|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > INFO, > glob_iolevel, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > #Top Generate Globals Decl > glob_h, > glob_subiter_method, > glob_max_minutes, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug2, > glob_warned2, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_smallish_float, > glob_dump_analytic, > glob_max_sec, > glob_abserr, > glob_not_yet_finished, > glob_normmax, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_hmin, > glob_initial_pass, > hours_in_day, > glob_display_flag, > glob_html_log, > glob_log10normmin, > glob_log10abserr, > glob_current_iter, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_max_hours, > glob_large_float, > glob_hmin_init, > djd_debug, > glob_log10relerr, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > glob_optimal_done, > glob_reached_optimal_h, > glob_clock_sec, > glob_almost_1, > years_in_century, > glob_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_hmax, > min_in_hour, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_max_opt_iter, > glob_percent_done, > glob_optimal_start, > glob_no_eqs, > centuries_in_millinium, > days_in_year, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_5, > #END CONST > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_norms, > array_m1, > array_y2, > array_y1, > array_1st_rel_error, > array_y1_init, > array_y2_init, > array_x, > array_last_rel_error, > array_y2_higher_work, > array_y1_set_initial, > array_y1_higher_work2, > array_complex_pole, > array_real_pole, > array_y2_higher, > array_y2_higher_work2, > array_poles, > array_y1_higher, > array_y2_set_initial, > array_y1_higher_work, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED, glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr, glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h, glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag, glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours, glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr, glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done, glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century, glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax, min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start, glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump, array_const_0D0, array_const_1D0, array_const_1, array_const_5, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error, array_y1_init, array_y2_init, array_x, array_last_rel_error, array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2, array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2, array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > INFO, > glob_iolevel, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > #Top Generate Globals Decl > glob_h, > glob_subiter_method, > glob_max_minutes, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug2, > glob_warned2, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_smallish_float, > glob_dump_analytic, > glob_max_sec, > glob_abserr, > glob_not_yet_finished, > glob_normmax, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_hmin, > glob_initial_pass, > hours_in_day, > glob_display_flag, > glob_html_log, > glob_log10normmin, > glob_log10abserr, > glob_current_iter, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_max_hours, > glob_large_float, > glob_hmin_init, > djd_debug, > glob_log10relerr, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > glob_optimal_done, > glob_reached_optimal_h, > glob_clock_sec, > glob_almost_1, > years_in_century, > glob_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_hmax, > min_in_hour, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_max_opt_iter, > glob_percent_done, > glob_optimal_start, > glob_no_eqs, > centuries_in_millinium, > days_in_year, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_5, > #END CONST > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_norms, > array_m1, > array_y2, > array_y1, > array_1st_rel_error, > array_y1_init, > array_y2_init, > array_x, > array_last_rel_error, > array_y2_higher_work, > array_y1_set_initial, > array_y1_higher_work2, > array_complex_pole, > array_real_pole, > array_y2_higher, > array_y2_higher_work2, > array_poles, > array_y1_higher, > array_y2_set_initial, > array_y1_higher_work, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED, glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr, glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h, glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag, glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours, glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr, glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done, glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century, glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax, min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start, glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump, array_const_0D0, array_const_1D0, array_const_1, array_const_5, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error, array_y1_init, array_y2_init, array_x, array_last_rel_error, array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2, array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2, array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > INFO, > glob_iolevel, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > #Top Generate Globals Decl > glob_h, > glob_subiter_method, > glob_max_minutes, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug2, > glob_warned2, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_smallish_float, > glob_dump_analytic, > glob_max_sec, > glob_abserr, > glob_not_yet_finished, > glob_normmax, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_hmin, > glob_initial_pass, > hours_in_day, > glob_display_flag, > glob_html_log, > glob_log10normmin, > glob_log10abserr, > glob_current_iter, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_max_hours, > glob_large_float, > glob_hmin_init, > djd_debug, > glob_log10relerr, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > glob_optimal_done, > glob_reached_optimal_h, > glob_clock_sec, > glob_almost_1, > years_in_century, > glob_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_hmax, > min_in_hour, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_max_opt_iter, > glob_percent_done, > glob_optimal_start, > glob_no_eqs, > centuries_in_millinium, > days_in_year, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_5, > #END CONST > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_norms, > array_m1, > array_y2, > array_y1, > array_1st_rel_error, > array_y1_init, > array_y2_init, > array_x, > array_last_rel_error, > array_y2_higher_work, > array_y1_set_initial, > array_y1_higher_work2, > array_complex_pole, > array_real_pole, > array_y2_higher, > array_y2_higher_work2, > array_poles, > array_y1_higher, > array_y2_set_initial, > array_y1_higher_work, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED, glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr, glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h, glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag, glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours, glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr, glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done, glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century, glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax, min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start, glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump, array_const_0D0, array_const_1D0, array_const_1, array_const_5, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error, array_y1_init, array_y2_init, array_x, array_last_rel_error, array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2, array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2, array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > glob_iolevel, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > #Top Generate Globals Decl > glob_h, > glob_subiter_method, > glob_max_minutes, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug2, > glob_warned2, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_smallish_float, > glob_dump_analytic, > glob_max_sec, > glob_abserr, > glob_not_yet_finished, > glob_normmax, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_hmin, > glob_initial_pass, > hours_in_day, > glob_display_flag, > glob_html_log, > glob_log10normmin, > glob_log10abserr, > glob_current_iter, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_max_hours, > glob_large_float, > glob_hmin_init, > djd_debug, > glob_log10relerr, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > glob_optimal_done, > glob_reached_optimal_h, > glob_clock_sec, > glob_almost_1, > years_in_century, > glob_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_hmax, > min_in_hour, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_max_opt_iter, > glob_percent_done, > glob_optimal_start, > glob_no_eqs, > centuries_in_millinium, > days_in_year, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_5, > #END CONST > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_norms, > array_m1, > array_y2, > array_y1, > array_1st_rel_error, > array_y1_init, > array_y2_init, > array_x, > array_last_rel_error, > array_y2_higher_work, > array_y1_set_initial, > array_y1_higher_work2, > array_complex_pole, > array_real_pole, > array_y2_higher, > array_y2_higher_work2, > array_poles, > array_y1_higher, > array_y2_set_initial, > array_y1_higher_work, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 5 - 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 - 5 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED, glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr, glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h, glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag, glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours, glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr, glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done, glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century, glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax, min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start, glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump, array_const_0D0, array_const_1D0, array_const_1, array_const_5, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error, array_y1_init, array_y2_init, array_x, array_last_rel_error, array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2, array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2, array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work, glob_last; n := glob_max_terms; m := n - 6; 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 - 6; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y2_higher[1, m]) or glob_large_float <= abs(array_y2_higher[1, m - 1]) or glob_large_float <= abs(array_y2_higher[1, m - 2]) or glob_large_float <= abs(array_y2_higher[1, m - 3]) or glob_large_float <= abs(array_y2_higher[1, m - 4]) or glob_large_float <= abs(array_y2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_y1_higher[1, m]) or glob_large_float <= abs(array_y1_higher[1, m - 1]) or glob_large_float <= abs(array_y1_higher[1, m - 2]) or glob_large_float <= abs(array_y1_higher[1, m - 3]) or glob_large_float <= abs(array_y1_higher[1, m - 4]) or glob_large_float <= abs(array_y1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > INFO, > glob_iolevel, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > #Top Generate Globals Decl > glob_h, > glob_subiter_method, > glob_max_minutes, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug2, > glob_warned2, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_smallish_float, > glob_dump_analytic, > glob_max_sec, > glob_abserr, > glob_not_yet_finished, > glob_normmax, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_hmin, > glob_initial_pass, > hours_in_day, > glob_display_flag, > glob_html_log, > glob_log10normmin, > glob_log10abserr, > glob_current_iter, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_max_hours, > glob_large_float, > glob_hmin_init, > djd_debug, > glob_log10relerr, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > glob_optimal_done, > glob_reached_optimal_h, > glob_clock_sec, > glob_almost_1, > years_in_century, > glob_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_hmax, > min_in_hour, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_max_opt_iter, > glob_percent_done, > glob_optimal_start, > glob_no_eqs, > centuries_in_millinium, > days_in_year, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_5, > #END CONST > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_norms, > array_m1, > array_y2, > array_y1, > array_1st_rel_error, > array_y1_init, > array_y2_init, > array_x, > array_last_rel_error, > array_y2_higher_work, > array_y1_set_initial, > array_y1_higher_work2, > array_complex_pole, > array_real_pole, > array_y2_higher, > array_y2_higher_work2, > array_poles, > array_y1_higher, > array_y2_set_initial, > array_y1_higher_work, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED, glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr, glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h, glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag, glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours, glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr, glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done, glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century, glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax, min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start, glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump, array_const_0D0, array_const_1D0, array_const_1, array_const_5, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error, array_y1_init, array_y2_init, array_x, array_last_rel_error, array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2, array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2, array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y2[iii]) then array_norms[iii] := abs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y1[iii]) then array_norms[iii] := abs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > INFO, > glob_iolevel, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > #Top Generate Globals Decl > glob_h, > glob_subiter_method, > glob_max_minutes, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug2, > glob_warned2, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_smallish_float, > glob_dump_analytic, > glob_max_sec, > glob_abserr, > glob_not_yet_finished, > glob_normmax, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_hmin, > glob_initial_pass, > hours_in_day, > glob_display_flag, > glob_html_log, > glob_log10normmin, > glob_log10abserr, > glob_current_iter, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_max_hours, > glob_large_float, > glob_hmin_init, > djd_debug, > glob_log10relerr, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > glob_optimal_done, > glob_reached_optimal_h, > glob_clock_sec, > glob_almost_1, > years_in_century, > glob_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_hmax, > min_in_hour, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_max_opt_iter, > glob_percent_done, > glob_optimal_start, > glob_no_eqs, > centuries_in_millinium, > days_in_year, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_5, > #END CONST > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_norms, > array_m1, > array_y2, > array_y1, > array_1st_rel_error, > array_y1_init, > array_y2_init, > array_x, > array_last_rel_error, > array_y2_higher_work, > array_y1_set_initial, > array_y1_higher_work2, > array_complex_pole, > array_real_pole, > array_y2_higher, > array_y2_higher_work2, > array_poles, > array_y1_higher, > array_y2_set_initial, > array_y1_higher_work, > 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 assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y2_set_initial[1,6] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[1] * (glob_h ^ (5)) * factorial_3(0,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,4] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,3] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,2] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult $eq_no = 2 i = 1 > array_tmp3[1] := (array_m1[1] * (array_y2[1])); > #emit pre add $eq_no = 2 i = 1 > array_tmp4[1] := array_tmp3[1] + array_const_1D0[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 assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y2_set_initial[1,7] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[2] * (glob_h ^ (5)) * factorial_3(1,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,5] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,4] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,3] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult $eq_no = 2 i = 2 > array_tmp3[2] := ats(2,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 2 > array_tmp4[2] := array_tmp3[2] + array_const_1D0[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 assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y2_set_initial[1,8] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[3] * (glob_h ^ (5)) * factorial_3(2,7); > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,7] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,6] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,5] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,4] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult $eq_no = 2 i = 3 > array_tmp3[3] := ats(3,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 3 > array_tmp4[3] := array_tmp3[3] + array_const_1D0[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 assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y2_set_initial[1,9] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[4] * (glob_h ^ (5)) * factorial_3(3,8); > array_y2[9] := temporary; > array_y2_higher[1,9] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,8] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,7] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,6] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,5] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult $eq_no = 2 i = 4 > array_tmp3[4] := ats(4,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 4 > array_tmp4[4] := array_tmp3[4] + array_const_1D0[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 assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y2_set_initial[1,10] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[5] * (glob_h ^ (5)) * factorial_3(4,9); > array_y2[10] := temporary; > array_y2_higher[1,10] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,9] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,8] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,7] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,6] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult $eq_no = 2 i = 5 > array_tmp3[5] := ats(5,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 5 > array_tmp4[5] := array_tmp3[5] + array_const_1D0[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 assign $eq_no = 1 > order_d := 5; > 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_tmp1[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 mult $eq_no = 2 > array_tmp3[kkk] := ats(kkk,array_m1,array_y2,1); > #emit add $eq_no = 2 > array_tmp4[kkk] := array_tmp3[kkk] + array_const_1D0[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 INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED, glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr, glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h, glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag, glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours, glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr, glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done, glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century, glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax, min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start, glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump, array_const_0D0, array_const_1D0, array_const_1, array_const_5, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error, array_y1_init, array_y2_init, array_x, array_last_rel_error, array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2, array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2, array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; if not array_y2_set_initial[1, 6] then if 1 <= glob_max_terms then temporary := array_tmp1[1]*glob_h^5*factorial_3(0, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 4] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 3] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 2] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 1] := temporary end if end if; kkk := 2; array_tmp3[1] := array_m1[1]*array_y2[1]; array_tmp4[1] := array_tmp3[1] + array_const_1D0[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]; if not array_y2_set_initial[1, 7] then if 2 <= glob_max_terms then temporary := array_tmp1[2]*glob_h^5*factorial_3(1, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 4] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 3] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 2] := temporary end if end if; kkk := 3; array_tmp3[2] := ats(2, array_m1, array_y2, 1); array_tmp4[2] := array_tmp3[2] + array_const_1D0[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]; if not array_y2_set_initial[1, 8] then if 3 <= glob_max_terms then temporary := array_tmp1[3]*glob_h^5*factorial_3(2, 7); array_y2[8] := temporary; array_y2_higher[1, 8] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 7] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 6] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 5] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 4] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 3] := temporary end if end if; kkk := 4; array_tmp3[3] := ats(3, array_m1, array_y2, 1); array_tmp4[3] := array_tmp3[3] + array_const_1D0[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]; if not array_y2_set_initial[1, 9] then if 4 <= glob_max_terms then temporary := array_tmp1[4]*glob_h^5*factorial_3(3, 8); array_y2[9] := temporary; array_y2_higher[1, 9] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 8] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 7] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 5] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 4] := temporary end if end if; kkk := 5; array_tmp3[4] := ats(4, array_m1, array_y2, 1); array_tmp4[4] := array_tmp3[4] + array_const_1D0[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]; if not array_y2_set_initial[1, 10] then if 5 <= glob_max_terms then temporary := array_tmp1[5]*glob_h^5*factorial_3(4, 9); array_y2[10] := temporary; array_y2_higher[1, 10] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 9] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 8] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 7] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 6] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 5] := temporary end if end if; kkk := 6; array_tmp3[5] := ats(5, array_m1, array_y2, 1); array_tmp4[5] := array_tmp3[5] + array_const_1D0[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]; order_d := 5; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp1[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_tmp3[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp4[kkk] := array_tmp3[kkk] + array_const_1D0[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) > 1.0 + cos(x); > end; exact_soln_y1 := proc(x) 1.0 + cos(x) end proc > exact_soln_y2 := proc(x) > 1.0 + sin(x); > end; exact_soln_y2 := proc(x) 1.0 + sin(x) end proc > exact_soln_y2p := proc(x) > cos(x); > end; exact_soln_y2p := proc(x) cos(x) end proc > exact_soln_y2pp := proc(x) > -sin(x); > end; exact_soln_y2pp := proc(x) -sin(x) end proc > exact_soln_y2ppp := proc(x) > -cos(x); > end; exact_soln_y2ppp := proc(x) -cos(x) end proc > exact_soln_y2pppp := proc(x) > sin(x); > end; exact_soln_y2pppp := proc(x) sin(x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > INFO, > glob_iolevel, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > #Top Generate Globals Decl > glob_h, > glob_subiter_method, > glob_max_minutes, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_start_msg, > glob_clock_start_sec, > djd_debug2, > glob_warned2, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_smallish_float, > glob_dump_analytic, > glob_max_sec, > glob_abserr, > glob_not_yet_finished, > glob_normmax, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_hmin, > glob_initial_pass, > hours_in_day, > glob_display_flag, > glob_html_log, > glob_log10normmin, > glob_log10abserr, > glob_current_iter, > glob_start, > glob_small_float, > glob_max_rel_trunc_err, > glob_max_hours, > glob_large_float, > glob_hmin_init, > djd_debug, > glob_log10relerr, > glob_log10_abserr, > glob_look_poles, > glob_disp_incr, > glob_optimal_done, > glob_reached_optimal_h, > glob_clock_sec, > glob_almost_1, > years_in_century, > glob_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_hmax, > min_in_hour, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_max_opt_iter, > glob_percent_done, > glob_optimal_start, > glob_no_eqs, > centuries_in_millinium, > days_in_year, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_5, > #END CONST > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_pole, > array_norms, > array_m1, > array_y2, > array_y1, > array_1st_rel_error, > array_y1_init, > array_y2_init, > array_x, > array_last_rel_error, > array_y2_higher_work, > array_y1_set_initial, > array_y1_higher_work2, > array_complex_pole, > array_real_pole, > array_y2_higher, > array_y2_higher_work2, > array_poles, > array_y1_higher, > array_y2_set_initial, > array_y1_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > glob_iolevel := 5; > ALWAYS := 1; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_h := 0.1; > glob_subiter_method := 3; > glob_max_minutes := 0.0; > glob_orig_start_sec := 0.0; > glob_warned := false; > glob_relerr := 0.1e-10; > glob_not_yet_start_msg := true; > glob_clock_start_sec := 0.0; > djd_debug2 := true; > glob_warned2 := false; > glob_optimal_expect_sec := 0.1; > MAX_UNCHANGED := 10; > glob_smallish_float := 0.1e-100; > glob_dump_analytic := false; > glob_max_sec := 10000.0; > glob_abserr := 0.1e-10; > glob_not_yet_finished := true; > glob_normmax := 0.0; > glob_unchanged_h_cnt := 0; > glob_last_good_h := 0.1; > glob_hmin := 0.00000000001; > glob_initial_pass := true; > hours_in_day := 24.0; > glob_display_flag := true; > glob_html_log := true; > glob_log10normmin := 0.1; > glob_log10abserr := 0.0; > glob_current_iter := 0; > glob_start := 0; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > djd_debug := true; > glob_log10relerr := 0.0; > glob_log10_abserr := 0.1e-10; > glob_look_poles := false; > glob_disp_incr := 0.1; > glob_optimal_done := false; > glob_reached_optimal_h := false; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > years_in_century := 100.0; > glob_iter := 0; > glob_curr_iter_when_opt := 0; > glob_max_trunc_err := 0.1e-10; > glob_hmax := 1.0; > min_in_hour := 60.0; > sec_in_min := 60.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_iter := 1000; > glob_log10_relerr := 0.1e-10; > glob_max_opt_iter := 10; > glob_percent_done := 0.0; > glob_optimal_start := 0.0; > glob_no_eqs := 0; > centuries_in_millinium := 10.0; > days_in_year := 365.0; > glob_dump := false; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 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/mtest7postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 5 ) = y1 ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > 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 := 0.0;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"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 := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"1.0 + cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"1.0 + sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"-sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"sin(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_type_pole:= 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_pole:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_m1:= 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_y1_init:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_y2_higher_work := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work2 := 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),[]); > array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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_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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_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_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 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 <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 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 <= 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 <=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 <=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_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 > ; > 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 <= 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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_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_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1D0[1] := 1.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_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_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 := 0.0; > x_end := 5.0; > 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 := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := 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 <= 6 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 6 + 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 , 5 ) = y1 ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > 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,"2012-06-13T03:17:17-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest7") > ; > logitem_str(html_log_file,"diff ( y2 , x , 5 ) = y1 ;") > ; > 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,"mtest7 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest7 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 ) = m1 * y2 + 1.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 5 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if glob_html_log then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `subiter` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global INFO, glob_iolevel, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_h, glob_subiter_method, glob_max_minutes, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2, glob_optimal_expect_sec, MAX_UNCHANGED, glob_smallish_float, glob_dump_analytic, glob_max_sec, glob_abserr, glob_not_yet_finished, glob_normmax, glob_unchanged_h_cnt, glob_last_good_h, glob_hmin, glob_initial_pass, hours_in_day, glob_display_flag, glob_html_log, glob_log10normmin, glob_log10abserr, glob_current_iter, glob_start, glob_small_float, glob_max_rel_trunc_err, glob_max_hours, glob_large_float, glob_hmin_init, djd_debug, glob_log10relerr, glob_log10_abserr, glob_look_poles, glob_disp_incr, glob_optimal_done, glob_reached_optimal_h, glob_clock_sec, glob_almost_1, years_in_century, glob_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_hmax, min_in_hour, sec_in_min, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_max_opt_iter, glob_percent_done, glob_optimal_start, glob_no_eqs, centuries_in_millinium, days_in_year, glob_dump, array_const_0D0, array_const_1D0, array_const_1, array_const_5, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_pole, array_norms, array_m1, array_y2, array_y1, array_1st_rel_error, array_y1_init, array_y2_init, array_x, array_last_rel_error, array_y2_higher_work, array_y1_set_initial, array_y1_higher_work2, array_complex_pole, array_real_pole, array_y2_higher, array_y2_higher_work2, array_poles, array_y1_higher, array_y2_set_initial, array_y1_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; glob_iolevel := 5; ALWAYS := 1; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; glob_h := 0.1; glob_subiter_method := 3; glob_max_minutes := 0.; glob_orig_start_sec := 0.; glob_warned := false; glob_relerr := 0.1*10^(-10); glob_not_yet_start_msg := true; glob_clock_start_sec := 0.; djd_debug2 := true; glob_warned2 := false; glob_optimal_expect_sec := 0.1; MAX_UNCHANGED := 10; glob_smallish_float := 0.1*10^(-100); glob_dump_analytic := false; glob_max_sec := 10000.0; glob_abserr := 0.1*10^(-10); glob_not_yet_finished := true; glob_normmax := 0.; glob_unchanged_h_cnt := 0; glob_last_good_h := 0.1; glob_hmin := 0.1*10^(-10); glob_initial_pass := true; hours_in_day := 24.0; glob_display_flag := true; glob_html_log := true; glob_log10normmin := 0.1; glob_log10abserr := 0.; glob_current_iter := 0; glob_start := 0; glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; djd_debug := true; glob_log10relerr := 0.; glob_log10_abserr := 0.1*10^(-10); glob_look_poles := false; glob_disp_incr := 0.1; glob_optimal_done := false; glob_reached_optimal_h := false; glob_clock_sec := 0.; glob_almost_1 := 0.9990; years_in_century := 100.0; glob_iter := 0; glob_curr_iter_when_opt := 0; glob_max_trunc_err := 0.1*10^(-10); glob_hmax := 1.0; min_in_hour := 60.0; sec_in_min := 60.0; glob_optimal_clock_start_sec := 0.; glob_max_iter := 1000; glob_log10_relerr := 0.1*10^(-10); glob_max_opt_iter := 10; glob_percent_done := 0.; glob_optimal_start := 0.; glob_no_eqs := 0; centuries_in_millinium := 10.0; days_in_year := 365.0; glob_dump := false; 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/mtest7postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); 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 := 0.0;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "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 := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "1.0 +\tcos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "1.0 +\tsin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "-sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "sin(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_type_pole := 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_pole := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_m1 := 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_y1_init := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_y2_higher_work := Array(1 .. 7, 1 .. max_terms + 1, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_y2_higher := Array(1 .. 7, 1 .. max_terms + 1, []); array_y2_higher_work2 := Array(1 .. 7, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); 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_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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_y1_init[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_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; 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 <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 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 <= 3 do array_real_pole[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 <= 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_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; 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 <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_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_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_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_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_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.; x_end := 5.0; 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 := 20; glob_h := 0.0001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := 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 <= 6 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 6 + 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 , 5 ) = y1 ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); 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, "2012-06-13T03:17:17-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest7") ; logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;"); 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, "mtest7 diffeq.mxt"); logitem_str(html_log_file, "mtest7 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 ) = m1 * y2 + 1.0;") ; 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/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 5.0; 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 := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) 1.0 + cos(x); end; exact_soln_y2 := proc(x) 1.0 + sin(x); end; exact_soln_y2p := proc(x) cos(x); end; exact_soln_y2pp := proc(x) -sin(x); end; exact_soln_y2ppp := proc(x) -cos(x); end; exact_soln_y2pppp := proc(x) sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % h = 0.0001 x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=3.1MB, time=0.19 x[1] = 0.0001 y2[1] (analytic) = 1.0000999999998333333334166666666 y2[1] (numeric) = 1.0000999999998333333335 absolute error = 8.33333334e-23 relative error = 8.3325000899923895110631980367746e-21 % h = 0.0001 y1[1] (analytic) = 1.9999999950000000041666666652778 y1[1] (numeric) = 1.9999999950000000041666665666667 absolute error = 9.86111e-26 relative error = 4.9305550123263875205439791957706e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0002 y2[1] (analytic) = 1.0001999999986666666693333333308 y2[1] (numeric) = 1.0001999999986666666719999999975 absolute error = 2.6666666667e-21 relative error = 2.6661334400155517342327311669123e-19 % h = 0.0001 y1[1] (analytic) = 1.9999999800000000666666665777778 y1[1] (numeric) = 1.9999999800000000666666662944445 absolute error = 2.833333e-25 relative error = 1.4166665141666650944444338685184e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.38 NO POLE NO POLE x[1] = 0.0003 y2[1] (analytic) = 1.0002999999955000000202499999566 y2[1] (numeric) = 1.0002999999955000000404999999566 absolute error = 2.02500000000e-20 relative error = 2.0243926822044484324991763133255e-18 % h = 0.0001 y1[1] (analytic) = 1.9999999550000003374999989875 y1[1] (numeric) = 1.9999999550000003374999976833334 absolute error = 1.3041666e-24 relative error = 6.5208331467187447007811655599598e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.4MB, time=0.58 NO POLE NO POLE x[1] = 0.0004 y2[1] (analytic) = 1.0003999999893333334186666663416 y2[1] (numeric) = 1.0003999999893333335039999996749 absolute error = 8.53333333333e-20 relative error = 8.5299213648750358128389781703723e-18 % h = 0.0001 y1[1] (analytic) = 1.9999999200000010666666609777778 y1[1] (numeric) = 1.9999999200000010666666549000001 absolute error = 6.0777777e-24 relative error = 3.0388889715555572414815134735808e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=0.78 NO POLE NO POLE x[1] = 0.0005 y2[1] (analytic) = 1.0004999999791666669270833317832 y2[1] (numeric) = 1.0004999999791666671874999984499 absolute error = 2.604166666667e-19 relative error = 2.6028652341041742712303922838289e-17 % h = 0.0001 y1[1] (analytic) = 1.9999998750000026041666449652779 y1[1] (numeric) = 1.999999875000002604166622777778 absolute error = 2.21874999e-23 relative error = 1.1093750643359400764974851311606e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=0.99 NO POLE NO POLE x[1] = 0.0006 y2[1] (analytic) = 1.0005999999640000006479999944457 y2[1] (numeric) = 1.0005999999640000012959999944457 absolute error = 6.480000000000e-19 relative error = 6.4761143316341596159727240608099e-17 % h = 0.0001 y1[1] (analytic) = 1.9999998200000053999999352000004 y1[1] (numeric) = 1.9999998200000053999998698166672 absolute error = 6.53833332e-23 relative error = 3.2691669542250170535008643285404e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.18 NO POLE NO POLE x[1] = 0.0007 y2[1] (analytic) = 1.0006999999428333347339166503265 y2[1] (numeric) = 1.0006999999428333361344999836598 absolute error = 1.4005833333333e-18 relative error = 1.3996036108856906876473507043409e-16 % h = 0.0001 y1[1] (analytic) = 1.9999997550000100041665032652792 y1[1] (numeric) = 1.9999997550000100041663391833349 absolute error = 1.640819443e-22 relative error = 8.2040982200019909126615857799349e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.38 NO POLE NO POLE x[1] = 0.0008 y2[1] (analytic) = 1.0007999999146666693973332917232 y2[1] (numeric) = 1.0007999999146666721279999583898 absolute error = 2.7306666666666e-18 relative error = 2.7284838797955941416453279035350e-16 % h = 0.0001 y1[1] (analytic) = 1.9999996800000170666663025777819 y1[1] (numeric) = 1.9999996800000170666659377111154 absolute error = 3.648666665e-22 relative error = 1.8243336243933643352916975997600e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.58 NO POLE NO POLE x[1] = 0.0009 y2[1] (analytic) = 1.0008999998785000049207499050998 y2[1] (numeric) = 1.0008999998785000098414999050998 absolute error = 4.9207500000000e-18 relative error = 4.9163253078202952349966615837303e-16 % h = 0.0001 y1[1] (analytic) = 1.9999995950000273374992618875107 y1[1] (numeric) = 1.9999995950000273374985229000108 absolute error = 7.389874999e-22 relative error = 3.6949382477249446591154835205820e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=34.3MB, alloc=4.4MB, time=1.78 x[1] = 0.001 y2[1] (analytic) = 1.000999999833333341666666468254 y2[1] (numeric) = 1.0009999998333333499999998015873 absolute error = 8.3333333333333e-18 relative error = 8.3250083263944069114458875295451e-16 % h = 0.0001 y1[1] (analytic) = 1.9999995000000416666652777778026 y1[1] (numeric) = 1.9999995000000416666638879166916 absolute error = 1.3898611110e-21 relative error = 6.9493072923266783044391452117439e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0011 y2[1] (analytic) = 1.0010999997781666800875829466831 y2[1] (numeric) = 1.0010999997781666935084996133498 absolute error = 1.34209166666667e-17 relative error = 1.3406169882769588624917227827023e-15 % h = 0.0001 y1[1] (analytic) = 1.9999993950000610041642061653309 y1[1] (numeric) = 1.9999993950000610041617445944978 absolute error = 2.4615708331e-21 relative error = 1.2307857888626635894265526052009e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=1.99 NO POLE NO POLE x[1] = 0.0012 y2[1] (analytic) = 1.0011999997120000207359992890514 y2[1] (numeric) = 1.0011999997120000414719992890515 absolute error = 2.07360000000001e-17 relative error = 2.0711146630008899121031003946817e-15 % h = 0.0001 y1[1] (analytic) = 1.9999992800000863999958528001066 y1[1] (numeric) = 1.9999992800000863999917044334402 absolute error = 4.1483666664e-21 relative error = 2.0741840799061791614765472126148e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.5MB, time=2.19 NO POLE NO POLE x[1] = 0.0013 y2[1] (analytic) = 1.0012999996338333642744154216564 y2[1] (numeric) = 1.0012999996338333952154987549898 absolute error = 3.09410833333334e-17 relative error = 3.0900912158841788720717975224660e-15 % h = 0.0001 y1[1] (analytic) = 1.9999991550001190041599627654801 y1[1] (numeric) = 1.9999991550001190041532576002026 absolute error = 6.7051652775e-21 relative error = 3.3525840552165638432736259786367e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.5MB, time=2.39 NO POLE NO POLE x[1] = 0.0014 y2[1] (analytic) = 1.0013999995426667114853312417956 y2[1] (numeric) = 1.0013999995426667563039979084623 absolute error = 4.48186666666667e-17 relative error = 4.4756008275549343364736079896743e-15 % h = 0.0001 y1[1] (analytic) = 1.9999990200001600666562089781438 y1[1] (numeric) = 1.9999990200001600666457499281441 absolute error = 1.04590499997e-20 relative error = 5.2295275623180869993674032176490e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.5MB, time=2.59 NO POLE NO POLE x[1] = 0.0015 y2[1] (analytic) = 1.0014999994375000632812466099331 y2[1] (numeric) = 1.0014999994375001265624966099332 absolute error = 6.32812500000001e-17 relative error = 6.3186470330047414440472350729720e-15 % h = 0.0001 y1[1] (analytic) = 1.9999988750002109374841796881356 y1[1] (numeric) = 1.9999988750002109374683579173027 absolute error = 1.58217708329e-20 relative error = 7.9108898663247154560494314653770e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.5MB, time=2.79 NO POLE NO POLE x[1] = 0.0016 y2[1] (analytic) = 1.0015999993173334207146613405665 y2[1] (numeric) = 1.0015999993173335080959946738999 absolute error = 8.73813333333334e-17 relative error = 8.7241746598333091774323464342129e-15 % h = 0.0001 y1[1] (analytic) = 1.999998720000273066643364978843 y1[1] (numeric) = 1.999998720000273066620061734399 absolute error = 2.33032444440e-20 relative error = 1.1651629679041403750795306708047e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.5MB, time=2.99 NO POLE NO POLE x[1] = 0.0017 y2[1] (analytic) = 1.0016999991811667849880751916933 y2[1] (numeric) = 1.00169999918116690330949185836 absolute error = 1.183214166666667e-16 relative error = 1.1812061172345790182359418021288e-14 % h = 0.0001 y1[1] (analytic) = 1.9999985550003480041331422670079 y1[1] (numeric) = 1.9999985550003480040996162128417 absolute error = 3.35260541662e-20 relative error = 1.6763039194392901145409240284449e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.5MB, time=3.20 NO POLE NO POLE x[1] = 0.0018 y2[1] (analytic) = 1.0017999990280001574639878527777 y2[1] (numeric) = 1.0017999990280003149279878527777 absolute error = 1.574640000000000e-16 relative error = 1.5718107421918544558862995765201e-14 % h = 0.0001 y1[1] (analytic) = 1.9999983800004373999527608027331 y1[1] (numeric) = 1.9999983800004373999055198527337 absolute error = 4.72409499994e-20 relative error = 2.3620494132295081357507073237365e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=64.8MB, alloc=4.5MB, time=3.40 x[1] = 0.0019 y2[1] (analytic) = 1.0018999988568335396748989311172 y2[1] (numeric) = 1.0018999988568337460164822644505 absolute error = 2.063415833333333e-16 relative error = 2.0595027804049181590030883458369e-14 % h = 0.0001 y1[1] (analytic) = 1.99999819500054300410132516949 y1[1] (numeric) = 1.9999981950005430040359818208795 absolute error = 6.53433486105e-20 relative error = 3.2671703791453801352477700359052e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.002 y2[1] (analytic) = 1.0019999986666669333333079365093 y2[1] (numeric) = 1.001999998666667199999974603176 absolute error = 2.666666666666667e-16 relative error = 2.6613439822506236859372959788106e-14 % h = 0.0001 y1[1] (analytic) = 1.999998000000666666577777784127 y1[1] (numeric) = 1.9999980000006666664888869507944 absolute error = 8.88908333326e-20 relative error = 4.4445461111746296594568032821926e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=3.60 NO POLE NO POLE x[1] = 0.0021 y2[1] (analytic) = 1.0020999984565003403417142641184 y2[1] (numeric) = 1.0020999984565006806834642641184 absolute error = 3.403417500000000e-16 relative error = 3.3962853060993565652797062674565e-14 % h = 0.0001 y1[1] (analytic) = 1.9999977950008103373808803968807 y1[1] (numeric) = 1.9999977950008103372617587427149 absolute error = 1.191216541658e-19 relative error = 5.9560892748760123299119473028844e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=3.80 NO POLE NO POLE x[1] = 0.0022 y2[1] (analytic) = 1.0021999982253337628026171754421 y2[1] (numeric) = 1.0021999982253341922719505087753 absolute error = 4.294693333333332e-16 relative error = 4.2852657562744446767894289890015e-14 % h = 0.0001 y1[1] (analytic) = 1.9999975800009760665091945913879 y1[1] (numeric) = 1.9999975800009760663517203636111 absolute error = 1.574742277768e-19 relative error = 7.8737209160384657688991353151169e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=4.00 NO POLE NO POLE x[1] = 0.0023 y2[1] (analytic) = 1.0022999979721672030285157772778 y2[1] (numeric) = 1.0022999979721677393904324439444 absolute error = 5.363619166666666e-16 relative error = 5.3513111618459845164031384494473e-14 % h = 0.0001 y1[1] (analytic) = 1.9999973550011660039610612847001 y1[1] (numeric) = 1.9999973550011660037554536472013 absolute error = 2.056076374988e-19 relative error = 1.0280395470757016585234344386440e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=4.20 NO POLE NO POLE x[1] = 0.0024 y2[1] (analytic) = 1.0023999976960006635519089985901 y2[1] (numeric) = 1.00239999769600132710390899859 absolute error = 6.635519999999999e-16 relative error = 6.6196328963005075824085437547900e-14 % h = 0.0001 y1[1] (analytic) = 1.9999971200013823997345792273004 y1[1] (numeric) = 1.9999971200013823994691560939684 absolute error = 2.654231333320e-19 relative error = 1.3271175777083945965946293403904e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=4.41 NO POLE NO POLE x[1] = 0.0025 y2[1] (analytic) = 1.0024999973958341471352955651767 y2[1] (numeric) = 1.0024999973958349609373788985099 absolute error = 8.138020833333332e-16 relative error = 8.1177265381279184573429779477856e-14 % h = 0.0001 y1[1] (analytic) = 1.999996875001627603827582503122 y1[1] (numeric) = 1.999996875001627603488495871179 absolute error = 3.390866319430e-19 relative error = 1.6954358088320715512058610008034e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=4.61 NO POLE NO POLE x[1] = 0.0026 y2[1] (analytic) = 1.0025999970706676567811739720353 y2[1] (numeric) = 1.0025999970706686468958406387018 absolute error = 9.901146666666665e-16 relative error = 9.8754704723670457402825502015967e-14 % h = 0.0001 y1[1] (analytic) = 1.9999966200019040662376170295702 y1[1] (numeric) = 1.9999966200019040658085648129051 absolute error = 4.290522166651e-19 relative error = 2.1452647088208155441268610530344e-17 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=91.5MB, alloc=4.5MB, time=4.82 x[1] = 0.0027 y2[1] (analytic) = 1.0026999967195011957420424533305 y2[1] (numeric) = 1.0026999967195023914842924533303 absolute error = 1.1957422499999998e-15 relative error = 1.1925224433151174322788677526042e-13 % h = 0.0001 y1[1] (analytic) = 1.999996355002214336961916057547 y1[1] (numeric) = 1.9999963550022143364238294200487 absolute error = 5.380866374983e-19 relative error = 2.6904380908119417365096989123237e-17 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0028 y2[1] (analytic) = 1.0027999963413347675303989498603 y2[1] (numeric) = 1.0027999963413362017277322831934 absolute error = 1.4341973333333331e-15 relative error = 1.4301927987294872042680181966792e-13 % h = 0.0001 y1[1] (analytic) = 1.9999960800025610659973746714787 y1[1] (numeric) = 1.9999960800025610653280798603694 absolute error = 6.692948111093e-19 relative error = 3.3464806146442194238135512738309e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=5.01 NO POLE NO POLE x[1] = 0.0029 y2[1] (analytic) = 1.0028999959351683759287410739227 y2[1] (numeric) = 1.0028999959351700851911577405892 absolute error = 1.7092624166666665e-15 relative error = 1.7043198958963405228569955017006e-13 % h = 0.0001 y1[1] (analytic) = 1.9999957950029470033405232893468 y1[1] (numeric) = 1.9999957950029470025143769685155 absolute error = 8.261463208313e-19 relative error = 4.1307402890318710367935493275877e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=5.22 NO POLE NO POLE x[1] = 0.003 y2[1] (analytic) = 1.0029999955000020249995660714828 y2[1] (numeric) = 1.0029999955000040499995660714826 absolute error = 2.0249999999999998e-15 relative error = 2.0189431795466002189438070592242e-13 % h = 0.0001 y1[1] (analytic) = 1.9999955000033749989875001627232 y1[1] (numeric) = 1.9999955000033749979749972460588 absolute error = 1.0125029166644e-18 relative error = 5.0625259739968984830033703538339e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=5.43 NO POLE NO POLE x[1] = 0.0031 y2[1] (analytic) = 1.0030999950348357190953707815389 y2[1] (numeric) = 1.003099995034838104857954114872 absolute error = 2.3857625833333331e-15 relative error = 2.3783895874214217182138781136047e-13 % h = 0.0001 y1[1] (analytic) = 1.9999951950038480029340228768083 y1[1] (numeric) = 1.999995195003848001701375861533 absolute error = 1.2326470152753e-18 relative error = 6.1632498835724871810829010093894e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=5.65 NO POLE NO POLE x[1] = 0.0032 y2[1] (analytic) = 1.0031999945386694628686515925897 y2[1] (numeric) = 1.0031999945386722590713182592561 absolute error = 2.7962026666666664e-15 relative error = 2.7872833750886585047948773992425e-13 % h = 0.0001 y1[1] (analytic) = 1.9999948800043690651753588504741 y1[1] (numeric) = 1.9999948800043690636840476504768 absolute error = 1.4913111999973e-18 relative error = 7.4565750888024382029678320672934e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=5.86 NO POLE NO POLE x[1] = 0.0033 y2[1] (analytic) = 1.0032999940105032612819043961006 y2[1] (numeric) = 1.0032999940105065225646543961003 absolute error = 3.2612827499999997e-15 relative error = 3.2505559348840764188267976136501e-13 % h = 0.0001 y1[1] (analytic) = 1.9999945550049413357062948363116 y1[1] (numeric) = 1.9999945550049413339125861154813 absolute error = 1.7937087208303e-18 relative error = 8.9685680210557789716598618739910e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.5MB, time=6.08 NO POLE NO POLE x[1] = 0.0034 y2[1] (analytic) = 1.0033999934493371196176245368708 y2[1] (numeric) = 1.0033999934493409059029578702038 absolute error = 3.7862853333333330e-15 relative error = 3.7734556089814317206750410782961e-13 % h = 0.0001 y1[1] (analytic) = 1.999994220005568064521105420683 y1[1] (numeric) = 1.9999942200055680623755404262418 absolute error = 2.1455649944412e-18 relative error = 1.0727855975679903017796865410566e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.5MB, time=6.29 NO POLE NO POLE x[1] = 0.0035 y2[1] (analytic) = 1.0034999928541710434883067601998 y2[1] (numeric) = 1.0034999928541754203112234268661 absolute error = 4.3768229166666663e-15 relative error = 4.3615574965955258143128642451123e-13 % h = 0.0001 y1[1] (analytic) = 1.9999938750062526016135205237785 y1[1] (numeric) = 1.9999938750062525990603704196154 absolute error = 2.5531501041631e-18 relative error = 1.2765789616006289320885592975992e-16 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=122.0MB, alloc=4.5MB, time=6.50 x[1] = 0.0036 y2[1] (analytic) = 1.0035999922240050388464451557542 y2[1] (numeric) = 1.0035999922240100776944451557537 absolute error = 5.0388479999999995e-15 relative error = 5.0207732553223465867687301162054e-13 % h = 0.0001 y1[1] (analytic) = 1.9999935200069983969766918996799 y1[1] (numeric) = 1.9999935200069983939533795996838 absolute error = 3.0233122999961e-18 relative error = 1.5116610477745551875055433397859e-16 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0037 y2[1] (analytic) = 1.0036999915578391119945330980341 y2[1] (numeric) = 1.0036999915578448906576164313669 absolute error = 5.7786630833333328e-15 relative error = 5.7573608966204042837310584382446e-13 % h = 0.0001 y1[1] (analytic) = 1.9999931550078090006031586364283 y1[1] (numeric) = 1.9999931550078089970396461378214 absolute error = 3.5635124986069e-18 relative error = 1.7817623473781270100170112123683e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=6.71 NO POLE NO POLE x[1] = 0.0038 y2[1] (analytic) = 1.0037999908546732695950631833404 y2[1] (numeric) = 1.0037999908546798725257298500065 absolute error = 6.6029306666666661e-15 relative error = 6.5779345754373650165393341439498e-13 % h = 0.0001 y1[1] (analytic) = 1.9999927800086880624848116560991 y1[1] (numeric) = 1.9999927800086880583029518727703 absolute error = 4.1818597833288e-18 relative error = 2.0909374399394750839400398841273e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=6.92 NO POLE NO POLE x[1] = 0.0039 y2[1] (analytic) = 1.0038999901135075186805271631411 y2[1] (numeric) = 1.0038999901135150373637771631405 absolute error = 7.5186832499999994e-15 relative error = 7.4894743739860857530115573469562e-13 % h = 0.0001 y1[1] (analytic) = 1.999992395009639332612857214883 y1[1] (numeric) = 1.9999923950096393277257093107213 absolute error = 4.8871479041617e-18 relative error = 2.4435832437943572722164584177831e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.5MB, time=7.12 NO POLE NO POLE x[1] = 0.004 y2[1] (analytic) = 1.0039999893333418666634158737383 y2[1] (numeric) = 1.003999989333350399996749207071 absolute error = 8.5333333333333327e-15 relative error = 8.4993360796741484285033196543085e-13 % h = 0.0001 y1[1] (analytic) = 1.9999920000106666609777794031743 y1[1] (numeric) = 1.9999920000106666552888866254019 absolute error = 5.6888927777724e-18 relative error = 2.8444577667020963750539888155551e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=7.32 NO POLE NO POLE x[1] = 0.0041 y2[1] (analytic) = 1.0040999885131763213462191621347 y2[1] (numeric) = 1.0040999885131859760296358288007 absolute error = 9.6546834166666660e-15 relative error = 9.6152609571909901797596690867590e-13 % h = 0.0001 y1[1] (analytic) = 1.9999915950117739975693016456656 y1[1] (numeric) = 1.9999915950117739909719306581714 absolute error = 6.5973709874942e-18 relative error = 3.2986993565117263014270687631785e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=7.53 NO POLE NO POLE x[1] = 0.0042 y2[1] (analytic) = 1.0041999876520108909314258080007 y2[1] (numeric) = 1.0041999876520217818674258079999 absolute error = 1.08909359999999992e-14 relative error = 1.0845385514756723182499591904629e-12 % h = 0.0001 y1[1] (analytic) = 1.9999911800129653923763472014509 y1[1] (numeric) = 1.9999911800129653847526879181238 absolute error = 7.6236592833271e-18 relative error = 3.8118464518816917557971265574465e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=7.73 NO POLE NO POLE x[1] = 0.0043 y2[1] (analytic) = 1.0042999867488455840315234416408 y2[1] (numeric) = 1.0042999867488578347351067749733 absolute error = 1.22507035833333325e-14 relative error = 1.2198251264536735647873163310447e-12 % h = 0.0001 y1[1] (analytic) = 1.9999907550142449953869986641364 y1[1] (numeric) = 1.9999907550142449866073235821986 absolute error = 8.7796750819378e-18 relative error = 4.3898578330554665466033841377331e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.5MB, time=7.94 NO POLE NO POLE x[1] = 0.0044 y2[1] (analytic) = 1.0043999858026804096789984578608 y2[1] (numeric) = 1.0043999858026941526976651245266 absolute error = 1.37430186666666658e-14 relative error = 1.3682814477226160721078041630669e-12 % h = 0.0001 y1[1] (analytic) = 1.9999903200156170565884564619595 y1[1] (numeric) = 1.9999903200156170465102384952999 absolute error = 1.00782179666596e-17 relative error = 5.0391333726959756330029774752740e-16 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0045 y2[1] (analytic) = 1.0044999848125153773363359256343 y2[1] (numeric) = 1.0044999848125307546800859256333 absolute error = 1.53773437499999990e-14 relative error = 1.5308455930808300692758023928823e-12 % h = 0.0001 y1[1] (analytic) = 1.9999898750170859259669963579171 y1[1] (numeric) = 1.9999898750170859144339841704246 absolute error = 1.15330121874925e-17 relative error = 5.7665352867818760357494173587131e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.5MB, time=8.16 NO POLE NO POLE x[1] = 0.0046 y2[1] (analytic) = 1.0045999837773504969060194934696 y2[1] (numeric) = 1.0045999837773676604873528268018 absolute error = 1.71635813333333322e-14 relative error = 1.7084990653491088328909521570372e-12 % h = 0.0001 y1[1] (analytic) = 1.9999894200186560535079259499027 y1[1] (numeric) = 1.9999894200186560403491757887996 absolute error = 1.31587501611031e-17 relative error = 6.5794098855684717457776639838701e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=8.38 NO POLE NO POLE x[1] = 0.0047 y2[1] (analytic) = 1.0046999826961857787405312903764 y2[1] (numeric) = 1.0046999826962048908244479570419 absolute error = 1.91120839166666655e-14 relative error = 1.9022677660825665107823179178635e-12 % h = 0.0001 y1[1] (analytic) = 1.9999889550203319891955401708534 y1[1] (numeric) = 1.9999889550203319742244032000286 absolute error = 1.49711369708248e-17 relative error = 7.4856098246165577759022508171977e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.5MB, time=8.59 NO POLE NO POLE x[1] = 0.0048 y2[1] (analytic) = 1.0047999815680212336523518223331 y2[1] (numeric) = 1.0047999815680424673163518223318 absolute error = 2.12336639999999987e-14 relative error = 2.1132229687011154037192474481902e-12 % h = 0.0001 y1[1] (analytic) = 1.999988480022118383013075788907 y1[1] (numeric) = 1.9999884800221183660261399222495 absolute error = 1.69869358666575e-17 relative error = 8.4935168558919085079196893811784e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.5MB, time=8.80 NO POLE NO POLE x[1] = 0.0049 y2[1] (analytic) = 1.0048999803918568729239598641532 y2[1] (numeric) = 1.004899980391880412528043197485 absolute error = 2.35396040833333318e-14 relative error = 2.3424822910389702610539566972553e-12 % h = 0.0001 y1[1] (analytic) = 1.9999879950240199849426649075699 y1[1] (numeric) = 1.9999879950240199657186501423018 absolute error = 1.92240147652681e-17 relative error = 9.6120650789392455035891173670958e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.5MB, time=9.02 NO POLE NO POLE x[1] = 0.005 y2[1] (analytic) = 1.0049999791666927083178323466521 y2[1] (numeric) = 1.0049999791667187499844990133171 absolute error = 2.60416666666666650e-14 relative error = 2.5912106673135866563470252450608e-12 % h = 0.0001 y1[1] (analytic) = 1.9999875000260416449652874658951 y1[1] (numeric) = 1.9999875000260416232638937159054 absolute error = 2.17013937499897e-17 relative error = 1.0850764692132889949704984919429e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.5MB, time=9.24 NO POLE NO POLE x[1] = 0.0051 y2[1] (analytic) = 1.0050999778915287520864442390147 y2[1] (numeric) = 1.0050999778915575041906942390128 absolute error = 2.87521042499999981e-14 relative error = 2.8606213195144403578286157982192e-12 % h = 0.0001 y1[1] (analytic) = 1.9999869950281883130607227386734 y1[1] (numeric) = 1.999986995028188288621429167851 absolute error = 2.44392935708224e-17 relative error = 1.2219726244008874933268027682964e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=9.46 NO POLE NO POLE x[1] = 0.0052 y2[1] (analytic) = 1.0051999765653650169822684262613 y2[1] (numeric) = 1.0051999765653967006516017595926 absolute error = 3.16836693333333313e-14 relative error = 3.1519767282120545469717330248179e-12 % h = 0.0001 y1[1] (analytic) = 1.999986480030465039207499836635 y1[1] (numeric) = 1.9999864800304650117483146922021 absolute error = 2.74591851444329e-17 relative error = 1.3729685384680512738490647548033e-15 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=179.2MB, alloc=4.5MB, time=9.68 x[1] = 0.0053 y2[1] (analytic) = 1.0052999751872015162677755817155 y2[1] (numeric) = 1.00529997518723636589219224838 absolute error = 3.48496244166666645e-14 relative error = 3.4665896027876809805750171702298e-12 % h = 0.0001 y1[1] (analytic) = 1.9999859550328769733828472066644 y1[1] (numeric) = 1.9999859550328769425990071525099 absolute error = 3.07838400541545e-17 relative error = 1.5392028117341682382603592687184e-15 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0054 y2[1] (analytic) = 1.0053999737560382637254340343706 y2[1] (numeric) = 1.0053999737560765274774340343682 absolute error = 3.82637519999999976e-14 relative error = 3.8058238510840414589722457431803e-12 % h = 0.0001 y1[1] (analytic) = 1.9999854200354293655626411320282 y1[1] (numeric) = 1.9999854200354293311252590820411 absolute error = 3.44373820499871e-17 relative error = 1.7218816549861172614897819295252e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.5MB, time=9.89 NO POLE NO POLE x[1] = 0.0055 y2[1] (analytic) = 1.0054999722708752736677096310567 y2[1] (numeric) = 1.0054999722709172140322929643874 absolute error = 4.19403645833333307e-14 relative error = 4.1710955484775353348413441945193e-12 % h = 0.0001 y1[1] (analytic) = 1.9999848750381275657213532326165 y1[1] (numeric) = 1.999984875038127527276013684019 absolute error = 3.84453395485975e-17 relative error = 1.9222815146471835619333606570829e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=10.11 NO POLE NO POLE x[1] = 0.0056 y2[1] (analytic) = 1.0055999707307125609470655933077 y2[1] (numeric) = 1.0055999707307584552617322599715 absolute error = 4.58943146666666638e-14 relative error = 4.5638739063723185970612099519909e-12 % h = 0.0001 y1[1] (analytic) = 1.9999843200409770238319969651979 y1[1] (numeric) = 1.9999843200409769809972978318789 absolute error = 4.28346991333190e-17 relative error = 2.1417517479557726670486072340473e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=10.33 NO POLE NO POLE x[1] = 0.0057 y2[1] (analytic) = 1.0056999691345501409659623688285 y2[1] (numeric) = 1.0056999691346002819707123688253 absolute error = 5.01410047499999968e-14 relative error = 4.9856822401166599138881035059122e-12 % h = 0.0001 y1[1] (analytic) = 1.9999837550439832898660731236897 y1[1] (numeric) = 1.9999837550439832422321130695382 absolute error = 4.76339600541515e-17 relative error = 2.3817173481543575015173420215803e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=10.54 NO POLE NO POLE x[1] = 0.0058 y2[1] (analytic) = 1.0057999674813880296868574774616 y2[1] (numeric) = 1.0057999674814427260841908107915 absolute error = 5.46963973333333299e-14 relative error = 5.4380989363419786807292065613294e-12 % h = 0.0001 y1[1] (analytic) = 1.9999831800471520137935143394429 y1[1] (numeric) = 1.9999831800471519609203246116811 absolute error = 5.28731897277618e-17 relative error = 2.6436817196890251262450924101240e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=10.75 NO POLE NO POLE x[1] = 0.0059 y2[1] (analytic) = 1.005899965770226243642205351555 y2[1] (numeric) = 1.0058999657702858206671220182179 absolute error = 5.95770249166666629e-14 relative error = 5.9227584197249696895804070831147e-12 % h = 0.0001 y1[1] (analytic) = 1.9999825950504889455826285815429 y1[1] (numeric) = 1.9999825950504888869985483440596 absolute error = 5.85840802374833e-17 relative error = 2.9292295034199716578047515000881e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=10.97 NO POLE NO POLE x[1] = 0.006 y2[1] (analytic) = 1.0059999640000647999444571706286 y2[1] (numeric) = 1.0059999640001295999444571706244 absolute error = 6.47999999999999958e-14 relative error = 6.4413521191732191560400975293425e-12 % h = 0.0001 y1[1] (analytic) = 1.9999820000539999352000416571262 y1[1] (numeric) = 1.9999820000539998704000358238105 absolute error = 6.48000058333157e-17 relative error = 3.2400294518433709001152167772152e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.5MB, time=11.17 NO POLE NO POLE x[1] = 0.0061 y2[1] (analytic) = 1.0060999621699037162960606902414 y2[1] (numeric) = 1.0060999621699740993211440235701 absolute error = 7.03830250833333287e-14 relative error = 6.9956294334347161335339919302886e-12 % h = 0.0001 y1[1] (analytic) = 1.9999813950576909326106387117147 y1[1] (numeric) = 1.9999813950576908610545572797888 absolute error = 7.15560814319259e-17 relative error = 3.5778373543250792221993674875799e-15 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0062 y2[1] (analytic) = 1.0061999602787430109994600649592 y2[1] (numeric) = 1.0061999602788193554021267316208 absolute error = 7.63444026666666616e-14 relative error = 7.5873986961316633343802585841497e-12 % h = 0.0001 y1[1] (analytic) = 1.9999807800615679877775047295666 y1[1] (numeric) = 1.9999807800615679088882826129193 absolute error = 7.88892221166473e-17 relative error = 3.9444990123464462158578716551545e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.5MB, time=11.37 NO POLE NO POLE x[1] = 0.0063 y2[1] (analytic) = 1.0062999583255827029670956653213 y2[1] (numeric) = 1.0062999583256654060123456653158 absolute error = 8.27030452499999945e-14 relative error = 8.2185281402189910890330804026445e-12 % h = 0.0001 y1[1] (analytic) = 1.9999801550656372506618640340453 y1[1] (numeric) = 1.9999801550656371638236603965657 absolute error = 8.68382036374796e-17 relative error = 4.3419532647627526710127122780338e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.5MB, time=11.59 NO POLE NO POLE x[1] = 0.0064 y2[1] (analytic) = 1.0063999563094228117314038887082 y2[1] (numeric) = 1.0063999563095122902167372220355 absolute error = 8.94784853333333273e-14 relative error = 8.8909468618679778172072063205117e-12 % h = 0.0001 y1[1] (analytic) = 1.9999795200699049712230187880081 y1[1] (numeric) = 1.9999795200699048757792948769183 absolute error = 9.54437239110898e-17 relative error = 4.7722350630747344079034766518640e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.6MB, time=11.80 NO POLE NO POLE x[1] = 0.0065 y2[1] (analytic) = 1.0064999542292633574548169640085 y2[1] (numeric) = 1.0064999542293600483402336306686 absolute error = 9.66908854166666601e-14 relative error = 9.6066457837753802259314308182967e-12 % h = 0.0001 y1[1] (analytic) = 1.9999788750743774994182864942121 y1[1] (numeric) = 1.9999788750743773946698209734011 absolute error = 1.047484655208110e-16 relative error = 5.2374785967134525052019148063640e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.6MB, time=12.01 NO POLE NO POLE x[1] = 0.0066 y2[1] (analytic) = 1.0065999520841043609397627499864 y2[1] (numeric) = 1.0065999520842087219877627499793 absolute error = 1.043610479999999929e-13 relative error = 1.0367678617898476022789246030280e-11 % h = 0.0001 y1[1] (analytic) = 1.9999782200790612852029364957421 y1[1] (numeric) = 1.9999782200790611704057772790987 absolute error = 1.147971592166434e-16 relative error = 5.7399204683391674689389688745672e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.6MB, time=12.22 NO POLE NO POLE x[1] = 0.0067 y2[1] (analytic) = 1.0066999498729458436386645272492 y2[1] (numeric) = 1.0066999498730583540642478605748 absolute error = 1.125104255833333256e-13 relative error = 1.1176162827616421853820219271128e-11 % h = 0.0001 y1[1] (analytic) = 1.9999775550839628785301254764571 y1[1] (numeric) = 1.9999775550839627528934770612037 absolute error = 1.256366484152534e-16 relative error = 6.2819029191544568850228890170383e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.6MB, time=12.43 NO POLE NO POLE x[1] = 0.0068 y2[1] (analytic) = 1.0067999475947878276639407837147 y2[1] (numeric) = 1.0067999475949089887946074503729 absolute error = 1.211611306666666582e-13 relative error = 1.2034280589318328808752929056974e-11 % h = 0.0001 y1[1] (analytic) = 1.9999768800890889293508319614595 y1[1] (numeric) = 1.999976880089088792034877261485 absolute error = 1.373159546999745e-16 relative error = 6.8658771042322131042482659277667e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.6MB, time=12.64 NO POLE NO POLE x[1] = 0.0069 y2[1] (analytic) = 1.0068999452486303357980049934784 y2[1] (numeric) = 1.0068999452487606717437549934692 absolute error = 1.303359457499999908e-13 relative error = 1.2944279753418457539238669465442e-11 % h = 0.0001 y1[1] (analytic) = 1.999976195094446187613789817585 y1[1] (numeric) = 1.9999761950944460377274454967783 absolute error = 1.498863443208067e-16 relative error = 7.4944064178588145072421304081198e-15 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=236.5MB, alloc=4.6MB, time=12.85 x[1] = 0.007 y2[1] (analytic) = 1.0069999428334733915032653889815 y2[1] (numeric) = 1.0069999428336134498365987223049 absolute error = 1.400583333333333234e-13 relative error = 1.3908474804798934808485336287345e-11 % h = 0.0001 y1[1] (analytic) = 1.9999755001000415032654207539152 y1[1] (numeric) = 1.9999755001000413398640250594986 absolute error = 1.634013956944166e-16 relative error = 8.1701698688930459020033465887451e-15 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0071 y2[1] (analytic) = 1.007099940348317018932124726378 y2[1] (numeric) = 1.007099940348467371378041393034 absolute error = 1.503524459166666560e-13 relative error = 1.4929247822680393073506738244690e-11 % h = 0.0001 y1[1] (analytic) = 1.9999747951058818262497658223139 y1[1] (numeric) = 1.9999747951058816483326979181762 absolute error = 1.779170679041377e-16 relative error = 8.8959655061412156076471182416502e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.6MB, time=13.07 NO POLE NO POLE x[1] = 0.0072 y2[1] (analytic) = 1.007199937792161242936980044003 y2[1] (numeric) = 1.0071999377923224860729800439914 absolute error = 1.612431359999999884e-13 relative error = 1.6009049439920934325309303940514e-11 % h = 0.0001 y1[1] (analytic) = 1.9999740801119742065084159179862 y1[1] (numeric) = 1.9999740801119740130166457180164 absolute error = 1.934917701999698e-16 relative error = 9.6747138937488937799391483663972e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.6MB, time=13.28 NO POLE NO POLE x[1] = 0.0073 y2[1] (analytic) = 1.0072999351640060890802224138395 y2[1] (numeric) = 1.0072999351641788450463057471603 absolute error = 1.727559660833333208e-13 relative error = 1.7150399801743819314704685594827e-11 % h = 0.0001 y1[1] (analytic) = 1.9999733551183257939804412800631 y1[1] (numeric) = 1.9999733551183255837940087814835 absolute error = 2.101864324985796e-16 relative error = 1.0509461636609863538677569054610e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.6MB, time=13.51 NO POLE NO POLE x[1] = 0.0074 y2[1] (analytic) = 1.0073999324628515836442366858868 y2[1] (numeric) = 1.00739993246303650086290335254 absolute error = 1.849172186666666532e-13 relative error = 1.8355889523894282717369567468105e-11 % h = 0.0001 y1[1] (analytic) = 1.9999726201249438386023199922106 y1[1] (numeric) = 1.9999726201249436105377431089101 absolute error = 2.280645768833005e-16 relative error = 1.1403384955792678457049734852635e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.6MB, time=13.72 NO POLE NO POLE x[1] = 0.0075 y2[1] (analytic) = 1.0074999296876977536414012253283 y2[1] (numeric) = 1.0074999296878955075476512253138 absolute error = 1.977539062499999855e-13 relative error = 1.9628180650225874912961951940621e-11 % h = 0.0001 y1[1] (analytic) = 1.999971875131835690307865483265 y1[1] (numeric) = 1.9999718751318354431154753791326 absolute error = 2.471923901041324e-16 relative error = 1.2359793313985366977417219306128e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.6MB, time=13.94 NO POLE NO POLE x[1] = 0.0076 y2[1] (analytic) = 1.0075999268375446268240876423992 y2[1] (numeric) = 1.0075999268377559206054209757169 absolute error = 2.112937813333333177e-13 relative error = 2.0970007609716730538963460406821e-11 % h = 0.0001 y1[1] (analytic) = 1.9999711201390087990281530278951 y1[1] (numeric) = 1.9999711201390085313893559501529 absolute error = 2.676387970777422e-16 relative error = 1.3382133090958826320747525708520e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.6MB, time=14.15 NO POLE NO POLE x[1] = 0.0077 y2[1] (analytic) = 1.0076999239113922316946605148542 y2[1] (numeric) = 1.0076999239116177970410771815041 absolute error = 2.255653464166666499e-13 relative error = 2.2384178172916163744050448850895e-11 % h = 0.0001 y1[1] (analytic) = 1.999970355146470714691445247291 y1[1] (numeric) = 1.999970355146470425215909859828 absolute error = 2.894755353874630e-16 relative error = 1.4473991309049320457815375404080e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.6MB, time=14.38 NO POLE NO POLE x[1] = 0.0078 y2[1] (analytic) = 1.0077999209082405975154771029362 y2[1] (numeric) = 1.0077999209084811953794771029182 absolute error = 2.405978639999999820e-13 relative error = 2.3873574407821989820171402200075e-11 % h = 0.0001 y1[1] (analytic) = 1.9999695801542290872231166098821 y1[1] (numeric) = 1.9999695801542287744458858265871 absolute error = 3.127772307832950e-16 relative error = 1.5639099408660753716669365150982e-14 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0079 y2[1] (analytic) = 1.0078999178270897543188870567438 y2[1] (numeric) = 1.0078999178273461756854703900578 absolute error = 2.564213665833333140e-13 relative error = 2.5441153635188972726428443788922e-11 % h = 0.0001 y1[1] (analytic) = 1.9999687951622916665455769320828 y1[1] (numeric) = 1.9999687951622913289241032501782 absolute error = 3.376214736819046e-16 relative error = 1.6881337073787073599204562992268e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.6MB, time=14.59 NO POLE NO POLE x[1] = 0.008 y2[1] (analytic) = 1.0079999146669397329172321158996 y2[1] (numeric) = 1.0079999146672127995838987825456 absolute error = 2.730666666666666460e-13 relative error = 2.7089949383268797574105121669222e-11 % h = 0.0001 y1[1] (analytic) = 1.9999680001706663025781938790692 y1[1] (numeric) = 1.9999680001706659384892972124439 absolute error = 3.640888966666253e-16 relative error = 1.8204736107555518387850084816154e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.6MB, time=14.81 NO POLE NO POLE x[1] = 0.0081 y2[1] (analytic) = 1.0080999114267905649128458014187 y2[1] (numeric) = 1.0080999114270811302795958013966 absolute error = 2.905653667499999779e-13 relative error = 2.8823072341981966966607236283276e-11 % h = 0.0001 y1[1] (analytic) = 1.9999671951793609452372144655848 y1[1] (numeric) = 1.9999671951793605529739614781278 absolute error = 3.922632529874570e-16 relative error = 1.9613484357791082121320130547420e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.6MB, time=15.03 NO POLE NO POLE x[1] = 0.0082 y2[1] (analytic) = 1.0081999081056422827080530996768 y2[1] (numeric) = 1.0081999081059512325773864329865 absolute error = 3.089498693333333097e-13 relative error = 3.0643711316522019912618376007546e-11 % h = 0.0001 y1[1] (analytic) = 1.9999663801883836444356855567786 y1[1] (numeric) = 1.9999663801883832222041894957121 absolute error = 4.222314960610665e-16 relative error = 2.1111929692602886526241258889800e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.6MB, time=15.25 NO POLE NO POLE x[1] = 0.0083 y2[1] (analytic) = 1.0082999047024949195151701383786 y2[1] (numeric) = 1.00829990470282317290208680502 absolute error = 3.282533869166666414e-13 relative error = 3.2555134180392471577721806775211e-11 % h = 0.0001 y1[1] (analytic) = 1.9999655551977425500833733690744 y1[1] (numeric) = 1.9999655551977420959995133982873 absolute error = 4.540838599707871e-16 relative error = 2.2704584025992911490977122221572e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.6MB, time=15.47 NO POLE NO POLE x[1] = 0.0084 y2[1] (analytic) = 1.0083999012163485093665038544264 y2[1] (numeric) = 1.0083999012166970193185038543994 absolute error = 3.485099519999999730e-13 relative error = 3.4560688827876872024216170004293e-11 % h = 0.0001 y1[1] (analytic) = 1.9999647202074459120866819710734 y1[1] (numeric) = 1.9999647202074454241727410044546 absolute error = 4.879139409666188e-16 relative error = 2.4396127393487722674165498329405e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.6MB, time=15.69 NO POLE NO POLE x[1] = 0.0085 y2[1] (analytic) = 1.0084998976462030871243516535888 y2[1] (numeric) = 1.0084998976465728415514349868933 absolute error = 3.697544270833333045e-13 relative error = 3.6663804125942381765154995796006e-11 % h = 0.0001 y1[1] (analytic) = 1.9999638752175020803485707844898 y1[1] (numeric) = 1.9999638752175015565297908192617 absolute error = 5.238187799652281e-16 relative error = 2.6191412077793716841917048987247e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.6MB, time=15.90 NO POLE NO POLE x[1] = 0.0086 y2[1] (analytic) = 1.008599893991058688491001061869 y2[1] (numeric) = 1.008599893991450711005667728505 absolute error = 3.920225146666666360e-13 relative error = 3.8867990865577261714503066931100e-11 % h = 0.0001 y1[1] (analytic) = 1.9999630202279195047684710851221 y1[1] (numeric) = 1.9999630202279189428695250351735 absolute error = 5.618989460499486e-16 relative error = 2.8095466784476522533023176717412e-14 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=293.7MB, alloc=4.6MB, time=16.13 x[1] = 0.0087 y2[1] (analytic) = 1.0086998902499153500187293684742 y2[1] (numeric) = 1.0086998902503307007859793684415 absolute error = 4.153507672499999673e-13 relative error = 4.1176842712562674782113571436123e-11 % h = 0.0001 y1[1] (analytic) = 1.9999621552387067352422015038579 y1[1] (numeric) = 1.9999621552387061329835805330778 absolute error = 6.022586209707801e-16 relative error = 3.0113500867665025652031140287421e-14 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0088 y2[1] (analytic) = 1.0087998864217731091198032602839 y2[1] (numeric) = 1.0087998864222128857171365935824 absolute error = 4.397765973333332985e-13 relative error = 4.3594037157679196306849517594624e-11 % h = 0.0001 y1[1] (analytic) = 1.9999612802498724216618825277167 y1[1] (numeric) = 1.9999612802498717766561978833273 absolute error = 6.450056846443894e-16 relative error = 3.2250908605780771598676905933017e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.6MB, time=16.34 NO POLE NO POLE x[1] = 0.0089 y2[1] (analytic) = 1.0088998825056320040764784477192 y2[1] (numeric) = 1.0088998825060973423638951143488 absolute error = 4.653382874166666296e-13 relative error = 4.6123336466348429910735705334739e-11 % h = 0.0001 y1[1] (analytic) = 1.9999603952614253139158500009278 y1[1] (numeric) = 1.9999603952614246236640483468181 absolute error = 6.902518016541097e-16 relative error = 3.4513273527293187540278157764480e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.6MB, time=16.56 NO POLE NO POLE x[1] = 0.009 y2[1] (analytic) = 1.0089998785004920740509992819119 y2[1] (numeric) = 1.0089998785009841490509992818725 absolute error = 4.920749999999999606e-13 relative error = 4.8768588627710125440845080505987e-11 % h = 0.0001 y1[1] (analytic) = 1.9999595002733742618885676260481 y1[1] (numeric) = 1.9999595002733735237760588761069 absolute error = 7.381125087499412e-16 relative error = 3.6906372786501360442801902618781e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.6MB, time=16.78 NO POLE NO POLE x[1] = 0.0091 y2[1] (analytic) = 1.0090998744053533590955983630738 y2[1] (numeric) = 1.0090998744058733858831816963651 absolute error = 5.200267875833332913e-13 relative error = 5.1533728303135195174550421493766e-11 % h = 0.0001 y1[1] (analytic) = 1.9999585952857282154605384651164 y1[1] (numeric) = 1.9999585952857274267532351165661 absolute error = 7.887073033485503e-16 relative error = 3.9436181589342853475373736381911e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.6MB, time=17.00 NO POLE NO POLE x[1] = 0.0092 y2[1] (analytic) = 1.0091998702192159001624961399656 y2[1] (numeric) = 1.0091998702197651347651628065876 absolute error = 5.492346026666666220e-13 relative error = 5.4422777774175024399171527790927e-11 % h = 0.0001 y1[1] (analytic) = 1.9999576802984962245082154408494 y1[1] (numeric) = 1.9999576802984953823484824075789 absolute error = 8.421597330332705e-16 relative error = 4.2108877669230335412625552189053e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.6MB, time=17.21 NO POLE NO POLE x[1] = 0.0093 y2[1] (analytic) = 1.0092998659410797391139005003671 y2[1] (numeric) = 1.0092998659416594794216505003196 absolute error = 5.797403077499999525e-13 relative error = 5.7439847889947471837803233099110e-11 % h = 0.0001 y1[1] (analytic) = 1.9999567553116874389039108378768 y1[1] (numeric) = 1.999956755311686540306424783775 absolute error = 8.985974860541018e-16 relative error = 4.4930845812916489657190389371959e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.6MB, time=17.43 NO POLE NO POLE x[1] = 0.0094 y2[1] (analytic) = 1.0093998615699449187320063524461 y2[1] (numeric) = 1.0093998615705565054173396857289 absolute error = 6.115866853333332828e-13 relative error = 6.0589139013959955725262733646664e-11 % h = 0.0001 y1[1] (analytic) = 1.9999558203253111085157048040181 y1[1] (numeric) = 1.9999558203253101503632219763073 absolute error = 9.581524828277108e-16 relative error = 4.7908682436387946514284380499451e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.6MB, time=17.65 NO POLE NO POLE x[1] = 0.0095 y2[1] (analytic) = 1.0094998571048114827289951969284 y2[1] (numeric) = 1.0094998571054563001769118635415 absolute error = 6.448174479166666131e-13 relative error = 6.3874941970370020501010325712645e-11 % h = 0.0001 y1[1] (analytic) = 1.9999548753393765832073528516022 y1[1] (numeric) = 1.9999548753393755622463844141714 absolute error = 1.0209609684374308e-15 relative error = 5.1049200210788844351797889956717e-14 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0096 y2[1] (analytic) = 1.0095998525446794757570346899679 y2[1] (numeric) = 1.009599852545358953005034689911 absolute error = 6.794772479999999431e-13 relative error = 6.7301638989683779061716654647213e-11 % h = 0.0001 y1[1] (analytic) = 1.9999539203538933128381923588301 y1[1] (numeric) = 1.9999539203538922256745862255681 absolute error = 1.0871636061332620e-15 relative error = 5.4359432738374672284555284442083e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.6MB, time=17.87 NO POLE NO POLE x[1] = 0.0097 y2[1] (analytic) = 1.0096998478885489434182781966159 y2[1] (numeric) = 1.009699847889264555106361529889 absolute error = 7.156116880833332731e-13 relative error = 7.0873704653892625501848373960108e-11 % h = 0.0001 y1[1] (analytic) = 1.9999529553688708472630480711808 y1[1] (numeric) = 1.9999529553688696903574762393099 absolute error = 1.1569055718318709e-15 relative error = 5.7846639278497004024787620242754e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.6MB, time=18.09 NO POLE NO POLE x[1] = 0.0098 y2[1] (analytic) = 1.0097998431354199322748643347922 y2[1] (numeric) = 1.009799843136173199605531001395 absolute error = 7.532673306666666028e-13 relative error = 7.4595706841048612355141317611547e-11 % h = 0.0001 y1[1] (analytic) = 1.9999519803843188363321366028639 y1[1] (numeric) = 1.9999519803843176059954869862731 absolute error = 1.2303366496165908e-15 relative error = 6.1518309523619879548689069547701e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.6MB, time=18.31 NO POLE NO POLE x[1] = 0.0099 y2[1] (analytic) = 1.0098998382842924898589165096544 y2[1] (numeric) = 1.0098998382850849815671665095867 absolute error = 7.924917082499999323e-13 relative error = 7.8472307669278886940197484999298e-11 % h = 0.0001 y1[1] (analytic) = 1.9999509954002470298909699383174 y1[1] (numeric) = 1.9999509954002457222796417008956 absolute error = 1.3076113282374218e-15 relative error = 6.5382168425368423229747753795773e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.6MB, time=18.52 NO POLE NO POLE x[1] = 0.01 y2[1] (analytic) = 1.0099998333341666646825424382691 y2[1] (numeric) = 1.0099998333349999980158757715307 absolute error = 8.333333333333332616e-13 relative error = 8.2508264440239580339871125591238e-11 % h = 0.0001 y1[1] (analytic) = 1.9999500004166652777802579337522 y1[1] (numeric) = 1.9999500004166638888913593227217 absolute error = 1.3888888986110305e-15 relative error = 6.9446181070610384096320425011773e-14 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 100 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 18 Seconds Expected Time Remaining = 2 Hours 33 Minutes 2 Seconds Optimized Time Remaining = 2 Hours 32 Minutes 58 Seconds Time to Timeout = 14 Minutes 41 Seconds Percent Done = 0.202 % > quit memory used=337.7MB, alloc=4.6MB, time=18.64