|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_log10abserr, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > djd_debug2, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_hmin, > glob_disp_incr, > glob_optimal_expect_sec, > glob_iter, > glob_h, > glob_initial_pass, > glob_clock_sec, > sec_in_min, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_max_iter, > glob_last_good_h, > glob_not_yet_start_msg, > glob_almost_1, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > centuries_in_millinium, > days_in_year, > hours_in_day, > djd_debug, > glob_subiter_method, > glob_current_iter, > glob_max_sec, > glob_optimal_start, > glob_curr_iter_when_opt, > glob_warned, > glob_log10_relerr, > glob_not_yet_finished, > min_in_hour, > glob_log10normmin, > glob_max_minutes, > glob_warned2, > glob_smallish_float, > glob_no_eqs, > glob_max_hours, > glob_relerr, > glob_look_poles, > glob_start, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3D0, > array_const_0D0, > #END CONST > array_norms, > array_y_init, > array_type_pole, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_fact_1, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y_higher, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_poles, > array_complex_pole, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, ALWAYS, INFO, glob_log10abserr, glob_abserr, glob_log10_abserr, glob_large_float, glob_clock_start_sec, djd_debug2, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_max_trunc_err, glob_hmin, glob_disp_incr, glob_optimal_expect_sec, glob_iter, glob_h, glob_initial_pass, glob_clock_sec, sec_in_min, MAX_UNCHANGED, glob_orig_start_sec, glob_max_iter, glob_last_good_h, glob_not_yet_start_msg, glob_almost_1, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_dump_analytic, glob_hmax, glob_optimal_done, centuries_in_millinium, days_in_year, hours_in_day, djd_debug, glob_subiter_method, glob_current_iter, glob_max_sec, glob_optimal_start, glob_curr_iter_when_opt, glob_warned, glob_log10_relerr, glob_not_yet_finished, min_in_hour, glob_log10normmin, glob_max_minutes, glob_warned2, glob_smallish_float, glob_no_eqs, glob_max_hours, glob_relerr, glob_look_poles, glob_start, glob_max_rel_trunc_err, glob_hmin_init, glob_dump, array_const_1, array_const_3D0, array_const_0D0, array_norms, array_y_init, array_type_pole, array_pole, array_y, array_x, array_1st_rel_error, array_fact_1, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y_higher, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_poles, array_complex_pole, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_log10abserr, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > djd_debug2, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_hmin, > glob_disp_incr, > glob_optimal_expect_sec, > glob_iter, > glob_h, > glob_initial_pass, > glob_clock_sec, > sec_in_min, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_max_iter, > glob_last_good_h, > glob_not_yet_start_msg, > glob_almost_1, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > centuries_in_millinium, > days_in_year, > hours_in_day, > djd_debug, > glob_subiter_method, > glob_current_iter, > glob_max_sec, > glob_optimal_start, > glob_curr_iter_when_opt, > glob_warned, > glob_log10_relerr, > glob_not_yet_finished, > min_in_hour, > glob_log10normmin, > glob_max_minutes, > glob_warned2, > glob_smallish_float, > glob_no_eqs, > glob_max_hours, > glob_relerr, > glob_look_poles, > glob_start, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3D0, > array_const_0D0, > #END CONST > array_norms, > array_y_init, > array_type_pole, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_fact_1, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y_higher, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_poles, > array_complex_pole, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, ALWAYS, INFO, glob_log10abserr, glob_abserr, glob_log10_abserr, glob_large_float, glob_clock_start_sec, djd_debug2, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_max_trunc_err, glob_hmin, glob_disp_incr, glob_optimal_expect_sec, glob_iter, glob_h, glob_initial_pass, glob_clock_sec, sec_in_min, MAX_UNCHANGED, glob_orig_start_sec, glob_max_iter, glob_last_good_h, glob_not_yet_start_msg, glob_almost_1, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_dump_analytic, glob_hmax, glob_optimal_done, centuries_in_millinium, days_in_year, hours_in_day, djd_debug, glob_subiter_method, glob_current_iter, glob_max_sec, glob_optimal_start, glob_curr_iter_when_opt, glob_warned, glob_log10_relerr, glob_not_yet_finished, min_in_hour, glob_log10normmin, glob_max_minutes, glob_warned2, glob_smallish_float, glob_no_eqs, glob_max_hours, glob_relerr, glob_look_poles, glob_start, glob_max_rel_trunc_err, glob_hmin_init, glob_dump, array_const_1, array_const_3D0, array_const_0D0, array_norms, array_y_init, array_type_pole, array_pole, array_y, array_x, array_1st_rel_error, array_fact_1, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y_higher, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_poles, array_complex_pole, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_log10abserr, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > djd_debug2, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_hmin, > glob_disp_incr, > glob_optimal_expect_sec, > glob_iter, > glob_h, > glob_initial_pass, > glob_clock_sec, > sec_in_min, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_max_iter, > glob_last_good_h, > glob_not_yet_start_msg, > glob_almost_1, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > centuries_in_millinium, > days_in_year, > hours_in_day, > djd_debug, > glob_subiter_method, > glob_current_iter, > glob_max_sec, > glob_optimal_start, > glob_curr_iter_when_opt, > glob_warned, > glob_log10_relerr, > glob_not_yet_finished, > min_in_hour, > glob_log10normmin, > glob_max_minutes, > glob_warned2, > glob_smallish_float, > glob_no_eqs, > glob_max_hours, > glob_relerr, > glob_look_poles, > glob_start, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3D0, > array_const_0D0, > #END CONST > array_norms, > array_y_init, > array_type_pole, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_fact_1, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y_higher, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_poles, > array_complex_pole, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, ALWAYS, INFO, glob_log10abserr, glob_abserr, glob_log10_abserr, glob_large_float, glob_clock_start_sec, djd_debug2, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_max_trunc_err, glob_hmin, glob_disp_incr, glob_optimal_expect_sec, glob_iter, glob_h, glob_initial_pass, glob_clock_sec, sec_in_min, MAX_UNCHANGED, glob_orig_start_sec, glob_max_iter, glob_last_good_h, glob_not_yet_start_msg, glob_almost_1, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_dump_analytic, glob_hmax, glob_optimal_done, centuries_in_millinium, days_in_year, hours_in_day, djd_debug, glob_subiter_method, glob_current_iter, glob_max_sec, glob_optimal_start, glob_curr_iter_when_opt, glob_warned, glob_log10_relerr, glob_not_yet_finished, min_in_hour, glob_log10normmin, glob_max_minutes, glob_warned2, glob_smallish_float, glob_no_eqs, glob_max_hours, glob_relerr, glob_look_poles, glob_start, glob_max_rel_trunc_err, glob_hmin_init, glob_dump, array_const_1, array_const_3D0, array_const_0D0, array_norms, array_y_init, array_type_pole, array_pole, array_y, array_x, array_1st_rel_error, array_fact_1, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y_higher, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_poles, array_complex_pole, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_log10abserr, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > djd_debug2, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_hmin, > glob_disp_incr, > glob_optimal_expect_sec, > glob_iter, > glob_h, > glob_initial_pass, > glob_clock_sec, > sec_in_min, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_max_iter, > glob_last_good_h, > glob_not_yet_start_msg, > glob_almost_1, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > centuries_in_millinium, > days_in_year, > hours_in_day, > djd_debug, > glob_subiter_method, > glob_current_iter, > glob_max_sec, > glob_optimal_start, > glob_curr_iter_when_opt, > glob_warned, > glob_log10_relerr, > glob_not_yet_finished, > min_in_hour, > glob_log10normmin, > glob_max_minutes, > glob_warned2, > glob_smallish_float, > glob_no_eqs, > glob_max_hours, > glob_relerr, > glob_look_poles, > glob_start, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3D0, > array_const_0D0, > #END CONST > array_norms, > array_y_init, > array_type_pole, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_fact_1, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y_higher, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_poles, > array_complex_pole, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, ALWAYS, INFO, glob_log10abserr, glob_abserr, glob_log10_abserr, glob_large_float, glob_clock_start_sec, djd_debug2, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_max_trunc_err, glob_hmin, glob_disp_incr, glob_optimal_expect_sec, glob_iter, glob_h, glob_initial_pass, glob_clock_sec, sec_in_min, MAX_UNCHANGED, glob_orig_start_sec, glob_max_iter, glob_last_good_h, glob_not_yet_start_msg, glob_almost_1, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_dump_analytic, glob_hmax, glob_optimal_done, centuries_in_millinium, days_in_year, hours_in_day, djd_debug, glob_subiter_method, glob_current_iter, glob_max_sec, glob_optimal_start, glob_curr_iter_when_opt, glob_warned, glob_log10_relerr, glob_not_yet_finished, min_in_hour, glob_log10normmin, glob_max_minutes, glob_warned2, glob_smallish_float, glob_no_eqs, glob_max_hours, glob_relerr, glob_look_poles, glob_start, glob_max_rel_trunc_err, glob_hmin_init, glob_dump, array_const_1, array_const_3D0, array_const_0D0, array_norms, array_y_init, array_type_pole, array_pole, array_y, array_x, array_1st_rel_error, array_fact_1, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y_higher, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_poles, array_complex_pole, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_log10abserr, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > djd_debug2, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_hmin, > glob_disp_incr, > glob_optimal_expect_sec, > glob_iter, > glob_h, > glob_initial_pass, > glob_clock_sec, > sec_in_min, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_max_iter, > glob_last_good_h, > glob_not_yet_start_msg, > glob_almost_1, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > centuries_in_millinium, > days_in_year, > hours_in_day, > djd_debug, > glob_subiter_method, > glob_current_iter, > glob_max_sec, > glob_optimal_start, > glob_curr_iter_when_opt, > glob_warned, > glob_log10_relerr, > glob_not_yet_finished, > min_in_hour, > glob_log10normmin, > glob_max_minutes, > glob_warned2, > glob_smallish_float, > glob_no_eqs, > glob_max_hours, > glob_relerr, > glob_look_poles, > glob_start, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3D0, > array_const_0D0, > #END CONST > array_norms, > array_y_init, > array_type_pole, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_fact_1, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y_higher, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_poles, > array_complex_pole, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, ALWAYS, INFO, glob_log10abserr, glob_abserr, glob_log10_abserr, glob_large_float, glob_clock_start_sec, djd_debug2, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_max_trunc_err, glob_hmin, glob_disp_incr, glob_optimal_expect_sec, glob_iter, glob_h, glob_initial_pass, glob_clock_sec, sec_in_min, MAX_UNCHANGED, glob_orig_start_sec, glob_max_iter, glob_last_good_h, glob_not_yet_start_msg, glob_almost_1, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_dump_analytic, glob_hmax, glob_optimal_done, centuries_in_millinium, days_in_year, hours_in_day, djd_debug, glob_subiter_method, glob_current_iter, glob_max_sec, glob_optimal_start, glob_curr_iter_when_opt, glob_warned, glob_log10_relerr, glob_not_yet_finished, min_in_hour, glob_log10normmin, glob_max_minutes, glob_warned2, glob_smallish_float, glob_no_eqs, glob_max_hours, glob_relerr, glob_look_poles, glob_start, glob_max_rel_trunc_err, glob_hmin_init, glob_dump, array_const_1, array_const_3D0, array_const_0D0, array_norms, array_y_init, array_type_pole, array_pole, array_y, array_x, array_1st_rel_error, array_fact_1, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y_higher, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_poles, array_complex_pole, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_log10abserr, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > djd_debug2, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_hmin, > glob_disp_incr, > glob_optimal_expect_sec, > glob_iter, > glob_h, > glob_initial_pass, > glob_clock_sec, > sec_in_min, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_max_iter, > glob_last_good_h, > glob_not_yet_start_msg, > glob_almost_1, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > centuries_in_millinium, > days_in_year, > hours_in_day, > djd_debug, > glob_subiter_method, > glob_current_iter, > glob_max_sec, > glob_optimal_start, > glob_curr_iter_when_opt, > glob_warned, > glob_log10_relerr, > glob_not_yet_finished, > min_in_hour, > glob_log10normmin, > glob_max_minutes, > glob_warned2, > glob_smallish_float, > glob_no_eqs, > glob_max_hours, > glob_relerr, > glob_look_poles, > glob_start, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3D0, > array_const_0D0, > #END CONST > array_norms, > array_y_init, > array_type_pole, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_fact_1, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y_higher, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_poles, > array_complex_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult $eq_no = 1 i = 1 > array_tmp1[1] := (array_m1[1] * (array_const_3D0[1])); > #emit pre div $eq_no = 1 i = 1 > array_tmp2[1] := (array_tmp1[1] / (array_x[1])); > #emit pre div $eq_no = 1 i = 1 > array_tmp3[1] := (array_tmp2[1] / (array_x[1])); > #emit pre div $eq_no = 1 i = 1 > array_tmp4[1] := (array_tmp3[1] / (array_x[1])); > #emit pre div $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp4[1] / (array_x[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_m1,array_const_3D0,1); > #emit pre div $eq_no = 1 i = 2 > array_tmp2[2] := ((array_tmp1[2] - ats(2,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 2 > array_tmp3[2] := ((array_tmp2[2] - ats(2,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 2 > array_tmp4[2] := ((array_tmp3[2] - ats(2,array_x,array_tmp4,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 2 > array_tmp5[2] := ((array_tmp4[2] - ats(2,array_x,array_tmp5,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 2 > array_tmp6[2] := array_const_0D0[2] + array_tmp5[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_tmp6[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_m1,array_const_3D0,1); > #emit pre div $eq_no = 1 i = 3 > array_tmp2[3] := ((array_tmp1[3] - ats(3,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 3 > array_tmp3[3] := ((array_tmp2[3] - ats(3,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 3 > array_tmp4[3] := ((array_tmp3[3] - ats(3,array_x,array_tmp4,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 3 > array_tmp5[3] := ((array_tmp4[3] - ats(3,array_x,array_tmp5,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 3 > array_tmp6[3] := array_const_0D0[3] + array_tmp5[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_tmp6[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_m1,array_const_3D0,1); > #emit pre div $eq_no = 1 i = 4 > array_tmp2[4] := ((array_tmp1[4] - ats(4,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 4 > array_tmp3[4] := ((array_tmp2[4] - ats(4,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 4 > array_tmp4[4] := ((array_tmp3[4] - ats(4,array_x,array_tmp4,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 4 > array_tmp5[4] := ((array_tmp4[4] - ats(4,array_x,array_tmp5,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 4 > array_tmp6[4] := array_const_0D0[4] + array_tmp5[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_tmp6[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_m1,array_const_3D0,1); > #emit pre div $eq_no = 1 i = 5 > array_tmp2[5] := ((array_tmp1[5] - ats(5,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 5 > array_tmp3[5] := ((array_tmp2[5] - ats(5,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 5 > array_tmp4[5] := ((array_tmp3[5] - ats(5,array_x,array_tmp4,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 5 > array_tmp5[5] := ((array_tmp4[5] - ats(5,array_x,array_tmp5,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 5 > array_tmp6[5] := array_const_0D0[5] + array_tmp5[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_tmp6[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_m1,array_const_3D0,1); > #emit div $eq_no = 1 > array_tmp2[kkk] := ((array_tmp1[kkk] - ats(kkk,array_x,array_tmp2,2))/array_x[1]); > #emit div $eq_no = 1 > array_tmp3[kkk] := ((array_tmp2[kkk] - ats(kkk,array_x,array_tmp3,2))/array_x[1]); > #emit div $eq_no = 1 > array_tmp4[kkk] := ((array_tmp3[kkk] - ats(kkk,array_x,array_tmp4,2))/array_x[1]); > #emit div $eq_no = 1 > array_tmp5[kkk] := ((array_tmp4[kkk] - ats(kkk,array_x,array_tmp5,2))/array_x[1]); > #emit add $eq_no = 1 > array_tmp6[kkk] := array_const_0D0[kkk] + array_tmp5[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_tmp6[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, ALWAYS, INFO, glob_log10abserr, glob_abserr, glob_log10_abserr, glob_large_float, glob_clock_start_sec, djd_debug2, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_max_trunc_err, glob_hmin, glob_disp_incr, glob_optimal_expect_sec, glob_iter, glob_h, glob_initial_pass, glob_clock_sec, sec_in_min, MAX_UNCHANGED, glob_orig_start_sec, glob_max_iter, glob_last_good_h, glob_not_yet_start_msg, glob_almost_1, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_dump_analytic, glob_hmax, glob_optimal_done, centuries_in_millinium, days_in_year, hours_in_day, djd_debug, glob_subiter_method, glob_current_iter, glob_max_sec, glob_optimal_start, glob_curr_iter_when_opt, glob_warned, glob_log10_relerr, glob_not_yet_finished, min_in_hour, glob_log10normmin, glob_max_minutes, glob_warned2, glob_smallish_float, glob_no_eqs, glob_max_hours, glob_relerr, glob_look_poles, glob_start, glob_max_rel_trunc_err, glob_hmin_init, glob_dump, array_const_1, array_const_3D0, array_const_0D0, array_norms, array_y_init, array_type_pole, array_pole, array_y, array_x, array_1st_rel_error, array_fact_1, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y_higher, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_poles, array_complex_pole, glob_last; array_tmp1[1] := array_m1[1]*array_const_3D0[1]; array_tmp2[1] := array_tmp1[1]/array_x[1]; array_tmp3[1] := array_tmp2[1]/array_x[1]; array_tmp4[1] := array_tmp3[1]/array_x[1]; array_tmp5[1] := array_tmp4[1]/array_x[1]; array_tmp6[1] := array_const_0D0[1] + array_tmp5[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp6[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_const_3D0, 1); array_tmp2[2] := (array_tmp1[2] - ats(2, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[2] := (array_tmp2[2] - ats(2, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[2] := (array_tmp3[2] - ats(2, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[2] := (array_tmp4[2] - ats(2, array_x, array_tmp5, 2))/array_x[1]; array_tmp6[2] := array_const_0D0[2] + array_tmp5[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp6[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_const_3D0, 1); array_tmp2[3] := (array_tmp1[3] - ats(3, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[3] := (array_tmp2[3] - ats(3, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[3] := (array_tmp3[3] - ats(3, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[3] := (array_tmp4[3] - ats(3, array_x, array_tmp5, 2))/array_x[1]; array_tmp6[3] := array_const_0D0[3] + array_tmp5[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp6[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_const_3D0, 1); array_tmp2[4] := (array_tmp1[4] - ats(4, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[4] := (array_tmp2[4] - ats(4, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[4] := (array_tmp3[4] - ats(4, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[4] := (array_tmp4[4] - ats(4, array_x, array_tmp5, 2))/array_x[1]; array_tmp6[4] := array_const_0D0[4] + array_tmp5[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp6[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_const_3D0, 1); array_tmp2[5] := (array_tmp1[5] - ats(5, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[5] := (array_tmp2[5] - ats(5, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[5] := (array_tmp3[5] - ats(5, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[5] := (array_tmp4[5] - ats(5, array_x, array_tmp5, 2))/array_x[1]; array_tmp6[5] := array_const_0D0[5] + array_tmp5[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp6[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_m1, array_const_3D0, 1); array_tmp2[kkk] := (array_tmp1[kkk] - ats(kkk, array_x, array_tmp2, 2))/array_x[1] ; array_tmp3[kkk] := (array_tmp2[kkk] - ats(kkk, array_x, array_tmp3, 2))/array_x[1] ; array_tmp4[kkk] := (array_tmp3[kkk] - ats(kkk, array_x, array_tmp4, 2))/array_x[1] ; array_tmp5[kkk] := (array_tmp4[kkk] - ats(kkk, array_x, array_tmp5, 2))/array_x[1] ; array_tmp6[kkk] := array_const_0D0[kkk] + array_tmp5[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_tmp6[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 13 > if array_fact_1[nnn] = 0 then # if number 14 > ret := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > if array_fact_2[mmm,nnn] = 0 then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0/x/x/x; > end; exact_soln_y := proc(x) 1.0/(x*x*x) end proc > > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_log10abserr, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > djd_debug2, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_hmin, > glob_disp_incr, > glob_optimal_expect_sec, > glob_iter, > glob_h, > glob_initial_pass, > glob_clock_sec, > sec_in_min, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_max_iter, > glob_last_good_h, > glob_not_yet_start_msg, > glob_almost_1, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_dump_analytic, > glob_hmax, > glob_optimal_done, > centuries_in_millinium, > days_in_year, > hours_in_day, > djd_debug, > glob_subiter_method, > glob_current_iter, > glob_max_sec, > glob_optimal_start, > glob_curr_iter_when_opt, > glob_warned, > glob_log10_relerr, > glob_not_yet_finished, > min_in_hour, > glob_log10normmin, > glob_max_minutes, > glob_warned2, > glob_smallish_float, > glob_no_eqs, > glob_max_hours, > glob_relerr, > glob_look_poles, > glob_start, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3D0, > array_const_0D0, > #END CONST > array_norms, > array_y_init, > array_type_pole, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_fact_1, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y_higher, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_fact_2, > array_poles, > array_complex_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > ALWAYS := 1; > INFO := 2; > glob_log10abserr := 0.0; > glob_abserr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_large_float := 9.0e100; > glob_clock_start_sec := 0.0; > djd_debug2 := true; > glob_reached_optimal_h := false; > years_in_century := 100.0; > glob_percent_done := 0.0; > glob_log10relerr := 0.0; > glob_unchanged_h_cnt := 0; > glob_max_trunc_err := 0.1e-10; > glob_hmin := 0.00000000001; > glob_disp_incr := 0.1; > glob_optimal_expect_sec := 0.1; > glob_iter := 0; > glob_h := 0.1; > glob_initial_pass := true; > glob_clock_sec := 0.0; > sec_in_min := 60.0; > MAX_UNCHANGED := 10; > glob_orig_start_sec := 0.0; > glob_max_iter := 1000; > glob_last_good_h := 0.1; > glob_not_yet_start_msg := true; > glob_almost_1 := 0.9990; > glob_display_flag := true; > glob_max_opt_iter := 10; > glob_html_log := true; > glob_normmax := 0.0; > glob_small_float := 0.1e-50; > glob_optimal_clock_start_sec := 0.0; > glob_dump_analytic := false; > glob_hmax := 1.0; > glob_optimal_done := false; > centuries_in_millinium := 10.0; > days_in_year := 365.0; > hours_in_day := 24.0; > djd_debug := true; > glob_subiter_method := 3; > glob_current_iter := 0; > glob_max_sec := 10000.0; > glob_optimal_start := 0.0; > glob_curr_iter_when_opt := 0; > glob_warned := false; > glob_log10_relerr := 0.1e-10; > glob_not_yet_finished := true; > min_in_hour := 60.0; > glob_log10normmin := 0.1; > glob_max_minutes := 0.0; > glob_warned2 := false; > glob_smallish_float := 0.1e-100; > glob_no_eqs := 0; > glob_max_hours := 0.0; > glob_relerr := 0.1e-10; > glob_look_poles := false; > glob_start := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_hmin_init := 0.001; > glob_dump := false; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sing5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -1.0;"); > omniout_str(ALWAYS,"x_end := -0.7;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"1.0/x/x/x;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_norms:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 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_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > 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_y_init[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_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_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_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[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 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_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 <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_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_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -1.0; > x_end := -0.7; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001; > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-18T01:16:44-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing5") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 092 ") > ; > logitem_str(html_log_file,"sing5 diffeq.mxt") > ; > logitem_str(html_log_file,"sing5 maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, ALWAYS, INFO, glob_log10abserr, glob_abserr, glob_log10_abserr, glob_large_float, glob_clock_start_sec, djd_debug2, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_max_trunc_err, glob_hmin, glob_disp_incr, glob_optimal_expect_sec, glob_iter, glob_h, glob_initial_pass, glob_clock_sec, sec_in_min, MAX_UNCHANGED, glob_orig_start_sec, glob_max_iter, glob_last_good_h, glob_not_yet_start_msg, glob_almost_1, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_dump_analytic, glob_hmax, glob_optimal_done, centuries_in_millinium, days_in_year, hours_in_day, djd_debug, glob_subiter_method, glob_current_iter, glob_max_sec, glob_optimal_start, glob_curr_iter_when_opt, glob_warned, glob_log10_relerr, glob_not_yet_finished, min_in_hour, glob_log10normmin, glob_max_minutes, glob_warned2, glob_smallish_float, glob_no_eqs, glob_max_hours, glob_relerr, glob_look_poles, glob_start, glob_max_rel_trunc_err, glob_hmin_init, glob_dump, array_const_1, array_const_3D0, array_const_0D0, array_norms, array_y_init, array_type_pole, array_pole, array_y, array_x, array_1st_rel_error, array_fact_1, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y_higher, array_real_pole, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_fact_2, array_poles, array_complex_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; glob_iolevel := 5; glob_max_terms := 30; DEBUGMASSIVE := 4; ALWAYS := 1; INFO := 2; glob_log10abserr := 0.; glob_abserr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_clock_start_sec := 0.; djd_debug2 := true; glob_reached_optimal_h := false; years_in_century := 100.0; glob_percent_done := 0.; glob_log10relerr := 0.; glob_unchanged_h_cnt := 0; glob_max_trunc_err := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_disp_incr := 0.1; glob_optimal_expect_sec := 0.1; glob_iter := 0; glob_h := 0.1; glob_initial_pass := true; glob_clock_sec := 0.; sec_in_min := 60.0; MAX_UNCHANGED := 10; glob_orig_start_sec := 0.; glob_max_iter := 1000; glob_last_good_h := 0.1; glob_not_yet_start_msg := true; glob_almost_1 := 0.9990; glob_display_flag := true; glob_max_opt_iter := 10; glob_html_log := true; glob_normmax := 0.; glob_small_float := 0.1*10^(-50); glob_optimal_clock_start_sec := 0.; glob_dump_analytic := false; glob_hmax := 1.0; glob_optimal_done := false; centuries_in_millinium := 10.0; days_in_year := 365.0; hours_in_day := 24.0; djd_debug := true; glob_subiter_method := 3; glob_current_iter := 0; glob_max_sec := 10000.0; glob_optimal_start := 0.; glob_curr_iter_when_opt := 0; glob_warned := false; glob_log10_relerr := 0.1*10^(-10); glob_not_yet_finished := true; min_in_hour := 60.0; glob_log10normmin := 0.1; glob_max_minutes := 0.; glob_warned2 := false; glob_smallish_float := 0.1*10^(-100); glob_no_eqs := 0; glob_max_hours := 0.; glob_relerr := 0.1*10^(-10); glob_look_poles := false; glob_start := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_hmin_init := 0.001; glob_dump := false; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sing5postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -1.0;"); omniout_str(ALWAYS, "x_end := -0.7;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "1.0/x/x/x;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_norms := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[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_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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[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; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_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 <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_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_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_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_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := -1.0; x_end := -0.7; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-18T01:16:44-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing5"); logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 092 "); logitem_str(html_log_file, "sing5 diffeq.mxt"); logitem_str(html_log_file, "sing5 maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.0; x_end := -0.7; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0/x/x/x; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -1 y[1] (analytic) = -1 y[1] (numeric) = -1 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.011 Order of pole = 5.626 x[1] = -0.999 y[1] (analytic) = -1.0030060100150210280360450550661 y[1] (numeric) = -1.0030060100150220097668844616095 absolute error = 9.817308394065434e-16 relative error = 9.7878859109911115002365659999998e-14 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.01 Order of pole = 5.626 x[1] = -0.998 y[1] (analytic) = -1.0060240802406737966195482277442 y[1] (numeric) = -1.0060240802406757689628960747482 absolute error = 1.9723433478470040e-15 relative error = 1.9605329401013493572719679999998e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.009 Order of pole = 5.626 x[1] = -0.997 y[1] (analytic) = -1.0090542712201234910283314761 y[1] (numeric) = -1.0090542712201264629552265850869 absolute error = 2.9719268951089869e-15 relative error = 2.9452597148371477926036537000000e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 5.626 x[1] = -0.996 y[1] (analytic) = -1.0120966438616192807876074547054 y[1] (numeric) = -1.0120966438616232613594486201324 absolute error = 3.9805718411654270e-15 relative error = 3.9329957917632199819086720000005e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 5.626 x[1] = -0.995 y[1] (analytic) = -1.0151512594410653301861952371894 y[1] (numeric) = -1.0151512594410703285557433920922 absolute error = 4.9983695481549028e-15 relative error = 4.9237682578524973563471500000003e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 5.626 x[1] = -0.994 y[1] (analytic) = -1.0182181796046125218370125452544 y[1] (numeric) = -1.0182181796046185472494050643931 absolute error = 6.0254123925191387e-15 relative error = 5.9176044125031094862456408000000e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 5.626 x[1] = -0.993 y[1] (analytic) = -1.0212974663712710812022922527324 y[1] (numeric) = -1.0212974663712781429960695526504 absolute error = 7.0617937772999180e-15 relative error = 6.9145317694666171960741260000005e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 5.626 x[1] = -0.992 y[1] (analytic) = -1.0243891821355442919002383270116 y[1] (numeric) = -1.0243891821355523995083829246753 absolute error = 8.1076081445976637e-15 relative error = 7.9145780587957124886265855999993e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 5.626 x[1] = -0.991 y[1] (analytic) = -1.0274933896700834935271733588728 y[1] (numeric) = -1.0274933896700926564781615528544 absolute error = 9.1629509881939816e-15 relative error = 8.9177712288116048409162135999994e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 5.626 x[1] = -0.99 y[1] (analytic) = -1.0306101521283645556678920621376 y[1] (numeric) = -1.0306101521283747835867584026233 absolute error = 1.02279188663404857e-14 relative error = 9.9241394480913069342242999999995e-13 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 5.626 x[1] = -0.989 y[1] (analytic) = -1.0337395330473860237271816069859 y[1] (numeric) = -1.0337395330473973263365963232598 absolute error = 1.13026094147162739e-14 relative error = 1.0933711107475047881365139100000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 5.626 memory used=3.8MB, alloc=3.1MB, time=0.21 x[1] = -0.988 y[1] (analytic) = -1.0368815963503891341975628073193 y[1] (numeric) = -1.0368815963504015213189223637659 absolute error = 1.23871213595564466e-14 relative error = 1.1946514822094033593791475200000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9991 Order of pole = 5.626 x[1] = -0.987 y[1] (analytic) = -1.040036406349599898982511894951 y[1] (numeric) = -1.0400364063496133805370428490568 absolute error = 1.34815545309541058e-14 relative error = 1.2962579433418784899270157400000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9981 Order of pole = 5.626 x[1] = -0.986 y[1] (analytic) = -1.0432040277489934604210102726637 y[1] (numeric) = -1.0432040277490080464308866109661 absolute error = 1.45860098763383024e-14 relative error = 1.3981934011328279948709414400001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9971 Order of pole = 5.626 x[1] = -0.985 y[1] (analytic) = -1.0463845256470809207085121942383 y[1] (numeric) = -1.0463845256470966212979863246817 absolute error = 1.57005894741304434e-14 relative error = 1.5004607856200136306048525000000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9961 Order of pole = 5.626 x[1] = -0.984 y[1] (analytic) = -1.0495779655397188514815943321043 y[1] (numeric) = -1.0495779655397356768781419138103 absolute error = 1.68253965475817060e-14 relative error = 1.6030630501022067967540224000001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9951 Order of pole = 5.626 x[1] = -0.983 y[1] (analytic) = -1.0527844133229416914289368831288 y[1] (numeric) = -1.0527844133229596519644156771712 absolute error = 1.79605354787940424e-14 relative error = 1.7060031713524853357230488800000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9941 Order of pole = 5.626 x[1] = -0.982 y[1] (analytic) = -1.0560039352958172419101671644937 y[1] (numeric) = -1.0560039352958363480219900918986 absolute error = 1.91061118229274049e-14 relative error = 1.8092841498337059160337423200000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9931 Order of pole = 5.626 x[1] = -0.981 y[1] (analytic) = -1.0592365981633254727067612653502 y[1] (numeric) = -1.0592365981633457349390838612046 absolute error = 2.02622323225958544e-14 relative error = 1.9129090099161761324549870399998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.992 Order of pole = 5.626 x[1] = -0.98 y[1] (analytic) = -1.0624824690392608521959387670103 y[1] (numeric) = -1.0624824690392822812008612222721 absolute error = 2.14290049224552618e-14 relative error = 2.0168808000975512764065600000001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.991 Order of pole = 5.626 x[1] = -0.979 y[1] (analytic) = -1.0657416154491584184295952209222 y[1] (numeric) = -1.0657416154491810249683792062703 absolute error = 2.26065387839853481e-14 relative error = 2.1212025932249805296927545899999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.99 Order of pole = 5.626 x[1] = -0.978 y[1] (analytic) = -1.0690141053332438098160963061637 y[1] (numeric) = -1.0690141053332676047603967750229 absolute error = 2.37949443004688592e-14 relative error = 2.2258774867195283883945638400001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.989 Order of pole = 5.626 x[1] = -0.977 y[1] (analytic) = -1.0723000070494074763435096902299 y[1] (numeric) = -1.0723000070494324706766218609329 absolute error = 2.49943331121707030e-14 relative error = 2.3309086028028963617717598999999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.988 Order of pole = 5.626 x[1] = -0.976 y[1] (analytic) = -1.0755993893762032945488829461497 y[1] (numeric) = -1.0755993893762294993670046660824 absolute error = 2.62048181217199327e-14 relative error = 2.4362990887264714932955955199999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.987 Order of pole = 5.626 x[1] = -0.975 y[1] (analytic) = -1.0789123215158718117297998954803 y[1] (numeric) = -1.0789123215158992382433095929743 absolute error = 2.74265135096974940e-14 relative error = 2.5420521170027275727906250000002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.986 Order of pole = 5.626 x[1] = -0.974 y[1] (analytic) = -1.0822388730973883472119790717858 y[1] (numeric) = -1.0822388730974170067467295044917 absolute error = 2.86595347504327059e-14 relative error = 2.6481708856390058762126301600002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.985 Order of pole = 5.626 x[1] = -0.973 y[1] (analytic) = -1.0855791141795361808304364754183 y[1] (numeric) = -1.0855791141795660848290644869063 absolute error = 2.99039986280114880e-14 relative error = 2.7546586183737023446137696000000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.984 Order of pole = 5.626 x[1] = -0.972 y[1] (analytic) = -1.0889331152540050611520445424867 y[1] (numeric) = -1.0889331152540362211752970418802 absolute error = 3.11600232524993935e-14 relative error = 2.8615185649148884152825888000001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9829 Order of pole = 5.626 x[1] = -0.971 y[1] (analytic) = -1.0923009472485152683645087474632 y[1] (numeric) = -1.0923009472485476960925851300183 absolute error = 3.24277280763825551e-14 relative error = 2.9687540011813931098680966100003e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9819 Order of pole = 5.626 x[1] = -0.97 y[1] (analytic) = -1.0956826815299674691811853752658 y[1] (numeric) = -1.0956826815300011764150966049661 absolute error = 3.37072339112297003e-14 relative error = 3.0763682295463744261901900000001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9809 Order of pole = 5.626 x[1] = -0.969 y[1] (analytic) = -1.0990783899076186035631160806292 y[1] (numeric) = -1.0990783899076536022260606590695 absolute error = 3.49986629445784403e-14 relative error = 3.1843645790834083059169922700001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9799 Order of pole = 5.626 memory used=7.6MB, alloc=4.3MB, time=0.48 x[1] = -0.968 y[1] (analytic) = -1.1024881446362840455394987810185 y[1] (numeric) = -1.1024881446363203476782558301046 absolute error = 3.63021387570490861e-14 relative error = 3.2927464058151237642445875200001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9789 Order of pole = 5.626 x[1] = -0.967 y[1] (analytic) = -1.1059120184195662829158966860222 y[1] (numeric) = -1.1059120184196039007022363753192 absolute error = 3.76177863396892970e-14 relative error = 3.4015170929644132116032710999999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9779 Order of pole = 5.626 x[1] = -0.966 y[1] (analytic) = -1.1093500844131103631961590004675 y[1] (numeric) = -1.1093500844131493089282705533869 absolute error = 3.89457321115529194e-14 relative error = 3.5106800512082474669735102399997e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9769 Order of pole = 5.626 x[1] = -0.965 y[1] (analytic) = -1.1128024162278863556096439352199 y[1] (numeric) = -1.1128024162279266417135814516422 absolute error = 4.02861039375164223e-14 relative error = 3.6202387189341249793846387499999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9759 Order of pole = 5.626 x[1] = -0.964 y[1] (analytic) = -1.1162690879334990817302578077933 y[1] (numeric) = -1.1162690879335407207614041441866 absolute error = 4.16390311463363933e-14 relative error = 3.7301965624991855249984595199998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9749 Order of pole = 5.626 x[1] = -0.963 y[1] (analytic) = -1.1197501740615253697984187777124 y[1] (numeric) = -1.1197501740615683744429677293237 absolute error = 4.30046445489516113e-14 relative error = 3.8405570764920188667341921099998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9738 Order of pole = 5.626 x[1] = -0.962 y[1] (analytic) = -1.1232457496088790905116906474093 y[1] (numeric) = -1.1232457496089234735881476806747 absolute error = 4.43830764570332654e-14 relative error = 3.9513237839971990920773771200000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9728 Order of pole = 5.626 x[1] = -0.961 y[1] (analytic) = -1.1267558900412042347348866939516 y[1] (numeric) = -1.1267558900412500091955884809006 absolute error = 4.57744607017869490e-14 relative error = 4.0625002368625760515259269000001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9718 Order of pole = 5.626 x[1] = -0.96 y[1] (analytic) = -1.1302806712962962962962962962964 y[1] (numeric) = -1.1302806712963434752289493064082 absolute error = 4.71789326530101118e-14 relative error = 4.1740900159693554273484799999996e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9708 Order of pole = 5.626 x[1] = -0.959 y[1] (analytic) = -1.1338201697875522257837239681508 y[1] (numeric) = -1.1338201697876008224129623768633 absolute error = 4.85966292384087125e-14 relative error = 4.2860967315049995632763287499999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9698 Order of pole = 5.626 x[1] = -0.958 y[1] (analytic) = -1.1373744624074492240326423195072 y[1] (numeric) = -1.1373744624074992517216054963779 absolute error = 5.00276889631768707e-14 relative error = 4.3985240232389813143547978400002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9688 Order of pole = 5.626 x[1] = -0.957 y[1] (analytic) = -1.1409436265310526468093437893195 y[1] (numeric) = -1.1409436265311041190612736327003 absolute error = 5.14722519298433808e-14 relative error = 4.5113755608014239852420334400001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9678 Order of pole = 5.626 x[1] = -0.956 y[1] (analytic) = -1.1445277400195532950349324516209 y[1] (numeric) = -1.144527740019606225494790840629 absolute error = 5.29304598583890081e-14 relative error = 4.6246550439646605380578809600000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9668 Order of pole = 5.626 x[1] = -0.955 y[1] (analytic) = -1.1481268812238343677717340059826 y[1] (numeric) = -1.1481268812238887702278406445312 absolute error = 5.44024561066385486e-14 relative error = 4.7383662029277456284003825000000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9658 Order of pole = 5.626 x[1] = -0.954 y[1] (analytic) = -1.1517411289880683581026319837056 y[1] (numeric) = -1.1517411289881242464883229154057 absolute error = 5.58883856909317001e-14 relative error = 4.8525127986039547390473866399999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9647 Order of pole = 5.626 x[1] = -0.953 y[1] (analytic) = -1.1553705626533441749763796331014 y[1] (numeric) = -1.1553705626534015633716867099546 absolute error = 5.73883953070768532e-14 relative error = 4.9670986229113048564826616399999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9637 Order of pole = 5.626 x[1] = -0.952 y[1] (analytic) = -1.1590152620613247770685140096572 y[1] (numeric) = -1.1590152620613836797018656016342 absolute error = 5.89026333515919770e-14 relative error = 5.0821274990661316797103616000002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9627 Order of pole = 5.626 x[1] = -0.951 y[1] (analytic) = -1.1626753075579356077185414125254 y[1] (numeric) = -1.1626753075579960389684846493652 absolute error = 6.04312499432368398e-14 relative error = 5.1976032818797587435513769800003e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9617 Order of pole = 5.626 x[1] = -0.95 y[1] (analytic) = -1.1663507799970841230500072896924 y[1] (numeric) = -1.1663507799971460974469521305657 absolute error = 6.19743969448408733e-14 relative error = 5.3135298580582943745587499999999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9607 Order of pole = 5.626 x[1] = -0.949 y[1] (analytic) = -1.170041760744410708461350868743 y[1] (numeric) = -1.1700417607444742406893362997994 absolute error = 6.35322279854310564e-14 relative error = 5.4299111465055927888826683599998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9597 Order of pole = 5.626 x[1] = -0.948 y[1] (analytic) = -1.1737483316810712817925229113796 y[1] (numeric) = -1.1737483316811363866910055756419 absolute error = 6.51048984826642623e-14 relative error = 5.5467510986294159420384121600002e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.75 Real estimate of pole used Radius of convergence = 0.9587 Order of pole = 5.626 x[1] = -0.947 y[1] (analytic) = -1.1774705752075518846256681452278 y[1] (numeric) = -1.1774705752076185771913337138161 absolute error = 6.66925656655685883e-14 relative error = 5.6640536986508336399183760900002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9577 Order of pole = 5.626 x[1] = -0.946 y[1] (analytic) = -1.1812085742475155663682023490042 y[1] (numeric) = -1.1812085742475838617567999472583 absolute error = 6.82953885975982541e-14 relative error = 5.7818229639168994251183197600004e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9566 Order of pole = 5.626 x[1] = -0.945 y[1] (analytic) = -1.1849624122516818689938143480878 y[1] (numeric) = -1.1849624122517517825220143548181 absolute error = 6.99135282000067303e-14 relative error = 5.9000629452166404758218837499997e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9556 Order of pole = 5.626 x[1] = -0.944 y[1] (analytic) = -1.1887321732017392235817683404827 y[1] (numeric) = -1.1887321732018107707290438833165 absolute error = 7.15471472755428338e-14 relative error = 6.0187777271004002971689779200001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9546 Order of pole = 5.626 x[1] = -0.943 y[1] (analytic) = -1.1925179416142905730978515695743 y[1] (numeric) = -1.1925179416143637695083840441725 absolute error = 7.31964105324745982e-14 relative error = 6.1379714282025731248190947399999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9536 Order of pole = 5.626 x[1] = -0.942 y[1] (analytic) = -1.196319802544832539201892566443 y[1] (numeric) = -1.1963198025449074006865015122543 absolute error = 7.48614846089458113e-14 relative error = 6.2576482015677700626305234399998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9526 Order of pole = 5.626 x[1] = -0.941 y[1] (analytic) = -1.2001378415917684542474589010426 y[1] (numeric) = -1.2001378415918449967855565712247 absolute error = 7.65425380976701821e-14 relative error = 6.3778122349804568175640784099999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9516 Order of pole = 5.626 x[1] = -0.94 y[1] (analytic) = -1.2039721449004555830596303323926 y[1] (numeric) = -1.2039721449005338228012013005778 absolute error = 7.82397415709681852e-14 relative error = 6.4984677512981039136156800000002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9506 Order of pole = 5.626 x[1] = -0.939 y[1] (analytic) = -1.207822799167286862537140083043 y[1] (numeric) = -1.2078227991673668158047462347512 absolute error = 7.99532676061517082e-14 relative error = 6.6196190087878905197157655800003e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9496 Order of pole = 5.626 x[1] = -0.938 y[1] (analytic) = -1.2116898916438074906261973616586 y[1] (numeric) = -1.2116898916438891739170086233698 absolute error = 8.16832908112617112e-14 relative error = 6.7412703014670036589251526400004e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9486 Order of pole = 5.626 x[1] = -0.937 y[1] (analytic) = -1.2155735101408666997554690332752 y[1] (numeric) = -1.2155735101409501297433201974656 absolute error = 8.34299878511641904e-14 relative error = 6.8634259594465750377175851199998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9475 Order of pole = 5.626 x[1] = -0.936 y[1] (analytic) = -1.2194737430328050534055355444793 y[1] (numeric) = -1.219473743032890246943009554304 absolute error = 8.51935374740098247e-14 relative error = 6.9860903492792984252027443199996e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9465 Order of pole = 5.626 x[1] = -0.935 y[1] (analytic) = -1.2233906792616776081121812551163 y[1] (numeric) = -1.2233906792617645822327193178831 absolute error = 8.69741205380627668e-14 relative error = 7.1092678743107707355857549999998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9455 Order of pole = 5.626 x[1] = -0.934 y[1] (analytic) = -1.2273244083415132868716750738552 y[1] (numeric) = -1.2273244083416020587917139779891 absolute error = 8.87719200389041339e-14 relative error = 7.2329629750346009826725485600002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9445 Order of pole = 5.626 x[1] = -0.933 y[1] (analytic) = -1.2312750203626108136282941788923 y[1] (numeric) = -1.2312750203627014007494311947304 absolute error = 9.05871211370158381e-14 relative error = 7.3571801294513314639078229700003e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9435 Order of pole = 5.626 x[1] = -0.932 y[1] (analytic) = -1.2352426059958715622802997500976 y[1] (numeric) = -1.2352426059959639821914855005872 absolute error = 9.24199111857504896e-14 relative error = 7.4819238534312162615385292799998e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9425 Order of pole = 5.626 x[1] = -0.931 y[1] (analytic) = -1.2392272564971696774409549695412 y[1] (numeric) = -1.2392272564972639479207146627399 absolute error = 9.42704797596931987e-14 relative error = 7.6071987010809027473120361699997e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9415 Order of pole = 5.626 x[1] = -0.93 y[1] (analytic) = -1.2432290637117598280365559073895 y[1] (numeric) = -1.2432290637118559670552393285847 absolute error = 9.61390186834211952e-14 relative error = 7.7330092651140622307486399999993e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9405 Order of pole = 5.626 x[1] = -0.929 y[1] (analytic) = -1.2472481200787229587144071821765 y[1] (numeric) = -1.2472481200788209844364678494596 absolute error = 9.80257220606672831e-14 relative error = 7.8593601772260167634059695900002e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9395 Order of pole = 5.626 x[1] = -0.928 y[1] (analytic) = -1.2512845186354504079708065111321 y[1] (numeric) = -1.2512845186355503387571104043729 absolute error = 9.99307863038932408e-14 relative error = 7.9862561084724092923779481599998e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=1.02 Real estimate of pole used Radius of convergence = 0.9384 Order of pole = 5.626 x[1] = -0.927 y[1] (analytic) = -1.2553383530221667658930037737743 y[1] (numeric) = -1.2553383530222686203031680531581 absolute error = 1.018544101642793838e-13 relative error = 8.1137017696519655783562875400000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9374 Order of pole = 5.626 x[1] = -0.926 y[1] (analytic) = -1.2594097174864918484403777354619 y[1] (numeric) = -1.25940971748659564523513987206 absolute error = 1.037967947621365981e-13 relative error = 8.2417019116933961314558325599996e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9364 Order of pole = 5.626 x[1] = -0.925 y[1] (analytic) = -1.2634987068880421692693423884075 y[1] (numeric) = -1.2634987068881479274129601356728 absolute error = 1.057581436177472653e-13 relative error = 8.3702613260464878581889062499993e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9354 Order of pole = 5.626 x[1] = -0.924 y[1] (analytic) = -1.2676054167030722942343789029571 y[1] (numeric) = -1.2676054167031800328970615445543 absolute error = 1.077386626826415972e-13 relative error = 8.4993848450774351356909132799999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9344 Order of pole = 5.626 x[1] = -0.923 y[1] (analytic) = -1.2717299430291564678747211762303 y[1] (numeric) = -1.2717299430292662064350924922387 absolute error = 1.097385603713160084e-13 relative error = 8.6290773424684610289747922800003e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9334 Order of pole = 5.626 x[1] = -0.922 y[1] (analytic) = -1.2758723825899109054232445840927 y[1] (numeric) = -1.2758723825900226634708379843547 absolute error = 1.117580475934002620e-13 relative error = 8.7593437336217798992891376000000e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9324 Order of pole = 5.626 x[1] = -0.921 y[1] (analytic) = -1.280032832739757148151669518471 y[1] (numeric) = -1.2800328327398709454894557987049 absolute error = 1.137973377862802339e-13 relative error = 8.8901889760679533464767877900001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9314 Order of pole = 5.626 x[1] = -0.92 y[1] (analytic) = -1.2842113914687268841949535629161 y[1] (numeric) = -1.2842113914688427408419017461685 absolute error = 1.158566469481832524e-13 relative error = 9.0216180698786920444851199999999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9304 Order of pole = 5.626 x[1] = -0.919 y[1] (analytic) = -1.288408157407308641378378008257 y[1] (numeric) = -1.2884081574074265775720497413427 absolute error = 1.179361936717330857e-13 relative error = 9.1536360580841568697935606300001e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9293 Order of pole = 5.626 x[1] = -0.918 y[1] (analytic) = -1.2926232298313367630040146085453 y[1] (numeric) = -1.2926232298314567992031925903086 absolute error = 1.200361991779817633e-13 relative error = 9.2862480270948132208620405599996e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9283 Order of pole = 5.626 x[1] = -0.917 y[1] (analytic) = -1.2968567086669230820396754298098 y[1] (numeric) = -1.2968567086670452389270263553478 absolute error = 1.221568873509255380e-13 relative error = 9.4194591071278933471249593999995e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9273 Order of pole = 5.626 x[1] = -0.916 y[1] (analytic) = -1.3011086944954317136938005355821 y[1] (numeric) = -1.3011086944955560121785730479945 absolute error = 1.242984847725124124e-13 relative error = 9.5532744726385220024004070400003e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9263 Order of pole = 5.626 x[1] = -0.915 y[1] (analytic) = -1.3053792885584973909547331992383 y[1] (numeric) = -1.3053792885586238521754913480162 absolute error = 1.264612207581487779e-13 relative error = 9.6876993427555616178254662499996e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9253 Order of pole = 5.626 x[1] = -0.914 y[1] (analytic) = -1.3096685927630877723231885321479 y[1] (numeric) = -1.3096685927632164176505812449877 absolute error = 1.286453273927128398e-13 relative error = 9.8227389817222340263050571199996e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9243 Order of pole = 5.626 x[1] = -0.913 y[1] (analytic) = -1.3139767096866101556731673040805 y[1] (numeric) = -1.3139767096867410067127343867031 absolute error = 1.308510395670826226e-13 relative error = 9.9583986993415760604548232199999e-12 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9233 Order of pole = 5.626 x[1] = -0.912 y[1] (analytic) = -1.3183037425820630369398411387039 y[1] (numeric) = -1.3183037425821961155348563251911 absolute error = 1.330785950151864872e-13 relative error = 1.0094683851426787788402524160000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9223 Order of pole = 5.626 x[1] = -0.911 y[1] (analytic) = -1.3226497953832329571537875774513 y[1] (numeric) = -1.3226497953833682853881391616655 absolute error = 1.353282343515842142e-13 relative error = 1.0231599840256532271873424019999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9213 Order of pole = 5.626 x[1] = -0.91 y[1] (analytic) = -1.3270149727099370862201438218827 y[1] (numeric) = -1.327014972710074686421253408731 absolute error = 1.376002011095868483e-13 relative error = 1.0369152115035247086027930000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9202 Order of pole = 5.626 x[1] = -0.909 y[1] (analytic) = -1.3313993798733119967795472727922 y[1] (numeric) = -1.3313993798734518915213271964172 absolute error = 1.398947417799236250e-13 relative error = 1.0507346172358527916486012500000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9192 Order of pole = 5.626 x[1] = -0.908 y[1] (analytic) = -1.335803122881149086485921319016 y[1] (numeric) = -1.3358031228812912985917712834681 absolute error = 1.422121058499644521e-13 relative error = 1.0646187556683646356884635520000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9182 Order of pole = 5.626 x[1] = -0.907 y[1] (analytic) = -1.3402263084432771120950394467669 y[1] (numeric) = -1.3402263084434216646408829533111 absolute error = 1.445525458435065442e-13 relative error = 1.0785681860805263727718432060001e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=1.29 Real estimate of pole used Radius of convergence = 0.9172 Order of pole = 5.626 x[1] = -0.906 y[1] (analytic) = -1.3446690439769923038781642926751 y[1] (numeric) = -1.3446690439771392201955254266385 absolute error = 1.469163173611339634e-13 relative error = 1.0925834726336404473115057439999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9162 Order of pole = 5.626 x[1] = -0.905 y[1] (analytic) = -1.3491314376125365340577269732354 y[1] (numeric) = -1.3491314376126858377368481321946 absolute error = 1.493036791211589592e-13 relative error = 1.1066651844194753098569590000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9152 Order of pole = 5.626 x[1] = -0.904 y[1] (analytic) = -1.3536135981986240182078138633596 y[1] (numeric) = -1.3536135981987757331008150175054 absolute error = 1.517148930011541458e-13 relative error = 1.1208138955094339251833989120000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9142 Order of pole = 5.626 x[1] = -0.903 y[1] (analytic) = -1.3581156353080170338720028735771 y[1] (numeric) = -1.3581156353081711840960829582939 absolute error = 1.541502240800847168e-13 relative error = 1.1350301850042677235357759360000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9132 Order of pole = 5.626 x[1] = -0.902 y[1] (analytic) = -1.3626376592431511460256912140318 y[1] (numeric) = -1.3626376592433077559663722640681 absolute error = 1.566099406810500363e-13 relative error = 1.1493146370843426042791033040000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9122 Order of pole = 5.626 x[1] = -0.901 y[1] (analytic) = -1.3671797810418104344503459655956 y[1] (numeric) = -1.3671797810419695287647606097088 absolute error = 1.590943144146441132e-13 relative error = 1.1636678410604637767162575320000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9111 Order of pole = 5.626 x[1] = -0.9 y[1] (analytic) = -1.3717421124828532235939643347051 y[1] (numeric) = -1.371742112483014827214187279323 absolute error = 1.616036202229446179e-13 relative error = 1.1780903914252662644910000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9101 Order of pole = 5.626 x[1] = -0.899 y[1] (analytic) = -1.3763247660919888210663417729105 y[1] (numeric) = -1.3763247660921529592027659131756 absolute error = 1.641381364241402651e-13 relative error = 1.1925828879051780116828250490000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9091 Order of pole = 5.626 x[1] = -0.898 y[1] (analytic) = -1.3809278551476057765604156102339 y[1] (numeric) = -1.3809278551477724747051734167844 absolute error = 1.666981447578065505e-13 relative error = 1.2071459355129626172736299599999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9081 Order of pole = 5.626 x[1] = -0.897 y[1] (analytic) = -1.3855514936866521787028949919356 y[1] (numeric) = -1.3855514936868214626333258319321 absolute error = 1.692839304308399965e-13 relative error = 1.2217801446008488165325004450000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9071 Order of pole = 5.626 x[1] = -0.896 y[1] (analytic) = -1.3901957965105685131195335276968 y[1] (numeric) = -1.3901957965107404089016975889288 absolute error = 1.718957821640612320e-13 relative error = 1.2364861309142539189826355200000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9061 Order of pole = 5.626 x[1] = -0.895 y[1] (analytic) = -1.3948608791912736108536914731631 y[1] (numeric) = -1.3948608791914481448459309705715 absolute error = 1.745339922394974084e-13 relative error = 1.2512645156461085334943095000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9051 Order of pole = 5.626 x[1] = -0.894 y[1] (analytic) = -1.399546858077204222202225496714 y[1] (numeric) = -1.3995468580773814210587738513383 absolute error = 1.771988565483546243e-13 relative error = 1.2661159254917899631728911120000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9041 Order of pole = 5.626 x[1] = -0.893 y[1] (analytic) = -1.4042538502994087570312061028052 y[1] (numeric) = -1.4042538502995886477058457940244 absolute error = 1.798906746396912192e-13 relative error = 1.2810409927046718089241997440000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9031 Order of pole = 5.626 x[1] = -0.892 y[1] (analytic) = -1.4089819737776957387064797029497 y[1] (numeric) = -1.4089819737778783484562495059226 absolute error = 1.826097497698029729e-13 relative error = 1.2960403551522973726551899519999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.902 Order of pole = 5.626 x[1] = -0.891 y[1] (analytic) = -1.413731347226837524921662636677 y[1] (numeric) = -1.4137313472270228813106149681159 absolute error = 1.853563889523314389e-13 relative error = 1.3111146563731845902542547190000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.901 Order of pole = 5.626 x[1] = -0.89 y[1] (analytic) = -1.4185020901628298549297912390473 y[1] (numeric) = -1.4185020901630179858328003458723 absolute error = 1.881309030091068250e-13 relative error = 1.3262645456342702931342500000001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9 Order of pole = 5.626 x[1] = -0.889 y[1] (analytic) = -1.4232943229092077889855832511187 y[1] (numeric) = -1.4232943229093987225922049881525 absolute error = 1.909336066217370338e-13 relative error = 1.3414906779890017468367647220000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.899 Order of pole = 5.626 x[1] = -0.888 y[1] (analytic) = -1.4281081666034186121841344631703 y[1] (numeric) = -1.4281081666036123770025184178369 absolute error = 1.937648183839546666e-13 relative error = 1.3567937143360834797405419520000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.898 Order of pole = 5.626 x[1] = -0.887 y[1] (analytic) = -1.4329437432032522813399387588215 y[1] (numeric) = -1.4329437432034489062007934928202 absolute error = 1.966248608547339987e-13 relative error = 1.3721743214788875530637866610001e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.56 Real estimate of pole used Radius of convergence = 0.897 Order of pole = 5.626 x[1] = -0.886 y[1] (analytic) = -1.4378011754933300000884535283164 y[1] (numeric) = -1.4378011754935295141490657184503 absolute error = 1.995140606121901339e-13 relative error = 1.3876331721855355042695445840000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.896 Order of pole = 5.626 x[1] = -0.885 y[1] (analytic) = -1.4426805870916515140121253696644 y[1] (numeric) = -1.4426805870918539467604336424266 absolute error = 2.024327483082727622e-13 relative error = 1.4031709452496603674407407500000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.895 Order of pole = 5.626 x[1] = -0.884 y[1] (analytic) = -1.4475821024562017242949487676374 y[1] (numeric) = -1.44758210245640710555367303478 absolute error = 2.053812587242671426e-13 relative error = 1.4187883255518571930186103040001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.894 Order of pole = 5.626 x[1] = -0.883 y[1] (analytic) = -1.4525058468916172251953750000215 y[1] (numeric) = -1.4525058468918255851262021151838 absolute error = 2.083599308271151623e-13 relative error = 1.4344860041218307030643731010001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8929 Order of pole = 5.626 x[1] = -0.882 y[1] (analytic) = -1.4574519465559133774978583909607 y[1] (numeric) = -1.4574519465561247466056849604941 absolute error = 2.113691078265695334e-13 relative error = 1.4502646782012487693198353120000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8919 Order of pole = 5.626 x[1] = -0.881 y[1] (analytic) = -1.4624205284672725370596775546123 y[1] (numeric) = -1.4624205284674869461969107490284 absolute error = 2.144091372331944161e-13 relative error = 1.4661250513073105526243564009999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8909 Order of pole = 5.626 x[1] = -0.88 y[1] (analytic) = -1.4674117205108940646130728775357 y[1] (numeric) = -1.467411720511111544983990103517 absolute error = 2.174803709172259813e-13 relative error = 1.4820678332970382392847360000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8899 Order of pole = 5.626 x[1] = -0.879 y[1] (analytic) = -1.4724256514459067501143879634775 y[1] (numeric) = -1.4724256514461273332795562701377 absolute error = 2.205831651683066602e-13 relative error = 1.4980937404323014546811402780000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8889 Order of pole = 5.626 x[1] = -0.878 y[1] (analytic) = -1.4774624509123442921529995342211 y[1] (numeric) = -1.4774624509125680100337556412848 absolute error = 2.237178807561070637e-13 relative error = 1.5142034954455835549472688240000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8879 Order of pole = 5.626 x[1] = -0.877 y[1] (analytic) = -1.4825222494381844802445926880049 y[1] (numeric) = -1.482522249438411365127584537796 absolute error = 2.268848829918497911e-13 relative error = 1.5303978276064991010754081630000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8869 Order of pole = 5.626 x[1] = -0.876 y[1] (analytic) = -1.4876051784464527352370300107803 y[1] (numeric) = -1.4876051784466828197788207603771 absolute error = 2.300845417907495968e-13 relative error = 1.5466774727890719803234119680000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8859 Order of pole = 5.626 x[1] = -0.875 y[1] (analytic) = -1.4927113702623906705539358600583 y[1] (numeric) = -1.4927113702626239877856712446872 absolute error = 2.333172317353846289e-13 relative error = 1.5630431735397837443886718750000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8848 Order of pole = 5.626 x[1] = -0.874 y[1] (analytic) = -1.4978409581206903445924520343095 y[1] (numeric) = -1.4978409581209269279245920480181 absolute error = 2.365833321400137086e-13 relative error = 1.5794956791464018760004636640000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8838 Order of pole = 5.626 x[1] = -0.873 y[1] (analytic) = -1.5029940761727948822787179358928 y[1] (numeric) = -1.5029940761730347655058337907713 absolute error = 2.398832271158548785e-13 relative error = 1.5960357457075978363389303450000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8828 Order of pole = 5.626 x[1] = -0.872 y[1] (analytic) = -1.5081708594942661515688065672661 y[1] (numeric) = -1.5081708594945093688744439079736 absolute error = 2.432173056373407075e-13 relative error = 1.6126641362033648593562496000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8818 Order of pole = 5.626 x[1] = -0.871 y[1] (analytic) = -1.513371444092220188565446317884 y[1] (numeric) = -1.513371444092466774527055683996 absolute error = 2.465859616093661120e-13 relative error = 1.6293816205662456253577283200001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8808 Order of pole = 5.626 x[1] = -0.87 y[1] (analytic) = -1.5185959669128310729032365835843 y[1] (numeric) = -1.5185959669130810624971721283053 absolute error = 2.499895939355447210e-13 relative error = 1.6461889757533800541266300000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8798 Order of pole = 5.626 x[1] = -0.869 y[1] (analytic) = -1.5238445658489039631386022470804 y[1] (numeric) = -1.5238445658491573917451897371778 absolute error = 2.534286065874900974e-13 relative error = 1.6630869858193836460569013660000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8788 Order of pole = 5.626 x[1] = -0.868 y[1] (analytic) = -1.529117379747518010066828056647 y[1] (numeric) = -1.5291173797477749134755031950468 absolute error = 2.569034086751383998e-13 relative error = 1.6800764419900668719843439359999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8778 Order of pole = 5.626 x[1] = -0.867 y[1] (analytic) = -1.5344145484177398741785901072737 y[1] (numeric) = -1.5344145484180002885931082366442 absolute error = 2.604144145181293705e-13 relative error = 1.6971581427370063464699849150000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8768 Order of pole = 5.626 x[1] = -0.866 y[1] (analytic) = -1.5397362126384085818639004496732 y[1] (numeric) = -1.5397362126386725439076187124894 absolute error = 2.639620437182628162e-13 relative error = 1.7143328938529785843555151520000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.82 Real estimate of pole used Radius of convergence = 0.8757 Order of pole = 5.626 x[1] = -0.865 y[1] (analytic) = -1.5450825141659924634737665268303 y[1] (numeric) = -1.5450825141662600101949995748878 absolute error = 2.675467212330480575e-13 relative error = 1.7316015085282673614184093750000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8747 Order of pole = 5.626 x[1] = -0.864 y[1] (analytic) = -1.5504535957425189249606259208454 y[1] (numeric) = -1.5504535957427900938380762849643 absolute error = 2.711688774503641189e-13 relative error = 1.7489648074278557949325148160000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8737 Order of pole = 5.626 x[1] = -0.863 y[1] (analytic) = -1.5558496011035778135392574546282 y[1] (numeric) = -1.555849601103852642487521703375 absolute error = 2.748289482642487468e-13 relative error = 1.7664236187695144524343717959999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8727 Order of pole = 5.626 x[1] = -0.862 y[1] (analytic) = -1.561270674986399146641923482474 y[1] (numeric) = -1.5612706749866776740170753171321 absolute error = 2.785273751518346581e-13 relative error = 1.7839787784027969491958701679999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8717 Order of pole = 5.626 x[1] = -0.861 y[1] (analytic) = -1.5667169631380059823865198193511 y[1] (numeric) = -1.5667169631382882469917712710913 absolute error = 2.822646052514517402e-13 relative error = 1.8016311298889546318274841620000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8707 Order of pole = 5.626 x[1] = -0.86 y[1] (analytic) = -1.5721886123234432188360773265248 y[1] (numeric) = -1.5721886123237292599275192407807 absolute error = 2.860410914419142559e-13 relative error = 1.8193815245817821395073039999999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8697 Order of pole = 5.626 x[1] = -0.859 y[1] (analytic) = -1.5776857703340831185036747275529 y[1] (numeric) = -1.5776857703343729757960977399905 absolute error = 2.898572924230124376e-13 relative error = 1.8372308217094057796263529040000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8687 Order of pole = 5.626 x[1] = -0.858 y[1] (analytic) = -1.5832085859960083638503121118408 y[1] (numeric) = -1.5832085859963020775231093400356 absolute error = 2.937136727972281948e-13 relative error = 1.8551798884570268185160909760000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8677 Order of pole = 5.626 x[1] = -0.857 y[1] (analytic) = -1.5887572091784734589362098299482 y[1] (numeric) = -1.5887572091787710696393625249572 absolute error = 2.976107031526950090e-13 relative error = 1.8732296000506319804194013699999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8666 Order of pole = 5.626 x[1] = -0.856 y[1] (analytic) = -1.594331790802445301920014236235 y[1] (numeric) = -1.5943317908027468507801616586743 absolute error = 3.015488601474224393e-13 relative error = 1.8913808398416835958138362880000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8656 Order of pole = 5.626 x[1] = -0.855 y[1] (analytic) = -1.5999324828492237627572116456687 y[1] (numeric) = -1.5999324828495292913838064516911 absolute error = 3.055286265948060224e-13 relative error = 1.9096344993928020200884079999998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8646 Order of pole = 5.626 x[1] = -0.854 y[1] (analytic) = -1.6055594383691431102304025318619 y[1] (numeric) = -1.6055594383694526607219529755832 absolute error = 3.095504915504437213e-13 relative error = 1.9279914785644531473926070320000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8636 Order of pole = 5.626 x[1] = -0.853 y[1] (analytic) = -1.6112128114903551423517233516925 y[1] (numeric) = -1.6112128114906687573021236321342 absolute error = 3.136149504002804417e-13 relative error = 1.9464526856026539707487569090000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8626 Order of pole = 5.626 x[1] = -0.852 y[1] (analytic) = -1.6168927574276948842134041806586 y[1] (numeric) = -1.6168927574280126067183542831854 absolute error = 3.177225049501025268e-13 relative error = 1.9650190372277093937132157440000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8616 Order of pole = 5.626 x[1] = -0.851 y[1] (analytic) = -1.6225994324916297275280245597819 y[1] (numeric) = -1.6225994324919516011915409642992 absolute error = 3.218736635164045173e-13 relative error = 1.9836914587239936132603388229999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8606 Order of pole = 5.626 x[1] = -0.85 y[1] (analytic) = -1.6283329940972928963973132505598 y[1] (numeric) = -1.6283329940976189653383319014274 absolute error = 3.260689410186508676e-13 relative error = 2.0024708840307896406484999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8596 Order of pole = 5.626 x[1] = -0.849 y[1] (analytic) = -1.6340936007736021342791937713569 y[1] (numeric) = -1.6340936007739324431382667270613 absolute error = 3.303088590729557044e-13 relative error = 2.0213582558342006743945351559999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8586 Order of pole = 5.626 x[1] = -0.848 y[1] (analytic) = -1.6398814121724645176890990549246 y[1] (numeric) = -1.6398814121727991116351862590548 absolute error = 3.345939460872041302e-13 relative error = 2.0403545256601472733915299839999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8575 Order of pole = 5.626 x[1] = -0.847 y[1] (analytic) = -1.6456965890780683128752868101502 y[1] (numeric) = -1.6456965890784072376126444491362 absolute error = 3.389247373576389860e-13 relative error = 2.0594606539684644392926107799999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8565 Order of pole = 5.626 x[1] = -0.846 y[1] (analytic) = -1.6515392934162628025509332405935 y[1] (numeric) = -1.6515392934166061043261001780113 absolute error = 3.433017751669374178e-13 relative error = 2.0786776102481129465675050079999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8555 Order of pole = 5.626 memory used=30.5MB, alloc=4.4MB, time=2.09 x[1] = -0.845 y[1] (analytic) = -1.6574096882640270207501477684324 y[1] (numeric) = -1.6574096882643747463590315704552 absolute error = 3.477256088838020228e-13 relative error = 2.0980063731135194473365565000002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8545 Order of pole = 5.626 x[1] = -0.844 y[1] (analytic) = -1.6633079378590283450027469863256 y[1] (numeric) = -1.6633079378593805417978110781183 absolute error = 3.521967950640917927e-13 relative error = 2.1174479304020600821056663679999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8535 Order of pole = 5.626 x[1] = -0.843 y[1] (analytic) = -1.6692342076092719062956949212883 y[1] (numeric) = -1.6692342076096286221932484398152 absolute error = 3.567158975535185269e-13 relative error = 2.1370032792727025676615367830000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8525 Order of pole = 5.626 x[1] = -0.842 y[1] (analytic) = -1.6751886641028417887096331295281 y[1] (numeric) = -1.6751886641032030721972250643647 absolute error = 3.612834875919348366e-13 relative error = 2.1566734263058218815502778080000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8515 Order of pole = 5.626 x[1] = -0.841 y[1] (analytic) = -1.6811714751177350021889945367492 y[1] (numeric) = -1.6811714751181009023329137770928 absolute error = 3.659001439192403436e-13 relative error = 2.1764593876042049697733309560000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8505 Order of pole = 5.626 x[1] = -0.84 y[1] (analytic) = -1.6871828096317892236259583198358 y[1] (numeric) = -1.6871828096321597900788412529764 absolute error = 3.705664528829331406e-13 relative error = 2.1963621888952600416618240000001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8495 Order of pole = 5.626 x[1] = -0.839 y[1] (analytic) = -1.6932228378327053133141317009617 y[1] (numeric) = -1.6932228378330805963226790350344 absolute error = 3.752830085473340727e-13 relative error = 2.2163828656344462819501857130001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8484 Order of pole = 5.626 x[1] = -0.838 y[1] (analytic) = -1.699291731128165625859544239898 y[1] (numeric) = -1.6992917311285456762723487517936 absolute error = 3.800504128045118956e-13 relative error = 2.2365224631099400405230272319999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8474 Order of pole = 5.626 x[1] = -0.837 y[1] (analytic) = -1.7053896621560491468265513132913 y[1] (numeric) = -1.7053896621564340161020382511578 absolute error = 3.848692754869378665e-13 relative error = 2.2567820365485537660208422450000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8464 Order of pole = 5.626 x[1] = -0.836 y[1] (analytic) = -1.7115168047947444987468410876636 y[1] (numeric) = -1.7115168047951342389613229865031 absolute error = 3.897402144818988395e-13 relative error = 2.2771626512229241923287651200002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8454 Order of pole = 5.626 x[1] = -0.835 y[1] (analytic) = -1.7176733341735618726332340160297 y[1] (numeric) = -1.7176733341739565364890817144958 absolute error = 3.946638558476984661e-13 relative error = 2.2976653825599865512718803750001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8444 Order of pole = 5.626 x[1] = -0.834 y[1] (analytic) = -1.7238594266832449538187023660578 y[1] (numeric) = -1.7238594266836445946526340426858 absolute error = 3.996408339316766280e-13 relative error = 2.3182913162507517806675011199999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8434 Order of pole = 5.626 x[1] = -0.833 y[1] (analytic) = -1.7300752599865839237874028365729 y[1] (numeric) = -1.7300752599869885955788929143533 absolute error = 4.046717914900777804e-13 relative error = 2.3390415483614039794299167480000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8424 Order of pole = 5.626 x[1] = -0.832 y[1] (analytic) = -1.7363210130291306326809285389167 y[1] (numeric) = -1.7363210130295403900607383383511 absolute error = 4.097573798097994344e-13 relative error = 2.3599171854457355826018385920000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8414 Order of pole = 5.626 x[1] = -0.831 y[1] (analytic) = -1.7425968660500170503519060230893 y[1] (numeric) = -1.7425968660504319486107380756688 absolute error = 4.148982588320525795e-13 relative error = 2.3809193446589380198359468450000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8404 Order of pole = 5.626 x[1] = -0.83 y[1] (analytic) = -1.7489030005928781172009856817312 y[1] (numeric) = -1.7489030005932982122982636481462 absolute error = 4.200950972779664150e-13 relative error = 2.4020491538727658253360499999999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8393 Order of pole = 5.626 x[1] = -0.829 y[1] (analytic) = -1.7552395995168801295747360388632 y[1] (numeric) = -1.7552395995173054781475122092197 absolute error = 4.253485727761703565e-13 relative error = 2.4233077517920924824430427850001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8383 Order of pole = 5.626 x[1] = -0.828 y[1] (analytic) = -1.7616068470078558082235302646312 y[1] (numeric) = -1.7616068470082864675955226515058 absolute error = 4.306593719923868746e-13 relative error = 2.4446962880728765019361457919999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8373 Order of pole = 5.626 x[1] = -0.827 y[1] (analytic) = -1.7680049285895472122228234362272 y[1] (numeric) = -1.7680049285899832404135845055703 absolute error = 4.360281907610693431e-13 relative error = 2.4662159234415565546407199729998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8363 Order of pole = 5.626 x[1] = -0.826 y[1] (analytic) = -1.774434031134957674850919505327 y[1] (numeric) = -1.7744340311353991305851386250131 absolute error = 4.414557342191196861e-13 relative error = 2.4878678298158946903964353360000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8353 Order of pole = 5.626 x[1] = -0.825 y[1] (analytic) = -1.7808943428778139521941174833737 y[1] (numeric) = -1.780894342878260894911059204633 absolute error = 4.469427169417212593e-13 relative error = 2.5096531904272870149162656250000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.37 Real estimate of pole used Radius of convergence = 0.8343 Order of pole = 5.626 x[1] = -0.824 y[1] (analytic) = -1.7873860534241397897187495138309 y[1] (numeric) = -1.7873860534245922795818298368719 absolute error = 4.524898630803230410e-13 relative error = 2.5315731999445614367887718400001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8333 Order of pole = 5.626 x[1] = -0.823 y[1] (analytic) = -1.7939093537639421267118651337083 y[1] (numeric) = -1.7939093537644002246183679455789 absolute error = 4.580979065028118706e-13 relative error = 2.5536290645992823961583935019999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8323 Order of pole = 5.626 x[1] = -0.822 y[1] (analytic) = -1.8004644362830111733510061160912 y[1] (numeric) = -1.8004644362834749409419420262389 absolute error = 4.637675909359101477e-13 relative error = 2.5758220023125827906006902960001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8313 Order of pole = 5.626 x[1] = -0.821 y[1] (analytic) = -1.8070514947748356102215296773666 y[1] (numeric) = -1.8070514947753051098916395144509 absolute error = 4.694996701098370843e-13 relative error = 2.5981532428235435717183682230000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8302 Order of pole = 5.626 x[1] = -0.82 y[1] (analytic) = -1.8136707244526341753601950058762 y[1] (numeric) = -1.8136707244531094702681002781899 absolute error = 4.752949079052723137e-13 relative error = 2.6206240278191418506014160000001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8292 Order of pole = 5.626 x[1] = -0.819 y[1] (analytic) = -1.8203223219615049193691959147911 y[1] (numeric) = -1.8203223219619860734476985761501 absolute error = 4.811540785026613590e-13 relative error = 2.6432356110657885774001898100001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8282 Order of pole = 5.626 x[1] = -0.818 y[1] (analytic) = -1.8270064853906934248185150415763 y[1] (numeric) = -1.8270064853911805027850489447803 absolute error = 4.870779665339032040e-13 relative error = 2.6659892585424772403315612800000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8272 Order of pole = 5.626 x[1] = -0.817 y[1] (analytic) = -1.8337234142859813020394545286774 y[1] (numeric) = -1.8337234142864743694066909896201 absolute error = 4.930673672364609427e-13 relative error = 2.6888862485755652987459620509999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8262 Order of pole = 5.626 x[1] = -0.816 y[1] (analytic) = -1.8404733096621962895115754875575 y[1] (numeric) = -1.8404733096626954125981854248016 absolute error = 4.991230866099372441e-13 relative error = 2.7119278719752104086367887360001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8252 Order of pole = 5.626 x[1] = -0.815 y[1] (analytic) = -1.8472563740158453033622144170508 y[1] (numeric) = -1.8472563740163505493037895741873 absolute error = 5.052459415751571365e-13 relative error = 2.7351154321734838042824568750002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8242 Order of pole = 5.626 x[1] = -0.814 y[1] (analytic) = -1.8540728113378717970354503022977 y[1] (numeric) = -1.8540728113383832337955861037059 absolute error = 5.114367601358014082e-13 relative error = 2.7584502453641835647229738080000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8232 Order of pole = 5.626 x[1] = -0.813 y[1] (analytic) = -1.8609228271265388089491339578728 y[1] (numeric) = -1.8609228271270565053306765925885 absolute error = 5.176963815426347157e-13 relative error = 2.7819336406443707875143031290000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8222 Order of pole = 5.626 x[1] = -0.812 y[1] (analytic) = -1.867806628400439092947676191544 y[1] (numeric) = -1.8678066284009631186041365648562 absolute error = 5.240256564603733122e-13 relative error = 2.8055669601576520550126780160001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8211 Order of pole = 5.626 x[1] = -0.811 y[1] (analytic) = -1.8747244237116337435780916486818 y[1] (numeric) = -1.8747244237121641690252288868266 absolute error = 5.304254471372381448e-13 relative error = 2.8293515592392319337699664880000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8201 Order of pole = 5.626 x[1] = -0.81 y[1] (analytic) = -1.8816764231589207456707329694172 y[1] (numeric) = -1.8816764231594576422983102093338 absolute error = 5.368966275772399166e-13 relative error = 2.8532888065627595851782059999999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8191 Order of pole = 5.626 x[1] = -0.809 y[1] (analytic) = -1.888662838401234895397702429192 y[1] (numeric) = -1.8886628384017783354814176727684 absolute error = 5.434400837152435764e-13 relative error = 2.8773800842889939188081135559999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8181 Order of pole = 5.626 x[1] = -0.808 y[1] (analytic) = -1.8956838826711805579146288317687 y[1] (numeric) = -1.8956838826717306146282236923553 absolute error = 5.500567135948605866e-13 relative error = 2.9016267882163121010409809919998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8171 Order of pole = 5.626 x[1] = -0.807 y[1] (analytic) = -1.9027397707886987448689363638825 y[1] (numeric) = -1.9027397707892554922964855821035 absolute error = 5.567474275492182210e-13 relative error = 2.9260303279330865948687940300000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8161 Order of pole = 5.626 x[1] = -0.806 y[1] (analytic) = -1.909830719174870013483557663832 y[1] (numeric) = -1.9098307191754335266319423198934 absolute error = 5.635131483846560614e-13 relative error = 2.9505921269719562663354222240002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8151 Order of pole = 5.626 x[1] = -0.805 y[1] (analytic) = -1.9169569458658547076029627528077 y[1] (numeric) = -1.9169569458664250624145301536135 absolute error = 5.703548115674008058e-13 relative error = 2.9753136229660175027872872500000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8141 Order of pole = 5.626 x[1] = -0.804 y[1] (analytic) = -1.924118670526972080022155995597 y[1] (numeric) = -1.9241186705275493533875692670516 absolute error = 5.772733654132714546e-13 relative error = 3.0001962678069616559975773439998e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.64 Real estimate of pole used Radius of convergence = 0.8131 Order of pole = 5.626 x[1] = -0.803 y[1] (analytic) = -1.931316114466919854612763229623 y[1] (numeric) = -1.9313161144675041243840436975397 absolute error = 5.842697712804679167e-13 relative error = 3.0252415278051855123022647090001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.812 Order of pole = 5.626 x[1] = -0.802 y[1] (analytic) = -1.9385495006521358062173810937547 y[1] (numeric) = -1.9385495006527271512211465908325 absolute error = 5.913450037654970778e-13 relative error = 3.0504508838519019150827550240001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.811 Order of pole = 5.626 x[1] = -0.801 y[1] (analytic) = -1.9458190537213029560079440864848 y[1] (numeric) = -1.9458190537219014560588463778716 absolute error = 5.985000509022913868e-13 relative error = 3.0758258315832780590587570679999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.81 Order of pole = 5.626 x[1] = -0.8 y[1] (analytic) = -1.953125 y[1] (numeric) = -1.9531250000006057359143645760507 absolute error = 6.057359143645760507e-13 relative error = 3.1013678815466293795840000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.809 Order of pole = 5.626 x[1] = -0.799 y[1] (analytic) = -1.9604675675154986086865545815472 y[1] (numeric) = -1.9604675675161116622962261235358 absolute error = 6.130536096715419886e-13 relative error = 3.1270785593686973957431865139999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.808 Order of pole = 5.626 x[1] = -0.798 y[1] (analytic) = -1.9678469860117092563067016414472 y[1] (numeric) = -1.9678469860123297104730985242208 absolute error = 6.204541663968827736e-13 relative error = 3.1529594059260402913214037120001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.807 Order of pole = 5.626 x[1] = -0.797 y[1] (analytic) = -1.975263486964277259099813210591 y[1] (numeric) = -1.97526348696490519772819446548 absolute error = 6.279386283812548890e-13 relative error = 3.1790119775175654381908039700001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.806 Order of pole = 5.626 x[1] = -0.796 y[1] (analytic) = -1.9827173035958307230199125726357 y[1] (numeric) = -1.9827173035964662310738607943885 absolute error = 6.355080539482217528e-13 relative error = 3.2052378460392335340121134079999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.805 Order of pole = 5.626 x[1] = -0.795 y[1] (analytic) = -1.9902086708913821228013480678431 y[1] (numeric) = -1.9902086708920252863174718109463 absolute error = 6.431635161237431032e-13 relative error = 3.2316385991609644416598410000002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8039 Order of pole = 5.626 x[1] = -0.794 y[1] (analytic) = -1.9977378256138852559804559230874 y[1] (numeric) = -1.9977378256145361620833151955978 absolute error = 6.509061028592725104e-13 relative error = 3.2582158405057752954702831359998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8029 Order of pole = 5.626 x[1] = -0.793 y[1] (analytic) = -2.0053050063199493374930471312832 y[1] (numeric) = -2.0053050063206080744103056582579 absolute error = 6.587369172585269747e-13 relative error = 3.2849711898311819160390439789999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8019 Order of pole = 5.626 x[1] = -0.792 y[1] (analytic) = -2.0129104533757120227888516838625 y[1] (numeric) = -2.0129104533763786798666596776382 absolute error = 6.666570778079937757e-13 relative error = 3.3119062832128949891478236159998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.8009 Order of pole = 5.626 x[1] = -0.791 y[1] (analytic) = -2.020554408972873170036153638601 y[1] (numeric) = -2.0205544089735478377547648795961 absolute error = 6.746677186112409951e-13 relative error = 3.3390227732308430275063401209999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7999 Order of pole = 5.626 x[1] = -0.79 y[1] (analytic) = -2.0282371171448911749374795908639 y[1] (numeric) = -2.0282371171455739449271066902492 absolute error = 6.827699896270993853e-13 relative error = 3.3663223291575545382892670000002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7989 Order of pole = 5.626 x[1] = -0.789 y[1] (analytic) = -2.0359588237833437349451661012474 y[1] (numeric) = -2.0359588237840347000020778858065 absolute error = 6.909650569117845591e-13 relative error = 3.3938066371489323702172247789998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7979 Order of pole = 5.626 x[1] = -0.788 y[1] (analytic) = -2.0437197766544549232588128793716 y[1] (numeric) = -2.0437197766551541773616779091627 absolute error = 6.992541028650297911e-13 relative error = 3.4214774004374537018058113920000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7969 Order of pole = 5.626 x[1] = -0.787 y[1] (analytic) = -2.0515202254157904769099931792492 y[1] (numeric) = -2.0515202254164981152364734803087 absolute error = 7.076383264803010595e-13 relative error = 3.4493363395278296090718547849999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7959 Order of pole = 5.626 x[1] = -0.786 y[1] (analytic) = -2.0593604216331232274981882982627 y[1] (numeric) = -2.0593604216338393464417874656077 absolute error = 7.161189435991673450e-13 relative error = 3.4773851923951587461029332000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7948 Order of pole = 5.626 x[1] = -0.785 y[1] (analytic) = -2.0672406187974706277408703548134 y[1] (numeric) = -2.0672406187981953249280402553999 absolute error = 7.246971871699005865e-13 relative error = 3.5056257146856101129903056250000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7938 Order of pole = 5.626 x[1] = -0.784 y[1] (analytic) = -2.0751610723423063519451929043171 y[1] (numeric) = -2.0751610723430397262527032854533 absolute error = 7.333743075103811362e-13 relative error = 3.5340596799196704887928340480000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7928 Order of pole = 5.626 x[1] = -0.783 y[1] (analytic) = -2.0831220396609479738041654095807 memory used=41.9MB, alloc=4.4MB, time=2.91 y[1] (numeric) = -2.0831220396616901253767407955898 absolute error = 7.421515725753860091e-13 relative error = 3.5626888796979926218662505169999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7918 Order of pole = 5.626 x[1] = -0.782 y[1] (analytic) = -2.0911237801241227505718763491408 y[1] (numeric) = -2.0911237801248737808401046878523 absolute error = 7.510302682283387115e-13 relative error = 3.5915151239098808292925693200000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7908 Order of pole = 5.626 x[1] = -0.781 y[1] (analytic) = -2.0991665550977135686857719189918 y[1] (numeric) = -2.0991665550984735803842895199454 absolute error = 7.600116985176009536e-13 relative error = 3.6205402409444512269713029760000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7898 Order of pole = 5.626 x[1] = -0.78 y[1] (analytic) = -2.1072506279606871322847654208601 y[1] (numeric) = -2.1072506279614562294707228089611 absolute error = 7.690971859573881010e-13 relative error = 3.6497660779045043810575200000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7888 Order of pole = 5.626 x[1] = -0.779 y[1] (analytic) = -2.1153762641232065028257122097987 y[1] (numeric) = -2.1153762641239847908975256016019 absolute error = 7.782880718133918032e-13 relative error = 3.6791945008231487579639344480003e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7878 Order of pole = 5.626 x[1] = -0.778 y[1] (analytic) = -2.1235437310449301251332969635414 y[1] (numeric) = -2.1235437310457177108496901583922 absolute error = 7.875857163931948508e-13 relative error = 3.7088273948832139351172596160000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7868 Order of pole = 5.626 x[1] = -0.777 y[1] (analytic) = -2.1317532982534995027355010062484 y[1] (numeric) = -2.1317532982542964942348425712147 absolute error = 7.969914993415649663e-13 relative error = 3.7386666646394931589406150789998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7857 Order of pole = 5.626 x[1] = -0.776 y[1] (analytic) = -2.140005237363217713244502686066 y[1] (numeric) = -2.1400052373640242200644434019746 absolute error = 8.065068199407159086e-13 relative error = 3.7687142342438554135024015360002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7847 Order of pole = 5.626 x[1] = -0.775 y[1] (analytic) = -2.1482998220939209828471686079689 y[1] (numeric) = -2.1482998220947371159445842339649 absolute error = 8.161330974156259960e-13 relative error = 3.7989720476732678198181249999999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7837 Order of pole = 5.626 x[1] = -0.774 y[1] (analytic) = -2.1566373282900455676763749335044 y[1] (numeric) = -2.1566373282908714394476194394103 absolute error = 8.258717712445059059e-13 relative error = 3.8294420689607698194420206160000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7827 Order of pole = 5.626 x[1] = -0.773 y[1] (analytic) = -2.1650180339398922189505167310244 y[1] (numeric) = -2.1650180339407279432519912404144 absolute error = 8.357243014745093900e-13 relative error = 3.8601262824294411976282063000001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7817 Order of pole = 5.626 x[1] = -0.772 y[1] (analytic) = -2.1734422191950905383000858109763 y[1] (numeric) = -2.1734422191959362304691285933606 absolute error = 8.456921690427823843e-13 relative error = 3.8910266929294067195703072640000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7807 Order of pole = 5.626 x[1] = -0.771 y[1] (analytic) = -2.1819101663902655596535974109681 y[1] (numeric) = -2.181910166391121336529700358816 absolute error = 8.557768761029478479e-13 relative error = 3.9221453260779207709486692690000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7797 Order of pole = 5.626 x[1] = -0.77 y[1] (analytic) = -2.1904221600629089244370067443099 y[1] (numeric) = -2.1904221600637749043833638698832 absolute error = 8.659799463571255733e-13 relative error = 3.9534842285025760935536889999999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7787 Order of pole = 5.626 x[1] = -0.769 y[1] (analytic) = -2.1989784869734570476577724679092 y[1] (numeric) = -2.1989784869743333505831660560628 absolute error = 8.763029253935881536e-13 relative error = 3.9850454680876813907370714240002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7777 Order of pole = 5.626 x[1] = -0.768 y[1] (analytic) = -2.2075794361255787037037037037036 y[1] (numeric) = -2.2075794361264654510847338599801 absolute error = 8.867473810301562765e-13 relative error = 4.0168311342238532784409804800002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7766 Order of pole = 5.626 x[1] = -0.767 y[1] (analytic) = -2.2162252987866744923945940476183 y[1] (numeric) = -2.2162252987875718072982574861612 absolute error = 8.973149036634385429e-13 relative error = 4.0488433380608687787146324269998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7756 Order of pole = 5.626 x[1] = -0.766 y[1] (analytic) = -2.224916368508590677988441363673 y[1] (numeric) = -2.2249163685094986850950653867458 absolute error = 9.080071066240230728e-13 relative error = 4.0810842127638252609153898879999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7746 Order of pole = 5.626 x[1] = -0.765 y[1] (analytic) = -2.2336529411485499264709372435661 y[1] (numeric) = -2.2336529411494687520974749738411 absolute error = 9.188256265377302750e-13 relative error = 4.1135559137726554814295937500001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7736 Order of pole = 5.626 x[1] = -0.764 y[1] (analytic) = -2.2424353148903014995541679804348 y[1] (numeric) = -2.2424353148912312716778610187512 absolute error = 9.297721236930383164e-13 relative error = 4.1462606190650461355087260159999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7726 Order of pole = 5.626 x[1] = -0.763 y[1] (analytic) = -2.251263790265493497385507179126 y[1] (numeric) = -2.2512637902664343456679219741504 absolute error = 9.408482824147950244e-13 relative error = 4.1792005294228090787922170680000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.5MB, time=3.18 Real estimate of pole used Radius of convergence = 0.7716 Order of pole = 5.626 x[1] = -0.762 y[1] (analytic) = -2.2601386701752697760280326626562 y[1] (numeric) = -2.2601386701762218318394769948601 absolute error = 9.520558114443322039e-13 relative error = 4.2123778687017551508939943919999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7706 Order of pole = 5.626 x[1] = -0.761 y[1] (analytic) = -2.2690602599120942003271299638595 y[1] (numeric) = -2.2690602599130575967714560645114 absolute error = 9.633964443261006519e-13 relative error = 4.2457948841051213481365370390000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7696 Order of pole = 5.626 x[1] = -0.76 y[1] (analytic) = -2.2780288671818049278320454876804 y[1] (numeric) = -2.2780288671827797997718464341698 absolute error = 9.748719398009464894e-13 relative error = 4.2794538464606028613085440000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7686 Order of pole = 5.626 x[1] = -0.759 y[1] (analytic) = -2.2870448021259014550039521392055 y[1] (numeric) = -2.287044802126887939086158291035 absolute error = 9.864840822061518295e-13 relative error = 4.3133570505010423343645383050001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7675 Order of pole = 5.626 x[1] = -0.758 y[1] (analytic) = -2.2961083773440671930216527244822 y[1] (numeric) = -2.2961083773450654277035350897261 absolute error = 9.982346818823652439e-13 relative error = 4.3475068151488295242908897680002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7665 Order of pole = 5.626 x[1] = -0.757 y[1] (analytic) = -2.3052199079169303771005742987441 y[1] (numeric) = -2.3052199079179405026761618487289 absolute error = 1.0101255755875499848e-12 relative error = 4.3819054838040653794841898640000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7655 Order of pole = 5.626 x[1] = -0.756 y[1] (analytic) = -2.3143797114290661503785436486089 y[1] (numeric) = -2.314379711430088309005461729081 absolute error = 1.0221586269180804721e-12 relative error = 4.4165554246365454277082207360000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7645 Order of pole = 5.626 x[1] = -0.755 y[1] (analytic) = -2.3235881079922427011014678977424 y[1] (numeric) = -2.3235881079932770368282050178974 absolute error = 1.0343357267371201550e-12 relative error = 4.4514590308816182184717562499999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7635 Order of pole = 5.626 x[1] = -0.754 y[1] (analytic) = -2.3328454202689143700721089984511 y[1] (numeric) = -2.3328454202699610288657194149731 absolute error = 1.0466587936104165220e-12 relative error = 4.4866187211399754780369940799999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7625 Order of pole = 5.626 x[1] = -0.753 y[1] (analytic) = -2.342151973495964684114420054234 y[1] (numeric) = -2.342151973497023813888669705979 absolute error = 1.0591297742496517450e-12 relative error = 4.5220369396814315206937086500001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7615 Order of pole = 5.626 x[1] = -0.752 y[1] (analytic) = -2.3515080955087023106633404929544 y[1] (numeric) = -2.3515080955097740613073039831729 absolute error = 1.0717506439634902185e-12 relative error = 4.5577161567527503853701324799999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7605 Order of pole = 5.626 x[1] = -0.751 y[1] (analytic) = -2.3609141167651129685246164405216 y[1] (numeric) = -2.3609141167661974919317329076128 absolute error = 1.0845234071164670912e-12 relative error = 4.5936588688895801148382229119998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7595 Order of pole = 5.626 x[1] = -0.75 y[1] (analytic) = -2.3703703703703703703703703703703 y[1] (numeric) = -2.3703703703714678204679662351451 absolute error = 1.0974500975958647748e-12 relative error = 4.6298675992325545186875000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7584 Order of pole = 5.626 x[1] = -0.749 y[1] (analytic) = -2.3798771921016093136531990931554 y[1] (numeric) = -2.3798771921027198464324858205343 absolute error = 1.1105327792867273789e-12 relative error = 4.6663448978476237637141889610000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7574 Order of pole = 5.626 x[1] = -0.748 y[1] (analytic) = -2.3894349204329640783441040138989 y[1] (numeric) = -2.3894349204340878518906591799357 absolute error = 1.1237735465551660368e-12 relative error = 4.7030933420506761045380290560001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7564 Order of pole = 5.626 x[1] = -0.747 y[1] (analytic) = -2.3990438965608753322372917444871 y[1] (numeric) = -2.3990438965620125067620318556561 absolute error = 1.1371745247401111690e-12 relative error = 4.7401155367365140589698318700001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7554 Order of pole = 5.626 x[1] = -0.746 y[1] (analytic) = -2.4087044644296687875277359910374 y[1] (numeric) = -2.4087044644308195253983896619263 absolute error = 1.1507378706536708889e-12 relative error = 4.7774141147122493807167601040001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7544 Order of pole = 5.626 x[1] = -0.745 y[1] (analytic) = -2.4184169707574088959654456583219 y[1] (numeric) = -2.4184169707585733617385359162904 absolute error = 1.1644657730902579685e-12 relative error = 4.8149917370351821958020081249998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7534 Order of pole = 5.626 x[1] = -0.744 y[1] (analytic) = -2.4281817650620309141338982566198 y[1] (numeric) = -2.4281817650632092745872429076943 absolute error = 1.1783604533446510745e-12 relative error = 4.8528510933552307421777740800002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7524 Order of pole = 5.626 x[1] = -0.743 y[1] (analytic) = -2.4379991996877547152995106274908 y[1] (numeric) = -2.437999199688947139465249786831 absolute error = 1.1924241657391593402e-12 relative error = 4.8909949022619792072636586140001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7514 Order of pole = 5.626 x[1] = -0.742 y[1] (analytic) = -2.4478696298317837698449525251352 y[1] (numeric) = -2.4478696298329904290431125879151 absolute error = 1.2066591981600627799e-12 relative error = 4.9294259116364122882982479119999e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.5MB, time=3.45 Real estimate of pole used Radius of convergence = 0.7504 Order of pole = 5.626 x[1] = -0.741 y[1] (analytic) = -2.4577934135712927625423710988308 y[1] (numeric) = -2.4577934135725138304149746033789 absolute error = 1.2210678726035045481e-12 relative error = 4.9681468990074061665449441010001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7493 Order of pole = 5.626 x[1] = -0.74 y[1] (analytic) = -2.4677709118907073618541843523582 y[1] (numeric) = -2.4677709118919430143999153669953 absolute error = 1.2356525457310146371e-12 relative error = 5.0071606719130467530421040000000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7483 Order of pole = 5.626 x[1] = -0.739 y[1] (analytic) = -2.4778024887092797040802114816317 y[1] (numeric) = -2.4778024887105301196896463298987 absolute error = 1.2504156094348482670e-12 relative error = 5.0464700682668472134208487300001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7473 Order of pole = 5.626 x[1] = -0.738 y[1] (analytic) = -2.4878885109089632035119273057289 y[1] (numeric) = -2.4878885109102285630033406316864 absolute error = 1.2653594914133259575e-12 relative error = 5.0860779567289379306391293999998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7463 Order of pole = 5.626 x[1] = -0.737 y[1] (analytic) = -2.4980293483625903488191476787313 y[1] (numeric) = -2.4980293483638708354749040448321 absolute error = 1.2804866557563661008e-12 relative error = 5.1259872370823032891220574240001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7453 Order of pole = 5.626 x[1] = -0.736 y[1] (analytic) = -2.5082253739623571956932686775704 y[1] (numeric) = -2.5082253739636529952968100823227 absolute error = 1.2957996035414047523e-12 relative error = 5.1662008406141408448459898880002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7443 Order of pole = 5.626 x[1] = -0.735 y[1] (analytic) = -2.51847696364861831631629929958 y[1] (numeric) = -2.5184769636499296171897392009363 absolute error = 1.3113008734399013563e-12 relative error = 5.2067217305024197200226811250002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7433 Order of pole = 5.626 x[1] = -0.734 y[1] (analytic) = -2.5287844964389960175285630760685 y[1] (numeric) = -2.5287844964403230105708977092623 absolute error = 1.3269930423346331938e-12 relative error = 5.2475529022077162846384199520000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7423 Order of pole = 5.626 x[1] = -0.733 y[1] (analytic) = -2.5391483544578076916425330983765 y[1] (numeric) = -2.5391483544591505703684810838896 absolute error = 1.3428787259479855131e-12 relative error = 5.2886973838704064905907366469999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7413 Order of pole = 5.626 x[1] = -0.732 y[1] (analytic) = -2.5495689229658152167084632797622 y[1] (numeric) = -2.5495689229671741772879447283231 absolute error = 1.3589605794814485609e-12 relative error = 5.3301582367132955178523893120000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7402 Order of pole = 5.626 x[1] = -0.731 y[1] (analytic) = -2.5600465903903003766921674358228 y[1] (numeric) = -2.5600465903916756179904339729086 absolute error = 1.3752412982665370858e-12 relative error = 5.3719385554497667232848204780001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7392 Order of pole = 5.626 x[1] = -0.73 y[1] (analytic) = -2.5705817483554703264895878586282 y[1] (numeric) = -2.5705817483568620501080152109623 absolute error = 1.3917236184273523341e-12 relative error = 5.4140414686975332295457970000002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7382 Order of pole = 5.626 x[1] = -0.729 y[1] (analytic) = -2.5811747917131971819900315081167 y[1] (numeric) = -2.5811747917146055923075865192227 absolute error = 1.4084103175550111060e-12 relative error = 5.4564701393980768708695083400001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7372 Order of pole = 5.626 x[1] = -0.728 y[1] (analytic) = -2.5918261185740958715237184021148 y[1] (numeric) = -2.5918261185755211757391125732013 absolute error = 1.4253042153941710865e-12 relative error = 5.4992277652418606071034444799999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7362 Order of pole = 5.626 x[1] = -0.727 y[1] (analytic) = -2.6025361303389444420034101395271 y[1] (numeric) = -2.602536130340386850177952025943 absolute error = 1.4424081745418864159e-12 relative error = 5.5423175790994019436519646970000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7352 Order of pole = 5.626 x[1] = -0.726 y[1] (analytic) = -2.6133052317304510709084415550069 y[1] (numeric) = -2.6133052317319107960096005873267 absolute error = 1.4597251011590323198e-12 relative error = 5.5857428494582963438739688480001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7342 Order of pole = 5.626 x[1] = -0.725 y[1] (analytic) = -2.6241338308253720939767928164335 y[1] (numeric) = -2.6241338308268493519224873590168 absolute error = 1.4772579456945425833e-12 relative error = 5.6295068808662811037662031250003e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7332 Order of pole = 5.626 x[1] = -0.724 y[1] (analytic) = -2.6350223390869854180814979946004 y[1] (numeric) = -2.6350223390884804277851207033232 absolute error = 1.4950097036227087228e-12 relative error = 5.6736130143804316445726686720001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7321 Order of pole = 5.626 x[1] = -0.723 y[1] (analytic) = -2.6459711713979237492865370258804 y[1] (numeric) = -2.6459711713994367327027308207811 absolute error = 1.5129834161937949007e-12 relative error = 5.7180646280225837319051144689998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7311 Order of pole = 5.626 x[1] = -0.722 y[1] (analytic) = -2.6569807460933721275195165332327 y[1] (numeric) = -2.656980746094903309690714761156 absolute error = 1.5311821711982279233e-12 relative error = 5.7628651372410766632359141840001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7301 Order of pole = 5.626 x[1] = -0.721 y[1] (analytic) = -2.6680514849946343216792995658351 y[1] (numeric) = -2.6680514849961839307830441929195 absolute error = 1.5496091037446270844e-12 relative error = 5.8080179953789140617891946840002e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.5MB, time=3.71 Real estimate of pole used Radius of convergence = 0.7291 Order of pole = 5.626 x[1] = -0.72 y[1] (analytic) = -2.6791838134430727023319615912208 y[1] (numeric) = -2.6791838134446409697290135353824 absolute error = 1.5682673970519441616e-12 relative error = 5.8535266941484405442887680000001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7281 Order of pole = 5.626 x[1] = -0.719 y[1] (analytic) = -2.6903781603344262734539803107741 y[1] (numeric) = -2.6903781603360134337372363003015 absolute error = 1.5871602832559895274e-12 relative error = 5.8993947641126341389137237660001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7271 Order of pole = 5.626 x[1] = -0.718 y[1] (analytic) = -2.7016349581535116099736495494029 y[1] (numeric) = -2.701634958155117901017880175539 absolute error = 1.6062910442306261361e-12 relative error = 5.9456257751731160327813417520001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7261 Order of pole = 5.626 x[1] = -0.717 y[1] (analytic) = -2.7129546430093115141568769223607 y[1] (numeric) = -2.7129546430109371771693008414254 absolute error = 1.6256630124239190647e-12 relative error = 5.9922233370649809181368430109999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7251 Order of pole = 5.626 x[1] = -0.716 y[1] (analytic) = -2.7243376546704562711986161585216 y[1] (numeric) = -2.7243376546721015507703256928632 absolute error = 1.6452795717095343416e-12 relative error = 6.0391910998585529479793935360003e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7241 Order of pole = 5.626 x[1] = -0.715 y[1] (analytic) = -2.7357844366011024527333393292608 y[1] (numeric) = -2.7357844366027675968915930162427 absolute error = 1.6651441582536869819e-12 relative error = 6.0865327544681740603510666250002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.723 Order of pole = 5.626 x[1] = -0.714 y[1] (analytic) = -2.747295435997214286384625800669 y[1] (numeric) = -2.7472954359988995466460237451563 absolute error = 1.6852602613979444873e-12 relative error = 6.1342520331681332660317983120001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.722 Order of pole = 5.626 x[1] = -0.713 y[1] (analytic) = -2.7588711038232526799529061806125 y[1] (numeric) = -2.7588711038249583113774643791391 absolute error = 1.7056314245581985266e-12 relative error = 6.1823527101158472748637928020002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.721 Order of pole = 5.626 x[1] = -0.712 y[1] (analytic) = -2.7705118948492770604097485137645 y[1] (numeric) = -2.770511894851003321655888637907 absolute error = 1.7262612461401241425e-12 relative error = 6.2308386018824047442641023999999e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.72 Order of pole = 5.626 x[1] = -0.711 y[1] (analytic) = -2.7822182676884652605452394936406 y[1] (numeric) = -2.7822182676902124139257109462341 absolute error = 1.7471533804714525935e-12 relative error = 6.2797135679905883161480529850000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.719 Order of pole = 5.626 x[1] = -0.71 y[1] (analytic) = -2.7939906848350567599207624241782 y[1] (numeric) = -2.7939906848368250714595138150337 absolute error = 1.7683115387513908555e-12 relative error = 6.3289815114604905248286049999997e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.718 Order of pole = 5.626 x[1] = -0.709 y[1] (analytic) = -2.805829612702724661731917576432 y[1] (numeric) = -2.8058296127045144012219351043287 absolute error = 1.7897394900175278967e-12 relative error = 6.3786463793628416691450636429998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.717 Order of pole = 5.626 x[1] = -0.708 y[1] (analytic) = -2.8177355216633818633049323626257 y[1] (numeric) = -2.8177355216651933043670629376895 absolute error = 1.8114410621305750638e-12 relative error = 6.4287121633801696977669538560000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.716 Order of pole = 5.626 x[1] = -0.707 y[1] (analytic) = -2.8297088860864269552544896847392 y[1] (numeric) = -2.8297088860882603753972669800709 absolute error = 1.8334201427772953317e-12 relative error = 6.4791829003759142403822370309998e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.715 Order of pole = 5.626 x[1] = -0.706 y[1] (analytic) = -2.8417501843784354628416497000919 y[1] (numeric) = -2.8417501843802911435221416838268 absolute error = 1.8556806804919837349e-12 relative error = 6.5300626729716189785136317840000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7139 Order of pole = 5.626 x[1] = -0.705 y[1] (analytic) = -2.8538598990233021228080126397455 y[1] (numeric) = -2.8538598990251803494937095087852 absolute error = 1.8782266856968690397e-12 relative error = 6.5813556101323286579210921250000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7129 Order of pole = 5.626 x[1] = -0.704 y[1] (analytic) = -2.8660385166228399699474079639368 y[1] (numeric) = -2.8660385166247410321791697785838 absolute error = 1.9010622317618146470e-12 relative error = 6.6330658877603192377363660800002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7119 Order of pole = 5.626 x[1] = -0.703 y[1] (analytic) = -2.8782865279378420899305255604119 y[1] (numeric) = -2.8782865279397662813866092652154 absolute error = 1.9241914560837048035e-12 relative error = 6.6851977292972918206475084450001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7109 Order of pole = 5.626 x[1] = -0.702 y[1] (analytic) = -2.890604427929611978442750920247 y[1] (numeric) = -2.8906044279315595970039368307474 absolute error = 1.9476185611859105004e-12 relative error = 6.7377554063351632964386336320001e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7099 Order of pole = 5.626 x[1] = -0.701 y[1] (analytic) = -2.9029927158019685315531547212295 y[1] (numeric) = -2.9029927158039398793689929591333 absolute error = 1.9713478158382379038e-12 relative error = 6.7907432392355888685982188380000e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7089 Order of pole = 5.626 memory used=57.2MB, alloc=4.5MB, time=3.98 x[1] = -0.7 y[1] (analytic) = -2.9154518950437317784256559766763 y[1] (numeric) = -2.9154518950457271619818537475181 absolute error = 1.9953835561977708418e-12 relative error = 6.8441655977583539873740000000002e-11 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.7079 Order of pole = 5.626 x[1] = -0.699 y[1] (analytic) = -2.9279824734716955550347845928237 y[1] (numeric) = -2.9279824734737152852217556205629 absolute error = 2.0197301869710277392e-12 relative error = 6.8980269016987755595620058080004e-11 % h = 0.001 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations = 301 Total Elapsed Time = 3 Seconds Elapsed Time(since restart) = 3 Seconds Time to Timeout = 14 Minutes 56 Seconds Percent Done = 100.7 % > quit memory used=57.4MB, alloc=4.5MB, time=4.00