y[1] (analytic) = 1.8450184501845018450184501845018 y[1] (numeric) = 1.8450184501845018450184501844983 absolute error = 3.5e-30 relative error = 1.8970000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.542 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.459 y[1] (analytic) = 1.8484288354898336414048059149723 y[1] (numeric) = 1.8484288354898336414048059149687 absolute error = 3.6e-30 relative error = 1.9476000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.541 Order of pole = 651 memory used=118.2MB, alloc=4.1MB, time=11.83 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 1.8518518518518518518518518518519 y[1] (numeric) = 1.8518518518518518518518518518483 absolute error = 3.6e-30 relative error = 1.9439999999999999999999999999999e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.54 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.461 y[1] (analytic) = 1.8552875695732838589981447124304 y[1] (numeric) = 1.8552875695732838589981447124269 absolute error = 3.5e-30 relative error = 1.8865000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.539 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.462 y[1] (analytic) = 1.8587360594795539033457249070632 y[1] (numeric) = 1.8587360594795539033457249070597 absolute error = 3.5e-30 relative error = 1.8830000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.538 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.463 y[1] (analytic) = 1.8621973929236499068901303538175 y[1] (numeric) = 1.862197392923649906890130353814 absolute error = 3.5e-30 relative error = 1.8795000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.537 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.464 y[1] (analytic) = 1.8656716417910447761194029850746 y[1] (numeric) = 1.8656716417910447761194029850711 absolute error = 3.5e-30 relative error = 1.8760000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.536 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.465 y[1] (analytic) = 1.869158878504672897196261682243 y[1] (numeric) = 1.8691588785046728971962616822395 absolute error = 3.5e-30 relative error = 1.8725000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.535 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.466 y[1] (analytic) = 1.8726591760299625468164794007491 y[1] (numeric) = 1.8726591760299625468164794007456 absolute error = 3.5e-30 relative error = 1.8690000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.534 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.467 y[1] (analytic) = 1.8761726078799249530956848030019 y[1] (numeric) = 1.8761726078799249530956848029984 absolute error = 3.5e-30 relative error = 1.8655000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.533 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.468 y[1] (analytic) = 1.8796992481203007518796992481203 y[1] (numeric) = 1.8796992481203007518796992481168 absolute error = 3.5e-30 relative error = 1.8620000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.532 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.469 y[1] (analytic) = 1.8832391713747645951035781544256 y[1] (numeric) = 1.8832391713747645951035781544221 absolute error = 3.5e-30 relative error = 1.8585000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.531 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 1.8867924528301886792452830188679 y[1] (numeric) = 1.8867924528301886792452830188644 absolute error = 3.5e-30 relative error = 1.8550000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.53 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.471 y[1] (analytic) = 1.8903591682419659735349716446125 y[1] (numeric) = 1.8903591682419659735349716446089 absolute error = 3.6e-30 relative error = 1.9044000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.529 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.472 y[1] (analytic) = 1.8939393939393939393939393939394 y[1] (numeric) = 1.8939393939393939393939393939358 absolute error = 3.6e-30 relative error = 1.9008000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.528 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.473 y[1] (analytic) = 1.8975332068311195445920303605313 y[1] (numeric) = 1.8975332068311195445920303605277 absolute error = 3.6e-30 relative error = 1.8972000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.527 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.474 y[1] (analytic) = 1.9011406844106463878326996197719 y[1] (numeric) = 1.9011406844106463878326996197682 absolute error = 3.7e-30 relative error = 1.9462000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.526 Order of pole = 651 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.1MB, time=12.21 x[1] = 0.475 y[1] (analytic) = 1.9047619047619047619047619047619 y[1] (numeric) = 1.9047619047619047619047619047582 absolute error = 3.7e-30 relative error = 1.9425000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.525 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.476 y[1] (analytic) = 1.9083969465648854961832061068702 y[1] (numeric) = 1.9083969465648854961832061068665 absolute error = 3.7e-30 relative error = 1.9388000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.524 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.477 y[1] (analytic) = 1.9120458891013384321223709369025 y[1] (numeric) = 1.9120458891013384321223709368987 absolute error = 3.8e-30 relative error = 1.9874000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.523 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.478 y[1] (analytic) = 1.9157088122605363984674329501916 y[1] (numeric) = 1.9157088122605363984674329501878 absolute error = 3.8e-30 relative error = 1.9836000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.522 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.479 y[1] (analytic) = 1.9193857965451055662188099808061 y[1] (numeric) = 1.9193857965451055662188099808024 absolute error = 3.7e-30 relative error = 1.9277000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.521 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 1.9230769230769230769230769230769 y[1] (numeric) = 1.9230769230769230769230769230732 absolute error = 3.7e-30 relative error = 1.9240000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.52 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.481 y[1] (analytic) = 1.9267822736030828516377649325626 y[1] (numeric) = 1.9267822736030828516377649325589 absolute error = 3.7e-30 relative error = 1.9203000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.519 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.482 y[1] (analytic) = 1.9305019305019305019305019305019 y[1] (numeric) = 1.9305019305019305019305019304982 absolute error = 3.7e-30 relative error = 1.9166000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.518 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.483 y[1] (analytic) = 1.9342359767891682785299806576402 y[1] (numeric) = 1.9342359767891682785299806576365 absolute error = 3.7e-30 relative error = 1.9129000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.517 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.484 y[1] (analytic) = 1.9379844961240310077519379844961 y[1] (numeric) = 1.9379844961240310077519379844924 absolute error = 3.7e-30 relative error = 1.9092000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.516 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.485 y[1] (analytic) = 1.9417475728155339805825242718447 y[1] (numeric) = 1.9417475728155339805825242718409 absolute error = 3.8e-30 relative error = 1.9570000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.515 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.486 y[1] (analytic) = 1.9455252918287937743190661478599 y[1] (numeric) = 1.9455252918287937743190661478561 absolute error = 3.8e-30 relative error = 1.9532000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.514 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.487 y[1] (analytic) = 1.9493177387914230019493177387914 y[1] (numeric) = 1.9493177387914230019493177387876 absolute error = 3.8e-30 relative error = 1.9494000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.513 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.488 y[1] (analytic) = 1.953125 y[1] (numeric) = 1.9531249999999999999999999999962 absolute error = 3.8e-30 relative error = 1.9456000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.512 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.489 y[1] (analytic) = 1.9569471624266144814090019569472 y[1] (numeric) = 1.9569471624266144814090019569433 absolute error = 3.9e-30 relative error = 1.9929000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.511 Order of pole = 651 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.1MB, time=12.59 x[1] = 0.49 y[1] (analytic) = 1.960784313725490196078431372549 y[1] (numeric) = 1.9607843137254901960784313725451 absolute error = 3.9e-30 relative error = 1.9890000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.51 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.491 y[1] (analytic) = 1.9646365422396856581532416502947 y[1] (numeric) = 1.9646365422396856581532416502908 absolute error = 3.9e-30 relative error = 1.9851000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.509 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.492 y[1] (analytic) = 1.968503937007874015748031496063 y[1] (numeric) = 1.9685039370078740157480314960591 absolute error = 3.9e-30 relative error = 1.9812000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.508 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.493 y[1] (analytic) = 1.972386587771203155818540433925 y[1] (numeric) = 1.9723865877712031558185404339211 absolute error = 3.9e-30 relative error = 1.9773000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.507 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.494 y[1] (analytic) = 1.9762845849802371541501976284585 y[1] (numeric) = 1.9762845849802371541501976284545 absolute error = 4.0e-30 relative error = 2.0240000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.506 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.495 y[1] (analytic) = 1.980198019801980198019801980198 y[1] (numeric) = 1.980198019801980198019801980194 absolute error = 4.0e-30 relative error = 2.0200000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.505 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.496 y[1] (analytic) = 1.984126984126984126984126984127 y[1] (numeric) = 1.9841269841269841269841269841229 absolute error = 4.1e-30 relative error = 2.0664000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.504 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.497 y[1] (analytic) = 1.9880715705765407554671968190855 y[1] (numeric) = 1.9880715705765407554671968190814 absolute error = 4.1e-30 relative error = 2.0623000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.503 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.498 y[1] (analytic) = 1.9920318725099601593625498007968 y[1] (numeric) = 1.9920318725099601593625498007927 absolute error = 4.1e-30 relative error = 2.0582000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.502 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.499 y[1] (analytic) = 1.9960079840319361277445109780439 y[1] (numeric) = 1.9960079840319361277445109780398 absolute error = 4.1e-30 relative error = 2.0541000000000000000000000000000e-28 % Correct digits = 29 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.501 Order of pole = 651 Finished! diff ( y , x , 1 ) = y * y; Iterations = 500 Total Elapsed Time = 12 Seconds Elapsed Time(since restart) = 12 Seconds Time to Timeout = 2 Minutes 47 Seconds Percent Done = 100.2 % > quit memory used=128.3MB, alloc=4.1MB, time=12.83