|\^/| 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 > INFO, > ALWAYS, > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_log10abserr, > glob_max_iter, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_iter, > glob_warned, > glob_small_float, > glob_max_hours, > glob_large_float, > glob_hmin, > glob_subiter_method, > glob_current_iter, > glob_disp_incr, > glob_initial_pass, > years_in_century, > days_in_year, > sec_in_min, > glob_optimal_done, > djd_debug2, > glob_display_flag, > glob_dump, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_max_trunc_err, > glob_h, > djd_debug, > glob_percent_done, > glob_no_eqs, > glob_relerr, > glob_hmax, > glob_clock_start_sec, > glob_clock_sec, > centuries_in_millinium, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_not_yet_finished, > hours_in_day, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_dump_analytic, > glob_smallish_float, > min_in_hour, > glob_optimal_expect_sec, > glob_max_minutes, > glob_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_hmin_init, > glob_almost_1, > glob_log10relerr, > MAX_UNCHANGED, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_2, > #END CONST > array_m1, > array_tmp1_g, > array_last_rel_error, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y_init, > array_norms, > array_pole, > array_y_set_initial, > array_y_higher, > array_y_higher_work2, > array_poles, > array_real_pole, > array_complex_pole, > array_y_higher_work, > 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 INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter, glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float, glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr, glob_initial_pass, years_in_century, days_in_year, sec_in_min, glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs, glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec, centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_dump_analytic, glob_smallish_float, min_in_hour, glob_optimal_expect_sec, glob_max_minutes, glob_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr, MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2, array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init, array_norms, array_pole, array_y_set_initial, array_y_higher, array_y_higher_work2, array_poles, array_real_pole, array_complex_pole, array_y_higher_work, 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 > INFO, > ALWAYS, > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_log10abserr, > glob_max_iter, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_iter, > glob_warned, > glob_small_float, > glob_max_hours, > glob_large_float, > glob_hmin, > glob_subiter_method, > glob_current_iter, > glob_disp_incr, > glob_initial_pass, > years_in_century, > days_in_year, > sec_in_min, > glob_optimal_done, > djd_debug2, > glob_display_flag, > glob_dump, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_max_trunc_err, > glob_h, > djd_debug, > glob_percent_done, > glob_no_eqs, > glob_relerr, > glob_hmax, > glob_clock_start_sec, > glob_clock_sec, > centuries_in_millinium, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_not_yet_finished, > hours_in_day, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_dump_analytic, > glob_smallish_float, > min_in_hour, > glob_optimal_expect_sec, > glob_max_minutes, > glob_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_hmin_init, > glob_almost_1, > glob_log10relerr, > MAX_UNCHANGED, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_2, > #END CONST > array_m1, > array_tmp1_g, > array_last_rel_error, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y_init, > array_norms, > array_pole, > array_y_set_initial, > array_y_higher, > array_y_higher_work2, > array_poles, > array_real_pole, > array_complex_pole, > array_y_higher_work, > 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 INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter, glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float, glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr, glob_initial_pass, years_in_century, days_in_year, sec_in_min, glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs, glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec, centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_dump_analytic, glob_smallish_float, min_in_hour, glob_optimal_expect_sec, glob_max_minutes, glob_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr, MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2, array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init, array_norms, array_pole, array_y_set_initial, array_y_higher, array_y_higher_work2, array_poles, array_real_pole, array_complex_pole, array_y_higher_work, 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 > INFO, > ALWAYS, > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_log10abserr, > glob_max_iter, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_iter, > glob_warned, > glob_small_float, > glob_max_hours, > glob_large_float, > glob_hmin, > glob_subiter_method, > glob_current_iter, > glob_disp_incr, > glob_initial_pass, > years_in_century, > days_in_year, > sec_in_min, > glob_optimal_done, > djd_debug2, > glob_display_flag, > glob_dump, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_max_trunc_err, > glob_h, > djd_debug, > glob_percent_done, > glob_no_eqs, > glob_relerr, > glob_hmax, > glob_clock_start_sec, > glob_clock_sec, > centuries_in_millinium, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_not_yet_finished, > hours_in_day, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_dump_analytic, > glob_smallish_float, > min_in_hour, > glob_optimal_expect_sec, > glob_max_minutes, > glob_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_hmin_init, > glob_almost_1, > glob_log10relerr, > MAX_UNCHANGED, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_2, > #END CONST > array_m1, > array_tmp1_g, > array_last_rel_error, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y_init, > array_norms, > array_pole, > array_y_set_initial, > array_y_higher, > array_y_higher_work2, > array_poles, > array_real_pole, > array_complex_pole, > array_y_higher_work, > 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 INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter, glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float, glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr, glob_initial_pass, years_in_century, days_in_year, sec_in_min, glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs, glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec, centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_dump_analytic, glob_smallish_float, min_in_hour, glob_optimal_expect_sec, glob_max_minutes, glob_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr, MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2, array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init, array_norms, array_pole, array_y_set_initial, array_y_higher, array_y_higher_work2, array_poles, array_real_pole, array_complex_pole, array_y_higher_work, 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 > INFO, > ALWAYS, > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_log10abserr, > glob_max_iter, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_iter, > glob_warned, > glob_small_float, > glob_max_hours, > glob_large_float, > glob_hmin, > glob_subiter_method, > glob_current_iter, > glob_disp_incr, > glob_initial_pass, > years_in_century, > days_in_year, > sec_in_min, > glob_optimal_done, > djd_debug2, > glob_display_flag, > glob_dump, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_max_trunc_err, > glob_h, > djd_debug, > glob_percent_done, > glob_no_eqs, > glob_relerr, > glob_hmax, > glob_clock_start_sec, > glob_clock_sec, > centuries_in_millinium, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_not_yet_finished, > hours_in_day, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_dump_analytic, > glob_smallish_float, > min_in_hour, > glob_optimal_expect_sec, > glob_max_minutes, > glob_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_hmin_init, > glob_almost_1, > glob_log10relerr, > MAX_UNCHANGED, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_2, > #END CONST > array_m1, > array_tmp1_g, > array_last_rel_error, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y_init, > array_norms, > array_pole, > array_y_set_initial, > array_y_higher, > array_y_higher_work2, > array_poles, > array_real_pole, > array_complex_pole, > array_y_higher_work, > 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 - 2 - 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 - 2 - 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 INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter, glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float, glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr, glob_initial_pass, years_in_century, days_in_year, sec_in_min, glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs, glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec, centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_dump_analytic, glob_smallish_float, min_in_hour, glob_optimal_expect_sec, glob_max_minutes, glob_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr, MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2, array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init, array_norms, array_pole, array_y_set_initial, array_y_higher, array_y_higher_work2, array_poles, array_real_pole, array_complex_pole, array_y_higher_work, glob_last; n := glob_max_terms; m := n - 3; 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 - 3; 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 > INFO, > ALWAYS, > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_log10abserr, > glob_max_iter, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_iter, > glob_warned, > glob_small_float, > glob_max_hours, > glob_large_float, > glob_hmin, > glob_subiter_method, > glob_current_iter, > glob_disp_incr, > glob_initial_pass, > years_in_century, > days_in_year, > sec_in_min, > glob_optimal_done, > djd_debug2, > glob_display_flag, > glob_dump, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_max_trunc_err, > glob_h, > djd_debug, > glob_percent_done, > glob_no_eqs, > glob_relerr, > glob_hmax, > glob_clock_start_sec, > glob_clock_sec, > centuries_in_millinium, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_not_yet_finished, > hours_in_day, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_dump_analytic, > glob_smallish_float, > min_in_hour, > glob_optimal_expect_sec, > glob_max_minutes, > glob_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_hmin_init, > glob_almost_1, > glob_log10relerr, > MAX_UNCHANGED, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_2, > #END CONST > array_m1, > array_tmp1_g, > array_last_rel_error, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y_init, > array_norms, > array_pole, > array_y_set_initial, > array_y_higher, > array_y_higher_work2, > array_poles, > array_real_pole, > array_complex_pole, > array_y_higher_work, > 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 INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter, glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float, glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr, glob_initial_pass, years_in_century, days_in_year, sec_in_min, glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs, glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec, centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_dump_analytic, glob_smallish_float, min_in_hour, glob_optimal_expect_sec, glob_max_minutes, glob_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr, MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2, array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init, array_norms, array_pole, array_y_set_initial, array_y_higher, array_y_higher_work2, array_poles, array_real_pole, array_complex_pole, array_y_higher_work, 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 > INFO, > ALWAYS, > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_log10abserr, > glob_max_iter, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_iter, > glob_warned, > glob_small_float, > glob_max_hours, > glob_large_float, > glob_hmin, > glob_subiter_method, > glob_current_iter, > glob_disp_incr, > glob_initial_pass, > years_in_century, > days_in_year, > sec_in_min, > glob_optimal_done, > djd_debug2, > glob_display_flag, > glob_dump, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_max_trunc_err, > glob_h, > djd_debug, > glob_percent_done, > glob_no_eqs, > glob_relerr, > glob_hmax, > glob_clock_start_sec, > glob_clock_sec, > centuries_in_millinium, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_not_yet_finished, > hours_in_day, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_dump_analytic, > glob_smallish_float, > min_in_hour, > glob_optimal_expect_sec, > glob_max_minutes, > glob_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_hmin_init, > glob_almost_1, > glob_log10relerr, > MAX_UNCHANGED, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_2, > #END CONST > array_m1, > array_tmp1_g, > array_last_rel_error, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y_init, > array_norms, > array_pole, > array_y_set_initial, > array_y_higher, > array_y_higher_work2, > array_poles, > array_real_pole, > array_complex_pole, > array_y_higher_work, > 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[1,3] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (2)) * factorial_3(0,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,1] := 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[1,4] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (2)) * factorial_3(1,3); > 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 > ; > 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[1,5] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (2)) * factorial_3(2,4); > 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 > ; > 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[1,6] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (2)) * factorial_3(3,5); > 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 > ; > 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[1,7] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (2)) * factorial_3(4,6); > 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 > ; > 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 := 2; > 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 INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter, glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float, glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr, glob_initial_pass, years_in_century, days_in_year, sec_in_min, glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs, glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec, centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_dump_analytic, glob_smallish_float, min_in_hour, glob_optimal_expect_sec, glob_max_minutes, glob_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr, MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2, array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init, array_norms, array_pole, array_y_set_initial, array_y_higher, array_y_higher_work2, array_poles, array_real_pole, array_complex_pole, array_y_higher_work, 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, 3] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h^2*factorial_3(0, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 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, 4] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h^2*factorial_3(1, 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 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, 5] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h^2*factorial_3(2, 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 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, 6] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h^2*factorial_3(3, 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 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, 7] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h^2*factorial_3(4, 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 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 := 2; 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) > 2.0 - cos(x); > end; exact_soln_y := proc(x) 2.0 - cos(x) end proc > exact_soln_yp := proc(x) > sin(x); > end; exact_soln_yp := 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 > INFO, > ALWAYS, > DEBUGL, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_log10abserr, > glob_max_iter, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_iter, > glob_warned, > glob_small_float, > glob_max_hours, > glob_large_float, > glob_hmin, > glob_subiter_method, > glob_current_iter, > glob_disp_incr, > glob_initial_pass, > years_in_century, > days_in_year, > sec_in_min, > glob_optimal_done, > djd_debug2, > glob_display_flag, > glob_dump, > glob_html_log, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_max_trunc_err, > glob_h, > djd_debug, > glob_percent_done, > glob_no_eqs, > glob_relerr, > glob_hmax, > glob_clock_start_sec, > glob_clock_sec, > centuries_in_millinium, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_not_yet_finished, > hours_in_day, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_dump_analytic, > glob_smallish_float, > min_in_hour, > glob_optimal_expect_sec, > glob_max_minutes, > glob_start, > glob_optimal_clock_start_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_look_poles, > glob_hmin_init, > glob_almost_1, > glob_log10relerr, > MAX_UNCHANGED, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_2, > #END CONST > array_m1, > array_tmp1_g, > array_last_rel_error, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_type_pole, > array_y_init, > array_norms, > array_pole, > array_y_set_initial, > array_y_higher, > array_y_higher_work2, > array_poles, > array_real_pole, > array_complex_pole, > array_y_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > ALWAYS := 1; > DEBUGL := 3; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > glob_log10abserr := 0.0; > glob_max_iter := 1000; > glob_not_yet_start_msg := true; > glob_max_opt_iter := 10; > glob_iter := 0; > glob_warned := false; > glob_small_float := 0.1e-50; > glob_max_hours := 0.0; > glob_large_float := 9.0e100; > glob_hmin := 0.00000000001; > glob_subiter_method := 3; > glob_current_iter := 0; > glob_disp_incr := 0.1; > glob_initial_pass := true; > years_in_century := 100.0; > days_in_year := 365.0; > sec_in_min := 60.0; > glob_optimal_done := false; > djd_debug2 := true; > glob_display_flag := true; > glob_dump := false; > glob_html_log := true; > glob_curr_iter_when_opt := 0; > glob_warned2 := false; > glob_optimal_start := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_h := 0.1; > djd_debug := true; > glob_percent_done := 0.0; > glob_no_eqs := 0; > glob_relerr := 0.1e-10; > glob_hmax := 1.0; > glob_clock_start_sec := 0.0; > glob_clock_sec := 0.0; > centuries_in_millinium := 10.0; > glob_unchanged_h_cnt := 0; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_last_good_h := 0.1; > glob_not_yet_finished := true; > hours_in_day := 24.0; > glob_log10normmin := 0.1; > glob_normmax := 0.0; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_dump_analytic := false; > glob_smallish_float := 0.1e-100; > min_in_hour := 60.0; > glob_optimal_expect_sec := 0.1; > glob_max_minutes := 0.0; > glob_start := 0; > glob_optimal_clock_start_sec := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_abserr := 0.1e-10; > glob_look_poles := false; > glob_hmin_init := 0.001; > glob_almost_1 := 0.9990; > glob_log10relerr := 0.0; > MAX_UNCHANGED := 10; > glob_reached_optimal_h := false; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/h2sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 2 ) = 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,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > 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,"2.0 - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_yp := 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_m1:= Array(1..(max_terms + 1),[]); > array_tmp1_g:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= 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_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[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_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_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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_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 <=3 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 <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 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 > ; > #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_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > 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); > glob_h := 0.00001; > glob_look_poles := true; > glob_max_iter := 100; > #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] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 2; > #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 := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #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 := 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 := 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 , 2 ) = 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,"2012-06-13T01:40:51-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"h2sin") > ; > logitem_str(html_log_file,"diff ( y , x , 2 ) = 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,"h2sin diffeq.mxt") > ; > logitem_str(html_log_file,"h2sin 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 INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter, glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float, glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr, glob_initial_pass, years_in_century, days_in_year, sec_in_min, glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs, glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec, centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr, glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_dump_analytic, glob_smallish_float, min_in_hour, glob_optimal_expect_sec, glob_max_minutes, glob_start, glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr, glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr, MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2, array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init, array_norms, array_pole, array_y_set_initial, array_y_higher, array_y_higher_work2, array_poles, array_real_pole, array_complex_pole, array_y_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; ALWAYS := 1; DEBUGL := 3; glob_iolevel := 5; glob_max_terms := 30; DEBUGMASSIVE := 4; glob_log10abserr := 0.; glob_max_iter := 1000; glob_not_yet_start_msg := true; glob_max_opt_iter := 10; glob_iter := 0; glob_warned := false; glob_small_float := 0.1*10^(-50); glob_max_hours := 0.; glob_large_float := 0.90*10^101; glob_hmin := 0.1*10^(-10); glob_subiter_method := 3; glob_current_iter := 0; glob_disp_incr := 0.1; glob_initial_pass := true; years_in_century := 100.0; days_in_year := 365.0; sec_in_min := 60.0; glob_optimal_done := false; djd_debug2 := true; glob_display_flag := true; glob_dump := false; glob_html_log := true; glob_curr_iter_when_opt := 0; glob_warned2 := false; glob_optimal_start := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_h := 0.1; djd_debug := true; glob_percent_done := 0.; glob_no_eqs := 0; glob_relerr := 0.1*10^(-10); glob_hmax := 1.0; glob_clock_start_sec := 0.; glob_clock_sec := 0.; centuries_in_millinium := 10.0; glob_unchanged_h_cnt := 0; glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_not_yet_finished := true; hours_in_day := 24.0; glob_log10normmin := 0.1; glob_normmax := 0.; glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_dump_analytic := false; glob_smallish_float := 0.1*10^(-100); min_in_hour := 60.0; glob_optimal_expect_sec := 0.1; glob_max_minutes := 0.; glob_start := 0; glob_optimal_clock_start_sec := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_look_poles := false; glob_hmin_init := 0.001; glob_almost_1 := 0.9990; glob_log10relerr := 0.; MAX_UNCHANGED := 10; glob_reached_optimal_h := false; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/h2sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 2 ) = 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, "glob_h := 0.00001;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); 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, "2.0 - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_yp := 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_m1 := Array(1 .. max_terms + 1, []); array_tmp1_g := Array(1 .. max_terms + 1, []); array_last_rel_error := 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_1st_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[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_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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 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 <= 3 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 <= 3 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 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; 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_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; 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); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; 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] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 2; 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 := 2; 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 := 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 := 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 , 2 ) = 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, "2012-06-13T01:40:51-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "h2sin"); logitem_str(html_log_file, "diff ( y , x , 2 ) = 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, "h2sin diffeq.mxt"); logitem_str(html_log_file, "h2sin 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/h2sinpostode.ode################# diff ( y , x , 2 ) = 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); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; #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) 2.0 - cos(x); end; exact_soln_yp := proc(x) sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.0049958347219742339044380121961 y[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1001 y[1] (analytic) = 1.00500582303864310006118068491 y[1] (numeric) = 1.0050058185629718335653003065756 absolute error = 4.4756712664958803783343078885500e-09 relative error = 4.4533784420906664036177363664867e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1002 y[1] (analytic) = 1.0050158213052537275398742184312 y[1] (numeric) = 1.0050158034032985980336186771541 absolute error = 1.7901955129506255541277083085533e-08 relative error = 1.7812610259464651614037120828114e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1003 y[1] (analytic) = 1.0050258295217061336744956568613 y[1] (numeric) = 1.0050257892439495164872211755182 absolute error = 4.0277756617187274481343172773774e-08 relative error = 4.0076339765671039495612297834371e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1004 y[1] (analytic) = 1.0050358476879002363006043406579 y[1] (numeric) = 1.0050357760859195681006943217376 absolute error = 7.1601980668199910018920299878927e-08 relative error = 7.1243210710266027492763204457086e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1005 y[1] (analytic) = 1.005045875803735853756342728278 y[1] (numeric) = 1.0050457639302037220354333126278 absolute error = 1.1187353213172090941565020935444e-07 relative error = 1.1131186627899504740387125942420e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1006 y[1] (analytic) = 1.0050559138691127048834382127963 y[1] (numeric) = 1.0050557527777969374296923301442 absolute error = 1.6109131576745374588265206930829e-07 relative error = 1.6028094909397497039978393467045e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1007 y[1] (analytic) = 1.0050659618839304090282059334865 y[1] (numeric) = 1.0050657426296941633886349500079 absolute error = 2.1925423624563957098347861188931e-07 relative error = 2.1814910121387639623620817604210e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1008 y[1] (analytic) = 1.0050760198480884860425525823578 y[1] (numeric) = 1.0050757334868903389743846506623 absolute error = 2.8636119814706816793169548990368e-07 relative error = 2.8491496413410602660925028135298e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1009 y[1] (analytic) = 1.0050860877614863562849812056346 y[1] (numeric) = 1.0050857253503803931960754226603 absolute error = 3.6241110596308890578297431618585e-07 relative error = 3.6057717878698912260333750880779e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=2.9MB, time=0.18 x[1] = 0.101 y[1] (analytic) = 1.005096165624023340621597000171 y[1] (numeric) = 1.0050957182211592449999024785812 absolute error = 4.4740286409562169452158984380309e-07 relative error = 4.4513438554195204618073437689388e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1011 y[1] (analytic) = 1.0051062534355986604271141047886 y[1] (numeric) = 1.0051057121002218032591730635769 absolute error = 5.4133537685716794104121173622873e-07 relative error = 5.3858522420570488566184432820356e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1012 y[1] (analytic) = 1.0051163511961114375858633865286 y[1] (numeric) = 1.0051157069885629667643573666473 absolute error = 6.4420754847082150601988136767629e-07 relative error = 6.4092833402242416514546516429475e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1013 y[1] (analytic) = 1.0051264589054606944928012218079 y[1] (numeric) = 1.0051257028871776242131395327438 absolute error = 7.5601828307027966168906408484491e-07 relative error = 7.5216235367393563781814441663656e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1014 y[1] (analytic) = 1.0051365765635453540545192724681 y[1] (numeric) = 1.0051356997970606542004687758007 absolute error = 8.7676648469985405049666735238545e-07 relative error = 8.7228592127989716310175859992715e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1015 y[1] (analytic) = 1.0051467041702642396902552567095 y[1] (numeric) = 1.0051456977192069252086105927943 absolute error = 1.0064510573144816446639151954574e-06 relative error = 0.00010012976743979816675884180986234 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1016 y[1] (analytic) = 1.0051568417255160753329047148974 y[1] (numeric) = 1.0051556966546112955971980789281 absolute error = 1.1450709047797357066359693438077e-06 relative error = 0.00011391962500240601897117772653927 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1017 y[1] (analytic) = 1.0051669892291994854300337702324 y[1] (numeric) = 1.0051656966042686135932833440449 absolute error = 1.2926249308718367504261874728657e-06 relative error = 0.00012859802845923850081038071613977 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1018 y[1] (analytic) = 1.0051771466812129949448928842737 y[1] (numeric) = 1.0051756975691737172813890303648 absolute error = 1.4491120392776635038539089284112e-06 relative error = 0.00014416484139757728535860662428607 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1019 y[1] (analytic) = 1.0051873140814550293574316073064 y[1] (numeric) = 1.005185699550321434593559931648 absolute error = 1.6145311335947638716756583124389e-06 relative error = 0.00016061992734857882047444821962379 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 1.0051974914298239146653143235401 y[1] (numeric) = 1.0051957025487065832994147138828 absolute error = 1.7888811173313658996096572989052e-06 relative error = 0.00017796314978729266670366360455694 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1021 y[1] (analytic) = 1.0052076787262178773849369911326 y[1] (numeric) = 1.0052057065653239709961977375976 absolute error = 1.9721608939063887392535350391154e-06 relative error = 0.00019619437213267984353805176001723 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1022 y[1] (analytic) = 1.0052178759705350445524448770242 y[1] (numeric) = 1.0052157116011683950988309818967 absolute error = 2.1643693666494536138951275075712e-06 relative error = 0.00021531345774763118401736992788155 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1023 y[1] (analytic) = 1.0052280831626734437247512865758 y[1] (numeric) = 1.0052257176572346428299660703197 absolute error = 2.3655054388008947852162561301728e-06 relative error = 0.00023532026993898569766918533378661 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1024 y[1] (analytic) = 1.0052383003025310029805572879987 y[1] (numeric) = 1.0052357247345174912100363986227 absolute error = 2.5755680135117705208893760277368e-06 relative error = 0.00025621467195754894178155155456401 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.0MB, time=0.39 NO POLE x[1] = 0.1025 y[1] (analytic) = 1.0052485273900055509213724315671 y[1] (numeric) = 1.0052457328340117070473093645829 absolute error = 2.7945559938438740630669841988633e-06 relative error = 0.00027799652699811140100339763833276 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1026 y[1] (analytic) = 1.0052587644249948166725364636016 y[1] (numeric) = 1.0052557419567120469279386999236 absolute error = 3.0224682827697445977636779572602e-06 relative error = 0.0003006656981994668752675158914409 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1027 y[1] (analytic) = 1.0052690114073964298842420352155 y[1] (numeric) = 1.0052657521036132572060169044616 absolute error = 3.2593037831726782251307539297006e-06 relative error = 0.00032422204864443087603103205494373 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1028 y[1] (analytic) = 1.0052792683371079207325584058118 y[1] (numeric) = 1.0052757632757100739936277825739 absolute error = 3.5050613978467389306232379118717e-06 relative error = 0.00034866544135985903082823940414455 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1029 y[1] (analytic) = 1.0052895352140267199204561413216 y[1] (numeric) = 1.0052857754739972231508990820857 absolute error = 3.7597400294967695570592358704407e-06 relative error = 0.00037399573931666549613067611790527 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 1.0052998120380501586788328071734 y[1] (numeric) = 1.005295788699469420276055235677 absolute error = 4.0233385807384027775714963707485e-06 relative error = 0.00040021280542984137850932307995991 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1031 y[1] (analytic) = 1.0053100988090754687675396559837 y[1] (numeric) = 1.005305802953121370695470204909 absolute error = 4.2958559540980720694510747006115e-06 relative error = 0.00042731650255847316409379709233424 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1032 y[1] (analytic) = 1.0053203955269997824764093099572 y[1] (numeric) = 1.0053158182359477694537204269683 absolute error = 4.5772910520130226888829889517986e-06 relative error = 0.00045530669350576115632341230119118 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1033 y[1] (analytic) = 1.005330702191720132626284437988 y[1] (numeric) = 1.0053258345489433013036378642297 absolute error = 4.8676427768313226465737583118248e-06 relative error = 0.00048418324101903792198498045798436 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1034 y[1] (analytic) = 1.0053410188031334525700474274499 y[1] (numeric) = 1.0053358518931026406963631567361 absolute error = 5.1669100308118736842707138097859e-06 relative error = 0.00051394600778978674553221846371212 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1035 y[1] (analytic) = 1.0053513453611365761936510506671 y[1] (numeric) = 1.0053458702694204517713988776953 absolute error = 5.4750917161244222521729717510437e-06 relative error = 0.00054459485645366009168162947132327 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1036 y[1] (analytic) = 1.0053616818656262379171501260534 y[1] (numeric) = 1.0053558896788913883466628920934 absolute error = 5.7921867348495704872339600666485e-06 relative error = 0.00057612964959049807627972165093295 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1037 y[1] (analytic) = 1.0053720283164990726957341739114 y[1] (numeric) = 1.0053659101225100939085418185236 absolute error = 6.1181939889787871923553877944769e-06 relative error = 0.00060855024972434694543642655446494 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1038 y[1] (analytic) = 1.0053823847136516160207610668791 y[1] (numeric) = 1.0053759316012712016019445943312 absolute error = 6.4531123804144188164725479001437e-06 relative error = 0.00064185651932347756291957685064496 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1039 y[1] (analytic) = 1.0053927510569803039207916750157 y[1] (numeric) = 1.005385954116169334220356144172 absolute error = 6.7969408109697004355308436368350e-06 relative error = 0.00067604832080040390580530103792939 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=4.1MB, time=0.60 x[1] = 0.104 y[1] (analytic) = 1.0054031273463814729626255055154 y[1] (numeric) = 1.0053959776681991041958911520867 absolute error = 7.1496781823687667343534286342979e-06 relative error = 0.00071112551651190156837919058196679 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1041 y[1] (analytic) = 1.005413513581751360252337337038 y[1] (numeric) = 1.0054060022583551135893479371872 absolute error = 7.5113233962466629893998508983101e-06 relative error = 0.00074708796875902627428309276555474 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1042 y[1] (analytic) = 1.005423909762986103436314848648 y[1] (numeric) = 1.0054160278876319540802624330572 absolute error = 7.8818753541493560524155908930431e-06 relative error = 0.00078393553978713239690238038277511 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1043 y[1] (analytic) = 1.0054343158899817407022972433492 y[1] (numeric) = 1.0054260545570242069569622709653 absolute error = 8.2613329575337453349723838698237e-06 relative error = 0.00082166809178589148798854725506554 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1044 y[1] (analytic) = 1.0054447319626342107804148662065 y[1] (numeric) = 1.0054360822675264431066209669899 absolute error = 8.6496951077676737938992165968910e-06 relative error = 0.00086028548688931081451197639541542 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1045 y[1] (analytic) = 1.0054551579808393529442298170443 y[1] (numeric) = 1.0054461110201332230053122131556 absolute error = 9.0469607061299389176038886358384e-06 relative error = 0.00089978758717575190373972549766268 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1046 y[1] (analytic) = 1.0054655939444929070117775577094 y[1] (numeric) = 1.0054561408158390967080642726811 absolute error = 9.4531286538103037132850283015257e-06 relative error = 0.00094017425466794909653317228101181 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1047 y[1] (analytic) = 1.0054760398534905133466095138901 y[1] (numeric) = 1.0054661716556386038389144794367 absolute error = 9.8681978519095076950344534333407e-06 relative error = 0.00098144535133302810886036007539728 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1048 y[1] (analytic) = 1.0054864957077277128588366714797 y[1] (numeric) = 1.0054762035405262735809638417126 absolute error = 1.0292167201439277872829767096787e-05 relative error = 0.0010236007390825246015178818911785 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1049 y[1] (analytic) = 1.0054969615070999470061741674745 y[1] (numeric) = 1.0054862364714966246664317503962 absolute error = 1.0725035603322339742417078325474e-05 relative error = 0.0010666402797724027580571390768745 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 1.0055074372515025577949868753959 y[1] (numeric) = 1.0054962704495441653667107916579 absolute error = 1.1166801958392428276083738004675e-05 relative error = 0.0011105638352030738709098085312302 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1051 y[1] (analytic) = 1.0055179229408307877813359852258 y[1] (numeric) = 1.0055063054756633934824216642459 absolute error = 1.1617465167394298914320979988739e-05 relative error = 0.0011553712671194149357073503008497 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1052 y[1] (analytic) = 1.0055284185749797800720265778451 y[1] (numeric) = 1.0055163415508487963334682014875 absolute error = 1.2077024130983738558376357535715e-05 relative error = 0.0012010624372107872537893852619393 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1053 y[1] (analytic) = 1.0055389241538445783256561939646 y[1] (numeric) = 1.0055263786760948507490924980995 absolute error = 1.2545477749727576563695865133675e-05 relative error = 0.0012476372071110550428957704543738 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1054 y[1] (analytic) = 1.0055494396773201267536643975387 y[1] (numeric) = 1.005536416852396023057930141903 absolute error = 1.3022824924103695734255635784313e-05 relative error = 0.0012950954383986040560371975083328 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1055 y[1] (analytic) = 1.0055599651453012701213833336496 y[1] (numeric) = 1.0055464560807467690780655505458 absolute error = 1.3509064554501043317783103800498e-05 relative error = 0.0013434369925963602085391374781534 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.81 NO POLE x[1] = 0.1056 y[1] (analytic) = 1.0055705005576827537490892808531 y[1] (numeric) = 1.0055564963621415341070874133299 absolute error = 1.4004195541219642001867523165573e-05 relative error = 0.0013926617311718082132539532748094 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1057 y[1] (analytic) = 1.0055810459143592235130551979753 y[1] (numeric) = 1.0055665376975747529121442382438 absolute error = 1.4508216784470600910959731493298e-05 relative error = 0.0014427695155370102239359987675603 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1058 y[1] (analytic) = 1.005591601215225225846604265349 y[1] (numeric) = 1.0055765800880408497200000042993 absolute error = 1.5021127184376126604261049618433e-05 relative error = 0.0014937602070486244867745215068088 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1059 y[1] (analytic) = 1.005602166460175207741164420479 y[1] (numeric) = 1.0055866235345342382070899192722 absolute error = 1.5542925640969534074501206839078e-05 relative error = 0.0015456336670079240000791839040751 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 1.0056127416491035167473238881278 y[1] (numeric) = 1.005596668038049321489576282946 absolute error = 1.6073611054195257747605181822984e-05 relative error = 0.0015983897566608151821130155912288 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1061 y[1] (analytic) = 1.005623326781904400975887704808 y[1] (numeric) = 1.0056067135995804921134044559588 absolute error = 1.6613182323908862483248849181177e-05 relative error = 0.0016520283371978565470676075697263 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1062 y[1] (analytic) = 1.0056339218584720090989352376741 y[1] (numeric) = 1.0056167602201221320443589343524 absolute error = 1.7161638349877054576303321703325e-05 relative error = 0.0017065492697542773891753566515764 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1063 y[1] (analytic) = 1.0056445268787003903508786978002 y[1] (numeric) = 1.0056268079006686126581195299219 absolute error = 1.7718978031777692759167878240420e-05 relative error = 0.0017619524154099964749535665871031 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1064 y[1] (analytic) = 1.0056551418424834945295226478354 y[1] (numeric) = 1.0056368566422142947303176564682 absolute error = 1.8285200269199799204991367211430e-05 relative error = 0.0018182376351896407435752101702938 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1065 y[1] (analytic) = 1.0056657667497151719971245040249 y[1] (numeric) = 1.0056469064457535284265927220492 absolute error = 1.8860303961643570531781975701724e-05 relative error = 0.0018754047900625640153611545106135 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1066 y[1] (analytic) = 1.0056764016002891736814560325861 y[1] (numeric) = 1.0056569573122806532926486273319 absolute error = 1.9444288008520388807405254112154e-05 relative error = 0.0019334537409428657083886495606305 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1067 y[1] (analytic) = 1.0056870463940991510768658404304 y[1] (numeric) = 1.0056670092427899982443103701441 absolute error = 2.0037151309152832555470286308830e-05 relative error = 0.0019923843486894095632108778916377 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1068 y[1] (analytic) = 1.005697701131038656245342860219 y[1] (numeric) = 1.0056770622382758815575807563238 absolute error = 2.0638892762774687762103895214715e-05 relative error = 0.0020521964741058423756823616146715 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1069 y[1] (analytic) = 1.0057083658110011418175808297414 y[1] (numeric) = 1.0056871162997326108586972169676 absolute error = 2.1249511268530958883612773775310e-05 relative error = 0.0021128899779406127378850202519198 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 1.0057190404338799609940437656082 y[1] (numeric) = 1.005697171428154483114188732177 absolute error = 2.1869005725477879855033431221788e-05 relative error = 0.0021744647208869897871496712734773 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.1MB, time=1.03 NO POLE x[1] = 0.1071 y[1] (analytic) = 1.0057297249995683675460324312455 y[1] (numeric) = 1.005707227624535784620932861401 absolute error = 2.2497375032582925099569844546105e-05 relative error = 0.0022369205635830819631677629267556 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1072 y[1] (analytic) = 1.0057404195079595158167517991808 y[1] (numeric) = 1.0057172848898707909962128804757 absolute error = 2.3134618088724820538918705093684e-05 relative error = 0.0023002573666118557731881269005763 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1073 y[1] (analytic) = 1.00575112395894646072237950761 y[1] (numeric) = 1.0057273432251537671677750254598 absolute error = 2.3780733792693554604482150170440e-05 relative error = 0.0023644749905011545652935362830797 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1074 y[1] (analytic) = 1.0057618383524221577531353112351 y[1] (numeric) = 1.0057374026313789673638858433655 absolute error = 2.4435721043190389249467869552008e-05 relative error = 0.0024295732957237173097518521920659 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1075 y[1] (analytic) = 1.0057725626882794629743515263608 y[1] (numeric) = 1.005747463109540635103389649884 absolute error = 2.5099578738827870961876476774177e-05 relative error = 0.0024955521426971973884365403782479 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1076 y[1] (analytic) = 1.0057832969664111330275444702404 y[1] (numeric) = 1.0057575246606330031857660942053 absolute error = 2.5772305778129841778376035074651e-05 relative error = 0.0025624113917841813923113370261414 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1077 y[1] (analytic) = 1.0057940411867098251314868946597 y[1] (numeric) = 1.0057675872856502936811878310318 absolute error = 2.6453901059531450299063627847410e-05 relative error = 0.0026301509032922079269738409039468 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1078 y[1] (analytic) = 1.0058047953490680970832814137484 y[1] (numeric) = 1.0057776509855867179205782998849 absolute error = 2.7144363481379162703113863462020e-05 relative error = 0.0026987705374737864262528069427847 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1079 y[1] (analytic) = 1.0058155594533784072594349260082 y[1] (numeric) = 1.0057877157614364764856696118039 absolute error = 2.7843691941930773765314204291450e-05 relative error = 0.0027682701545264159738539142570468 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 1.0058263334995331146169340305467 y[1] (numeric) = 1.0057977816141937591990605435369 absolute error = 2.8551885339355417873487009783009e-05 relative error = 0.0028386496145926041330487795513993 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1081 y[1] (analytic) = 1.0058371174874244786943214375069 y[1] (numeric) = 1.0058078485448527451142746393235 absolute error = 2.9268942571733580046798183398198e-05 relative error = 0.0029099087777598857844019847961426 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1082 y[1] (analytic) = 1.0058479114169446596127733726807 y[1] (numeric) = 1.0058179165544076025058184203674 absolute error = 2.9994862537057106954952313238390e-05 relative error = 0.0029820475040608419715308859911812 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1083 y[1] (analytic) = 1.0058587152879857180771779762961 y[1] (numeric) = 1.0058279856438524888592397021 absolute error = 3.0729644133229217938274196164380e-05 relative error = 0.003055065653473118754892967779798 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1084 y[1] (analytic) = 1.0058695291004396153772146959678 y[1] (numeric) = 1.0058380558141815508611860193326 absolute error = 3.1473286258064516028676635209001e-05 relative error = 0.0031289630859194460735955066167485 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1085 y[1] (analytic) = 1.0058803528541982133884346737992 y[1] (numeric) = 1.0058481270663889243894631593991 absolute error = 3.2225787809288998971514400073115e-05 relative error = 0.0032037396612676566152223031409095 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=22.8MB, alloc=4.2MB, time=1.24 x[1] = 0.1086 y[1] (analytic) = 1.005891186549153274573342127626 y[1] (numeric) = 1.0058581994014687345030938033855 absolute error = 3.2987147684540070248324240486448e-05 relative error = 0.0032793952393307046936722423508173 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1087 y[1] (analytic) = 1.0059020301851964619824767263904 y[1] (numeric) = 1.0058682728204150954323762755482 absolute error = 3.3757364781366550100450842205871e-05 relative error = 0.0033559296798666851350044381319233 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1088 y[1] (analytic) = 1.0059128837622193392554969596347 y[1] (numeric) = 1.0058783473242221105689434010193 absolute error = 3.4536437997228686553558615414856e-05 relative error = 0.0034333428425788521712847166372833 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1089 y[1] (analytic) = 1.0059237472801133706222645011039 y[1] (numeric) = 1.0058884229138838724558214718986 absolute error = 3.5324366229498166443029205279005e-05 relative error = 0.0035116345871156383424281909786657 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 1.0059346207387699209039295664461 y[1] (numeric) = 1.0058984995903944627774893218317 absolute error = 3.6121148375458126440244614403660e-05 relative error = 0.0035908047730706734060326776427387 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1091 y[1] (analytic) = 1.005945504138080255514017265 y[1] (numeric) = 1.005908577354747952349937509173 absolute error = 3.6926783332303164079755826930777e-05 relative error = 0.0036708532599828032551977030070533 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1092 y[1] (analytic) = 1.0059563974779355404595149456589 y[1] (numeric) = 1.0059186562079384011107276088349 absolute error = 3.7741269997139348787336824003372e-05 relative error = 0.0037517799073361088443238462929946 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1093 y[1] (analytic) = 1.0059673007582268423419605368001 y[1] (numeric) = 1.0059287361509598581090516129198 absolute error = 3.8564607266984232908923880316999e-05 relative error = 0.0038335845745599251228871632577237 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1094 y[1] (analytic) = 1.0059782139788451283585318802682 y[1] (numeric) = 1.0059388171848063614957914402367 absolute error = 3.9396794038766862740440031468867e-05 relative error = 0.0039162671210288599771834328943778 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1095 y[1] (analytic) = 1.0059891371396812663031370594024 y[1] (numeric) = 1.0059488993104719385135785548006 absolute error = 4.0237829209327789558504601806347e-05 relative error = 0.0039998274060628131800369673794346 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1096 y[1] (analytic) = 1.0060000702406260245675057210971 y[1] (numeric) = 1.0059589825289506054868536934146 absolute error = 4.1087711675419080652027682467791e-05 relative error = 0.0040842652889269953484687234781864 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1097 y[1] (analytic) = 1.0060110132815700721422813918831 y[1] (numeric) = 1.0059690668412363678119267024338 absolute error = 4.1946440333704330354689449299691e-05 relative error = 0.0041695806288319469093184515937036 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1098 y[1] (analytic) = 1.0060219662624039786181147880204 y[1] (numeric) = 1.0059791522483232199470364838101 absolute error = 4.2814014080758671078304210325414e-05 relative error = 0.0042557732849335570728156166215013 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1099 y[1] (analytic) = 1.006032929183018214186758119591 y[1] (numeric) = 1.0059892387512051454024110505185 absolute error = 4.3690431813068784347069072431845e-05 relative error = 0.0043428431163330828140938227513525 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 1.0060439020433031496421603885802 y[1] (numeric) = 1.0059993263508761167303276914632 absolute error = 4.4575692427032911832697116931477e-05 relative error = 0.0044307899820771678626434723393273 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 2 ) = sin(x); Iterations = 100 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Expected Time Remaining = 11 Minutes 15 Seconds Optimized Time Remaining = 11 Minutes 12 Seconds Time to Timeout = 14 Minutes 58 Seconds Percent Done = 0.2061 % > quit memory used=26.5MB, alloc=4.2MB, time=1.43