|\^/| 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 > glob_iolevel, > INFO, > ALWAYS, > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_max_iter, > glob_hmin_init, > glob_initial_pass, > glob_smallish_float, > glob_h, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_reached_optimal_h, > glob_not_yet_finished, > days_in_year, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug, > glob_normmax, > glob_warned, > glob_abserr, > centuries_in_millinium, > glob_display_flag, > glob_log10relerr, > glob_current_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_almost_1, > min_in_hour, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmax, > glob_subiter_method, > glob_dump_analytic, > glob_large_float, > glob_clock_sec, > years_in_century, > sec_in_min, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_start, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > hours_in_day, > djd_debug2, > glob_small_float, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_percent_done, > glob_unchanged_h_cnt, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_1, > #END CONST > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_y_init, > array_norms, > array_type_pole, > array_poles, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_complex_pole, > array_y_higher, > 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 glob_iolevel, INFO, ALWAYS, DEBUGL, DEBUGMASSIVE, glob_max_terms, glob_iter, glob_max_iter, glob_hmin_init, glob_initial_pass, glob_smallish_float, glob_h, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_reached_optimal_h, glob_not_yet_finished, days_in_year, glob_log10normmin, glob_curr_iter_when_opt, glob_max_sec, glob_max_hours, glob_log10_relerr, glob_hmin, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug, glob_normmax, glob_warned, glob_abserr, centuries_in_millinium, glob_display_flag, glob_log10relerr, glob_current_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_almost_1, min_in_hour, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_hmax, glob_subiter_method, glob_dump_analytic, glob_large_float, glob_clock_sec, years_in_century, sec_in_min, glob_dump, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_start, glob_log10_abserr, glob_look_poles, glob_disp_incr, hours_in_day, djd_debug2, glob_small_float, glob_no_eqs, glob_relerr, glob_last_good_h, glob_percent_done, glob_unchanged_h_cnt, glob_optimal_done, array_const_2D0, array_const_0D0, array_const_1, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_last_rel_error, array_1st_rel_error, array_pole, array_y_init, array_norms, array_type_pole, array_poles, array_y_higher_work, array_real_pole, array_y_higher_work2, array_y_set_initial, array_complex_pole, array_y_higher, 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 > glob_iolevel, > INFO, > ALWAYS, > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_max_iter, > glob_hmin_init, > glob_initial_pass, > glob_smallish_float, > glob_h, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_reached_optimal_h, > glob_not_yet_finished, > days_in_year, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug, > glob_normmax, > glob_warned, > glob_abserr, > centuries_in_millinium, > glob_display_flag, > glob_log10relerr, > glob_current_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_almost_1, > min_in_hour, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmax, > glob_subiter_method, > glob_dump_analytic, > glob_large_float, > glob_clock_sec, > years_in_century, > sec_in_min, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_start, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > hours_in_day, > djd_debug2, > glob_small_float, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_percent_done, > glob_unchanged_h_cnt, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_1, > #END CONST > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_y_init, > array_norms, > array_type_pole, > array_poles, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_complex_pole, > array_y_higher, > 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 glob_iolevel, INFO, ALWAYS, DEBUGL, DEBUGMASSIVE, glob_max_terms, glob_iter, glob_max_iter, glob_hmin_init, glob_initial_pass, glob_smallish_float, glob_h, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_reached_optimal_h, glob_not_yet_finished, days_in_year, glob_log10normmin, glob_curr_iter_when_opt, glob_max_sec, glob_max_hours, glob_log10_relerr, glob_hmin, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug, glob_normmax, glob_warned, glob_abserr, centuries_in_millinium, glob_display_flag, glob_log10relerr, glob_current_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_almost_1, min_in_hour, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_hmax, glob_subiter_method, glob_dump_analytic, glob_large_float, glob_clock_sec, years_in_century, sec_in_min, glob_dump, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_start, glob_log10_abserr, glob_look_poles, glob_disp_incr, hours_in_day, djd_debug2, glob_small_float, glob_no_eqs, glob_relerr, glob_last_good_h, glob_percent_done, glob_unchanged_h_cnt, glob_optimal_done, array_const_2D0, array_const_0D0, array_const_1, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_last_rel_error, array_1st_rel_error, array_pole, array_y_init, array_norms, array_type_pole, array_poles, array_y_higher_work, array_real_pole, array_y_higher_work2, array_y_set_initial, array_complex_pole, array_y_higher, 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 > glob_iolevel, > INFO, > ALWAYS, > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_max_iter, > glob_hmin_init, > glob_initial_pass, > glob_smallish_float, > glob_h, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_reached_optimal_h, > glob_not_yet_finished, > days_in_year, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug, > glob_normmax, > glob_warned, > glob_abserr, > centuries_in_millinium, > glob_display_flag, > glob_log10relerr, > glob_current_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_almost_1, > min_in_hour, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmax, > glob_subiter_method, > glob_dump_analytic, > glob_large_float, > glob_clock_sec, > years_in_century, > sec_in_min, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_start, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > hours_in_day, > djd_debug2, > glob_small_float, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_percent_done, > glob_unchanged_h_cnt, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_1, > #END CONST > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_y_init, > array_norms, > array_type_pole, > array_poles, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_complex_pole, > array_y_higher, > 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 glob_iolevel, INFO, ALWAYS, DEBUGL, DEBUGMASSIVE, glob_max_terms, glob_iter, glob_max_iter, glob_hmin_init, glob_initial_pass, glob_smallish_float, glob_h, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_reached_optimal_h, glob_not_yet_finished, days_in_year, glob_log10normmin, glob_curr_iter_when_opt, glob_max_sec, glob_max_hours, glob_log10_relerr, glob_hmin, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug, glob_normmax, glob_warned, glob_abserr, centuries_in_millinium, glob_display_flag, glob_log10relerr, glob_current_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_almost_1, min_in_hour, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_hmax, glob_subiter_method, glob_dump_analytic, glob_large_float, glob_clock_sec, years_in_century, sec_in_min, glob_dump, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_start, glob_log10_abserr, glob_look_poles, glob_disp_incr, hours_in_day, djd_debug2, glob_small_float, glob_no_eqs, glob_relerr, glob_last_good_h, glob_percent_done, glob_unchanged_h_cnt, glob_optimal_done, array_const_2D0, array_const_0D0, array_const_1, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_last_rel_error, array_1st_rel_error, array_pole, array_y_init, array_norms, array_type_pole, array_poles, array_y_higher_work, array_real_pole, array_y_higher_work2, array_y_set_initial, array_complex_pole, array_y_higher, 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 > glob_iolevel, > INFO, > ALWAYS, > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_max_iter, > glob_hmin_init, > glob_initial_pass, > glob_smallish_float, > glob_h, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_reached_optimal_h, > glob_not_yet_finished, > days_in_year, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug, > glob_normmax, > glob_warned, > glob_abserr, > centuries_in_millinium, > glob_display_flag, > glob_log10relerr, > glob_current_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_almost_1, > min_in_hour, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmax, > glob_subiter_method, > glob_dump_analytic, > glob_large_float, > glob_clock_sec, > years_in_century, > sec_in_min, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_start, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > hours_in_day, > djd_debug2, > glob_small_float, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_percent_done, > glob_unchanged_h_cnt, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_1, > #END CONST > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_y_init, > array_norms, > array_type_pole, > array_poles, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_complex_pole, > array_y_higher, > 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 glob_iolevel, INFO, ALWAYS, DEBUGL, DEBUGMASSIVE, glob_max_terms, glob_iter, glob_max_iter, glob_hmin_init, glob_initial_pass, glob_smallish_float, glob_h, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_reached_optimal_h, glob_not_yet_finished, days_in_year, glob_log10normmin, glob_curr_iter_when_opt, glob_max_sec, glob_max_hours, glob_log10_relerr, glob_hmin, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug, glob_normmax, glob_warned, glob_abserr, centuries_in_millinium, glob_display_flag, glob_log10relerr, glob_current_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_almost_1, min_in_hour, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_hmax, glob_subiter_method, glob_dump_analytic, glob_large_float, glob_clock_sec, years_in_century, sec_in_min, glob_dump, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_start, glob_log10_abserr, glob_look_poles, glob_disp_incr, hours_in_day, djd_debug2, glob_small_float, glob_no_eqs, glob_relerr, glob_last_good_h, glob_percent_done, glob_unchanged_h_cnt, glob_optimal_done, array_const_2D0, array_const_0D0, array_const_1, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_last_rel_error, array_1st_rel_error, array_pole, array_y_init, array_norms, array_type_pole, array_poles, array_y_higher_work, array_real_pole, array_y_higher_work2, array_y_set_initial, array_complex_pole, array_y_higher, 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 > glob_iolevel, > INFO, > ALWAYS, > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_max_iter, > glob_hmin_init, > glob_initial_pass, > glob_smallish_float, > glob_h, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_reached_optimal_h, > glob_not_yet_finished, > days_in_year, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug, > glob_normmax, > glob_warned, > glob_abserr, > centuries_in_millinium, > glob_display_flag, > glob_log10relerr, > glob_current_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_almost_1, > min_in_hour, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmax, > glob_subiter_method, > glob_dump_analytic, > glob_large_float, > glob_clock_sec, > years_in_century, > sec_in_min, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_start, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > hours_in_day, > djd_debug2, > glob_small_float, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_percent_done, > glob_unchanged_h_cnt, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_1, > #END CONST > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_y_init, > array_norms, > array_type_pole, > array_poles, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_complex_pole, > array_y_higher, > 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 glob_iolevel, INFO, ALWAYS, DEBUGL, DEBUGMASSIVE, glob_max_terms, glob_iter, glob_max_iter, glob_hmin_init, glob_initial_pass, glob_smallish_float, glob_h, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_reached_optimal_h, glob_not_yet_finished, days_in_year, glob_log10normmin, glob_curr_iter_when_opt, glob_max_sec, glob_max_hours, glob_log10_relerr, glob_hmin, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug, glob_normmax, glob_warned, glob_abserr, centuries_in_millinium, glob_display_flag, glob_log10relerr, glob_current_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_almost_1, min_in_hour, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_hmax, glob_subiter_method, glob_dump_analytic, glob_large_float, glob_clock_sec, years_in_century, sec_in_min, glob_dump, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_start, glob_log10_abserr, glob_look_poles, glob_disp_incr, hours_in_day, djd_debug2, glob_small_float, glob_no_eqs, glob_relerr, glob_last_good_h, glob_percent_done, glob_unchanged_h_cnt, glob_optimal_done, array_const_2D0, array_const_0D0, array_const_1, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_last_rel_error, array_1st_rel_error, array_pole, array_y_init, array_norms, array_type_pole, array_poles, array_y_higher_work, array_real_pole, array_y_higher_work2, array_y_set_initial, array_complex_pole, array_y_higher, 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 > glob_iolevel, > INFO, > ALWAYS, > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_max_iter, > glob_hmin_init, > glob_initial_pass, > glob_smallish_float, > glob_h, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_reached_optimal_h, > glob_not_yet_finished, > days_in_year, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug, > glob_normmax, > glob_warned, > glob_abserr, > centuries_in_millinium, > glob_display_flag, > glob_log10relerr, > glob_current_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_almost_1, > min_in_hour, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmax, > glob_subiter_method, > glob_dump_analytic, > glob_large_float, > glob_clock_sec, > years_in_century, > sec_in_min, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_start, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > hours_in_day, > djd_debug2, > glob_small_float, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_percent_done, > glob_unchanged_h_cnt, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_1, > #END CONST > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_y_init, > array_norms, > array_type_pole, > array_poles, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_complex_pole, > array_y_higher, > 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_2D0[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 add $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * (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_2D0,1); > #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 add $eq_no = 1 i = 2 > array_tmp5[2] := array_const_0D0[2] + array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * (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_2D0,1); > #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 add $eq_no = 1 i = 3 > array_tmp5[3] := array_const_0D0[3] + array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * (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_2D0,1); > #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 add $eq_no = 1 i = 4 > array_tmp5[4] := array_const_0D0[4] + array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * (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_2D0,1); > #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 add $eq_no = 1 i = 5 > array_tmp5[5] := array_const_0D0[5] + array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * (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_2D0,1); > #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 add $eq_no = 1 > array_tmp5[kkk] := array_const_0D0[kkk] + array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp5[kkk] * (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 glob_iolevel, INFO, ALWAYS, DEBUGL, DEBUGMASSIVE, glob_max_terms, glob_iter, glob_max_iter, glob_hmin_init, glob_initial_pass, glob_smallish_float, glob_h, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_reached_optimal_h, glob_not_yet_finished, days_in_year, glob_log10normmin, glob_curr_iter_when_opt, glob_max_sec, glob_max_hours, glob_log10_relerr, glob_hmin, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug, glob_normmax, glob_warned, glob_abserr, centuries_in_millinium, glob_display_flag, glob_log10relerr, glob_current_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_almost_1, min_in_hour, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_hmax, glob_subiter_method, glob_dump_analytic, glob_large_float, glob_clock_sec, years_in_century, sec_in_min, glob_dump, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_start, glob_log10_abserr, glob_look_poles, glob_disp_incr, hours_in_day, djd_debug2, glob_small_float, glob_no_eqs, glob_relerr, glob_last_good_h, glob_percent_done, glob_unchanged_h_cnt, glob_optimal_done, array_const_2D0, array_const_0D0, array_const_1, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_last_rel_error, array_1st_rel_error, array_pole, array_y_init, array_norms, array_type_pole, array_poles, array_y_higher_work, array_real_pole, array_y_higher_work2, array_y_set_initial, array_complex_pole, array_y_higher, glob_last; array_tmp1[1] := array_m1[1]*array_const_2D0[1]; array_tmp2[1] := array_tmp1[1]/array_x[1]; array_tmp3[1] := array_tmp2[1]/array_x[1]; array_tmp4[1] := array_tmp3[1]/array_x[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*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_2D0, 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_const_0D0[2] + array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[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_2D0, 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_const_0D0[3] + array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[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_2D0, 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_const_0D0[4] + array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[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_2D0, 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_const_0D0[5] + array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[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_2D0, 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_const_0D0[kkk] + array_tmp4[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0/x/x; > end; exact_soln_y := proc(x) 1.0/(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, > 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 > glob_iolevel, > INFO, > ALWAYS, > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_max_iter, > glob_hmin_init, > glob_initial_pass, > glob_smallish_float, > glob_h, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_reached_optimal_h, > glob_not_yet_finished, > days_in_year, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug, > glob_normmax, > glob_warned, > glob_abserr, > centuries_in_millinium, > glob_display_flag, > glob_log10relerr, > glob_current_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_almost_1, > min_in_hour, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmax, > glob_subiter_method, > glob_dump_analytic, > glob_large_float, > glob_clock_sec, > years_in_century, > sec_in_min, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_start, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > hours_in_day, > djd_debug2, > glob_small_float, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_percent_done, > glob_unchanged_h_cnt, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_1, > #END CONST > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_y_init, > array_norms, > array_type_pole, > array_poles, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > array_y_set_initial, > array_complex_pole, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_iolevel := 5; > INFO := 2; > ALWAYS := 1; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_max_terms := 30; > glob_iter := 0; > glob_max_iter := 1000; > glob_hmin_init := 0.001; > glob_initial_pass := true; > glob_smallish_float := 0.1e-100; > glob_h := 0.1; > glob_warned2 := false; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_reached_optimal_h := false; > glob_not_yet_finished := true; > days_in_year := 365.0; > glob_log10normmin := 0.1; > glob_curr_iter_when_opt := 0; > glob_max_sec := 10000.0; > glob_max_hours := 0.0; > glob_log10_relerr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_not_yet_start_msg := true; > glob_clock_start_sec := 0.0; > djd_debug := true; > glob_normmax := 0.0; > glob_warned := false; > glob_abserr := 0.1e-10; > centuries_in_millinium := 10.0; > glob_display_flag := true; > glob_log10relerr := 0.0; > glob_current_iter := 0; > glob_orig_start_sec := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_almost_1 := 0.9990; > min_in_hour := 60.0; > glob_max_minutes := 0.0; > glob_log10abserr := 0.0; > MAX_UNCHANGED := 10; > glob_hmax := 1.0; > glob_subiter_method := 3; > glob_dump_analytic := false; > glob_large_float := 9.0e100; > glob_clock_sec := 0.0; > years_in_century := 100.0; > sec_in_min := 60.0; > glob_dump := false; > glob_max_opt_iter := 10; > glob_html_log := true; > glob_optimal_expect_sec := 0.1; > glob_start := 0; > glob_log10_abserr := 0.1e-10; > glob_look_poles := false; > glob_disp_incr := 0.1; > hours_in_day := 24.0; > djd_debug2 := true; > glob_small_float := 0.1e-50; > glob_no_eqs := 0; > glob_relerr := 0.1e-10; > glob_last_good_h := 0.1; > glob_percent_done := 0.0; > glob_unchanged_h_cnt := 0; > glob_optimal_done := 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/sing3postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 100;"); > 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 := 0.1;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > 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;"); > 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 := 100; > 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_m1:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_pole[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_norms[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 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > 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_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_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -1.0; > x_end := -0.7; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.1; > glob_look_poles := true; > glob_max_iter := 100000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-13T04:05:18-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing3") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"sing3 diffeq.mxt") > ; > logitem_str(html_log_file,"sing3 maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global glob_iolevel, INFO, ALWAYS, DEBUGL, DEBUGMASSIVE, glob_max_terms, glob_iter, glob_max_iter, glob_hmin_init, glob_initial_pass, glob_smallish_float, glob_h, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_reached_optimal_h, glob_not_yet_finished, days_in_year, glob_log10normmin, glob_curr_iter_when_opt, glob_max_sec, glob_max_hours, glob_log10_relerr, glob_hmin, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug, glob_normmax, glob_warned, glob_abserr, centuries_in_millinium, glob_display_flag, glob_log10relerr, glob_current_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_almost_1, min_in_hour, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_hmax, glob_subiter_method, glob_dump_analytic, glob_large_float, glob_clock_sec, years_in_century, sec_in_min, glob_dump, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_start, glob_log10_abserr, glob_look_poles, glob_disp_incr, hours_in_day, djd_debug2, glob_small_float, glob_no_eqs, glob_relerr, glob_last_good_h, glob_percent_done, glob_unchanged_h_cnt, glob_optimal_done, array_const_2D0, array_const_0D0, array_const_1, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_last_rel_error, array_1st_rel_error, array_pole, array_y_init, array_norms, array_type_pole, array_poles, array_y_higher_work, array_real_pole, array_y_higher_work2, array_y_set_initial, array_complex_pole, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_iolevel := 5; INFO := 2; ALWAYS := 1; DEBUGL := 3; DEBUGMASSIVE := 4; glob_max_terms := 30; glob_iter := 0; glob_max_iter := 1000; glob_hmin_init := 0.001; glob_initial_pass := true; glob_smallish_float := 0.1*10^(-100); glob_h := 0.1; glob_warned2 := false; glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_reached_optimal_h := false; glob_not_yet_finished := true; days_in_year := 365.0; glob_log10normmin := 0.1; glob_curr_iter_when_opt := 0; glob_max_sec := 10000.0; glob_max_hours := 0.; glob_log10_relerr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_not_yet_start_msg := true; glob_clock_start_sec := 0.; djd_debug := true; glob_normmax := 0.; glob_warned := false; glob_abserr := 0.1*10^(-10); centuries_in_millinium := 10.0; glob_display_flag := true; glob_log10relerr := 0.; glob_current_iter := 0; glob_orig_start_sec := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_almost_1 := 0.9990; min_in_hour := 60.0; glob_max_minutes := 0.; glob_log10abserr := 0.; MAX_UNCHANGED := 10; glob_hmax := 1.0; glob_subiter_method := 3; glob_dump_analytic := false; glob_large_float := 0.90*10^101; glob_clock_sec := 0.; years_in_century := 100.0; sec_in_min := 60.0; glob_dump := false; glob_max_opt_iter := 10; glob_html_log := true; glob_optimal_expect_sec := 0.1; glob_start := 0; glob_log10_abserr := 0.1*10^(-10); glob_look_poles := false; glob_disp_incr := 0.1; hours_in_day := 24.0; djd_debug2 := true; glob_small_float := 0.1*10^(-50); glob_no_eqs := 0; glob_relerr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_percent_done := 0.; glob_unchanged_h_cnt := 0; glob_optimal_done := 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/sing3postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 100;"); 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 := 0.1;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); 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;"); 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 := 100; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_m1 := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[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_pole[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_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; 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_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_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := -1.0; x_end := -0.7; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.1; glob_look_poles := true; glob_max_iter := 100000; glob_h := 0.0001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-13T04:05:18-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing3"); logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "sing3 diffeq.mxt"); logitem_str(html_log_file, "sing3 maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! #BEGIN FIRST INPUT BLOCK Digits := 100; 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 := 0.1; glob_look_poles := true; glob_max_iter := 100000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0/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 = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9999 y[1] (analytic) = 1.0002000300040005000600070008001 y[1] (numeric) = 1.0002000300040005000602520392058 absolute error = 2.4503840567080010891440185923523e-22 relative error = 2.4498940044005000560062006800740e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9998 y[1] (analytic) = 1.000400120032008001920448102423 y[1] (numeric) = 1.0004001200320080019209383753572 absolute error = 4.9027293415396864307773666192589e-22 relative error = 4.9007684459122442177925129037058e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9997 y[1] (analytic) = 1.0006002701080405145851047501907 y[1] (numeric) = 1.0006002701080405145858404539527 absolute error = 7.3570376206062313890173758661958e-22 relative error = 7.3526240601672535047447904522399e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9996 y[1] (analytic) = 1.0008004802561280614686851131009 y[1] (numeric) = 1.000800480256128061469666444167 absolute error = 9.8133106617861057608869762110668e-22 relative error = 9.8054615833863827620551883720141e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9995 y[1] (analytic) = 1.0010007505003126876094375351758 y[1] (numeric) = 1.0010007505003126876106646901993 absolute error = 1.2271550234727019297317806672402e-21 relative error = 1.2259281752379850959775313195181e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9994 y[1] (analytic) = 1.0012010808646484668868161000663 y[1] (numeric) = 1.0012010808646484668882892758774 absolute error = 1.4731758110847869560810298645917e-21 relative error = 1.4714085304547772022570368179249e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9993 y[1] (analytic) = 1.0014014713732015092442023536359 y[1] (numeric) = 1.0014014713732015092459217472423 absolute error = 1.7193936063340692122791333298766e-21 relative error = 1.7169872977880686190758565599901e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9992 y[1] (analytic) = 1.0016019220500499679166872328928 y[1] (numeric) = 1.0016019220500499679186530414795 absolute error = 1.9658085867172613103714336491168e-21 relative error = 1.9626645510960091913220779929958e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9991 y[1] (analytic) = 1.0018024329192840466639172532829 y[1] (numeric) = 1.0018024329192840466661296742128 absolute error = 2.2124209299087804058950942395054e-21 relative error = 2.2084403642958978272766118449007e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.999 y[1] (analytic) = 1.002003004005006007008009010011 y[1] (numeric) = 1.0020030040050060070104682408248 absolute error = 2.4592308137609439213527631189132e-21 relative error = 2.4543148113642357944539789454385e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9989 y[1] (analytic) = 1.0022036353313301754765360527073 y[1] (numeric) = 1.0022036353313301754792422911236 absolute error = 2.7062384163041655048765026839688e-21 relative error = 2.7002879663367800688060352786323e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.45 Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9988 y[1] (analytic) = 1.0024043269223829508505921964186 y[1] (numeric) = 1.0024043269223829508535456403344 absolute error = 2.9534439157471512243881828036699e-21 relative error = 2.9463599033085967373474142839243e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9987 y[1] (analytic) = 1.0026050788023028114179353355617 y[1] (numeric) = 1.0026050788023028114211361830522 absolute error = 3.2008474904770959975629638855839e-21 relative error = 3.1925306964341144542615360608904e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9986 y[1] (analytic) = 1.0028058909952403222312158311442 y[1] (numeric) = 1.0028058909952403222346642804632 absolute error = 3.4484493190598802579029265668937e-21 relative error = 3.4388004199271779505461038622425e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9985 y[1] (analytic) = 1.0030067635253581423712935452252 y[1] (numeric) = 1.0030067635253581423749897948054 absolute error = 3.6962495802402668572283353238830e-21 relative error = 3.6851691480611015972570790816658e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9984 y[1] (analytic) = 1.003207696416831032215647600263 y[1] (numeric) = 1.0032076964168310322195918487159 absolute error = 3.9442484529420982048944545819635e-21 relative error = 3.9316369551687230224101968571050e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9983 y[1] (analytic) = 1.0034086896938458607118829446702 y[1] (numeric) = 1.0034086896938458607160753907864 absolute error = 4.1924461162684936440422678450642e-21 relative error = 4.1782039156424567815991554165451e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9982 y[1] (analytic) = 1.00360974338060161265633780958 y[1] (numeric) = 1.0036097433806016126607786523295 absolute error = 4.4408427495020470651918829491678e-21 relative error = 4.4248701039343480823896833922516e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9981 y[1] (analytic) = 1.0038108575013093959777961455088 y[1] (numeric) = 1.003810857501309395982485584041 absolute error = 4.6894385321050247574878397810391e-21 relative error = 4.6716355945561265625487605209728e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.998 y[1] (analytic) = 1.0040120320801924490263091312886 y[1] (numeric) = 1.0040120320801924490312473649323 absolute error = 4.9382336437195634979059706907750e-21 relative error = 4.9185004620792601221683384318947e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9979 y[1] (analytic) = 1.004213267141486147867129851333 y[1] (numeric) = 1.0042132671414861478723170795971 absolute error = 5.1872282641678688787318983667753e-21 relative error = 5.1654647811350088097429796013067e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9978 y[1] (analytic) = 1.0044145627094380135797652409966 y[1] (numeric) = 1.0044145627094380135852016635701 absolute error = 5.4364225734524138736216911351206e-21 relative error = 5.4125286264144787622609040231112e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9977 y[1] (analytic) = 1.0046159188083077195621494034857 y[1] (numeric) = 1.0046159188083077195678352202374 absolute error = 5.6858167517561376425556314932061e-21 relative error = 5.6596920726686761993680047076280e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9976 y[1] (analytic) = 1.004817335462367098839942405478 y[1] (numeric) = 1.0048173354623670988458778164575 absolute error = 5.9354109794426445759964901908638e-21 relative error = 5.9069551947085614716644647777311e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9975 y[1] (analytic) = 1.00501881269590015138095866232 y[1] (numeric) = 1.005018812695900151387143867757 absolute error = 6.1852054370564035785641353321599e-21 relative error = 6.1543180674051031631936806813450e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9974 y[1] (analytic) = 1.0052203505332030514147290273741 y[1] (numeric) = 1.0052203505332030514211642276794 absolute error = 6.4352003053229475925387437886411e-21 relative error = 6.4017807656893322481832678828482e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9973 y[1] (analytic) = 1.0054219489985841547572007038074 y[1] (numeric) = 1.0054219489985841547638860995726 absolute error = 6.6853957651490733615053206910656e-21 relative error = 6.6493433645523963020979973331217e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9972 y[1] (analytic) = 1.0056236081163640061405791008245 y[1] (numeric) = 1.0056236081163640061475148928221 absolute error = 6.9357919976230414344526719026632e-21 relative error = 6.8970059390456137670645830489560e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9971 y[1] (analytic) = 1.0058253279108753465483157600729 y[1] (numeric) = 1.0058253279108753465555021492569 absolute error = 7.1863891840147764106404141737708e-21 relative error = 7.1447685642805282717283132574462e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.2MB, time=0.99 Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.997 y[1] (analytic) = 1.0060271084064631205552464816717 y[1] (numeric) = 1.0060271084064631205626836691775 absolute error = 7.4371875057760674255480481363532e-21 relative error = 7.3926313154289630056015897799683e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9969 y[1] (analytic) = 1.0062289496274844836728837830417 y[1] (numeric) = 1.0062289496274844836805719701862 absolute error = 7.6881871445407688782205604185025e-21 relative error = 7.6405942677230751479645126434934e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9968 y[1] (analytic) = 1.0064308515983088096998678274491 y[1] (numeric) = 1.0064308515983088097078072157312 absolute error = 7.9393882821250014003254629445832e-21 relative error = 7.8886574964554103513777193144784e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9967 y[1] (analytic) = 1.0066328143433176980775799629094 y[1] (numeric) = 1.0066328143433176980857707540099 absolute error = 8.1907911005273530672366199373089e-21 relative error = 8.1368210769789572798677604525138e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9966 y[1] (analytic) = 1.0068348378869049812509230158376 y[1] (numeric) = 1.0068348378869049812593654116196 absolute error = 8.4423957819290808514606562547831e-21 relative error = 8.3850850847072022018453666774369e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9965 y[1] (analytic) = 1.0070369222534767320342724875751 y[1] (numeric) = 1.0070369222534767320429666900837 absolute error = 8.6942025086943123187221844794679e-21 relative error = 8.6334495951141836378170335348715e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9964 y[1] (analytic) = 1.0072390674674512709826028056685 y[1] (numeric) = 1.0072390674674512709915490171318 absolute error = 8.9462114633702475670245326282407e-21 relative error = 8.8819146837345470629504246312602e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9963 y[1] (analytic) = 1.0074412735532591737677927855297 y[1] (numeric) = 1.0074412735532591737769912083584 absolute error = 9.1984228286873614090030994742284e-21 relative error = 9.1304804261635996645541657905509e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9962 y[1] (analytic) = 1.0076435405353432785601144618573 y[1] (numeric) = 1.0076435405353432785695652986448 absolute error = 9.4508367875596057978889102630504e-21 relative error = 9.3791468980573651545326760609155e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9961 y[1] (analytic) = 1.0078458684381586934149094529603 y[1] (numeric) = 1.0078458684381586934246129064834 absolute error = 9.7034535230846124974003920695282e-21 relative error = 9.6279141751326386368767544713493e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.996 y[1] (analytic) = 1.0080482572861728036644570248867 y[1] (numeric) = 1.0080482572861728036744132981052 absolute error = 9.9562732185438959958818351769174e-21 relative error = 9.8767823331670415302507146048649e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9959 y[1] (analytic) = 1.0082507071038652793150380260242 y[1] (numeric) = 1.0082507071038652793252473220816 absolute error = 1.0209296057403056665007454670358e-20 relative error = 1.0125751447999076545736932317375e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9958 y[1] (analytic) = 1.0084532179157280824491988666115 y[1] (numeric) = 1.0084532179157280824596613888348 absolute error = 1.0462522223311984163370414920616e-20 relative error = 1.0374821595528182719798745289402e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9957 y[1] (analytic) = 1.0086557897462654746332197213711 y[1] (numeric) = 1.0086557897462654746439356732712 absolute error = 1.0715951900105061085276628794362e-20 relative error = 1.0623992851714790502522716551597e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9956 y[1] (analytic) = 1.0088584226199940243297911372514 y[1] (numeric) = 1.0088584226199940243407607225232 absolute error = 1.0969585271801366855063593264357e-20 relative error = 1.0873265292580376901201347674797e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9955 y[1] (analytic) = 1.009061116561442614315903232048 y[1] (numeric) = 1.0090611165614426143271266545706 absolute error = 1.1223422522604881867264973607938e-20 relative error = 1.1122638994207520679317400961182e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9954 y[1] (analytic) = 1.0092638715951524491059516734584 y[1] (numeric) = 1.0092638715951524491174291372953 absolute error = 1.1477463836904691872942099576408e-20 relative error = 1.1372114032739957610991063715132e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9953 y[1] (analytic) = 1.0094666877456770623800646319123 y[1] (numeric) = 1.0094666877456770623917963413115 absolute error = 1.1731709399275192612503988792233e-20 relative error = 1.1621690484382635790951261510699e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=1.54 Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9952 y[1] (analytic) = 1.0096695650375823244176549043124 y[1] (numeric) = 1.0096695650375823244296410637069 absolute error = 1.1986159394476294695337965186549e-20 relative error = 1.1871368425401771000092501307476e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9951 y[1] (analytic) = 1.0098725034954464495362014096184 y[1] (numeric) = 1.0098725034954464495484422236259 absolute error = 1.2240814007453628726573393527430e-20 relative error = 1.2121147932124902126678699298040e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.995 y[1] (analytic) = 1.0100755031438600035352642610035 y[1] (numeric) = 1.0100755031438600035477599344268 absolute error = 1.2495673423338750681301505010808e-20 relative error = 1.2371029080940946643255522498326e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9949 y[1] (analytic) = 1.0102785640074259111457376231202 y[1] (numeric) = 1.0102785640074259111584883609477 absolute error = 1.2750737827449347526574743491863e-20 relative error = 1.2621011948300256139332847317324e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9948 y[1] (analytic) = 1.0104816861107594634843445668178 y[1] (numeric) = 1.0104816861107594634973505742231 absolute error = 1.3006007405289443091509517226372e-20 relative error = 1.2871096610714671909899012664563e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9947 y[1] (analytic) = 1.0106848694784883255133781374653 y[1] (numeric) = 1.0106848694784883255266396198078 absolute error = 1.3261482342549604185816696969881e-20 relative error = 1.3121283144757580599828619573018e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9946 y[1] (analytic) = 1.0108881141352525435056928568503 y[1] (numeric) = 1.0108881141352525435192100196754 absolute error = 1.3517162825107146967084657948813e-20 relative error = 1.3371571627063969904245703831591e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9945 y[1] (analytic) = 1.0110914201057045525149508824427 y[1] (numeric) = 1.0110914201057045525287239314817 absolute error = 1.3773049039026343557140120572883e-20 relative error = 1.3621962134330484324904182735229e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9944 y[1] (analytic) = 1.011294787414509183851127051634 y[1] (numeric) = 1.0112947874145091838651561928045 absolute error = 1.4029141170558628907812502803495e-20 relative error = 1.3872454743315480982647551772184e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9943 y[1] (analytic) = 1.0114982160863436725612770423922 y[1] (numeric) = 1.0114982160863436725755624817983 absolute error = 1.4285439406142807916427955829302e-20 relative error = 1.4123049530839085486009881877132e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9942 y[1] (analytic) = 1.0117017061458976649155728856011 y[1] (numeric) = 1.0117017061458976649301148295335 absolute error = 1.4541943932405262791359714128943e-20 relative error = 1.4373746573783247856020242785830e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9941 y[1] (analytic) = 1.0119052576178732258986100681881 y[1] (numeric) = 1.0119052576178732259134087231243 absolute error = 1.4798654936160160667961851123205e-20 relative error = 1.4624545949091798507272753031989e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.994 y[1] (analytic) = 1.0121088705269848467059904699829 y[1] (numeric) = 1.0121088705269848467210460425873 absolute error = 1.5055572604409661475213992435629e-20 relative error = 1.4875447733770504285324532230129e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9939 y[1] (analytic) = 1.0123125448979594522461853810913 y[1] (numeric) = 1.0123125448979594522614980782156 absolute error = 1.5312697124344126053405000293017e-20 relative error = 1.5126452004887124560483906489503e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9938 y[1] (analytic) = 1.0125162807555364086476828504164 y[1] (numeric) = 1.0125162807555364086632528790997 absolute error = 1.5570028683342324523184104806516e-20 relative error = 1.5377558839571467378051293103904e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9937 y[1] (analytic) = 1.0127200781244675307714236198061 y[1] (numeric) = 1.0127200781244675307872511872751 absolute error = 1.5827567468971644906308420781048e-20 relative error = 1.5628768315015445665075266060428e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9936 y[1] (analytic) = 1.0129239370295170897285299021629 y[1] (numeric) = 1.0129239370295170897446152158319 absolute error = 1.6085313668988301998416252306998e-20 relative error = 1.5880080508473133493686379407163e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9935 y[1] (analytic) = 1.0131278574954618204033312657082 y[1] (numeric) = 1.0131278574954618204196745331796 absolute error = 1.6343267471337546494156051694347e-20 relative error = 1.6131495497260822401071401115504e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=2.10 Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9934 y[1] (analytic) = 1.0133318395470909289816918904553 y[1] (numeric) = 1.0133318395470909289982933195194 absolute error = 1.6601429064153874365001364316996e-20 relative error = 1.6383013358757077766150685767441e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9933 y[1] (analytic) = 1.01353588320920610048464346681 y[1] (numeric) = 1.0135358832092061005015032654458 absolute error = 1.6859798635761236490082556644996e-20 relative error = 1.6634634170402795243021490191921e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9932 y[1] (analytic) = 1.01373998850662150630732801009 y[1] (numeric) = 1.0137399885066215063244463864647 absolute error = 1.7118376374673248540366591155886e-20 relative error = 1.6886358009701257251230112067341e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9931 y[1] (analytic) = 1.0139441554641638117632548686227 y[1] (numeric) = 1.0139441554641638117806320310923 absolute error = 1.7377162469593401116516578934537e-20 relative error = 1.7138184954218189522935807499563e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.993 y[1] (analytic) = 1.0141483841066721836338762069633 y[1] (numeric) = 1.0141483841066721836515123640728 absolute error = 1.7636157109415270140763308594870e-20 relative error = 1.7390115081581817707029519676663e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9929 y[1] (analytic) = 1.0143526744589982977234852496536 y[1] (numeric) = 1.0143526744589982977413806101369 absolute error = 1.7895360483222727503121418687744e-20 relative error = 1.7642148469482924030270526893094e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9928 y[1] (analytic) = 1.0145570265460063464194415748263 y[1] (numeric) = 1.0145570265460063464375963476065 absolute error = 1.8154772780290151962283349998333e-20 relative error = 1.7894285195674904015504194527220e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9927 y[1] (analytic) = 1.0147614403925730462577277508506 y[1] (numeric) = 1.0147614403925730462761421450407 absolute error = 1.8414394190082640301524684084540e-20 relative error = 1.8146525337973823257024091947321e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9926 y[1] (analytic) = 1.0149659160235876454938416131073 y[1] (numeric) = 1.0149659160235876455125158380095 absolute error = 1.8674224902256218739954945066635e-20 relative error = 1.8398868974258474253141811812441e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9925 y[1] (analytic) = 1.015170453463951931679028481876 y[1] (numeric) = 1.0151704534639519316979627469827 absolute error = 1.8934265106658054599448413048384e-20 relative error = 1.8651316182470433296027905825892e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9924 y[1] (analytic) = 1.0153750527385802392418576262221 y[1] (numeric) = 1.0153750527385802392610521412154 absolute error = 1.9194514993326668227589969632780e-20 relative error = 1.8903867040614117418887427691008e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9923 y[1] (analytic) = 1.0155797138723994570751472826707 y[1] (numeric) = 1.0155797138723994570946022574232 absolute error = 1.9454974752492145176971468792058e-20 relative error = 1.9156521626756841400533650811045e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9922 y[1] (analytic) = 1.0157844368903490361282425413691 y[1] (numeric) = 1.0157844368903490361479581859437 absolute error = 1.9715644574576348641174599863255e-20 relative error = 1.9409280019028874827423605168044e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9921 y[1] (analytic) = 1.0159892218173809970046504163458 y[1] (numeric) = 1.015989221817380997024626940996 absolute error = 1.9976524650193132147776683668263e-20 relative error = 1.9662142295623499213219154809132e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.992 y[1] (analytic) = 1.0161940686784599375650364203954 y[1] (numeric) = 1.0161940686784599375852740355656 absolute error = 2.0237615170148552508716317702283e-20 relative error = 1.9915108534797065175937414463380e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9999 Order of pole = 4.437 x[1] = -0.9919 y[1] (analytic) = 1.0163989774985630405355869690374 y[1] (numeric) = 1.0163989774985630405560858853628 absolute error = 2.0498916325441083028356261997970e-20 relative error = 2.0168178814869049672754381007953e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9998 Order of pole = 4.437 x[1] = -0.9918 y[1] (analytic) = 1.0166039483026800811217419419193 y[1] (numeric) = 1.0166039483026800811425023702266 absolute error = 2.0760428307261826969581433655555e-20 relative error = 2.0421353214222113292525732799203e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9997 Order of pole = 4.437 x[1] = -0.9917 y[1] (analytic) = 1.0168089811158134346273017339674 y[1] (numeric) = 1.0168089811158134346483238852744 absolute error = 2.1022151306994731278270355132940e-20 relative error = 2.0674631811302157606088827282498e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=2.66 Real estimate of pole used Radius of convergence = 0.9996 Order of pole = 4.437 x[1] = -0.9916 y[1] (analytic) = 1.0170140759629780840789131325156 y[1] (numeric) = 1.0170140759629780841001972180318 absolute error = 2.1284085516216800566478879215423e-20 relative error = 2.0928014684618382574410004794321e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9995 Order of pole = 4.437 x[1] = -0.9915 y[1] (analytic) = 1.0172192328692016278559383605834 y[1] (numeric) = 1.0172192328692016278774845917101 absolute error = 2.1546231126698311354675492133427e-20 relative error = 2.1181501912743344014641384071465e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9994 Order of pole = 4.437 x[1] = -0.9914 y[1] (analytic) = 1.0174244518595242873257116304109 y[1] (numeric) = 1.0174244518595242873475202187413 absolute error = 2.1808588330403026573367975569575e-20 relative error = 2.1435093574313011124151412685252e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9993 Order of pole = 4.437 x[1] = -0.9913 y[1] (analytic) = 1.0176297329589989144841875553063 y[1] (numeric) = 1.0176297329589989145062587126258 absolute error = 2.2071157319488410324461688294852e-20 relative error = 2.1688789748026824062593513423709e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9992 Order of pole = 4.437 x[1] = -0.9912 y[1] (analytic) = 1.0178350761926909996019857718056 y[1] (numeric) = 1.0178350761926909996243197100919 absolute error = 2.2333938286305842902690208898550e-20 relative error = 2.1942590512647751592077245551712e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9991 Order of pole = 4.437 x[1] = -0.9911 y[1] (analytic) = 1.0180404815856786788758361281005 y[1] (numeric) = 1.0180404815856786788984330595239 absolute error = 2.2596931423400836077459562529447e-20 relative error = 2.2196495947002348775506477888371e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.999 Order of pole = 4.437 x[1] = -0.991 y[1] (analytic) = 1.0182459491630527420854287986429 y[1] (numeric) = 1.0182459491630527421082889355664 absolute error = 2.2860136923513248635447736747338e-20 relative error = 2.2450506129980814733149148752562e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9989 Order of pole = 4.437 x[1] = -0.9909 y[1] (analytic) = 1.018451478949916640255673688798 y[1] (numeric) = 1.0184514789499166402787972437775 absolute error = 2.3123554979577502184301674495794e-20 relative error = 2.2704621140537050457503266041635e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9988 Order of pole = 4.437 x[1] = -0.9908 y[1] (analytic) = 1.018657070971386493324373497379 y[1] (numeric) = 1.0186570709713864933477606831637 absolute error = 2.3387185784722797217774415850152e-20 relative error = 2.2958841057688716686523879025067e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9987 Order of pole = 4.437 x[1] = -0.9907 y[1] (analytic) = 1.0188627252525910978153148088671 y[1] (numeric) = 1.0188627252525910978389658383994 absolute error = 2.3651029532273329442645544570245e-20 relative error = 2.3213165960517291835275831854388e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9986 Order of pole = 4.437 x[1] = -0.9906 y[1] (analytic) = 1.0190684418186719345167815910911 y[1] (numeric) = 1.0190684418186719345406966775069 absolute error = 2.3915086415748506367768580596601e-20 relative error = 2.3467595928168129986077187313166e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9985 Order of pole = 4.437 x[1] = -0.9905 y[1] (analytic) = 1.0192742206947831761654954781173 y[1] (numeric) = 1.0192742206947831761896748347462 absolute error = 2.4179356628863164155589445472919e-20 relative error = 2.3722131039850518937198287956387e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9984 Order of pole = 4.437 x[1] = -0.9904 y[1] (analytic) = 1.0194800619060916951359872220816 y[1] (numeric) = 1.0194800619060916951604310624471 absolute error = 2.4443840365527784736480614257663e-20 relative error = 2.3976771374837738310181500517325e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9983 Order of pole = 4.437 x[1] = -0.9903 y[1] (analytic) = 1.0196859654777770711354037016783 y[1] (numeric) = 1.0196859654777770711601122394981 absolute error = 2.4708537819848713186236054804962e-20 relative error = 2.4231517012467117715846768292142e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9982 Order of pole = 4.437 x[1] = -0.9902 y[1] (analytic) = 1.01989193143503159890375487901 y[1] (numeric) = 1.0198919314350315989287283281961 absolute error = 2.4973449186128375367072543350689e-20 relative error = 2.4486368032140094979048175148079e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9981 Order of pole = 4.437 x[1] = -0.9901 y[1] (analytic) = 1.0200979598030602959196051004939 y[1] (numeric) = 1.0200979598030602959448436751527 absolute error = 2.5238574658865495832483434134915e-20 relative error = 2.4741324513322274422246803840423e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.998 Order of pole = 4.437 x[1] = -0.99 y[1] (analytic) = 1.0203040506070809101112131415162 y[1] (numeric) = 1.0203040506070809101367170559489 absolute error = 2.5503914432755315996291450328067e-20 relative error = 2.4996386535543485207965250466538e-18 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 100 Total Elapsed Time = 3 Seconds Elapsed Time(since restart) = 3 Seconds Expected Time Remaining = 1 Minutes 28 Seconds Optimized Time Remaining = 1 Minutes 27 Seconds Time to Timeout = 14 Minutes 56 Seconds Percent Done = 3.367 % > quit memory used=22.7MB, alloc=4.3MB, time=3.17