|\^/| 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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > centuries_in_millinium, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_dump_analytic, > glob_reached_optimal_h, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_warned2, > years_in_century, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_iter, > glob_look_poles, > glob_h, > glob_almost_1, > glob_current_iter, > glob_max_trunc_err, > glob_log10_abserr, > glob_last_good_h, > djd_debug2, > glob_log10relerr, > glob_start, > glob_optimal_start, > glob_max_hours, > glob_disp_incr, > glob_clock_start_sec, > days_in_year, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_large_float, > glob_hmax, > glob_optimal_done, > glob_no_eqs, > glob_hmin, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_initial_pass, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > sec_in_min, > glob_display_flag, > glob_dump, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_y1_init, > array_y2, > array_y1, > array_1st_rel_error, > array_pole, > array_y2_init, > array_type_pole, > array_x, > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y2_higher_work2, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work, > array_y1_higher_work, > array_y2_higher, > array_poles, > array_y1_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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr, glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter, glob_normmax, glob_warned2, years_in_century, hours_in_day, glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err, glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter, glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2, glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours, glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour, glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done, glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished, glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag, glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1, array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y2_higher_work2, array_real_pole, array_y1_set_initial, array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles, array_y1_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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > centuries_in_millinium, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_dump_analytic, > glob_reached_optimal_h, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_warned2, > years_in_century, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_iter, > glob_look_poles, > glob_h, > glob_almost_1, > glob_current_iter, > glob_max_trunc_err, > glob_log10_abserr, > glob_last_good_h, > djd_debug2, > glob_log10relerr, > glob_start, > glob_optimal_start, > glob_max_hours, > glob_disp_incr, > glob_clock_start_sec, > days_in_year, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_large_float, > glob_hmax, > glob_optimal_done, > glob_no_eqs, > glob_hmin, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_initial_pass, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > sec_in_min, > glob_display_flag, > glob_dump, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_y1_init, > array_y2, > array_y1, > array_1st_rel_error, > array_pole, > array_y2_init, > array_type_pole, > array_x, > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y2_higher_work2, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work, > array_y1_higher_work, > array_y2_higher, > array_poles, > array_y1_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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr, glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter, glob_normmax, glob_warned2, years_in_century, hours_in_day, glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err, glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter, glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2, glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours, glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour, glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done, glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished, glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag, glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1, array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y2_higher_work2, array_real_pole, array_y1_set_initial, array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles, array_y1_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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > centuries_in_millinium, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_dump_analytic, > glob_reached_optimal_h, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_warned2, > years_in_century, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_iter, > glob_look_poles, > glob_h, > glob_almost_1, > glob_current_iter, > glob_max_trunc_err, > glob_log10_abserr, > glob_last_good_h, > djd_debug2, > glob_log10relerr, > glob_start, > glob_optimal_start, > glob_max_hours, > glob_disp_incr, > glob_clock_start_sec, > days_in_year, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_large_float, > glob_hmax, > glob_optimal_done, > glob_no_eqs, > glob_hmin, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_initial_pass, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > sec_in_min, > glob_display_flag, > glob_dump, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_y1_init, > array_y2, > array_y1, > array_1st_rel_error, > array_pole, > array_y2_init, > array_type_pole, > array_x, > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y2_higher_work2, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work, > array_y1_higher_work, > array_y2_higher, > array_poles, > array_y1_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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr, glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter, glob_normmax, glob_warned2, years_in_century, hours_in_day, glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err, glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter, glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2, glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours, glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour, glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done, glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished, glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag, glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1, array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y2_higher_work2, array_real_pole, array_y1_set_initial, array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles, array_y1_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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > centuries_in_millinium, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_dump_analytic, > glob_reached_optimal_h, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_warned2, > years_in_century, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_iter, > glob_look_poles, > glob_h, > glob_almost_1, > glob_current_iter, > glob_max_trunc_err, > glob_log10_abserr, > glob_last_good_h, > djd_debug2, > glob_log10relerr, > glob_start, > glob_optimal_start, > glob_max_hours, > glob_disp_incr, > glob_clock_start_sec, > days_in_year, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_large_float, > glob_hmax, > glob_optimal_done, > glob_no_eqs, > glob_hmin, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_initial_pass, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > sec_in_min, > glob_display_flag, > glob_dump, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_y1_init, > array_y2, > array_y1, > array_1st_rel_error, > array_pole, > array_y2_init, > array_type_pole, > array_x, > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y2_higher_work2, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work, > array_y1_higher_work, > array_y2_higher, > array_poles, > array_y1_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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr, glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter, glob_normmax, glob_warned2, years_in_century, hours_in_day, glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err, glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter, glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2, glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours, glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour, glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done, glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished, glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag, glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1, array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y2_higher_work2, array_real_pole, array_y1_set_initial, array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles, array_y1_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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > centuries_in_millinium, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_dump_analytic, > glob_reached_optimal_h, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_warned2, > years_in_century, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_iter, > glob_look_poles, > glob_h, > glob_almost_1, > glob_current_iter, > glob_max_trunc_err, > glob_log10_abserr, > glob_last_good_h, > djd_debug2, > glob_log10relerr, > glob_start, > glob_optimal_start, > glob_max_hours, > glob_disp_incr, > glob_clock_start_sec, > days_in_year, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_large_float, > glob_hmax, > glob_optimal_done, > glob_no_eqs, > glob_hmin, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_initial_pass, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > sec_in_min, > glob_display_flag, > glob_dump, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_y1_init, > array_y2, > array_y1, > array_1st_rel_error, > array_pole, > array_y2_init, > array_type_pole, > array_x, > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y2_higher_work2, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work, > array_y1_higher_work, > array_y2_higher, > array_poles, > array_y1_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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr, glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter, glob_normmax, glob_warned2, years_in_century, hours_in_day, glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err, glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter, glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2, glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours, glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour, glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done, glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished, glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag, glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1, array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y2_higher_work2, array_real_pole, array_y1_set_initial, array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles, array_y1_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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > centuries_in_millinium, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_dump_analytic, > glob_reached_optimal_h, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_warned2, > years_in_century, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_iter, > glob_look_poles, > glob_h, > glob_almost_1, > glob_current_iter, > glob_max_trunc_err, > glob_log10_abserr, > glob_last_good_h, > djd_debug2, > glob_log10relerr, > glob_start, > glob_optimal_start, > glob_max_hours, > glob_disp_incr, > glob_clock_start_sec, > days_in_year, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_large_float, > glob_hmax, > glob_optimal_done, > glob_no_eqs, > glob_hmin, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_initial_pass, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > sec_in_min, > glob_display_flag, > glob_dump, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_y1_init, > array_y2, > array_y1, > array_1st_rel_error, > array_pole, > array_y2_init, > array_type_pole, > array_x, > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y2_higher_work2, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work, > array_y1_higher_work, > array_y2_higher, > array_poles, > array_y1_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre add $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp2[1] := (array_tmp1[1] - (array_const_2D0[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 diff $eq_no = 2 i = 1 > array_tmp4[1] := array_y2_higher[6,1]; > #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 add $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D0[2] + array_y1[2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp2[2] := (array_tmp1[2] - (array_const_2D0[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 diff $eq_no = 2 i = 2 > array_tmp4[2] := array_y2_higher[6,2]; > #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 add $eq_no = 1 i = 3 > array_tmp1[3] := array_const_0D0[3] + array_y1[3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp2[3] := (array_tmp1[3] - (array_const_2D0[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 diff $eq_no = 2 i = 3 > array_tmp4[3] := array_y2_higher[6,3]; > #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 add $eq_no = 1 i = 4 > array_tmp1[4] := array_const_0D0[4] + array_y1[4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp2[4] := (array_tmp1[4] - (array_const_2D0[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 diff $eq_no = 2 i = 4 > array_tmp4[4] := array_y2_higher[6,4]; > #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 add $eq_no = 1 i = 5 > array_tmp1[5] := array_const_0D0[5] + array_y1[5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp2[5] := (array_tmp1[5] - (array_const_2D0[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 diff $eq_no = 2 i = 5 > array_tmp4[5] := array_y2_higher[6,5]; > #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 add $eq_no = 1 > array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk]; > #emit sub $eq_no = 1 > array_tmp2[kkk] := (array_tmp1[kkk] - (array_const_2D0[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 diff $eq_no = 2 > array_tmp4[kkk] := array_y2_higher[6,kkk]; > #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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr, glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter, glob_normmax, glob_warned2, years_in_century, hours_in_day, glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err, glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter, glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2, glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours, glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour, glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done, glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished, glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag, glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1, array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y2_higher_work2, array_real_pole, array_y1_set_initial, array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles, array_y1_higher, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; array_tmp2[1] := array_tmp1[1] - array_const_2D0[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] := array_y2_higher[6, 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_const_0D0[2] + array_y1[2]; array_tmp2[2] := array_tmp1[2] - array_const_2D0[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] := array_y2_higher[6, 2]; 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_const_0D0[3] + array_y1[3]; array_tmp2[3] := array_tmp1[3] - array_const_2D0[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] := array_y2_higher[6, 3]; 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_const_0D0[4] + array_y1[4]; array_tmp2[4] := array_tmp1[4] - array_const_2D0[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] := array_y2_higher[6, 4]; 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_const_0D0[5] + array_y1[5]; array_tmp2[5] := array_tmp1[5] - array_const_2D0[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] := array_y2_higher[6, 5]; 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_const_0D0[kkk] + array_y1[kkk]; array_tmp2[kkk] := array_tmp1[kkk] - array_const_2D0[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] := array_y2_higher[6, kkk]; 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 + sin(x); > end; exact_soln_y1 := proc(x) 2.0 + sin(x) end proc > exact_soln_y2 := proc(x) > 2.0 - cos(x); > end; exact_soln_y2 := proc(x) 2.0 - cos(x) end proc > exact_soln_y2p := proc(x) > sin(x); > end; exact_soln_y2p := proc(x) sin(x) end proc > exact_soln_y2pp := proc(x) > cos(x); > end; exact_soln_y2pp := proc(x) cos(x) end proc > exact_soln_y2ppp := proc(x) > -sin(x); > end; exact_soln_y2ppp := proc(x) -sin(x) end proc > exact_soln_y2pppp := proc(x) > -cos(x); > end; exact_soln_y2pppp := proc(x) -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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > centuries_in_millinium, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_dump_analytic, > glob_reached_optimal_h, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_warned2, > years_in_century, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_iter, > glob_look_poles, > glob_h, > glob_almost_1, > glob_current_iter, > glob_max_trunc_err, > glob_log10_abserr, > glob_last_good_h, > djd_debug2, > glob_log10relerr, > glob_start, > glob_optimal_start, > glob_max_hours, > glob_disp_incr, > glob_clock_start_sec, > days_in_year, > min_in_hour, > glob_max_sec, > glob_relerr, > glob_large_float, > glob_hmax, > glob_optimal_done, > glob_no_eqs, > glob_hmin, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_initial_pass, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > sec_in_min, > glob_display_flag, > glob_dump, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_y1_init, > array_y2, > array_y1, > array_1st_rel_error, > array_pole, > array_y2_init, > array_type_pole, > array_x, > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y2_set_initial, > array_complex_pole, > array_y1_higher_work2, > array_y2_higher_work2, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work, > array_y1_higher_work, > array_y2_higher, > array_poles, > array_y1_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > DEBUGMASSIVE := 4; > glob_max_terms := 30; > INFO := 2; > DEBUGL := 3; > glob_iolevel := 5; > MAX_UNCHANGED := 10; > glob_warned := false; > glob_unchanged_h_cnt := 0; > centuries_in_millinium := 10.0; > glob_subiter_method := 3; > glob_optimal_clock_start_sec := 0.0; > glob_log10_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_reached_optimal_h := false; > djd_debug := true; > glob_max_opt_iter := 10; > glob_normmax := 0.0; > glob_warned2 := false; > years_in_century := 100.0; > hours_in_day := 24.0; > glob_log10normmin := 0.1; > glob_smallish_float := 0.1e-100; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_iter := 1000; > glob_look_poles := false; > glob_h := 0.1; > glob_almost_1 := 0.9990; > glob_current_iter := 0; > glob_max_trunc_err := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_last_good_h := 0.1; > djd_debug2 := true; > glob_log10relerr := 0.0; > glob_start := 0; > glob_optimal_start := 0.0; > glob_max_hours := 0.0; > glob_disp_incr := 0.1; > glob_clock_start_sec := 0.0; > days_in_year := 365.0; > min_in_hour := 60.0; > glob_max_sec := 10000.0; > glob_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmax := 1.0; > glob_optimal_done := false; > glob_no_eqs := 0; > glob_hmin := 0.00000000001; > glob_optimal_expect_sec := 0.1; > glob_log10abserr := 0.0; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_small_float := 0.1e-50; > glob_abserr := 0.1e-10; > glob_hmin_init := 0.001; > glob_not_yet_start_msg := true; > glob_clock_sec := 0.0; > glob_curr_iter_when_opt := 0; > glob_initial_pass := true; > glob_not_yet_finished := true; > glob_percent_done := 0.0; > glob_max_minutes := 0.0; > sec_in_min := 60.0; > glob_display_flag := true; > glob_dump := false; > glob_html_log := true; > #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/mtest9_revpostode.ode#################"); > omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);"); > 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 := 0.5;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > 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,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"glob_subiter_method := 3;"); > 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 + sin(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,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"-sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_y1_init:= Array(1..(max_terms + 1),[]); > array_y2:= Array(1..(max_terms + 1),[]); > array_y1:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_norms:= 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_m1:= Array(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_y2_higher_work2 := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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_y1_init[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_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_m1[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_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 <=6 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 <=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 <=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 <=6 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 <= 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 <=6 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 > ; > 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_y1_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_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_5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_5[1] := 5; > 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_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_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 := 0.5; > x_end := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > glob_subiter_method := 3; > #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] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := true; > array_y2_set_initial[1,5] := true; > 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 := 5; > #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 := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[6,iii] := array_y2_higher[6,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 := 6; > 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 := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > 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 := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > 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 := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 3; > #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 := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 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 := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_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 := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 4; > #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 := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 3; > #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 := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_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 := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_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 := 2; > calc_term := 5; > #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 := 5; > #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 := 2; > calc_term := 4; > #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 := 4; > #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 := 2; > calc_term := 3; > #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 := 3; > #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 := 2; > calc_term := 2; > #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 := 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 := 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 := 6; > #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 := 6; > #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 := 5; > #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 := 5; > #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 := 4; > #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 := 4; > #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 := 3; > #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 := 3; > #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) = y1 - 2.0;"); > omniout_str(INFO,"diff(y1,x,1) = diff(y2,x,5);"); > 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,"2012-06-13T03:52:26-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest9_rev") > ; > logitem_str(html_log_file,"diff(y2,x,1) = y1 - 2.0;") > ; > 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,"mtest9_rev diffeq.mxt") > ; > logitem_str(html_log_file,"mtest9_rev 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) = diff(y2,x,5);") > ; > 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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, DEBUGL, glob_iolevel, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, centuries_in_millinium, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_relerr, glob_dump_analytic, glob_reached_optimal_h, djd_debug, glob_max_opt_iter, glob_normmax, glob_warned2, years_in_century, hours_in_day, glob_log10normmin, glob_smallish_float, glob_max_rel_trunc_err, glob_max_iter, glob_look_poles, glob_h, glob_almost_1, glob_current_iter, glob_max_trunc_err, glob_log10_abserr, glob_last_good_h, djd_debug2, glob_log10relerr, glob_start, glob_optimal_start, glob_max_hours, glob_disp_incr, glob_clock_start_sec, days_in_year, min_in_hour, glob_max_sec, glob_relerr, glob_large_float, glob_hmax, glob_optimal_done, glob_no_eqs, glob_hmin, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_curr_iter_when_opt, glob_initial_pass, glob_not_yet_finished, glob_percent_done, glob_max_minutes, sec_in_min, glob_display_flag, glob_dump, glob_html_log, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_y1_init, array_y2, array_y1, array_1st_rel_error, array_pole, array_y2_init, array_type_pole, array_x, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y2_set_initial, array_complex_pole, array_y1_higher_work2, array_y2_higher_work2, array_real_pole, array_y1_set_initial, array_y2_higher_work, array_y1_higher_work, array_y2_higher, array_poles, array_y1_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; DEBUGMASSIVE := 4; glob_max_terms := 30; INFO := 2; DEBUGL := 3; glob_iolevel := 5; MAX_UNCHANGED := 10; glob_warned := false; glob_unchanged_h_cnt := 0; centuries_in_millinium := 10.0; glob_subiter_method := 3; glob_optimal_clock_start_sec := 0.; glob_log10_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_reached_optimal_h := false; djd_debug := true; glob_max_opt_iter := 10; glob_normmax := 0.; glob_warned2 := false; years_in_century := 100.0; hours_in_day := 24.0; glob_log10normmin := 0.1; glob_smallish_float := 0.1*10^(-100); glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_iter := 1000; glob_look_poles := false; glob_h := 0.1; glob_almost_1 := 0.9990; glob_current_iter := 0; glob_max_trunc_err := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; djd_debug2 := true; glob_log10relerr := 0.; glob_start := 0; glob_optimal_start := 0.; glob_max_hours := 0.; glob_disp_incr := 0.1; glob_clock_start_sec := 0.; days_in_year := 365.0; min_in_hour := 60.0; glob_max_sec := 10000.0; glob_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmax := 1.0; glob_optimal_done := false; glob_no_eqs := 0; glob_hmin := 0.1*10^(-10); glob_optimal_expect_sec := 0.1; glob_log10abserr := 0.; glob_iter := 0; glob_orig_start_sec := 0.; glob_small_float := 0.1*10^(-50); glob_abserr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_not_yet_start_msg := true; glob_clock_sec := 0.; glob_curr_iter_when_opt := 0; glob_initial_pass := true; glob_not_yet_finished := true; glob_percent_done := 0.; glob_max_minutes := 0.; sec_in_min := 60.0; glob_display_flag := true; glob_dump := false; glob_html_log := true; 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/mtest9_revpostode.ode#################"); omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"); 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 := 0.5;"); omniout_str(ALWAYS, "x_end := 10.0;"); 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, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "glob_subiter_method := 3;"); 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 + sin(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, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "-sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_last_rel_error := Array(1 .. max_terms + 1, []); array_y1_init := Array(1 .. max_terms + 1, []); array_y2 := Array(1 .. max_terms + 1, []); array_y1 := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_norms := 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_m1 := Array(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_y2_higher_work2 := Array(1 .. 7, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y2_higher_work := Array(1 .. 7, 1 .. max_terms + 1, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_higher := Array(1 .. 7, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); 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_y1_init[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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_m1[term] := 0.; term := term + 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 <= 6 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 <= 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 <= 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 <= 6 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 <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_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_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_y1_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_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_5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5[term] := 0.; term := term + 1 end do; array_const_5[1] := 5; 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_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_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 := 0.5; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[4] := exact_soln_y2ppp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; 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] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := true; array_y2_set_initial[1, 5] := true; 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 := 5; 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 := 5; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 6; 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 := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; 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 := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; 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 := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 3; 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 := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 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 := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_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 := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 4; 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 := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 3; 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 := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_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 := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_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 := 2; calc_term := 5; 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 := 5; 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 := 2; calc_term := 4; 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 := 4; 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 := 2; calc_term := 3; 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 := 3; 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 := 2; calc_term := 2; 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 := 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 := 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 := 6; 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 := 6; 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 := 5; 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 := 5; 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 := 4; 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 := 4; 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 := 3; 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 := 3; 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) = y1 - 2.0;"); omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"); 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, "2012-06-13T03:52:26-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest9_rev"); logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"); 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, "mtest9_rev diffeq.mxt"); logitem_str(html_log_file, "mtest9_rev 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) = diff(y2,x,5);"); 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/mtest9_revpostode.ode################# diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; #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 + sin(x); end; exact_soln_y2 := proc(x) 2.0 - cos(x); end; exact_soln_y2p := proc(x) sin(x); end; exact_soln_y2pp := proc(x) cos(x); end; exact_soln_y2ppp := proc(x) -sin(x); end; exact_soln_y2pppp := proc(x) -cos(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.0001 x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5001 y2[1] (analytic) = 1.1224653850513206057226212384082 y2[1] (numeric) = 1.1224653850513206057225812850612 absolute error = 3.99533470e-23 relative error = 3.5594279816631744060018373993147e-21 % h = 0.0001 y1[1] (analytic) = 2.4795132944631180827612490419532 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 8.77558589150824879611067376e-05 relative error = 0.0035392372814070356873465959087753 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5002 y2[1] (analytic) = 1.122513340768360069735529546726 y2[1] (numeric) = 1.122513340768360069734251000617 absolute error = 1.2785461090e-21 relative error = 1.1390030412688329777726287466527e-19 % h = 0.0001 y1[1] (analytic) = 2.4796010455269002246139734402722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001755069226972243406855050566 relative error = 0.0070780306781137923396978378563839 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.19 NO POLE NO POLE x[1] = 0.5003 y2[1] (analytic) = 1.1225613052602661187524483331957 y2[1] (numeric) = 1.1225613052602661187427390775074 absolute error = 9.7092556883e-21 relative error = 8.6491986164166834930999012427343e-19 % h = 0.0001 y1[1] (analytic) = 2.4796887917946719151943709705102 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002632531904689149210830352946 relative error = 0.010616380222390154323420137410111 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5004 y2[1] (analytic) = 1.122609278526559107854716811747 y2[1] (numeric) = 1.122609278526559107813800840139 absolute error = 4.09159716080e-20 relative error = 3.6447205978648959407660893371546e-18 % h = 0.0001 y1[1] (analytic) = 2.479776533265555691825455945761 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003509946613526915521680105454 relative error = 0.014154285946503230345708760152732 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5005 y2[1] (analytic) = 1.1226572605667593043798048685764 y2[1] (numeric) = 1.122657260566759304254935423881 absolute error = 1.248694446954e-19 relative error = 1.1122668429753996493912495105327e-17 % h = 0.0001 y1[1] (analytic) = 2.4798642699386741397991217786374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004387313344711395258338434218 relative error = 0.017691747882717353010916621593082 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5006 y2[1] (analytic) = 1.1227052513803868879261103887678 y2[1] (numeric) = 1.1227052513803868876153857750655 absolute error = 3.107246137023e-19 relative error = 2.7676419373674286810216521185989e-17 % h = 0.0001 y1[1] (analytic) = 2.4799520018131498923849151283452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005264632089468921116271931296 relative error = 0.021228766063294078377159362912004 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=0.40 NO POLE NO POLE x[1] = 0.5007 y2[1] (analytic) = 1.1227532509669619503577574603049 y2[1] (numeric) = 1.1227532509669619496861386509872 absolute error = 6.716188093177e-19 relative error = 5.9818914684885023123308063921464e-17 % h = 0.0001 y1[1] (analytic) = 2.4800397288881056308388095679803 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006141902839026305655216327647 relative error = 0.024765340520492185513196598099757 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5008 y2[1] (analytic) = 1.1228012593260044958093954554259 y2[1] (numeric) = 1.1228012593260044944999246199035 absolute error = 1.3094708355224e-18 relative error = 1.1662534439162007869017965741049e-16 % h = 0.0001 y1[1] (analytic) = 2.4801274511626640844119787719614 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007019125584610841386908367458 relative error = 0.02830147128656767605558922409793 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5009 y2[1] (analytic) = 1.122849276457034440690998989273 y2[1] (numeric) = 1.1228492764570344383312180610346 absolute error = 2.3597809282384e-18 relative error = 2.1016007915900335475301034839687e-16 % h = 0.0001 y1[1] (analytic) = 2.4802151686359480303595692235113 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007896300317450300862812882957 relative error = 0.031837158393773773766132685611939 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.501 y2[1] (analytic) = 1.1228973023595716136926687557886 y2[1] (numeric) = 1.1228973023595716096962371645635 absolute error = 3.9964315912251e-18 relative error = 3.5590357041799818917528935659069e-16 % h = 0.0001 y1[1] (analytic) = 2.4803028813070802939494724420977 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008773427028772936761845068821 relative error = 0.035372401874360924089566086208289 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=3.9MB, time=0.62 x[1] = 0.5011 y2[1] (analytic) = 1.1229453370331357557894332408103 y2[1] (numeric) = 1.1229453370331357493529439316358 absolute error = 6.4364893091745e-18 relative error = 5.7317921869464717621046234700062e-16 % h = 0.0001 y1[1] (analytic) = 2.4803905891751837484710967307476 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000965050570980748197808795532 relative error = 0.038907201760576793711557037472634 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5012 y2[1] (analytic) = 1.1229933804772465202460513123167 y2[1] (numeric) = 1.1229933804772465103010441743599 absolute error = 9.9450071379568e-18 relative error = 8.8558021007482691157362098073858e-16 % h = 0.0001 y1[1] (analytic) = 2.4804782922393813152441384431453 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0010527536351783149708505079297 relative error = 0.04244155808466627011696213787216 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5013 y2[1] (analytic) = 1.1230414326914234726218156877758 y2[1] (numeric) = 1.1230414326914234577819875158068 absolute error = 1.48398281719690e-17 relative error = 1.3213963207398883990633889562694e-15 % h = 0.0001 y1[1] (analytic) = 2.4805659904987959636273527704284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0011404518945929633540648352128 relative error = 0.045975470878871461148362973176003 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5014 y2[1] (analytic) = 1.123089493675186090775357278548 y2[1] (numeric) = 1.1230894936751860692789673900104 absolute error = 2.14963898885376e-17 relative error = 1.9140406895084596337380334996386e-15 % h = 0.0001 y1[1] (analytic) = 2.4806536839525507110273240475931 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0012281453483477107540361123775 relative error = 0.049508940175431694564877530195195 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5015 y2[1] (analytic) = 1.1231375634280537648694504112957 y2[1] (numeric) = 1.1231375634280537345169210419673 absolute error = 3.03525293693284e-17 relative error = 2.7024765583198954362990474455866e-15 % h = 0.0001 y1[1] (analytic) = 2.4807413725997686229072355794206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.001315833995565622633947644205 relative error = 0.05304196600658351760124691565663 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=0.83 NO POLE NO POLE x[1] = 0.5016 y2[1] (analytic) = 1.1231856419495457973758189263517 y2[1] (numeric) = 1.1231856419495457554625295276368 absolute error = 4.19132893987149e-17 relative error = 3.7316439805947654034543240004214e-15 % h = 0.0001 y1[1] (analytic) = 2.4808290564395728127956389858385 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0014035178353698125223510506229 relative error = 0.056574548404560696527197272142876 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5017 y2[1] (analytic) = 1.123233729239181403079943152998 y2[1] (numeric) = 1.1232337292391813463242177139408 absolute error = 5.67557254390572e-17 relative error = 5.0528864974078458410914509585353e-15 % h = 0.0001 y1[1] (analytic) = 2.4809167354710864422952230666275 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0014911968668834420219351314119 relative error = 0.060106687401594216207076782917388 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5018 y2[1] (analytic) = 1.1232818252964797090858677616068 y2[1] (numeric) = 1.1232818252964796335521542787641 absolute error = 7.55337134828427e-17 relative error = 6.7243777814090675165908313209214e-15 % h = 0.0001 y1[1] (analytic) = 2.4810044096934327210915821853874 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0015788710892297208182942501718 relative error = 0.063638383029912279659767657636522 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5019 y2[1] (analytic) = 1.1233299301209597548210104925963 y2[1] (numeric) = 1.1233299301209596558382517109542 absolute error = 9.89827587816421e-17 relative error = 8.8115482484281063216010204630400e-15 % h = 0.0001 y1[1] (analytic) = 2.4810920791057349069619841726739 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0016665405015319066886962374583 relative error = 0.067169635321740307618872990881736 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=3.9MB, time=1.05 NO POLE NO POLE x[1] = 0.502 y2[1] (analytic) = 1.1233780437121404920409717621522 y2[1] (numeric) = 1.1233780437121403641161663103213 absolute error = 1.279248054518309e-16 relative error = 1.1387511636698049527321551304247e-14 % h = 0.0001 y1[1] (analytic) = 2.4811797437071163057841377482187 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0017542051029133055108498130031 relative error = 0.070700444309300938093178385518425 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5021 y2[1] (analytic) = 1.1234261660695407848343451446679 y2[1] (numeric) = 1.1234261660695406215612981876383 absolute error = 1.632730469570296e-16 relative error = 1.4533491553633876808755916091875e-14 % h = 0.0001 y1[1] (analytic) = 2.4812674034967002715449594621449 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0018418648924972712716715269293 relative error = 0.074230810024814025927388232900411 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5022 y2[1] (analytic) = 1.1234742971926794096275287318546 y2[1] (numeric) = 1.1234742971926792035907912646409 absolute error = 2.060367374672137e-16 relative error = 1.8339247990101347662833473303597e-14 % h = 0.0001 y1[1] (analytic) = 2.4813550584736102063493401550904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0019295198694072060760522198748 relative error = 0.077760732500496642363136542000036 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5023 y2[1] (analytic) = 1.1235224370810750551895373684732 y2[1] (numeric) = 1.1235224370810747978635332740275 absolute error = 2.573260040944457e-16 relative error = 2.2903503802112024190229846458462e-14 % h = 0.0001 y1[1] (analytic) = 2.4814427086369695604289109371521 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0020171700327665601556230019365 relative error = 0.081290211768563074600272209580537 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=3.9MB, time=1.27 NO POLE NO POLE x[1] = 0.5024 y2[1] (analytic) = 1.12357058573424632263681576464 y2[1] (numeric) = 1.1235705857342460042801557594592 absolute error = 3.183566600051808e-16 relative error = 2.8334371159880153120626016900052e-14 % h = 0.0001 y1[1] (analytic) = 2.4815303539859018321508086855622 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0021048153816988318775207503466 relative error = 0.084819247861224825358418623499678 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5025 y2[1] (analytic) = 1.1236187431517117254380524846586 y2[1] (numeric) = 1.1236187431517113349830340755598 absolute error = 3.904550184090988e-16 relative error = 3.4749777964177241591693042711944e-14 % h = 0.0001 y1[1] (analytic) = 2.4816179945195305680264410610091 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0021924559153275677531531257935 relative error = 0.088347840810690612438807491314677 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5026 y2[1] (analytic) = 1.1236669093329896894189948123286 y2[1] (numeric) = 1.1236669093329892143562873879159 absolute error = 4.750627074244127e-16 relative error = 4.2277894229920022616853460099026e-14 % h = 0.0001 y1[1] (analytic) = 2.4817056302369793627202510425165 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0022800916327763624469631073009 relative error = 0.091875990649166368286386786435399 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5027 y2[1] (analytic) = 1.1237150842775985527672644926845 y2[1] (numeric) = 1.1237150842775979790257786730768 absolute error = 5.737414858196077e-16 relative error = 5.1057558436927830426879629990958e-14 % h = 0.0001 y1[1] (analytic) = 2.4817932611373718590584809807915 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0023677225331688587851930455759 relative error = 0.095403697408855239552202703992763 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=3.9MB, time=1.49 NO POLE NO POLE x[1] = 0.5028 y2[1] (analytic) = 1.1237632679850565660371743501153 y2[1] (numeric) = 1.1237632679850558778591147185545 absolute error = 6.881780596315608e-16 relative error = 6.1238703847785133805350909704015e-14 % h = 0.0001 y1[1] (analytic) = 2.4818808872198317480379361699548 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0024553486156287477646482347392 relative error = 0.098930961121957586656055518714595 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5029 y2[1] (analytic) = 1.123811460454881892154545782817 y2[1] (numeric) = 1.1238114604548810719656461228238 absolute error = 8.201888996599932e-16 relative error = 7.2982784792745193004855153482851e-14 % h = 0.0001 y1[1] (analytic) = 2.4819685084834827688347479375655 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0025429698792797685614600023499 relative error = 0.10245778182067098334942923710964 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.503 y2[1] (analytic) = 1.1238596616865926064215271335312 y2[1] (numeric) = 1.1238596616865916346964672953222 absolute error = 9.717250598382090e-16 relative error = 8.6463202921610960949418515093497e-14 % h = 0.0001 y1[1] (analytic) = 2.4820561249274487088131362528522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0026305863232457085398483176366 relative error = 0.10598415953719021627869493626097 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5031 y2[1] (analytic) = 1.1239078716797066965214129365188 y2[1] (numeric) = 1.1239078716797055516444164564499 absolute error = 1.1448769964800689e-15 relative error = 1.0186573342252896175921696720981e-13 % h = 0.0001 y1[1] (analytic) = 2.4821437365508534035341718530639 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0027181979466504032608839178483 relative error = 0.10951009430370728454858768163501 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=30.5MB, alloc=3.9MB, time=1.71 x[1] = 0.5032 y2[1] (analytic) = 1.1239560904337420625234640407234 y2[1] (numeric) = 1.1239560904337407206440756375698 absolute error = 1.3418793884031536e-15 relative error = 1.1938895120763245302642408999210e-13 % h = 0.0001 y1[1] (analytic) = 2.4822313433528207367645378878518 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0028058047486177364912499526362 relative error = 0.11303558615241139928595691624867 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5033 y2[1] (analytic) = 1.1240043179482165168877286090746 y2[1] (numeric) = 1.1240043179482149517717706810076 absolute error = 1.5651159579280670e-15 relative error = 1.3924465706546980840657569167657e-13 % h = 0.0001 y1[1] (analytic) = 2.4823189453324746404852910815948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0028934067282716402120031463792 relative error = 0.11656063511548898320379021363783 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5034 y2[1] (analytic) = 1.1240525542226477844698639938838 y2[1] (numeric) = 1.1240525542226459673455712400517 absolute error = 1.8171242927538321e-15 relative error = 1.6165830378015434572126989312331e-13 % h = 0.0001 y1[1] (analytic) = 2.4824065424889390949006224135825 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0029810038847360946273344783669 relative error = 0.12008524122512367016551028714358 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5035 y2[1] (analytic) = 1.1241007992565535025259594882828 y2[1] (numeric) = 1.1241007992565514019252907789532 absolute error = 2.1006006687093296e-15 relative error = 1.8686942221717160723696120595262e-13 % h = 0.0001 y1[1] (analytic) = 2.4824941348213381284466173159652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0030685962171351281733293807496 relative error = 0.12360940451349630474954514789207 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5036 y2[1] (analytic) = 1.1241490530494512207173599536599 y2[1] (numeric) = 1.124149053049448802312486572926 absolute error = 2.4184048733807339e-15 relative error = 2.1513204737578055642577029106497e-13 % h = 0.0001 y1[1] (analytic) = 2.4825817223287958178000153893858 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0031561837245928175267274541702 relative error = 0.12713312501278494181417130409372 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=3.9MB, time=1.92 NO POLE NO POLE x[1] = 0.5037 y2[1] (analytic) = 1.1241973156008584011154903230418 y2[1] (numeric) = 1.1241973156008556275504597081467 absolute error = 2.7735650306148951e-15 relative error = 2.4671514440794465231405135742305e-13 % h = 0.0001 y1[1] (analytic) = 2.4826693050104362878869696362058 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0032437664062332876136817009902 relative error = 0.13065640275516484606262989421157 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5038 y2[1] (analytic) = 1.1242455869102924182066809803753 y2[1] (numeric) = 1.1242455869102892489242550817546 absolute error = 3.1692824258986207e-15 relative error = 2.8190303460372925576313503835395e-13 % h = 0.0001 y1[1] (analytic) = 2.4827568828653837118918052112356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.00333134426118071161851727602 relative error = 0.13417923777280849160851564650062 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5039 y2[1] (analytic) = 1.1242938669772705588969940156605 y2[1] (numeric) = 1.1242938669772669499606614018517 absolute error = 3.6089363326138088e-15 relative error = 3.2099582134310169248261945844324e-13 % h = 0.0001 y1[1] (analytic) = 2.4828444558927623112657776898846 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.003418917288559310992489754669 relative error = 0.1377016300978855615414385576659 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.504 y2[1] (analytic) = 1.1243421558013100225170503558855 y2[1] (numeric) = 1.1243421558013059264282111875028 absolute error = 4.0960888391683827e-15 relative error = 3.6430981601407016810339461234989e-13 % h = 0.0001 y1[1] (analytic) = 2.4829320240916963557358308536409 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0035064854874933554625429184253 relative error = 0.14122357976256294749295818319025 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.0MB, time=2.14 NO POLE NO POLE x[1] = 0.5041 y2[1] (analytic) = 1.1243904533819279208268577717167 y2[1] (numeric) = 1.1243904533819232863371807687354 absolute error = 4.6344896770029813e-15 relative error = 4.1217796389709817043255671342151e-13 % h = 0.0001 y1[1] (analytic) = 2.4830195874613101633133539927949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0035940488571071630400660575793 relative error = 0.14474508679900474920279043209641 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5042 y2[1] (analytic) = 1.1244387597186412780206397598942 y2[1] (numeric) = 1.1244387597186360499395902865397 absolute error = 5.2280810494733545e-15 relative error = 4.6495027001573057100556050862084e-13 % h = 0.0001 y1[1] (analytic) = 2.4831071460007281003029387263179 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0036816073965251000296507911023 relative error = 0.14826615123937227408528675881179 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5043 y2[1] (analytic) = 1.1244870748109670307316653012861 y2[1] (numeric) = 1.1244870748109611497292036928686 absolute error = 5.8810024616084175e-15 relative error = 5.2299422495336809562984666182024e-13 % h = 0.0001 y1[1] (analytic) = 2.483194699709074581311135338809 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0037691611048715810378474035934 relative error = 0.1517867731158240367961856449255 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5044 y2[1] (analytic) = 1.1245353986584220280370794945515 y2[1] (numeric) = 1.1245353986584154304415287506379 absolute error = 6.5975955507439136e-15 relative error = 5.8669523063612649070641305265234e-13 % h = 0.0001 y1[1] (analytic) = 2.4832822485854740692552086344221 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0038567099812710689819206992065 relative error = 0.15530695246051575879963626359932 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.0MB, time=2.36 NO POLE NO POLE x[1] = 0.5045 y2[1] (analytic) = 1.1245837312605230314627350653647 y2[1] (numeric) = 1.124583731260515649053817033726 absolute error = 7.3824089180316387e-15 relative error = 6.5645702608171707184351871962644e-13 % h = 0.0001 y1[1] (analytic) = 2.4833697926290510753718933076862 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0039442540248480750986053724706 relative error = 0.15882668930560036793549421948315 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5046 y2[1] (analytic) = 1.1246320726167867149880247511533 y2[1] (numeric) = 1.124632072616778474785063926974 absolute error = 8.2402029608241793e-15 relative error = 7.3270211311428525629620837216456e-13 % h = 0.0001 y1[1] (analytic) = 2.4834573318389301592261488311309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0040317932347271589528608959153 relative error = 0.1623459836832279979868892569658 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5047 y2[1] (analytic) = 1.1246804227267296650507145612998 y2[1] (numeric) = 1.1246804227267204890960086261857 absolute error = 9.1759547059351141e-15 relative error = 8.1587218204514356916416315044141e-13 % h = 0.0001 y1[1] (analytic) = 2.4835448662142359287199138596289 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0041193276100329284466259244133 relative error = 0.16586483562554598824806482962048 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5048 y2[1] (analytic) = 1.12472878158986838055177791276 y2[1] (numeric) = 1.1247287815898581856891341381278 absolute error = 1.01948626437746322e-14 relative error = 9.0642853731933591073057686542243e-13 % h = 0.0001 y1[1] (analytic) = 2.4836323957540930401008601513698 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0042068571498900398275722161542 relative error = 0.16938324516469888309248942383736 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.0MB, time=2.58 NO POLE NO POLE x[1] = 0.5049 y2[1] (analytic) = 1.1247771492057192728602306410493 y2[1] (numeric) = 1.1247771492057079705086672805296 absolute error = 1.13023515633605197e-14 relative error = 1.0048525231279698051639080362516e-12 % h = 0.0001 y1[1] (analytic) = 2.4837199204576261979711460053762 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0042943818534231976978580701606 relative error = 0.17290121233282843154123952953543 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.505 y2[1] (analytic) = 1.1248255255737986658179668865485 y2[1] (numeric) = 1.1248255255737861617405786820832 absolute error = 1.25040773882044653e-14 relative error = 1.1116459489862532836901440217852e-12 % h = 0.0001 y1[1] (analytic) = 2.4838074403239601552961692154743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0043819017197571550228812802587 relative error = 0.17641873716207358683165415092659 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5051 y2[1] (analytic) = 1.1248739106936227957445958560807 y2[1] (numeric) = 1.1248739106936089898125827824433 absolute error = 1.38059320130736374e-14 relative error = 1.2273315152771732638620767021862e-12 % h = 0.0001 y1[1] (analytic) = 2.4838949553522197134133195406332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0044694167480167131400316054176 relative error = 0.17993581968457050598626075041799 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5052 y2[1] (analytic) = 1.1249223045647078114422794597113 y2[1] (numeric) = 1.1249223045646925973941378322274 absolute error = 1.52140481416274839e-14 relative error = 1.3524532387607522105467943310908e-12 % h = 0.0001 y1[1] (analytic) = 2.4839824655415297220407306915832 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0045569269373267217674427563676 relative error = 0.1834524599324525493819725186141 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=49.5MB, alloc=4.0MB, time=2.80 x[1] = 0.5053 y2[1] (analytic) = 1.1249707071865697742005708227225 y2[1] (numeric) = 1.1249707071865530393964458930158 absolute error = 1.67348041249297067e-14 relative error = 1.4875768780488199749688607474205e-12 % h = 0.0001 y1[1] (analytic) = 2.4840699708910150792860318336276 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.004644432286812079012743898412 relative error = 0.18696865793785028031955686358144 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5054 y2[1] (analytic) = 1.1250191185587246578012536727134 y2[1] (numeric) = 1.1250191185587062829724528373515 absolute error = 1.83748288008353619e-14 relative error = 1.6332903590452376588433787333975e-12 % h = 0.0001 y1[1] (analytic) = 2.4841574713998007316550986055588 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0047319327955977313818106703432 relative error = 0.1904844137328914645933750124228 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5055 y2[1] (analytic) = 1.1250675386806883485231826017783 y2[1] (numeric) = 1.1250675386806682075168483487401 absolute error = 2.01410063342530382e-14 relative error = 1.7902042003515105235784214681932e-12 % h = 0.0001 y1[1] (analytic) = 2.4842449670670116740608036545925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0048194284628086737875157193769 relative error = 0.1939997273497010700613926183604 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5056 y2[1] (analytic) = 1.1251159675519766451471242037142 y2[1] (numeric) = 1.1251159675519546046660659216501 absolute error = 2.20404810582820641e-14 relative error = 1.9589519386377268352341251832706e-12 % h = 0.0001 y1[1] (analytic) = 2.4843324578917729498317666872315 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0049069192875699495584787520159 relative error = 0.19751459882040126621546126646809 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5057 y2[1] (analytic) = 1.1251644051721052589605990862088 y2[1] (numeric) = 1.1251644051720811782982828615126 absolute error = 2.40806623162246962e-14 relative error = 2.1401905539787597266574190464716e-12 % h = 0.0001 y1[1] (analytic) = 2.4844199438732096507211040359722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0049944052690066504478161007566 relative error = 0.20102902817711142375187077128874 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.0MB, time=3.01 NO POLE NO POLE x[1] = 0.5058 y2[1] (analytic) = 1.1252128515405898137627247579617 y2[1] (numeric) = 1.1252128515405635445334202847215 absolute error = 2.62692293044732402e-14 relative error = 2.3346008951556691355967337004784e-12 % h = 0.0001 y1[1] (analytic) = 2.4845074250104469169151777417664 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0050818864062439166418898065508 relative error = 0.20454301545194811414217215958604 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5059 y2[1] (analytic) = 1.125261306656945845869059390689 y2[1] (numeric) = 1.1252613066569172317331431186334 absolute error = 2.86141359162720556e-14 relative error = 2.5428881049222408639024943325617e-12 % h = 0.0001 y1[1] (analytic) = 2.4845949013026099370423441521499 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0051693626984069367690562169343 relative error = 0.20805656067702510920427123146752 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.506 y2[1] (analytic) = 1.1253097705206888041164464559634 y2[1] (numeric) = 1.1253097705206576805008601015676 absolute error = 3.11236155863543958e-14 relative error = 2.7657820452365999047702352938993e-12 % h = 0.0001 y1[1] (analytic) = 2.4846823727488239481817020349524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0052568341446209479084140997368 relative error = 0.2115696638844533806737925932691 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5061 y2[1] (analytic) = 1.125358243131334049867860236842 y2[1] (numeric) = 1.1253582431313002436817237828062 absolute error = 3.38061861364540358e-14 relative error = 3.0040377224578352690431124989298e-12 % h = 0.0001 y1[1] (analytic) = 2.4847698393482142358718402074983 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0053443007440112355985522722827 relative error = 0.21508232510634109977571405542669 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.0MB, time=3.23 NO POLE NO POLE x[1] = 0.5062 y2[1] (analytic) = 1.1254067244883968570172522142328 y2[1] (numeric) = 1.1254067244883601863626305225941 absolute error = 3.66706546216916387e-14 relative error = 3.2584357125075734923532679076673e-12 % h = 0.0001 y1[1] (analytic) = 2.4848573010999061341195846812144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0054317624957031338462967459988 relative error = 0.21859454437479363679627128885001 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5063 y2[1] (analytic) = 1.1254552145913924119943983279504 y2[1] (numeric) = 1.1254552145913526858722204921387 absolute error = 3.97261221778358117e-14 relative error = 3.5297825859964380001101863411506e-12 % h = 0.0001 y1[1] (analytic) = 2.4849447580030250254087453215537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0055192193988220251354573863381 relative error = 0.22210632172191356065513263307314 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5064 y2[1] (analytic) = 1.1255037134398358137697471124149 y2[1] (numeric) = 1.1255037134397928317808776736103 absolute error = 4.29819888694388046e-14 relative error = 3.8189113333153317513726772595572e-12 % h = 0.0001 y1[1] (analytic) = 2.4850322100566963407088620231503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0056066714524933404355740879347 relative error = 0.22561765717980063847784394972158 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5065 y2[1] (analytic) = 1.1255522210332420738592687069431 y2[1] (numeric) = 1.1255522210331956259007298601418 absolute error = 4.64479585388468013e-14 relative error = 4.1266817896914804001380728790430e-12 % h = 0.0001 y1[1] (analytic) = 2.4851196572600455594839504001169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0056941186558425592106624649013 relative error = 0.22912855078055183516854341472728 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.0MB, time=3.45 NO POLE NO POLE x[1] = 0.5066 y2[1] (analytic) = 1.1256007373711261163293047405846 y2[1] (numeric) = 1.125600737371075982285648655829 absolute error = 5.01340436560847556e-14 relative error = 4.4539810602091733233471490516041e-12 % h = 0.0001 y1[1] (analytic) = 2.4852070996121982097012469913967 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0057815610079952094279590561811 relative error = 0.23263900255626131298294614276802 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5067 y2[1] (analytic) = 1.1256492624530027778014190914547 y2[1] (numeric) = 1.1256492624529487272312494757303 absolute error = 5.40505701696157244e-14 relative error = 4.8017239447951400644832596296155e-12 % h = 0.0001 y1[1] (analytic) = 2.4852945371122798678399539810846 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.005868998508076867566666045869 relative error = 0.23614901253902043110159853756371 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5068 y2[1] (analytic) = 1.1256977962783868074572495205144 y2[1] (numeric) = 1.1256977962783285992748915458669 absolute error = 5.82081823579746475e-14 relative error = 5.1708533631684994348145102154945e-12 % h = 0.0001 y1[1] (analytic) = 2.4853819697594161588999834336272 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0059564311552131586266954984116 relative error = 0.23965858076091774520340226147838 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5069 y2[1] (analytic) = 1.1257463388467928670433601797501 y2[1] (numeric) = 1.1257463388467302491956779032226 absolute error = 6.26178476822765275e-14 relative error = 5.5623407797552189360431910220380e-12 % h = 0.0001 y1[1] (analytic) = 2.4854693975527327564107010438169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0060438589485297561374131086013 relative error = 0.2431677072540390070394077181413 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.0MB, time=3.66 NO POLE NO POLE x[1] = 0.507 y2[1] (analytic) = 1.1257948901577355308760949947039 y2[1] (numeric) = 1.1257948901576682400144553957441 absolute error = 6.72908616395989598e-14 relative error = 5.9771866285670218968550162568950e-12 % h = 0.0001 y1[1] (analytic) = 2.4855568204913553824396694014904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0061312818871523821663814662748 relative error = 0.24667639205046716400687694163286 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5071 y2[1] (analytic) = 1.1258434502107292858464319213063 y2[1] (numeric) = 1.1258434502106570469938146823407 absolute error = 7.22388526172389656e-14 relative error = 6.4164207380446800131773284727611e-12 % h = 0.0001 y1[1] (analytic) = 2.4856442385744098076013907708465 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0062186999702068073281028356309 relative error = 0.25018463518228235872361578599722 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5072 y2[1] (analytic) = 1.125892019005288531424838076962 y2[1] (numeric) = 1.1258920190052110576380902328845 absolute error = 7.74737867478440775e-14 relative error = 6.8811027558656287285024841520392e-12 % h = 0.0001 y1[1] (analytic) = 2.4857316518010218510660493842931 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0063061131968188507927614490775 relative error = 0.25369243668156192860257530867599 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5073 y2[1] (analytic) = 1.1259405965409275796661257458414 y2[1] (numeric) = 1.1259405965408445716933603282104 absolute error = 8.30079727654176310e-14 relative error = 7.3723225737158432590008025600716e-12 % h = 0.0001 y1[1] (analytic) = 2.4858190601703173805682532507384 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0063935215661143802949653155228 relative error = 0.25719979658038040542672224169378 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=68.6MB, alloc=4.0MB, time=3.89 x[1] = 0.5074 y2[1] (analytic) = 1.1259891828171606552143092583286 y2[1] (numeric) = 1.1259891828170718011474470601158 absolute error = 8.88540668621982128e-14 relative error = 7.8912007520259128946470242922356e-12 % h = 0.0001 y1[1] (analytic) = 2.4859064636814223124157754782377 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0064809250772193121424875430221 relative error = 0.2607067149108095149241784443146 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5075 y2[1] (analytic) = 1.1260377778335018953074627445769 y2[1] (numeric) = 1.126037777833406870229916331361 absolute error = 9.50250775464132159e-14 relative error = 8.4388889446712511673818542269546e-12 % h = 0.0001 y1[1] (analytic) = 2.485993862333462611498295110908 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0065683237292596112250071756924 relative error = 0.26421319170491817634362923095228 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5076 y2[1] (analytic) = 1.126086381589465349782578762124 y2[1] (numeric) = 1.126086381589363815412077855669 absolute error = 1.015343705009064550e-13 relative error = 9.0165703236363798278974674618470e-12 % h = 0.0001 y1[1] (analytic) = 2.4860812561255642912961374800242 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0066557175213612910228495448086 relative error = 0.2677192269947725020300004682148 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5077 y2[1] (analytic) = 1.1261349940845649810804277975184 y2[1] (numeric) = 1.1261349940844565854069851577255 absolute error = 1.083956734426397929e-13 relative error = 9.6254600036432243636516425070035e-12 % h = 0.0001 y1[1] (analytic) = 2.4861686450568534138890140692085 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0067431064526504136157261339929 relative error = 0.27122482081243579700040433490639 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5078 y2[1] (analytic) = 1.1261836153183146642504186419074 y2[1] (numeric) = 1.126183615318199041169435573179 absolute error = 1.156230809830687284e-13 relative error = 1.0266805466743358812700560453097e-11 % h = 0.0001 y1[1] (analytic) = 2.486256029126456089964761893626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0068304905222530896914739584104 relative error = 0.2747299731899685585203536388995 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.0MB, time=4.11 NO POLE NO POLE x[1] = 0.5079 y2[1] (analytic) = 1.1262322452902281869554596405387 y2[1] (numeric) = 1.1262322452901049558959702486407 absolute error = 1.232310594893918980e-13 relative error = 1.0941886986874137827520629868585e-11 % h = 0.0001 y1[1] (analytic) = 2.486343408333498478828082393099 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0069178697292954785547944578834 relative error = 0.2782346841594284756802445848015 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.508 y2[1] (analytic) = 1.1262808839998192494768208161278 y2[1] (numeric) = 1.1262808839996880150248741416844 absolute error = 1.312344519466744434e-13 relative error = 1.1652018054378653956058284869067e-11 % h = 0.0001 y1[1] (analytic) = 2.4864307826771067884092798390526 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.007005244072903788135991903837 relative error = 0.28173895375287042897210788637658 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5081 y2[1] (analytic) = 1.1263295314466014647189968660408 y2[1] (numeric) = 1.1263295314464618162361760208468 absolute error = 1.396484828208451940e-13 relative error = 1.2398545800489457898370455326369e-11 % h = 0.0001 y1[1] (analytic) = 2.4865181521564072752729992552048 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0070926135522042749997113199892 relative error = 0.28524278200234648986662811774034 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5082 y2[1] (analytic) = 1.1263781876300883582145710332457 y2[1] (numeric) = 1.1263781876299398694516484656273 absolute error = 1.484887629225676184e-13 relative error = 1.3182851421775979963172483994906e-11 % h = 0.0001 y1[1] (analytic) = 2.4866055167705262446269638519124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0071799781663232443536759166968 relative error = 0.28874616893990592039043119730001 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.0MB, time=4.33 NO POLE NO POLE x[1] = 0.5083 y2[1] (analytic) = 1.1264268525497933681290798509824 y2[1] (numeric) = 1.1264268525496355968348078664879 absolute error = 1.577712942719844945e-13 relative error = 1.4006350604555590597661469857467e-11 % h = 0.0001 y1[1] (analytic) = 2.4866928765185900503307119740863 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0072673379143870500574240388707 relative error = 0.2922491145975951727036398985382 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5084 y2[1] (analytic) = 1.1264755262052298452658787611032 y2[1] (numeric) = 1.1264755262050623327909144248535 absolute error = 1.675124749643362497e-13 relative error = 1.4870493949268238072457237858129e-11 % h = 0.0001 y1[1] (analytic) = 2.4867802313997250949043335625894 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0073546927955220946310456273738 relative error = 0.29575161900745788867769728175415 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5085 y2[1] (analytic) = 1.1265242085959110530710086060352 y2[1] (numeric) = 1.1265242085957333239669721531116 absolute error = 1.777291040364529236e-13 relative error = 1.5776767394814601523147807762084e-11 % h = 0.0001 y1[1] (analytic) = 2.4868675814130578295372061290281 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0074420428088548292639181938125 relative error = 0.29925368220153489947345794082024 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5086 y2[1] (analytic) = 1.126572899721350167638062994316 y2[1] (numeric) = 1.1265728997211617292517288746125 absolute error = 1.884383863341197035e-13 relative error = 1.6726692642857697403250106967312e-11 % h = 0.0001 y1[1] (analytic) = 2.4869549265577147540967302438511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0075293879535117538234423086355 relative error = 0.30275530421186422511954695915242 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.0MB, time=4.55 NO POLE NO POLE x[1] = 0.5087 y2[1] (analytic) = 1.1266215995810602777130565396536 y2[1] (numeric) = 1.1266215995808606197756762236692 absolute error = 1.996579373803159844e-13 relative error = 1.7721827582087877567460973709140e-11 % h = 0.0001 y1[1] (analytic) = 2.4870422668328224171370645376684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0076167282286194168637766024528 relative error = 0.3062564850704810740909864690931 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5088 y2[1] (analytic) = 1.1266703081745543846992939734623 y2[1] (numeric) = 1.1266703081743429789110496455574 absolute error = 2.114057882443279049e-13 relative error = 1.8763766712451157217206964985886e-11 % h = 0.0001 y1[1] (analytic) = 2.4871296022375074159078602157024 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0077040636333044156345722804868 relative error = 0.30975722480941784288808970889725 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5089 y2[1] (analytic) = 1.1267190255013454026622401308252 y2[1] (numeric) = 1.1267190255011217022718283965156 absolute error = 2.237003904117343096e-13 relative error = 1.9854141569340810909273242252550e-11 % h = 0.0001 y1[1] (analytic) = 2.4872169327708963963629950852839 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0077913941666933960897071500683 relative error = 0.31325752346070411561562247158066 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.509 y2[1] (analytic) = 1.126767751560946158334390809836 y2[1] (numeric) = 1.1267677515607095977137355437449 absolute error = 2.365606206552660911e-13 relative error = 2.0994621147752175089968880977799e-11 % h = 0.0001 y1[1] (analytic) = 2.4873042584321160531693070963062 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0078787198279130528960191610906 relative error = 0.31675738105636666356223183993781 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.0MB, time=4.79 NO POLE NO POLE x[1] = 0.5091 y2[1] (analytic) = 1.1268164863528693911201445042698 y2[1] (numeric) = 1.1268164863526193853342379654093 absolute error = 2.500057859065388605e-13 relative error = 2.2186912326400595284285708557927e-11 % h = 0.0001 y1[1] (analytic) = 2.4873915792202931297153273945494 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0079660406160901294420394593338 relative error = 0.32025679762842944478014210202461 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5092 y2[1] (analytic) = 1.1268652298766277531006750095348 y2[1] (numeric) = 1.1268652298763636974725463506354 absolute error = 2.640556281286588994e-13 relative error = 2.3432760291802456473213705750257e-11 % h = 0.0001 y1[1] (analytic) = 2.487478895134554418120012887788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0080533565303514178467249525724 relative error = 0.32375577320891360366511774147363 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5093 y2[1] (analytic) = 1.1269139821317338090388049018571 y2[1] (numeric) = 1.1269139821314550787096151995126 absolute error = 2.787303291897023445e-13 relative error = 2.4733948962319235063517289138662e-11 % h = 0.0001 y1[1] (analytic) = 2.4875662061740267592414783245936 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.008140667569823758968190389378 relative error = 0.32725430782983747053669339698971 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5094 y2[1] (analytic) = 1.1269627431177000363838798906477 y2[1] (numeric) = 1.1269627431174059858681428230931 absolute error = 2.940505157370675546e-13 relative error = 2.6092301412164510778728624243945e-11 % h = 0.0001 y1[1] (analytic) = 2.4876535123378370426857278857469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0082279737336340424124399505313 relative error = 0.3307524015232165612186706855019 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=87.7MB, alloc=4.0MB, time=5.01 x[1] = 0.5095 y2[1] (analytic) = 1.1270115128340388252766440440054 y2[1] (numeric) = 1.1270115128337287880125713433916 absolute error = 3.100372640727006138e-13 relative error = 2.7509680295373877194885591658868e-11 % h = 0.0001 y1[1] (analytic) = 2.4877408136251122068153862881703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0083152750209092065420983529547 relative error = 0.33425005432106357661988178336379 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5096 y2[1] (analytic) = 1.1270602912802624785541158873053 y2[1] (numeric) = 1.1270602912799357664490866933857 absolute error = 3.267121050291939196e-13 relative error = 2.8987988269737689231769481234105e-11 % h = 0.0001 y1[1] (analytic) = 2.4878281100349792387584294012944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0084025714307762384851414660788 relative error = 0.3377472662553884023152196601067 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5097 y2[1] (analytic) = 1.1271090784558832117544653748244 y2[1] (numeric) = 1.1271090784555391147256186170157 absolute error = 3.440970288467578087e-13 relative error = 3.0529168420696586314053129185082e-11 % h = 0.0001 y1[1] (analytic) = 2.4879154015665651744169143757705 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0084898629623621741436264405549 relative error = 0.34124403735819810812693485923398 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5098 y2[1] (analytic) = 1.1271578743604131531218917343559 y2[1] (numeric) = 1.1271578743600509386318406691846 absolute error = 3.622144900510651713e-13 relative error = 3.2135204685199729779104375153932e-11 % h = 0.0001 y1[1] (analytic) = 2.4880026882189970984757092844435 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0085771496147940982024213492279 relative error = 0.34474036766149694770619872066933 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5099 y2[1] (analytic) = 1.1272066789933643436115021847631 y2[1] (numeric) = 1.1272066789929832561991702157581 absolute error = 3.810874123319690050e-13 relative error = 3.3808122275525693174641584394278e-11 % h = 0.0001 y1[1] (analytic) = 2.4880899699914021444112222754956 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.00866443138719914413793434028 relative error = 0.34823625719728635811493293934347 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.0MB, time=5.23 NO POLE NO POLE x[1] = 0.51 y2[1] (analytic) = 1.1272554923542487368941915264245 y2[1] (numeric) = 1.1272554923538479977007684335648 absolute error = 4.007391934230928597e-13 relative error = 3.5549988103065944155883831730206e-11 % h = 0.0001 y1[1] (analytic) = 2.4881772468829074945001302376746 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.008751708278704494226842302459 relative error = 0.35173170599756495940790535457244 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); Iterations = 100 Total Elapsed Time = 5 Seconds Elapsed Time(since restart) = 5 Seconds Expected Time Remaining = 1 Hours 22 Minutes 4 Seconds Optimized Time Remaining = 1 Hours 21 Minutes 50 Seconds Time to Timeout = 14 Minutes 54 Seconds Percent Done = 0.1063 % > quit memory used=92.4MB, alloc=4.0MB, time=5.28