|\^/| 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 > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_iter, > glob_start, > glob_orig_start_sec, > glob_max_sec, > glob_log10_abserr, > glob_last_good_h, > years_in_century, > glob_look_poles, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump, > glob_max_opt_iter, > glob_log10abserr, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > MAX_UNCHANGED, > glob_clock_sec, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_smallish_float, > glob_disp_incr, > glob_clock_start_sec, > glob_html_log, > glob_max_rel_trunc_err, > days_in_year, > djd_debug2, > glob_abserr, > glob_optimal_done, > sec_in_min, > glob_normmax, > glob_warned2, > glob_unchanged_h_cnt, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > hours_in_day, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_relerr, > glob_dump_analytic, > glob_h, > glob_display_flag, > glob_log10normmin, > glob_max_iter, > glob_not_yet_finished, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp1_g, > array_pole, > array_y_init, > array_1st_rel_error, > array_norms, > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_type_pole, > array_complex_pole, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_y_higher_work2, > 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 DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_hours, glob_log10_relerr, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_iter, glob_start, glob_orig_start_sec, glob_max_sec, glob_log10_abserr, glob_last_good_h, years_in_century, glob_look_poles, glob_not_yet_start_msg, glob_almost_1, glob_dump, glob_max_opt_iter, glob_log10abserr, glob_large_float, glob_hmin_init, glob_hmax, glob_initial_pass, glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_clock_sec, glob_percent_done, glob_current_iter, glob_warned, glob_smallish_float, glob_disp_incr, glob_clock_start_sec, glob_html_log, glob_max_rel_trunc_err, days_in_year, djd_debug2, glob_abserr, glob_optimal_done, sec_in_min, glob_normmax, glob_warned2, glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_max_trunc_err, hours_in_day, glob_optimal_start, glob_optimal_clock_start_sec, glob_relerr, glob_dump_analytic, glob_h, glob_display_flag, glob_log10normmin, glob_max_iter, glob_not_yet_finished, glob_subiter_method, array_const_3, array_const_0D0, array_tmp1_g, array_pole, array_y_init, array_1st_rel_error, array_norms, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_type_pole, array_complex_pole, array_y_set_initial, array_poles, array_y_higher_work, array_y_higher, array_real_pole, array_y_higher_work2, 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 > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_iter, > glob_start, > glob_orig_start_sec, > glob_max_sec, > glob_log10_abserr, > glob_last_good_h, > years_in_century, > glob_look_poles, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump, > glob_max_opt_iter, > glob_log10abserr, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > MAX_UNCHANGED, > glob_clock_sec, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_smallish_float, > glob_disp_incr, > glob_clock_start_sec, > glob_html_log, > glob_max_rel_trunc_err, > days_in_year, > djd_debug2, > glob_abserr, > glob_optimal_done, > sec_in_min, > glob_normmax, > glob_warned2, > glob_unchanged_h_cnt, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > hours_in_day, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_relerr, > glob_dump_analytic, > glob_h, > glob_display_flag, > glob_log10normmin, > glob_max_iter, > glob_not_yet_finished, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp1_g, > array_pole, > array_y_init, > array_1st_rel_error, > array_norms, > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_type_pole, > array_complex_pole, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_y_higher_work2, > 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 DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_hours, glob_log10_relerr, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_iter, glob_start, glob_orig_start_sec, glob_max_sec, glob_log10_abserr, glob_last_good_h, years_in_century, glob_look_poles, glob_not_yet_start_msg, glob_almost_1, glob_dump, glob_max_opt_iter, glob_log10abserr, glob_large_float, glob_hmin_init, glob_hmax, glob_initial_pass, glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_clock_sec, glob_percent_done, glob_current_iter, glob_warned, glob_smallish_float, glob_disp_incr, glob_clock_start_sec, glob_html_log, glob_max_rel_trunc_err, days_in_year, djd_debug2, glob_abserr, glob_optimal_done, sec_in_min, glob_normmax, glob_warned2, glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_max_trunc_err, hours_in_day, glob_optimal_start, glob_optimal_clock_start_sec, glob_relerr, glob_dump_analytic, glob_h, glob_display_flag, glob_log10normmin, glob_max_iter, glob_not_yet_finished, glob_subiter_method, array_const_3, array_const_0D0, array_tmp1_g, array_pole, array_y_init, array_1st_rel_error, array_norms, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_type_pole, array_complex_pole, array_y_set_initial, array_poles, array_y_higher_work, array_y_higher, array_real_pole, array_y_higher_work2, 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 > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_iter, > glob_start, > glob_orig_start_sec, > glob_max_sec, > glob_log10_abserr, > glob_last_good_h, > years_in_century, > glob_look_poles, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump, > glob_max_opt_iter, > glob_log10abserr, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > MAX_UNCHANGED, > glob_clock_sec, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_smallish_float, > glob_disp_incr, > glob_clock_start_sec, > glob_html_log, > glob_max_rel_trunc_err, > days_in_year, > djd_debug2, > glob_abserr, > glob_optimal_done, > sec_in_min, > glob_normmax, > glob_warned2, > glob_unchanged_h_cnt, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > hours_in_day, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_relerr, > glob_dump_analytic, > glob_h, > glob_display_flag, > glob_log10normmin, > glob_max_iter, > glob_not_yet_finished, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp1_g, > array_pole, > array_y_init, > array_1st_rel_error, > array_norms, > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_type_pole, > array_complex_pole, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_y_higher_work2, > 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 DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_hours, glob_log10_relerr, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_iter, glob_start, glob_orig_start_sec, glob_max_sec, glob_log10_abserr, glob_last_good_h, years_in_century, glob_look_poles, glob_not_yet_start_msg, glob_almost_1, glob_dump, glob_max_opt_iter, glob_log10abserr, glob_large_float, glob_hmin_init, glob_hmax, glob_initial_pass, glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_clock_sec, glob_percent_done, glob_current_iter, glob_warned, glob_smallish_float, glob_disp_incr, glob_clock_start_sec, glob_html_log, glob_max_rel_trunc_err, days_in_year, djd_debug2, glob_abserr, glob_optimal_done, sec_in_min, glob_normmax, glob_warned2, glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_max_trunc_err, hours_in_day, glob_optimal_start, glob_optimal_clock_start_sec, glob_relerr, glob_dump_analytic, glob_h, glob_display_flag, glob_log10normmin, glob_max_iter, glob_not_yet_finished, glob_subiter_method, array_const_3, array_const_0D0, array_tmp1_g, array_pole, array_y_init, array_1st_rel_error, array_norms, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_type_pole, array_complex_pole, array_y_set_initial, array_poles, array_y_higher_work, array_y_higher, array_real_pole, array_y_higher_work2, 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 > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_iter, > glob_start, > glob_orig_start_sec, > glob_max_sec, > glob_log10_abserr, > glob_last_good_h, > years_in_century, > glob_look_poles, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump, > glob_max_opt_iter, > glob_log10abserr, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > MAX_UNCHANGED, > glob_clock_sec, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_smallish_float, > glob_disp_incr, > glob_clock_start_sec, > glob_html_log, > glob_max_rel_trunc_err, > days_in_year, > djd_debug2, > glob_abserr, > glob_optimal_done, > sec_in_min, > glob_normmax, > glob_warned2, > glob_unchanged_h_cnt, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > hours_in_day, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_relerr, > glob_dump_analytic, > glob_h, > glob_display_flag, > glob_log10normmin, > glob_max_iter, > glob_not_yet_finished, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp1_g, > array_pole, > array_y_init, > array_1st_rel_error, > array_norms, > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_type_pole, > array_complex_pole, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_y_higher_work2, > 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 - 3 - 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 - 3 - 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 DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_hours, glob_log10_relerr, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_iter, glob_start, glob_orig_start_sec, glob_max_sec, glob_log10_abserr, glob_last_good_h, years_in_century, glob_look_poles, glob_not_yet_start_msg, glob_almost_1, glob_dump, glob_max_opt_iter, glob_log10abserr, glob_large_float, glob_hmin_init, glob_hmax, glob_initial_pass, glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_clock_sec, glob_percent_done, glob_current_iter, glob_warned, glob_smallish_float, glob_disp_incr, glob_clock_start_sec, glob_html_log, glob_max_rel_trunc_err, days_in_year, djd_debug2, glob_abserr, glob_optimal_done, sec_in_min, glob_normmax, glob_warned2, glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_max_trunc_err, hours_in_day, glob_optimal_start, glob_optimal_clock_start_sec, glob_relerr, glob_dump_analytic, glob_h, glob_display_flag, glob_log10normmin, glob_max_iter, glob_not_yet_finished, glob_subiter_method, array_const_3, array_const_0D0, array_tmp1_g, array_pole, array_y_init, array_1st_rel_error, array_norms, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_type_pole, array_complex_pole, array_y_set_initial, array_poles, array_y_higher_work, array_y_higher, array_real_pole, array_y_higher_work2, glob_last; n := glob_max_terms; m := n - 4; 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 - 4; 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 > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_iter, > glob_start, > glob_orig_start_sec, > glob_max_sec, > glob_log10_abserr, > glob_last_good_h, > years_in_century, > glob_look_poles, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump, > glob_max_opt_iter, > glob_log10abserr, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > MAX_UNCHANGED, > glob_clock_sec, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_smallish_float, > glob_disp_incr, > glob_clock_start_sec, > glob_html_log, > glob_max_rel_trunc_err, > days_in_year, > djd_debug2, > glob_abserr, > glob_optimal_done, > sec_in_min, > glob_normmax, > glob_warned2, > glob_unchanged_h_cnt, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > hours_in_day, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_relerr, > glob_dump_analytic, > glob_h, > glob_display_flag, > glob_log10normmin, > glob_max_iter, > glob_not_yet_finished, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp1_g, > array_pole, > array_y_init, > array_1st_rel_error, > array_norms, > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_type_pole, > array_complex_pole, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_y_higher_work2, > 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 DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_hours, glob_log10_relerr, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_iter, glob_start, glob_orig_start_sec, glob_max_sec, glob_log10_abserr, glob_last_good_h, years_in_century, glob_look_poles, glob_not_yet_start_msg, glob_almost_1, glob_dump, glob_max_opt_iter, glob_log10abserr, glob_large_float, glob_hmin_init, glob_hmax, glob_initial_pass, glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_clock_sec, glob_percent_done, glob_current_iter, glob_warned, glob_smallish_float, glob_disp_incr, glob_clock_start_sec, glob_html_log, glob_max_rel_trunc_err, days_in_year, djd_debug2, glob_abserr, glob_optimal_done, sec_in_min, glob_normmax, glob_warned2, glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_max_trunc_err, hours_in_day, glob_optimal_start, glob_optimal_clock_start_sec, glob_relerr, glob_dump_analytic, glob_h, glob_display_flag, glob_log10normmin, glob_max_iter, glob_not_yet_finished, glob_subiter_method, array_const_3, array_const_0D0, array_tmp1_g, array_pole, array_y_init, array_1st_rel_error, array_norms, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_type_pole, array_complex_pole, array_y_set_initial, array_poles, array_y_higher_work, array_y_higher, array_real_pole, array_y_higher_work2, 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 > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_iter, > glob_start, > glob_orig_start_sec, > glob_max_sec, > glob_log10_abserr, > glob_last_good_h, > years_in_century, > glob_look_poles, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump, > glob_max_opt_iter, > glob_log10abserr, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > MAX_UNCHANGED, > glob_clock_sec, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_smallish_float, > glob_disp_incr, > glob_clock_start_sec, > glob_html_log, > glob_max_rel_trunc_err, > days_in_year, > djd_debug2, > glob_abserr, > glob_optimal_done, > sec_in_min, > glob_normmax, > glob_warned2, > glob_unchanged_h_cnt, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > hours_in_day, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_relerr, > glob_dump_analytic, > glob_h, > glob_display_flag, > glob_log10normmin, > glob_max_iter, > glob_not_yet_finished, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp1_g, > array_pole, > array_y_init, > array_1st_rel_error, > array_norms, > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_type_pole, > array_complex_pole, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_y_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin $eq_no = 1 iii = 1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (3)) * factorial_3(0,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,2] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin $eq_no = 1 iii = 2 > #emit pre sin 2 $eq_no = 1 > array_tmp1[2] := att(1,array_tmp1_g,array_x,1); > array_tmp1_g[2] := -att(1,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (3)) * factorial_3(1,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,3] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin $eq_no = 1 iii = 3 > #emit pre sin 3 $eq_no = 1 > array_tmp1[3] := att(2,array_tmp1_g,array_x,1); > array_tmp1_g[3] := -att(2,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (3)) * factorial_3(2,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,4] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin $eq_no = 1 iii = 4 > #emit pre sin 4 $eq_no = 1 > array_tmp1[4] := att(3,array_tmp1_g,array_x,1); > array_tmp1_g[4] := -att(3,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,7] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (3)) * factorial_3(3,6); > array_y[7] := temporary; > array_y_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,5] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin $eq_no = 1 iii = 5 > #emit pre sin 5 $eq_no = 1 > array_tmp1[5] := att(4,array_tmp1_g,array_x,1); > array_tmp1_g[5] := -att(4,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,8] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (3)) * factorial_3(4,7); > array_y[8] := temporary; > array_y_higher[1,8] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,7] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,6] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,5] := 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 sin $eq_no = 1 > array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1); > array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 3; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (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 DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_hours, glob_log10_relerr, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_iter, glob_start, glob_orig_start_sec, glob_max_sec, glob_log10_abserr, glob_last_good_h, years_in_century, glob_look_poles, glob_not_yet_start_msg, glob_almost_1, glob_dump, glob_max_opt_iter, glob_log10abserr, glob_large_float, glob_hmin_init, glob_hmax, glob_initial_pass, glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_clock_sec, glob_percent_done, glob_current_iter, glob_warned, glob_smallish_float, glob_disp_incr, glob_clock_start_sec, glob_html_log, glob_max_rel_trunc_err, days_in_year, djd_debug2, glob_abserr, glob_optimal_done, sec_in_min, glob_normmax, glob_warned2, glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_max_trunc_err, hours_in_day, glob_optimal_start, glob_optimal_clock_start_sec, glob_relerr, glob_dump_analytic, glob_h, glob_display_flag, glob_log10normmin, glob_max_iter, glob_not_yet_finished, glob_subiter_method, array_const_3, array_const_0D0, array_tmp1_g, array_pole, array_y_init, array_1st_rel_error, array_norms, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_type_pole, array_complex_pole, array_y_set_initial, array_poles, array_y_higher_work, array_y_higher, array_real_pole, array_y_higher_work2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 4] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h^3*factorial_3(0, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 2] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := att(1, array_tmp1_g, array_x, 1); array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 5] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h^3*factorial_3(1, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 3] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := att(2, array_tmp1_g, array_x, 1); array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 6] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h^3*factorial_3(2, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 4] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := att(3, array_tmp1_g, array_x, 1); array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 7] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h^3*factorial_3(3, 6); array_y[7] := temporary; array_y_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := att(4, array_tmp1_g, array_x, 1); array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 8] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h^3*factorial_3(4, 7); array_y[8] := temporary; array_y_higher[1, 8] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 7] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 6] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 3; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[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 - sin(x); > end; exact_soln_y := proc(x) 1.0 - sin(x) end proc > exact_soln_yp := proc(x) > -cos(x); > end; exact_soln_yp := proc(x) -cos(x) end proc > exact_soln_ypp := proc(x) > sin(x); > end; exact_soln_ypp := proc(x) sin(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 > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_hours, > glob_log10_relerr, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_iter, > glob_start, > glob_orig_start_sec, > glob_max_sec, > glob_log10_abserr, > glob_last_good_h, > years_in_century, > glob_look_poles, > glob_not_yet_start_msg, > glob_almost_1, > glob_dump, > glob_max_opt_iter, > glob_log10abserr, > glob_large_float, > glob_hmin_init, > glob_hmax, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > MAX_UNCHANGED, > glob_clock_sec, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_smallish_float, > glob_disp_incr, > glob_clock_start_sec, > glob_html_log, > glob_max_rel_trunc_err, > days_in_year, > djd_debug2, > glob_abserr, > glob_optimal_done, > sec_in_min, > glob_normmax, > glob_warned2, > glob_unchanged_h_cnt, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > hours_in_day, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_relerr, > glob_dump_analytic, > glob_h, > glob_display_flag, > glob_log10normmin, > glob_max_iter, > glob_not_yet_finished, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp1_g, > array_pole, > array_y_init, > array_1st_rel_error, > array_norms, > array_m1, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_type_pole, > array_complex_pole, > array_y_set_initial, > array_poles, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_y_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_iolevel := 5; > glob_max_terms := 30; > ALWAYS := 1; > INFO := 2; > glob_curr_iter_when_opt := 0; > glob_max_hours := 0.0; > glob_log10_relerr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_reached_optimal_h := false; > centuries_in_millinium := 10.0; > min_in_hour := 60.0; > djd_debug := true; > glob_optimal_expect_sec := 0.1; > glob_iter := 0; > glob_start := 0; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_log10_abserr := 0.1e-10; > glob_last_good_h := 0.1; > years_in_century := 100.0; > glob_look_poles := false; > glob_not_yet_start_msg := true; > glob_almost_1 := 0.9990; > glob_dump := false; > glob_max_opt_iter := 10; > glob_log10abserr := 0.0; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_hmax := 1.0; > glob_initial_pass := true; > glob_max_minutes := 0.0; > glob_log10relerr := 0.0; > MAX_UNCHANGED := 10; > glob_clock_sec := 0.0; > glob_percent_done := 0.0; > glob_current_iter := 0; > glob_warned := false; > glob_smallish_float := 0.1e-100; > glob_disp_incr := 0.1; > glob_clock_start_sec := 0.0; > glob_html_log := true; > glob_max_rel_trunc_err := 0.1e-10; > days_in_year := 365.0; > djd_debug2 := true; > glob_abserr := 0.1e-10; > glob_optimal_done := false; > sec_in_min := 60.0; > glob_normmax := 0.0; > glob_warned2 := false; > glob_unchanged_h_cnt := 0; > glob_small_float := 0.1e-50; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > hours_in_day := 24.0; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_h := 0.1; > glob_display_flag := true; > glob_log10normmin := 0.1; > glob_max_iter := 1000; > glob_not_yet_finished := true; > glob_subiter_method := 3; > #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/h3sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 3 ) = sin(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 50;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);"); > omniout_str(ALWAYS,"array_y_init[2 + 1] := exact_soln_ypp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > 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 - sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_yp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_ypp := proc(x)"); > omniout_str(ALWAYS,"sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 50; > 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_tmp1_g:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > 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_last_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work2 := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[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_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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=4 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 <=4 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=4 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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[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_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_const_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3[1] := 3; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > array_y_init[1 + 1] := exact_soln_yp(x_start); > array_y_init[2 + 1] := exact_soln_ypp(x_start); > glob_h := 0.00001; > glob_look_poles := true; > glob_max_iter := 20; > #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] := true; > array_y_set_initial[1,3] := true; > 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 := 3; > #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 := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[4,iii] := array_y_higher[4,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 := 4; > 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 := 3; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[3,iii] := array_y_higher[3,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 := 3; > 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 := 3; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[3,iii] := array_y_higher[3,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 := 3; > 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 := 2; > calc_term := 3; > #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 := 3; > #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 := 2; > calc_term := 2; > #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 := 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 := 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 := 4; > #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 := 4; > #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 := 3; > #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 := 3; > #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 , 3 ) = sin(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,"2012-06-13T01:42:49-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"h3sin") > ; > logitem_str(html_log_file,"diff ( y , x , 3 ) = sin(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,"h3sin diffeq.mxt") > ; > logitem_str(html_log_file,"h3sin 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 DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_hours, glob_log10_relerr, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_iter, glob_start, glob_orig_start_sec, glob_max_sec, glob_log10_abserr, glob_last_good_h, years_in_century, glob_look_poles, glob_not_yet_start_msg, glob_almost_1, glob_dump, glob_max_opt_iter, glob_log10abserr, glob_large_float, glob_hmin_init, glob_hmax, glob_initial_pass, glob_max_minutes, glob_log10relerr, MAX_UNCHANGED, glob_clock_sec, glob_percent_done, glob_current_iter, glob_warned, glob_smallish_float, glob_disp_incr, glob_clock_start_sec, glob_html_log, glob_max_rel_trunc_err, days_in_year, djd_debug2, glob_abserr, glob_optimal_done, sec_in_min, glob_normmax, glob_warned2, glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_max_trunc_err, hours_in_day, glob_optimal_start, glob_optimal_clock_start_sec, glob_relerr, glob_dump_analytic, glob_h, glob_display_flag, glob_log10normmin, glob_max_iter, glob_not_yet_finished, glob_subiter_method, array_const_3, array_const_0D0, array_tmp1_g, array_pole, array_y_init, array_1st_rel_error, array_norms, array_m1, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_type_pole, array_complex_pole, array_y_set_initial, array_poles, array_y_higher_work, array_y_higher, array_real_pole, array_y_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; DEBUGL := 3; glob_iolevel := 5; glob_max_terms := 30; ALWAYS := 1; INFO := 2; glob_curr_iter_when_opt := 0; glob_max_hours := 0.; glob_log10_relerr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_reached_optimal_h := false; centuries_in_millinium := 10.0; min_in_hour := 60.0; djd_debug := true; glob_optimal_expect_sec := 0.1; glob_iter := 0; glob_start := 0; glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_log10_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; years_in_century := 100.0; glob_look_poles := false; glob_not_yet_start_msg := true; glob_almost_1 := 0.9990; glob_dump := false; glob_max_opt_iter := 10; glob_log10abserr := 0.; glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_hmax := 1.0; glob_initial_pass := true; glob_max_minutes := 0.; glob_log10relerr := 0.; MAX_UNCHANGED := 10; glob_clock_sec := 0.; glob_percent_done := 0.; glob_current_iter := 0; glob_warned := false; glob_smallish_float := 0.1*10^(-100); glob_disp_incr := 0.1; glob_clock_start_sec := 0.; glob_html_log := true; glob_max_rel_trunc_err := 0.1*10^(-10); days_in_year := 365.0; djd_debug2 := true; glob_abserr := 0.1*10^(-10); glob_optimal_done := false; sec_in_min := 60.0; glob_normmax := 0.; glob_warned2 := false; glob_unchanged_h_cnt := 0; glob_small_float := 0.1*10^(-50); glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); hours_in_day := 24.0; glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_h := 0.1; glob_display_flag := true; glob_log10normmin := 0.1; glob_max_iter := 1000; glob_not_yet_finished := true; glob_subiter_method := 3; 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/h3sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 3 ) = sin(x);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 50;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);"); omniout_str(ALWAYS, "array_y_init[2 + 1] := exact_soln_ypp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 20;"); 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 - sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_yp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_ypp := proc(x)"); omniout_str(ALWAYS, "sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 50; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp1_g := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); 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_last_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 5, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 5, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work2 := Array(1 .. 5, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_tmp1_g[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_1st_rel_error[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_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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; 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_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 4 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 <= 4 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 4 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; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[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_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_const_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); array_y_init[2] := exact_soln_yp(x_start); array_y_init[3] := exact_soln_ypp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 20; 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] := true; array_y_set_initial[1, 3] := true; 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 := 3; 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 := 3; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[4, iii] := array_y_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; 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 := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[3, iii] := array_y_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; 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 := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[3, iii] := array_y_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; 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 := 2; calc_term := 3; 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 := 3; 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 := 2; calc_term := 2; 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 := 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 := 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 := 4; 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 := 4; 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 := 3; 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 := 3; 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 , 3 ) = sin(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, "2012-06-13T01:42:49-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "h3sin"); logitem_str(html_log_file, "diff ( y , x , 3 ) = sin(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, "h3sin diffeq.mxt"); logitem_str(html_log_file, "h3sin 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/h3sinpostode.ode################# diff ( y , x , 3 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK Digits := 50; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); array_y_init[1 + 1] := exact_soln_yp(x_start); array_y_init[2 + 1] := exact_soln_ypp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 20; #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 - sin(x); end; exact_soln_yp := proc(x) -cos(x); end; exact_soln_ypp := proc(x) sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.90016658335317184769318580158938 y[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 0.90006708343597696196220785831547 y[1] (numeric) = 0.90006708343582777139933384610852 absolute error = 1.4919056287401220695185208014167e-13 relative error = 1.6575493718143992274990384678530e-11 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002 y[1] (analytic) = 0.89996758451811124103868599099689 y[1] (numeric) = 0.899967584516917753032070213845 absolute error = 1.1934880066157771518847895384279e-12 relative error = 1.3261455491808983151116968720892e-10 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003 y[1] (analytic) = 0.89986808660056967410044825122023 y[1] (numeric) = 0.89986808659654177525741786069892 absolute error = 4.0278988430303905213115136208160e-12 relative error = 4.4760992227722820585170685445118e-10 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004 y[1] (analytic) = 0.89976858968434724032208115905533 y[1] (numeric) = 0.89976858967479992023981744621432 absolute error = 9.5473200822637128410071583346345e-12 relative error = 1.0610861716803273411085500688076e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005 y[1] (analytic) = 0.89966909377043890886497991131759 y[1] (numeric) = 0.89966909375179236964112651193558 absolute error = 1.8646539223853399382008160272895e-11 relative error = 2.0725997317199474611501960436509e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006 y[1] (analytic) = 0.8995695988598396388673986899624 y[1] (numeric) = 0.89956959882761940461961766478971 absolute error = 3.2220234247781025172692268397588e-11 relative error = 3.5817388992045298485730837002388e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007 y[1] (analytic) = 0.89947010495354437943450107071087 y[1] (numeric) = 0.89947010490238140582897576550445 absolute error = 5.1162973605525305206418443586605e-11 relative error = 5.6881238546741649008603243535197e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.44 NO POLE x[1] = 0.1008 y[1] (analytic) = 0.89937061205254806962841053200644 y[1] (numeric) = 0.89937061197617885341729412207225 absolute error = 7.6369216211116409934194445793311e-11 relative error = 8.4914066779240435800060829345541e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009 y[1] (analytic) = 0.89927112015784563845826106440201 y[1] (numeric) = 0.89927112004911232702606968827018 absolute error = 1.0873331143219137613182895381758e-10 relative error = 1.2091271363535596656360464802646e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 0.89917162927043200487024788047681 y[1] (numeric) = 0.8991716291212825057891972672458 absolute error = 1.4914949908105061323101410894218e-10 relative error = 1.6587433836415326150228241830357e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1011 y[1] (analytic) = 0.89907213939130207773767822538281 y[1] (numeric) = 0.89907213919279016833196272017904 absolute error = 1.9851190940571550520377341904922e-10 relative error = 2.2079641967341333377535171160261e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1012 y[1] (analytic) = 0.8989726505214507558510222881199 y[1] (numeric) = 0.8989726502637361927700351800302 absolute error = 2.5771456308098710808969900429762e-10 relative error = 2.8667675588517548008658021815768e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1013 y[1] (analytic) = 0.89887316266187292790796421363949 y[1] (numeric) = 0.8988731623342215567084582703841 absolute error = 3.2765137119950594325539120901467e-10 relative error = 3.6451346509135662552298729682871e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1014 y[1] (analytic) = 0.89877367581356347250345321587596 y[1] (numeric) = 0.89877367540434733724064032940046 absolute error = 4.0921613526281288647550264713295e-10 relative error = 4.5530498530944776679069351749947e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1015 y[1] (analytic) = 0.89867418997751725811975479180544 y[1] (numeric) = 0.89867418947421471094734363888066 absolute error = 5.0330254717241115292477779028743e-10 relative error = 5.6005007463828755802242687384549e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1016 y[1] (analytic) = 0.89857470515472914311650203663147 y[1] (numeric) = 0.898574704543924953895672658461 absolute error = 6.1080418922082937817046824857809e-10 relative error = 6.7974781141391308335913579326489e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1017 y[1] (analytic) = 0.89847522134619397572074706019696 y[1] (numeric) = 0.89847522061357944163806126494247 absolute error = 7.3261453408268579525449293399936e-10 relative error = 8.1539759436548786053608001473813e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1018 y[1] (analytic) = 0.89837573855290659401701250472195 y[1] (numeric) = 0.89837573768327964921125899676725 absolute error = 8.6962694480575350795470133564022e-10 relative error = 9.6799914277130711973171085921976e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.1MB, time=0.93 NO POLE x[1] = 0.1019 y[1] (analytic) = 0.89827625677586182593734316396666 y[1] (numeric) = 0.89827625575312715113531630365207 absolute error = 1.0227346748020268603145871739680e-09 relative error = 1.1385524966148804019656123957741e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 0.89817677601605448925135770391935 y[1] (numeric) = 0.89817677482322362141256880138856 absolute error = 1.1928308678387889025307887388244e-09 relative error = 1.3280580167410915213597545249678e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1021 y[1] (analytic) = 0.89807729627447939155630048510842 y[1] (numeric) = 0.89807729489367083352662053182072 absolute error = 1.3808085580296799532877012521836e-09 relative error = 1.5375163850124359356053080739584e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1022 y[1] (analytic) = 0.89797781755213133026709348663827 y[1] (numeric) = 0.89797781596457066044132622800976 absolute error = 1.5875606698257672586285156322533e-09 relative error = 1.7679286044653355690052906402118e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1023 y[1] (analytic) = 0.89787833985000509260638833204834 y[1] (numeric) = 0.89787833803602507459977258459636 absolute error = 1.8139800180066157474519870701323e-09 relative error = 2.0202959994665311324913501478040e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1024 y[1] (analytic) = 0.89777886316909545559461841709491 y[1] (numeric) = 0.89777886110813614792325853337069 absolute error = 2.0609593076713598837242258639835e-09 relative error = 2.2956202158695519850410509067815e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1025 y[1] (analytic) = 0.89767938751039718604005113955504 y[1] (numeric) = 0.89767938518100605181027452406025 absolute error = 2.3293911342297766154947919885298e-09 relative error = 2.5949032211712635809501044070489e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1026 y[1] (analytic) = 0.89757991287490504052884023115219 y[1] (numeric) = 0.89757991025473705713548081034583 absolute error = 2.6201679833933594208063639096376e-09 relative error = 2.9191473046684925474420841487259e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1027 y[1] (analytic) = 0.89748043926361376541507819170298 y[1] (numeric) = 0.89748043632943153424868474111574 absolute error = 2.9341822311663934505872411848166e-09 relative error = 3.2693550776147294371262805258624e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1028 y[1] (analytic) = 0.89738096667751809681084882558455 y[1] (numeric) = 0.89738096340519195297381705696862 absolute error = 3.2723261438370317686159294206364e-09 relative error = 3.6465294733769091998424881548548e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1029 y[1] (analytic) = 0.89728149511761276057627988062199 y[1] (numeric) = 0.89728149148212088260790719197495 absolute error = 3.6354918779683726886470451873408e-09 relative error = 4.0516737475922694184596740878853e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=4.2MB, time=1.41 x[1] = 0.103 y[1] (analytic) = 0.89718202458489247230959578949541 y[1] (numeric) = 0.89718202056032099192005758070764 absolute error = 4.0245714803895382087877675193246e-09 relative error = 4.4857914783252863532236510902673e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1031 y[1] (analytic) = 0.89708255508035193733717051376591 y[1] (numeric) = 0.89708255063989504915041697055186 absolute error = 4.4404568881867535432140516576354e-09 relative error = 4.9498865662246888392770756037723e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1032 y[1] (analytic) = 0.89698308660498585070358049062019 y[1] (numeric) = 0.89698308172094592200915273930438 absolute error = 4.8840399286944277513158097172634e-09 relative error = 5.4449632346805500820033051809069e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1033 y[1] (analytic) = 0.89688361915978889716165768243304 y[1] (numeric) = 0.89688361380357657767542221807279 absolute error = 5.3562123194862354643602519876935e-09 relative error = 5.9720260299814573948738850727939e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1034 y[1] (analytic) = 0.89678415274575575116254272924732 y[1] (numeric) = 0.89678414688789008279634301948475 absolute error = 5.8578656683661997097625716000109e-09 relative error = 6.5320798214717599245076883008684e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1035 y[1] (analytic) = 0.89668468736388107684573820427085 y[1] (numeric) = 0.8966846809739896034859623712177 absolute error = 6.3898914733597758330531443177806e-09 relative error = 7.1261298017088944076780079551488e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1036 y[1] (analytic) = 0.89658522301515952802916197248966 y[1] (numeric) = 0.89658521606197840532422545485925 absolute error = 6.9531811227049365176304042319531e-09 relative error = 7.7551814866207890050321946544998e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1037 y[1] (analytic) = 0.8964857597005857481992006524971 y[1] (numeric) = 0.89648575215195985335594275010856 absolute error = 7.5486258948432579023885451621941e-09 relative error = 8.4202407156633452563167460921957e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1038 y[1] (analytic) = 0.8963862974211543705007631816383 y[1] (numeric) = 0.89638628924403741208975638432911 absolute error = 8.1771169584110067973091865882864e-09 relative error = 9.1223136519779982019290893883720e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1039 y[1] (analytic) = 0.8962868361778600177273344845693 y[1] (numeric) = 0.89628682733831464549710548746316 absolute error = 8.8395453722302289971061319556136e-09 relative error = 9.8624067825493547156456505947741e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 0.89618737597169730231102924533054 y[1] (numeric) = 0.89618736643489521701119055231821 absolute error = 9.5368020852998386930123362182034e-09 relative error = 1.0641526918362910093404179161742e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1041 y[1] (analytic) = 0.89608791680366082631264578303401 y[1] (numeric) = 0.89608790653388288952593680023582 absolute error = 1.0269777936786708982798188501386e-08 relative error = 1.1460681194562842943046688497797e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.2MB, time=1.90 x[1] = 0.1042 y[1] (analytic) = 0.8959884586747451814117200312635 y[1] (numeric) = 0.8959884476353815253949565521533 absolute error = 1.1039363656016763479110204783813e-08 relative error = 1.2320877070609888419957786943717e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1043 y[1] (analytic) = 0.89588900158594494889657962128759 y[1] (numeric) = 0.89588898973949508643051060506838 absolute error = 1.1846449862466069016219214515371e-08 relative error = 1.3223122330439289853561606560793e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1044 y[1] (analytic) = 0.89578954553825469965439806918463 y[1] (numeric) = 0.89578953284632763390246861391751 absolute error = 1.2691927065751929455267114103438e-08 relative error = 1.4168425082618828809668990112297e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1045 y[1] (analytic) = 0.89569009053266899416124906697927 y[1] (numeric) = 0.89569007695598332853726847887803 absolute error = 1.3576685665623980588101249214941e-08 relative error = 1.5157793760506933633695069513284e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1046 y[1] (analytic) = 0.89559063657018238247216087789009 y[1] (numeric) = 0.89559062206856643051687473810461 absolute error = 1.4501615951955286139785476855792e-08 relative error = 1.6192237122410866519795861851919e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1047 y[1] (analytic) = 0.89549118365178940421117083578751 y[1] (numeric) = 0.89549116818418129947773596591056 absolute error = 1.5467608104733434869876947202524e-08 relative error = 1.7272764251744989151001021860876e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1048 y[1] (analytic) = 0.89539173177848458856137994896177 y[1] (numeric) = 0.89539171530293239450974117640413 absolute error = 1.6475552194051638772557634173279e-08 relative error = 1.8400384557189106955448422455207e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1049 y[1] (analytic) = 0.89529228095126245425500760830018 y[1] (numeric) = 0.89529226342492427415517523259054 absolute error = 1.7526338180099832375709632736763e-08 relative error = 1.9576107772846892023854787668780e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 0.89519283117111750956344639997322 y[1] (numeric) = 0.89519281255026159640767326094999 absolute error = 1.8620855913155773139023229968341e-08 relative error = 2.0800943958404384733385175030159e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1051 y[1] (analytic) = 0.89509338243904425228731702272891 y[1] (numeric) = 0.89509336267904911871117407150216 absolute error = 1.9759995133576142951226745872107e-08 relative error = 2.2075903499288574123112697136009e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1052 y[1] (analytic) = 0.89499393475603716974652330989487 y[1] (numeric) = 0.89499391381139169795887258336774 absolute error = 2.0944645471787650726527128996577e-08 relative error = 2.3401997106826057066288484921072e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1053 y[1] (analytic) = 0.89489448812309073877030735618759 y[1] (numeric) = 0.89489446594739429049217125583731 absolute error = 2.2175696448278136100350280879503e-08 relative error = 2.4780235818401776284670527903771e-06 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=2.38 NO POLE x[1] = 0.1054 y[1] (analytic) = 0.89479504254119942568730474942828 y[1] (numeric) = 0.89479501908716195209963052495821 absolute error = 2.3454037473587674224470072364345e-08 relative error = 2.6211630997617837250188679520952e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1055 y[1] (analytic) = 0.89469559801135768631559990726483 y[1] (numeric) = 0.89469557323079983801591824564982 absolute error = 2.4780557848299681661615003837029e-08 relative error = 2.7697194334452404019251788569528e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1056 y[1] (analytic) = 0.8945961545345599659527815189992 y[1] (numeric) = 0.89459612837841320292075813935775 absolute error = 2.6156146763032023379641450436854e-08 relative error = 2.9237937845418674045031610762137e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1057 y[1] (analytic) = 0.89449671211180069936599809261988 y[1] (numeric) = 0.89449668453010740093787724725746 absolute error = 2.7581693298428120845362422299745e-08 relative error = 3.0834873873723932013086867493925e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1058 y[1] (analytic) = 0.89439727074407431078201360713865 y[1] (numeric) = 0.89439724168598788563395238901789 absolute error = 2.9058086425148061218120758895479e-08 relative error = 3.2489015089428682745719552123390e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1059 y[1] (analytic) = 0.89429783043237521387726327033124 y[1] (numeric) = 0.89429779984616021001755562713558 absolute error = 3.0586215003859707643195665523090e-08 relative error = 3.4201374489605863220484337407493e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 0.89419839117769781176790938198128 y[1] (numeric) = 0.89419835901073002653809873684979 absolute error = 3.2166967785229810645131489030304e-08 relative error = 3.5972965398500133748300711215244e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1061 y[1] (analytic) = 0.89409895298103649699989730272694 y[1] (numeric) = 0.89409891917980308708477668164932 absolute error = 3.3801233409915120621077618823652e-08 relative error = 3.7804801467687248356646261290213e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1062 y[1] (analytic) = 0.89399951584338565153901152860976 y[1] (numeric) = 0.89399948035348524298551009438137 absolute error = 3.5489900408553501434228388235779e-08 relative error = 3.9697896676233504423338343656307e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1063 y[1] (analytic) = 0.89390007976573964676093187142512 y[1] (numeric) = 0.89390004253188244500588676397328 absolute error = 3.7233857201755045107451840315481e-08 relative error = 4.1653265330855271606440203278198e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1064 y[1] (analytic) = 0.89380064474909284344128974497372 y[1] (numeric) = 0.89380060571510074334810212777751 absolute error = 3.9033992100093187617196211104106e-08 relative error = 4.3671922066078600115856469813426e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=22.8MB, alloc=4.3MB, time=2.89 x[1] = 0.1065 y[1] (analytic) = 0.89370121079443959174572455731352 y[1] (numeric) = 0.89370116990324628764989876955055 absolute error = 4.0891193304095825787762972459178e-08 relative error = 4.5754881844398908372211825742929e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1066 y[1] (analytic) = 0.89360177790277423121994020911169 y[1] (numeric) = 0.89360173509642532698350492307642 absolute error = 4.2806348904236435286035265482452e-08 relative error = 4.7903159956440750098635538856100e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1067 y[1] (analytic) = 0.89350234607509109077976169819579 y[1] (numeric) = 0.89350230129474420985457198144524 absolute error = 4.4780346880925189716750544605020e-08 relative error = 5.0117772021117660891103466010912e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1068 y[1] (analytic) = 0.89340291531238448870119183040385 y[1] (numeric) = 0.89340286849830938420111101199761 absolute error = 4.6814075104500080818406241376688e-08 relative error = 5.2399733985792084313018070304752e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1069 y[1] (analytic) = 0.89330348561564873261046803683264 y[1] (numeric) = 0.8933034367072273973924282769454 absolute error = 4.8908421335218039759887246000482e-08 relative error = 5.4750062126435377559735949292864e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 0.89320405698587811947411929758354 y[1] (numeric) = 0.89320400592160489622805975967954 absolute error = 5.1064273223246059537903993645937e-08 relative error = 5.7169773047787896738781347694321e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1071 y[1] (analytic) = 0.89310462942406693558902317210554 y[1] (numeric) = 0.89310457614154862693670469677561 absolute error = 5.3282518308652318475329931566718e-08 relative error = 5.9659883683519161811513124145756e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1072 y[1] (analytic) = 0.89300520293120945657246293623481 y[1] (numeric) = 0.89300514736716543517515811570768 absolute error = 5.5564044021397304820527132039114e-08 relative error = 6.2221411296388101242041658016272e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1073 y[1] (analytic) = 0.89290577750829994735218482603007 y[1] (numeric) = 0.89290571959856226602724237828126 absolute error = 5.7909737681324942447748805128089e-08 relative error = 6.4855373478403376399221219098616e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1074 y[1] (analytic) = 0.89280635315633266215645538850346 y[1] (numeric) = 0.892806292835846164002737729796 absolute error = 6.0320486498153717658707454276775e-08 relative error = 6.7562788150983785757572380157467e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1075 y[1] (analytic) = 0.89270692987630184450411893934616 y[1] (numeric) = 0.89270686707912427303631185394875 absolute error = 6.2797177571467807085397406703673e-08 relative error = 7.0344673565118748943018129861109e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1076 y[1] (analytic) = 0.89260750766920172719465512774823 y[1] (numeric) = 0.89260744232850383648644843348779 absolute error = 6.5340697890708206694260439579235e-08 relative error = 7.3202048301528870669346441563574e-06 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=3.38 NO POLE x[1] = 0.1077 y[1] (analytic) = 0.89250808653602653229823660841207 y[1] (numeric) = 0.89250801858409219713437471662885 absolute error = 6.7951934335163861891783211940123e-08 relative error = 7.6135931270826584611341171756056e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1078 y[1] (analytic) = 0.89240866647777047114578682085902 y[1] (numeric) = 0.89240859584599679718298808924382 absolute error = 7.0631773673962798731615201285077e-08 relative error = 7.9147341713676877260552300784823e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1079 y[1] (analytic) = 0.89230924749542774431903787612839 y[1] (numeric) = 0.89230917411432517825578165283255 absolute error = 7.3381102566063256223295832781158e-08 relative error = 8.2237299200958091809705687653512e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 0.89220982958999254164058855096841 y[1] (numeric) = 0.89220975338918498139576880828894 absolute error = 7.6200807560244819742679477992996e-08 relative error = 8.5406823633922812111781690406407e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1081 y[1] (analytic) = 0.89211041276245904216396238961858 y[1] (numeric) = 0.89211033367068394706440684547159 absolute error = 7.9091775095099555544146989030745e-08 relative error = 8.8656935244358826759821203741632e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1082 y[1] (analytic) = 0.89201099701382141416366591328264 y[1] (numeric) = 0.89201091495892991514051953859022 absolute error = 8.2054891499023146374692422994538e-08 relative error = 9.1988654594750173333546886144983e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1083 y[1] (analytic) = 0.89191158234507381512524693739185 y[1] (numeric) = 0.89191149725403082491921874741825 absolute error = 8.5091042990206028189973600574506e-08 relative error = 9.5403002578438262858916589981977e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1084 y[1] (analytic) = 0.89181216875721039173535299675779 y[1] (numeric) = 0.89181208055609471511082502434266 absolute error = 8.8201115676624527972415131645789e-08 relative error = 9.8901000419783084526755269653449e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1085 y[1] (analytic) = 0.89171275625122527987178987871414 y[1] (numeric) = 0.89171266486522972383978722726161 absolute error = 9.1385995556032002651452529677418e-08 relative error = 1.0248366967432449071664092512436e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1086 y[1] (analytic) = 0.89161334482811260459358026434694 y[1] (numeric) = 0.89161325018154408864360113834091 absolute error = 9.4646568515949979126006025752573e-08 relative error = 1.0615203222894356237224944089221e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1087 y[1] (analytic) = 0.89151393448886648013102247791261 y[1] (numeric) = 0.89151383650514614647172708863993 absolute error = 9.7983720333659295389272681975388e-08 relative error = 1.0990711030202405477439250378617e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.3MB, time=3.88 x[1] = 0.1088 y[1] (analytic) = 0.89141452523448100987574934454329 y[1] (numeric) = 0.8914144238361443336845065886179 absolute error = 1.0139833667619124275592539301632e-07 relative error = 1.1374992644361392375801212689714e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1089 y[1] (analytic) = 0.89131511706595028637078715633878 y[1] (numeric) = 0.89131501217464718605207796453143 absolute error = 1.0489130310031870919180735352401e-07 relative error = 1.1768150353558693241942467144699e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 0.89121570998426839130061474694456 y[1] (numeric) = 0.891215601520763338753291000734 absolute error = 1.0846350505254732374621055810663e-07 relative error = 1.2170286479180433836013664352977e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1091 y[1] (analytic) = 0.89111630399042939548122267471527 y[1] (numeric) = 0.89111619187460152637462058788838 absolute error = 1.1211582786910660208682688955983e-07 relative error = 1.2581503375827666151358394841281e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1092 y[1] (analytic) = 0.89101689908542735885017251456312 y[1] (numeric) = 0.89101678323627058290907937710278 absolute error = 1.1584915677594109313746033999173e-07 relative error = 1.3001903431332553260117571148832e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1093 y[1] (analytic) = 0.89091749527025633045665625859053 y[1] (numeric) = 0.89091737560587944175512944000163 absolute error = 1.1966437688870152681858889846776e-07 relative error = 1.3431589066774562226405322203211e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1094 y[1] (analytic) = 0.89081809254591034845155582560653 y[1] (numeric) = 0.8908179689835371357155929347419 absolute error = 1.2356237321273596289086462776962e-07 relative error = 1.3870662736496665091700402367023e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1095 y[1] (analytic) = 0.89071869091338344007750267962617 y[1] (numeric) = 0.89071856336935279699656177798573 absolute error = 1.2754403064308094090164044183334e-07 relative error = 1.4319226928121547937100066389441e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1096 y[1] (analytic) = 0.89061929037366962165893755745254 y[1] (numeric) = 0.89061915876343565720630632284045 absolute error = 1.3161023396445263123461208440103e-07 relative error = 1.4777384162567828027086312411679e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1097 y[1] (analytic) = 0.89051989092776289859217030544061 y[1] (numeric) = 0.89051975516589504735418304277681 absolute error = 1.3576186785123798726266379838991e-07 relative error = 1.5245236994066279039457348163191e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1098 y[1] (analytic) = 0.89042049257665726533543982554245 y[1] (numeric) = 0.89042035257684039784954122153629 absolute error = 1.3999981686748589860400616445002e-07 relative error = 1.5722888010176064386080090547270e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1099 y[1] (analytic) = 0.89032109532134670539897413073309 y[1] (numeric) = 0.89032095099638123850062864903852 absolute error = 1.4432496546689834548169457614918e-07 relative error = 1.6210439831800978629122465952557e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=34.3MB, alloc=4.3MB, time=4.39 x[1] = 0.11 y[1] (analytic) = 0.89022169916282519133505050991655 y[1] (numeric) = 0.89022155042462719851349632329974 absolute error = 1.4873819799282155418661680818994e-07 relative error = 1.6707995113205696997427237842174e-05 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 3 ) = sin(x); Iterations = 100 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Expected Time Remaining = 34 Minutes 45 Seconds Optimized Time Remaining = 34 Minutes 34 Seconds Time to Timeout = 14 Minutes 55 Seconds Percent Done = 0.2061 % > quit memory used=34.6MB, alloc=4.3MB, time=4.42