|\^/| 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_max_terms, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_warned2, > glob_smallish_float, > years_in_century, > days_in_year, > min_in_hour, > glob_log10normmin, > glob_max_hours, > glob_disp_incr, > glob_max_minutes, > glob_start, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_look_poles, > glob_last_good_h, > glob_display_flag, > djd_debug, > glob_max_sec, > glob_hmax, > djd_debug2, > glob_iter, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_not_yet_start_msg, > glob_dump, > glob_html_log, > glob_current_iter, > glob_warned, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_clock_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_large_float, > glob_h, > glob_initial_pass, > glob_not_yet_finished, > hours_in_day, > sec_in_min, > glob_log10relerr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_max_iter, > glob_almost_1, > glob_optimal_expect_sec, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_clock_start_sec, > centuries_in_millinium, > glob_subiter_method, > glob_percent_done, > glob_log10_abserr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_last_rel_error, > array_y2, > array_y1, > array_type_pole, > array_pole, > array_tmp4_g, > array_y1_init, > array_x, > array_y2_init, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_y1_set_initial, > array_y2_higher_work, > array_poles, > array_y2_higher_work2, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[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," "); > ; > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[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[2] := relerr; > else > array_last_rel_error[2] := 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_max_terms, DEBUGMASSIVE, glob_iolevel, glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century, days_in_year, min_in_hour, glob_log10normmin, glob_max_hours, glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt, glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag, djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump, glob_html_log, glob_current_iter, glob_warned, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h, glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min, glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter, glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium, glob_subiter_method, glob_percent_done, glob_log10_abserr, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole, array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_y1_set_initial, array_y2_higher_work, array_poles, array_y2_higher_work2, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_real_pole, array_y2_higher, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[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, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[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[2] := relerr else array_last_rel_error[2] := 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_max_terms, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_warned2, > glob_smallish_float, > years_in_century, > days_in_year, > min_in_hour, > glob_log10normmin, > glob_max_hours, > glob_disp_incr, > glob_max_minutes, > glob_start, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_look_poles, > glob_last_good_h, > glob_display_flag, > djd_debug, > glob_max_sec, > glob_hmax, > djd_debug2, > glob_iter, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_not_yet_start_msg, > glob_dump, > glob_html_log, > glob_current_iter, > glob_warned, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_clock_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_large_float, > glob_h, > glob_initial_pass, > glob_not_yet_finished, > hours_in_day, > sec_in_min, > glob_log10relerr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_max_iter, > glob_almost_1, > glob_optimal_expect_sec, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_clock_start_sec, > centuries_in_millinium, > glob_subiter_method, > glob_percent_done, > glob_log10_abserr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_last_rel_error, > array_y2, > array_y1, > array_type_pole, > array_pole, > array_tmp4_g, > array_y1_init, > array_x, > array_y2_init, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_y1_set_initial, > array_y2_higher_work, > array_poles, > array_y2_higher_work2, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y1_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_max_terms, DEBUGMASSIVE, glob_iolevel, glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century, days_in_year, min_in_hour, glob_log10normmin, glob_max_hours, glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt, glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag, djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump, glob_html_log, glob_current_iter, glob_warned, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h, glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min, glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter, glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium, glob_subiter_method, glob_percent_done, glob_log10_abserr, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole, array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_y1_set_initial, array_y2_higher_work, array_poles, array_y2_higher_work2, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_real_pole, array_y2_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_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_max_terms, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_warned2, > glob_smallish_float, > years_in_century, > days_in_year, > min_in_hour, > glob_log10normmin, > glob_max_hours, > glob_disp_incr, > glob_max_minutes, > glob_start, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_look_poles, > glob_last_good_h, > glob_display_flag, > djd_debug, > glob_max_sec, > glob_hmax, > djd_debug2, > glob_iter, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_not_yet_start_msg, > glob_dump, > glob_html_log, > glob_current_iter, > glob_warned, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_clock_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_large_float, > glob_h, > glob_initial_pass, > glob_not_yet_finished, > hours_in_day, > sec_in_min, > glob_log10relerr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_max_iter, > glob_almost_1, > glob_optimal_expect_sec, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_clock_start_sec, > centuries_in_millinium, > glob_subiter_method, > glob_percent_done, > glob_log10_abserr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_last_rel_error, > array_y2, > array_y1, > array_type_pole, > array_pole, > array_tmp4_g, > array_y1_init, > array_x, > array_y2_init, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_y1_set_initial, > array_y2_higher_work, > array_poles, > array_y2_higher_work2, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel, glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century, days_in_year, min_in_hour, glob_log10normmin, glob_max_hours, glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt, glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag, djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump, glob_html_log, glob_current_iter, glob_warned, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h, glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min, glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter, glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium, glob_subiter_method, glob_percent_done, glob_log10_abserr, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole, array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_y1_set_initial, array_y2_higher_work, array_poles, array_y2_higher_work2, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_real_pole, array_y2_higher, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > ALWAYS, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_warned2, > glob_smallish_float, > years_in_century, > days_in_year, > min_in_hour, > glob_log10normmin, > glob_max_hours, > glob_disp_incr, > glob_max_minutes, > glob_start, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_look_poles, > glob_last_good_h, > glob_display_flag, > djd_debug, > glob_max_sec, > glob_hmax, > djd_debug2, > glob_iter, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_not_yet_start_msg, > glob_dump, > glob_html_log, > glob_current_iter, > glob_warned, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_clock_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_large_float, > glob_h, > glob_initial_pass, > glob_not_yet_finished, > hours_in_day, > sec_in_min, > glob_log10relerr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_max_iter, > glob_almost_1, > glob_optimal_expect_sec, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_clock_start_sec, > centuries_in_millinium, > glob_subiter_method, > glob_percent_done, > glob_log10_abserr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_last_rel_error, > array_y2, > array_y1, > array_type_pole, > array_pole, > array_tmp4_g, > array_y1_init, > array_x, > array_y2_init, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_y1_set_initial, > array_y2_higher_work, > array_poles, > array_y2_higher_work2, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(array_y2_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_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_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 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y1_higher[1,m]) < glob_small_float) or (abs(array_y1_higher[1,m-1]) < glob_small_float) or (abs(array_y1_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_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_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[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y2_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_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y2_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_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_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 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_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 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > 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 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > 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 3 > 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 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > 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 3 > 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 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > 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 3 > 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 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > 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 3 > 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 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > 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 3 > 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 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > 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 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > 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 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #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_max_terms, DEBUGMASSIVE, glob_iolevel, glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century, days_in_year, min_in_hour, glob_log10normmin, glob_max_hours, glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt, glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag, djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump, glob_html_log, glob_current_iter, glob_warned, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h, glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min, glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter, glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium, glob_subiter_method, glob_percent_done, glob_log10_abserr, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole, array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_y1_set_initial, array_y2_higher_work, array_poles, array_y2_higher_work2, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_real_pole, array_y2_higher, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or abs(array_y2_higher[1, m - 1]) < glob_small_float or abs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_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; m := n - 2; while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or abs(array_y1_higher[1, m - 1]) < glob_small_float or abs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_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[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y2_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_y2_higher[1, m]) or glob_large_float <= abs(array_y2_higher[1, m - 1]) or glob_large_float <= abs(array_y2_higher[1, m - 2]) or glob_large_float <= abs(array_y2_higher[1, m - 3]) or glob_large_float <= abs(array_y2_higher[1, m - 4]) or glob_large_float <= abs(array_y2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_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; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y1_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[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_y1_higher[1, m]) or glob_large_float <= abs(array_y1_higher[1, m - 1]) or glob_large_float <= abs(array_y1_higher[1, m - 2]) or glob_large_float <= abs(array_y1_higher[1, m - 3]) or glob_large_float <= abs(array_y1_higher[1, m - 4]) or glob_large_float <= abs(array_y1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_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[2, 1] := glob_large_float; array_complex_pole[2, 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[2, 1] := rad_c; array_complex_pole[2, 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; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 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[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 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[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 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[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 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[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 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; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > INFO, > ALWAYS, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_warned2, > glob_smallish_float, > years_in_century, > days_in_year, > min_in_hour, > glob_log10normmin, > glob_max_hours, > glob_disp_incr, > glob_max_minutes, > glob_start, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_look_poles, > glob_last_good_h, > glob_display_flag, > djd_debug, > glob_max_sec, > glob_hmax, > djd_debug2, > glob_iter, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_not_yet_start_msg, > glob_dump, > glob_html_log, > glob_current_iter, > glob_warned, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_clock_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_large_float, > glob_h, > glob_initial_pass, > glob_not_yet_finished, > hours_in_day, > sec_in_min, > glob_log10relerr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_max_iter, > glob_almost_1, > glob_optimal_expect_sec, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_clock_start_sec, > centuries_in_millinium, > glob_subiter_method, > glob_percent_done, > glob_log10_abserr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_last_rel_error, > array_y2, > array_y1, > array_type_pole, > array_pole, > array_tmp4_g, > array_y1_init, > array_x, > array_y2_init, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_y1_set_initial, > array_y2_higher_work, > array_poles, > array_y2_higher_work2, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > 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_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel, glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century, days_in_year, min_in_hour, glob_log10normmin, glob_max_hours, glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt, glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag, djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump, glob_html_log, glob_current_iter, glob_warned, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h, glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min, glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter, glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium, glob_subiter_method, glob_percent_done, glob_log10_abserr, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole, array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_y1_set_initial, array_y2_higher_work, array_poles, array_y2_higher_work2, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_real_pole, array_y2_higher, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y2[iii]) then array_norms[iii] := abs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y1[iii]) then array_norms[iii] := abs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > INFO, > ALWAYS, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_warned2, > glob_smallish_float, > years_in_century, > days_in_year, > min_in_hour, > glob_log10normmin, > glob_max_hours, > glob_disp_incr, > glob_max_minutes, > glob_start, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_look_poles, > glob_last_good_h, > glob_display_flag, > djd_debug, > glob_max_sec, > glob_hmax, > djd_debug2, > glob_iter, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_not_yet_start_msg, > glob_dump, > glob_html_log, > glob_current_iter, > glob_warned, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_clock_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_large_float, > glob_h, > glob_initial_pass, > glob_not_yet_finished, > hours_in_day, > sec_in_min, > glob_log10relerr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_max_iter, > glob_almost_1, > glob_optimal_expect_sec, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_clock_start_sec, > centuries_in_millinium, > glob_subiter_method, > glob_percent_done, > glob_log10_abserr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_last_rel_error, > array_y2, > array_y1, > array_type_pole, > array_pole, > array_tmp4_g, > array_y1_init, > array_x, > array_y2_init, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_y1_set_initial, > array_y2_higher_work, > array_poles, > array_y2_higher_work2, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_y1_higher[2,1]; > #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_y2_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre sin $eq_no = 2 iii = 1 > #emit pre sin 1 $eq_no = 2 > array_tmp4[1] := sin(array_x[1]); > array_tmp4_g[1] := cos(array_x[1]); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_y1_set_initial[2,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_y1_higher[2,2]; > #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_y2_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre sin $eq_no = 2 iii = 2 > #emit pre sin 2 $eq_no = 2 > array_tmp4[2] := att(1,array_tmp4_g,array_x,1); > array_tmp4_g[2] := -att(1,array_tmp4,array_x,1); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_y1_higher[2,3]; > #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_y2_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre sin $eq_no = 2 iii = 3 > #emit pre sin 3 $eq_no = 2 > array_tmp4[3] := att(2,array_tmp4_g,array_x,1); > array_tmp4_g[3] := -att(2,array_tmp4,array_x,1); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_y1_higher[2,4]; > #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_y2_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre sin $eq_no = 2 iii = 4 > #emit pre sin 4 $eq_no = 2 > array_tmp4[4] := att(3,array_tmp4_g,array_x,1); > array_tmp4_g[4] := -att(3,array_tmp4,array_x,1); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_y1_higher[2,5]; > #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_y2_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre sin $eq_no = 2 iii = 5 > #emit pre sin 5 $eq_no = 2 > array_tmp4[5] := att(4,array_tmp4_g,array_x,1); > array_tmp4_g[5] := -att(4,array_tmp4,array_x,1); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_y1_higher[2,kkk]; > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y2_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_y2[kkk + order_d] := temporary; > array_y2_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_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit sin $eq_no = 2 > array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_x,1); > array_tmp4_g[kkk] := -att(kkk-1,array_tmp4,array_x,1); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp4[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_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_y1_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_max_terms, DEBUGMASSIVE, glob_iolevel, glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century, days_in_year, min_in_hour, glob_log10normmin, glob_max_hours, glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt, glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag, djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump, glob_html_log, glob_current_iter, glob_warned, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h, glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min, glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter, glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium, glob_subiter_method, glob_percent_done, glob_log10_abserr, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole, array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_y1_set_initial, array_y2_higher_work, array_poles, array_y2_higher_work2, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_real_pole, array_y2_higher, glob_last; array_tmp1[1] := array_y1_higher[2, 1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y2_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp4[1] := sin(array_x[1]); array_tmp4_g[1] := cos(array_x[1]); if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*glob_h*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_y1_higher[2, 2]; array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y2_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp4[2] := att(1, array_tmp4_g, array_x, 1); array_tmp4_g[2] := -att(1, array_tmp4, array_x, 1); if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*glob_h*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_y1_higher[2, 3]; array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y2_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp4[3] := att(2, array_tmp4_g, array_x, 1); array_tmp4_g[3] := -att(2, array_tmp4, array_x, 1); if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*glob_h*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_y1_higher[2, 4]; array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y2_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp4[4] := att(3, array_tmp4_g, array_x, 1); array_tmp4_g[4] := -att(3, array_tmp4, array_x, 1); if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*glob_h*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_y1_higher[2, 5]; array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y2_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp4[5] := att(4, array_tmp4_g, array_x, 1); array_tmp4_g[5] := -att(4, array_tmp4, array_x, 1); if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*glob_h*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y1_higher[2, kkk]; array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_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_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_x, 1); array_tmp4_g[kkk] := -att(kkk - 1, array_tmp4, array_x, 1); order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp4[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_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_y1_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_y1 := proc(x) > 2.0 - cos(x); > end; exact_soln_y1 := proc(x) 2.0 - cos(x) end proc > exact_soln_y2 := proc(x) > 2.0 - cos(x); > end; exact_soln_y2 := proc(x) 2.0 - cos(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_max_terms, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_warned2, > glob_smallish_float, > years_in_century, > days_in_year, > min_in_hour, > glob_log10normmin, > glob_max_hours, > glob_disp_incr, > glob_max_minutes, > glob_start, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_look_poles, > glob_last_good_h, > glob_display_flag, > djd_debug, > glob_max_sec, > glob_hmax, > djd_debug2, > glob_iter, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_not_yet_start_msg, > glob_dump, > glob_html_log, > glob_current_iter, > glob_warned, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_clock_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_large_float, > glob_h, > glob_initial_pass, > glob_not_yet_finished, > hours_in_day, > sec_in_min, > glob_log10relerr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_max_iter, > glob_almost_1, > glob_optimal_expect_sec, > glob_normmax, > glob_small_float, > glob_optimal_clock_start_sec, > glob_clock_start_sec, > centuries_in_millinium, > glob_subiter_method, > glob_percent_done, > glob_log10_abserr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_last_rel_error, > array_y2, > array_y1, > array_type_pole, > array_pole, > array_tmp4_g, > array_y1_init, > array_x, > array_y2_init, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_norms, > array_y1_set_initial, > array_y2_higher_work, > array_poles, > array_y2_higher_work2, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > ALWAYS := 1; > DEBUGL := 3; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_log10abserr := 0.0; > glob_warned2 := false; > glob_smallish_float := 0.1e-100; > years_in_century := 100.0; > days_in_year := 365.0; > min_in_hour := 60.0; > glob_log10normmin := 0.1; > glob_max_hours := 0.0; > glob_disp_incr := 0.1; > glob_max_minutes := 0.0; > glob_start := 0; > glob_unchanged_h_cnt := 0; > glob_max_trunc_err := 0.1e-10; > glob_look_poles := false; > glob_last_good_h := 0.1; > glob_display_flag := true; > djd_debug := true; > glob_max_sec := 10000.0; > glob_hmax := 1.0; > djd_debug2 := true; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_hmin := 0.00000000001; > glob_optimal_done := false; > glob_not_yet_start_msg := true; > glob_dump := false; > glob_html_log := true; > glob_current_iter := 0; > glob_warned := false; > glob_optimal_start := 0.0; > glob_hmin_init := 0.001; > glob_reached_optimal_h := false; > glob_clock_sec := 0.0; > glob_no_eqs := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_h := 0.1; > glob_initial_pass := true; > glob_not_yet_finished := true; > hours_in_day := 24.0; > sec_in_min := 60.0; > glob_log10relerr := 0.0; > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_max_iter := 1000; > glob_almost_1 := 0.9990; > glob_optimal_expect_sec := 0.1; > glob_normmax := 0.0; > glob_small_float := 0.1e-50; > glob_optimal_clock_start_sec := 0.0; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > glob_subiter_method := 3; > glob_percent_done := 0.0; > glob_log10_abserr := 0.1e-10; > glob_max_opt_iter := 10; > #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 := 2; > 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/mtest5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = sin ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"2.0 - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"2.0 - cos(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 := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_m1:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_y2:= Array(1..(max_terms + 1),[]); > array_y1:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_tmp4_g:= Array(1..(max_terms + 1),[]); > array_y1_init:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1_init[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_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 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_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_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 <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4_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_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_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_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_h := 0.00001 ; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := false; > array_y2_set_initial[1,3] := false; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_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 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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_y2(); > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_y1(); > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > 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; > if glob_subiter_method = 1 then # if number 3 > atomall(); > elif glob_subiter_method = 2 then # if number 4 > subiter := 1; > while subiter <= 2 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 2 + glob_max_terms do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y2_higher[ord,term_no] := array_y2_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 > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #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_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y1_higher[ord,term_no] := array_y1_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 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = sin ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-13T02:27:00-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest5") > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;") > ; > 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 5 > 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 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 5 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"mtest5 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest5 maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = sin ( x ) ;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 5 > 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 5 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 5 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if glob_html_log then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `subiter` is implicitly declared local to procedure `mainprog` 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, subiter; global INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel, glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century, days_in_year, min_in_hour, glob_log10normmin, glob_max_hours, glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt, glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag, djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump, glob_html_log, glob_current_iter, glob_warned, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h, glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min, glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter, glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float, glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium, glob_subiter_method, glob_percent_done, glob_log10_abserr, glob_max_opt_iter, array_const_1, array_const_0D0, array_m1, array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole, array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms, array_y1_set_initial, array_y2_higher_work, array_poles, array_y2_higher_work2, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_real_pole, array_y2_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; ALWAYS := 1; DEBUGL := 3; glob_max_terms := 30; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_log10abserr := 0.; glob_warned2 := false; glob_smallish_float := 0.1*10^(-100); years_in_century := 100.0; days_in_year := 365.0; min_in_hour := 60.0; glob_log10normmin := 0.1; glob_max_hours := 0.; glob_disp_incr := 0.1; glob_max_minutes := 0.; glob_start := 0; glob_unchanged_h_cnt := 0; glob_max_trunc_err := 0.1*10^(-10); glob_look_poles := false; glob_last_good_h := 0.1; glob_display_flag := true; djd_debug := true; glob_max_sec := 10000.0; glob_hmax := 1.0; djd_debug2 := true; glob_iter := 0; glob_orig_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_hmin := 0.1*10^(-10); glob_optimal_done := false; glob_not_yet_start_msg := true; glob_dump := false; glob_html_log := true; glob_current_iter := 0; glob_warned := false; glob_optimal_start := 0.; glob_hmin_init := 0.001; glob_reached_optimal_h := false; glob_clock_sec := 0.; glob_no_eqs := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_h := 0.1; glob_initial_pass := true; glob_not_yet_finished := true; hours_in_day := 24.0; sec_in_min := 60.0; glob_log10relerr := 0.; MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_max_iter := 1000; glob_almost_1 := 0.9990; glob_optimal_expect_sec := 0.1; glob_normmax := 0.; glob_small_float := 0.1*10^(-50); glob_optimal_clock_start_sec := 0.; glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; glob_subiter_method := 3; glob_percent_done := 0.; glob_log10_abserr := 0.1*10^(-10); glob_max_opt_iter := 10; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; 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/mtest5postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = sin ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "2.0 - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "2.0 - cos(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 := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_m1 := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_y2 := Array(1 .. max_terms + 1, []); array_y1 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_tmp4_g := Array(1 .. max_terms + 1, []); array_y1_init := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y2_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_y2_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_y2_higher := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[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_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work2[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_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_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_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_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_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_h := 0.00001; glob_max_iter := 20; glob_h := 0.0001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := false; array_y2_set_initial[1, 3] := false; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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_y2(); if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_y1(); if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_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 ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = 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, "2012-06-13T02:27:00-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest5") ; logitem_str(html_log_file, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); 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, "mtest5 diffeq.mxt"); logitem_str(html_log_file, "mtest5 maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = sin ( x ) ;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 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; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_h := 0.00001 ; glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) 2.0 - cos(x); end; exact_soln_y2 := proc(x) 2.0 - cos(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.0049958347219742339044380121961 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 1.0049958347219742339044380121961 y1[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % h = 0.0001 x[1] = 0.1 y2[1] (analytic) = 1.0049958347219742339044380121961 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 1.0049958347219742339044380121961 y1[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.52 NO POLE NO POLE x[1] = 0.1001 y2[1] (analytic) = 1.00500582303864310006118068491 y2[1] (numeric) = 1.0050158063803133312502571383936 absolute error = 9.9833416702311890764534836e-06 relative error = 0.00099336157476645022077122473146728 % h = 0.0001 y1[1] (analytic) = 1.00500582303864310006118068491 y1[1] (numeric) = 1.0050058230386431000611807332781 absolute error = 4.83681e-26 relative error = 4.8127183834376864520341527729514e-24 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.1MB, time=1.18 NO POLE NO POLE x[1] = 0.1002 y2[1] (analytic) = 1.0050158213052537275398742184312 y2[1] (numeric) = 1.0050357979385859149343525867125 absolute error = 1.99766333321873944783682813e-05 relative error = 0.0019876934182233023998511670430243 % h = 0.0001 y1[1] (analytic) = 1.0050158213052537275398742184312 y1[1] (numeric) = 1.005015821305253727539874315167 absolute error = 9.67358e-26 relative error = 9.6253012091257824360361950283837e-24 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=1.78 NO POLE NO POLE x[1] = 0.1003 y2[1] (analytic) = 1.0050258295217061336744956568614 y2[1] (numeric) = 1.0050558093965920693741651166307 absolute error = 2.99798748859356996694597693e-05 relative error = 0.0029829954619378473085290392480137 % h = 0.0001 y1[1] (analytic) = 1.0050258295217061336744956568614 y1[1] (numeric) = 1.0050258295217061336744958019643 absolute error = 1.451029e-25 relative error = 1.4437728438188973666138600203973e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=2.38 NO POLE NO POLE x[1] = 0.1004 y2[1] (analytic) = 1.0050358476879002363006043406579 y2[1] (numeric) = 1.0050758407541316799897999459 absolute error = 3.99930662314436891956052421e-05 relative error = 0.0039792676374129665958877951691437 % h = 0.0001 y1[1] (analytic) = 1.0050358476879002363006043406579 y1[1] (numeric) = 1.0050358476879002363006045341276 absolute error = 1.934697e-25 relative error = 1.9250029782030152765434432154408e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.1MB, time=2.98 NO POLE NO POLE x[1] = 0.1005 y2[1] (analytic) = 1.005045875803735853756342728278 y2[1] (numeric) = 1.0050958920110044332060278963436 absolute error = 5.00162072685794496851680656e-05 relative error = 0.0049765098760871443351111054990432 % h = 0.0001 y1[1] (analytic) = 1.005045875803735853756342728278 y1[1] (numeric) = 1.0050458758037358537563429701139 absolute error = 2.418359e-25 relative error = 2.4062175252110125849240987802809e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=3.59 NO POLE NO POLE x[1] = 0.1006 y2[1] (analytic) = 1.0050559138691127048834382127963 y2[1] (numeric) = 1.0051159631670098164542885296064 absolute error = 6.00492978971115708503168101e-05 relative error = 0.0059747221093344785800599641550778 % h = 0.0001 y1[1] (analytic) = 1.0050559138691127048834382127963 y1[1] (numeric) = 1.0050559138691127048834385029979 absolute error = 2.902016e-25 relative error = 2.8874174659877940502277959895574e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=4.19 NO POLE NO POLE x[1] = 0.1007 y2[1] (analytic) = 1.0050659618839304090282059334865 y2[1] (numeric) = 1.0051360542219471181746952728391 absolute error = 7.00923380167091464893393526e-05 relative error = 0.0069739042684646929321153161155742 % h = 0.0001 y1[1] (analytic) = 1.0050659618839304090282059334865 y1[1] (numeric) = 1.0050659618839304090282062720534 absolute error = 3.385669e-25 relative error = 3.3686037816401471797937681806910e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=4.79 NO POLE NO POLE x[1] = 0.1008 y2[1] (analytic) = 1.0050760198480884860425525823578 y2[1] (numeric) = 1.0051561651756154278180425342954 absolute error = 8.01453275269417754899519376e-05 relative error = 0.0079740562847231481172830942425244 % h = 0.0001 y1[1] (analytic) = 1.0050760198480884860425525823578 y1[1] (numeric) = 1.0050760198480884860425529692894 absolute error = 3.869316e-25 relative error = 3.8497744683877992312337905298146e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=34.3MB, alloc=4.1MB, time=5.41 x[1] = 0.1009 y2[1] (analytic) = 1.0050860877614863562849812056346 y2[1] (numeric) = 1.0051762960278136358478148088223 absolute error = 9.02082663272795628336031877e-05 relative error = 0.0089751780892908535735580498444113 % h = 0.0001 y1[1] (analytic) = 1.0050860877614863562849812056346 y1[1] (numeric) = 1.0050860877614863562849816409305 absolute error = 4.352959e-25 relative error = 4.3309315022903652540571582180656e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.101 y2[1] (analytic) = 1.005096165624023340621597000171 y2[1] (numeric) = 1.0051964467783404337421977732237 absolute error = 0.0001002811543170931206007730527 relative error = 0.0099772696132844790485427585155033 % h = 0.0001 y1[1] (analytic) = 1.005096165624023340621597000171 y1[1] (numeric) = 1.0050961656240233406215974838307 absolute error = 4.836597e-25 relative error = 4.8120738745403068824677547641046e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=6.05 NO POLE NO POLE x[1] = 0.1011 y2[1] (analytic) = 1.0051062534355986604271141047886 y2[1] (numeric) = 1.0052166174269943139960913714768 absolute error = 0.0001103639913956535689772666882 relative error = 0.010980330787756366207318180060042 % h = 0.0001 y1[1] (analytic) = 1.0051062534355986604271141047886 y1[1] (numeric) = 1.0051062534355986604271146368116 absolute error = 5.320230e-25 relative error = 5.2932015712912776856187998661957e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.2MB, time=6.65 NO POLE NO POLE x[1] = 0.1012 y2[1] (analytic) = 1.0051163511961114375858633865286 y2[1] (numeric) = 1.0052368079735735701231248897814 absolute error = 0.0001204567774621325372615032528 relative error = 0.011984361543694540250562148165706 % h = 0.0001 y1[1] (analytic) = 1.0051163511961114375858633865286 y1[1] (numeric) = 1.0051163511961114375858639669144 absolute error = 5.803858e-25 relative error = 5.7743145786985519519206566891596e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.2MB, time=7.30 NO POLE NO POLE x[1] = 0.1013 y2[1] (analytic) = 1.0051264589054606944928012218078 y2[1] (numeric) = 1.0052570184178762966576740214219 absolute error = 0.0001305595124156021648727996141 relative error = 0.012989361812022721542912162647019 % h = 0.0001 y1[1] (analytic) = 1.0051264589054606944928012218078 y1[1] (numeric) = 1.0051264589054606944928018505559 absolute error = 6.287481e-25 relative error = 6.2554128829190262014701862302364e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.2MB, time=7.90 NO POLE NO POLE x[1] = 0.1014 y2[1] (analytic) = 1.0051365765635453540545192724681 y2[1] (numeric) = 1.005277248759700389156879921422 absolute error = 0.0001406721961550351023606489539 relative error = 0.013995331523600337251568854147865 % h = 0.0001 y1[1] (analytic) = 1.0051365765635453540545192724681 y1[1] (numeric) = 1.005136576563545354054519949578 absolute error = 6.771099e-25 relative error = 6.7364964701112206980956116612208e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.2MB, time=8.51 NO POLE NO POLE x[1] = 0.1015 y2[1] (analytic) = 1.0051467041702642396902552567095 y2[1] (numeric) = 1.0052974989988435442026702509714 absolute error = 0.0001507948285793045124149942619 relative error = 0.015002270609222532995136488133315 % h = 0.0001 y1[1] (analytic) = 1.0051467041702642396902552567095 y1[1] (numeric) = 1.0051467041702642396902559821808 absolute error = 7.254713e-25 relative error = 7.2175663213149297238180277784591e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.2MB, time=9.15 NO POLE NO POLE x[1] = 0.1016 y2[1] (analytic) = 1.0051568417255160753329047148974 y2[1] (numeric) = 1.005317769135103259403782211605 absolute error = 0.0001609274095871840708774967076 relative error = 0.016010178999620184502696872092922 % h = 0.0001 y1[1] (analytic) = 1.0051568417255160753329047148974 y1[1] (numeric) = 1.0051568417255160753329054887295 absolute error = 7.738321e-25 relative error = 7.6986204329225941347677617648527e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.2MB, time=9.76 NO POLE NO POLE x[1] = 0.1017 y2[1] (analytic) = 1.0051669892291994854300337702324 y2[1] (numeric) = 1.0053380591682768333977875691138 absolute error = 0.0001710699390773479677537988814 relative error = 0.017019056625459909283113027061137 % h = 0.0001 y1[1] (analytic) = 1.0051669892291994854300337702324 y1[1] (numeric) = 1.0051669892291994854300345924248 absolute error = 8.221924e-25 relative error = 8.1796597859872875173171584801195e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.2MB, time=10.40 NO POLE NO POLE x[1] = 0.1018 y2[1] (analytic) = 1.0051771466812129949448928842738 y2[1] (numeric) = 1.0053583690981613658531196671674 absolute error = 0.0001812224169483709082267828936 relative error = 0.018028903417344078304558981387419 % h = 0.0001 y1[1] (analytic) = 1.0051771466812129949448928842738 y1[1] (numeric) = 1.005177146681212994944893754826 absolute error = 8.705522e-25 relative error = 8.6606843666740402236578150436321e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.2MB, time=11.04 NO POLE NO POLE x[1] = 0.1019 y2[1] (analytic) = 1.0051873140814550293574316073064 y2[1] (numeric) = 1.0053786989245537574711024306282 absolute error = 0.0001913848430987281136708233218 relative error = 0.019039719305810827684272041925437 % h = 0.0001 y1[1] (analytic) = 1.0051873140814550293574316073064 y1[1] (numeric) = 1.005187314081455029357432526218 absolute error = 9.189116e-25 relative error = 9.1416951559889691889727014580308e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.2MB, time=11.67 NO POLE NO POLE x[1] = 0.102 y2[1] (analytic) = 1.0051974914298239146653143235401 y2[1] (numeric) = 1.0053990486472507099879813585363 absolute error = 0.0002015572174267953226670349962 relative error = 0.020051504221334070388523894770719 % h = 0.0001 y1[1] (analytic) = 1.0051974914298239146653143235401 y1[1] (numeric) = 1.0051974914298239146653152908106 absolute error = 9.672705e-25 relative error = 9.6226911452407686345263232488593e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.2MB, time=12.28 NO POLE NO POLE x[1] = 0.1021 y2[1] (analytic) = 1.0052076787262178773849369911326 y2[1] (numeric) = 1.0054194182660487261769565067452 absolute error = 0.0002117395398308487920195156126 relative error = 0.021064258094323507942806884767262 % h = 0.0001 y1[1] (analytic) = 1.0052076787262178773849369911326 y1[1] (numeric) = 1.0052076787262178773849380067615 absolute error = 1.0156289e-24 relative error = 1.0103672320599338412078272912172e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.2MB, time=12.92 NO POLE NO POLE x[1] = 0.1022 y2[1] (analytic) = 1.0052178759705350445524448770242 y2[1] (numeric) = 1.0054398077807441098502174601885 absolute error = 0.0002219318102090652977725831643 relative error = 0.02207798085512464215223182020599 % h = 0.0001 y1[1] (analytic) = 1.0052178759705350445524448770242 y1[1] (numeric) = 1.005217875970535044552445941011 absolute error = 1.0639868e-24 relative error = 1.0584638668236214202370640334355e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.2MB, time=13.53 NO POLE NO POLE x[1] = 0.1023 y2[1] (analytic) = 1.0052280831626734437247512865758 y2[1] (numeric) = 1.005460217191132965860980294756 absolute error = 0.0002321340284595221362290081802 relative error = 0.023092672434018786832133645814892 % h = 0.0001 y1[1] (analytic) = 1.0052280831626734437247512865758 y1[1] (numeric) = 1.0052280831626734437247523989199 absolute error = 1.1123441e-24 relative error = 1.1065589179525461488050416990782e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.2MB, time=14.13 NO POLE NO POLE x[1] = 0.1024 y2[1] (analytic) = 1.0052383003025310029805572879987 y2[1] (numeric) = 1.0054806464970112001055265287599 absolute error = 0.0002423461944801971249692407612 relative error = 0.024108332761223079548881324684939 % h = 0.0001 y1[1] (analytic) = 1.0052383003025310029805572879987 y1[1] (numeric) = 1.0052383003025310029805584486997 absolute error = 1.1607010e-24 relative error = 1.1546525830250218241419461943290e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.2MB, time=14.74 NO POLE NO POLE x[1] = 0.1025 y2[1] (analytic) = 1.0052485273900055509213724315671 y2[1] (numeric) = 1.0055010956981745195252440639703 absolute error = 0.0002525683081689686038716324032 relative error = 0.025124961766890493370888266466393 % h = 0.0001 y1[1] (analytic) = 1.0052485273900055509213724315671 y1[1] (numeric) = 1.0052485273900055509213736406244 absolute error = 1.2090573e-24 relative error = 1.2027446616998851922674805044983e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.2MB, time=15.35 NO POLE NO POLE x[1] = 0.1026 y2[1] (analytic) = 1.0052587644249948166725364636016 y2[1] (numeric) = 1.0055215647944184321086701161997 absolute error = 0.0002628003694236154361336525981 relative error = 0.026142559381109848629819636548939 % h = 0.0001 y1[1] (analytic) = 1.0052587644249948166725364636016 y1[1] (numeric) = 1.0052587644249948166725377210148 absolute error = 1.2574132e-24 relative error = 1.2508353515517338569353106093491e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.2MB, time=15.99 NO POLE NO POLE x[1] = 0.1027 y2[1] (analytic) = 1.0052690114073964298842420352155 y2[1] (numeric) = 1.0055420537855382468935361354158 absolute error = 0.0002730423781418170092941002003 relative error = 0.027161125533905824691992877623219 % h = 0.0001 y1[1] (analytic) = 1.0052690114073964298842420352155 y1[1] (numeric) = 1.0052690114073964298842433409841 absolute error = 1.3057686e-24 relative error = 1.2989245517196419127858984468072e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.2MB, time=16.61 NO POLE NO POLE x[1] = 0.1028 y2[1] (analytic) = 1.0052792683371079207325584058118 y2[1] (numeric) = 1.0055625626713290739688147153626 absolute error = 0.0002832943342211532362563095508 relative error = 0.028180660155238971739967772553084 % h = 0.0001 y1[1] (analytic) = 1.0052792683371079207325584058118 y1[1] (numeric) = 1.0052792683371079207325597599353 absolute error = 1.3541235e-24 relative error = 1.3470122608217475917877160719193e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.2MB, time=17.23 NO POLE NO POLE x[1] = 0.1029 y2[1] (analytic) = 1.0052895352140267199204561413216 y2[1] (numeric) = 1.0055830914515858244767684926688 absolute error = 0.0002935562375591045563123513472 relative error = 0.029201163175005722564322374185628 % h = 0.0001 y1[1] (analytic) = 1.0052895352140267199204561413216 y1[1] (numeric) = 1.0052895352140267199204575437994 absolute error = 1.4024778e-24 relative error = 1.3950983780025240889330168206187e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.2MB, time=17.87 NO POLE NO POLE x[1] = 0.103 y2[1] (analytic) = 1.0052998120380501586788328071734 y2[1] (numeric) = 1.0056036401261032106150010354236 absolute error = 0.0003038280880530519361682282502 relative error = 0.03022263452303840436561112503259 % h = 0.0001 y1[1] (analytic) = 1.0052998120380501586788328071734 y1[1] (numeric) = 1.0052998120380501586788342580051 absolute error = 1.4508317e-24 relative error = 1.4431831008291152988008737400215e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.2MB, time=18.48 NO POLE NO POLE x[1] = 0.1031 y2[1] (analytic) = 1.0053100988090754687675396559837 y2[1] (numeric) = 1.005624208694675745638509721199 absolute error = 0.0003141098856002768709700652153 relative error = 0.03124507412910525056650148664717 % h = 0.0001 y1[1] (analytic) = 1.0053100988090754687675396559837 y1[1] (numeric) = 1.0053100988090754687675411551688 absolute error = 1.4991851e-24 relative error = 1.4912663284453082219570667171403e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.2MB, time=19.09 NO POLE NO POLE x[1] = 0.1032 y2[1] (analytic) = 1.0053203955269997824764093099572 y2[1] (numeric) = 1.0056447971570977438617406044979 absolute error = 0.0003244016300979613853312945407 relative error = 0.032268481922910412634085395830497 % h = 0.0001 y1[1] (analytic) = 1.0053203955269997824764093099572 y1[1] (numeric) = 1.0053203955269997824764108574952 absolute error = 1.5475380e-24 relative error = 1.5393480594699005459885051172232e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1033 y2[1] (analytic) = 1.005330702191720132626284437988 y2[1] (numeric) = 1.0056654055131633206606452736081 absolute error = 0.0003347033214431880343608356201 relative error = 0.033292857834093971912361861656263 % h = 0.0001 y1[1] (analytic) = 1.005330702191720132626284437988 y1[1] (numeric) = 1.0053307021917201326262860338784 absolute error = 1.5958904e-24 relative error = 1.5874282925218551986717239163730e-22 % h = 0.0001 memory used=122.0MB, alloc=4.2MB, time=19.72 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1034 y2[1] (analytic) = 1.0053410188031334525700474274499 y2[1] (numeric) = 1.0056860337626663924747396968411 absolute error = 0.0003450149595329399046922693912 relative error = 0.034318201792231951464887014596017 % h = 0.0001 y1[1] (analytic) = 1.0053410188031334525700474274499 y1[1] (numeric) = 1.0053410188031334525700490716922 absolute error = 1.6442423e-24 relative error = 1.6355070262203004984017462772698e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.2MB, time=20.38 NO POLE NO POLE x[1] = 0.1035 y2[1] (analytic) = 1.0053513453611365761936510506671 y2[1] (numeric) = 1.005706681905400676809165058135 absolute error = 0.0003553365442641006155140074679 relative error = 0.03534451372683632792758791583583 % h = 0.0001 y1[1] (analytic) = 1.0053513453611365761936510506671 y1[1] (numeric) = 1.0053513453611365761936527432607 absolute error = 1.6925936e-24 relative error = 1.6835841597168163940000537388593e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.2MB, time=21.05 NO POLE NO POLE x[1] = 0.1036 y2[1] (analytic) = 1.0053616818656262379171501260534 y2[1] (numeric) = 1.0057273499411596922367505820017 absolute error = 0.0003656680755334543196004559483 relative error = 0.036371793567355043371736432371609 % h = 0.0001 y1[1] (analytic) = 1.0053616818656262379171501260534 y1[1] (numeric) = 1.0053616818656262379171518669979 absolute error = 1.7409445e-24 relative error = 1.7316598905673129226577246409324e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.2MB, time=21.71 NO POLE NO POLE x[1] = 0.1037 y2[1] (analytic) = 1.0053720283164990726957341739114 y2[1] (numeric) = 1.0057480378697367584000783477965 absolute error = 0.0003760095532376857043441738851 relative error = 0.037400041243172017177079480013657 % h = 0.0001 y1[1] (analytic) = 1.0053720283164990726957341739114 y1[1] (numeric) = 1.0053720283164990726957359632062 absolute error = 1.7892948e-24 relative error = 1.7797340184570122469264710583752e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.2MB, time=22.39 NO POLE NO POLE x[1] = 0.1038 y2[1] (analytic) = 1.0053823847136516160207610668791 y2[1] (numeric) = 1.005768745690924996013550093291 absolute error = 0.0003863609772733799927890264119 relative error = 0.038429256683607157915121934209843 % h = 0.0001 y1[1] (analytic) = 1.0053823847136516160207610668791 y1[1] (numeric) = 1.0053823847136516160207629045237 absolute error = 1.8376446e-24 relative error = 1.8278066414734225505775443940977e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.2MB, time=23.02 NO POLE NO POLE x[1] = 0.1039 y2[1] (analytic) = 1.0053927510569803039207916750157 y2[1] (numeric) = 1.0057894734045173268654560075269 absolute error = 0.0003967223475370229446643325112 relative error = 0.039459439817916375242558504924905 % h = 0.0001 y1[1] (analytic) = 1.0053927510569803039207916750157 y1[1] (numeric) = 1.0053927510569803039207935610097 absolute error = 1.8859940e-24 relative error = 1.8758778577001217204419285359615e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.2MB, time=23.68 NO POLE NO POLE x[1] = 0.104 y2[1] (analytic) = 1.0054031273463814729626255055154 y2[1] (numeric) = 1.0058102210103064738200455129318 absolute error = 0.0004070936639250008574200074164 relative error = 0.040490590575291591804850869555984 % h = 0.0001 y1[1] (analytic) = 1.0054031273463814729626255055154 y1[1] (numeric) = 1.0054031273463814729626274398582 absolute error = 1.9343428e-24 relative error = 1.9239474668289750033143347914607e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.2MB, time=24.33 NO POLE NO POLE x[1] = 0.1041 y2[1] (analytic) = 1.005413513581751360252337337038 y2[1] (numeric) = 1.0058309885080849608196000366746 absolute error = 0.0004174749263336005672626996366 relative error = 0.041522708884860755149946354614275 % h = 0.0001 y1[1] (analytic) = 1.005413513581751360252337337038 y1[1] (numeric) = 1.0054135135817513602523393197293 absolute error = 1.9826913e-24 relative error = 1.9720157658680455250328525555774e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.2MB, time=25.01 NO POLE NO POLE x[1] = 0.1042 y2[1] (analytic) = 1.005423909762986103436314848648 y2[1] (numeric) = 1.0058517758976451128865077712411 absolute error = 0.0004278661346590094501929225931 relative error = 0.042555794675687849652134454012123 % h = 0.0001 y1[1] (analytic) = 1.005423909762986103436314848648 y1[1] (numeric) = 1.0054239097629861034363168796871 absolute error = 2.0310391e-24 relative error = 2.0200823555894822418514107060752e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.2MB, time=25.70 NO POLE NO POLE x[1] = 0.1043 y2[1] (analytic) = 1.0054343158899817407022972433492 y2[1] (numeric) = 1.0058725831787790561253404242086 absolute error = 0.0004382672887973154230431808594 relative error = 0.043589847876772908446037469185112 % h = 0.0001 y1[1] (analytic) = 1.0054343158899817407022972433492 y1[1] (numeric) = 1.0054343158899817407022993227356 absolute error = 2.0793864e-24 relative error = 2.0681474335390935479160455397712e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.2MB, time=26.36 NO POLE NO POLE x[1] = 0.1044 y2[1] (analytic) = 1.0054447319626342107804148662065 y2[1] (numeric) = 1.0058934103512787177249319571981 absolute error = 0.0004486783886445069445170909916 relative error = 0.044624868417052025370731552894447 % h = 0.0001 y1[1] (analytic) = 1.0054447319626342107804148662065 y1[1] (numeric) = 1.0054447319626342107804169939398 absolute error = 2.1277333e-24 relative error = 2.1162110977961480808916284930599e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.2MB, time=27.01 NO POLE NO POLE x[1] = 0.1045 y2[1] (analytic) = 1.0054551579808393529442298170443 y2[1] (numeric) = 1.0059142574149358259604593139845 absolute error = 0.0004590994340964730162294969402 relative error = 0.045660856225397366923994436068092 % h = 0.0001 y1[1] (analytic) = 1.0054551579808393529442298170443 y1[1] (numeric) = 1.0054551579808393529442319931239 absolute error = 2.1760796e-24 relative error = 2.1642731480636244087201030105707e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.2MB, time=27.68 NO POLE NO POLE x[1] = 0.1046 y2[1] (analytic) = 1.0054655939444929070117775577094 y2[1] (numeric) = 1.005935124369541910195525137743 absolute error = 0.0004695304250490031837475800336 relative error = 0.046697811230617184226676114076557 % h = 0.0001 y1[1] (analytic) = 1.0054655939444929070117775577094 y1[1] (numeric) = 1.0054655939444929070117797821348 absolute error = 2.2244254e-24 relative error = 2.2123336824221557713800629343517e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.2MB, time=28.34 NO POLE NO POLE x[1] = 0.1047 y2[1] (analytic) = 1.0054760398534905133466095138901 y2[1] (numeric) = 1.0059560112148883008842424774112 absolute error = 0.0004799713613977875376329635211 relative error = 0.047735733361455824997188765699378 % h = 0.0001 y1[1] (analytic) = 1.0054760398534905133466095138901 y1[1] (numeric) = 1.0054760398534905133466117866608 absolute error = 2.2727707e-24 relative error = 2.2603926994930371230305959495516e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.2MB, time=29.01 NO POLE NO POLE x[1] = 0.1048 y2[1] (analytic) = 1.0054864957077277128588366714797 y2[1] (numeric) = 1.0059769179507661295733214831464 absolute error = 0.0004904222430384167144848116667 relative error = 0.048774622546593745536112175497317 % h = 0.0001 y1[1] (analytic) = 1.0054864957077277128588366714797 y1[1] (numeric) = 1.0054864957077277128588389925952 absolute error = 2.3211155e-24 relative error = 2.3084501978977309100440081085363e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.2MB, time=29.70 NO POLE NO POLE x[1] = 0.1049 y2[1] (analytic) = 1.0054969615070999470061741674745 y2[1] (numeric) = 1.0059978445769663289041580908568 absolute error = 0.0005008830698663818979839233823 relative error = 0.049814478714647522720910927149292 % h = 0.0001 y1[1] (analytic) = 1.0054969615070999470061741674745 y1[1] (numeric) = 1.0054969615070999470061765369343 absolute error = 2.3694598e-24 relative error = 2.3565061762578672208437568914643e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.2MB, time=30.38 NO POLE NO POLE x[1] = 0.105 y2[1] (analytic) = 1.0055074372515025577949868753959 y2[1] (numeric) = 1.0060187910932796326149246957856 absolute error = 0.0005113538417770748199378203897 relative error = 0.050855301794169866010759632507108 % h = 0.0001 y1[1] (analytic) = 1.0055074372515025577949868753959 y1[1] (numeric) = 1.0055074372515025577949892931995 absolute error = 2.4178036e-24 relative error = 2.4045606331952439357027479901654e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.3MB, time=31.05 NO POLE NO POLE x[1] = 0.1051 y2[1] (analytic) = 1.0055179229408307877813359852258 y2[1] (numeric) = 1.0060397574994965755426628151277 absolute error = 0.0005218345586657877613268299019 relative error = 0.051897091713649629461472458346761 % h = 0.0001 y1[1] (analytic) = 1.0055179229408307877813359852258 y1[1] (numeric) = 1.0055179229408307877813384513727 absolute error = 2.4661469e-24 relative error = 2.4526135673318268765019631262460e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.3MB, time=31.70 NO POLE NO POLE x[1] = 0.1052 y2[1] (analytic) = 1.0055284185749797800720265778451 y2[1] (numeric) = 1.0060607437954074936253777396574 absolute error = 0.0005323252204277135533511618123 relative error = 0.052939848401511823750533209724283 % h = 0.0001 y1[1] (analytic) = 1.0055284185749797800720265778451 y1[1] (numeric) = 1.0055284185749797800720290923347 absolute error = 2.5144896e-24 relative error = 2.5006648778395522765881421595194e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.3MB, time=32.35 NO POLE NO POLE x[1] = 0.1053 y2[1] (analytic) = 1.0055389241538445783256561939646 y2[1] (numeric) = 1.0060817499808025239041351743468 absolute error = 0.0005428258269579455784789803822 relative error = 0.05398357178611762821222222614313 % h = 0.0001 y1[1] (analytic) = 1.0055389241538445783256561939646 y1[1] (numeric) = 1.0055389241538445783256587567965 absolute error = 2.5628319e-24 relative error = 2.5487147622421566767021346289422e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.3MB, time=32.98 NO POLE NO POLE x[1] = 0.1054 y2[1] (analytic) = 1.0055494396773201267536643975387 y2[1] (numeric) = 1.0061027760554716045251598679533 absolute error = 0.0005533363781514777714954704146 relative error = 0.055028261795764402882836343623256 % h = 0.0001 y1[1] (analytic) = 1.0055494396773201267536643975387 y1[1] (numeric) = 1.0055494396773201267536670087124 absolute error = 2.6111737e-24 relative error = 2.5967631197108748768425191599945e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.3MB, time=33.60 NO POLE NO POLE x[1] = 0.1055 y2[1] (analytic) = 1.0055599651453012701213833336496 y2[1] (numeric) = 1.0061238220192044747419362315554 absolute error = 0.0005638568739032046205528979058 relative error = 0.056073918358685700555998173233956 % h = 0.0001 y1[1] (analytic) = 1.0055599651453012701213833336496 y1[1] (numeric) = 1.0055599651453012701213859931645 absolute error = 2.6595149e-24 relative error = 2.6448098494212682479354129041646e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=205.9MB, alloc=4.3MB, time=34.25 x[1] = 0.1056 y2[1] (analytic) = 1.0055705005576827537490892808531 y2[1] (numeric) = 1.0061448878717906749173109460164 absolute error = 0.0005743873141079211682216651633 relative error = 0.057120541403051278848050943479644 % h = 0.0001 y1[1] (analytic) = 1.0055705005576827537490892808531 y1[1] (numeric) = 1.0055705005576827537490919887087 absolute error = 2.7078556e-24 relative error = 2.6928550494453061029318200137719e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1057 y2[1] (analytic) = 1.0055810459143592235130551979753 y2[1] (numeric) = 1.0061659736130195465255975583541 absolute error = 0.0005849276986603230125423603788 relative error = 0.058168130856967112273535151085055 % h = 0.0001 y1[1] (analytic) = 1.0055810459143592235130551979753 y1[1] (numeric) = 1.0055810459143592235130579541712 absolute error = 2.7561959e-24 relative error = 2.7408988178509608692772689486619e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.3MB, time=34.91 NO POLE NO POLE x[1] = 0.1058 y2[1] (analytic) = 1.005591601215225225846604265349 y2[1] (numeric) = 1.0061870792426802321546830669958 absolute error = 0.0005954780274550063080788016468 relative error = 0.059216686648475404330743262024834 % h = 0.0001 y1[1] (analytic) = 1.005591601215225225846604265349 y1[1] (numeric) = 1.0055916012152252258466070698846 absolute error = 2.8045356e-24 relative error = 2.7889409543703513422869142393034e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.3MB, time=35.56 NO POLE NO POLE x[1] = 0.1059 y2[1] (analytic) = 1.005602166460175207741164420479 y2[1] (numeric) = 1.0062082047605616755081364958977 absolute error = 0.0006060383003864677669720754187 relative error = 0.060266208705554599597348701713883 % h = 0.0001 y1[1] (analytic) = 1.005602166460175207741164420479 y1[1] (numeric) = 1.0056021664601752077411672733539 absolute error = 2.8528749e-24 relative error = 2.8369816565157352463926562076170e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.3MB, time=36.25 NO POLE NO POLE x[1] = 0.106 y2[1] (analytic) = 1.0056127416491035167473238881278 y2[1] (numeric) = 1.0062293501664526214073194575076 absolute error = 0.0006166085173491046599955693798 relative error = 0.061316696956119395836105370159174 % h = 0.0001 y1[1] (analytic) = 1.0056127416491035167473238881278 y1[1] (numeric) = 1.0056127416491035167473267893413 absolute error = 2.9012135e-24 relative error = 2.8850206245818866038962970388680e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.3MB, time=36.91 NO POLE NO POLE x[1] = 0.1061 y2[1] (analytic) = 1.005623326781904400975887704808 y2[1] (numeric) = 1.0062505154601416157934987045494 absolute error = 0.0006271886782372148176109997414 relative error = 0.062368151328020756110613915486248 % h = 0.0001 y1[1] (analytic) = 1.005623326781904400975887704808 y1[1] (numeric) = 1.0056233267819044009758906543597 absolute error = 2.9495517e-24 relative error = 2.9330581555211746548923765245987e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.3MB, time=37.58 NO POLE NO POLE x[1] = 0.1062 y2[1] (analytic) = 1.0056339218584720090989352376741 y2[1] (numeric) = 1.0062717006414170057299606706086 absolute error = 0.0006377787829449966310254329345 relative error = 0.063420571749045920911150995823191 % h = 0.0001 y1[1] (analytic) = 1.0056339218584720090989352376741 y1[1] (numeric) = 1.0056339218584720090989382355634 absolute error = 2.9978893e-24 relative error = 2.9810940490747568989152202688354e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.3MB, time=38.25 NO POLE NO POLE x[1] = 0.1063 y2[1] (analytic) = 1.0056445268787003903508786978002 y2[1] (numeric) = 1.0062929057100669394041279994979 absolute error = 0.0006483788313665490532493016977 relative error = 0.064473958146918420290557757270473 % h = 0.0001 y1[1] (analytic) = 1.0056445268787003903508786978002 y1[1] (numeric) = 1.0056445268787003903508817440266 absolute error = 3.0462264e-24 relative error = 3.0291284033084904293407306229443e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.3MB, time=38.94 NO POLE NO POLE x[1] = 0.1064 y2[1] (analytic) = 1.0056551418424834945295226478354 y2[1] (numeric) = 1.0063141306658793661296780633809 absolute error = 0.0006589888233958716001554155455 relative error = 0.065528310449298086010183752188799 % h = 0.0001 y1[1] (analytic) = 1.0056551418424834945295226478354 y1[1] (numeric) = 1.0056551418424834945295257423985 absolute error = 3.0945631e-24 relative error = 3.0771613162842095797786145938714e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.3MB, time=39.62 NO POLE NO POLE x[1] = 0.1065 y2[1] (analytic) = 1.0056657667497151719971245040248 y2[1] (numeric) = 1.0063353755086420363486634696338 absolute error = 0.000669608758926864351538965609 relative error = 0.066583628583781063695882519756475 % h = 0.0001 y1[1] (analytic) = 1.0056657667497151719971245040248 y1[1] (numeric) = 1.0056657667497151719971276469241 absolute error = 3.1428993e-24 relative error = 3.1251926871864858000961604586420e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.3MB, time=40.29 NO POLE NO POLE x[1] = 0.1066 y2[1] (analytic) = 1.0056764016002891736814560325861 y2[1] (numeric) = 1.0063566402381425016336345564231 absolute error = 0.000680238637853327952178523837 relative error = 0.06763991247789982500405504749416 % h = 0.0001 y1[1] (analytic) = 1.0056764016002891736814560325861 y1[1] (numeric) = 1.0056764016002891736814592238209 absolute error = 3.1912348e-24 relative error = 3.1732223157686972493248873392804e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.3MB, time=40.95 NO POLE NO POLE x[1] = 0.1067 y2[1] (analytic) = 1.0056870463940991510768658404304 y2[1] (numeric) = 1.0063779248541681146897638769782 absolute error = 0.0006908784600689636128980365478 relative error = 0.068697162059123179797737329829774 % h = 0.0001 y1[1] (analytic) = 1.0056870463940991510768658404304 y1[1] (numeric) = 1.0056870463940991510768690800004 absolute error = 3.2395700e-24 relative error = 3.2212505983998802285107300755262e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.3MB, time=41.63 NO POLE NO POLE x[1] = 0.1068 y2[1] (analytic) = 1.005697701131038656245342860219 y2[1] (numeric) = 1.0063992293565060293569726725379 absolute error = 0.0007015282254673731116298123189 relative error = 0.069755377254856288332728236615874 % h = 0.0001 y1[1] (analytic) = 1.005697701131038656245342860219 y1[1] (numeric) = 1.0056977011310386562453461481235 absolute error = 3.2879045e-24 relative error = 3.2692771359647349111416115989128e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.3MB, time=42.31 NO POLE NO POLE x[1] = 0.1069 y2[1] (analytic) = 1.0057083658110011418175808297414 y2[1] (numeric) = 1.0064205537449432006120593339496 absolute error = 0.0007121879339420587944785042082 relative error = 0.070814557992440673453753902298473 % h = 0.0001 y1[1] (analytic) = 1.0057083658110011418175808297414 y1[1] (numeric) = 1.0057083658110011418175841659799 absolute error = 3.3362385e-24 relative error = 3.3173021259594118898404793650151e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.3MB, time=42.98 NO POLE NO POLE x[1] = 0.107 y2[1] (analytic) = 1.0057190404338799609940437656082 y2[1] (numeric) = 1.0064418980192663845708298518993 absolute error = 0.0007228575853864235767860862911 relative error = 0.071874704199154232800664842672675 % h = 0.0001 y1[1] (analytic) = 1.0057190404338799609940437656082 y1[1] (numeric) = 1.0057190404338799609940471501803 absolute error = 3.3845721e-24 relative error = 3.3653256664404530226578606905771e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.3MB, time=43.65 NO POLE NO POLE x[1] = 0.1071 y2[1] (analytic) = 1.0057297249995683675460324312455 y2[1] (numeric) = 1.006463262179262138490230255752 absolute error = 0.0007335371796937709441978245065 relative error = 0.072935815802211251024662004169717 % h = 0.0001 y1[1] (analytic) = 1.0057297249995683675460324312455 y1[1] (numeric) = 1.0057297249995683675460358641506 absolute error = 3.4329051e-24 relative error = 3.4133475571694704674084732503249e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.3MB, time=44.33 NO POLE NO POLE x[1] = 0.1072 y2[1] (analytic) = 1.0057404195079595158167517991808 y2[1] (numeric) = 1.0064846462247168207704810409802 absolute error = 0.0007442267167573049537292417994 relative error = 0.073997892728762412014547947248261 % h = 0.0001 y1[1] (analytic) = 1.0057404195079595158167517991808 y1[1] (numeric) = 1.0057404195079595158167552804183 absolute error = 3.4812375e-24 relative error = 3.4613677967751689711959246908875e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.3MB, time=45.01 NO POLE NO POLE x[1] = 0.1073 y2[1] (analytic) = 1.00575112395894646072237950761 y2[1] (numeric) = 1.0065060501554165909572135851601 absolute error = 0.0007549261964701302348340775501 relative error = 0.075060934905894811132999362848909 % h = 0.0001 y1[1] (analytic) = 1.00575112395894646072237950761 y1[1] (numeric) = 1.0057511239589464607223830371795 absolute error = 3.5295695e-24 relative error = 3.5093865827427827362935019589606e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.3MB, time=45.68 NO POLE NO POLE x[1] = 0.1074 y2[1] (analytic) = 1.0057618383524221577531353112351 y2[1] (numeric) = 1.0065274739711474097436085525136 absolute error = 0.0007656356187252519904732412785 relative error = 0.076124942260631967462857117880994 % h = 0.0001 y1[1] (analytic) = 1.0057618383524221577531353112351 y1[1] (numeric) = 1.005761838352422157753138889136 absolute error = 3.5779009e-24 relative error = 3.5574037148407813290056373947457e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.3MB, time=46.36 NO POLE NO POLE x[1] = 0.1075 y2[1] (analytic) = 1.0057725626882794629743515263608 y2[1] (numeric) = 1.0065489176716950389725362869743 absolute error = 0.0007763549834155759981847606135 relative error = 0.077189914719933836063430023021088 % h = 0.0001 y1[1] (analytic) = 1.0057725626882794629743515263608 y1[1] (numeric) = 1.0057725626882794629743551525926 absolute error = 3.6262318e-24 relative error = 3.6054192911244519976351224170153e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.3MB, time=47.01 NO POLE NO POLE x[1] = 0.1076 y2[1] (analytic) = 1.0057832969664111330275444702404 y2[1] (numeric) = 1.0065703812568450416386991937575 absolute error = 0.0007870842904339086111547235171 relative error = 0.078255852210696820236808513225789 % h = 0.0001 y1[1] (analytic) = 1.0057832969664111330275444702404 y1[1] (numeric) = 1.0057832969664111330275481448026 absolute error = 3.6745622e-24 relative error = 3.6534333102200191791907616853759e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.3MB, time=47.68 NO POLE NO POLE x[1] = 0.1077 y2[1] (analytic) = 1.0057940411867098251314868946597 y2[1] (numeric) = 1.0065918647263827818907761094111 absolute error = 0.0007978235396729567592892147514 relative error = 0.079322754659753783804184428387132 % h = 0.0001 y1[1] (analytic) = 1.0057940411867098251314868946597 y1[1] (numeric) = 1.0057940411867098251314906175518 absolute error = 3.7228921e-24 relative error = 3.7014457707538791308158699851220e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.3MB, time=48.37 NO POLE NO POLE x[1] = 0.1078 y2[1] (analytic) = 1.0058047953490680970832814137484 y2[1] (numeric) = 1.0066133680800934250335686603271 absolute error = 0.0008085727310253279502872465787 relative error = 0.080390621993874063392173078924598 % h = 0.0001 y1[1] (analytic) = 1.0058047953490680970832814137484 y1[1] (numeric) = 1.0058047953490680970832851849698 absolute error = 3.7712214e-24 relative error = 3.7494565719297294952149096319252e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.3MB, time=49.05 NO POLE NO POLE x[1] = 0.1079 y2[1] (analytic) = 1.0058155594533784072594349260082 y2[1] (numeric) = 1.0066348913177619375301496096918 absolute error = 0.0008193318643835302707146836836 relative error = 0.081459454139763480729133778147125 % h = 0.0001 y1[1] (analytic) = 1.0058155594533784072594349260082 y1[1] (numeric) = 1.0058155594533784072594387455584 absolute error = 3.8195502e-24 relative error = 3.7974658117993092196978751651724e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.108 y2[1] (analytic) = 1.0058263334995331146169340305467 y2[1] (numeric) = 1.0066564344391730870040131928531 absolute error = 0.0008301009396399723870791623064 relative error = 0.082529251024064354951485020428877 % h = 0.0001 y1[1] (analytic) = 1.0058263334995331146169340305467 y1[1] (numeric) = 1.0058263334995331146169378984252 absolute error = 3.8678785e-24 relative error = 3.8454734889895337934726849230498e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.3MB, time=49.71 NO POLE NO POLE x[1] = 0.1081 y2[1] (analytic) = 1.0058371174874244786943214375069 y2[1] (numeric) = 1.0066779974441114422412274410842 absolute error = 0.0008408799566869635469060035773 relative error = 0.083600012573355514920010481434804 % h = 0.0001 y1[1] (analytic) = 1.0058371174874244786943214375069 y1[1] (numeric) = 1.0058371174874244786943253537132 absolute error = 3.9162063e-24 relative error = 3.8934796021274911200418880516526e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.3MB, time=50.38 NO POLE NO POLE x[1] = 0.1082 y2[1] (analytic) = 1.0058479114169446596127733726807 y2[1] (numeric) = 1.0066995803323613731925884937207 absolute error = 0.00085166891541671357981512104 relative error = 0.08467173871415231154615201371703 % h = 0.0001 y1[1] (analytic) = 1.0058479114169446596127733726807 y1[1] (numeric) = 1.0058479114169446596127773372142 absolute error = 3.9645335e-24 relative error = 3.9414840504218328830706231963024e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.3MB, time=51.05 NO POLE NO POLE x[1] = 0.1083 y2[1] (analytic) = 1.0058587152879857180771779762961 y2[1] (numeric) = 1.0067211831037070509757768986509 absolute error = 0.0008624678157213328985989223548 relative error = 0.08574442937290663012828580832834 % h = 0.0001 y1[1] (analytic) = 1.0058587152879857180771779762961 y1[1] (numeric) = 1.0058587152879857180771819891564 absolute error = 4.0128603e-24 relative error = 3.9894870313382776750315843983461e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.3MB, time=51.73 NO POLE NO POLE x[1] = 0.1084 y2[1] (analytic) = 1.0058695291004396153772146959678 y2[1] (numeric) = 1.0067428057579324478775159011375 absolute error = 0.0008732766574928325003012051697 relative error = 0.086818084476006902697977890118142 % h = 0.0001 y1[1] (analytic) = 1.0058695291004396153772146959678 y1[1] (numeric) = 1.0058695291004396153772187571543 absolute error = 4.0611865e-24 relative error = 4.0374883446682837367981651429046e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.3MB, time=52.41 NO POLE NO POLE x[1] = 0.1085 y2[1] (analytic) = 1.0058803528541982133884346737992 y2[1] (numeric) = 1.0067644482948213373557317209483 absolute error = 0.0008840954406231239672970471491 relative error = 0.087892703949778120376215111665762 % h = 0.0001 y1[1] (analytic) = 1.0058803528541982133884346737992 y1[1] (numeric) = 1.0058803528541982133884387833114 absolute error = 4.1095122e-24 relative error = 4.0854880884582417750806596107500e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.3MB, time=53.09 NO POLE NO POLE x[1] = 0.1086 y2[1] (analytic) = 1.005891186549153274573342127626 y2[1] (numeric) = 1.0067861107141572940417158177751 absolute error = 0.0008949241650040194683736901491 relative error = 0.088968287720481845739607807928072 % h = 0.0001 y1[1] (analytic) = 1.005891186549153274573342127626 y1[1] (numeric) = 1.0058911865491532745733462854633 absolute error = 4.1578373e-24 relative error = 4.1334861619217752433681840041726e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.3MB, time=53.77 NO POLE NO POLE x[1] = 0.1087 y2[1] (analytic) = 1.0059020301851964619824767263904 y2[1] (numeric) = 1.0068077930157236937422891449191 absolute error = 0.0009057628305272317598124185287 relative error = 0.090044835714316225196560270892142 % h = 0.0001 y1[1] (analytic) = 1.0059020301851964619824767263904 y1[1] (numeric) = 1.0059020301851964619824809325523 absolute error = 4.2061619e-24 relative error = 4.1814826631034875284546045052404e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.3MB, time=54.45 NO POLE NO POLE x[1] = 0.1088 y2[1] (analytic) = 1.0059128837622193392554969596347 y2[1] (numeric) = 1.0068294951993037134419683912209 absolute error = 0.0009166114370843741864714315862 relative error = 0.091122347857416001373405200709408 % h = 0.0001 y1[1] (analytic) = 1.0059128837622193392554969596347 y1[1] (numeric) = 1.0059128837622193392555012141207 absolute error = 4.2544860e-24 relative error = 4.2294775906316833457562816227405e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.3MB, time=55.11 NO POLE NO POLE x[1] = 0.1089 y2[1] (analytic) = 1.0059237472801133706222645011039 y2[1] (numeric) = 1.0068512172646803313051342112135 absolute error = 0.0009274699845669606828697101096 relative error = 0.092200824075852525510498286925634 % h = 0.0001 y1[1] (analytic) = 1.0059237472801133706222645011039 y1[1] (numeric) = 1.0059237472801133706222688039135 absolute error = 4.3028096e-24 relative error = 4.2774709431348410113432812690942e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.3MB, time=55.79 NO POLE NO POLE x[1] = 0.109 y2[1] (analytic) = 1.0059346207387699209039295664461 y2[1] (numeric) = 1.0068729592116363266782014434767 absolute error = 0.0009383384728664057742718770306 relative error = 0.093280264295633769868269070690092 % h = 0.0001 y1[1] (analytic) = 1.0059346207387699209039295664461 y1[1] (numeric) = 1.0059346207387699209039339175787 absolute error = 4.3511326e-24 relative error = 4.3254626198315734699280202758346e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.3MB, time=56.46 NO POLE NO POLE x[1] = 0.1091 y2[1] (analytic) = 1.005945504138080255514017265 y2[1] (numeric) = 1.006894721039954280091791317171 absolute error = 0.000949216901874024577774052171 relative error = 0.094360668442704340143224235939252 % h = 0.0001 y1[1] (analytic) = 1.005945504138080255514017265 y1[1] (numeric) = 1.0059455041380802555140216644551 absolute error = 4.3994551e-24 relative error = 4.3734527187628968528246891125008e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.3MB, time=57.14 NO POLE NO POLE x[1] = 0.1092 y2[1] (analytic) = 1.0059563974779355404595149456589 y2[1] (numeric) = 1.0069165027494165732629056467298 absolute error = 0.0009601052714810328033907010709 relative error = 0.095442036442945487893899474803192 % h = 0.0001 y1[1] (analytic) = 1.0059563974779355404595149456589 y1[1] (numeric) = 1.0059563974779355404595193934361 absolute error = 4.4477772e-24 relative error = 4.4214413379657011560604666450074e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.3MB, time=57.83 NO POLE NO POLE x[1] = 0.1093 y2[1] (analytic) = 1.0059673007582268423419605368001 y2[1] (numeric) = 1.0069383043398053890971030146874 absolute error = 0.0009710035815785467551424778873 relative error = 0.096524368222175122976756069598711 % h = 0.0001 y1[1] (analytic) = 1.0059673007582268423419605368001 y1[1] (numeric) = 1.0059673007582268423419650328988 absolute error = 4.4960987e-24 relative error = 4.4694282772523117901199284522462e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.3MB, time=58.51 NO POLE NO POLE x[1] = 0.1094 y2[1] (analytic) = 1.0059782139788451283585318802682 y2[1] (numeric) = 1.0069601258109027116906769426216 absolute error = 0.0009819118320575833321450623534 relative error = 0.097607663706147825992018331139314 % h = 0.0001 y1[1] (analytic) = 1.0059782139788451283585318802682 y1[1] (numeric) = 1.0059782139788451283585364246877 absolute error = 4.5444195e-24 relative error = 4.5174134358495812329657880335896e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.3MB, time=59.16 NO POLE NO POLE x[1] = 0.1095 y2[1] (analytic) = 1.0059891371396812663031370594024 y2[1] (numeric) = 1.0069819671624903263328360501892 absolute error = 0.0009928300228090600296989907868 relative error = 0.098691922820554860739448030082325 % h = 0.0001 y1[1] (analytic) = 1.0059891371396812663031370594024 y1[1] (numeric) = 1.0059891371396812663031416521423 absolute error = 4.5927399e-24 relative error = 4.5653971106074672756766218309236e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.3MB, time=59.84 NO POLE NO POLE x[1] = 0.1096 y2[1] (analytic) = 1.0060000702406260245675057210971 y2[1] (numeric) = 1.0070038283943498195078862022317 absolute error = 0.0010037581537237949403804811346 relative error = 0.099777145491024186684051955214565 % h = 0.0001 y1[1] (analytic) = 1.0060000702406260245675057210971 y1[1] (numeric) = 1.0060000702406260245675103621569 absolute error = 4.6410598e-24 relative error = 4.6133792007488636686689137336489e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.3MB, time=60.51 NO POLE NO POLE x[1] = 0.1097 y2[1] (analytic) = 1.0060110132815700721422813918831 y2[1] (numeric) = 1.0070257095062625788974146439307 absolute error = 0.0010146962246925067551332520476 relative error = 0.10086333164312047143171873019858 % h = 0.0001 y1[1] (analytic) = 1.0060110132815700721422813918831 y1[1] (numeric) = 1.0060110132815700721422860812622 absolute error = 4.6893791e-24 relative error = 4.6613596055011583055084532430424e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.3MB, time=61.20 NO POLE NO POLE x[1] = 0.1098 y2[1] (analytic) = 1.0060219662624039786181147880204 y2[1] (numeric) = 1.0070476104980097933824761239902 absolute error = 0.0010256442356058147643613359698 relative error = 0.10195048120234510321478101690938 % h = 0.0001 y1[1] (analytic) = 1.0060219662624039786181147880204 y1[1] (numeric) = 1.0060219662624039786181195257183 absolute error = 4.7376979e-24 relative error = 4.7093384228990591058049808797048e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.3MB, time=61.85 NO POLE NO POLE x[1] = 0.1099 y2[1] (analytic) = 1.006032929183018214186758119591 y2[1] (numeric) = 1.007069531369372453045781005824 absolute error = 0.001036602186354238859022886233 relative error = 0.10303859409413620338749923105644 % h = 0.0001 y1[1] (analytic) = 1.006032929183018214186758119591 y1[1] (numeric) = 1.0060329291830182141867629056072 absolute error = 4.7860162e-24 relative error = 4.7573156515727971615195838655554e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.3MB, time=62.51 NO POLE NO POLE x[1] = 0.11 y2[1] (analytic) = 1.0060439020433031496421603885802 y2[1] (numeric) = 1.0070914721201313491738853667271 absolute error = 0.0010475700768281995317249781469 relative error = 0.10412767024386863893146289305392 % h = 0.0001 y1[1] (analytic) = 1.0060439020433031496421603885802 y1[1] (numeric) = 1.0060439020433031496421652229141 absolute error = 4.8343339e-24 relative error = 4.8052911907535380662668580645539e-22 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; Iterations = 100 Total Elapsed Time = 1 Minutes 2 Seconds Elapsed Time(since restart) = 1 Minutes 2 Seconds Expected Time Remaining = 8 Hours 24 Minutes 12 Seconds Optimized Time Remaining = 8 Hours 23 Minutes 59 Seconds Time to Timeout = 13 Minutes 57 Seconds Percent Done = 0.2061 % > quit memory used=366.8MB, alloc=4.3MB, time=62.59