|\^/| 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.
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> #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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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_1D0, 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_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_1D0,
> #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_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 LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
> #emit pre div CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_1D0[1] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * 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 LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre div CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := -ats(2,array_tmp2,array_tmp3,2) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * 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 LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp1[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre div CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := -ats(3,array_tmp2,array_tmp3,2) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * 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 add FULL CONST $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre div CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := -ats(4,array_tmp2,array_tmp3,2) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * 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 add FULL CONST $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre div CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := -ats(5,array_tmp2,array_tmp3,2) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * 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 LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit div CONST FULL $eq_no = 1 i = 1
> array_tmp3[kkk] := -ats(kkk,array_tmp2,array_tmp3,2) / array_tmp2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp4[kkk] * 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_1D0, 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_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_x[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
array_tmp3[1] := array_const_1D0[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*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] := 2*array_x[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := -ats(2, array_tmp2, array_tmp3, 2)/array_tmp2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[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_x[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := -ats(3, array_tmp2, array_tmp3, 2)/array_tmp2[1];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[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_tmp2[4] := array_tmp1[4];
array_tmp3[4] := -ats(4, array_tmp2, array_tmp3, 2)/array_tmp2[1];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[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_tmp2[5] := array_tmp1[5];
array_tmp3[5] := -ats(5, array_tmp2, array_tmp3, 2)/array_tmp2[1];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[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_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] :=
-ats(kkk, array_tmp2, array_tmp3, 2)/array_tmp2[1];
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp4[kkk]*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(arctan(x));
> end;
exact_soln_y := proc(x) return arctan(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_1D0,
> #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_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/sing2postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -2.0;");
> omniout_str(ALWAYS,"x_end := -1.5;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 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(arctan(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:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= 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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1D0[1] := 1.0;
> 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 := -2.0;
> x_end := -1.5;
> 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;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> if (glob_max_h < glob_h) then # if number 2
> glob_h := glob_max_h;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
> 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,"2013-01-28T19:03:30-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing2")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;")
> ;
> 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,"sing2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing2 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_1D0, 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_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/sing2postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -2.0;");
omniout_str(ALWAYS, "x_end := -1.5;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 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(arctan(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 := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := 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_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := -2.0;
x_end := -1.5;
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;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
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, "2013-01-28T19:03:30-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing2");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;");
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,
"sing2 diffeq.mxt");
logitem_str(html_log_file,
"sing2 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/sing2postode.ode#################
diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.0;
x_end := -1.5;
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(arctan(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.5
estimated_steps = 500
step_error = 2.0000000000000000000000000000000e-13
est_needed_step_err = 2.0000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.5423793205590851374391492714693e-89
max_value3 = 1.5423793205590851374391492714693e-89
value3 = 1.5423793205590851374391492714693e-89
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -2
y[1] (analytic) = -1.1071487177940905030170654601785
y[1] (numeric) = -1.1071487177940905030170654601785
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.236
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -1.999
y[1] (analytic) = -1.106948637764747567059262846648
y[1] (numeric) = -1.106948637764747567059262846648
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.998
y[1] (analytic) = -1.1067483975592701523523682753958
y[1] (numeric) = -1.1067483975592701523523682753957
absolute error = 1e-31
relative error = 9.0354772792562059120416505345611e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.234
Order of pole = 1.81e-28
TOP MAIN SOLVE Loop
x[1] = -1.997
y[1] (analytic) = -1.1065479970013122650430381404474
y[1] (numeric) = -1.1065479970013122650430381404474
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.996
y[1] (analytic) = -1.1063474359142968807862186779712
y[1] (numeric) = -1.1063474359142968807862186779711
absolute error = 1e-31
relative error = 9.0387519104574028519967794944694e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.995
y[1] (analytic) = -1.1061467141214156290212504508558
y[1] (numeric) = -1.1061467141214156290212504508557
absolute error = 1e-31
relative error = 9.0403920857304604426210877964644e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.994
y[1] (analytic) = -1.1059458314456284769108753479934
y[1] (numeric) = -1.1059458314456284769108753479933
absolute error = 1e-31
relative error = 9.0420341717175948049497190083926e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.231
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.993
y[1] (analytic) = -1.105744787709663412943428695263
y[1] (numeric) = -1.1057447877096634129434286952629
absolute error = 1e-31
relative error = 9.0436781716268063971992603060437e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.23
Order of pole = 2.18e-28
TOP MAIN SOLVE Loop
x[1] = -1.992
y[1] (analytic) = -1.1055435827360161301985035103973
y[1] (numeric) = -1.1055435827360161301985035103972
absolute error = 1e-31
relative error = 9.0453240886730556478989646583430e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.991
y[1] (analytic) = -1.1053422163469497092763783943778
y[1] (numeric) = -1.1053422163469497092763783943777
absolute error = 1e-31
relative error = 9.0469719260782813712921493917677e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.228
Order of pole = 8.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (analytic) = -1.1051406883644943008915050378617
y[1] (numeric) = -1.1051406883644943008915050378616
absolute error = 1e-31
relative error = 9.0486216870714192400987702792324e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.989
y[1] (analytic) = -1.1049389986104468081303558325205
y[1] (numeric) = -1.1049389986104468081303558325204
absolute error = 1e-31
relative error = 9.0502733748884203158446404492898e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.226
Order of pole = 1.89e-28
TOP MAIN SOLVE Loop
x[1] = -1.988
y[1] (analytic) = -1.1047371469063705683739366141761
y[1] (numeric) = -1.104737146906370568373936614176
absolute error = 1e-31
relative error = 9.0519269927722696369635959928604e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.225
Order of pole = 8.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.987
y[1] (analytic) = -1.1045351330735950348852741273846
y[1] (numeric) = -1.1045351330735950348852741273845
absolute error = 1e-31
relative error = 9.0535825439730048648797464965443e-30 %
Correct digits = 31
h = 0.001
memory used=3.8MB, alloc=2.9MB, time=0.39
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.986
y[1] (analytic) = -1.1043329569332154580621923897538
y[1] (numeric) = -1.1043329569332154580621923897537
absolute error = 1e-31
relative error = 9.0552400317477349882777888728361e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.985
y[1] (analytic) = -1.1041306183060925663556967489111
y[1] (numeric) = -1.104130618306092566355696748911
absolute error = 1e-31
relative error = 9.0568994593606590857702068072494e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.984
y[1] (analytic) = -1.103928117012852246854289065787
y[1] (numeric) = -1.1039281170128522468542890657869
absolute error = 1e-31
relative error = 9.0585608300830851471710259195647e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.983
y[1] (analytic) = -1.1037254528738852255345421248616
y[1] (numeric) = -1.1037254528738852255345421248615
absolute error = 1e-31
relative error = 9.0602241471934489535866463604083e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.221
Order of pole = 2.46e-28
TOP MAIN SOLVE Loop
x[1] = -1.982
y[1] (analytic) = -1.1035226257093467471782660653698
y[1] (numeric) = -1.1035226257093467471782660653697
absolute error = 1e-31
relative error = 9.0618894139773330165351300543921e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.981
y[1] (analytic) = -1.1033196353391562549566043472836
y[1] (numeric) = -1.1033196353391562549566043472834
absolute error = 2e-31
relative error = 1.8127113267454971152612358353300e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.219
Order of pole = 1.20e-28
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (analytic) = -1.103116481582997069681401512326
y[1] (numeric) = -1.1031164815829970696814015123258
absolute error = 2e-31
relative error = 1.8130451619487679319549811460408e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.979
y[1] (analytic) = -1.1029131642603160687241897734317
y[1] (numeric) = -1.1029131642603160687241897734315
absolute error = 2e-31
relative error = 1.8133793890667064395766718593860e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.978
y[1] (analytic) = -1.1027096831903233646031462660842
y[1] (numeric) = -1.102709683190323364603146266084
absolute error = 2e-31
relative error = 1.8137140087621846406009302369409e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.216
Order of pole = 1.36e-28
TOP MAIN SOLVE Loop
x[1] = -1.977
y[1] (analytic) = -1.1025060381919919832383776219549
y[1] (numeric) = -1.1025060381919919832383776219547
absolute error = 2e-31
relative error = 1.8140490216995230012810776614791e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.976
y[1] (analytic) = -1.1023022290840575418758933793661
y[1] (numeric) = -1.1023022290840575418758933793659
absolute error = 2e-31
relative error = 1.8143844285444943112046018465636e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.215
Order of pole = 1.32e-28
TOP MAIN SOLVE Loop
x[1] = -1.975
y[1] (analytic) = -1.1020982556850179266806346264257
y[1] (numeric) = -1.1020982556850179266806346264256
absolute error = 1e-31
relative error = 9.0736011498216377747754979365750e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.974
y[1] (analytic) = -1.1018941178131329699989291813655
y[1] (numeric) = -1.1018941178131329699989291813653
absolute error = 2e-31
relative error = 1.8150564266277117959243675854204e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.213
Order of pole = 1.49e-28
TOP MAIN SOLVE Loop
x[1] = -1.973
y[1] (analytic) = -1.1016898152864241272907495507763
y[1] (numeric) = -1.1016898152864241272907495507761
absolute error = 2e-31
relative error = 1.8153930192048000723184921159141e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.212
Order of pole = 2.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.972
y[1] (analytic) = -1.1014853479226741537321548702117
y[1] (numeric) = -1.1014853479226741537321548702116
absolute error = 1e-31
relative error = 9.0786500418360665270098367538807e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.971
y[1] (analytic) = -1.1012807155394267804883030231387
y[1] (numeric) = -1.1012807155394267804883030231386
absolute error = 1e-31
relative error = 9.0803369739402211001202600955206e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.21
Order of pole = 6.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (analytic) = -1.1010759179539863906574241535935
y[1] (numeric) = -1.1010759179539863906574241535935
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.969
y[1] (analytic) = -1.1008709549834176948861518352737
y[1] (numeric) = -1.1008709549834176948861518352737
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.968
y[1] (analytic) = -1.1006658264445454066566132352894
y[1] (numeric) = -1.1006658264445454066566132352894
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.207
Order of pole = 2.22e-28
TOP MAIN SOLVE Loop
x[1] = -1.967
y[1] (analytic) = -1.1004605321539539172456847145512
y[1] (numeric) = -1.1004605321539539172456847145512
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.966
y[1] (analytic) = -1.1002550719279869703568244389027
y[1] (numeric) = -1.1002550719279869703568244389027
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.965
y[1] (analytic) = -1.1000494455827473364248987357562
y[1] (numeric) = -1.1000494455827473364248987357562
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.205
Order of pole = 1.30e-28
TOP MAIN SOLVE Loop
x[1] = -1.964
y[1] (analytic) = -1.0998436529340964865944241202885
y[1] (numeric) = -1.0998436529340964865944241202884
absolute error = 1e-31
relative error = 9.0922013991012302698553316089919e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.963
y[1] (analytic) = -1.0996376937976542663716521333248
y[1] (numeric) = -1.0996376937976542663716521333247
absolute error = 1e-31
relative error = 9.0939043435883826168198000358170e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=0.87
x[1] = -1.962
y[1] (analytic) = -1.0994315679887985689509293800305
y[1] (numeric) = -1.0994315679887985689509293800304
absolute error = 1e-31
relative error = 9.0956093049912169162666286652321e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.961
y[1] (analytic) = -1.0992252753226650082157704345585
y[1] (numeric) = -1.0992252753226650082157704345583
absolute error = 2e-31
relative error = 1.8194632573499757573522657907884e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (analytic) = -1.0990188156141465914150865810103
y[1] (numeric) = -1.0990188156141465914150865810101
absolute error = 2e-31
relative error = 1.8198050584624185222028007802136e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.2
Order of pole = 3.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.959
y[1] (analytic) = -1.0988121886778933915150186955938
y[1] (numeric) = -1.0988121886778933915150186955936
absolute error = 2e-31
relative error = 1.8201472650266363786040457441318e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.958
y[1] (analytic) = -1.0986053943283122192268279388266
y[1] (numeric) = -1.0986053943283122192268279388265
absolute error = 1e-31
relative error = 9.1024493886760896795704879744568e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.199
Order of pole = 3.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.957
y[1] (analytic) = -1.0983984323795662947113033201895
y[1] (numeric) = -1.0983984323795662947113033201894
absolute error = 1e-31
relative error = 9.1041644864113990463622488837287e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.198
Order of pole = 6.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.956
y[1] (analytic) = -1.0981913026455749189601506209025
y[1] (numeric) = -1.0981913026455749189601506209023
absolute error = 2e-31
relative error = 1.8211763243634707297899427387834e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.197
Order of pole = 3.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.955
y[1] (analytic) = -1.0979840049400131448548326136238
y[1] (numeric) = -1.0979840049400131448548326136236
absolute error = 2e-31
relative error = 1.8215201596759756677534523102427e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.196
Order of pole = 1.4e-29
TOP MAIN SOLVE Loop
x[1] = -1.954
y[1] (analytic) = -1.0977765390763114479033360009882
y[1] (numeric) = -1.0977765390763114479033360009881
absolute error = 1e-31
relative error = 9.1093220195925998444635623885240e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.195
Order of pole = 7.6e-29
TOP MAIN SOLVE Loop
x[1] = -1.953
y[1] (analytic) = -1.0975689048676553966553460081481
y[1] (numeric) = -1.097568904867655396655346008148
absolute error = 1e-31
relative error = 9.1110452889568675187843218323314e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.952
y[1] (analytic) = -1.0973611021269853227963151079938
y[1] (numeric) = -1.0973611021269853227963151079937
absolute error = 1e-31
relative error = 9.1127706099817741512425971545534e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.951
y[1] (analytic) = -1.0971531306669959909209179316523
y[1] (numeric) = -1.0971531306669959909209179316522
absolute error = 1e-31
relative error = 9.1144979861841768468166098275057e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (analytic) = -1.0969449903001362679863900213251
y[1] (numeric) = -1.096944990300136267986390021325
absolute error = 1e-31
relative error = 9.1162274210887179709159703187133e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.949
y[1] (analytic) = -1.0967366808386087924462537176792
y[1] (numeric) = -1.0967366808386087924462537176791
absolute error = 1e-31
relative error = 9.1179589182278461608582254086509e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.948
y[1] (analytic) = -1.0965282020943696430649401399777
y[1] (numeric) = -1.0965282020943696430649401399776
absolute error = 1e-31
relative error = 9.1196924811418374040986375519891e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.19
Order of pole = 1.60e-28
TOP MAIN SOLVE Loop
x[1] = -1.947
y[1] (analytic) = -1.0963195538791280074138219140809
y[1] (numeric) = -1.0963195538791280074138219140807
absolute error = 2e-31
relative error = 1.8242856226757632366914219309903e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.189
Order of pole = 2.66e-28
TOP MAIN SOLVE Loop
x[1] = -1.946
y[1] (analytic) = -1.0961107360043458500491770314935
y[1] (numeric) = -1.0961107360043458500491770314934
absolute error = 1e-31
relative error = 9.1231658184947766895871771316607e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.188
Order of pole = 1.61e-28
TOP MAIN SOLVE Loop
x[1] = -1.945
y[1] (analytic) = -1.095901748281237580372609981937
y[1] (numeric) = -1.0959017482812375803726099819368
absolute error = 2e-31
relative error = 1.8249811200107208201866004508942e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.187
Order of pole = 2.48e-28
TOP MAIN SOLVE Loop
x[1] = -1.944
y[1] (analytic) = -1.0956925905207697201744620926103
y[1] (numeric) = -1.0956925905207697201744620926102
absolute error = 1e-31
relative error = 9.1266474616270959314213236512886e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.943
y[1] (analytic) = -1.0954832625336605708607488295345
y[1] (numeric) = -1.0954832625336605708607488295344
absolute error = 1e-31
relative error = 9.1283914067949834461363363505802e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.185
Order of pole = 1.42e-28
TOP MAIN SOLVE Loop
x[1] = -1.942
y[1] (analytic) = -1.0952737641303798803641676702742
y[1] (numeric) = -1.0952737641303798803641676702741
absolute error = 1e-31
relative error = 9.1301374391449531452265050565231e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.184
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.941
y[1] (analytic) = -1.0950640951211485097397260430628
y[1] (numeric) = -1.0950640951211485097397260430627
absolute error = 1e-31
relative error = 9.1318855622726683162933453765985e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.183
Order of pole = 1.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (analytic) = -1.094854255315938099445544745049
y[1] (numeric) = -1.0948542553159380994455447450489
absolute error = 1e-31
relative error = 9.1336357797817906555132445465154e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.183
Order of pole = 5.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.939
y[1] (analytic) = -1.0946442445244707353093982021949
y[1] (numeric) = -1.0946442445244707353093982021948
absolute error = 1e-31
relative error = 9.1353880952840019577444348270348e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.182
Order of pole = 2.67e-28
TOP MAIN SOLVE Loop
x[1] = -1.938
y[1] (analytic) = -1.0944340625562186141815589154218
y[1] (numeric) = -1.0944340625562186141815589154217
absolute error = 1e-31
relative error = 9.1371425123990258758722792088744e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.181
Order of pole = 1.02e-28
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=1.33
x[1] = -1.937
y[1] (analytic) = -1.0942237092204037092745194520772
y[1] (numeric) = -1.0942237092204037092745194520771
absolute error = 1e-31
relative error = 9.1388990347546497496470803801347e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.936
y[1] (analytic) = -1.0940131843259974351901713888221
y[1] (numeric) = -1.094013184325997435190171388822
absolute error = 1e-31
relative error = 9.1406576659867465042696801106602e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.935
y[1] (analytic) = -1.0938024876817203126350266917691
y[1] (numeric) = -1.093802487681720312635026691769
absolute error = 1e-31
relative error = 9.1424184097392966189811773144578e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.934
y[1] (analytic) = -1.0935916190960416328240731322788
y[1] (numeric) = -1.0935916190960416328240731322787
absolute error = 1e-31
relative error = 9.1441812696644101659141590900677e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.177
Order of pole = 1.68e-28
TOP MAIN SOLVE Loop
x[1] = -1.933
y[1] (analytic) = -1.0933805783771791215738614824
y[1] (numeric) = -1.0933805783771791215738614823999
absolute error = 1e-31
relative error = 9.1459462494223489194639100349531e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.932
y[1] (analytic) = -1.093169365333098603085428412664
y[1] (numeric) = -1.093169365333098603085428412664
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.175
Order of pole = 7.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.931
y[1] (analytic) = -1.0929579797715136634176652269667
y[1] (numeric) = -1.0929579797715136634176652269666
absolute error = 1e-31
relative error = 9.1494825831186408072528603110266e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (analytic) = -1.0927464214998853136517488147424
y[1] (numeric) = -1.0927464214998853136517488147423
absolute error = 1e-31
relative error = 9.1512539444184759784150934509128e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.174
Order of pole = 3.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.929
y[1] (analytic) = -1.0925346903254216527472574797095
y[1] (numeric) = -1.0925346903254216527472574797094
absolute error = 1e-31
relative error = 9.1530274402741451465902543897967e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.928
y[1] (analytic) = -1.0923227860550775300906006172872
y[1] (numeric) = -1.0923227860550775300906006172871
absolute error = 1e-31
relative error = 9.1548030743870027244830602811850e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.172
Order of pole = 8.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.927
y[1] (analytic) = -1.0921107084955542077363975595155
y[1] (numeric) = -1.0921107084955542077363975595155
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.171
Order of pole = 8.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.926
y[1] (analytic) = -1.0918984574532990223424472870959
y[1] (numeric) = -1.0918984574532990223424472870958
absolute error = 1e-31
relative error = 9.1583607722311526406783794450876e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.925
y[1] (analytic) = -1.0916860327345050467989371231669
y[1] (numeric) = -1.0916860327345050467989371231669
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.169
Order of pole = 1.34e-28
TOP MAIN SOLVE Loop
x[1] = -1.924
y[1] (analytic) = -1.0914734341451107515525449727968
y[1] (numeric) = -1.0914734341451107515525449727968
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.923
y[1] (analytic) = -1.0912606614907996656260961560552
y[1] (numeric) = -1.0912606614907996656260961560551
absolute error = 1e-31
relative error = 9.1637134489377992004496602860778e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.167
Order of pole = 1.18e-28
TOP MAIN SOLVE Loop
x[1] = -1.922
y[1] (analytic) = -1.0910477145770000373344424010914
y[1] (numeric) = -1.0910477145770000373344424010914
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.921
y[1] (analytic) = -1.0908345932088844946972371170395
y[1] (numeric) = -1.0908345932088844946972371170395
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (analytic) = -1.0906212971913697055492876549513
y[1] (numeric) = -1.0906212971913697055492876549513
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.165
Order of pole = 6.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.919
y[1] (analytic) = -1.0904078263291160373491718884929
y[1] (numeric) = -1.0904078263291160373491718884929
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.918
y[1] (analytic) = -1.0901941804265272166868131049712
y[1] (numeric) = -1.0901941804265272166868131049712
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.917
y[1] (analytic) = -1.0899803592877499884907138915571
y[1] (numeric) = -1.0899803592877499884907138915571
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.162
Order of pole = 3.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.916
y[1] (analytic) = -1.0897663627166737749355564314937
y[1] (numeric) = -1.0897663627166737749355564314936
absolute error = 1e-31
relative error = 9.1762788264734506583807129225455e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.161
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -1.915
y[1] (analytic) = -1.0895521905169303340508833907792
y[1] (numeric) = -1.0895521905169303340508833907791
absolute error = 1e-31
relative error = 9.1780825985541552593114430261943e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.16
Order of pole = 2.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.914
y[1] (analytic) = -1.0893378424918934180315803774641
y[1] (numeric) = -1.089337842491893418031580377464
absolute error = 1e-31
relative error = 9.1798885615914123713052762040903e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.913
y[1] (analytic) = -1.089123318444678431250887793451
y[1] (numeric) = -1.0891233184446784312508877934509
absolute error = 1e-31
relative error = 9.1816967194132717178587516586951e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.159
Order of pole = 6.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.912
memory used=15.2MB, alloc=4.2MB, time=1.81
y[1] (analytic) = -1.088908618178142087976676772703
y[1] (numeric) = -1.088908618178142087976676772703
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.911
y[1] (analytic) = -1.0886937414948820697917308102142
y[1] (numeric) = -1.0886937414948820697917308102142
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.157
Order of pole = 1.53e-28
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (analytic) = -1.0884786881972366827187816331298
y[1] (numeric) = -1.0884786881972366827187816331298
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.156
Order of pole = 1.28e-28
TOP MAIN SOLVE Loop
x[1] = -1.909
y[1] (analytic) = -1.0882634580872845140510548491992
y[1] (numeric) = -1.0882634580872845140510548491991
absolute error = 1e-31
relative error = 9.1889513754103713041870176103847e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.908
y[1] (analytic) = -1.0880480509668440888890879284541
y[1] (numeric) = -1.088048050966844088889087928454
absolute error = 1e-31
relative error = 9.1907705648789663351824837155424e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.907
y[1] (analytic) = -1.0878324666374735263845901318031
y[1] (numeric) = -1.087832466637473526384590131803
absolute error = 1e-31
relative error = 9.1925919722825830598204883418474e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.153
Order of pole = 9.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.906
y[1] (analytic) = -1.0876167049004701956921210952779
y[1] (numeric) = -1.0876167049004701956921210952778
absolute error = 1e-31
relative error = 9.1944156015102015057258789205689e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.905
y[1] (analytic) = -1.0874007655568703716293719111304
y[1] (numeric) = -1.0874007655568703716293719111304
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.904
y[1] (analytic) = -1.0871846484074488900468397170265
y[1] (numeric) = -1.0871846484074488900468397170265
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.903
y[1] (analytic) = -1.0869683532527188029076940123762
y[1] (numeric) = -1.0869683532527188029076940123762
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.902
y[1] (analytic) = -1.0867518798929310330786401665586
y[1] (numeric) = -1.0867518798929310330786401665585
absolute error = 1e-31
relative error = 9.2017324147488201111130775904820e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.901
y[1] (analytic) = -1.0865352281280740288325928675998
y[1] (numeric) = -1.0865352281280740288325928675998
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (analytic) = -1.0863183977578734180639795819257
y[1] (numeric) = -1.0863183977578734180639795819256
absolute error = 1e-31
relative error = 9.2054042540747552241846705235362e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.147
Order of pole = 4.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.899
y[1] (analytic) = -1.0861013885817916622175014562941
y[1] (numeric) = -1.086101388581791662217501456294
absolute error = 1e-31
relative error = 9.2072435457041350112918090220349e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.898
y[1] (analytic) = -1.0858842003990277099311864921022
y[1] (numeric) = -1.0858842003990277099311864921021
absolute error = 1e-31
relative error = 9.2090850905882228194692844273728e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.897
y[1] (analytic) = -1.085666833008516650394577260115
y[1] (numeric) = -1.0856668330085166503945772601149
absolute error = 1e-31
relative error = 9.2109288926960834390817176372048e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.144
Order of pole = 4e-30
TOP MAIN SOLVE Loop
x[1] = -1.896
y[1] (analytic) = -1.0854492862089293664229029004597
y[1] (numeric) = -1.0854492862089293664229029004597
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.895
y[1] (analytic) = -1.0852315597986721872480926686421
y[1] (numeric) = -1.0852315597986721872480926686421
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.894
y[1] (analytic) = -1.0850136535758865410274958435374
y[1] (numeric) = -1.0850136535758865410274958435373
absolute error = 1e-31
relative error = 9.2164738821884269280400018914311e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.142
Order of pole = 1.94e-28
TOP MAIN SOLVE Loop
x[1] = -1.893
y[1] (analytic) = -1.0847955673384486070711804079716
y[1] (numeric) = -1.0847955673384486070711804079716
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.141
Order of pole = 2.99e-28
TOP MAIN SOLVE Loop
x[1] = -1.892
y[1] (analytic) = -1.0845773008839689677886905468049
y[1] (numeric) = -1.0845773008839689677886905468048
absolute error = 1e-31
relative error = 9.2201819011421733813010714595852e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.891
y[1] (analytic) = -1.0843588540097922603561506815363
y[1] (numeric) = -1.0843588540097922603561506815363
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (analytic) = -1.084140226512996828104611474551
y[1] (numeric) = -1.084140226512996828104611474551
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.138
Order of pole = 3.48e-28
TOP MAIN SOLVE Loop
x[1] = -1.889
y[1] (analytic) = -1.0839214181903943716305409903873
y[1] (numeric) = -1.0839214181903943716305409903873
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.137
Order of pole = 2.89e-28
TOP MAIN SOLVE Loop
x[1] = -1.888
y[1] (analytic) = -1.0837024288385295996293719960113
y[1] (numeric) = -1.0837024288385295996293719960113
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.136
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.887
y[1] (analytic) = -1.0834832582536798794530242172078
y[1] (numeric) = -1.0834832582536798794530242172078
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=2.30
x[1] = -1.886
y[1] (analytic) = -1.0832639062318548873923282440222
y[1] (numeric) = -1.0832639062318548873923282440222
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.135
Order of pole = 1.40e-28
TOP MAIN SOLVE Loop
x[1] = -1.885
y[1] (analytic) = -1.0830443725687962586852856948912
y[1] (numeric) = -1.0830443725687962586852856948912
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.884
y[1] (analytic) = -1.0828246570599772372521082068612
y[1] (numeric) = -1.0828246570599772372521082068612
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.133
Order of pole = 1.84e-28
TOP MAIN SOLVE Loop
x[1] = -1.883
y[1] (analytic) = -1.0826047595006023251579858182959
y[1] (numeric) = -1.0826047595006023251579858182959
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.132
Order of pole = 2.92e-28
TOP MAIN SOLVE Loop
x[1] = -1.882
y[1] (analytic) = -1.0823846796856069318045433508962
y[1] (numeric) = -1.0823846796856069318045433508963
absolute error = 1e-31
relative error = 9.2388595179531120030967885518493e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.881
y[1] (analytic) = -1.0821644174096570228509514798842
y[1] (numeric) = -1.0821644174096570228509514798843
absolute error = 1e-31
relative error = 9.2407399828731071368025313317981e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.13
Order of pole = 5.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (analytic) = -1.0819439724671487688656673050121
y[1] (numeric) = -1.0819439724671487688656673050121
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.129
Order of pole = 1.12e-28
TOP MAIN SOLVE Loop
x[1] = -1.879
y[1] (analytic) = -1.0817233446522081937097874008434
y[1] (numeric) = -1.0817233446522081937097874008434
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.878
y[1] (analytic) = -1.0815025337586908226530045326886
y[1] (numeric) = -1.0815025337586908226530045326886
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.128
Order of pole = 2.44e-28
TOP MAIN SOLVE Loop
x[1] = -1.877
y[1] (analytic) = -1.0812815395801813302231674748537
y[1] (numeric) = -1.0812815395801813302231674748537
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.876
y[1] (analytic) = -1.0810603619099931877904516606612
y[1] (numeric) = -1.0810603619099931877904516606612
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.126
Order of pole = 7.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.875
y[1] (analytic) = -1.0808390005411683108871567292172
y[1] (numeric) = -1.0808390005411683108871567292172
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.125
Order of pole = 9.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.874
y[1] (analytic) = -1.0806174552664767062641554123057
y[1] (numeric) = -1.0806174552664767062641554123057
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.124
Order of pole = 1.68e-28
TOP MAIN SOLVE Loop
x[1] = -1.873
y[1] (analytic) = -1.0803957258784161186850266262912
y[1] (numeric) = -1.0803957258784161186850266262912
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.123
Order of pole = 1.52e-28
TOP MAIN SOLVE Loop
x[1] = -1.872
y[1] (analytic) = -1.0801738121692116774589140986807
y[1] (numeric) = -1.0801738121692116774589140986807
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.871
y[1] (analytic) = -1.0799517139308155427131603672314
y[1] (numeric) = -1.0799517139308155427131603672314
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (analytic) = -1.0797294309549065514067745413803
y[1] (numeric) = -1.0797294309549065514067745413803
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.121
Order of pole = 1.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.869
y[1] (analytic) = -1.0795069630328898630858008115048
y[1] (numeric) = -1.0795069630328898630858008115048
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.868
y[1] (analytic) = -1.0792843099558966053816633312927
y[1] (numeric) = -1.0792843099558966053816633312927
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.119
Order of pole = 3.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.867
y[1] (analytic) = -1.0790614715147835192535717824957
y[1] (numeric) = -1.0790614715147835192535717824957
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.866
y[1] (analytic) = -1.07883844750013260397608065976
y[1] (numeric) = -1.07883844750013260397608065976
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.117
Order of pole = 7.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.865
y[1] (analytic) = -1.0786152377022507618729040862557
y[1] (numeric) = -1.0786152377022507618729040862557
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.864
y[1] (analytic) = -1.0783918419111694427980967886686
y[1] (numeric) = -1.0783918419111694427980967886686
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.863
y[1] (analytic) = -1.0781682599166442883657207229581
y[1] (numeric) = -1.0781682599166442883657207229581
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.114
Order of pole = 1.22e-28
TOP MAIN SOLVE Loop
x[1] = -1.862
y[1] (analytic) = -1.0779444915081547759291257503268
y[1] (numeric) = -1.0779444915081547759291257503268
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.861
y[1] (analytic) = -1.0777205364749038623109817162831
y[1] (numeric) = -1.0777205364749038623109817162831
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.113
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=2.78
x[1] = -1.86
y[1] (analytic) = -1.0774963946058176272852082847049
y[1] (numeric) = -1.0774963946058176272852082847049
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.859
y[1] (analytic) = -1.0772720656895449168119579236318
y[1] (numeric) = -1.0772720656895449168119579236318
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.858
y[1] (analytic) = -1.0770475495144569860268165303173
y[1] (numeric) = -1.0770475495144569860268165303174
absolute error = 1e-31
relative error = 9.2846411511804586976718044742353e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.857
y[1] (analytic) = -1.0768228458686471419853953200687
y[1] (numeric) = -1.0768228458686471419853953200688
absolute error = 1e-31
relative error = 9.2865786033107795344102001548831e-30 %
Correct digits = 31
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.109
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -1.856
y[1] (analytic) = -1.0765979545399303861644967867803
y[1] (numeric) = -1.0765979545399303861644967867804
absolute error = 1e-31
relative error = 9.2885184834605831215698755590492e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.855
y[1] (analytic) = -1.0763728753158430567210467730395
y[1] (numeric) = -1.0763728753158430567210467730397
absolute error = 2e-31
relative error = 1.8580921592000676278365345927323e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.854
y[1] (analytic) = -1.0761476079836424705099939644419
y[1] (numeric) = -1.076147607983642470509993964442
absolute error = 1e-31
relative error = 9.2924055453106585335090153478525e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.853
y[1] (analytic) = -1.0759221523303065648623874465032
y[1] (numeric) = -1.0759221523303065648623874465034
absolute error = 2e-31
relative error = 1.8588705471564664420487561209757e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.106
Order of pole = 1.28e-28
TOP MAIN SOLVE Loop
x[1] = -1.852
y[1] (analytic) = -1.0756965081425335391248523335068
y[1] (numeric) = -1.0756965081425335391248523335069
absolute error = 1e-31
relative error = 9.2963023718163498232442498154181e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.851
y[1] (analytic) = -1.0754706752067414959616928969641
y[1] (numeric) = -1.0754706752067414959616928969642
absolute error = 1e-31
relative error = 9.2982544578239336591460294742795e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (analytic) = -1.0752446533090680824208620873218
y[1] (numeric) = -1.075244653309068082420862087322
absolute error = 2e-31
relative error = 1.8600417996453133236468869531471e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.849
y[1] (analytic) = -1.0750184422353701307650458563007
y[1] (numeric) = -1.0750184422353701307650458563009
absolute error = 2e-31
relative error = 1.8604331994912042583880831782527e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.102
Order of pole = 1.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.848
y[1] (analytic) = -1.0747920417712232990691202490252
y[1] (numeric) = -1.0747920417712232990691202490254
absolute error = 2e-31
relative error = 1.8608250919908778274663424217194e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.101
Order of pole = 4.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.847
y[1] (analytic) = -1.0745654517019217115852488450957
y[1] (numeric) = -1.074565451701921711585248845096
absolute error = 3e-31
relative error = 2.7918262170522329246914585753719e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.846
y[1] (analytic) = -1.0743386718124775988768977861754
y[1] (numeric) = -1.0743386718124775988768977861757
absolute error = 3e-31
relative error = 2.7924155377734000685555948314660e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.845
y[1] (analytic) = -1.0741117018876209377230553347201
y[1] (numeric) = -1.0741117018876209377230553347204
absolute error = 3e-31
relative error = 2.7930056014917853957333579491231e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.099
Order of pole = 1.33e-28
TOP MAIN SOLVE Loop
x[1] = -1.844
y[1] (analytic) = -1.073884541711799090793952664386
y[1] (numeric) = -1.0738845417117990907939526643863
absolute error = 3e-31
relative error = 2.7935964095524870914733552053890e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.843
y[1] (analytic) = -1.0736571910691764460995923876043
y[1] (numeric) = -1.0736571910691764460995923876046
absolute error = 3e-31
relative error = 2.7941879633037432028566264928496e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.842
y[1] (analytic) = -1.0734296497436340562124011800399
y[1] (numeric) = -1.0734296497436340562124011800401
absolute error = 2e-31
relative error = 1.8631868427312937120652895760835e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.096
Order of pole = 3.38e-28
TOP MAIN SOLVE Loop
x[1] = -1.841
y[1] (analytic) = -1.0732019175187692772653327653487
y[1] (numeric) = -1.0732019175187692772653327653489
absolute error = 2e-31
relative error = 1.8635822088577491838251468937032e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (analytic) = -1.0729739941778954077267574770421
y[1] (numeric) = -1.0729739941778954077267574770423
absolute error = 2e-31
relative error = 1.8639780748203361025599096246503e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.094
Order of pole = 1.41e-28
TOP MAIN SOLVE Loop
x[1] = -1.839
y[1] (analytic) = -1.0727458795040413269534846175545
y[1] (numeric) = -1.0727458795040413269534846175547
absolute error = 2e-31
relative error = 1.8643744415263125262072580928954e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.093
Order of pole = 1.6e-29
TOP MAIN SOLVE Loop
x[1] = -1.838
y[1] (analytic) = -1.0725175732799511335232738880207
y[1] (numeric) = -1.0725175732799511335232738880209
absolute error = 2e-31
relative error = 1.8647713098850597183044918728758e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.837
y[1] (analytic) = -1.0722890752880837833482022660042
y[1] (numeric) = -1.0722890752880837833482022660045
absolute error = 3e-31
relative error = 2.7977530212121323018938206931445e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.092
Order of pole = 8.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.836
y[1] (analytic) = -1.0720603853106127275702628626984
y[1] (numeric) = -1.0720603853106127275702628626987
absolute error = 3e-31
relative error = 2.7983498328135657449314193947025e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.835
memory used=26.7MB, alloc=4.3MB, time=3.26
y[1] (analytic) = -1.0718315031294255502405824961646
y[1] (numeric) = -1.0718315031294255502405824961649
absolute error = 3e-31
relative error = 2.7989474010055708285431928474344e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.09
Order of pole = 7.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.834
y[1] (analytic) = -1.0716024285261236057836549731896
y[1] (numeric) = -1.0716024285261236057836549731899
absolute error = 3e-31
relative error = 2.7995457271650497860459305013785e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.833
y[1] (analytic) = -1.0713731612820216562479973795565
y[1] (numeric) = -1.0713731612820216562479973795568
absolute error = 3e-31
relative error = 2.8001448126721353646042716422842e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.832
y[1] (analytic) = -1.0711437011781475083446470371482
y[1] (numeric) = -1.0711437011781475083446470371485
absolute error = 3e-31
relative error = 2.8007446589102000586806134943257e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.087
Order of pole = 8.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.831
y[1] (analytic) = -1.0709140479952416502749271965605
y[1] (numeric) = -1.0709140479952416502749271965608
absolute error = 3e-31
relative error = 2.8013452672658653745499550395080e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (analytic) = -1.0706842015137568883489199960067
y[1] (numeric) = -1.0706842015137568883489199960071
absolute error = 4e-31
relative error = 3.7359288521720148346665977727177e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.085
Order of pole = 3.32e-28
TOP MAIN SOLVE Loop
x[1] = -1.829
y[1] (analytic) = -1.0704541615138579833960957314775
y[1] (numeric) = -1.0704541615138579833960957314778
absolute error = 3e-31
relative error = 2.8025487758927847613369564835552e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.828
y[1] (analytic) = -1.0702239277754212869695580495882
y[1] (numeric) = -1.0702239277754212869695580495885
absolute error = 3e-31
relative error = 2.8031516789536107218194475717391e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.827
y[1] (analytic) = -1.0699935000780343773453752935366
y[1] (numeric) = -1.0699935000780343773453752935369
absolute error = 3e-31
relative error = 2.8037553497111998316405861944994e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.083
Order of pole = 2.80e-28
TOP MAIN SOLVE Loop
x[1] = -1.826
y[1] (analytic) = -1.0697628782009956953184789043136
y[1] (numeric) = -1.0697628782009956953184789043139
absolute error = 3e-31
relative error = 2.8043597895685587195824197938997e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.082
Order of pole = 1.05e-28
TOP MAIN SOLVE Loop
x[1] = -1.825
y[1] (analytic) = -1.0695320619233141797966205039994
y[1] (numeric) = -1.0695320619233141797966205039997
absolute error = 3e-31
relative error = 2.8049649999319992724645945924283e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.824
y[1] (analytic) = -1.0693010510237089031938900658457
y[1] (numeric) = -1.069301051023708903193890065846
absolute error = 3e-31
relative error = 2.8055709822111481205110765585664e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.08
Order of pole = 6.29e-28
TOP MAIN SOLVE Loop
x[1] = -1.823
y[1] (analytic) = -1.0690698452806087066253084071283
y[1] (numeric) = -1.0690698452806087066253084071286
absolute error = 3e-31
relative error = 2.8061777378189561547588959632361e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.079
Order of pole = 3.93e-28
TOP MAIN SOLVE Loop
x[1] = -1.822
y[1] (analytic) = -1.068838444472151834904018125674
y[1] (numeric) = -1.0688384444721518349040181256743
absolute error = 3e-31
relative error = 2.8067852681717080766334799306703e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.078
Order of pole = 6.94e-28
TOP MAIN SOLVE Loop
x[1] = -1.821
y[1] (analytic) = -1.068606848376185571342608039746
y[1] (numeric) = -1.0686068483761855713426080397463
absolute error = 3e-31
relative error = 2.8073935746890319798156859161509e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.078
Order of pole = 1.143e-27
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (analytic) = -1.0683750567702658723601171838498
y[1] (numeric) = -1.0683750567702658723601171838501
absolute error = 3e-31
relative error = 2.8080026587939089645262002760789e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.819
y[1] (analytic) = -1.0681430694316570018962754602112
y[1] (numeric) = -1.0681430694316570018962754602115
absolute error = 3e-31
relative error = 2.8086125219126827843535200477993e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.076
Order of pole = 1.313e-25
TOP MAIN SOLVE Loop
x[1] = -1.818
y[1] (analytic) = -1.0679108861373311656345491474241
y[1] (numeric) = -1.0679108861373311656345491474244
absolute error = 3e-31
relative error = 2.8092231654750695257522927423330e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.075
Order of pole = 4.296e-27
TOP MAIN SOLVE Loop
x[1] = -1.817
y[1] (analytic) = -1.0676785066639681450355706242843
y[1] (numeric) = -1.0676785066639681450355706242846
absolute error = 3e-31
relative error = 2.8098345909141673203393483876693e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.816
y[1] (analytic) = -1.0674459307879549311825428783578
y[1] (numeric) = -1.0674459307879549311825428783581
absolute error = 3e-31
relative error = 2.8104467996664660901153202585791e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.815
y[1] (analytic) = -1.0672131582853853584402206356041
y[1] (numeric) = -1.0672131582853853584402206356044
absolute error = 3e-31
relative error = 2.8110597931718573257403157061688e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.072
Order of pole = 2.72e-28
TOP MAIN SOLVE Loop
x[1] = -1.814
y[1] (analytic) = -1.0669801889320597379290812696193
y[1] (numeric) = -1.0669801889320597379290812696196
absolute error = 3e-31
relative error = 2.8116735728736438979926662718547e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.813
y[1] (analytic) = -1.0667470225034844908163100270173
y[1] (numeric) = -1.0667470225034844908163100270177
absolute error = 4e-31
relative error = 3.7497175202913998700538091352118e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.812
y[1] (analytic) = -1.0665136587748717814252355393604
y[1] (numeric) = -1.0665136587748717814252355393608
absolute error = 4e-31
relative error = 3.7505379955423073842070761075278e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.811
y[1] (analytic) = -1.0662800975211391501648630821168
y[1] (numeric) = -1.0662800975211391501648630821172
absolute error = 4e-31
relative error = 3.7513595248557093580016724809298e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (analytic) = -1.0660463385169091462811645876063
y[1] (numeric) = -1.0660463385169091462811645876067
memory used=30.5MB, alloc=4.3MB, time=3.75
absolute error = 4e-31
relative error = 3.7521821101743353568354227243260e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.068
Order of pole = 3.14e-28
TOP MAIN SOLVE Loop
x[1] = -1.809
y[1] (analytic) = -1.0658123815365089604317960220182
y[1] (numeric) = -1.0658123815365089604317960220186
absolute error = 4e-31
relative error = 3.7530057534455295323918643603915e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.808
y[1] (analytic) = -1.0655782263539700570859243966009
y[1] (numeric) = -1.0655782263539700570859243966013
absolute error = 4e-31
relative error = 3.7538304566212639737055677664421e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.807
y[1] (analytic) = -1.0653438727430278067508584002558
y[1] (numeric) = -1.0653438727430278067508584002562
absolute error = 4e-31
relative error = 3.7546562216581521036973481518940e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.065
Order of pole = 5.49e-28
TOP MAIN SOLVE Loop
x[1] = -1.806
y[1] (analytic) = -1.0651093204771211180271884152658
y[1] (numeric) = -1.0651093204771211180271884152661
absolute error = 3e-31
relative error = 2.8166122878880965910182010904529e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.805
y[1] (analytic) = -1.0648745693293920694941535099859
y[1] (numeric) = -1.0648745693293920694941535099863
absolute error = 4e-31
relative error = 3.7563109451651304897567873866394e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.063
Order of pole = 4.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.804
y[1] (analytic) = -1.0646396190726855414269648922663
y[1] (numeric) = -1.0646396190726855414269648922667
absolute error = 4e-31
relative error = 3.7571399075717754700628783078964e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.063
Order of pole = 8.65e-28
TOP MAIN SOLVE Loop
x[1] = -1.803
y[1] (analytic) = -1.0644044694795488473478272553968
y[1] (numeric) = -1.0644044694795488473478272553972
absolute error = 4e-31
relative error = 3.7579699397127107017463919551986e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.062
Order of pole = 2.80e-28
TOP MAIN SOLVE Loop
x[1] = -1.802
y[1] (analytic) = -1.0641691203222313654124114547175
y[1] (numeric) = -1.0641691203222313654124114547179
absolute error = 4e-31
relative error = 3.7588010435679588291544294668560e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.801
y[1] (analytic) = -1.0639335713726841696335440179519
y[1] (numeric) = -1.0639335713726841696335440179523
absolute error = 4e-31
relative error = 3.7596332211222651746359474721922e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.06
Order of pole = 3.83e-28
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (analytic) = -1.0636978224025596609438911160525
y[1] (numeric) = -1.063697822402559660943891116053
absolute error = 5e-31
relative error = 4.7005830929563893230016305303638e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.059
Order of pole = 4.33e-28
TOP MAIN SOLVE Loop
x[1] = -1.799
y[1] (analytic) = -1.0634618731832111980994268041349
y[1] (numeric) = -1.0634618731832111980994268041354
absolute error = 5e-31
relative error = 4.7016260066134119566249209805795e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.058
Order of pole = 6.78e-28
TOP MAIN SOLVE Loop
x[1] = -1.798
y[1] (analytic) = -1.0632257234856927284254875841644
y[1] (numeric) = -1.0632257234856927284254875841648
absolute error = 4e-31
relative error = 3.7621362158981153587008401710518e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.797
y[1] (analytic) = -1.0629893730807584184072276426995
y[1] (numeric) = -1.0629893730807584184072276426999
absolute error = 4e-31
relative error = 3.7629727081910425416613541789994e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.796
y[1] (analytic) = -1.0627528217388622841263014784297
y[1] (numeric) = -1.0627528217388622841263014784301
absolute error = 4e-31
relative error = 3.7638102841780765655705772834783e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.056
Order of pole = 1.155e-27
TOP MAIN SOLVE Loop
x[1] = -1.795
y[1] (analytic) = -1.0625160692301578215456130557209
y[1] (numeric) = -1.0625160692301578215456130557213
absolute error = 4e-31
relative error = 3.7646489458725885864545700835308e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.055
Order of pole = 1.72e-28
TOP MAIN SOLVE Loop
x[1] = -1.794
y[1] (analytic) = -1.0622791153244976366439831021563
y[1] (numeric) = -1.0622791153244976366439831021567
absolute error = 4e-31
relative error = 3.7654886952927694691313411430901e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.054
Order of pole = 4.69e-28
TOP MAIN SOLVE Loop
x[1] = -1.793
y[1] (analytic) = -1.0620419597914330754025987103692
y[1] (numeric) = -1.0620419597914330754025987103696
absolute error = 4e-31
relative error = 3.7663295344616438394044498699751e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.792
y[1] (analytic) = -1.061804602400213853645122007572
y[1] (numeric) = -1.0618046024002138536451220075723
absolute error = 3e-31
relative error = 2.8253785990553131383636789462704e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.052
Order of pole = 3.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.791
y[1] (analytic) = -1.0615670429197876867333473203349
y[1] (numeric) = -1.0615670429197876867333473203352
absolute error = 3e-31
relative error = 2.8260108676213687513739159726227e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (analytic) = -1.061329281118799919120308987613
y[1] (numeric) = -1.0613292811187999191203089876133
absolute error = 3e-31
relative error = 2.8266439580726077474527569644484e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.05
Order of pole = 6.6e-29
TOP MAIN SOLVE Loop
x[1] = -1.789
y[1] (analytic) = -1.0610913167655931537627547620153
y[1] (numeric) = -1.0610913167655931537627547620156
absolute error = 3e-31
relative error = 2.8272778719409059959332584798323e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.788
y[1] (analytic) = -1.0608531496282068813949125881078
y[1] (numeric) = -1.0608531496282068813949125881081
absolute error = 3e-31
relative error = 2.8279126107618179280495052171179e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.787
y[1] (analytic) = -1.0606147794743771096654914573981
y[1] (numeric) = -1.0606147794743771096654914573984
absolute error = 3e-31
relative error = 2.8285481760745872952654185695514e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.048
Order of pole = 2.06e-28
TOP MAIN SOLVE Loop
x[1] = -1.786
y[1] (analytic) = -1.0603762060715359921398700128174
y[1] (numeric) = -1.0603762060715359921398700128177
absolute error = 3e-31
relative error = 2.8291845694221579646418197554602e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.047
Order of pole = 6.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.785
y[1] (analytic) = -1.0601374291868114571694396112554
y[1] (numeric) = -1.0601374291868114571694396112556
absolute error = 2e-31
relative error = 1.8865478615674565009256863159005e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.046
memory used=34.3MB, alloc=4.3MB, time=4.24
Order of pole = 2.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.784
y[1] (analytic) = -1.0598984485870268366300816512671
y[1] (numeric) = -1.0598984485870268366300816512673
absolute error = 2e-31
relative error = 1.8869732309413628591659634640842e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.045
Order of pole = 3.95e-28
TOP MAIN SOLVE Loop
x[1] = -1.783
y[1] (analytic) = -1.0596592640387004945317721347226
y[1] (numeric) = -1.0596592640387004945317721347229
absolute error = 3e-31
relative error = 2.8310987331588459353651996807241e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.044
Order of pole = 2.26e-28
TOP MAIN SOLVE Loop
x[1] = -1.782
y[1] (analytic) = -1.0594198753080454555013196561638
y[1] (numeric) = -1.0594198753080454555013196561641
absolute error = 3e-31
relative error = 2.8317384541494427202726701073615e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.781
y[1] (analytic) = -1.0591802821609690331402563022281
y[1] (numeric) = -1.0591802821609690331402563022284
absolute error = 3e-31
relative error = 2.8323790109454423256732763898785e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (analytic) = -1.0589404843630724582599142959644
y[1] (numeric) = -1.0589404843630724582599142959647
absolute error = 3e-31
relative error = 2.8330204051122181076376797600840e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.779
y[1] (analytic) = -1.0587004816796505069957346374499
y[1] (numeric) = -1.0587004816796505069957346374502
absolute error = 3e-31
relative error = 2.8336626382189201548871686384311e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.041
Order of pole = 3.6e-29
TOP MAIN SOLVE Loop
x[1] = -1.778
y[1] (analytic) = -1.0584602738756911288028674730938
y[1] (numeric) = -1.0584602738756911288028674730941
absolute error = 3e-31
relative error = 2.8343057118384863858066981396865e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.04
Order of pole = 3.20e-28
TOP MAIN SOLVE Loop
x[1] = -1.777
y[1] (analytic) = -1.0582198607158750743351374716394
y[1] (numeric) = -1.0582198607158750743351374716397
absolute error = 3e-31
relative error = 2.8349496275476536838412323221305e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.776
y[1] (analytic) = -1.0579792419645755232094610954174
y[1] (numeric) = -1.0579792419645755232094610954177
absolute error = 3e-31
relative error = 2.8355943869269690714282244963984e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.775
y[1] (analytic) = -1.057738417385857711657816331125
y[1] (numeric) = -1.0577384173858577116578163311254
absolute error = 4e-31
relative error = 3.7816533220810678968263474455773e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.774
y[1] (analytic) = -1.0574973867434785600688791855726
y[1] (numeric) = -1.0574973867434785600688791855729
absolute error = 3e-31
relative error = 2.8368864430373502145485836770791e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.036
Order of pole = 1.57e-28
TOP MAIN SOLVE Loop
x[1] = -1.773
y[1] (analytic) = -1.057256149800886300421455058718
y[1] (numeric) = -1.0572561498008863004214550587183
absolute error = 3e-31
relative error = 2.8375337429486618178929146114313e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.772
y[1] (analytic) = -1.0570147063212201036118469791709
y[1] (numeric) = -1.0570147063212201036118469791712
absolute error = 3e-31
relative error = 2.8381818928906358264956835658017e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.035
Order of pole = 2.13e-28
TOP MAIN SOLVE Loop
x[1] = -1.771
y[1] (analytic) = -1.0567730560673097066773166264532
y[1] (numeric) = -1.0567730560673097066773166264535
absolute error = 3e-31
relative error = 2.8388308944630389262944914234223e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (analytic) = -1.0565311988016750399178080699299
y[1] (numeric) = -1.0565311988016750399178080699302
absolute error = 3e-31
relative error = 2.8394807492695158037193269426314e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.033
Order of pole = 1.57e-28
TOP MAIN SOLVE Loop
x[1] = -1.769
y[1] (analytic) = -1.0562891342865258539181182267354
y[1] (numeric) = -1.0562891342865258539181182267358
absolute error = 4e-31
relative error = 3.7868419452234674582877022184918e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.032
Order of pole = 2.00e-28
TOP MAIN SOLVE Loop
x[1] = -1.768
y[1] (analytic) = -1.0560468622837613464727121804917
y[1] (numeric) = -1.0560468622837613464727121804921
absolute error = 4e-31
relative error = 3.7877107000249711567362386299793e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.031
Order of pole = 4.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.767
y[1] (analytic) = -1.055804382554969789415395709414
y[1] (numeric) = -1.0558043825549697894153957094144
absolute error = 4e-31
relative error = 3.7885805989176622140931891369171e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.03
Order of pole = 2.75e-28
TOP MAIN SOLVE Loop
x[1] = -1.766
y[1] (analytic) = -1.0555616948614281553560716468066
y[1] (numeric) = -1.055561694861428155356071646807
absolute error = 4e-31
relative error = 3.7894516440605693867154208397767e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.029
Order of pole = 2.24e-28
TOP MAIN SOLVE Loop
x[1] = -1.765
y[1] (analytic) = -1.0553187989641017443268210392272
y[1] (numeric) = -1.0553187989641017443268210392275
absolute error = 3e-31
relative error = 2.8427428782134767132630374264652e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.029
Order of pole = 8.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.764
y[1] (analytic) = -1.0550756946236438103395644780314
y[1] (numeric) = -1.0550756946236438103395644780317
absolute error = 3e-31
relative error = 2.8433978863195501761451931728028e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.763
y[1] (analytic) = -1.0548323816003951878575734588655
y[1] (numeric) = -1.0548323816003951878575734588659
absolute error = 4e-31
relative error = 3.7920716786596812030571677804760e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.762
y[1] (analytic) = -1.0545888596543839181831161712323
y[1] (numeric) = -1.0545888596543839181831161712327
absolute error = 4e-31
relative error = 3.7929473304989240972115401056360e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.026
Order of pole = 2.49e-28
TOP MAIN SOLVE Loop
x[1] = -1.761
y[1] (analytic) = -1.0543451285453248757635367367935
y[1] (numeric) = -1.0543451285453248757635367367939
absolute error = 4e-31
relative error = 3.7938241394625511301066851748945e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.025
Order of pole = 1.60e-28
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (analytic) = -1.0541011880326193944180816008678
y[1] (numeric) = -1.0541011880326193944180816008681
absolute error = 3e-31
relative error = 2.8460265808059826761492516831447e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=38.1MB, alloc=4.3MB, time=4.74
TOP MAIN SOLVE Loop
x[1] = -1.759
y[1] (analytic) = -1.0538570378753548934878015369111
y[1] (numeric) = -1.0538570378753548934878015369115
absolute error = 4e-31
relative error = 3.7955812375312908691015353878470e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.758
y[1] (analytic) = -1.0536126778323045039108725489141
y[1] (numeric) = -1.0536126778323045039108725489145
absolute error = 4e-31
relative error = 3.7964615310339398742789472009923e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.023
Order of pole = 1.36e-28
TOP MAIN SOLVE Loop
x[1] = -1.757
y[1] (analytic) = -1.0533681076619266942256938518897
y[1] (numeric) = -1.0533681076619266942256938518901
absolute error = 4e-31
relative error = 3.7973429904560773905093162026308e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.756
y[1] (analytic) = -1.053123327122364896504136076245
y[1] (numeric) = -1.0531233271223648965041360762454
absolute error = 4e-31
relative error = 3.7982256180099128270025099635819e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.755
y[1] (analytic) = -1.0528783359714471322173278781071
y[1] (numeric) = -1.0528783359714471322173278781075
absolute error = 4e-31
relative error = 3.7991094159130608883992369836028e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.02
Order of pole = 3.42e-28
TOP MAIN SOLVE Loop
x[1] = -1.754
y[1] (analytic) = -1.0526331339666856380363842448938
y[1] (numeric) = -1.0526331339666856380363842448942
absolute error = 4e-31
relative error = 3.7999943863885576572092365430905e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.753
y[1] (analytic) = -1.0523877208652764915704949638652
y[1] (numeric) = -1.0523877208652764915704949638656
absolute error = 4e-31
relative error = 3.8008805316648767325814271866611e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.752
y[1] (analytic) = -1.0521420964240992370448069713523
y[1] (numeric) = -1.0521420964240992370448069713527
absolute error = 4e-31
relative error = 3.8017678539759454256332011881731e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.751
y[1] (analytic) = -1.0518962603997165109205496221103
y[1] (numeric) = -1.0518962603997165109205496221107
absolute error = 4e-31
relative error = 3.8026563555611610115670909960087e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.016
Order of pole = 2.34e-28
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (analytic) = -1.0516502125483736674598673120863
y[1] (numeric) = -1.0516502125483736674598673120867
absolute error = 4e-31
relative error = 3.8035460386654070388040776269875e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.016
Order of pole = 3.46e-28
TOP MAIN SOLVE Loop
x[1] = -1.749
y[1] (analytic) = -1.0514039526259984042378393540978
y[1] (numeric) = -1.0514039526259984042378393540982
absolute error = 4e-31
relative error = 3.8044369055390696953638602974722e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.015
Order of pole = 5.89e-28
TOP MAIN SOLVE Loop
x[1] = -1.748
y[1] (analytic) = -1.0511574803882003876041825447895
y[1] (numeric) = -1.0511574803882003876041825447899
absolute error = 4e-31
relative error = 3.8053289584380542327234612814242e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.747
y[1] (analytic) = -1.0509107955902708780971474730531
y[1] (numeric) = -1.0509107955902708780971474730536
absolute error = 5e-31
relative error = 4.7577777495297518092332501225537e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.746
y[1] (analytic) = -1.0506638979871823558121353051524
y[1] (numeric) = -1.0506638979871823558121353051528
absolute error = 4e-31
relative error = 3.8071166313633042203973366869802e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.012
Order of pole = 2.64e-28
TOP MAIN SOLVE Loop
x[1] = -1.745
y[1] (analytic) = -1.0504167873335881457275775403811
y[1] (numeric) = -1.0504167873335881457275775403815
absolute error = 4e-31
relative error = 3.8080122559291241150325542579905e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.744
y[1] (analytic) = -1.0501694633838220429906370634934
y[1] (numeric) = -1.0501694633838220429906370634938
absolute error = 4e-31
relative error = 3.8089090755994080329089290354394e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.743
y[1] (analytic) = -1.0499219258918979381653047266663
y[1] (numeric) = -1.0499219258918979381653047266667
absolute error = 4e-31
relative error = 3.8098070926579049287411161878086e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.742
y[1] (analytic) = -1.0496741746115094424454816746877
y[1] (numeric) = -1.0496741746115094424454816746881
absolute error = 4e-31
relative error = 3.8107063093939825839889688697394e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.009
Order of pole = 3.59e-28
TOP MAIN SOLVE Loop
x[1] = -1.741
y[1] (analytic) = -1.0494262092960295128356536826984
y[1] (numeric) = -1.0494262092960295128356536826988
absolute error = 4e-31
relative error = 3.8116067281026444396327005411097e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.008
Order of pole = 6.60e-28
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (analytic) = -1.0491780296985100773017799064475
y[1] (numeric) = -1.0491780296985100773017799064479
absolute error = 4e-31
relative error = 3.8125083510845464883159995961140e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.007
Order of pole = 6.29e-28
TOP MAIN SOLVE Loop
x[1] = -1.739
y[1] (analytic) = -1.0489296355716816598950346509516
y[1] (numeric) = -1.048929635571681659895034650952
absolute error = 4e-31
relative error = 3.8134111806460142260982098675114e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.006
Order of pole = 1.76e-28
TOP MAIN SOLVE Loop
x[1] = -1.738
y[1] (analytic) = -1.048681026667953005851057044964
y[1] (numeric) = -1.0486810266679530058510570449644
absolute error = 4e-31
relative error = 3.8143152190990596640578007995642e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.005
Order of pole = 7.47e-28
TOP MAIN SOLVE Loop
x[1] = -1.737
y[1] (analytic) = -1.0484322027394107066673798660733
y[1] (numeric) = -1.0484322027394107066673798660737
absolute error = 4e-31
relative error = 3.8152204687613983999904670402652e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.004
Order of pole = 7.31e-28
TOP MAIN SOLVE Loop
x[1] = -1.736
y[1] (analytic) = -1.0481831635378188251617251948455
y[1] (numeric) = -1.0481831635378188251617251948459
absolute error = 4e-31
relative error = 3.8161269319564667504463189221229e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.003
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.735
y[1] (analytic) = -1.0479339088146185205138710865148
y[1] (numeric) = -1.0479339088146185205138710865152
absolute error = 4e-31
relative error = 3.8170346110134389433517528140051e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.003
Order of pole = 1.296e-27
memory used=41.9MB, alloc=4.3MB, time=5.22
TOP MAIN SOLVE Loop
x[1] = -1.734
y[1] (analytic) = -1.0476844383209276732938100356012
y[1] (numeric) = -1.0476844383209276732938100356016
absolute error = 4e-31
relative error = 3.8179435082672443714627236676171e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.002
Order of pole = 3.393e-27
TOP MAIN SOLVE Loop
x[1] = -1.733
y[1] (analytic) = -1.0474347518075405104789366728037
y[1] (numeric) = -1.0474347518075405104789366728041
absolute error = 4e-31
relative error = 3.8188536260585849068972812845094e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.001
Order of pole = 3.249e-27
TOP MAIN SOLVE Loop
x[1] = -1.732
y[1] (analytic) = -1.0471848490249272304630188748779
y[1] (numeric) = -1.0471848490249272304630188748783
absolute error = 4e-31
relative error = 3.8197649667339522769963769267513e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2
Order of pole = 2.934e-26
TOP MAIN SOLVE Loop
x[1] = -1.731
y[1] (analytic) = -1.0469347297232336280597232872656
y[1] (numeric) = -1.046934729723233628059723287266
absolute error = 4e-31
relative error = 3.8206775326456455017630979204307e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.999
Order of pole = 2.252e-27
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (analytic) = -1.0466843936522807195034831563044
y[1] (numeric) = -1.0466843936522807195034831563048
absolute error = 4e-31
relative error = 3.8215913261517883931316448900140e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.998
Order of pole = 2.31e-28
TOP MAIN SOLVE Loop
x[1] = -1.729
y[1] (analytic) = -1.0464338405615643674505133432104
y[1] (numeric) = -1.0464338405615643674505133432108
absolute error = 4e-31
relative error = 3.8225063496163471163185292476433e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.728
y[1] (analytic) = -1.0461830702002549059827944460079
y[1] (numeric) = -1.0461830702002549059827944460084
absolute error = 5e-31
relative error = 4.7792782567614347668870469739315e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.727
y[1] (analytic) = -1.0459320823171967656178650884773
y[1] (numeric) = -1.0459320823171967656178650884777
absolute error = 4e-31
relative error = 3.8243400959058942901379846526326e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.996
Order of pole = 3.47e-28
TOP MAIN SOLVE Loop
x[1] = -1.726
y[1] (analytic) = -1.0456808766609080983272786473166
y[1] (numeric) = -1.0456808766609080983272786473171
absolute error = 5e-31
relative error = 4.7815735293602322050101974513059e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.995
Order of pole = 6.12e-28
TOP MAIN SOLVE Loop
x[1] = -1.725
y[1] (analytic) = -1.0454294529795804025665979803791
y[1] (numeric) = -1.0454294529795804025665979803796
absolute error = 5e-31
relative error = 4.7827234881794183469058050399155e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.724
y[1] (analytic) = -1.0451778110210781483198190903494
y[1] (numeric) = -1.0451778110210781483198190903499
absolute error = 5e-31
relative error = 4.7838749993317307166030252896632e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.723
y[1] (analytic) = -1.0449259505329384021611321098912
y[1] (numeric) = -1.0449259505329384021611321098918
absolute error = 6e-31
relative error = 5.7420336789796920499190932397685e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.722
y[1] (analytic) = -1.0446738712623704523369455264271
y[1] (numeric) = -1.0446738712623704523369455264277
absolute error = 6e-31
relative error = 5.7434192287681870230172340091213e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.991
Order of pole = 3.6e-29
TOP MAIN SOLVE Loop
x[1] = -1.721
y[1] (analytic) = -1.0444215729562554338711171776211
y[1] (numeric) = -1.0444215729562554338711171776216
absolute error = 5e-31
relative error = 4.7873388768171490671404385032056e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (analytic) = -1.0441690553611459536963532426421
y[1] (numeric) = -1.0441690553611459536963532426426
absolute error = 5e-31
relative error = 4.7884966273690746550011717184458e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.99
Order of pole = 1.29e-28
TOP MAIN SOLVE Loop
x[1] = -1.719
y[1] (analytic) = -1.0439163182232657158147542296939
y[1] (numeric) = -1.0439163182232657158147542296944
absolute error = 5e-31
relative error = 4.7896559453251443827517487773139e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.718
y[1] (analytic) = -1.0436633612885091464905048174304
y[1] (numeric) = -1.043663361288509146490504817431
absolute error = 6e-31
relative error = 5.7489802004665435689014153575557e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.717
y[1] (analytic) = -1.0434101843024410194777223470474
y[1] (numeric) = -1.043410184302441019477722347048
absolute error = 6e-31
relative error = 5.7503751547252012213688962444618e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.716
y[1] (analytic) = -1.0431567870102960812864967833629
y[1] (numeric) = -1.0431567870102960812864967833635
absolute error = 6e-31
relative error = 5.7517720008284615493165304171181e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.986
Order of pole = 5.21e-28
TOP MAIN SOLVE Loop
x[1] = -1.715
y[1] (analytic) = -1.0429031691569786764901730673983
y[1] (numeric) = -1.0429031691569786764901730673989
absolute error = 6e-31
relative error = 5.7531707424477821979161718333440e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.985
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.714
y[1] (analytic) = -1.0426493304870623730769449701572
y[1] (numeric) = -1.0426493304870623730769449701578
absolute error = 6e-31
relative error = 5.7545713832637909104366471811133e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.713
y[1] (analytic) = -1.0423952707447895878488478277957
y[1] (numeric) = -1.0423952707447895878488478277964
absolute error = 7e-31
relative error = 6.7153029147940323154098600135898e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.712
y[1] (analytic) = -1.0421409896740712118712558925046
y[1] (numeric) = -1.0421409896740712118712558925053
absolute error = 7e-31
relative error = 6.7169414401301349671634699667004e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.711
y[1] (analytic) = -1.0418864870184862359760084715006
y[1] (numeric) = -1.0418864870184862359760084715013
absolute error = 7e-31
relative error = 6.7185821941424207223976352897077e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.982
Order of pole = 1.03e-28
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (analytic) = -1.0416317625212813763213075488757
y[1] (numeric) = -1.0416317625212813763213075488764
absolute error = 7e-31
relative error = 6.7202251811680755644734239599977e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.981
Order of pole = 1.93e-28
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=5.70
x[1] = -1.709
y[1] (analytic) = -1.0413768159253707000115481919974
y[1] (numeric) = -1.041376815925370700011548191998
absolute error = 6e-31
relative error = 5.7616032047615552197799028329262e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.98
Order of pole = 3.14e-28
TOP MAIN SOLVE Loop
x[1] = -1.708
y[1] (analytic) = -1.0411216469733352507802617360203
y[1] (numeric) = -1.041121646973335250780261736021
absolute error = 7e-31
relative error = 6.7235178716625809605535087668396e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.707
y[1] (analytic) = -1.0408662554074226747393705171791
y[1] (numeric) = -1.0408662554074226747393705171798
absolute error = 7e-31
relative error = 6.7251675838602474771488754777273e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.706
y[1] (analytic) = -1.0406106409695468461979717882109
y[1] (numeric) = -1.0406106409695468461979717882116
absolute error = 7e-31
relative error = 6.7268195465289816023022358730615e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.977
Order of pole = 4.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.705
y[1] (analytic) = -1.0403548034012874935538873978328
y[1] (numeric) = -1.0403548034012874935538873978335
absolute error = 7e-31
relative error = 6.7284737640606131058319593706494e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.704
y[1] (analytic) = -1.0400987424438898252612348509983
y[1] (numeric) = -1.040098742443889825261234850999
absolute error = 7e-31
relative error = 6.7301302408580008295021950822365e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.703
y[1] (analytic) = -1.0398424578382641558772944880061
y[1] (numeric) = -1.0398424578382641558772944880069
absolute error = 8e-31
relative error = 7.6934731215257901784438578874278e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.975
Order of pole = 2.60e-28
TOP MAIN SOLVE Loop
x[1] = -1.702
y[1] (analytic) = -1.0395859493249855321919667287672
y[1] (numeric) = -1.039585949324985532191966728768
absolute error = 8e-31
relative error = 7.6953714170478035430006282420110e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.974
Order of pole = 1.66e-28
TOP MAIN SOLVE Loop
x[1] = -1.701
y[1] (analytic) = -1.0393292166442933594431326239748
y[1] (numeric) = -1.0393292166442933594431326239756
absolute error = 8e-31
relative error = 7.6972723097593540226204367943251e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (analytic) = -1.0390722595360910276212503379073
y[1] (numeric) = -1.0390722595360910276212503379081
absolute error = 8e-31
relative error = 7.6991758047430856596457476662046e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.972
Order of pole = 1.47e-28
TOP MAIN SOLVE Loop
x[1] = -1.699
y[1] (analytic) = -1.0388150777399455378665396584461
y[1] (numeric) = -1.0388150777399455378665396584469
absolute error = 8e-31
relative error = 7.7010819070944412237296847526919e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.698
y[1] (analytic) = -1.038557670995087128962126188953
y[1] (numeric) = -1.0385576709950871289621261889538
absolute error = 8e-31
relative error = 7.7029906219217014473637763950644e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.971
Order of pole = 3.24e-28
TOP MAIN SOLVE Loop
x[1] = -1.697
y[1] (analytic) = -1.038300039040408903926536524248
y[1] (numeric) = -1.0383000390404089039265365242489
absolute error = 9e-31
relative error = 8.6680146986392774534114016289536e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.696
y[1] (analytic) = -1.0380421816144664567089554494038
y[1] (numeric) = -1.0380421816144664567089554494047
absolute error = 9e-31
relative error = 8.6701678981891706504053602752383e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.969
Order of pole = 1.03e-28
TOP MAIN SOLVE Loop
x[1] = -1.695
y[1] (analytic) = -1.037784098455477498990676025748
y[1] (numeric) = -1.0377840984554774989906760257489
absolute error = 9e-31
relative error = 8.6723240541020041043266583237422e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.694
y[1] (analytic) = -1.0375257893013214870961933436928
y[1] (numeric) = -1.0375257893013214870961933436937
absolute error = 9e-31
relative error = 8.6744831721828090682447329456986e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.967
Order of pole = 1.76e-28
TOP MAIN SOLVE Loop
x[1] = -1.693
y[1] (analytic) = -1.0372672538895392490174127271123
y[1] (numeric) = -1.0372672538895392490174127271132
absolute error = 9e-31
relative error = 8.6766452582512826065132309356567e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.966
Order of pole = 2.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.692
y[1] (analytic) = -1.0370084919573326115544632693128
y[1] (numeric) = -1.0370084919573326115544632693137
absolute error = 9e-31
relative error = 8.6788103181418327007193782847749e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.691
y[1] (analytic) = -1.0367495032415640275766277665203
y[1] (numeric) = -1.0367495032415640275766277665212
absolute error = 9e-31
relative error = 8.6809783577036235189857361992371e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.965
Order of pole = 1.68e-28
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (analytic) = -1.0364902874787562034069203915875
y[1] (numeric) = -1.0364902874787562034069203915884
absolute error = 9e-31
relative error = 8.6831493828006208493058755591423e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.964
Order of pole = 3.14e-28
TOP MAIN SOLVE Loop
x[1] = -1.689
y[1] (analytic) = -1.0362308444050917263338638186339
y[1] (numeric) = -1.0362308444050917263338638186348
absolute error = 9e-31
relative error = 8.6853233993116376975987275640567e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.688
y[1] (analytic) = -1.0359711737564126922540379689265
y[1] (numeric) = -1.0359711737564126922540379689274
absolute error = 9e-31
relative error = 8.6875004131303800511696111823296e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.962
Order of pole = 1.02e-28
TOP MAIN SOLVE Loop
x[1] = -1.687
y[1] (analytic) = -1.0357112752682203334489930998183
y[1] (numeric) = -1.0357112752682203334489930998192
absolute error = 9e-31
relative error = 8.6896804301654928082691981132353e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.961
Order of pole = 1.05e-28
TOP MAIN SOLVE Loop
x[1] = -1.686
y[1] (analytic) = -1.0354511486756746465001406023373
y[1] (numeric) = -1.0354511486756746465001406023382
absolute error = 9e-31
relative error = 8.6918634563406058744449533855470e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.96
Order of pole = 2.53e-28
TOP MAIN SOLVE Loop
x[1] = -1.685
y[1] (analytic) = -1.0351907937135940203452556094
y[1] (numeric) = -1.0351907937135940203452556094008
absolute error = 8e-31
relative error = 7.7280439978616714901181196049292e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=6.19
x[1] = -1.684
y[1] (analytic) = -1.034930210116454864480246345955
y[1] (numeric) = -1.0349302101164548644802463459558
absolute error = 8e-31
relative error = 7.7299898310049380835028842974328e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.959
Order of pole = 7.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.683
y[1] (analytic) = -1.0346693976183912373098660749934
y[1] (numeric) = -1.0346693976183912373098660749942
absolute error = 8e-31
relative error = 7.7319383548159944987352582000105e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.682
y[1] (analytic) = -1.034408355953194474651064509632
y[1] (numeric) = -1.0344083559531944746510645096329
absolute error = 9e-31
relative error = 8.7006257714407300863845404765298e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.957
Order of pole = 1.20e-28
TOP MAIN SOLVE Loop
x[1] = -1.681
y[1] (analytic) = -1.0341470848543128183926966717421
y[1] (numeric) = -1.034147084854312818392696671743
absolute error = 9e-31
relative error = 8.7028239326980164439368522511271e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (analytic) = -1.0338855840548510453153283821921
y[1] (numeric) = -1.033885584054851045315328382193
absolute error = 9e-31
relative error = 8.7050251389543702851670104034777e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.955
Order of pole = 6.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.679
y[1] (analytic) = -1.0336238532875700960748988670659
y[1] (numeric) = -1.0336238532875700960748988670668
absolute error = 9e-31
relative error = 8.7072293962396214224916773582519e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.678
y[1] (analytic) = -1.0333618922848867043540223585378
y[1] (numeric) = -1.0333618922848867043540223585386
absolute error = 8e-31
relative error = 7.7417215205324084759155327089157e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.953
Order of pole = 2.09e-28
TOP MAIN SOLVE Loop
x[1] = -1.677
y[1] (analytic) = -1.0330997007788730261847320588002
y[1] (numeric) = -1.0330997007788730261847320588011
absolute error = 9e-31
relative error = 8.7116470880929817997658988712602e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.676
y[1] (analytic) = -1.0328372785012562694464914208908
y[1] (numeric) = -1.0328372785012562694464914208917
absolute error = 9e-31
relative error = 8.7138605347977406910077425187299e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.675
y[1] (analytic) = -1.0325746251834183235433193818035
y[1] (numeric) = -1.0325746251834183235433193818044
absolute error = 9e-31
relative error = 8.7160770568047919620012700987214e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.674
y[1] (analytic) = -1.0323117405563953892638979612579
y[1] (numeric) = -1.0323117405563953892638979612588
absolute error = 9e-31
relative error = 8.7182966602212427963069179800391e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.673
y[1] (analytic) = -1.0320486243508776088285525142806
y[1] (numeric) = -1.0320486243508776088285525142815
absolute error = 9e-31
relative error = 8.7205193511698001375547789031812e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.672
y[1] (analytic) = -1.0317852762972086961270168976902
y[1] (numeric) = -1.0317852762972086961270168976911
absolute error = 9e-31
relative error = 8.7227451357888191956946728991485e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.948
Order of pole = 1.87e-28
TOP MAIN SOLVE Loop
x[1] = -1.671
y[1] (analytic) = -1.0315216961253855671509178800198
y[1] (numeric) = -1.0315216961253855671509178800207
absolute error = 9e-31
relative error = 8.7249740202323521308621534548575e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.947
Order of pole = 1.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (analytic) = -1.0312578835650579706249352917186
y[1] (numeric) = -1.0312578835650579706249352917196
absolute error = 1.0e-30
relative error = 9.6968955674113299062331856211358e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.947
Order of pole = 3.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.669
y[1] (analytic) = -1.0309938383455281188406166780065
y[1] (numeric) = -1.0309938383455281188406166780075
absolute error = 1.0e-30
relative error = 9.6993790147643848625080804012649e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.668
y[1] (analytic) = -1.0307295601957503186968475808608
y[1] (numeric) = -1.0307295601957503186968475808618
absolute error = 1.0e-30
relative error = 9.7018659269855971267948139373768e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.945
Order of pole = 6.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.667
y[1] (analytic) = -1.0304650488443306029510010396658
y[1] (numeric) = -1.0304650488443306029510010396668
absolute error = 1.0e-30
relative error = 9.7043563109831115637182458424735e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.944
Order of pole = 1.63e-28
TOP MAIN SOLVE Loop
x[1] = -1.666
y[1] (analytic) = -1.0302003040195263616848124624
y[1] (numeric) = -1.0302003040195263616848124624011
absolute error = 1.1e-30
relative error = 1.0677535191051066304050735111573e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.943
Order of pole = 1.75e-28
TOP MAIN SOLVE Loop
x[1] = -1.665
y[1] (analytic) = -1.0299353254492459739890486812413
y[1] (numeric) = -1.0299353254492459739890486812423
absolute error = 1.0e-30
relative error = 9.7093475220282542650610227557985e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.942
Order of pole = 1.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.664
y[1] (analytic) = -1.0296701128610484398710627684934
y[1] (numeric) = -1.0296701128610484398710627684944
absolute error = 1.0e-30
relative error = 9.7118483629809661978329853148130e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.941
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -1.663
y[1] (analytic) = -1.0294046659821430123893490511472
y[1] (numeric) = -1.0294046659821430123893490511482
absolute error = 1.0e-30
relative error = 9.7143527035202588404356958804048e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.941
Order of pole = 1.76e-28
TOP MAIN SOLVE Loop
x[1] = -1.662
y[1] (analytic) = -1.0291389845393888300192357255379
y[1] (numeric) = -1.0291389845393888300192357255389
absolute error = 1.0e-30
relative error = 9.7168605506434045997895920567524e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.661
y[1] (analytic) = -1.0288730682592945492538755378225
y[1] (numeric) = -1.0288730682592945492538755378235
absolute error = 1.0e-30
relative error = 9.7193719113656689099103332099530e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (analytic) = -1.0286069168680179774447181617342
y[1] (numeric) = -1.0286069168680179774447181617352
absolute error = 1.0e-30
relative error = 9.7218867927203665517998028665419e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.938
Order of pole = 1.94e-28
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=6.68
x[1] = -1.659
y[1] (analytic) = -1.0283405300913657058856711726431
y[1] (numeric) = -1.0283405300913657058856711726441
absolute error = 1.0e-30
relative error = 9.7244052017589181809482933071420e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.658
y[1] (analytic) = -1.0280739076547927431451798867289
y[1] (numeric) = -1.0280739076547927431451798867299
absolute error = 1.0e-30
relative error = 9.7269271455509070633298420408727e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.936
Order of pole = 1.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.657
y[1] (analytic) = -1.0278070492834021486504798064199
y[1] (numeric) = -1.0278070492834021486504798064209
absolute error = 1.0e-30
relative error = 9.7294526311841360207769421554954e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.935
Order of pole = 5.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.656
y[1] (analytic) = -1.0275399547019446665282989885398
y[1] (numeric) = -1.0275399547019446665282989885408
absolute error = 1.0e-30
relative error = 9.7319816657646845866251238467509e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.655
y[1] (analytic) = -1.0272726236348183597063113302
y[1] (numeric) = -1.027272623634818359706311330201
absolute error = 1.0e-30
relative error = 9.7345142564169663725222028761654e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.934
Order of pole = 1.13e-28
TOP MAIN SOLVE Loop
x[1] = -1.654
y[1] (analytic) = -1.0270050558060682442796655497461
y[1] (numeric) = -1.0270050558060682442796655497471
absolute error = 1.0e-30
relative error = 9.7370504102837866473013134289214e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.653
y[1] (analytic) = -1.0267372509393859241469385263886
y[1] (numeric) = -1.0267372509393859241469385263896
absolute error = 1.0e-30
relative error = 9.7395901345264001288211879822197e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.932
Order of pole = 9.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.652
y[1] (analytic) = -1.0264692087581092259198856528828
y[1] (numeric) = -1.0264692087581092259198856528838
absolute error = 1.0e-30
relative error = 9.7421334363245689896815154909437e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.651
y[1] (analytic) = -1.0262009289852218341113849511525
y[1] (numeric) = -1.0262009289852218341113849511535
absolute error = 1.0e-30
relative error = 9.7446803228766210777256015932192e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (analytic) = -1.0259324113433529266059959014387
y[1] (numeric) = -1.0259324113433529266059959014397
absolute error = 1.0e-30
relative error = 9.7472308013995083522469707765860e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.649
y[1] (analytic) = -1.0256636555547768104175782417792
y[1] (numeric) = -1.0256636555547768104175782417802
absolute error = 1.0e-30
relative error = 9.7497848791288655368209906697059e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.648
y[1] (analytic) = -1.025394661341412557738440406758
y[1] (numeric) = -1.025394661341412557738440406759
absolute error = 1.0e-30
relative error = 9.7523425633190689896870629796178e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.928
Order of pole = 2.86e-28
TOP MAIN SOLVE Loop
x[1] = -1.647
y[1] (analytic) = -1.0251254284248236422845117928801
y[1] (numeric) = -1.0251254284248236422845117928812
absolute error = 1.1e-30
relative error = 1.0730394247367625371872555648869e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.927
Order of pole = 1.27e-28
TOP MAIN SOLVE Loop
x[1] = -1.646
y[1] (analytic) = -1.0248559565262175759410576630018
y[1] (numeric) = -1.0248559565262175759410576630029
absolute error = 1.1e-30
relative error = 1.0733215658212941365081535728946e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.926
Order of pole = 1.23e-28
TOP MAIN SOLVE Loop
x[1] = -1.645
y[1] (analytic) = -1.0245862453664455457134802343583
y[1] (numeric) = -1.0245862453664455457134802343593
absolute error = 1.0e-30
relative error = 9.7600373274808874633558339411926e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.644
y[1] (analytic) = -1.0243162946660020509877743342532
y[1] (numeric) = -1.0243162946660020509877743342542
absolute error = 1.0e-30
relative error = 9.7626095104351449895587055214438e-29 %
Correct digits = 30
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.924
Order of pole = 1.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.643
y[1] (analytic) = -1.0240461041450245411052309547881
y[1] (numeric) = -1.0240461041450245411052309547891
absolute error = 1.0e-30
relative error = 9.7651853364053309046916568504042e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.642
y[1] (analytic) = -1.0237756735232930532560070934894
y[1] (numeric) = -1.0237756735232930532560070934905
absolute error = 1.1e-30
relative error = 1.0744541294035471948950020036250e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.923
Order of pole = 6e-30
TOP MAIN SOLVE Loop
x[1] = -1.641
y[1] (analytic) = -1.0235050025202298506962054307213
y[1] (numeric) = -1.0235050025202298506962054307224
absolute error = 1.1e-30
relative error = 1.0747382741573441456396784230304e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (analytic) = -1.0232340908548990612931326677265
y[1] (numeric) = -1.0232340908548990612931326677276
absolute error = 1.1e-30
relative error = 1.0750228220806873220325624945279e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.921
Order of pole = 4.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.639
y[1] (analytic) = -1.0229629382460063164034307314038
y[1] (numeric) = -1.022962938246006316403430731405
absolute error = 1.2e-30
relative error = 1.1730630261713539088378233753015e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.92
Order of pole = 2.77e-28
TOP MAIN SOLVE Loop
x[1] = -1.638
y[1] (analytic) = -1.022691544411898390088800543882
y[1] (numeric) = -1.0226915444118983900888005438832
absolute error = 1.2e-30
relative error = 1.1733743244059608698648345655191e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.919
Order of pole = 1.53e-28
TOP MAIN SOLVE Loop
x[1] = -1.637
y[1] (analytic) = -1.0224199090705628386740636569746
y[1] (numeric) = -1.0224199090705628386740636569758
absolute error = 1.2e-30
relative error = 1.1736860651421268240692871100263e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.636
y[1] (analytic) = -1.0221480319396276406523327640814
y[1] (numeric) = -1.0221480319396276406523327640827
absolute error = 1.3e-30
relative error = 1.2718314367177527026997045257713e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.635
y[1] (analytic) = -1.0218759127363608369420879254161
y[1] (numeric) = -1.0218759127363608369420879254174
absolute error = 1.3e-30
relative error = 1.2721701175232553554191825692513e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.634
y[1] (analytic) = -1.0216035511776701715009812769787
y[1] (numeric) = -1.02160355117767017150098127698
memory used=57.2MB, alloc=4.3MB, time=7.16
absolute error = 1.3e-30
relative error = 1.2725092806318104290473006868527e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.916
Order of pole = 1.49e-28
TOP MAIN SOLVE Loop
x[1] = -1.633
y[1] (analytic) = -1.0213309469801027323012190398388
y[1] (numeric) = -1.0213309469801027323012190398401
absolute error = 1.3e-30
relative error = 1.2728489270239710222362449007390e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.915
Order of pole = 7.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.632
y[1] (analytic) = -1.0210580998598445926713958044295
y[1] (numeric) = -1.0210580998598445926713958044309
absolute error = 1.4e-30
relative error = 1.3711266775046109697232453997719e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.631
y[1] (analytic) = -1.0207850095327204530096823350723
y[1] (numeric) = -1.0207850095327204530096823350737
absolute error = 1.4e-30
relative error = 1.3714934946398466988415858830250e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.913
Order of pole = 8.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (analytic) = -1.0205116757141932828732945232312
y[1] (numeric) = -1.0205116757141932828732945232326
absolute error = 1.4e-30
relative error = 1.3718608354188855373035156497589e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.629
y[1] (analytic) = -1.0202380981193639634491976144342
y[1] (numeric) = -1.0202380981193639634491976144355
absolute error = 1.3e-30
relative error = 1.2742123651296003276895416834180e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.628
y[1] (analytic) = -1.0199642764629709304110264437729
y[1] (numeric) = -1.0199642764629709304110264437742
absolute error = 1.3e-30
relative error = 1.2745544427380693319361400016283e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.911
Order of pole = 1.54e-28
TOP MAIN SOLVE Loop
x[1] = -1.627
y[1] (analytic) = -1.0196902104593898171672291388033
y[1] (numeric) = -1.0196902104593898171672291388046
absolute error = 1.3e-30
relative error = 1.2748970095675678752154615819022e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.626
y[1] (analytic) = -1.0194158998226330985054685868957
y[1] (numeric) = -1.019415899822633098505468586897
absolute error = 1.3e-30
relative error = 1.2752400666167610091989880941140e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.909
Order of pole = 7e-30
TOP MAIN SOLVE Loop
x[1] = -1.625
y[1] (analytic) = -1.0191413442663497346383429170231
y[1] (numeric) = -1.0191413442663497346383429170244
absolute error = 1.3e-30
relative error = 1.2755836148869343118964339065388e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.624
y[1] (analytic) = -1.0188665435038248156555133140183
y[1] (numeric) = -1.0188665435038248156555133140196
absolute error = 1.3e-30
relative error = 1.2759276553820022572253522241694e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.623
y[1] (analytic) = -1.0185914972479792063873546668637
y[1] (numeric) = -1.0185914972479792063873546668651
absolute error = 1.4e-30
relative error = 1.3744469728860948173045707541970e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.906
Order of pole = 9.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.622
y[1] (analytic) = -1.018316205211369191685271852
y[1] (numeric) = -1.0183162052113691916852718520013
absolute error = 1.3e-30
relative error = 1.2766172170756748889557476582648e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.621
y[1] (analytic) = -1.0180406671061861221238518683366
y[1] (numeric) = -1.018040667106186122123851868338
absolute error = 1.4e-30
relative error = 1.3751906433949694451615490816207e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.905
Order of pole = 7.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (analytic) = -1.0177648826442560601300495730236
y[1] (numeric) = -1.017764882644256060130049573025
absolute error = 1.4e-30
relative error = 1.3755632797652228492974160066266e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.619
y[1] (analytic) = -1.0174888515370394265446324164765
y[1] (numeric) = -1.0174888515370394265446324164778
absolute error = 1.3e-30
relative error = 1.2776552765528521186305682270860e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.618
y[1] (analytic) = -1.0172125734956306476211373420518
y[1] (numeric) = -1.0172125734956306476211373420532
absolute error = 1.4e-30
relative error = 1.3763101602145243086425397765465e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.902
Order of pole = 8.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.617
y[1] (analytic) = -1.0169360482307578024676209005257
y[1] (numeric) = -1.016936048230757802467620900527
absolute error = 1.3e-30
relative error = 1.2783498060293077623065708313905e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.616
y[1] (analytic) = -1.016659275452782270936511632536
y[1] (numeric) = -1.0166592754527822709365116325374
absolute error = 1.4e-30
relative error = 1.3770591916121475525887027587768e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.9
Order of pole = 1.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.615
y[1] (analytic) = -1.0163822548716983819679018938144
y[1] (numeric) = -1.0163822548716983819679018938158
absolute error = 1.4e-30
relative error = 1.3774345166786949435900350176530e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.614
y[1] (analytic) = -1.0161049861971330623916445387347
y[1] (numeric) = -1.0161049861971330623916445387361
absolute error = 1.4e-30
relative error = 1.3778103828026959606348201617706e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.613
y[1] (analytic) = -1.0158274691383454861936482378634
y[1] (numeric) = -1.0158274691383454861936482378648
absolute error = 1.4e-30
relative error = 1.3781867910970362609086096703912e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.898
Order of pole = 1.89e-28
TOP MAIN SOLVE Loop
x[1] = -1.612
y[1] (analytic) = -1.015549703404226724251793685188
y[1] (numeric) = -1.0155497034042267242517936851894
absolute error = 1.4e-30
relative error = 1.3785637426775434684216179327237e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.611
y[1] (analytic) = -1.015271688703299394546921550942
y[1] (numeric) = -1.0152716887032993945469215509434
absolute error = 1.4e-30
relative error = 1.3789412386629966399028871688824e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.896
Order of pole = 3.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (analytic) = -1.0149934247437173128543717568226
y[1] (numeric) = -1.014993424743717312854371756824
absolute error = 1.4e-30
relative error = 1.3793192801751357665741110277636e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.895
Order of pole = 1.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.609
y[1] (analytic) = -1.0147149112332651439215824923232
y[1] (numeric) = -1.0147149112332651439215824923246
absolute error = 1.4e-30
relative error = 1.3796978683386713119599355762587e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
memory used=61.0MB, alloc=4.3MB, time=7.65
TOP MAIN SOLVE Loop
x[1] = -1.608
y[1] (analytic) = -1.0144361478793580531372863542673
y[1] (numeric) = -1.0144361478793580531372863542687
absolute error = 1.4e-30
relative error = 1.3800770042812937858923348199567e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.894
Order of pole = 2.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.607
y[1] (analytic) = -1.0141571343890413586978700768424
y[1] (numeric) = -1.0141571343890413586978700768439
absolute error = 1.5e-30
relative error = 1.4790607383575178802151149914799e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.893
Order of pole = 6.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.606
y[1] (analytic) = -1.0138778704689901842764935268911
y[1] (numeric) = -1.0138778704689901842764935268926
absolute error = 1.5e-30
relative error = 1.4794681328887708809792796158084e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.605
y[1] (analytic) = -1.0135983558255091122005929693204
y[1] (numeric) = -1.0135983558255091122005929693219
absolute error = 1.5e-30
relative error = 1.4798761179701685483571904321267e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.891
Order of pole = 1.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.604
y[1] (analytic) = -1.0133185901645318371434230606528
y[1] (numeric) = -1.0133185901645318371434230606542
absolute error = 1.4e-30
relative error = 1.3815990485013039880719796069428e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.89
Order of pole = 7.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.603
y[1] (analytic) = -1.0130385731916208203353216053524
y[1] (numeric) = -1.0130385731916208203353216053538
absolute error = 1.4e-30
relative error = 1.3819809403596951470874505915554e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.889
Order of pole = 9.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.602
y[1] (analytic) = -1.0127583046119669443004108100369
y[1] (numeric) = -1.0127583046119669443004108100384
absolute error = 1.5e-30
relative error = 1.4811036287426121545048654929333e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.888
Order of pole = 1.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.601
y[1] (analytic) = -1.0124777841303891681244785954202
y[1] (numeric) = -1.0124777841303891681244785954216
absolute error = 1.4e-30
relative error = 1.3827463890503545592903573581796e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (analytic) = -1.0121970114513341832598134752381
y[1] (numeric) = -1.0121970114513341832598134752395
absolute error = 1.4e-30
relative error = 1.3831299481833247327130182554885e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.887
Order of pole = 2.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.599
y[1] (analytic) = -1.0119159862788760698727965858925
y[1] (numeric) = -1.0119159862788760698727965858939
absolute error = 1.4e-30
relative error = 1.3835140653802963389818486513479e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.886
Order of pole = 6.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.598
y[1] (analytic) = -1.0116347083167159537400846505073
y[1] (numeric) = -1.0116347083167159537400846505087
absolute error = 1.4e-30
relative error = 1.3838987417992949982013993268947e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.597
y[1] (analytic) = -1.011353177268181663699247986941
y[1] (numeric) = -1.0113531772681816636992479869424
absolute error = 1.4e-30
relative error = 1.3842839786014341255057462450085e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.596
y[1] (analytic) = -1.0110713928362273896597581214427
y[1] (numeric) = -1.0110713928362273896597581214442
absolute error = 1.5e-30
relative error = 1.4835747610188481628289499893797e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.595
y[1] (analytic) = -1.0107893547234333411802501484831
y[1] (numeric) = -1.0107893547234333411802501484845
absolute error = 1.4e-30
relative error = 1.3850561380150865838596201021123e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.883
Order of pole = 5.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.594
y[1] (analytic) = -1.0105070626320054066180156832441
y[1] (numeric) = -1.0105070626320054066180156832456
absolute error = 1.5e-30
relative error = 1.4844032817475243931882971323650e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.593
y[1] (analytic) = -1.0102245162637748128567130867272
y[1] (numeric) = -1.0102245162637748128567130867287
absolute error = 1.5e-30
relative error = 1.4848184496131771675664712562815e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.592
y[1] (analytic) = -1.0099417153201977856183126048325
y[1] (numeric) = -1.009941715320197785618312604834
absolute error = 1.5e-30
relative error = 1.4852342241595905267657615121840e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.88
Order of pole = 9e-30
TOP MAIN SOLVE Loop
x[1] = -1.591
y[1] (analytic) = -1.0096586595023552103653251525016
y[1] (numeric) = -1.0096586595023552103653251525032
absolute error = 1.6e-30
relative error = 1.5846939804276176886604799138806e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.879
Order of pole = 1.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (analytic) = -1.0093753485109522937993946924935
y[1] (numeric) = -1.0093753485109522937993946924951
absolute error = 1.6e-30
relative error = 1.5851387715782312811861420427006e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.878
Order of pole = 5.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.589
y[1] (analytic) = -1.0090917820463182259623655059993
y[1] (numeric) = -1.0090917820463182259623655060008
absolute error = 1.5e-30
relative error = 1.4864852005415981502776741995469e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.877
Order of pole = 6.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.588
y[1] (analytic) = -1.008807959808405842945967129505
y[1] (numeric) = -1.0088079598084058429459671295065
absolute error = 1.5e-30
relative error = 1.4869034144862239254329945223074e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.877
Order of pole = 8.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.587
y[1] (analytic) = -1.0085238814967912902162913394908
y[1] (numeric) = -1.0085238814967912902162913394923
absolute error = 1.5e-30
relative error = 1.4873222414662001094395701636065e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.586
y[1] (analytic) = -1.0082395468106736865592673041213
y[1] (numeric) = -1.0082395468106736865592673041228
absolute error = 1.5e-30
relative error = 1.4877416827626864036801875947434e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.875
Order of pole = 4.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.585
y[1] (analytic) = -1.0079549554488747886533728894521
y[1] (numeric) = -1.0079549554488747886533728894536
absolute error = 1.5e-30
relative error = 1.4881617396602824514394643625479e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.874
Order of pole = 4.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.584
y[1] (analytic) = -1.0076701071098386562758521072564
y[1] (numeric) = -1.0076701071098386562758521072579
absolute error = 1.5e-30
relative error = 1.4885824134470390793790931666164e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.873
Order of pole = 4.0e-29
memory used=64.8MB, alloc=4.3MB, time=8.14
TOP MAIN SOLVE Loop
x[1] = -1.583
y[1] (analytic) = -1.0073850014916313181487408227815
y[1] (numeric) = -1.007385001491631318148740822783
absolute error = 1.5e-30
relative error = 1.4890037054144695822989774161978e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.582
y[1] (analytic) = -1.0070996382919404384310351039872
y[1] (numeric) = -1.0070996382919404384310351039886
absolute error = 1.4e-30
relative error = 1.3901305757337236479514149816216e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.872
Order of pole = 6.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.581
y[1] (analytic) = -1.0068140172080749838633689895111
y[1] (numeric) = -1.0068140172080749838633689895125
absolute error = 1.4e-30
relative error = 1.3905249391364666963387812526720e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.871
Order of pole = 4.6e-29
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (analytic) = -1.0065281379369648915716009811645
y[1] (numeric) = -1.0065281379369648915716009811659
absolute error = 1.4e-30
relative error = 1.3909198831435716759357711401764e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.579
y[1] (analytic) = -1.0062420001751607375357412285954
y[1] (numeric) = -1.0062420001751607375357412285968
absolute error = 1.4e-30
relative error = 1.3913154089734836816783270409033e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.869
Order of pole = 6e-30
TOP MAIN SOLVE Loop
x[1] = -1.578
y[1] (analytic) = -1.0059556036188334057306841692848
y[1] (numeric) = -1.0059556036188334057306841692862
absolute error = 1.4e-30
relative error = 1.3917115178479327199647238789628e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.868
Order of pole = 1.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.577
y[1] (analytic) = -1.0056689479637737579452443166746
y[1] (numeric) = -1.0056689479637737579452443166761
absolute error = 1.5e-30
relative error = 1.4915445117770833792504439656851e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.867
Order of pole = 4.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.576
y[1] (analytic) = -1.0053820329053923042860259533815
y[1] (numeric) = -1.0053820329053923042860259533829
absolute error = 1.4e-30
relative error = 1.3925054896338511906183207418525e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.866
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.575
y[1] (analytic) = -1.0050948581387188743726906855402
y[1] (numeric) = -1.0050948581387188743726906855416
absolute error = 1.4e-30
relative error = 1.3929033550053024094604611731702e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.866
Order of pole = 5.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.574
y[1] (analytic) = -1.0048074233584022892312201487656
y[1] (numeric) = -1.004807423358402289231220148767
absolute error = 1.4e-30
relative error = 1.3933018083412760002077412369442e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.573
y[1] (analytic) = -1.0045197282587100338918046264291
y[1] (numeric) = -1.0045197282587100338918046264305
absolute error = 1.4e-30
relative error = 1.3937008508800890425456882794909e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.572
y[1] (analytic) = -1.004231772533527930698021947339
y[1] (numeric) = -1.0042317725335279306980219473404
absolute error = 1.4e-30
relative error = 1.3941004838634088283548594502460e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.863
Order of pole = 1.7e-29
TOP MAIN SOLVE Loop
x[1] = -1.571
y[1] (analytic) = -1.0039435558763598133340047729067
y[1] (numeric) = -1.0039435558763598133340047729081
absolute error = 1.4e-30
relative error = 1.3945007085362638932156124836620e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.862
Order of pole = 2.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (analytic) = -1.0036550779803272015763282638849
y[1] (numeric) = -1.0036550779803272015763282638863
absolute error = 1.4e-30
relative error = 1.3949015261470550907178921127193e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.569
y[1] (analytic) = -1.0033663385381689767773841342047
y[1] (numeric) = -1.003366338538168976777384134206
absolute error = 1.3e-30
relative error = 1.2956384423798833733556789835119e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.861
Order of pole = 1.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.568
y[1] (analytic) = -1.0030773372422410580870412547239
y[1] (numeric) = -1.0030773372422410580870412547252
absolute error = 1.3e-30
relative error = 1.2960117348220506611480591337277e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.86
Order of pole = 1e-30
TOP MAIN SOLVE Loop
x[1] = -1.567
y[1] (analytic) = -1.0027880737845160794194272632517
y[1] (numeric) = -1.0027880737845160794194272632531
absolute error = 1.4e-30
relative error = 1.3961075491418725510702726147951e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.566
y[1] (analytic) = -1.0024985478565830671717000694497
y[1] (numeric) = -1.0024985478565830671717000694511
absolute error = 1.4e-30
relative error = 1.3965107510562531892846525598510e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.565
y[1] (analytic) = -1.0022087591496471187017127145426
y[1] (numeric) = -1.002208759149647118701712714544
absolute error = 1.4e-30
relative error = 1.3969145522015496196541870792763e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.564
y[1] (analytic) = -1.001918707354529081571509756627
y[1] (numeric) = -1.0019187073545290815715097566285
absolute error = 1.5e-30
relative error = 1.4971274505499624132290265103813e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.563
y[1] (analytic) = -1.0016283921616652335636282031507
y[1] (numeric) = -1.0016283921616652335636282031522
absolute error = 1.5e-30
relative error = 1.4975613827826641612177568731801e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.856
Order of pole = 4.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.562
y[1] (analytic) = -1.0013378132611069634772110032747
y[1] (numeric) = -1.0013378132611069634772110032762
absolute error = 1.5e-30
relative error = 1.4979959611381047719268574988990e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.855
Order of pole = 4.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.561
y[1] (analytic) = -1.0010469703425204527109762447437
y[1] (numeric) = -1.0010469703425204527109762447453
absolute error = 1.6e-30
relative error = 1.5983265994527114442746498497754e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (analytic) = -1.0007558630951863576401204729864
y[1] (numeric) = -1.0007558630951863576401204729879
absolute error = 1.5e-30
relative error = 1.4988670617034679354256225631317e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.853
Order of pole = 8e-30
TOP MAIN SOLVE Loop
x[1] = -1.559
y[1] (analytic) = -1.0004644912079994927942699648733
y[1] (numeric) = -1.0004644912079994927942699648749
absolute error = 1.6e-30
relative error = 1.5992571591102630368692017763526e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=8.61
x[1] = -1.558
y[1] (analytic) = -1.0001728543694685148436293462945
y[1] (numeric) = -1.0001728543694685148436293462961
absolute error = 1.6e-30
relative error = 1.5997234808064012317074721774728e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.557
y[1] (analytic) = -0.99988095226771560740051264188759
y[1] (numeric) = -0.99988095226771560740051264188919
absolute error = 1.60e-30
relative error = 1.6001904990501349490556788548400e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.85
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -1.556
y[1] (analytic) = -0.99958878459047616664347768728934
y[1] (numeric) = -0.99958878459047616664347768729095
absolute error = 1.61e-30
relative error = 1.6106623291692939625011439359222e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.85
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.555
y[1] (analytic) = -0.99929635102509848777132081959536
y[1] (numeric) = -0.99929635102509848777132081959696
absolute error = 1.60e-30
relative error = 1.6011266311126699419206450725263e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.849
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -1.554
y[1] (analytic) = -0.99900365125854345229422489073047
y[1] (numeric) = -0.99900365125854345229422489073207
absolute error = 1.60e-30
relative error = 1.6015957479077500450057706464663e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.553
y[1] (analytic) = -0.99871068497738421616938992156386
y[1] (numeric) = -0.99871068497738421616938992156546
absolute error = 1.60e-30
relative error = 1.6020655672030103177982190154784e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.847
Order of pole = 3.3e-29
TOP MAIN SOLVE Loop
x[1] = -1.552
y[1] (analytic) = -0.99841745186780589878851213227124
y[1] (numeric) = -0.99841745186780589878851213227284
absolute error = 1.60e-30
relative error = 1.6025360904967893311045555018496e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.846
Order of pole = 1.4e-29
TOP MAIN SOLVE Loop
x[1] = -1.551
y[1] (analytic) = -0.99812395161560527282451364706925
y[1] (numeric) = -0.99812395161560527282451364707085
absolute error = 1.60e-30
relative error = 1.6030073192915297970520752896770e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.845
Order of pole = 1.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (analytic) = -0.9978301839061904549449618794427
y[1] (numeric) = -0.99783018390619045494496187944431
absolute error = 1.61e-30
relative error = 1.6135010004381284529241597820835e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.549
y[1] (analytic) = -0.99753614842458059739965445777235
y[1] (numeric) = -0.99753614842458059739965445777395
absolute error = 1.60e-30
relative error = 1.6039518994142687893315113032413e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.548
y[1] (analytic) = -0.99724184485540558048988255126777
y[1] (numeric) = -0.99724184485540558048988255126937
absolute error = 1.60e-30
relative error = 1.6044252537677968559531589495527e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.843
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -1.547
y[1] (analytic) = -0.99694727288290570592692260273558
y[1] (numeric) = -0.99694727288290570592692260273717
absolute error = 1.59e-30
relative error = 1.5948686989254145082955844787212e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.546
y[1] (analytic) = -0.99665243219093139108734376838494
y[1] (numeric) = -0.99665243219093139108734376838654
absolute error = 1.60e-30
relative error = 1.6053740986541672233920452628235e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.545
y[1] (analytic) = -0.9963573224629428641727558060101
y[1] (numeric) = -0.9963573224629428641727558060117
absolute error = 1.60e-30
relative error = 1.6058495922375360336227880499818e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.544
y[1] (analytic) = -0.99606194338200986028165974190967
y[1] (numeric) = -0.99606194338200986028165974191127
absolute error = 1.60e-30
relative error = 1.6063258019550373533630037941782e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.543
y[1] (analytic) = -0.99576629463081131840110138422489
y[1] (numeric) = -0.99576629463081131840110138422649
absolute error = 1.60e-30
relative error = 1.6068027293424441336764153856554e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.839
Order of pole = 7e-30
TOP MAIN SOLVE Loop
x[1] = -1.542
y[1] (analytic) = -0.99547037589163507932586563642001
y[1] (numeric) = -0.99547037589163507932586563642161
absolute error = 1.60e-30
relative error = 1.6072803759397585633827086330784e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.838
Order of pole = 5e-30
TOP MAIN SOLVE Loop
x[1] = -1.541
y[1] (analytic) = -0.9951741868463775845129875998069
y[1] (numeric) = -0.9951741868463775845129875998085
absolute error = 1.60e-30
relative error = 1.6077587432912262440592841345728e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (analytic) = -0.99487772717654357587939463874932
y[1] (numeric) = -0.99487772717654357587939463875092
absolute error = 1.60e-30
relative error = 1.6082378329453504210445544821359e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.836
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.539
y[1] (analytic) = -0.99458099656324579655053191688854
y[1] (numeric) = -0.99458099656324579655053191689014
absolute error = 1.60e-30
relative error = 1.6087176464549062706981476748627e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.538
y[1] (analytic) = -0.99428399468720469256786239782779
y[1] (numeric) = -0.99428399468720469256786239782939
absolute error = 1.60e-30
relative error = 1.6091981853769552441747014861439e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.537
y[1] (analytic) = -0.99398672122874811556317093961612
y[1] (numeric) = -0.99398672122874811556317093961773
absolute error = 1.61e-30
relative error = 1.6197399478433148396440730184757e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.536
y[1] (analytic) = -0.99368917586781102640764089949904
y[1] (numeric) = -0.99368917586781102640764089950065
absolute error = 1.61e-30
relative error = 1.6202249547439730527529991657919e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.833
Order of pole = 1.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.535
y[1] (analytic) = -0.99339135828393519984371060417091
y[1] (numeric) = -0.99339135828393519984371060417252
absolute error = 1.61e-30
relative error = 1.6207106963173553041441823714637e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.534
y[1] (analytic) = -0.99309326815626893010775613158899
y[1] (numeric) = -0.9930932681562689301077561315906
absolute error = 1.61e-30
relative error = 1.6211971741476524157670845866080e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.831
Order of pole = 1e-30
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=9.10
x[1] = -1.533
y[1] (analytic) = -0.99279490516356673755168609370703
y[1] (numeric) = -0.99279490516356673755168609370864
absolute error = 1.61e-30
relative error = 1.6216843898234413028319106590675e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.532
y[1] (analytic) = -0.99249626898418907627157350567385
y[1] (numeric) = -0.99249626898418907627157350567546
absolute error = 1.61e-30
relative error = 1.6221723449376997539324480070386e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.531
y[1] (analytic) = -0.99219735929610204275148937653489
y[1] (numeric) = -0.9921973592961020427514893765365
absolute error = 1.61e-30
relative error = 1.6226610410878212698816886153014e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.829
Order of pole = 6.2e-29
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (analytic) = -0.99189817577687708553074235968741
y[1] (numeric) = -0.99189817577687708553074235968902
absolute error = 1.61e-30
relative error = 1.6231504798756299615294631599976e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.828
Order of pole = 2.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.529
y[1] (analytic) = -0.99159871810369071590276865868826
y[1] (numeric) = -0.99159871810369071590276865868988
absolute error = 1.62e-30
relative error = 1.6337253875217271559434831342807e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.827
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -1.528
y[1] (analytic) = -0.9912989859533242196539563959113
y[1] (numeric) = -0.99129898595332421965395639591291
absolute error = 1.61e-30
relative error = 1.6241315917938481674505009651609e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.527
y[1] (analytic) = -0.99099897900216336985072881841382
y[1] (numeric) = -0.99099897900216336985072881841543
absolute error = 1.61e-30
relative error = 1.6246232681501938651370612057585e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.825
Order of pole = 2e-30
TOP MAIN SOLVE Loop
x[1] = -1.526
y[1] (analytic) = -0.99069869692619814068325103761255
y[1] (numeric) = -0.99069869692619814068325103761416
absolute error = 1.61e-30
relative error = 1.6251156935961293182080590226054e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.525
y[1] (analytic) = -0.99039813940102242237416547740178
y[1] (numeric) = -0.99039813940102242237416547740339
absolute error = 1.61e-30
relative error = 1.6256088697558572383561161586224e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.824
Order of pole = 9e-30
TOP MAIN SOLVE Loop
x[1] = -1.524
y[1] (analytic) = -0.99009730610183373716080183958421
y[1] (numeric) = -0.99009730610183373716080183958583
absolute error = 1.62e-30
relative error = 1.6362028156385866911251814406580e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.523
y[1] (analytic) = -0.98979619670343295635934818633987
y[1] (numeric) = -0.98979619670343295635934818634149
absolute error = 1.62e-30
relative error = 1.6367005706785832897791131225197e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.822
Order of pole = 1.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.522
y[1] (analytic) = -0.98949481088022401851951068734359
y[1] (numeric) = -0.98949481088022401851951068734522
absolute error = 1.63e-30
relative error = 1.6473052532231092250798714781341e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.521
y[1] (analytic) = -0.98919314830621364867823068446841
y[1] (numeric) = -0.98919314830621364867823068447004
absolute error = 1.63e-30
relative error = 1.6478076124880505325338848840615e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (analytic) = -0.9888912086550110787210689901915
y[1] (numeric) = -0.98889120865501107872106899019313
absolute error = 1.63e-30
relative error = 1.6483107400832895301365860198905e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.819
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.519
y[1] (analytic) = -0.98858899159982776885990875726318
y[1] (numeric) = -0.9885889915998277688599087572648
absolute error = 1.62e-30
relative error = 1.6386992104558675069847737452605e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.819
Order of pole = 1.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.518
y[1] (analytic) = -0.9882864968134771302356698373165
y[1] (numeric) = -0.98828649681347713023566983731812
absolute error = 1.62e-30
relative error = 1.6392007836020736750766286527804e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.818
Order of pole = 6.9e-29
TOP MAIN SOLVE Loop
x[1] = -1.517
y[1] (analytic) = -0.98798372396837424865476928529662
y[1] (numeric) = -0.98798372396837424865476928529825
absolute error = 1.63e-30
relative error = 1.6498247495949406422548486447027e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.817
Order of pole = 1.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.516
y[1] (analytic) = -0.98768067273653560946810456528295
y[1] (numeric) = -0.98768067273653560946810456528458
absolute error = 1.63e-30
relative error = 1.6503309672789389921271235897473e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.816
Order of pole = 1.6e-29
TOP MAIN SOLVE Loop
x[1] = -1.515
y[1] (analytic) = -0.98737734278957882360137807187295
y[1] (numeric) = -0.98737734278957882360137807187458
absolute error = 1.63e-30
relative error = 1.6508379617004957606613032126865e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.514
y[1] (analytic) = -0.98707373379872235474562380020178
y[1] (numeric) = -0.98707373379872235474562380020341
absolute error = 1.63e-30
relative error = 1.6513457345552049518441849529639e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.513
y[1] (analytic) = -0.98676984543478524771683937729389
y[1] (numeric) = -0.98676984543478524771683937729551
absolute error = 1.62e-30
relative error = 1.6417202121597101205239995322559e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.512
y[1] (analytic) = -0.98646567736818685799366920818855
y[1] (numeric) = -0.98646567736818685799366920819017
absolute error = 1.62e-30
relative error = 1.6422264222329894742844163397107e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.511
y[1] (analytic) = -0.98616122926894658244212719255684
y[1] (numeric) = -0.98616122926894658244212719255847
absolute error = 1.63e-30
relative error = 1.6528737407455563802317643672053e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.812
Order of pole = 3.8e-29
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (analytic) = -0.98585650080668359123639033173802
y[1] (numeric) = -0.98585650080668359123639033173965
absolute error = 1.63e-30
relative error = 1.6533846443840880872349491979335e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.811
Order of pole = 3.0e-29
TOP MAIN SOLVE Loop
x[1] = -1.509
y[1] (analytic) = -0.98555149165061656098473757267363
y[1] (numeric) = -0.98555149165061656098473757267526
absolute error = 1.63e-30
relative error = 1.6538963350053393144261040859491e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.508
y[1] (analytic) = -0.98524620146956340906975142451197
y[1] (numeric) = -0.9852462014695634090697514245136
absolute error = 1.63e-30
relative error = 1.6544088143336572552249226731848e-28 %
Correct digits = 29
h = 0.001
memory used=76.2MB, alloc=4.3MB, time=9.59
Complex estimate of poles used for equation 1
Radius of convergence = 1.809
Order of pole = 4.1e-29
TOP MAIN SOLVE Loop
x[1] = -1.507
y[1] (analytic) = -0.98494062993194102921194323609649
y[1] (numeric) = -0.98494062993194102921194323609812
absolute error = 1.63e-30
relative error = 1.6549220840982387880355306825292e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.809
Order of pole = 5.5e-29
TOP MAIN SOLVE Loop
x[1] = -1.506
y[1] (analytic) = -0.9846347767057650282660065385424
y[1] (numeric) = -0.98463477670576502826600653854403
absolute error = 1.63e-30
relative error = 1.6554361460331470778789017956323e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.505
y[1] (analytic) = -0.98432864145864946425894653704764
y[1] (numeric) = -0.98432864145864946425894653704926
absolute error = 1.62e-30
relative error = 1.6457917932768538386274590761773e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.504
y[1] (analytic) = -0.98402222385780658567937768037798
y[1] (numeric) = -0.9840222238578065856793776803796
absolute error = 1.62e-30
relative error = 1.6463042812680352905974205766580e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.806
Order of pole = 8e-30
TOP MAIN SOLVE Loop
x[1] = -1.503
y[1] (analytic) = -0.9837155235700465720273252455123
y[1] (numeric) = -0.98371552357004657202732524551392
absolute error = 1.62e-30
relative error = 1.6468175617690616580411006200903e-28 %
Correct digits = 29
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = -1.502
y[1] (analytic) = -0.98340854026177727563391104913087
y[1] (numeric) = -0.98340854026177727563391104913249
absolute error = 1.62e-30
relative error = 1.6473316365228697445778648181251e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.804
Order of pole = 1.17e-28
TOP MAIN SOLVE Loop
x[1] = -1.501
y[1] (analytic) = -0.98310127359900396476034773737684
y[1] (numeric) = -0.98310127359900396476034773737846
absolute error = 1.62e-30
relative error = 1.6478465072773162901035083204430e-28 %
Correct digits = 29
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.804
Order of pole = 1.0e-29
Finished!
diff ( y , x , 1 ) = 1.0/ (x * x + 1.0) ;
Iterations = 500
Total Elapsed Time = 9 Seconds
Elapsed Time(since restart) = 9 Seconds
Time to Timeout = 2 Minutes 50 Seconds
Percent Done = 100.2 %
> quit
memory used=77.4MB, alloc=4.3MB, time=9.73