|\^/| 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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 CONST $eq_no = 1 i = 1 > array_tmp1[1] := array_m1[1] * array_const_2D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * 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 CONST $eq_no = 1 i = 2 > array_tmp1[2] := array_m1[2] * array_const_2D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp2[2] := (array_tmp1[2] - array_tmp2[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * 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 CONST $eq_no = 1 i = 3 > array_tmp1[3] := array_m1[3] * array_const_2D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp2[3] := (array_tmp1[3] - array_tmp2[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * 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 CONST $eq_no = 1 i = 4 > array_tmp1[4] := array_m1[4] * array_const_2D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp2[4] := (array_tmp1[4] - array_tmp2[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * 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 CONST $eq_no = 1 i = 5 > array_tmp1[5] := array_m1[5] * array_const_2D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp2[5] := (array_tmp1[5] - array_tmp2[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * 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 CONST $eq_no = 1 i = 1 > array_tmp1[kkk] := array_m1[kkk] * array_const_2D0[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp2[kkk] := -ats(kkk,array_x,array_tmp2,2) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp3[kkk] := -ats(kkk,array_x,array_tmp3,2) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp4[kkk] := -ats(kkk,array_x,array_tmp4,2) / array_x[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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_m1[1]*array_const_2D0[1]; array_tmp2[1] := array_tmp1[1]/array_x[1]; array_tmp3[1] := array_tmp2[1]/array_x[1]; array_tmp4[1] := array_tmp3[1]/array_x[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*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] := array_m1[2]*array_const_2D0[1]; array_tmp2[2] := (array_tmp1[2] - array_tmp2[1]*array_x[2])/array_x[1]; array_tmp3[2] := (array_tmp2[2] - array_tmp3[1]*array_x[2])/array_x[1]; array_tmp4[2] := (array_tmp3[2] - array_tmp4[1]*array_x[2])/array_x[1]; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[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] := array_m1[3]*array_const_2D0[1]; array_tmp2[3] := (array_tmp1[3] - array_tmp2[2]*array_x[2])/array_x[1]; array_tmp3[3] := (array_tmp2[3] - array_tmp3[2]*array_x[2])/array_x[1]; array_tmp4[3] := (array_tmp3[3] - array_tmp4[2]*array_x[2])/array_x[1]; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[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] := array_m1[4]*array_const_2D0[1]; array_tmp2[4] := (array_tmp1[4] - array_tmp2[3]*array_x[2])/array_x[1]; array_tmp3[4] := (array_tmp2[4] - array_tmp3[3]*array_x[2])/array_x[1]; array_tmp4[4] := (array_tmp3[4] - array_tmp4[3]*array_x[2])/array_x[1]; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[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] := array_m1[5]*array_const_2D0[1]; array_tmp2[5] := (array_tmp1[5] - array_tmp2[4]*array_x[2])/array_x[1]; array_tmp3[5] := (array_tmp2[5] - array_tmp3[4]*array_x[2])/array_x[1]; array_tmp4[5] := (array_tmp3[5] - array_tmp4[4]*array_x[2])/array_x[1]; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[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] := array_m1[kkk]*array_const_2D0[1]; array_tmp2[kkk] := -ats(kkk, array_x, array_tmp2, 2)/array_x[1]; array_tmp3[kkk] := -ats(kkk, array_x, array_tmp3, 2)/array_x[1]; array_tmp4[kkk] := -ats(kkk, array_x, array_tmp4, 2)/array_x[1]; array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*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/x/x); > end; exact_soln_y := proc(x) return 1.0/(x*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, > array_const_2D0, > #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_tmp3, > array_tmp4, > array_tmp5, > 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/sing3postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=20;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -1.0;"); > omniout_str(ALWAYS,"x_end := -0.7;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_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/x/x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=20; > #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_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= 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_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > 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_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_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_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_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_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_2D0[1] := 2.0; > array_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 := -1.0; > x_end := -0.7; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 100; > #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; > #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 ) = m1 * 2.0 / x / x / x ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T19:06:53-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing3") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_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,"sing3 diffeq.mxt") > ; > logitem_str(html_log_file,"sing3 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_const_2D0, 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_tmp3, array_tmp4, array_tmp5, 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/sing3postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=20;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -1.0;"); omniout_str(ALWAYS, "x_end := -0.7;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_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/x/x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 20; 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_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := 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_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; 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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[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_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[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_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_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 := -1.0; x_end := -0.7; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 100; 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; 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 ) = m1 * 2.0 / x / x / x ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T19:06:53-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing3"); logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_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, "sing3 diffeq.mxt"); logitem_str(html_log_file, "sing3 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/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=20; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.0; x_end := -0.7; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 100; #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/x/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 = 0.3 estimated_steps = 300 step_error = 3.3333333333333333333333333333333e-13 est_needed_step_err = 3.3333333333333333333333333333333e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.8758827696078431372549019607843e-48 max_value3 = 1.8758827696078431372549019607843e-48 value3 = 1.8758827696078431372549019607843e-48 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 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 = 0.9963 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.999 y[1] (analytic) = 1.002003004005006007008009010011 y[1] (numeric) = 1.0020030040050060050042894676221 absolute error = 2.0037195423889e-18 relative error = 1.9997141070236645889000000000000e-16 % Correct digits = 17 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9953 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.998 y[1] (analytic) = 1.0040120320801924490263091312887 y[1] (numeric) = 1.0040120320801924450027641566564 absolute error = 4.0235449746323e-18 relative error = 4.0074668889136693291999999999997e-16 % Correct digits = 17 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9943 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.997 y[1] (analytic) = 1.0060271084064631205552464816717 y[1] (numeric) = 1.0060271084064631144956243970799 absolute error = 6.0596220845918e-18 relative error = 6.0233188886830105262000000000000e-16 % Correct digits = 17 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9933 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.996 y[1] (analytic) = 1.0080482572861728036644570248866 y[1] (numeric) = 1.0080482572861727955523588970067 absolute error = 8.1120981278799e-18 relative error = 8.0473311364269068784000000000008e-16 % Correct digits = 17 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9924 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.995 y[1] (analytic) = 1.0100755031438600035352642610035 y[1] (numeric) = 1.0100755031438599933541424168727 absolute error = 1.01811218441308e-17 relative error = 1.0079565153735595270000000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9914 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.994 y[1] (analytic) = 1.0121088705269848467059904699829 y[1] (numeric) = 1.0121088705269848344391469965151 absolute error = 1.22668434734678e-17 relative error = 1.2120082958151231240800000000000e-15 % Correct digits = 16 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.4899 Order of pole = 4.944e-28 TOP MAIN SOLVE Loop x[1] = -0.993 y[1] (analytic) = 1.0141483841066721836338762069633 y[1] (numeric) = 1.014148384106672169264461433792 absolute error = 1.43694147731713e-17 relative error = 1.4168947067670787193700000000001e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9894 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.992 y[1] (analytic) = 1.0161940686784599375650364203955 y[1] (numeric) = 1.0161940686784599210760473858469 absolute error = 1.64889890345486e-17 relative error = 1.6226220505294033510399999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9884 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.991 y[1] (analytic) = 1.0182459491630527420854287986429 y[1] (numeric) = 1.0182459491630527234597076986353 absolute error = 1.86257211000076e-17 relative error = 1.8291966803616563815600000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9874 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 1.0203040506070809101112131415162 y[1] (numeric) = 1.0203040506070808893314457611764 absolute error = 2.07797673803398e-17 relative error = 2.0366250009471037979999999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9864 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.989 y[1] (analytic) = 1.0223683981838647774661826093091 y[1] (numeric) = 1.0223683981838647545148967370972 absolute error = 2.29512858722119e-17 relative error = 2.2449134688613775839899999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9854 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.988 y[1] (analytic) = 1.0244390171941844645871920536315 y[1] (numeric) = 1.0244390171941844394467558777599 absolute error = 2.51404361758716e-17 relative error = 2.4540685930460007110399999999998e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9844 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.987 y[1] (analytic) = 1.0265159330670551002957392403166 y[1] (numeric) = 1.0265159330670550729483597272483 absolute error = 2.73473795130683e-17 relative error = 2.6640969352866232742700000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9834 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.986 y[1] (analytic) = 1.0285991713605075519751161288464 y[1] (numeric) = 1.0285991713605075224028373836527 absolute error = 2.95722787451937e-17 relative error = 2.8750051106962334365200000000001e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9824 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.985 y[1] (analytic) = 1.0306887577623747068978845113247 y[1] (numeric) = 1.030688757762374675082586119682 absolute error = 3.18152983916427e-17 relative error = 3.0867997882031538607500000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9814 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.984 y[1] (analytic) = 1.0327847180910833498578888227906 y[1] (numeric) = 1.032784718091083315781284174391 absolute error = 3.40766046483996e-17 relative error = 3.2994876910440803097600000000002e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9804 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.983 y[1] (analytic) = 1.0348870782964516826746449561156 y[1] (numeric) = 1.0348870782964516463182795492634 absolute error = 3.63563654068522e-17 relative error = 3.5130755972621805485800000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9794 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.982 y[1] (analytic) = 1.0369958644604925315557841555328 y[1] (numeric) = 1.0369958644604924929010338826977 absolute error = 3.86547502728351e-17 relative error = 3.7275703402101434972400000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9784 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.981 y[1] (analytic) = 1.0391111027982222887253328013085 y[1] (numeric) = 1.0391111027982222477534022154004 absolute error = 4.09719305859081e-17 relative error = 3.9429788090585105024099999999998e-15 % Correct digits = 16 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.9691 Order of pole = 4.446e-28 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.18 x[1] = -0.98 y[1] (analytic) = 1.0412328196584756351520199916701 y[1] (numeric) = 1.0412328196584755918439405527999 absolute error = 4.33080794388702e-17 relative error = 4.1593079493090940080000000000001e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9764 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.979 y[1] (analytic) = 1.0433610415247260916425737212828 y[1] (numeric) = 1.0433610415247260459792020237682 absolute error = 4.56633716975146e-17 relative error = 4.3765647633137590738600000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9754 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.978 y[1] (analytic) = 1.0454957950159124460001421874281 y[1] (numeric) = 1.0454957950159123979621581668031 absolute error = 4.80379840206250e-17 relative error = 4.5947563107983482500000000000001e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9744 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.977 y[1] (analytic) = 1.0476371068872711043876089673546 y[1] (numeric) = 1.0476371068872710539555140871343 absolute error = 5.04320948802203e-17 relative error = 4.8138897093921802738699999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9734 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.976 y[1] (analytic) = 1.0497850040311744154797097554421 y[1] (numeric) = 1.049785004031174362633825173395 absolute error = 5.28458845820471e-17 relative error = 5.0339721351628098329599999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9724 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.975 y[1] (analytic) = 1.0519395134779750164365548980933 y[1] (numeric) = 1.0519395134779749611570196117669 absolute error = 5.52795352863264e-17 relative error = 5.2550108231564034000000000000003e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9714 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.974 y[1] (analytic) = 1.0541006623968562501844676159194 y[1] (numeric) = 1.0541006623968561924512365871633 absolute error = 5.77332310287561e-17 relative error = 5.4770130679436221923600000000003e-15 % Correct digits = 16 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.7873 Order of pole = 3.363e-28 TOP MAIN SOLVE Loop x[1] = -0.973 y[1] (analytic) = 1.056268478096688703948014690582 y[1] (numeric) = 1.0562684780966886437408569488092 absolute error = 6.02071577417728e-17 relative error = 5.6999862241710821171200000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9694 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.972 y[1] (analytic) = 1.0584429880268929194397872952971 y[1] (numeric) = 1.0584429880268928567382840192193 absolute error = 6.27015032760778e-17 relative error = 5.9239377071185888195200000000001e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9684 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.971 y[1] (analytic) = 1.0606242197783083255819379937868 y[1] (numeric) = 1.0606242197783082603654805713576 absolute error = 6.52164574224292e-17 relative error = 6.1488749932620569357200000000004e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9674 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 1.0628122010840684451057498140078 y[1] (numeric) = 1.0628122010840683773535378803033 absolute error = 6.77522119337045e-17 relative error = 6.3748056208422564050000000000004e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9664 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.969 y[1] (analytic) = 1.0650069598204824268526594821297 y[1] (numeric) = 1.0650069598204823565436989348924 absolute error = 7.03089605472373e-17 relative error = 6.6017371904394482445300000000001e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9655 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.968 y[1] (analytic) = 1.0672085240079229560822348200259 y[1] (numeric) = 1.0672085240079228831953358125945 absolute error = 7.28868990074314e-17 relative error = 6.8296773655539400153600000000003e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9645 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.967 y[1] (analytic) = 1.0694169218117205955796720953835 y[1] (numeric) = 1.0694169218117205200934470067265 absolute error = 7.54862250886570e-17 relative error = 7.0586338731927185472999999999996e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9635 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.966 y[1] (analytic) = 1.0716321815430646108474895944516 y[1] (numeric) = 1.0716321815430645327403509760207 absolute error = 7.81071386184309e-17 relative error = 7.2886145044620504920399999999994e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9625 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.965 y[1] (analytic) = 1.0738543316599103331633063974872 y[1] (numeric) = 1.0738543316599102524134648966001 absolute error = 8.07498415008871e-17 relative error = 7.5196271151663589697499999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9615 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.964 y[1] (analytic) = 1.0760834007678931147879685267127 y[1] (numeric) = 1.0760834007678930313734307861728 absolute error = 8.34145377405399e-17 relative error = 7.7516796264132766910400000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9605 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.963 y[1] (analytic) = 1.078319417621248931115877282937 y[1] (numeric) = 1.0783194176212488450144438165935 absolute error = 8.61014334663435e-17 relative error = 7.9847800252249505251500000000000e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9595 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.962 y[1] (analytic) = 1.0805624111237416850722464028077 y[1] (numeric) = 1.0805624111237415962615094467548 absolute error = 8.88107369560529e-17 relative error = 8.2189363651557419987600000000003e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9585 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.961 y[1] (analytic) = 1.0828124103295972695802261128875 y[1] (numeric) = 1.0828124103295971780375674519971 absolute error = 9.15426586608904e-17 relative error = 8.4541567669164163098400000000002e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9575 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 1.0850694444444444444444444444445 y[1] (numeric) = 1.0850694444444443501470332139242 absolute error = 9.42974112305203e-17 relative error = 8.6904494190047508479999999999996e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9565 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.959 y[1] (analytic) = 1.0873335428262625845265912854566 y[1] (numeric) = 1.0873335428262624874513817471191 absolute error = 9.70752095383375e-17 relative error = 8.9278225783427770337499999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9555 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.958 y[1] (analytic) = 1.0896047349863363566232713420879 y[1] (numeric) = 1.0896047349863362567470006350136 absolute error = 9.98762707070743e-17 relative error = 9.1662845709207337865200000000004e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9545 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.957 y[1] (analytic) = 1.0918830505902173829965420063788 y[1] (numeric) = 1.0918830505902172802957278716504 absolute error = 1.027008141347284e-16 relative error = 9.4058437924476870411599999999998e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9535 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.956 y[1] (analytic) = 1.0941685194586929500533954237496 y[1] (numeric) = 1.0941685194586928445043339029325 absolute error = 1.055490615208171e-16 relative error = 9.6465087090089497105599999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9525 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.955 y[1] (analytic) = 1.0964611715687618212220059757134 y[1] (numeric) = 1.0964611715687617128007690827497 absolute error = 1.084212368929637e-16 relative error = 9.8882878577305218492499999999999e-15 % Correct digits = 16 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9515 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.954 y[1] (analytic) = 1.0987610370546172136299109124551 y[1] (numeric) = 1.0987610370546171023123442786374 absolute error = 1.113175666338177e-16 relative error = 1.0131189847450362985320000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9505 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.953 y[1] (analytic) = 1.1010681462086369987524897903456 y[1] (numeric) = 1.1010681462086368845142102820296 absolute error = 1.142382795083160e-16 relative error = 1.0375223359396816604400000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9495 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.952 y[1] (analytic) = 1.1033825294823811877692253371937 y[1] (numeric) = 1.1033825294823810705856186459057 absolute error = 1.171836066912880e-16 relative error = 1.0620397147874107955200000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9485 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.951 y[1] (analytic) = 1.1057042174875967629403328833117 y[1] (numeric) = 1.1057042174875966427865510879009 absolute error = 1.201537817954108e-16 relative error = 1.0866720040955132293080000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9475 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 1.1080332409972299168975069252078 y[1] (numeric) = 1.1080332409972297937484660256899 absolute error = 1.231490408995179e-16 relative error = 1.1114200941181490475000000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9465 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.949 y[1] (analytic) = 1.1103696309464457623298219744371 y[1] (numeric) = 1.1103696309464456361601993971702 absolute error = 1.261696225772669e-16 relative error = 1.1362848826270914740690000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9455 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.948 y[1] (analytic) = 1.1127134184336555751393117199879 y[1] (numeric) = 1.1127134184336554459235437938161 absolute error = 1.292157679261718e-16 relative error = 1.1612672749832230134720000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9445 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.947 y[1] (analytic) = 1.1150646347215516347405077335307 y[1] (numeric) = 1.1150646347215515024527871365274 absolute error = 1.322877205970033e-16 relative error = 1.1863681842087793246970000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9435 Order of pole = 225.1 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.0MB, time=0.39 x[1] = -0.946 y[1] (analytic) = 1.117423311238149725784319422158 y[1] (numeric) = 1.1174233112381495903985925985938 absolute error = 1.353857268235642e-16 relative error = 1.2115885310603677960720000000001e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.5675 Order of pole = 7.373e-28 TOP MAIN SOLVE Loop x[1] = -0.945 y[1] (analytic) = 1.119789479577839366199154558943 y[1] (numeric) = 1.1197894795778392276891191061003 absolute error = 1.385100354528427e-16 relative error = 1.2369292441027485216749999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9415 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.944 y[1] (analytic) = 1.1221631715024418270611893134157 y[1] (numeric) = 1.1221631715024416854002913378649 absolute error = 1.416608979755508e-16 relative error = 1.2623912597834043770880000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9405 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.943 y[1] (analytic) = 1.1245444189422760104312740301086 y[1] (numeric) = 1.1245444189422758655927054730551 absolute error = 1.448385685570535e-16 relative error = 1.2879755225079126782149999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9395 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.942 y[1] (analytic) = 1.1269332539972322519281827975893 y[1] (numeric) = 1.1269332539972321038848787288984 absolute error = 1.480433040686909e-16 relative error = 1.3136829847160983178760000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9385 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.941 y[1] (analytic) = 1.1293297089378541154468588258811 y[1] (numeric) = 1.1293297089378539641714947063784 absolute error = 1.512753641195027e-16 relative error = 1.3395146069590137029870000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9376 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = 1.131733816206428248076052512449 y[1] (numeric) = 1.1317338162064280935410414240911 absolute error = 1.545350110883579e-16 relative error = 1.3654713579767304044000000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9366 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.939 y[1] (analytic) = 1.1341456084180823639223745379774 y[1] (numeric) = 1.1341456084180822060998643814802 absolute error = 1.578225101564972e-16 relative error = 1.3915542147769686768120000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9356 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.938 y[1] (analytic) = 1.1365651183618914262073731252358 y[1] (numeric) = 1.1365651183618912650692437847442 absolute error = 1.611381293404916e-16 relative error = 1.4177641627145549131040000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9346 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.937 y[1] (analytic) = 1.1389923790019920976708744841789 y[1] (numeric) = 1.138992379001991933188734958553 absolute error = 1.644821395256259e-16 relative error = 1.4441021955717424579709999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9336 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.936 y[1] (analytic) = 1.1414274234787055299875812696326 y[1] (numeric) = 1.1414274234787053621327667699228 absolute error = 1.678548144997098e-16 relative error = 1.4705693156393775694079999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9326 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.935 y[1] (analytic) = 1.1438702851096685635848894735337 y[1] (numeric) = 1.1438702851096683923284584862076 absolute error = 1.712564309873261e-16 relative error = 1.4971665337989515977250000000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.6058 Order of pole = 3.898e-28 TOP MAIN SOLVE Loop x[1] = -0.934 y[1] (analytic) = 1.1463209973909734099381445189808 y[1] (numeric) = 1.1463209973909732352508758344625 absolute error = 1.746872686845183e-16 relative error = 1.5238948696055164611480000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9306 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.933 y[1] (analytic) = 1.1487795939983158891151984689065 y[1] (numeric) = 1.1487795939983157109675881749796 absolute error = 1.781476102939269e-16 relative error = 1.5507553513715013325410000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9296 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.932 y[1] (analytic) = 1.151246108788152296045239367091 y[1] (numeric) = 1.1512461087881521144074978067119 absolute error = 1.816377415603791e-16 relative error = 1.5777490162514273535839999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9286 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.931 y[1] (analytic) = 1.1537205757988649696975290766429 y[1] (numeric) = 1.1537205757988647845395777697049 absolute error = 1.851579513069380e-16 relative error = 1.6048769103275288781799999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9276 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = 1.1562030292519366400739969938722 y[1] (numeric) = 1.1562030292519364513654655224526 absolute error = 1.887085314714196e-16 relative error = 1.6321400886963081203999999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9266 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.929 y[1] (analytic) = 1.158693503553133628645684272242 y[1] (numeric) = 1.1586935035531334363559071288605 absolute error = 1.922897771433815e-16 relative error = 1.6595396155560111314150000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9256 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.928 y[1] (analytic) = 1.1611920332936979785969084423306 y[1] (numeric) = 1.1611920332936977826949218407382 absolute error = 1.959019866015924e-16 relative error = 1.6870765642950574940159999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9246 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.927 y[1] (analytic) = 1.1636986532515485919828144982888 y[1] (numeric) = 1.1636986532515483924373531463017 absolute error = 1.995454613519871e-16 relative error = 1.7147520175814172265590000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9236 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.926 y[1] (analytic) = 1.1662133983924914516557897830377 y[1] (numeric) = 1.166213398392491248435283616922 absolute error = 2.032205061661157e-16 relative error = 1.7425670674529622597319999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9226 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.925 y[1] (analytic) = 1.1687363038714390065741417092769 y[1] (numeric) = 1.1687363038714387996467125891844 absolute error = 2.069274291200925e-16 relative error = 1.7705228154087914531249999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9216 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.924 y[1] (analytic) = 1.1712674050336387998725661063324 y[1] (numeric) = 1.17126740503363858920602447228 absolute error = 2.106665416340524e-16 relative error = 1.7986203725015472186239999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9206 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.923 y[1] (analytic) = 1.1738067374159114198483676456606 y[1] (numeric) = 1.1738067374159112054102091335387 absolute error = 2.144381585121219e-16 relative error = 1.8268608594307349814510000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9196 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.922 y[1] (analytic) = 1.1763543367478978548002315065335 y[1] (numeric) = 1.1763543367478976365576335236216 absolute error = 2.182425979829119e-16 relative error = 1.8552454066370567959960000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9186 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.921 y[1] (analytic) = 1.1789102389533163334476876265118 y[1] (numeric) = 1.1789102389533161113675058859729 absolute error = 2.220801817405389e-16 relative error = 1.8837751543977645707490000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9176 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (analytic) = 1.1814744801512287334593572778828 y[1] (numeric) = 1.1814744801512285075081222916985 absolute error = 2.259512349861843e-16 relative error = 1.9124512529230639152000000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9166 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.919 y[1] (analytic) = 1.1840470966573166414267293895882 y[1] (numeric) = 1.1840470966573164115706429193915 absolute error = 2.298560864701967e-16 relative error = 1.9412748624535579514870000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9156 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.918 y[1] (analytic) = 1.1866281249851671484376854106446 y[1] (numeric) = 1.1866281249851669146426168758979 absolute error = 2.337950685347467e-16 relative error = 1.9702471533587587801079999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9146 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.917 y[1] (analytic) = 1.1892176018475684662303823691356 y[1] (numeric) = 1.1892176018475682284618652120942 absolute error = 2.377685171570414e-16 relative error = 1.9993693062366738580459999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9136 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.916 y[1] (analytic) = 1.1918155641578154497435212905932 y[1] (numeric) = 1.1918155641578152079667492974862 absolute error = 2.417767719931070e-16 relative error = 2.0286425120144838699200000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9126 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.915 y[1] (analytic) = 1.194422049031025112723580877303 y[1] (numeric) = 1.1944220490310248669034044551554 absolute error = 2.458201764221476e-16 relative error = 2.0580679720503252441000000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9116 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.914 y[1] (analytic) = 1.1970370937854622239033943183832 y[1] (numeric) = 1.1970370937854619740043167268966 absolute error = 2.498990775914866e-16 relative error = 2.0876468982361753969359999999999e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.4967 Order of pole = 5.877e-28 TOP MAIN SOLVE Loop x[1] = -0.913 y[1] (analytic) = 1.1996607359438750721296017486255 y[1] (numeric) = 1.1996607359438748181157752865233 absolute error = 2.540138264621022e-16 relative error = 2.1173805131018806875180000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9097 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.912 y[1] (analytic) = 1.202293013234841489689135118498 y[1] (numeric) = 1.2022930132348412315243572637345 absolute error = 2.581647778547635e-16 relative error = 2.1472700499203241254400000000000e-14 % memory used=11.4MB, alloc=4.1MB, time=0.61 Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9087 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.911 y[1] (analytic) = 1.2049339635941252239671004830581 y[1] (numeric) = 1.2049339635941249616148099862824 absolute error = 2.623522904967757e-16 relative error = 2.1773167528137458571969999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9077 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = 1.2075836251660427484603308779133 y[1] (numeric) = 1.20758362516604248188360380857 absolute error = 2.665767270693433e-16 relative error = 2.2075218768612318673000000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9067 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.909 y[1] (analytic) = 1.2102420363048406050726084709681 y[1] (numeric) = 1.2102420363048403342341542154061 absolute error = 2.708384542555620e-16 relative error = 2.2378866882074002492200000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9057 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.908 y[1] (analytic) = 1.2129092355760833705292165576665 y[1] (numeric) = 1.212909235576083095391373768622 absolute error = 2.751378427890445e-16 relative error = 2.2684124641722678464800000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9047 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.907 y[1] (analytic) = 1.2155852617580523406702007782176 y[1] (numeric) = 1.2155852617580520611949332750239 absolute error = 2.794752675031937e-16 relative error = 2.2991004933623479411130000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9037 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.906 y[1] (analytic) = 1.2182701538431550273136168491636 y[1] (numeric) = 1.2182701538431547434625094680346 absolute error = 2.838511073811290e-16 relative error = 2.3299520757829640384399999999999e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.8576 Order of pole = 1.175e-28 TOP MAIN SOLVE Loop x[1] = -0.905 y[1] (analytic) = 1.220963951039345563322242910778 y[1] (numeric) = 1.2209639510393452750564973045011 absolute error = 2.882657456062769e-16 relative error = 2.3609685229518093802250000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9017 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.904 y[1] (analytic) = 1.2236666927715561124598637324771 y[1] (numeric) = 1.2236666927715558197402941188403 absolute error = 2.927195696136368e-16 relative error = 2.3921511580137781114880000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.9007 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.903 y[1] (analytic) = 1.2263784186831393815864185948401 y[1] (numeric) = 1.2263784186831390843734474531133 absolute error = 2.972129711417268e-16 relative error = 2.4235013158570430826120000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8997 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.902 y[1] (analytic) = 1.2290991686373223337151734750567 y[1] (numeric) = 1.2290991686373220319688271898302 absolute error = 3.017463462852265e-16 relative error = 2.4550203432304542130599999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8987 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.901 y[1] (analytic) = 1.2318289827186712014397617150016 y[1] (numeric) = 1.2318289827186708951196661666818 absolute error = 3.063200955483198e-16 relative error = 2.4867095988622156195980000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8977 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = 1.2345679012345679012345679012346 y[1] (numeric) = 1.2345679012345675902999440024812 absolute error = 3.109346238987534e-16 relative error = 2.5185704535799025399999999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8967 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.899 y[1] (analytic) = 1.2373159647166979501386412538465 y[1] (numeric) = 1.2373159647166976345483004312289 absolute error = 3.155903408226176e-16 relative error = 2.5506042904318036693760000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8957 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.898 y[1] (analytic) = 1.24007321392254998735125321799 y[1] (numeric) = 1.2400732139225496670635928381276 absolute error = 3.202876603798624e-16 relative error = 2.5828125048096255880960000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8947 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.897 y[1] (analytic) = 1.2428396898369270042964968077662 y[1] (numeric) = 1.2428396898369266792694955472085 absolute error = 3.250270012605577e-16 relative error = 2.6151965045725607043930000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8937 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.896 y[1] (analytic) = 1.2456154336734693877551020408163 y[1] (numeric) = 1.2456154336734690579463151989063 absolute error = 3.298087868419100e-16 relative error = 2.6477577101727481856000000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8927 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.895 y[1] (analytic) = 1.248400486876189881714053868481 y[1] (numeric) = 1.2484004868761895470806086224358 absolute error = 3.346334452460452e-16 relative error = 2.6804975547821335633000000000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.8683 Order of pole = 6.467e-28 TOP MAIN SOLVE Loop x[1] = -0.894 y[1] (analytic) = 1.2511948911210205746487895940623 y[1] (numeric) = 1.2511948911210202351473801954923 absolute error = 3.395014093985700e-16 relative error = 2.7134174844207549252000000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8907 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.893 y[1] (analytic) = 1.253998688317372020028867049805 y[1] (numeric) = 1.2539986883173716756157499618826 absolute error = 3.444131170879224e-16 relative error = 2.7465189580864662995760000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8897 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.892 y[1] (analytic) = 1.2568119206097045989261798950311 y[1] (numeric) = 1.256811920609704249557168869508 absolute error = 3.493690110255231e-16 relative error = 2.7798034478861181183839999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8887 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.891 y[1] (analytic) = 1.2596346303791122347052014092792 y[1] (numeric) = 1.2596346303791118803356625025402 absolute error = 3.543695389067390e-16 relative error = 2.8132724391682086405900000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8877 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (analytic) = 1.2624668602449185708875142027521 y[1] (numeric) = 1.2624668602449182114723607300795 absolute error = 3.594151534726726e-16 relative error = 2.8469274306570396646000000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8867 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.889 y[1] (analytic) = 1.2653086530662857244081835102445 y[1] (numeric) = 1.2653086530662853599018709374581 absolute error = 3.645063125727864e-16 relative error = 2.8807699345883712043440000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8857 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.888 y[1] (analytic) = 1.2681600519438357276195114032952 y[1] (numeric) = 1.2681600519438353579760321749181 absolute error = 3.696434792283771e-16 relative error = 2.9148014768466139194240000000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.2889 Order of pole = 9.300e-28 TOP MAIN SOLVE Loop x[1] = -0.887 y[1] (analytic) = 1.2710211002212847735485256790747 y[1] (numeric) = 1.271021100221284398721403982164 absolute error = 3.748271216969107e-16 relative error = 2.9490235971035673452830000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8838 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.886 y[1] (analytic) = 1.2738918414870903800783698260883 y[1] (numeric) = 1.2738918414870900000206562888556 absolute error = 3.800577135372327e-16 relative error = 2.9834378489587352056920000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8828 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.885 y[1] (analytic) = 1.276772319576111589900730952153 y[1] (numeric) = 1.2767723195761112045649972764897 absolute error = 3.853357336756633e-16 relative error = 3.0180458000812138814249999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8818 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.884 y[1] (analytic) = 1.2796625785712823242767347105915 y[1] (numeric) = 1.2796625785712819336150682375971 absolute error = 3.906616664729944e-16 relative error = 3.0528490323532031184640000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8808 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.883 y[1] (analytic) = 1.282562662805298009847516125019 y[1] (numeric) = 1.2825626628052976138115143326196 absolute error = 3.960360017923994e-16 relative error = 3.0878491420151409578660000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8798 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.882 y[1] (analytic) = 1.2854726168623155989531111008273 y[1] (numeric) = 1.2854726168623151974938760325579 absolute error = 4.014592350682694e-16 relative error = 3.1230477398124840472560000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8788 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.881 y[1] (analytic) = 1.2883924855796671051495759256134 y[1] (numeric) = 1.2883924855796666982177085496236 absolute error = 4.069318673759898e-16 relative error = 3.1584464511441561915779999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8778 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = 1.2913223140495867768595041322314 y[1] (numeric) = 1.2913223140495863644050986295592 absolute error = 4.124544055026722e-16 relative error = 3.1940469162126935168000000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8768 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.879 y[1] (analytic) = 1.2942621476209520333505470198967 y[1] (numeric) = 1.2942621476209516153231850010424 absolute error = 4.180273620188543e-16 relative error = 3.2298507901760960520630000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8758 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.878 y[1] (analytic) = 1.2972120319010382885103335910461 y[1] (numeric) = 1.2972120319010378648590782398632 absolute error = 4.236512553511829e-16 relative error = 3.2658597433014127868360000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8748 Order of pole = 225.1 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.82 x[1] = -0.877 y[1] (analytic) = 1.3001720127572877891745077873803 y[1] (numeric) = 1.3001720127572873598478979312856 absolute error = 4.293266098560947e-16 relative error = 3.3020754611200826051629999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8738 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.876 y[1] (analytic) = 1.3031421363190925960676382894435 y[1] (numeric) = 1.3031421363190921610136823949344 absolute error = 4.350539558945091e-16 relative error = 3.3384996445850481512160000000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.555 Order of pole = 5.360e-28 TOP MAIN SOLVE Loop x[1] = -0.875 y[1] (analytic) = 1.306122448979591836734693877551 y[1] (numeric) = 1.3061224489795913959008639700017 absolute error = 4.408338299075493e-16 relative error = 3.3751340102296743281250000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8718 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.874 y[1] (analytic) = 1.3091129973974833611738030779865 y[1] (numeric) = 1.3091129973974829145070285846809 absolute error = 4.466667744933056e-16 relative error = 3.4119802903284830850559999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8708 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.873 y[1] (analytic) = 1.3121138284988499322293207580344 y[1] (numeric) = 1.3121138284988494796759822733769 absolute error = 4.525533384846575e-16 relative error = 3.4490402330597353581750000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8698 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.872 y[1] (analytic) = 1.315124989479000084167999326656 y[1] (numeric) = 1.3151249894789996256739222984857 absolute error = 4.584940770281703e-16 relative error = 3.4863156026698824539520000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8688 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.871 y[1] (analytic) = 1.318146527804323784240503742877 y[1] (numeric) = 1.3181465278043233197509520787955 absolute error = 4.644895516640815e-16 relative error = 3.5238081796399045324150000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8678 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = 1.3211784912141630334258158277183 y[1] (numeric) = 1.3211784912141625628854854203237 absolute error = 4.705403304073946e-16 relative error = 3.5615197608535697274000000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8668 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.869 y[1] (analytic) = 1.3242209277226975439674453527129 y[1] (numeric) = 1.3242209277226970673204575226173 absolute error = 4.766469878300956e-16 relative error = 3.5994521597676282339159999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8658 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.868 y[1] (analytic) = 1.3272738856208456327380067531696 y[1] (numeric) = 1.3272738856208451499279016086593 absolute error = 4.828101051445103e-16 relative error = 3.6376072065839752826719999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8648 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.867 y[1] (analytic) = 1.3303374134781804709128376230063 y[1] (numeric) = 1.3303374134781799818825673351879 absolute error = 4.890302702878184e-16 relative error = 3.6759867484237992527760000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8638 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.866 y[1] (analytic) = 1.333411560144861831894137789417 y[1] (numeric) = 1.3334115601448613365860597816737 absolute error = 4.953080780077433e-16 relative error = 3.7145926495037513429479999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8628 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.865 y[1] (analytic) = 1.3364963747535834809048080457082 y[1] (numeric) = 1.3364963747535829792606780962752 absolute error = 5.016441299494330e-16 relative error = 3.7534267913141450642499999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8618 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.864 y[1] (analytic) = 1.3395919067215363511659807956104 y[1] (numeric) = 1.3395919067215358431269460520576 absolute error = 5.080390347435528e-16 relative error = 3.7924910727992319098880000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8608 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.863 y[1] (analytic) = 1.3426982057523876530843791833441 y[1] (numeric) = 1.3426982057523871385909710877377 absolute error = 5.144934080956064e-16 relative error = 3.8317874105395668292160000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8598 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.862 y[1] (analytic) = 1.3458153218382760644053380418926 y[1] (numeric) = 1.3458153218382755433974651653888 absolute error = 5.210078728765038e-16 relative error = 3.8713177389364888956719999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8588 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.861 y[1] (analytic) = 1.3489433052618231508347935644613 y[1] (numeric) = 1.3489433052618226232517343500649 absolute error = 5.275830592143964e-16 relative error = 3.9110840103987555364439999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8578 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (analytic) = 1.3520822065981611681990265008113 y[1] (numeric) = 1.3520822065981606339794219130141 absolute error = 5.342196045877972e-16 relative error = 3.9510881955313480911999999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8568 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.859 y[1] (analytic) = 1.3552320767169773987946565909679 y[1] (numeric) = 1.3552320767169768578765026709625 absolute error = 5.409181539200054e-16 relative error = 3.9913322833264750455740000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8559 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.858 y[1] (analytic) = 1.3583929667845751761835677919594 y[1] (numeric) = 1.3583929667845746285042081171021 absolute error = 5.476793596748573e-16 relative error = 4.0318182813568164939720000000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.1826 Order of pole = 6.045e-28 TOP MAIN SOLVE Loop x[1] = -0.857 y[1] (analytic) = 1.3615649282659517543083318242656 y[1] (numeric) = 1.3615649282659511998044498704451 absolute error = 5.545038819538205e-16 relative error = 4.0725482159710151240449999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8539 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.856 y[1] (analytic) = 1.3647480129268931784435321862172 y[1] (numeric) = 1.3647480129268926170511435917625 absolute error = 5.613923885944547e-16 relative error = 4.1135241324914635905919999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8529 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.855 y[1] (analytic) = 1.3679422728360863171574159570467 y[1] (numeric) = 1.367942272836085748811860686788 absolute error = 5.683455552702587e-16 relative error = 4.1547480954144086616749999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8519 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.854 y[1] (analytic) = 1.3711477603672482161367637622101 y[1] (numeric) = 1.3711477603672476407726981702859 absolute error = 5.753640655919242e-16 relative error = 4.1962221886123978984719999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8509 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.853 y[1] (analytic) = 1.3743645282012729364260200189937 y[1] (numeric) = 1.374364528201272353977408808974 absolute error = 5.824486112100197e-16 relative error = 4.2379485155391122389730000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8499 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.852 y[1] (analytic) = 1.3775926293283960413498203619211 y[1] (numeric) = 1.3775926293283954517499284427968 absolute error = 5.895998919191243e-16 relative error = 4.2799291994366000586720000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8489 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.851 y[1] (analytic) = 1.3808321170503768981263489003744 y[1] (numeric) = 1.3808321170503763013077331369392 absolute error = 5.968186157634352e-16 relative error = 4.3221663835449553527519999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8479 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = 1.3840830449826989619377162629758 y[1] (numeric) = 1.3840830449826983578322171191057 absolute error = 6.041054991438701e-16 relative error = 4.3646622313144614724999999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8469 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.849 y[1] (analytic) = 1.387345467056788212003035511882 y[1] (numeric) = 1.3873454670567876005417685851918 absolute error = 6.114612669266902e-16 relative error = 4.4074189266202522285019999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8459 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.848 y[1] (analytic) = 1.3906194375222499110003559985761 y[1] (numeric) = 1.3906194375222492921137034449135 absolute error = 6.188866525536626e-16 relative error = 4.4504386739794899031039999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8449 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.847 y[1] (analytic) = 1.3939050109491238610053679281972 y[1] (numeric) = 1.3939050109491232346229697744066 absolute error = 6.263823981537906e-16 relative error = 4.4937236987711276055539999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8439 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.846 y[1] (analytic) = 1.3972022422301583309580895215421 y[1] (numeric) = 1.3972022422301576970088348649087 absolute error = 6.339492546566334e-16 relative error = 4.5372762474582703051439999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8429 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.845 y[1] (analytic) = 1.4005111865831028325338748643254 y[1] (numeric) = 1.4005111865831021909458929570862 absolute error = 6.415879819072392e-16 relative error = 4.5810985878131646978000000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8419 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.844 y[1] (analytic) = 1.4038318995530199231823184564588 y[1] (numeric) = 1.4038318995530192738829696737389 absolute error = 6.492993487827199e-16 relative error = 4.6251930091448756268639999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8409 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.843 y[1] (analytic) = 1.407164437014616217007270818646 y[1] (numeric) = 1.4071644370146155599231375081584 absolute error = 6.570841333104876e-16 relative error = 4.6695618225296470245240000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8399 Order of pole = 225.1 memory used=19.0MB, alloc=4.1MB, time=1.03 TOP MAIN SOLVE Loop x[1] = -0.842 y[1] (analytic) = 1.4105088551745927860935110950627 y[1] (numeric) = 1.4105088551745921211503883068776 absolute error = 6.649431227881851e-16 relative error = 4.7142073610440286123639999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8389 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.841 y[1] (analytic) = 1.4138652105740151368409444054061 y[1] (numeric) = 1.4138652105740144639638305000761 absolute error = 6.728771139053300e-16 relative error = 4.7591319800007570772999999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8379 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = 1.4172335600907029478458049886621 y[1] (numeric) = 1.4172335600907022669588921219575 absolute error = 6.808869128667046e-16 relative error = 4.8043380571874676576000000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8369 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.839 y[1] (analytic) = 1.4206139609416397578705564971069 y[1] (numeric) = 1.4206139609416390688972209795915 absolute error = 6.889733355175154e-16 relative error = 4.8498279931082495788340000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8359 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.838 y[1] (analytic) = 1.4240064706854027944702980730345 y[1] (numeric) = 1.4240064706854020973330906026843 absolute error = 6.971372074703502e-16 relative error = 4.8956042112280860584879999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8349 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.837 y[1] (analytic) = 1.4274111472246131358938234492248 y[1] (numeric) = 1.4274111472246124305144592152628 absolute error = 7.053793642339620e-16 relative error = 4.9416691582202252437800000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8339 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.836 y[1] (analytic) = 1.4308280488084064009523591492868 y[1] (numeric) = 1.4308280488084056872517078053787 absolute error = 7.137006513439081e-16 relative error = 4.9880253042165199545760000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8329 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.835 y[1] (analytic) = 1.4342572340349241636487504033848 y[1] (numeric) = 1.4342572340349234415468259083136 absolute error = 7.221019244950712e-16 relative error = 5.0346751430607601742000000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8319 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.834 y[1] (analytic) = 1.4376987618538262914847977732922 y[1] (numeric) = 1.4376987618538255609007480971973 absolute error = 7.305840496760949e-16 relative error = 5.0816211925650586426439999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8309 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.833 y[1] (analytic) = 1.4411526915688244085149065628652 y[1] (numeric) = 1.4411526915688236693670032571042 absolute error = 7.391479033057610e-16 relative error = 5.1288659947693119452900000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8299 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.832 y[1] (analytic) = 1.4446190828402366863905325443787 y[1] (numeric) = 1.4446190828402359385961601730364 absolute error = 7.477943723713423e-16 relative error = 5.1764121162038005227520000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.829 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.831 y[1] (analytic) = 1.4480979956875641688424339051872 y[1] (numeric) = 1.4480979956875634123180793362303 absolute error = 7.565243545689569e-16 relative error = 5.2242621481549344582090000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.828 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = 1.4515894904920888372768181158369 y[1] (numeric) = 1.4515894904920880719380596698757 absolute error = 7.653387584459612e-16 relative error = 5.2724187069342267067999999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.827 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.829 y[1] (analytic) = 1.4550936279994936274174561762176 y[1] (numeric) = 1.455093627999492853178952630809 absolute error = 7.742385035454086e-16 relative error = 5.3208844341505015167260000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.826 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.828 y[1] (analytic) = 1.4586104693225046092090830591146 y[1] (numeric) = 1.4586104693225038259845625065035 absolute error = 7.832245205526111e-16 relative error = 5.3696619969854132838239999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.825 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.827 y[1] (analytic) = 1.4621400759435555445082749817599 y[1] (numeric) = 1.4621400759435547522105235379281 absolute error = 7.922977514438318e-16 relative error = 5.4187540884722843914219999999996e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.824 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.826 y[1] (analytic) = 1.4656825097174750394268595114001 y[1] (numeric) = 1.4656825097174742379677098742531 absolute error = 8.014591496371470e-16 relative error = 5.4681634277783410657199999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.823 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.825 y[1] (analytic) = 1.4692378328741965105601469237833 y[1] (numeric) = 1.4692378328741956998504667782743 absolute error = 8.107096801455090e-16 relative error = 5.5178927604903706312500000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.822 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.824 y[1] (analytic) = 1.4728061080214911867282495993967 y[1] (numeric) = 1.4728061080214903666779298673514 absolute error = 8.200503197320453e-16 relative error = 5.5679448589038518961280000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.821 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.823 y[1] (analytic) = 1.4763873981477243702838650050419 y[1] (numeric) = 1.4763873981477235408018079374119 absolute error = 8.294820570676300e-16 relative error = 5.6183225223156076026999999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.82 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.822 y[1] (analytic) = 1.479981766624635184494527027427 y[1] (numeric) = 1.4799817666246343454886341366644 absolute error = 8.390058928907626e-16 relative error = 5.6690285773200203661840000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.819 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.821 y[1] (analytic) = 1.483589277210140035991875865118 y[1] (numeric) = 1.4835892772101391873690356953254 absolute error = 8.486228401697926e-16 relative error = 5.7200658781088717389660000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.818 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = 1.4872099940511600237953599048185 y[1] (numeric) = 1.4872099940511591654614356372941 absolute error = 8.583339242675244e-16 relative error = 5.7714373067748340656000000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.817 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.819 y[1] (analytic) = 1.4908439816864725289633714542139 y[1] (numeric) = 1.4908439816864716608231883459703 absolute error = 8.681401831082436e-16 relative error = 5.8231457736186858537960000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.816 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.818 y[1] (analytic) = 1.4944913050495872215015453040094 y[1] (numeric) = 1.4944913050495863434588779568088 absolute error = 8.780426673472006e-16 relative error = 5.8751942174602825427440000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.815 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.817 y[1] (analytic) = 1.4981520294716467237662343499294 y[1] (numeric) = 1.4981520294716458357237938073368 absolute error = 8.880424405425926e-16 relative error = 5.9275856059533459198139999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.814 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.816 y[1] (analytic) = 1.5018262206843521722414455978469 y[1] (numeric) = 1.5018262206843512741008662677644 absolute error = 8.981405793300825e-16 relative error = 5.9803229359041141312000000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.813 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.815 y[1] (analytic) = 1.5055139448229139222402047498964 y[1] (numeric) = 1.5055139448229130139020311499991 absolute error = 9.083381735998973e-16 relative error = 6.0334092335939178409250000000004e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.812 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.814 y[1] (analytic) = 1.5092152684290276427868565460703 y[1] (numeric) = 1.5092152684290267241505298695259 absolute error = 9.186363266765444e-16 relative error = 6.0868475551057161326240000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.811 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.813 y[1] (analytic) = 1.5129302584538760516756459077506 y[1] (numeric) = 1.5129302584538751226394904065602 absolute error = 9.290361555011904e-16 relative error = 6.1406409866546631749760000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.81 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.812 y[1] (analytic) = 1.5166589822611565434735130675337 y[1] (numeric) = 1.5166589822611556039347222507893 absolute error = 9.395387908167444e-16 relative error = 6.1947926449227551967360000000004e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.809 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.811 y[1] (analytic) = 1.5204015076301349660418323270809 y[1] (numeric) = 1.5204015076301340158964549713919 absolute error = 9.501453773556890e-16 relative error = 6.2493056773976112476900000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.808 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (analytic) = 1.5241579027587258039932937052279 y[1] (numeric) = 1.5241579027587248431362196745255 absolute error = 9.608570740307024e-16 relative error = 6.3041832627154384463999999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.807 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.809 y[1] (analytic) = 1.5279282362665990303767412652163 y[1] (numeric) = 1.5279282362665980587016871370976 absolute error = 9.716750541281187e-16 relative error = 6.3594286110082525489469999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.806 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.808 y[1] (analytic) = 1.5317125771983138907950200960691 y[1] (numeric) = 1.5317125771983129081945145917979 absolute error = 9.826005055042712e-16 relative error = 6.4150449642554051271679999999996e-14 % Correct digits = 15 h = 0.001 memory used=22.8MB, alloc=4.1MB, time=1.25 Real estimate of pole used for equation 1 Radius of convergence = 0.805 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.807 y[1] (analytic) = 1.5355109950264798871092316456532 y[1] (numeric) = 1.5355109950264788934746008608893 absolute error = 9.936346307847639e-16 relative error = 6.4710355966394670511110000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.804 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.806 y[1] (analytic) = 1.5393235596549452308677474770486 y[1] (numeric) = 1.539323559654944226089099910327 absolute error = 1.0047786475667216e-15 relative error = 6.5274038149065475333760000000004e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.803 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.805 y[1] (analytic) = 1.5431503414220130396203850160102 y[1] (numeric) = 1.5431503414220120235865963919465 absolute error = 1.0160337886240637e-15 relative error = 6.5841529587310887919249999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8021 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.804 y[1] (analytic) = 1.54699141110368555233781342046 y[1] (numeric) = 1.5469914111036845249365113046074 absolute error = 1.0274013021158526e-15 relative error = 6.6412864010852097428159999999995e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8011 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.803 y[1] (analytic) = 1.5508468399169366432540488733873 y[1] (numeric) = 1.5508468399169356043715970756209 absolute error = 1.0388824517977664e-15 relative error = 6.6988075486126595461760000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.8001 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.802 y[1] (analytic) = 1.5547166995230129165863396371913 y[1] (numeric) = 1.5547166995230118661078224004437 absolute error = 1.0504785172367476e-15 relative error = 6.7567198420074500331040000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7991 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.801 y[1] (analytic) = 1.5586010620307636677623632132743 y[1] (numeric) = 1.5586010620307626055715691843985 absolute error = 1.0621907940288758e-15 relative error = 6.8150267563972074215580000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7981 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 1.5625 y[1] (numeric) = 1.5624999999999989259794059794775 absolute error = 1.0740205940205225e-15 relative error = 6.8737318017313440000000000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7971 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.799 y[1] (analytic) = 1.5664135864448833883405571106562 y[1] (numeric) = 1.5664135864448823023713115778193 absolute error = 1.0859692455328369e-15 relative error = 6.9328385231740860979689999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7961 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.798 y[1] (analytic) = 1.5703418948373439865327479098749 y[1] (numeric) = 1.5703418948373428884946543202551 absolute error = 1.0980380935896198e-15 relative error = 6.9923505015024424711920000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7951 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.797 y[1] (analytic) = 1.574284999110528975502551128841 y[1] (numeric) = 1.5742849991105278652740509802008 absolute error = 1.1102285001486402e-15 relative error = 7.0522713535091759280180000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7941 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.796 y[1] (analytic) = 1.578242973662281255523850407818 y[1] (numeric) = 1.5782429736622801329820060713674 absolute error = 1.1225418443364506e-15 relative error = 7.1126047324108448336959999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7931 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.795 y[1] (analytic) = 1.5822158933586487876270717139353 y[1] (numeric) = 1.5822158933586476526475490271762 absolute error = 1.1349795226867591e-15 relative error = 7.1733543282609892017750000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7921 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.794 y[1] (analytic) = 1.5862038335374248932484820029314 y[1] (numeric) = 1.5862038335374237457055326205142 absolute error = 1.1475429493824172e-15 relative error = 7.2345238683685356989919999999996e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7911 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.793 y[1] (analytic) = 1.5902068700117198246319863751076 y[1] (numeric) = 1.5902068700117186643984298740273 absolute error = 1.1602335565010803e-15 relative error = 7.2961171177214784557469999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7901 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.792 y[1] (analytic) = 1.5942250790735639220487705336191 y[1] (numeric) = 1.5942250790735627489959762690137 absolute error = 1.1730527942646054e-15 relative error = 7.3581378794159344162559999999996e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7891 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.791 y[1] (analytic) = 1.5982585374975426774985975281334 y[1] (numeric) = 1.5982585374975414914964662358897 absolute error = 1.1860021312922437e-15 relative error = 7.4205899950906233045969999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7881 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = 1.6023073225444640282006088767825 y[1] (numeric) = 1.6023073225444628291175540190894 absolute error = 1.1990830548576931e-15 relative error = 7.4834773453668626371000000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7871 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.789 y[1] (analytic) = 1.6063715119650582068717360538842 y[1] (numeric) = 1.6063715119650569945746649038098 absolute error = 1.2122970711500744e-15 relative error = 7.5468038502941546556239999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7861 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.788 y[1] (analytic) = 1.6104511840037104795279445489448 y[1] (numeric) = 1.6104511840037092538822390100514 absolute error = 1.2256457055388934e-15 relative error = 7.6105734698014262336960000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7851 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.787 y[1] (analytic) = 1.6145464174022271053281646320691 y[1] (numeric) = 1.6145464174022258661976617890088 absolute error = 1.2391305028430603e-15 relative error = 7.6747902041540341495070000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7841 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.786 y[1] (analytic) = 1.6186572914036348568135760024345 y[1] (numeric) = 1.6186572914036336040605483984069 absolute error = 1.2527530276040276e-15 relative error = 7.7394580944165783516959999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7831 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.785 y[1] (analytic) = 1.6227838857560144427765832285285 y[1] (numeric) = 1.6227838857560131762617188654088 absolute error = 1.2665148643631197e-15 relative error = 7.8045812229216343713250000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7821 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.784 y[1] (analytic) = 1.6269262807163681799250312369846 y[1] (numeric) = 1.6269262807163668995074132938629 absolute error = 1.2804176179431217e-15 relative error = 7.8701637137444741163520000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7811 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.783 y[1] (analytic) = 1.6310845570545222634886615157017 y[1] (numeric) = 1.6310845570545209690257477815037 absolute error = 1.2944629137341980e-15 relative error = 7.9362097331838571762199999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7801 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.782 y[1] (analytic) = 1.6352587960570639909472073050281 y[1] (numeric) = 1.6352587960570626822948093208133 absolute error = 1.3086523979842148e-15 relative error = 8.0027234902489897135520000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7791 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.781 y[1] (analytic) = 1.6394490795313142971435878687326 y[1] (numeric) = 1.6394490795313129741558497751938 absolute error = 1.3229877380935388e-15 relative error = 8.0697092371527301998680000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7781 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = 1.6436554898093359631821170282709 y[1] (numeric) = 1.6436554898093346257114941138844 absolute error = 1.3374706229143865e-15 relative error = 8.1371712698111274659999999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7771 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.779 y[1] (analytic) = 1.6478781097519778657012298114332 y[1] (numeric) = 1.6478781097519765135984667566319 absolute error = 1.3521027630548013e-15 relative error = 8.2051139283493867569330000000005e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7761 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.778 y[1] (analytic) = 1.6521170227529556373537050376352 y[1] (numeric) = 1.6521170227529542704678138502985 absolute error = 1.3668858911873367e-15 relative error = 8.2735415976143590712280000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7752 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.777 y[1] (analytic) = 1.656372312742969113625484281855 y[1] (numeric) = 1.6563723127429677318037219193338 absolute error = 1.3818217623625212e-15 relative error = 8.3424587076936256155479999999997e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7742 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.776 y[1] (analytic) = 1.6606440641938569454777340843872 y[1] (numeric) = 1.6606440641938555485655797571975 absolute error = 1.3969121543271897e-15 relative error = 8.4118697344412978478720000000004e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7732 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.775 y[1] (analytic) = 1.6649323621227887617065556711759 y[1] (numeric) = 1.6649323621227873495476878234144 absolute error = 1.4121588678477615e-15 relative error = 8.4817792000106175093749999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7722 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.774 y[1] (analytic) = 1.6692372920964952693815141985324 y[1] (numeric) = 1.6692372920964938418177871599869 absolute error = 1.4275637270385455e-15 relative error = 8.5521916733934368395800000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7712 Order of pole = 225.1 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.2MB, time=1.47 x[1] = -0.773 y[1] (analytic) = 1.6735589402355366852487494330819 y[1] (numeric) = 1.6735589402355352421201697379185 absolute error = 1.4431285796951634e-15 relative error = 8.6231117709667129123860000000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.5888 Order of pole = 1.095e-27 TOP MAIN SOLVE Loop x[1] = -0.772 y[1] (analytic) = 1.6778973932186098955676662460737 y[1] (numeric) = 1.6778973932186084367123686129026 absolute error = 1.4588552976331711e-15 relative error = 8.6945441570460784486240000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7692 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.771 y[1] (analytic) = 1.6822527382868947464929236038564 y[1] (numeric) = 1.6822527382868932717471465718854 absolute error = 1.4747457770319710e-15 relative error = 8.7664935444466187321100000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7682 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = 1.6866250632484398718164951931186 y[1] (numeric) = 1.6866250632484383810145564090166 absolute error = 1.4908019387841020e-15 relative error = 8.8389646950509407579999999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7672 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.769 y[1] (analytic) = 1.6910144564825884696488270278222 y[1] (numeric) = 1.6910144564825869626230981778224 absolute error = 1.5070257288499998e-15 relative error = 8.9119624203846473172780000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7662 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.768 y[1] (analytic) = 1.6954210069444444444444444444444 y[1] (numeric) = 1.6954210069444429210253258261238 absolute error = 1.5234191186183206e-15 relative error = 8.9854915821993232957440000000002e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7652 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.767 y[1] (analytic) = 1.6998448041693793356666536345232 y[1] (numeric) = 1.6998448041693777956825483626025 absolute error = 1.5399841052719207e-15 relative error = 9.0595570930631295668229999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7642 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.766 y[1] (analytic) = 1.7042859382775804593391460845735 y[1] (numeric) = 1.7042859382775789026164339249819 absolute error = 1.5567227121595916e-15 relative error = 9.1341639169591332884959999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7632 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.765 y[1] (analytic) = 1.7087444999786406937502669913281 y[1] (numeric) = 1.7087444999786391201132778176819 absolute error = 1.5736369891736462e-15 relative error = 9.2093170698914709739500000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7622 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.764 y[1] (analytic) = 1.7132205805761903456593843370522 y[1] (numeric) = 1.713220580576188754930371203595 absolute error = 1.5907290131334572e-15 relative error = 9.2850216204994643381119999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7612 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.763 y[1] (analytic) = 1.7177142719725715385051419776731 y[1] (numeric) = 1.7177142719725699305042538026246 absolute error = 1.6080008881750485e-15 relative error = 9.3612826906797981019650000000003e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7602 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.762 y[1] (analytic) = 1.722225666673555569333360888944 y[1] (numeric) = 1.7222256666735539438786147420986 absolute error = 1.6254547461468454e-15 relative error = 9.4381054562168890043760000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7592 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.761 y[1] (analytic) = 1.7267548577931036864489459024971 y[1] (numeric) = 1.7267548577931020433561988908116 absolute error = 1.6430927470116855e-15 relative error = 9.5154951474215431844549999999998e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7582 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (analytic) = 1.7313019390581717451523545706371 y[1] (numeric) = 1.7313019390581700842352753154352 absolute error = 1.6609170792552019e-15 relative error = 9.5934570497780461744000000000001e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.2564 Order of pole = 1.536e-28 TOP MAIN SOLVE Loop x[1] = -0.759 y[1] (analytic) = 1.735867004813559204347999673657 y[1] (numeric) = 1.7358670048135575254180393729714 absolute error = 1.6789299603006856e-15 relative error = 9.6719965045997926113360000000000e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7562 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.758 y[1] (analytic) = 1.7404501500268029323104127651575 y[1] (numeric) = 1.7404501500268012351767758346187 absolute error = 1.6971336369305388e-15 relative error = 9.7511189096935809508320000000004e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7552 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.757 y[1] (analytic) = 1.7450514702931162954651347441493 y[1] (numeric) = 1.745051470293114579934749029715 absolute error = 1.7155303857144343e-15 relative error = 9.8308297200327086118069999999999e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7542 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.756 y[1] (analytic) = 1.7496710618403740096861789983483 y[1] (numeric) = 1.749671061840372275563665554054 absolute error = 1.7341225134442943e-15 relative error = 9.9111344484389818704480000000001e-14 % Correct digits = 15 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7532 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.755 y[1] (analytic) = 1.7543090215341432393316082627955 y[1] (numeric) = 1.7543090215341414864192506865864 absolute error = 1.7529123575762091e-15 relative error = 9.9920386662737859222750000000000e-14 % Correct digits = 15 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.1886 Order of pole = 7.63e-29 TOP MAIN SOLVE Loop x[1] = -0.754 y[1] (analytic) = 1.7589654468827614350343701848321 y[1] (numeric) = 1.7589654468827596631320835054184 absolute error = 1.7719022866794137e-15 relative error = 1.0073548004138335590692000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7512 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.753 y[1] (analytic) = 1.7636404360424614071381583008382 y[1] (numeric) = 1.7636404360424596160434574083928 absolute error = 1.7910947008924454e-15 relative error = 1.0155668152583245738086000000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.4195 Order of pole = 4.858e-28 TOP MAIN SOLVE Loop x[1] = -0.752 y[1] (analytic) = 1.7683340878225441376188320507017 y[1] (numeric) = 1.7683340878225423271267996640942 absolute error = 1.8104920323866075e-15 relative error = 1.0238404862827560876800000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7492 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.751 y[1] (analytic) = 1.7730465016905998393619869468317 y[1] (numeric) = 1.7730465016905980092652411099671 absolute error = 1.8300967458368646e-15 relative error = 1.0321763947487374712646000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7482 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (analytic) = 1.7777777777777777777777777777777 y[1] (numeric) = 1.7777777777777759278664388774772 absolute error = 1.8499113389003005e-15 relative error = 1.0405751281314190312500000000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.4637 Order of pole = 2.366e-28 TOP MAIN SOLVE Loop x[1] = -0.749 y[1] (analytic) = 1.7825280168841053759262461207734 y[1] (numeric) = 1.7825280168841035059879034185038 absolute error = 1.8699383427022696e-15 relative error = 1.0490372801943159478696000000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.233 Order of pole = 2.083e-28 TOP MAIN SOLVE Loop x[1] = -0.748 y[1] (analytic) = 1.7872973204838571306013898023964 y[1] (numeric) = 1.7872973204838552404210674720216 absolute error = 1.8901803223303748e-15 relative error = 1.0575634510651340220992000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7453 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.747 y[1] (analytic) = 1.7920857907309738731812569331319 y[1] (numeric) = 1.7920857907309719625413795967204 absolute error = 1.9106398773364115e-15 relative error = 1.0661542473126136447035000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7443 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.746 y[1] (analytic) = 1.7968935304645329154956910493139 y[1] (numeric) = 1.7968935304645309841760488028995 absolute error = 1.9313196422464144e-15 relative error = 1.0748102820244055562304000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7433 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.745 y[1] (analytic) = 1.8017206432142696274942570154498 y[1] (numeric) = 1.8017206432142676752719699364998 absolute error = 1.9522222870789500e-15 relative error = 1.0835321748859942237500000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7423 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.744 y[1] (analytic) = 1.8065672332061510001156203029251 y[1] (numeric) = 1.8065672332061490267651024311261 absolute error = 1.9733505178717990e-15 relative error = 1.0923205522606841312640000000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7413 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.743 y[1] (analytic) = 1.8114334053680017534675363962257 y[1] (numeric) = 1.8114334053679997587604591790477 absolute error = 1.9947070772171780e-15 relative error = 1.1011760472706658977220000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7403 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.742 y[1] (analytic) = 1.8163192653351835572249547736503 y[1] (numeric) = 1.8163192653351815409302099680041 absolute error = 2.0162947448056462e-15 relative error = 1.1100992998791757944568000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7393 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.741 y[1] (analytic) = 1.8212249194563279370438969842336 y[1] (numeric) = 1.8212249194563258989275590053782 absolute error = 2.0381163379788554e-15 relative error = 1.1190909569737679018874000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7383 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (analytic) = 1.8261504747991234477720964207451 y[1] (numeric) = 1.82615047479912138759738412945 absolute error = 2.0601747122912951e-15 relative error = 1.1281516724507131967600000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7373 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.739 y[1] (analytic) = 1.8310960391561577013152762849258 y[1] (numeric) = 1.8310960391561556188425142037327 absolute error = 2.0824727620811931e-15 relative error = 1.1372821073005432569651000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7363 Order of pole = 225.1 memory used=30.5MB, alloc=4.2MB, time=1.69 TOP MAIN SOLVE Loop x[1] = -0.738 y[1] (analytic) = 1.8360617210508148441918023516279 y[1] (numeric) = 1.8360617210508127391783813008933 absolute error = 2.1050134210507346e-15 relative error = 1.1464829296947562954824000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7353 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.737 y[1] (analytic) = 1.841047629743229087079711839225 y[1] (numeric) = 1.8410476297432269592800489834635 absolute error = 2.1277996628557615e-15 relative error = 1.1557548150737011181935000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7343 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.736 y[1] (analytic) = 1.8460538752362948960302457466918 y[1] (numeric) = 1.8460538752362927451957440415674 absolute error = 2.1508345017051244e-15 relative error = 1.1650984462356590669824000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7333 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.735 y[1] (analytic) = 1.8510805682817344624924799851913 y[1] (numeric) = 1.8510805682817322883714870153365 absolute error = 2.1741209929698548e-15 relative error = 1.1745145134271398093300000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7323 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.734 y[1] (analytic) = 1.8561278203862230768659652978343 y[1] (numeric) = 1.8561278203862208792037314955007 absolute error = 2.1976622338023336e-15 relative error = 1.1840037144344100410016000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7313 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.733 y[1] (analytic) = 1.86119574381757303797397676111 y[1] (numeric) = 1.8611957438175708165126129954753 absolute error = 2.2214613637656347e-15 relative error = 1.1935667546762741023283000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7303 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.732 y[1] (analytic) = 1.8662844516109767386305951207859 y[1] (numeric) = 1.8662844516109744931090296475625 absolute error = 2.2455215654732234e-15 relative error = 1.2032043472981244550816000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7293 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.731 y[1] (analytic) = 1.8713940575753095753619743955865 y[1] (numeric) = 1.8713940575753073055159091563903 absolute error = 2.2698460652391962e-15 relative error = 1.2129172132672821206282000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7283 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (analytic) = 1.8765246762994933383373991367986 y[1] (numeric) = 1.8765246762994910438992653975507 absolute error = 2.2944381337392479e-15 relative error = 1.2227060814696452059100000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7273 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.729 y[1] (analytic) = 1.8816764231589207456707329694171 y[1] (numeric) = 1.8816764231589184263696462868556 absolute error = 2.3193010866825615e-15 relative error = 1.2325716888076671661215000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7263 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.728 y[1] (analytic) = 1.8868494143219417944692669967396 y[1] (numeric) = 1.8868494143219394500309815019263 absolute error = 2.3444382854948133e-15 relative error = 1.2425147802996831319872000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7253 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.727 y[1] (analytic) = 1.8920437667564126093364791714362 y[1] (numeric) = 1.8920437667564102394833411589415 absolute error = 2.3698531380124947e-15 relative error = 1.2525361091806058112963000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7243 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.726 y[1] (analytic) = 1.897259598236307477479528568935 y[1] (numeric) = 1.8972595982363050819304293801809 absolute error = 2.3955490991887541e-15 relative error = 1.2626364370040117560116000000000e-13 % Correct digits = 14 h = 0.001 Complex estimate of poles used for equation 1 Radius of convergence = 0.6403 Order of pole = 3.008e-28 TOP MAIN SOLVE Loop x[1] = -0.725 y[1] (analytic) = 1.9024970273483947681331747919143 y[1] (numeric) = 1.9024970273483923466035029809494 absolute error = 2.4215296718109649e-15 relative error = 1.2728165337456384255625000000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7223 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.724 y[1] (analytic) = 1.9077561734989774426910045480907 y[1] (numeric) = 1.9077561734989749948925973178585 absolute error = 2.4477984072302322e-15 relative error = 1.2830771779083141936672000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7213 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.723 y[1] (analytic) = 1.9130371569206988707341662697115 y[1] (numeric) = 1.9130371569206963963752601666586 absolute error = 2.4743589061030529e-15 relative error = 1.2934191566283427393641000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7204 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.722 y[1] (analytic) = 1.918340098679414676069090936994 y[1] (numeric) = 1.9183400986794121748542717916442 absolute error = 2.5012148191453498e-15 relative error = 1.3038432657833645251432000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7194 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.721 y[1] (analytic) = 1.9236651206811313459307749869671 y[1] (numeric) = 1.9236651206811288175609270878642 absolute error = 2.5283698478991029e-15 relative error = 1.3143503101017175506389000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7184 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (analytic) = 1.929012345679012345679012345679 y[1] (numeric) = 1.9290123456790097898512668338731 absolute error = 2.5558277455118059e-15 relative error = 1.3249411032733201785600000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7174 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.719 y[1] (analytic) = 1.9343818972804524906134118434466 y[1] (numeric) = 1.9343818972804499070210943144653 absolute error = 2.5835923175289813e-15 relative error = 1.3356164680620997018293000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7164 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.718 y[1] (analytic) = 1.9397738999542213359610803764713 y[1] (numeric) = 1.9397738999542187242936576764792 absolute error = 2.6116674226999921e-15 relative error = 1.3463772364199907273604000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7154 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.717 y[1] (analytic) = 1.9451884790376763556504807533326 y[1] (numeric) = 1.9451884790376737155935069559425 absolute error = 2.6400569737973901e-15 relative error = 1.3572242496025264791189000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7144 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.716 y[1] (analytic) = 1.9506257607440466901782091695015 y[1] (numeric) = 1.9506257607440440214132707194523 absolute error = 2.6687649384500492e-15 relative error = 1.3681583582860484226752000000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7134 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.715 y[1] (analytic) = 1.9560858721697882537043376204215 y[1] (numeric) = 1.9560858721697855559089976300859 absolute error = 2.6977953399903356e-15 relative error = 1.3791804226865593171100000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7124 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.714 y[1] (analytic) = 1.9615689413020110004786228216777 y[1] (numeric) = 1.961568941302008273326364506109 absolute error = 2.7271522583155687e-15 relative error = 1.3902913126802436609852000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7114 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.713 y[1] (analytic) = 1.9670750970259791608064221067767 y[1] (numeric) = 1.9670750970259764039665913427386 absolute error = 2.7568398307640381e-15 relative error = 1.4014919079256832848589000000001e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7104 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.712 y[1] (analytic) = 1.9726044691326852670117409418003 y[1] (numeric) = 1.9726044691326824801494879359593 absolute error = 2.7868622530058410e-15 relative error = 1.4127830979877930599040000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7094 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.711 y[1] (analytic) = 1.9781571883264988002476652799785 y[1] (numeric) = 1.9781571883264959830238853311667 absolute error = 2.8172237799488118e-15 relative error = 1.4241657824635032899478000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7084 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (analytic) = 1.9837333862328902995437413211665 y[1] (numeric) = 1.9837333862328874516150146613432 absolute error = 2.8479287266598233e-15 relative error = 1.4356408711092169255300000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7074 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.709 y[1] (analytic) = 1.9893331954062317851679295616903 y[1] (numeric) = 1.9893331954062289061864602599496 absolute error = 2.8789814693017407e-15 relative error = 1.4472092839700683168166999999999e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7064 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.708 y[1] (analytic) = 1.994956749337674359219892112739 y[1] (numeric) = 1.9949567493376714488334460264219 absolute error = 2.9103864460863171e-15 relative error = 1.4588719515110116548144000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7054 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.707 y[1] (analytic) = 2.0006041824631038573649242071106 y[1] (numeric) = 2.0006041824631009152167659637845 absolute error = 2.9421481582433261e-15 relative error = 1.4706298147497683077589000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7044 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.706 y[1] (analytic) = 2.0062756301711754367662046882649 y[1] (numeric) = 2.0062756301711724624950336820355 absolute error = 2.9742711710062294e-15 relative error = 1.4824838253916609572184000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7034 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.705 y[1] (analytic) = 2.0119712288114279965796489110206 y[1] (numeric) = 2.0119712288114249898195342963325 absolute error = 3.0067601146146881e-15 relative error = 1.4944349459663653529025000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7024 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.704 y[1] (analytic) = 2.0176911157024793388429752066115 y[1] (numeric) = 2.0176911157024762992232898723844 absolute error = 3.0396196853342271e-15 relative error = 1.5064841499666082983936000000001e-13 % Correct digits = 14 h = 0.001 memory used=34.3MB, alloc=4.2MB, time=1.91 Real estimate of pole used for equation 1 Radius of convergence = 0.7014 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.703 y[1] (analytic) = 2.0234354291403029892211594689696 y[1] (numeric) = 2.0234354291402999163665129755953 absolute error = 3.0728546464933743e-15 relative error = 1.5186324219888440194287000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.7004 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.702 y[1] (analytic) = 2.0292043084065876088668111460134 y[1] (numeric) = 2.0292043084065845023969816074179 absolute error = 3.1064698295385955e-15 relative error = 1.5308807578759380167820000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.6994 Order of pole = 225.1 TOP MAIN SOLVE Loop x[1] = -0.701 y[1] (analytic) = 2.0349978937771799406187614595819 y[1] (numeric) = 2.0349978937771768001486263522211 absolute error = 3.1404701351073608e-15 relative error = 1.5432301648618922044808000000000e-13 % Correct digits = 14 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.6984 Order of pole = 225.1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 300 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Time to Timeout = 2 Minutes 58 Seconds Percent Done = 100.3 % > quit memory used=34.7MB, alloc=4.2MB, time=1.93