|\^/| 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 > glob_iolevel, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_h, > glob_initial_pass, > djd_debug, > glob_iter, > glob_max_rel_trunc_err, > glob_look_poles, > sec_in_min, > glob_smallish_float, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_hmax, > glob_start, > centuries_in_millinium, > years_in_century, > glob_dump, > glob_percent_done, > glob_log10relerr, > glob_normmax, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_dump_analytic, > glob_last_good_h, > glob_disp_incr, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_max_iter, > glob_log10_relerr, > hours_in_day, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_small_float, > glob_optimal_start, > glob_relerr, > glob_clock_sec, > glob_almost_1, > min_in_hour, > djd_debug2, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmin, > days_in_year, > glob_log10normmin, > glob_warned, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_max_trunc_err, > glob_log10_abserr, > glob_display_flag, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_1D0, > array_const_4, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_init, > array_pole, > array_y2, > array_y1, > array_y2_init, > array_x, > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_norms, > array_poles, > array_y1_set_initial, > array_y2_higher, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_set_initial, > 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 glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO, glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err, glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours, glob_abserr, glob_large_float, glob_hmax, glob_start, centuries_in_millinium, years_in_century, glob_dump, glob_percent_done, glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs, glob_dump_analytic, glob_last_good_h, glob_disp_incr, glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter, glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr, glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr, MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned, glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished, glob_max_trunc_err, glob_log10_abserr, glob_display_flag, glob_subiter_method, array_const_3, array_const_1, array_const_1D0, array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole, array_y2, array_y1, array_y2_init, array_x, array_type_pole, array_last_rel_error, array_1st_rel_error, array_norms, array_poles, array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work, array_y1_higher_work2, array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial, 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 > glob_iolevel, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_h, > glob_initial_pass, > djd_debug, > glob_iter, > glob_max_rel_trunc_err, > glob_look_poles, > sec_in_min, > glob_smallish_float, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_hmax, > glob_start, > centuries_in_millinium, > years_in_century, > glob_dump, > glob_percent_done, > glob_log10relerr, > glob_normmax, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_dump_analytic, > glob_last_good_h, > glob_disp_incr, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_max_iter, > glob_log10_relerr, > hours_in_day, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_small_float, > glob_optimal_start, > glob_relerr, > glob_clock_sec, > glob_almost_1, > min_in_hour, > djd_debug2, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmin, > days_in_year, > glob_log10normmin, > glob_warned, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_max_trunc_err, > glob_log10_abserr, > glob_display_flag, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_1D0, > array_const_4, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_init, > array_pole, > array_y2, > array_y1, > array_y2_init, > array_x, > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_norms, > array_poles, > array_y1_set_initial, > array_y2_higher, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_set_initial, > 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 glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO, glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err, glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours, glob_abserr, glob_large_float, glob_hmax, glob_start, centuries_in_millinium, years_in_century, glob_dump, glob_percent_done, glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs, glob_dump_analytic, glob_last_good_h, glob_disp_incr, glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter, glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr, glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr, MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned, glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished, glob_max_trunc_err, glob_log10_abserr, glob_display_flag, glob_subiter_method, array_const_3, array_const_1, array_const_1D0, array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole, array_y2, array_y1, array_y2_init, array_x, array_type_pole, array_last_rel_error, array_1st_rel_error, array_norms, array_poles, array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work, array_y1_higher_work2, array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial, 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 > glob_iolevel, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_h, > glob_initial_pass, > djd_debug, > glob_iter, > glob_max_rel_trunc_err, > glob_look_poles, > sec_in_min, > glob_smallish_float, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_hmax, > glob_start, > centuries_in_millinium, > years_in_century, > glob_dump, > glob_percent_done, > glob_log10relerr, > glob_normmax, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_dump_analytic, > glob_last_good_h, > glob_disp_incr, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_max_iter, > glob_log10_relerr, > hours_in_day, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_small_float, > glob_optimal_start, > glob_relerr, > glob_clock_sec, > glob_almost_1, > min_in_hour, > djd_debug2, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmin, > days_in_year, > glob_log10normmin, > glob_warned, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_max_trunc_err, > glob_log10_abserr, > glob_display_flag, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_1D0, > array_const_4, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_init, > array_pole, > array_y2, > array_y1, > array_y2_init, > array_x, > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_norms, > array_poles, > array_y1_set_initial, > array_y2_higher, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_set_initial, > 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 glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO, glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err, glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours, glob_abserr, glob_large_float, glob_hmax, glob_start, centuries_in_millinium, years_in_century, glob_dump, glob_percent_done, glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs, glob_dump_analytic, glob_last_good_h, glob_disp_incr, glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter, glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr, glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr, MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned, glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished, glob_max_trunc_err, glob_log10_abserr, glob_display_flag, glob_subiter_method, array_const_3, array_const_1, array_const_1D0, array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole, array_y2, array_y1, array_y2_init, array_x, array_type_pole, array_last_rel_error, array_1st_rel_error, array_norms, array_poles, array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work, array_y1_higher_work2, array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial, 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 > glob_iolevel, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_h, > glob_initial_pass, > djd_debug, > glob_iter, > glob_max_rel_trunc_err, > glob_look_poles, > sec_in_min, > glob_smallish_float, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_hmax, > glob_start, > centuries_in_millinium, > years_in_century, > glob_dump, > glob_percent_done, > glob_log10relerr, > glob_normmax, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_dump_analytic, > glob_last_good_h, > glob_disp_incr, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_max_iter, > glob_log10_relerr, > hours_in_day, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_small_float, > glob_optimal_start, > glob_relerr, > glob_clock_sec, > glob_almost_1, > min_in_hour, > djd_debug2, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmin, > days_in_year, > glob_log10normmin, > glob_warned, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_max_trunc_err, > glob_log10_abserr, > glob_display_flag, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_1D0, > array_const_4, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_init, > array_pole, > array_y2, > array_y1, > array_y2_init, > array_x, > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_norms, > array_poles, > array_y1_set_initial, > array_y2_higher, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_set_initial, > 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 - 4 - 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 - 4 - 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 glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO, glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err, glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours, glob_abserr, glob_large_float, glob_hmax, glob_start, centuries_in_millinium, years_in_century, glob_dump, glob_percent_done, glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs, glob_dump_analytic, glob_last_good_h, glob_disp_incr, glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter, glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr, glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr, MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned, glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished, glob_max_trunc_err, glob_log10_abserr, glob_display_flag, glob_subiter_method, array_const_3, array_const_1, array_const_1D0, array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole, array_y2, array_y1, array_y2_init, array_x, array_type_pole, array_last_rel_error, array_1st_rel_error, array_norms, array_poles, array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work, array_y1_higher_work2, array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial, glob_last; n := glob_max_terms; m := n - 5; 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 - 5; 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 > glob_iolevel, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_h, > glob_initial_pass, > djd_debug, > glob_iter, > glob_max_rel_trunc_err, > glob_look_poles, > sec_in_min, > glob_smallish_float, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_hmax, > glob_start, > centuries_in_millinium, > years_in_century, > glob_dump, > glob_percent_done, > glob_log10relerr, > glob_normmax, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_dump_analytic, > glob_last_good_h, > glob_disp_incr, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_max_iter, > glob_log10_relerr, > hours_in_day, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_small_float, > glob_optimal_start, > glob_relerr, > glob_clock_sec, > glob_almost_1, > min_in_hour, > djd_debug2, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmin, > days_in_year, > glob_log10normmin, > glob_warned, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_max_trunc_err, > glob_log10_abserr, > glob_display_flag, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_1D0, > array_const_4, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_init, > array_pole, > array_y2, > array_y1, > array_y2_init, > array_x, > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_norms, > array_poles, > array_y1_set_initial, > array_y2_higher, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_set_initial, > 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 glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO, glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err, glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours, glob_abserr, glob_large_float, glob_hmax, glob_start, centuries_in_millinium, years_in_century, glob_dump, glob_percent_done, glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs, glob_dump_analytic, glob_last_good_h, glob_disp_incr, glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter, glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr, glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr, MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned, glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished, glob_max_trunc_err, glob_log10_abserr, glob_display_flag, glob_subiter_method, array_const_3, array_const_1, array_const_1D0, array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole, array_y2, array_y1, array_y2_init, array_x, array_type_pole, array_last_rel_error, array_1st_rel_error, array_norms, array_poles, array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work, array_y1_higher_work2, array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial, 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 > glob_iolevel, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_h, > glob_initial_pass, > djd_debug, > glob_iter, > glob_max_rel_trunc_err, > glob_look_poles, > sec_in_min, > glob_smallish_float, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_hmax, > glob_start, > centuries_in_millinium, > years_in_century, > glob_dump, > glob_percent_done, > glob_log10relerr, > glob_normmax, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_dump_analytic, > glob_last_good_h, > glob_disp_incr, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_max_iter, > glob_log10_relerr, > hours_in_day, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_small_float, > glob_optimal_start, > glob_relerr, > glob_clock_sec, > glob_almost_1, > min_in_hour, > djd_debug2, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmin, > days_in_year, > glob_log10normmin, > glob_warned, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_max_trunc_err, > glob_log10_abserr, > glob_display_flag, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_1D0, > array_const_4, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_init, > array_pole, > array_y2, > array_y1, > array_y2_init, > array_x, > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_norms, > array_poles, > array_y1_set_initial, > array_y2_higher, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_set_initial, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre add $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp2[1] := (array_tmp1[1] - (array_const_1D0[1])); > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y2_set_initial[1,5] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (4)) * factorial_3(0,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,3] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,2] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre diff $eq_no = 2 i = 1 > array_tmp4[1] := array_y2_higher[4,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp5[1] := (array_m1[1] * (array_tmp4[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_tmp5[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre add $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D0[2] + array_y1[2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp2[2] := (array_tmp1[2] - (array_const_1D0[2])); > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y2_set_initial[1,6] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (4)) * factorial_3(1,5); > 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 > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre diff $eq_no = 2 i = 2 > array_tmp4[2] := array_y2_higher[4,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp5[2] := ats(2,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre add $eq_no = 1 i = 3 > array_tmp1[3] := array_const_0D0[3] + array_y1[3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp2[3] := (array_tmp1[3] - (array_const_1D0[3])); > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y2_set_initial[1,7] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (4)) * factorial_3(2,6); > 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 > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre diff $eq_no = 2 i = 3 > array_tmp4[3] := array_y2_higher[4,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp5[3] := ats(3,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre add $eq_no = 1 i = 4 > array_tmp1[4] := array_const_0D0[4] + array_y1[4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp2[4] := (array_tmp1[4] - (array_const_1D0[4])); > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y2_set_initial[1,8] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (4)) * factorial_3(3,7); > 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 > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre diff $eq_no = 2 i = 4 > array_tmp4[4] := array_y2_higher[4,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp5[4] := ats(4,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre add $eq_no = 1 i = 5 > array_tmp1[5] := array_const_0D0[5] + array_y1[5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp2[5] := (array_tmp1[5] - (array_const_1D0[5])); > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y2_set_initial[1,9] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (4)) * factorial_3(4,8); > 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 > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre diff $eq_no = 2 i = 5 > array_tmp4[5] := array_y2_higher[4,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp5[5] := ats(5,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit add $eq_no = 1 > array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk]; > #emit sub $eq_no = 1 > array_tmp2[kkk] := (array_tmp1[kkk] - (array_const_1D0[kkk])); > #emit assign $eq_no = 1 > order_d := 4; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y2_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit diff $eq_no = 2 > array_tmp4[kkk] := array_y2_higher[4,kkk]; > #emit mult $eq_no = 2 > array_tmp5[kkk] := ats(kkk,array_m1,array_tmp4,1); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp5[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 glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO, glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err, glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours, glob_abserr, glob_large_float, glob_hmax, glob_start, centuries_in_millinium, years_in_century, glob_dump, glob_percent_done, glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs, glob_dump_analytic, glob_last_good_h, glob_disp_incr, glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter, glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr, glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr, MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned, glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished, glob_max_trunc_err, glob_log10_abserr, glob_display_flag, glob_subiter_method, array_const_3, array_const_1, array_const_1D0, array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole, array_y2, array_y1, array_y2_init, array_x, array_type_pole, array_last_rel_error, array_1st_rel_error, array_norms, array_poles, array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work, array_y1_higher_work2, array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; array_tmp2[1] := array_tmp1[1] - array_const_1D0[1]; if not array_y2_set_initial[1, 5] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h^4*factorial_3(0, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 3] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 2] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 1] := temporary end if end if; kkk := 2; array_tmp4[1] := array_y2_higher[4, 1]; array_tmp5[1] := array_m1[1]*array_tmp4[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*glob_h*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D0[2] + array_y1[2]; array_tmp2[2] := array_tmp1[2] - array_const_1D0[2]; if not array_y2_set_initial[1, 6] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h^4*factorial_3(1, 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 end if end if; kkk := 3; array_tmp4[2] := array_y2_higher[4, 2]; array_tmp5[2] := ats(2, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*glob_h*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_const_0D0[3] + array_y1[3]; array_tmp2[3] := array_tmp1[3] - array_const_1D0[3]; if not array_y2_set_initial[1, 7] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h^4*factorial_3(2, 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 end if end if; kkk := 4; array_tmp4[3] := array_y2_higher[4, 3]; array_tmp5[3] := ats(3, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*glob_h*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_const_0D0[4] + array_y1[4]; array_tmp2[4] := array_tmp1[4] - array_const_1D0[4]; if not array_y2_set_initial[1, 8] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h^4*factorial_3(3, 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 end if end if; kkk := 5; array_tmp4[4] := array_y2_higher[4, 4]; array_tmp5[4] := ats(4, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*glob_h*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_const_0D0[5] + array_y1[5]; array_tmp2[5] := array_tmp1[5] - array_const_1D0[5]; if not array_y2_set_initial[1, 9] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h^4*factorial_3(4, 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 end if end if; kkk := 6; array_tmp4[5] := array_y2_higher[4, 5]; array_tmp5[5] := ats(5, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*glob_h*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk]; array_tmp2[kkk] := array_tmp1[kkk] - array_const_1D0[kkk]; order_d := 4; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp4[kkk] := array_y2_higher[4, kkk]; array_tmp5[kkk] := ats(kkk, array_m1, array_tmp4, 1); order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp5[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 + sin(x); > end; exact_soln_y1 := proc(x) 1.0 + sin(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 > > > > #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 > glob_iolevel, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_h, > glob_initial_pass, > djd_debug, > glob_iter, > glob_max_rel_trunc_err, > glob_look_poles, > sec_in_min, > glob_smallish_float, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_hmax, > glob_start, > centuries_in_millinium, > years_in_century, > glob_dump, > glob_percent_done, > glob_log10relerr, > glob_normmax, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_dump_analytic, > glob_last_good_h, > glob_disp_incr, > glob_not_yet_start_msg, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_max_iter, > glob_log10_relerr, > hours_in_day, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_small_float, > glob_optimal_start, > glob_relerr, > glob_clock_sec, > glob_almost_1, > min_in_hour, > djd_debug2, > glob_log10abserr, > MAX_UNCHANGED, > glob_hmin, > days_in_year, > glob_log10normmin, > glob_warned, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_max_trunc_err, > glob_log10_abserr, > glob_display_flag, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_1D0, > array_const_4, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_init, > array_pole, > array_y2, > array_y1, > array_y2_init, > array_x, > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_norms, > array_poles, > array_y1_set_initial, > array_y2_higher, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_set_initial, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_iolevel := 5; > DEBUGMASSIVE := 4; > ALWAYS := 1; > glob_max_terms := 30; > DEBUGL := 3; > INFO := 2; > glob_h := 0.1; > glob_initial_pass := true; > djd_debug := true; > glob_iter := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_look_poles := false; > sec_in_min := 60.0; > glob_smallish_float := 0.1e-100; > glob_max_hours := 0.0; > glob_abserr := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmax := 1.0; > glob_start := 0; > centuries_in_millinium := 10.0; > years_in_century := 100.0; > glob_dump := false; > glob_percent_done := 0.0; > glob_log10relerr := 0.0; > glob_normmax := 0.0; > glob_unchanged_h_cnt := 0; > glob_no_eqs := 0; > glob_dump_analytic := false; > glob_last_good_h := 0.1; > glob_disp_incr := 0.1; > glob_not_yet_start_msg := true; > glob_max_opt_iter := 10; > glob_max_minutes := 0.0; > glob_hmin_init := 0.001; > glob_optimal_done := false; > glob_clock_start_sec := 0.0; > glob_html_log := true; > glob_curr_iter_when_opt := 0; > glob_orig_start_sec := 0.0; > glob_warned2 := false; > glob_max_iter := 1000; > glob_log10_relerr := 0.1e-10; > hours_in_day := 24.0; > glob_optimal_expect_sec := 0.1; > glob_current_iter := 0; > glob_max_sec := 10000.0; > glob_small_float := 0.1e-50; > glob_optimal_start := 0.0; > glob_relerr := 0.1e-10; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > min_in_hour := 60.0; > djd_debug2 := true; > glob_log10abserr := 0.0; > MAX_UNCHANGED := 10; > glob_hmin := 0.00000000001; > days_in_year := 365.0; > glob_log10normmin := 0.1; > glob_warned := false; > glob_optimal_clock_start_sec := 0.0; > glob_reached_optimal_h := false; > glob_not_yet_finished := true; > glob_max_trunc_err := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_display_flag := true; > glob_subiter_method := 3; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 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/mtest8postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 4 ) = y1 - 1.0;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.1;"); > 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,"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 + sin(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,""); > omniout_str(ALWAYS,""); > 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_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_tmp5:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_y1_init:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y2:= Array(1..(max_terms + 1),[]); > array_y1:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher := Array(1..(5+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher_work := Array(1..(5+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work2 := Array(1..(5+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > 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_tmp5[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_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y2[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_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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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 <=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 <=5 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 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 <=5 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_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 <=5 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 <= max_terms do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3[1] := 3; > array_const_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_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_4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4[1] := 4; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.1; > 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); > 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] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 4; > #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 <= 5 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 5 + 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 := 4; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #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 := 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 := 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 := 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 := 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 , 4 ) = y1 - 1.0;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"); > 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,"2012-06-13T03:32:03-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest8") > ; > logitem_str(html_log_file,"diff ( y2 , x , 4 ) = y1 - 1.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 5 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"mtest8 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest8 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 * diff ( y2 , x , 3 ) ;") > ; > 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 glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO, glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err, glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours, glob_abserr, glob_large_float, glob_hmax, glob_start, centuries_in_millinium, years_in_century, glob_dump, glob_percent_done, glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs, glob_dump_analytic, glob_last_good_h, glob_disp_incr, glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter, glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr, glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr, MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned, glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished, glob_max_trunc_err, glob_log10_abserr, glob_display_flag, glob_subiter_method, array_const_3, array_const_1, array_const_1D0, array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole, array_y2, array_y1, array_y2_init, array_x, array_type_pole, array_last_rel_error, array_1st_rel_error, array_norms, array_poles, array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work, array_y1_higher_work2, array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_iolevel := 5; DEBUGMASSIVE := 4; ALWAYS := 1; glob_max_terms := 30; DEBUGL := 3; INFO := 2; glob_h := 0.1; glob_initial_pass := true; djd_debug := true; glob_iter := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_look_poles := false; sec_in_min := 60.0; glob_smallish_float := 0.1*10^(-100); glob_max_hours := 0.; glob_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmax := 1.0; glob_start := 0; centuries_in_millinium := 10.0; years_in_century := 100.0; glob_dump := false; glob_percent_done := 0.; glob_log10relerr := 0.; glob_normmax := 0.; glob_unchanged_h_cnt := 0; glob_no_eqs := 0; glob_dump_analytic := false; glob_last_good_h := 0.1; glob_disp_incr := 0.1; glob_not_yet_start_msg := true; glob_max_opt_iter := 10; glob_max_minutes := 0.; glob_hmin_init := 0.001; glob_optimal_done := false; glob_clock_start_sec := 0.; glob_html_log := true; glob_curr_iter_when_opt := 0; glob_orig_start_sec := 0.; glob_warned2 := false; glob_max_iter := 1000; glob_log10_relerr := 0.1*10^(-10); hours_in_day := 24.0; glob_optimal_expect_sec := 0.1; glob_current_iter := 0; glob_max_sec := 10000.0; glob_small_float := 0.1*10^(-50); glob_optimal_start := 0.; glob_relerr := 0.1*10^(-10); glob_clock_sec := 0.; glob_almost_1 := 0.9990; min_in_hour := 60.0; djd_debug2 := true; glob_log10abserr := 0.; MAX_UNCHANGED := 10; glob_hmin := 0.1*10^(-10); days_in_year := 365.0; glob_log10normmin := 0.1; glob_warned := false; glob_optimal_clock_start_sec := 0.; glob_reached_optimal_h := false; glob_not_yet_finished := true; glob_max_trunc_err := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_display_flag := true; glob_subiter_method := 3; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 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/mtest8postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.1;"); 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, "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 +\tsin(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, ""); omniout_str(ALWAYS, ""); 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_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_tmp5 := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_y1_init := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y2 := Array(1 .. max_terms + 1, []); array_y1 := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y2_higher := Array(1 .. 6, 1 .. max_terms + 1, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_y2_higher_work := Array(1 .. 6, 1 .. max_terms + 1, []); array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_higher_work2 := Array(1 .. 6, 1 .. max_terms + 1, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); 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_tmp5[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_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[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_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_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; 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 <= 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 <= 5 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 5 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 5 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 <= max_terms do array_y1_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_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_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_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; array_const_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_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_4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4[term] := 0.; term := term + 1 end do; array_const_4[1] := 4; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.1; x_end := 5.1; 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); 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] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 4; 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 <= 5 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 5 + 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 := 4; 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 := 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 := 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 := 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 := 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 , 4 ) = y1 - 1.0;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"); 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, "2012-06-13T03:32:03-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest8") ; logitem_str(html_log_file, "diff ( y2 , x , 4 ) = y1 - 1.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "mtest8 diffeq.mxt"); logitem_str(html_log_file, "mtest8 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 * diff ( y2 , x , 3 ) ;"); 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/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.1; 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); 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 + sin(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; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 1.0998334166468281523068141984106 y1[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.0001 x[1] = 0.1 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 1.0998334166468281523068141984106 y1[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.18 NO POLE NO POLE x[1] = 0.1001 y2[1] (analytic) = 1.0999329165640230380377921416845 y2[1] (numeric) = 1.0999329165640230380377921416845 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 1.0999329165640230380377921416845 y1[1] (numeric) = 1.0999329165641225381214627433772 absolute error = 9.95000836706016927e-14 relative error = 9.0460138224993432887702211551991e-12 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002 y2[1] (analytic) = 1.1000324154818887589613140090031 y2[1] (numeric) = 1.1000324154818887589613140090045 absolute error = 1.4e-30 relative error = 1.2726897683162410327729518353249e-28 % h = 0.0001 y1[1] (analytic) = 1.1000324154818887589613140090031 y1[1] (numeric) = 1.1000324154823862580468709308103 absolute error = 4.974990855569218072e-13 relative error = 4.5225856852498613587116343421850e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.37 NO POLE NO POLE x[1] = 0.1003 y2[1] (analytic) = 1.1001319133994303258995517487798 y2[1] (numeric) = 1.1001319133994303258995517488002 absolute error = 2.04e-29 relative error = 1.8543230817624023666774426885434e-27 % h = 0.0001 y1[1] (analytic) = 1.1001319133994303258995517487798 y1[1] (numeric) = 1.1001319134006243199033095627653 absolute error = 1.1939940037578139855e-12 relative error = 1.0853189414970681674906284838449e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.4MB, time=0.58 NO POLE NO POLE x[1] = 0.1004 y2[1] (analytic) = 1.1002314103156527596779188409447 y2[1] (numeric) = 1.1002314103156527596779188410728 absolute error = 1.281e-28 relative error = 1.1643005171361953106497222382901e-26 % h = 0.0001 y1[1] (analytic) = 1.1002314103156527596779188409447 y1[1] (numeric) = 1.1002314103178417415083210454471 absolute error = 2.1889818304022045024e-12 relative error = 1.9895649314121952228589177065676e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=0.78 NO POLE NO POLE x[1] = 0.1005 y2[1] (analytic) = 1.1003309062295610911350200886824 y2[1] (numeric) = 1.1003309062295610911350200892023 absolute error = 5.199e-28 relative error = 4.7249422610649973863407507113785e-26 % h = 0.0001 y1[1] (analytic) = 1.1003309062295610911350200886824 y1[1] (numeric) = 1.1003309062330435506866692410265 absolute error = 3.4824595516491523441e-12 relative error = 3.1649202362062979273629316159172e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=1.00 NO POLE NO POLE x[1] = 0.1006 y2[1] (analytic) = 1.1004304011401603611326013100376 y2[1] (numeric) = 1.1004304011401603611326013116524 absolute error = 1.6148e-27 relative error = 1.4674258347705581655075063918353e-25 % h = 0.0001 y1[1] (analytic) = 1.1004304011401603611326013100376 y1[1] (numeric) = 1.1004304011452347852802892194142 absolute error = 5.0744241476879093766e-12 relative error = 4.6113085774713949411215396433950e-10 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007 y2[1] (analytic) = 1.1005298950464556205654989292891 y2[1] (numeric) = 1.1005298950464556205654989334745 absolute error = 4.1854e-27 relative error = 3.8030770620940975847112305765611e-25 % h = 0.0001 y1[1] (analytic) = 1.1005298950464556205654989292891 y1[1] (numeric) = 1.1005298950534204931582369098929 absolute error = 6.9648725927379806038e-12 relative error = 6.3286537004467098722489559672347e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.20 NO POLE NO POLE x[1] = 0.1008 y2[1] (analytic) = 1.1006293879474519303715894679936 y2[1] (numeric) = 1.1006293879474519303715894775101 absolute error = 9.5165e-27 relative error = 8.6464164088396597415659209941650e-25 % h = 0.0001 y1[1] (analytic) = 1.1006293879474519303715894679936 y1[1] (numeric) = 1.1006293879566057322266386525082 absolute error = 9.1538018550491845146e-12 relative error = 8.3168793740097919964286451967413e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.41 NO POLE NO POLE x[1] = 0.1009 y2[1] (analytic) = 1.100728879842154361541738935598 y2[1] (numeric) = 1.1007288798421543615417389551925 absolute error = 1.95945e-26 relative error = 1.7801386298513282567575559361485e-24 % h = 0.0001 y1[1] (analytic) = 1.100728879842154361541738935598 y1[1] (numeric) = 1.1007288798537955704386406491186 absolute error = 1.16412088969017135206e-11 relative error = 1.0575909390667640782393801187117e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.61 NO POLE NO POLE x[1] = 0.101 y2[1] (analytic) = 1.1008283707295679951297521195232 y2[1] (numeric) = 1.1008283707295679951297521568492 absolute error = 3.73260e-26 relative error = 3.3907192976197004443007167945504e-24 % h = 0.0001 y1[1] (analytic) = 1.1008283707295679951297521195232 y1[1] (numeric) = 1.1008283707439950858043583140049 absolute error = 1.44270906746061944817e-11 relative error = 1.3105667566547834219004257105695e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=34.3MB, alloc=4.4MB, time=1.82 x[1] = 0.1011 y2[1] (analytic) = 1.1009278606086979222623217746172 y2[1] (numeric) = 1.1009278606086979222623218414041 absolute error = 6.67869e-26 relative error = 6.0664192804670990780518423165325e-24 % h = 0.0001 y1[1] (analytic) = 1.1009278606086979222623217746172 y1[1] (numeric) = 1.1009278606262093664008255239401 absolute error = 1.75114441385037493229e-11 relative error = 1.5906077741389660945062421665063e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1012 y2[1] (analytic) = 1.1010273494785492441489777118801 y2[1] (numeric) = 1.1010273494785492441489778253806 absolute error = 1.135005e-25 relative error = 1.0308599514240429185039002887606e-23 % h = 0.0001 y1[1] (analytic) = 1.1010273494785492441489777118801 y1[1] (numeric) = 1.1010273494994435103819437676198 absolute error = 2.08942662329660557397e-11 relative error = 1.8977063778535256177651051417170e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.03 NO POLE NO POLE x[1] = 0.1013 y2[1] (analytic) = 1.1011268373381270720920357863605 y2[1] (numeric) = 1.101126837338127072092035971107 absolute error = 1.847465e-25 relative error = 1.6777949073206469496090767862522e-23 % h = 0.0001 y1[1] (analytic) = 1.1011268373381270720920357863605 y1[1] (numeric) = 1.1011268373627026259884311943538 absolute error = 2.45755538963954079933e-11 relative error = 2.2318549564920741438229400384498e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=2.24 NO POLE NO POLE x[1] = 0.1014 y2[1] (analytic) = 1.101226324186436527496546784124 y2[1] (numeric) = 1.1012263241864365274965470740229 absolute error = 2.898989e-25 relative error = 2.6325097178744921008613354181322e-23 % h = 0.0001 y1[1] (analytic) = 1.101226324186436527496546784124 y1[1] (numeric) = 1.1012263242149918315577715619194 absolute error = 2.85553040612247777954e-11 relative error = 2.5930459011067368074453203227608e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.44 NO POLE NO POLE x[1] = 0.1015 y2[1] (analytic) = 1.1013258100224827418802452081946 y2[1] (numeric) = 1.1013258100224827418802456489886 absolute error = 4.407940e-25 relative error = 4.0023941688155071976380199302566e-23 % h = 0.0001 y1[1] (analytic) = 1.1013258100224827418802452081946 y1[1] (numeric) = 1.1013258100553162555341630834766 absolute error = 3.28335136539178752820e-11 relative error = 2.9812716051072664575321893221544e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1016 y2[1] (analytic) = 1.1014252948452708568834979633685 y2[1] (numeric) = 1.1014252948452708568834986154977 absolute error = 6.521292e-25 relative error = 5.9207755900649771563815915852942e-23 % h = 0.0001 y1[1] (analytic) = 1.1014252948452708568834979633685 y1[1] (numeric) = 1.1014252948826810364784671734467 absolute error = 3.74101795949692100782e-11 relative error = 3.3965244642601587679618439421856e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=2.65 NO POLE NO POLE x[1] = 0.1017 y2[1] (analytic) = 1.101524778653806024279252939803 y2[1] (numeric) = 1.1015247786538060242792538816925 absolute error = 9.418895e-25 relative error = 8.5507790496651443868365739384499e-23 % h = 0.0001 y1[1] (analytic) = 1.101524778653806024279252939803 y1[1] (numeric) = 1.1015247786960913230781570922533 absolute error = 4.22852987989041524503e-11 relative error = 3.8387968766877677272432241008508e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=2.86 NO POLE NO POLE x[1] = 0.1018 y2[1] (analytic) = 1.101624261447093405982987495278 y2[1] (numeric) = 1.1016242614470934059829888270844 absolute error = 1.3318064e-24 relative error = 1.2089479567657119166817662778208e-22 % h = 0.0001 y1[1] (analytic) = 1.101624261447093405982987495278 y1[1] (numeric) = 1.1016242614945522741572664898276 absolute error = 4.74588681742789945496e-11 relative error = 4.3080812428674215071911733835710e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=3.07 NO POLE NO POLE x[1] = 0.1019 y2[1] (analytic) = 1.1017237432241381740626568360333 y2[1] (numeric) = 1.101723743224138174062658683878 absolute error = 1.8478447e-24 relative error = 1.6772305320319021309030924535472e-22 % h = 0.0001 y1[1] (analytic) = 1.1017237432241381740626568360333 y1[1] (numeric) = 1.1017237432770690586863378477777 absolute error = 5.29308846236810117444e-11 relative error = 4.8043699656305387101220906280288e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=61.0MB, alloc=4.4MB, time=3.27 x[1] = 0.102 y2[1] (analytic) = 1.1018232239839455107486422960806 y2[1] (numeric) = 1.1018232239839455107486448168008 absolute error = 2.5207202e-24 relative error = 2.2877718903815091568842156062779e-22 % h = 0.0001 y1[1] (analytic) = 1.1018232239839455107486422960806 y1[1] (numeric) = 1.1018232240426468557923708201226 absolute error = 5.87013450437285240420e-11 relative error = 5.3276554501617449945487435328030e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1021 y2[1] (analytic) = 1.1019227037255206084436995148916 y2[1] (numeric) = 1.1019227037255206084437029013381 absolute error = 3.3864465e-24 relative error = 3.0732160146539048548574804935938e-22 % h = 0.0001 y1[1] (analytic) = 1.1019227037255206084436995148916 y1[1] (numeric) = 1.1019227037902908547687704724917 absolute error = 6.47702463250709576001e-11 relative error = 5.8779301039979900791351970822378e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=3.48 NO POLE NO POLE x[1] = 0.1022 y2[1] (analytic) = 1.1020221824478686697329065133617 y2[1] (numeric) = 1.1020221824478686697329110002743 absolute error = 4.4869126e-24 relative error = 4.0715265731161941438273795124900e-22 % h = 0.0001 y1[1] (analytic) = 1.1020221824478686697329065133617 y1[1] (numeric) = 1.10202218251900625508529541969 absolute error = 7.11375853523889063283e-11 relative error = 6.4551863370276651247909146832501e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=3.70 NO POLE NO POLE x[1] = 0.1023 y2[1] (analytic) = 1.1021216601499949073936116679517 y2[1] (numeric) = 1.102121660149994907393617538441 absolute error = 5.8704893e-24 relative error = 5.3265347304770753860088683786306e-22 % h = 0.0001 y1[1] (analytic) = 1.1021216601499949073936116679517 y1[1] (numeric) = 1.1021216602277982663980058615294 absolute error = 7.78033590043941935777e-11 relative error = 7.0594165614897204945381627518617e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=3.91 NO POLE NO POLE x[1] = 0.1024 y2[1] (analytic) = 1.1022211368309045444053815829051 y2[1] (numeric) = 1.1022211368309045444053891755714 absolute error = 7.5926663e-24 relative error = 6.8885145151819171657881464561988e-22 % h = 0.0001 y1[1] (analytic) = 1.1022211368309045444053815829051 y1[1] (numeric) = 1.1022211369156721085592115168272 absolute error = 8.47675641538299339221e-11 relative error = 7.6906131919727838912860736424198e-09 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1025 y2[1] (analytic) = 1.102320612489602813959948860445 y2[1] (numeric) = 1.1023206124896028139599585771634 absolute error = 9.7167184e-24 relative error = 8.8147842741094065788421720542393e-22 % h = 0.0001 y1[1] (analytic) = 1.102320612489602813959948860445 y1[1] (numeric) = 1.1023206125816330116274194554716 absolute error = 9.20301976674705950266e-11 relative error = 8.3487686454142788729460667711390e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=4.11 NO POLE NO POLE x[1] = 0.1026 y2[1] (analytic) = 1.1024200871250949594711597688478 y2[1] (numeric) = 1.1024200871250949594711720832502 absolute error = 1.23144024e-23 relative error = 1.1170335649555927689332415162079e-21 % h = 0.0001 y1[1] (analytic) = 1.1024200871250949594711597688478 y1[1] (numeric) = 1.1024200872246862158772818284554 absolute error = 9.95912564061220596076e-11 relative error = 9.0338753410995437450675215633836e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=4.32 NO POLE NO POLE x[1] = 0.1027 y2[1] (analytic) = 1.102519560736386234584921808297 y2[1] (numeric) = 1.1025195607363862345849372749798 absolute error = 1.54666828e-23 relative error = 1.4028488337811997000760816399814e-21 % h = 0.0001 y1[1] (analytic) = 1.102519560736386234584921808297 y1[1] (numeric) = 1.1025195608438369718095434957776 absolute error = 1.074507372246216874806e-10 relative error = 9.7459257006609508304831041933828e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=4.53 NO POLE NO POLE x[1] = 0.1028 y2[1] (analytic) = 1.1026190333224819031891511744154 y2[1] (numeric) = 1.1026190333224819031891704389039 absolute error = 1.92644885e-23 relative error = 1.7471572608311518248174716117714e-21 % h = 0.0001 y1[1] (analytic) = 1.1026190333224819031891511744154 y1[1] (numeric) = 1.1026190334380905401609895521145 absolute error = 1.156086369718383776991e-10 relative error = 1.0484912148077026116079269040747e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=87.7MB, alloc=4.5MB, time=4.74 x[1] = 0.1029 y2[1] (analytic) = 1.102718504882387239423720119378 y2[1] (numeric) = 1.1027185048823872394237439288761 absolute error = 2.38094981e-23 relative error = 2.1591637389398350650449237701550e-21 % h = 0.0001 y1[1] (analytic) = 1.102718504882387239423720119378 y1[1] (numeric) = 1.10271850500645219191439275016 absolute error = 1.240649524906726307820e-10 relative error = 1.1250827109671569276272298758398e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.103 y2[1] (analytic) = 1.1028179754151075276904042105046 y2[1] (numeric) = 1.102817975415107527690433425461 absolute error = 2.92149564e-23 relative error = 2.6491186262178315660044586430199e-21 % h = 0.0001 y1[1] (analytic) = 1.1028179754151075276904042105046 y1[1] (numeric) = 1.1028179755479272083084608215356 absolute error = 1.328196806180566110310e-10 relative error = 1.2043663014112774073142292226916e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.5MB, time=4.94 NO POLE NO POLE x[1] = 0.1031 y2[1] (analytic) = 1.1029174449196480626628294862341 y2[1] (numeric) = 1.1029174449196480626628650927535 absolute error = 3.56065194e-23 relative error = 3.2283938896799367458760854526067e-21 % h = 0.0001 y1[1] (analytic) = 1.1029174449196480626628294862341 y1[1] (numeric) = 1.1029174450615208808477836951712 absolute error = 1.418728181849542089371e-10 relative error = 1.2863412292412349132959907064457e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=5.15 NO POLE NO POLE x[1] = 0.1032 y2[1] (analytic) = 1.1030169133950141492964195093798 y2[1] (numeric) = 1.10301691339501414929646263251 absolute error = 4.31231302e-23 relative error = 3.9095620090964712966782556299873e-21 % h = 0.0001 y1[1] (analytic) = 1.1030169133950141492964195093798 y1[1] (numeric) = 1.1030169135462385113127806130571 absolute error = 1.512243620163611036773e-10 relative error = 1.3710067377924639099022143329945e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=5.36 NO POLE NO POLE x[1] = 0.1033 y2[1] (analytic) = 1.103116380840211102838342317567 y2[1] (numeric) = 1.103116380840211102838394235491 absolute error = 5.19179240e-23 relative error = 4.7064774761531193737487332164444e-21 % h = 0.0001 y1[1] (analytic) = 1.103116380840211102838342317567 y1[1] (numeric) = 1.103116381001085411769647143267 absolute error = 1.608743089313048257000e-10 relative error = 1.4583620706345746160477787342816e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1034 y2[1] (analytic) = 1.1032158472542442488374572707527 y2[1] (numeric) = 1.1032158472542442488375194299164 absolute error = 6.21591637e-23 relative error = 5.6343610232490579098479865745046e-21 % h = 0.0001 y1[1] (analytic) = 1.1032158472542442488374572707527 y1[1] (numeric) = 1.1032158474250669045803020901534 absolute error = 1.708226557428448194007e-10 relative error = 1.5484064715712651957104329414243e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=5.56 NO POLE NO POLE x[1] = 0.1035 y2[1] (analytic) = 1.1033153126361189231542617957292 y2[1] (numeric) = 1.1033153126361189231543358269334 absolute error = 7.40312042e-23 relative error = 6.7098864080042009637703187944274e-21 % h = 0.0001 y1[1] (analytic) = 1.1033153126361189231542617957292 y1[1] (numeric) = 1.1033153128171883224123343016158 absolute error = 1.810693992580725058866e-10 relative error = 1.6411391846402339859726256900810e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=5.77 NO POLE NO POLE x[1] = 0.1036 y2[1] (analytic) = 1.1034147769848404719708380275103 y2[1] (numeric) = 1.1034147769848404719709257629984 absolute error = 8.77354881e-23 relative error = 7.9512699965595417256046762126644e-21 % h = 0.0001 y1[1] (analytic) = 1.1034147769848404719708380275103 y1[1] (numeric) = 1.1034147771764550082489493733416 absolute error = 1.916145362781113458313e-10 relative error = 1.7365594541130917626200447637920e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=5.97 NO POLE NO POLE x[1] = 0.1037 y2[1] (analytic) = 1.1035142402994142518007993475029 y2[1] (numeric) = 1.1035142402994142518009028390722 absolute error = 1.034915693e-22 relative error = 9.3783628267379535683344023061879e-21 % h = 0.0001 y1[1] (analytic) = 1.1035142402994142518007993475029 y1[1] (numeric) = 1.1035142405018723153989162499209 absolute error = 2.024580635981169024180e-10 relative error = 1.8346665244952740432640675426129e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=114.4MB, alloc=4.5MB, time=6.18 x[1] = 0.1038 y2[1] (analytic) = 1.1036137025788456294992368183617 y2[1] (numeric) = 1.1036137025788456294993583565305 absolute error = 1.215381688e-22 relative error = 1.1012745539131880383165353760052e-20 % h = 0.0001 y1[1] (analytic) = 1.1036137025788456294992368183617 y1[1] (numeric) = 1.1036137027924456075065137227357 absolute error = 2.135999780072769043740e-10 relative error = 1.9354596405259534279952133868520e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1039 y2[1] (analytic) = 1.1037131638221399822726655154307 y2[1] (numeric) = 1.1037131638221399822728076496887 absolute error = 1.421342580e-22 relative error = 1.2877825748475398555555652378097e-20 % h = 0.0001 y1[1] (analytic) = 1.1037131638221399822726655154307 y1[1] (numeric) = 1.1037131640471802585614768245235 absolute error = 2.250402762888113090928e-10 relative error = 2.0389380471779519775157880552008e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.5MB, time=6.41 NO POLE NO POLE x[1] = 0.104 y2[1] (analytic) = 1.1038126240283026976889707546695 y2[1] (numeric) = 1.1038126240283026976891363148427 absolute error = 1.655601732e-22 relative error = 1.4998938188965203922855442289756e-20 % h = 0.0001 y1[1] (analytic) = 1.1038126240283026976889707546695 y1[1] (numeric) = 1.1038126242650816529089431205162 absolute error = 2.367789552199723658467e-10 relative error = 2.1451009896576536287597372576594e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.5MB, time=6.64 NO POLE NO POLE x[1] = 0.1041 y2[1] (analytic) = 1.103912083196339173687354216966 y2[1] (numeric) = 1.1039120831963391736875463357261 absolute error = 1.921187601e-22 relative error = 1.7403447523078721019858147939421e-20 % h = 0.0001 y1[1] (analytic) = 1.103912083196339173687354216966 y1[1] (numeric) = 1.1039120834451551852593988960551 absolute error = 2.488160115720446790891e-10 relative error = 2.2539477134049166479742003019393e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=6.85 NO POLE NO POLE x[1] = 0.1042 y2[1] (analytic) = 1.1040115413252548185882799687365 y2[1] (numeric) = 1.1040115413252548185885021052833 absolute error = 2.221365468e-22 relative error = 2.0120853676343583973149372645620e-20 % h = 0.0001 y1[1] (analytic) = 1.1040115413252548185882799687365 y1[1] (numeric) = 1.1040115415864062606986252405822 absolute error = 2.611514421103452718457e-10 relative error = 2.3654774640929861212372699783552e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1043 y2[1] (analytic) = 1.1041109984140550511034203787124 y2[1] (numeric) = 1.1041109984140550511036763436607 absolute error = 2.559649483e-22 relative error = 2.3182899968179651416668427897635e-20 % h = 0.0001 y1[1] (analytic) = 1.1041109984140550511034203787124 y1[1] (numeric) = 1.104110998687840294697644027908 absolute error = 2.737852435942236491956e-10 relative error = 2.4796894876284064824027827127760e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=7.06 NO POLE NO POLE x[1] = 0.1044 y2[1] (analytic) = 1.1042104544617453003456019308154 y2[1] (numeric) = 1.1042104544617453003458959123149 absolute error = 2.939814995e-22 relative error = 2.6623683765365473657664712927605e-20 % h = 0.0001 y1[1] (analytic) = 1.1042104544617453003456019308154 y1[1] (numeric) = 1.1042104547484627131226637926571 absolute error = 2.867174127770618618417e-10 relative error = 2.5965830301509340784484764440782e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.5MB, time=7.27 NO POLE NO POLE x[1] = 0.1045 y2[1] (analytic) = 1.1043099094673310058387509330207 y2[1] (numeric) = 1.1043099094673310058390875241398 absolute error = 3.365911191e-22 relative error = 3.0479769873871392099507117317212e-20 % h = 0.0001 y1[1] (analytic) = 1.1043099094673310058387509330207 y1[1] (numeric) = 1.1043099097672789522450255027917 absolute error = 2.999479464062745697710e-10 relative error = 2.7161573380334497722147340550824e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=7.48 NO POLE NO POLE x[1] = 0.1046 y2[1] (analytic) = 1.1044093634298176175278391221099 y2[1] (numeric) = 1.104409363429817617528223349512 absolute error = 3.842274021e-22 relative error = 3.4790306459079262047776716243949e-20 % h = 0.0001 y1[1] (analytic) = 1.1044093634298176175278391221099 y1[1] (numeric) = 1.1044093637432944587511482281136 absolute error = 3.134768412233091060037e-10 relative error = 2.8384116578818715825057433628662e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=7.69 NO POLE NO POLE x[1] = 0.1047 y2[1] (analytic) = 1.1045088163482105957888291642125 y2[1] (numeric) = 1.1045088163482105957892665181561 absolute error = 4.373539436e-22 relative error = 3.9597143737250038380604703722220e-20 % h = 0.0001 y1[1] (analytic) = 1.1045088163482105957888291642125 y1[1] (numeric) = 1.1045088166755146897524747046453 absolute error = 3.273040939636455404328e-10 relative error = 2.9633452365350673615502724149016e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1048 y2[1] (analytic) = 1.1046082682215154114386200510382 y2[1] (numeric) = 1.1046082682215154114391165167295 absolute error = 4.964656913e-22 relative error = 4.4944955201117505809339197791633e-20 % h = 0.0001 y1[1] (analytic) = 1.1046082682215154114386200510382 y1[1] (numeric) = 1.1046082685629451127954167947905 absolute error = 3.414297013567967437523e-10 relative error = 3.0909573210647675097866669322521e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=7.89 NO POLE NO POLE x[1] = 0.1049 y2[1] (analytic) = 1.1047077190487375457449923916998 y2[1] (numeric) = 1.1047077190487375457455544820279 absolute error = 5.620903281e-22 relative error = 5.0881361504744013937767229185864e-20 % h = 0.0001 y1[1] (analytic) = 1.1047077190487375457449923916998 y1[1] (numeric) = 1.104707719404591205871300843175 absolute error = 3.558536601263084514752e-10 relative error = 3.2212471587754777279647607715000e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.5MB, time=8.11 NO POLE NO POLE x[1] = 0.105 y2[1] (analytic) = 1.1048071688288824904365536000268 y2[1] (numeric) = 1.1048071688288824904371883897118 absolute error = 6.347896850e-22 relative error = 5.7457057024067797757749168382422e-20 % h = 0.0001 y1[1] (analytic) = 1.1048071688288824904365536000268 y1[1] (numeric) = 1.1048071691994584574263129280681 absolute error = 3.705759669897593280413e-10 relative error = 3.3542139972043918065465307378547e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.5MB, time=8.32 NO POLE NO POLE x[1] = 0.1051 y2[1] (analytic) = 1.1049066175609557477126829772711 y2[1] (numeric) = 1.1049066175609557477133981384545 absolute error = 7.151611834e-22 relative error = 6.4725939010003786126513722163957e-20 % h = 0.0001 y1[1] (analytic) = 1.1049066175609557477126829772711 y1[1] (numeric) = 1.1049066179465523663714440082854 absolute error = 3.855966186587610310143e-10 relative error = 3.4898570841213044523828117189536e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1052 y2[1] (analytic) = 1.1050060652439628302534766901051 y2[1] (numeric) = 1.1050060652439628302542805294122 absolute error = 8.038393071e-22 relative error = 7.2745239359616424836873059867355e-20 % h = 0.0001 y1[1] (analytic) = 1.1050060652439628302534766901051 y1[1] (numeric) = 1.1050060656448784420924349654732 absolute error = 4.009156118389582753681e-10 relative error = 3.6281756675285241526470211570032e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=8.52 NO POLE NO POLE x[1] = 0.1053 y2[1] (analytic) = 1.1051055118769092612296926438124 y2[1] (numeric) = 1.105105511876909261230594140917 absolute error = 9.014971046e-22 relative error = 8.1575659058011474418494573083695e-20 % h = 0.0001 y1[1] (analytic) = 1.1051055118769092612296926438124 y1[1] (numeric) = 1.1051055122934422044597215416755 absolute error = 4.165329432300288978631e-10 relative error = 3.7691689956607860760149964393884e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.5MB, time=8.73 NO POLE NO POLE x[1] = 0.1054 y2[1] (analytic) = 1.1052049574588005743126952505717 y2[1] (numeric) = 1.1052049574588005743137040982927 absolute error = 1.0088477210e-21 relative error = 9.1281505225930680455874675355306e-20 % h = 0.0001 y1[1] (analytic) = 1.1052049574588005743126952505717 y1[1] (numeric) = 1.1052049578912491838383791720836 absolute error = 4.324486095256839215119e-10 relative error = 3.9128363169851650110673861290434e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.5MB, time=8.94 NO POLE NO POLE x[1] = 0.1055 y2[1] (analytic) = 1.1053044019886423136844000927352 y2[1] (numeric) = 1.1053044019886423136855267386948 absolute error = 1.1266459596e-21 relative error = 1.0193083078045833965826632209473e-19 % h = 0.0001 y1[1] (analytic) = 1.1053044019886423136844000927352 y1[1] (numeric) = 1.1053044024373049210980677128692 absolute error = 4.486626074136676201340e-10 relative error = 4.0591768802009883418928592029978e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.5MB, time=9.15 NO POLE NO POLE x[1] = 0.1056 y2[1] (analytic) = 1.1054038454654400340472184810008 y2[1] (numeric) = 1.1054038454654400340484741708744 absolute error = 1.2556898736e-21 relative error = 1.1359557674338293159541744534187e-19 % h = 0.0001 y1[1] (analytic) = 1.1054038454654400340472184810008 y1[1] (numeric) = 1.1054038459306149676229760640018 absolute error = 4.651749335757575830010e-10 relative error = 4.2081899342397490608875972351004e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1057 y2[1] (analytic) = 1.1055032878881993006340019073801 y2[1] (numeric) = 1.1055032878881993006353987297674 absolute error = 1.3968223873e-21 relative error = 1.2635171714127566696345220530105e-19 % h = 0.0001 y1[1] (analytic) = 1.1055032878881993006340019073801 y1[1] (numeric) = 1.1055032883701848853217666869502 absolute error = 4.819855846877647795701e-10 relative error = 4.3598747282650188187130656419965e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.5MB, time=9.36 NO POLE NO POLE x[1] = 0.1058 y2[1] (analytic) = 1.1056027292559256892179863928614 y2[1] (numeric) = 1.1056027292559256892195373258089 absolute error = 1.5509329475e-21 relative error = 1.4027940655897105351058265357332e-19 % h = 0.0001 y1[1] (analytic) = 1.1056027292559256892179863928614 y1[1] (numeric) = 1.1056027297550202466375200171692 absolute error = 4.990945574195336243078e-10 relative error = 4.5142305116723610114111681431220e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=9.57 NO POLE NO POLE x[1] = 0.1059 y2[1] (analytic) = 1.1057021695676247861227367296688 y2[1] (numeric) = 1.1057021695676247861244556888735 absolute error = 1.7189592047e-21 relative error = 1.5546313030860598222142619237739e-19 % h = 0.0001 y1[1] (analytic) = 1.1057021695676247861227367296688 y1[1] (numeric) = 1.1057021700841266345576787712725 absolute error = 5.165018484349420416037e-10 relative error = 4.6712565340892439046577980198198e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.5MB, time=9.77 NO POLE NO POLE x[1] = 0.106 y2[1] (analytic) = 1.1058016088223021882320906180187 y2[1] (numeric) = 1.1058016088223021882339925067424 absolute error = 1.9018887237e-21 relative error = 1.7199185717640113929527234397506e-19 % h = 0.0001 y1[1] (analytic) = 1.1058016088223021882320906180187 y1[1] (numeric) = 1.1058016093565096426239921487908 absolute error = 5.342074543919015307721e-10 relative error = 4.8309520453749537951159151941182e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1061 y2[1] (analytic) = 1.1059010470189635030001026972731 y2[1] (numeric) = 1.1059010470189635030022034579974 absolute error = 2.1007607243e-21 relative error = 1.8995919480886223289681454504362e-19 % h = 0.0001 y1[1] (analytic) = 1.1059010470189635030001026972731 y1[1] (numeric) = 1.1059010475711748749424599284175 absolute error = 5.522113719423572311444e-10 relative error = 4.9933162956205082088972276791341e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.5MB, time=9.98 NO POLE NO POLE x[1] = 0.1062 y2[1] (analytic) = 1.1060004841566143484609884713902 y2[1] (numeric) = 1.1060004841566143484633051392427 absolute error = 2.3166678525e-21 relative error = 2.0946354777290947635717187407442e-19 % h = 0.0001 y1[1] (analytic) = 1.1060004841566143484609884713902 y1[1] (numeric) = 1.1060004847271279461932764586416 absolute error = 5.705135977322879872514e-10 relative error = 5.1583485351485691371062840830937e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=10.19 NO POLE NO POLE x[1] = 0.1063 y2[1] (analytic) = 1.1060999202342603532390681285749 y2[1] (numeric) = 1.1060999202342603532416188865546 absolute error = 2.5507579797e-21 relative error = 2.3060827806223656839364676569941e-19 % h = 0.0001 y1[1] (analytic) = 1.1060999202342603532390681285749 y1[1] (numeric) = 1.106099920823374481640774542668 absolute error = 5.891141284017064140931e-10 relative error = 5.3260480145133563084272383786478e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=10.40 NO POLE NO POLE x[1] = 0.1064 y2[1] (analytic) = 1.1061993552509071565587102550263 y2[1] (numeric) = 1.1061993552509071565615144910606 absolute error = 2.8042360343e-21 relative error = 2.5350186844612160075419985790483e-19 % h = 0.0001 y1[1] (analytic) = 1.1061993552509071565587102550263 y1[1] (numeric) = 1.1061993558589201171433692175269 absolute error = 6.080129605846589625006e-10 relative error = 5.4964139845005604987768533148670e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=10.61 NO POLE NO POLE x[1] = 0.1065 y2[1] (analytic) = 1.1062987892055604082542754426865 y2[1] (numeric) = 1.1062987892055604082573538085472 absolute error = 3.0783658607e-21 relative error = 2.7825808820694745765298464374471e-19 % h = 0.0001 y1[1] (analytic) = 1.1062987892055604082542754426865 y1[1] (numeric) = 1.1062987898327704991635014272717 absolute error = 6.272100909092259845852e-10 relative error = 5.6694456961272568779614168429462e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1066 y2[1] (analytic) = 1.1063982220972257687800597908883 y2[1] (numeric) = 1.1063982220972257687834342629981 absolute error = 3.3744721098e-21 relative error = 3.0499616163550424949075950450043e-19 % h = 0.0001 y1[1] (analytic) = 1.1063982220972257687800597908883 y1[1] (numeric) = 1.1063982227439312847775815901668 absolute error = 6.467055159975217992785e-10 relative error = 5.8451424006418183933539211300655e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=10.81 NO POLE NO POLE x[1] = 0.1067 y2[1] (analytic) = 1.1064976539249089092202383018042 y2[1] (numeric) = 1.1064976539249089092239322439624 absolute error = 3.6939421582e-21 relative error = 3.3384093902929185989819499900417e-19 % h = 0.0001 y1[1] (analytic) = 1.1064976539249089092202383018042 y1[1] (numeric) = 1.1064976545914081416859330597652 absolute error = 6.664992324656947579610e-10 relative error = 6.0235033495238291905509024385198e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=11.02 NO POLE NO POLE x[1] = 0.1068 y2[1] (analytic) = 1.1065970846876155112988081695962 y2[1] (numeric) = 1.1065970846876155113028463976544 absolute error = 4.0382280582e-21 relative error = 3.6492307038202283603210218443323e-19 % h = 0.0001 y1[1] (analytic) = 1.1065970846876155112988081695962 y1[1] (numeric) = 1.1065970853742067482227354797772 absolute error = 6.865912369239273101810e-10 relative error = 6.2045277944839980710072240634992e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.5MB, time=11.23 NO POLE NO POLE x[1] = 0.1069 y2[1] (analytic) = 1.1066965143843512673895319631674 y2[1] (numeric) = 1.1066965143843512673939408116845 absolute error = 4.4088485171e-21 relative error = 3.9837918162709822779835759915299e-19 % h = 0.0001 y1[1] (analytic) = 1.1066965143843512673895319631674 y1[1] (numeric) = 1.1066965150913327933659680326301 absolute error = 7.069815259764360694627e-10 relative error = 6.3882149874640719866208785128249e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=209.8MB, alloc=4.5MB, time=11.44 x[1] = 0.107 y2[1] (analytic) = 1.1067959430141218805258807024165 y2[1] (numeric) = 1.1067959430141218805306880933226 absolute error = 4.8073909061e-21 relative error = 4.3435205346055928955899600185838e-19 % h = 0.0001 y1[1] (analytic) = 1.1067959430141218805258807024165 y1[1] (numeric) = 1.1067959437417919767473525816199 absolute error = 7.276700962214718792034e-10 relative error = 6.5745641806367495712489371399595e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1071 y2[1] (analytic) = 1.1068953705759330644109768278945 y2[1] (numeric) = 1.1068953705759330644162123411941 absolute error = 5.2355132996e-21 relative error = 4.7299080281417109685536615606587e-19 % h = 0.0001 y1[1] (analytic) = 1.1068953705759330644109768278945 y1[1] (numeric) = 1.1068953713245900086622967065551 absolute error = 7.486569442513198786606e-10 relative error = 6.7635746264055947091439167256004e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.5MB, time=11.65 NO POLE NO POLE x[1] = 0.1072 y2[1] (analytic) = 1.1069947970687905434275370637652 y2[1] (numeric) = 1.1069947970687905434332320103092 absolute error = 5.6949465440e-21 relative error = 5.1445106689567451647324258116553e-19 % h = 0.0001 y1[1] (analytic) = 1.1069947970687905434275370637652 y1[1] (numeric) = 1.1069947978387326100798366327939 absolute error = 7.699420666522995690287e-10 relative error = 6.9552455774049501402899002758655e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.5MB, time=11.86 NO POLE NO POLE x[1] = 0.1073 y2[1] (analytic) = 1.1070942224917000526478151739699 y2[1] (numeric) = 1.1070942224917000526540026703262 absolute error = 6.1874963563e-21 relative error = 5.5889518982169451313427788130799e-19 % h = 0.0001 y1[1] (analytic) = 1.1070942224917000526478151739699 y1[1] (numeric) = 1.1070942232832255126525800535747 absolute error = 7.915254600047648796048e-10 relative error = 7.1495762864998511026159544973233e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.5MB, time=12.06 NO POLE NO POLE x[1] = 0.1074 y2[1] (analytic) = 1.1071936468436673378435446114965 y2[1] (numeric) = 1.1071936468436673378502596569492 absolute error = 6.7150454527e-21 relative error = 6.0649241185974270074882659886241e-19 % h = 0.0001 y1[1] (analytic) = 1.1071936468436673378435446114965 y1[1] (numeric) = 1.1071936476570744587266488455404 absolute error = 8.134071208831042340439e-10 relative error = 7.3465660067859390110716248975449e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1075 y2[1] (analytic) = 1.1072930701236981554958810606538 y2[1] (numeric) = 1.1072930701236981555031606163608 absolute error = 7.2795557070e-21 relative error = 6.5741906125961618700851423216030e-19 % h = 0.0001 y1[1] (analytic) = 1.1072930701236981554958810606538 y1[1] (numeric) = 1.1072930709592852013516216773583 absolute error = 8.355870458557406167045e-10 relative error = 7.5462139915893751735556189973793e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.5MB, time=12.27 NO POLE NO POLE x[1] = 0.1076 y2[1] (analytic) = 1.1073924923307982728053448722518 y2[1] (numeric) = 1.1073924923307982728132279425904 absolute error = 7.8830703386e-21 relative error = 7.1185874865450898818601915237033e-19 % h = 0.0001 y1[1] (analytic) = 1.1073924923307982728053448722518 y1[1] (numeric) = 1.1073924931888635042904765113342 absolute error = 8.580652314851316390824e-10 relative error = 7.7485194944667545436598947007284e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.5MB, time=12.48 NO POLE NO POLE x[1] = 0.1077 y2[1] (analytic) = 1.1074919134639734677017633915879 y2[1] (numeric) = 1.1074919134639734677102911077186 absolute error = 8.5277161307e-21 relative error = 7.7000256408440179752582157814606e-19 % h = 0.0001 y1[1] (analytic) = 1.1074919134639734677017633915879 y1[1] (numeric) = 1.1074919143448151420295329979231 absolute error = 8.808416743277696063352e-10 relative error = 7.9534817692050195102338331230273e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.5MB, time=12.69 NO POLE NO POLE x[1] = 0.1078 y2[1] (analytic) = 1.107591333522229528854213179141 y2[1] (numeric) = 1.1075913335222295288634288848187 absolute error = 9.2157056777e-21 relative error = 8.3204927654980060982827201421564e-19 % h = 0.0001 y1[1] (analytic) = 1.107591333522229528854213179141 y1[1] (numeric) = 1.1075913344261458997883947630358 absolute error = 9.039163709341815838948e-10 relative error = 8.1611000698213737237262199848009e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=236.5MB, alloc=4.5MB, time=12.89 x[1] = 0.1079 y2[1] (analytic) = 1.1076907525045722556809621238716 y2[1] (numeric) = 1.1076907525045722556909114635352 absolute error = 9.9493396636e-21 relative error = 8.9820553625673892644885874364761e-19 % h = 0.0001 y1[1] (analytic) = 1.1076907525045722556809621238716 y1[1] (numeric) = 1.107690753431861573529891588043 absolute error = 9.272893178489294641714e-10 relative error = 8.3713736505631959593187592253089e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.108 y2[1] (analytic) = 1.1077901704100074583594114490316 y2[1] (numeric) = 1.1077901704100074583701424582001 absolute error = 1.07310091685e-20 relative error = 9.6868607928957474201304579793484e-19 % h = 0.0001 y1[1] (analytic) = 1.1077901704100074583594114490316 y1[1] (numeric) = 1.1077901713609679699700214823764 absolute error = 9.509605116106100333448e-10 relative error = 8.5843017659079540167953217846150e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.5MB, time=13.10 NO POLE NO POLE x[1] = 0.1081 y2[1] (analytic) = 1.1078895872375409578360376103814 y2[1] (numeric) = 1.1078895872375409578476008083882 absolute error = 1.15631980068e-20 relative error = 1.0437139350350038014798718965931e-18 % h = 0.0001 y1[1] (analytic) = 1.1078895872375409578360376103814 y1[1] (numeric) = 1.1078895882124709065878926486283 absolute error = 9.749299487518550382469e-10 relative error = 8.7998836705631186571642814345729e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.5MB, time=13.31 NO POLE NO POLE x[1] = 0.1082 y2[1] (analytic) = 1.1079890029861785858363340867174 y2[1] (numeric) = 1.107989002986178585848782571811 absolute error = 1.24484850936e-20 relative error = 1.1235206360396779534030535323011e-18 % h = 0.0001 y1[1] (analytic) = 1.1079890029861785858363340867174 y1[1] (numeric) = 1.10798900398537621163566534005 absolute error = 9.991976257993312533326e-10 relative error = 9.0181186194660775759908040685487e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.5MB, time=13.52 NO POLE NO POLE x[1] = 0.1083 y2[1] (analytic) = 1.1080884176549261848747530626082 y2[1] (numeric) = 1.1080884176549261848881426094505 absolute error = 1.33895468423e-20 relative error = 1.2083464305706412615802518900321e-18 % h = 0.0001 y1[1] (analytic) = 1.1080884176549261848747530626082 y1[1] (numeric) = 1.1080884186786897241484936103493 absolute error = 1.0237635392737405477411e-09 relative error = 9.2390058677840494134393025636054e-08 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1084 y2[1] (analytic) = 1.1081878312427896082646470032422 y2[1] (numeric) = 1.1081878312427896082790361628331 absolute error = 1.43891595909e-20 relative error = 1.2984404976512976528256861318913e-18 % h = 0.0001 y1[1] (analytic) = 1.1081878312427896082646470032422 y1[1] (numeric) = 1.1081878322914172939544669556877 absolute error = 1.0486276856898199524455e-09 relative error = 9.4625446709139978009892687424593e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.5MB, time=13.72 NO POLE NO POLE x[1] = 0.1085 y2[1] (analytic) = 1.1082872437487747201282101212859 y2[1] (numeric) = 1.1082872437487747201436603233444 absolute error = 1.54502020585e-20 relative error = 1.3940611647067043264298683575551e-18 % h = 0.0001 y1[1] (analytic) = 1.1082872437487747201282101212859 y1[1] (numeric) = 1.1082872448225647816845518487787 absolute error = 1.0737900615563417274928e-09 relative error = 9.6887342844825454448256135814270e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.5MB, time=13.93 NO POLE NO POLE x[1] = 0.1086 y2[1] (analytic) = 1.1083866551718873954064197356531 y2[1] (numeric) = 1.1083866551718873954229953934854 absolute error = 1.65756578323e-20 relative error = 1.4954761278436237609631645482182e-18 % h = 0.0001 y1[1] (analytic) = 1.1083866551718873954064197356531 y1[1] (numeric) = 1.1083866562711380587825331649864 absolute error = 1.0992506633761134293333e-09 relative error = 9.9175739643458882458766743285497e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.5MB, time=14.14 NO POLE NO POLE x[1] = 0.1087 y2[1] (analytic) = 1.1084860655111335198689775220874 y2[1] (numeric) = 1.1084860655111335198867461399707 absolute error = 1.77686178833e-20 relative error = 1.6029626746013014118607312888524e-18 % h = 0.0001 y1[1] (analytic) = 1.1084860655111335198689775220874 y1[1] (numeric) = 1.1084860666361430075149555003264 absolute error = 1.1250094876459779782390e-09 relative error = 1.0149062966589709456478476153064e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=263.2MB, alloc=4.5MB, time=14.36 x[1] = 0.1088 y2[1] (analytic) = 1.1085854747655189901242506554567 y2[1] (numeric) = 1.1085854747655189901432829385692 absolute error = 1.90322831125e-20 relative error = 1.7168079093337921032595718354278e-18 % h = 0.0001 y1[1] (analytic) = 1.1085854747655189901242506554567 y1[1] (numeric) = 1.1085854759165855209810643812684 absolute error = 1.1510665308568137258117e-09 relative error = 1.0383200547529093873653770776773e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1089 y2[1] (analytic) = 1.1086848829340497136292128436612 y2[1] (numeric) = 1.108684882934049713649582810588 absolute error = 2.03699669268e-20 relative error = 1.8373089811500307553651957836440e-18 % h = 0.0001 y1[1] (analytic) = 1.1086848829340497136292128436612 y1[1] (numeric) = 1.1086848841114715031227473662421 absolute error = 1.1774217894935345225809e-09 relative error = 1.0619985963708442068988967869697e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.5MB, time=14.58 NO POLE NO POLE x[1] = 0.109 y2[1] (analytic) = 1.1087842900157316086993852530554 y2[1] (numeric) = 1.1087842900157316087211703509003 absolute error = 2.17850978449e-20 relative error = 1.9647733144371038617748464488771e-18 % h = 0.0001 y1[1] (analytic) = 1.1087842900157316086993852530554 y1[1] (numeric) = 1.1087842912198068687344750387459 absolute error = 1.2040752600350897856905e-09 relative error = 1.0859418471901384655082163245606e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.5MB, time=14.81 NO POLE NO POLE x[1] = 0.1091 y2[1] (analytic) = 1.1088836960095706045187773252847 y2[1] (numeric) = 1.1088836960095706045420585474172 absolute error = 2.32812221325e-20 relative error = 2.0995188419019791733726011797442e-18 % h = 0.0001 y1[1] (analytic) = 1.1088836960095706045187773252847 y1[1] (numeric) = 1.1088836972405975434732418919603 absolute error = 1.2310269389544645666756e-09 relative error = 1.1101497329110696588556225611361e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.5MB, time=15.02 NO POLE NO POLE x[1] = 0.1092 y2[1] (analytic) = 1.1089831009145726411498274854369 y2[1] (numeric) = 1.1089831009145726411746894919047 absolute error = 2.48620064678e-20 relative error = 2.2418742402202911432969226737613e-18 % h = 0.0001 y1[1] (analytic) = 1.1089831009145726411498274854369 y1[1] (numeric) = 1.1089831021728494638685071047653 absolute error = 1.2582768227186796193284e-09 relative error = 1.1346221792568211509610165156367e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1093 y2[1] (analytic) = 1.1090825047297436695433437414095 y2[1] (numeric) = 1.1090825047297436695698749820463 absolute error = 2.65312406368e-20 relative error = 2.3921791682454693159233240860635e-18 % h = 0.0001 y1[1] (analytic) = 1.1090825047297436695433437414095 y1[1] (numeric) = 1.1090825060155685773321352090634 absolute error = 1.2858249077887914676539e-09 relative error = 1.1593591119734736118097351378887e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.5MB, time=15.22 NO POLE NO POLE x[1] = 0.1094 y2[1] (analytic) = 1.1091819074540896515484441743935 y2[1] (numeric) = 1.1091819074540896515767370146515 absolute error = 2.82928402580e-20 relative error = 2.5507845077405460705057513464211e-18 % h = 0.0001 y1[1] (analytic) = 1.1091819074540896515484441743935 y1[1] (numeric) = 1.1091819087677608421683366483078 absolute error = 1.3136711906198924739143e-09 relative error = 1.1843604568299964586102924493953e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.5MB, time=15.46 NO POLE NO POLE x[1] = 0.1095 y2[1] (analytic) = 1.1092813090866165599224973203738 y2[1] (numeric) = 1.1092813090866165599526481699113 absolute error = 3.01508495375e-20 relative error = 2.7180526067212150543117389110909e-18 % h = 0.0001 y1[1] (analytic) = 1.1092813090866165599224973203738 y1[1] (numeric) = 1.1092813104284322275836082271379 absolute error = 1.3418156676611109067641e-09 relative error = 1.2096261396182393007020707546085e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.5MB, time=15.68 NO POLE NO POLE x[1] = 0.1096 y2[1] (analytic) = 1.1093807096263303783410624425475 y2[1] (numeric) = 1.1093807096263303783731718866007 absolute error = 3.21094440532e-20 relative error = 2.8943575252913253570285248053919e-18 % h = 0.0001 y1[1] (analytic) = 1.1093807096263303783410624425475 y1[1] (numeric) = 1.1093807109965887136966734520206 absolute error = 1.3702583353556110094731e-09 relative error = 1.2351560861529233881086655679805e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=289.9MB, alloc=4.5MB, time=15.90 x[1] = 0.1097 y2[1] (analytic) = 1.1094801090722371014078296945594 y2[1] (numeric) = 1.1094801090722371014420026281293 absolute error = 3.41729335699e-20 relative error = 3.0800852841314918670483613727185e-18 % h = 0.0001 y1[1] (analytic) = 1.1094801090722371014078296945594 y1[1] (numeric) = 1.1094801104712362915484227628001 absolute error = 1.3989991901405930682407e-09 relative error = 1.2609502222716330637381788779200e-07 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1098 y2[1] (analytic) = 1.1095795074233427346645601744576 y2[1] (numeric) = 1.1095795074233427347009059393406 absolute error = 3.63457648830e-20 relative error = 3.2756341154318778310066078654218e-18 % h = 0.0001 y1[1] (analytic) = 1.1095795074233427346645601744576 y1[1] (numeric) = 1.1095795088513809631118536550555 absolute error = 1.4280382284472934805979e-09 relative error = 1.2870084738348072192254454385395e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.5MB, time=16.13 NO POLE NO POLE x[1] = 0.1099 y2[1] (analytic) = 1.1096789046786532946010258692669 y2[1] (numeric) = 1.1096789046786532946396583939598 absolute error = 3.86325246929e-20 relative error = 3.4814147164568665466889430953209e-18 % h = 0.0001 y1[1] (analytic) = 1.1096789046786532946010258692669 y1[1] (numeric) = 1.109678906136028741302010693167 absolute error = 1.4573754467009848239001e-09 relative error = 1.3133307667257307544172178506616e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.5MB, time=16.36 NO POLE NO POLE x[1] = 0.11 y2[1] (analytic) = 1.1097783008371748086649494900834 y2[1] (numeric) = 1.1097783008371748087059874325921 absolute error = 4.10379425087e-20 relative error = 3.6978505056138263926147755452642e-18 % h = 0.0001 y1[1] (analytic) = 1.1097783008371748086649494900834 y1[1] (numeric) = 1.1097783023241856499859254139916 absolute error = 1.4870108413209759239082e-09 relative error = 1.3399170268505260404962890998952e-07 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 100 Total Elapsed Time = 16 Seconds Elapsed Time(since restart) = 16 Seconds Expected Time Remaining = 2 Hours 15 Minutes 0 Seconds Optimized Time Remaining = 2 Hours 14 Minutes 53 Seconds Time to Timeout = 14 Minutes 43 Seconds Percent Done = 0.202 % > quit memory used=299.1MB, alloc=4.5MB, time=16.44