|\^/| 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 > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_max_opt_iter, > glob_log10normmin, > glob_log10relerr, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > glob_last_good_h, > glob_not_yet_start_msg, > glob_subiter_method, > glob_initial_pass, > centuries_in_millinium, > hours_in_day, > glob_small_float, > glob_max_iter, > glob_unchanged_h_cnt, > glob_max_rel_trunc_err, > glob_abserr, > glob_not_yet_finished, > glob_percent_done, > glob_max_sec, > glob_no_eqs, > glob_max_trunc_err, > glob_h, > glob_clock_start_sec, > years_in_century, > glob_current_iter, > glob_relerr, > glob_clock_sec, > djd_debug2, > glob_max_minutes, > glob_start, > glob_warned2, > glob_warned, > glob_look_poles, > glob_almost_1, > glob_orig_start_sec, > glob_optimal_done, > days_in_year, > min_in_hour, > sec_in_min, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_log10_relerr, > glob_large_float, > glob_hmax, > glob_disp_incr, > glob_display_flag, > djd_debug, > glob_dump, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_hmin, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_m1, > array_x2, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_last_rel_error, > array_pole, > array_x2_init, > array_1st_rel_error, > array_norms, > array_x1_init, > array_t, > array_type_pole, > array_real_pole, > array_x1_higher_work, > array_x2_higher, > array_x2_higher_work2, > array_complex_pole, > array_x1_set_initial, > array_x1_higher, > array_x2_set_initial, > array_poles, > array_x2_higher_work, > array_x1_higher_work2, > 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_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x2[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_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x1[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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin, glob_log10relerr, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg, glob_subiter_method, glob_initial_pass, centuries_in_millinium, hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished, glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h, glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr, glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2, glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec, glob_optimal_done, days_in_year, min_in_hour, sec_in_min, glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float, glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump, glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec, glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2, array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0, array_m1, array_x2, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error, array_pole, array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t, array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher, array_x2_higher_work2, array_complex_pole, array_x1_set_initial, array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work, array_x1_higher_work2, glob_last; if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x2[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_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x1[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 > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_max_opt_iter, > glob_log10normmin, > glob_log10relerr, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > glob_last_good_h, > glob_not_yet_start_msg, > glob_subiter_method, > glob_initial_pass, > centuries_in_millinium, > hours_in_day, > glob_small_float, > glob_max_iter, > glob_unchanged_h_cnt, > glob_max_rel_trunc_err, > glob_abserr, > glob_not_yet_finished, > glob_percent_done, > glob_max_sec, > glob_no_eqs, > glob_max_trunc_err, > glob_h, > glob_clock_start_sec, > years_in_century, > glob_current_iter, > glob_relerr, > glob_clock_sec, > djd_debug2, > glob_max_minutes, > glob_start, > glob_warned2, > glob_warned, > glob_look_poles, > glob_almost_1, > glob_orig_start_sec, > glob_optimal_done, > days_in_year, > min_in_hour, > sec_in_min, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_log10_relerr, > glob_large_float, > glob_hmax, > glob_disp_incr, > glob_display_flag, > djd_debug, > glob_dump, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_hmin, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_m1, > array_x2, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_last_rel_error, > array_pole, > array_x2_init, > array_1st_rel_error, > array_norms, > array_x1_init, > array_t, > array_type_pole, > array_real_pole, > array_x1_higher_work, > array_x2_higher, > array_x2_higher_work2, > array_complex_pole, > array_x1_set_initial, > array_x1_higher, > array_x2_set_initial, > array_poles, > array_x2_higher_work, > array_x1_higher_work2, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x2_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_x1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x1_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_t[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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin, glob_log10relerr, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg, glob_subiter_method, glob_initial_pass, centuries_in_millinium, hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished, glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h, glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr, glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2, glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec, glob_optimal_done, days_in_year, min_in_hour, sec_in_min, glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float, glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump, glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec, glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2, array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0, array_m1, array_x2, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error, array_pole, array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t, array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher, array_x2_higher_work2, array_complex_pole, array_x1_set_initial, array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work, array_x1_higher_work2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_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_t[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(t_start,t_end) > global > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_max_opt_iter, > glob_log10normmin, > glob_log10relerr, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > glob_last_good_h, > glob_not_yet_start_msg, > glob_subiter_method, > glob_initial_pass, > centuries_in_millinium, > hours_in_day, > glob_small_float, > glob_max_iter, > glob_unchanged_h_cnt, > glob_max_rel_trunc_err, > glob_abserr, > glob_not_yet_finished, > glob_percent_done, > glob_max_sec, > glob_no_eqs, > glob_max_trunc_err, > glob_h, > glob_clock_start_sec, > years_in_century, > glob_current_iter, > glob_relerr, > glob_clock_sec, > djd_debug2, > glob_max_minutes, > glob_start, > glob_warned2, > glob_warned, > glob_look_poles, > glob_almost_1, > glob_orig_start_sec, > glob_optimal_done, > days_in_year, > min_in_hour, > sec_in_min, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_log10_relerr, > glob_large_float, > glob_hmax, > glob_disp_incr, > glob_display_flag, > djd_debug, > glob_dump, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_hmin, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_m1, > array_x2, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_last_rel_error, > array_pole, > array_x2_init, > array_1st_rel_error, > array_norms, > array_x1_init, > array_t, > array_type_pole, > array_real_pole, > array_x1_higher_work, > array_x2_higher, > array_x2_higher_work2, > array_complex_pole, > array_x1_set_initial, > array_x1_higher, > array_x2_set_initial, > array_poles, > array_x2_higher_work, > array_x1_higher_work2, > 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(t_end),convfloat(t_start),convfloat(array_t[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(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[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(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin, glob_log10relerr, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg, glob_subiter_method, glob_initial_pass, centuries_in_millinium, hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished, glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h, glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr, glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2, glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec, glob_optimal_done, days_in_year, min_in_hour, sec_in_min, glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float, glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump, glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec, glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2, array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0, array_m1, array_x2, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error, array_pole, array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t, array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher, array_x2_higher_work2, array_complex_pole, array_x1_set_initial, array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work, array_x1_higher_work2, 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(t_end), convfloat(t_start), convfloat(array_t[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(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[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 > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_max_opt_iter, > glob_log10normmin, > glob_log10relerr, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > glob_last_good_h, > glob_not_yet_start_msg, > glob_subiter_method, > glob_initial_pass, > centuries_in_millinium, > hours_in_day, > glob_small_float, > glob_max_iter, > glob_unchanged_h_cnt, > glob_max_rel_trunc_err, > glob_abserr, > glob_not_yet_finished, > glob_percent_done, > glob_max_sec, > glob_no_eqs, > glob_max_trunc_err, > glob_h, > glob_clock_start_sec, > years_in_century, > glob_current_iter, > glob_relerr, > glob_clock_sec, > djd_debug2, > glob_max_minutes, > glob_start, > glob_warned2, > glob_warned, > glob_look_poles, > glob_almost_1, > glob_orig_start_sec, > glob_optimal_done, > days_in_year, > min_in_hour, > sec_in_min, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_log10_relerr, > glob_large_float, > glob_hmax, > glob_disp_incr, > glob_display_flag, > djd_debug, > glob_dump, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_hmin, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_m1, > array_x2, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_last_rel_error, > array_pole, > array_x2_init, > array_1st_rel_error, > array_norms, > array_x1_init, > array_t, > array_type_pole, > array_real_pole, > array_x1_higher_work, > array_x2_higher, > array_x2_higher_work2, > array_complex_pole, > array_x1_set_initial, > array_x1_higher, > array_x2_set_initial, > array_poles, > array_x2_higher_work, > array_x1_higher_work2, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_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_x2_higher[1,m]/array_x2_higher[1,m-1]; > rm1 := array_x2_higher[1,m-1]/array_x2_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_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_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_x1_higher[1,m]/array_x1_higher[1,m-1]; > rm1 := array_x1_higher[1,m-1]/array_x1_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 - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x2_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_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_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_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_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_x1_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_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_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_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin, glob_log10relerr, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg, glob_subiter_method, glob_initial_pass, centuries_in_millinium, hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished, glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h, glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr, glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2, glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec, glob_optimal_done, days_in_year, min_in_hour, sec_in_min, glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float, glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump, glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec, glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2, array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0, array_m1, array_x2, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error, array_pole, array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t, array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher, array_x2_higher_work2, array_complex_pole, array_x1_set_initial, array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work, array_x1_higher_work2, glob_last; n := glob_max_terms; m := n - 3; while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or abs(array_x2_higher[1, m - 1]) < glob_small_float or abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_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_x1_higher[1, m]) < glob_small_float or abs(array_x1_higher[1, m - 1]) < glob_small_float or abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_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 - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x2_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_x2_higher[1, m]) or glob_large_float <= abs(array_x2_higher[1, m - 1]) or glob_large_float <= abs(array_x2_higher[1, m - 2]) or glob_large_float <= abs(array_x2_higher[1, m - 3]) or glob_large_float <= abs(array_x2_higher[1, m - 4]) or glob_large_float <= abs(array_x2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_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_x1_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_x1_higher[1, m]) or glob_large_float <= abs(array_x1_higher[1, m - 1]) or glob_large_float <= abs(array_x1_higher[1, m - 2]) or glob_large_float <= abs(array_x1_higher[1, m - 3]) or glob_large_float <= abs(array_x1_higher[1, m - 4]) or glob_large_float <= abs(array_x1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_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 > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_max_opt_iter, > glob_log10normmin, > glob_log10relerr, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > glob_last_good_h, > glob_not_yet_start_msg, > glob_subiter_method, > glob_initial_pass, > centuries_in_millinium, > hours_in_day, > glob_small_float, > glob_max_iter, > glob_unchanged_h_cnt, > glob_max_rel_trunc_err, > glob_abserr, > glob_not_yet_finished, > glob_percent_done, > glob_max_sec, > glob_no_eqs, > glob_max_trunc_err, > glob_h, > glob_clock_start_sec, > years_in_century, > glob_current_iter, > glob_relerr, > glob_clock_sec, > djd_debug2, > glob_max_minutes, > glob_start, > glob_warned2, > glob_warned, > glob_look_poles, > glob_almost_1, > glob_orig_start_sec, > glob_optimal_done, > days_in_year, > min_in_hour, > sec_in_min, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_log10_relerr, > glob_large_float, > glob_hmax, > glob_disp_incr, > glob_display_flag, > djd_debug, > glob_dump, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_hmin, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_m1, > array_x2, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_last_rel_error, > array_pole, > array_x2_init, > array_1st_rel_error, > array_norms, > array_x1_init, > array_t, > array_type_pole, > array_real_pole, > array_x1_higher_work, > array_x2_higher, > array_x2_higher_work2, > array_complex_pole, > array_x1_set_initial, > array_x1_higher, > array_x2_set_initial, > array_poles, > array_x2_higher_work, > array_x1_higher_work2, > 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_x2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x2[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_x1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x1[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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin, glob_log10relerr, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg, glob_subiter_method, glob_initial_pass, centuries_in_millinium, hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished, glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h, glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr, glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2, glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec, glob_optimal_done, days_in_year, min_in_hour, sec_in_min, glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float, glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump, glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec, glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2, array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0, array_m1, array_x2, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error, array_pole, array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t, array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher, array_x2_higher_work2, array_complex_pole, array_x1_set_initial, array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work, array_x1_higher_work2, 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_x2[iii]) then array_norms[iii] := abs(array_x2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x1[iii]) then array_norms[iii] := abs(array_x1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_max_opt_iter, > glob_log10normmin, > glob_log10relerr, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > glob_last_good_h, > glob_not_yet_start_msg, > glob_subiter_method, > glob_initial_pass, > centuries_in_millinium, > hours_in_day, > glob_small_float, > glob_max_iter, > glob_unchanged_h_cnt, > glob_max_rel_trunc_err, > glob_abserr, > glob_not_yet_finished, > glob_percent_done, > glob_max_sec, > glob_no_eqs, > glob_max_trunc_err, > glob_h, > glob_clock_start_sec, > years_in_century, > glob_current_iter, > glob_relerr, > glob_clock_sec, > djd_debug2, > glob_max_minutes, > glob_start, > glob_warned2, > glob_warned, > glob_look_poles, > glob_almost_1, > glob_orig_start_sec, > glob_optimal_done, > days_in_year, > min_in_hour, > sec_in_min, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_log10_relerr, > glob_large_float, > glob_hmax, > glob_disp_incr, > glob_display_flag, > djd_debug, > glob_dump, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_hmin, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_m1, > array_x2, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_last_rel_error, > array_pole, > array_x2_init, > array_1st_rel_error, > array_norms, > array_x1_init, > array_t, > array_type_pole, > array_real_pole, > array_x1_higher_work, > array_x2_higher, > array_x2_higher_work2, > array_complex_pole, > array_x1_set_initial, > array_x1_higher, > array_x2_set_initial, > array_poles, > array_x2_higher_work, > array_x1_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp4[1] := (array_const_2D0[1] * (array_x2[1])); > #emit pre sub $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp6[1] := array_x1_higher[3,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp8[1] := array_x1_higher[2,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp10[1] := array_tmp9[1] + array_x1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_x2_set_initial[1,3] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2); > array_x2[3] := temporary; > array_x2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,2] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult $eq_no = 2 i = 1 > array_tmp12[1] := (array_const_4D0[1] * (array_x2[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp13[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1])); > # emit pre mult $eq_no = 2 i = 1 > array_tmp16[1] := (array_const_2D0[1] * (array_x1[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_x1_set_initial[2,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_x1[2] := temporary; > array_x1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp4[2] := ats(2,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp6[2] := array_x1_higher[3,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp8[2] := array_x1_higher[2,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2])); > #emit pre add $eq_no = 1 i = 2 > array_tmp10[2] := array_tmp9[2] + array_x1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_x2_set_initial[1,4] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3); > array_x2[4] := temporary; > array_x2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult $eq_no = 2 i = 2 > array_tmp12[2] := ats(2,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 2 > array_tmp13[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2])); > # emit pre mult $eq_no = 2 i = 2 > array_tmp16[2] := ats(2,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2])); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_x1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_x1[3] := temporary; > array_x1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp4[3] := ats(3,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp6[3] := array_x1_higher[3,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp8[3] := array_x1_higher[2,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3])); > #emit pre add $eq_no = 1 i = 3 > array_tmp10[3] := array_tmp9[3] + array_x1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_x2_set_initial[1,5] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4); > array_x2[5] := temporary; > array_x2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult $eq_no = 2 i = 3 > array_tmp12[3] := ats(3,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 3 > array_tmp13[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3])); > # emit pre mult $eq_no = 2 i = 3 > array_tmp16[3] := ats(3,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3])); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_x1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_x1[4] := temporary; > array_x1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp4[4] := ats(4,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp6[4] := array_x1_higher[3,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp8[4] := array_x1_higher[2,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4])); > #emit pre add $eq_no = 1 i = 4 > array_tmp10[4] := array_tmp9[4] + array_x1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_x2_set_initial[1,6] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5); > array_x2[6] := temporary; > array_x2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult $eq_no = 2 i = 4 > array_tmp12[4] := ats(4,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 4 > array_tmp13[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4])); > # emit pre mult $eq_no = 2 i = 4 > array_tmp16[4] := ats(4,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4])); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_x1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_x1[5] := temporary; > array_x1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp4[5] := ats(5,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp6[5] := array_x1_higher[3,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp8[5] := array_x1_higher[2,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5])); > #emit pre add $eq_no = 1 i = 5 > array_tmp10[5] := array_tmp9[5] + array_x1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_x2_set_initial[1,7] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6); > array_x2[7] := temporary; > array_x2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult $eq_no = 2 i = 5 > array_tmp12[5] := ats(5,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 5 > array_tmp13[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5])); > # emit pre mult $eq_no = 2 i = 5 > array_tmp16[5] := ats(5,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5])); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_x1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_x1[6] := temporary; > array_x1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 1 > array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1); > #emit add $eq_no = 1 > array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; > #emit mult $eq_no = 1 > array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1); > #emit sub $eq_no = 1 > array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk])); > #emit diff $eq_no = 1 > array_tmp6[kkk] := array_x1_higher[3,kkk]; > #emit sub $eq_no = 1 > array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk])); > #emit diff $eq_no = 1 > array_tmp8[kkk] := array_x1_higher[2,kkk]; > #emit sub $eq_no = 1 > array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk])); > #emit add $eq_no = 1 > array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_x2_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x2[kkk + order_d] := temporary; > array_x2_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_x2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit mult $eq_no = 2 > array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1); > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 2 > array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1); > #emit sub $eq_no = 2 > array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk])); > #emit mult $eq_no = 2 > array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1); > #emit sub $eq_no = 2 > array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk])); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_x1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x1[kkk + order_d] := temporary; > array_x1_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_x1_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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin, glob_log10relerr, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg, glob_subiter_method, glob_initial_pass, centuries_in_millinium, hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished, glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h, glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr, glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2, glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec, glob_optimal_done, days_in_year, min_in_hour, sec_in_min, glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float, glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump, glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec, glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2, array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0, array_m1, array_x2, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error, array_pole, array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t, array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher, array_x2_higher_work2, array_complex_pole, array_x1_set_initial, array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work, array_x1_higher_work2, glob_last; array_tmp1[1] := array_x2_higher[2, 1]; array_tmp2[1] := array_const_3D0[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; array_tmp4[1] := array_const_2D0[1]*array_x2[1]; array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; array_tmp6[1] := array_x1_higher[3, 1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; array_tmp8[1] := array_x1_higher[2, 1]; array_tmp9[1] := array_tmp7[1] - array_tmp8[1]; array_tmp10[1] := array_tmp9[1] + array_x1[1]; if not array_x2_set_initial[1, 3] then if 1 <= glob_max_terms then temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2); array_x2[3] := temporary; array_x2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 2] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 1] := temporary end if end if; kkk := 2; array_tmp12[1] := array_const_4D0[1]*array_x2[1]; array_tmp13[1] := array_x2_higher[2, 1]; array_tmp14[1] := array_const_2D0[1]*array_tmp13[1]; array_tmp15[1] := array_tmp12[1] - array_tmp14[1]; array_tmp16[1] := array_const_2D0[1]*array_x1[1]; array_tmp17[1] := array_tmp15[1] - array_tmp16[1]; if not array_x1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp17[1]*glob_h*factorial_3(0, 1); array_x1[2] := temporary; array_x1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_x2_higher[2, 2]; array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1); array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1); array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; array_tmp6[2] := array_x1_higher[3, 2]; array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; array_tmp8[2] := array_x1_higher[2, 2]; array_tmp9[2] := array_tmp7[2] - array_tmp8[2]; array_tmp10[2] := array_tmp9[2] + array_x1[2]; if not array_x2_set_initial[1, 4] then if 2 <= glob_max_terms then temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3); array_x2[4] := temporary; array_x2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 2] := temporary end if end if; kkk := 3; array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1); array_tmp13[2] := array_x2_higher[2, 2]; array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1); array_tmp15[2] := array_tmp12[2] - array_tmp14[2]; array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1); array_tmp17[2] := array_tmp15[2] - array_tmp16[2]; if not array_x1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp17[2]*glob_h*factorial_3(1, 2); array_x1[3] := temporary; array_x1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_x2_higher[2, 3]; array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1); array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1); array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; array_tmp6[3] := array_x1_higher[3, 3]; array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; array_tmp8[3] := array_x1_higher[2, 3]; array_tmp9[3] := array_tmp7[3] - array_tmp8[3]; array_tmp10[3] := array_tmp9[3] + array_x1[3]; if not array_x2_set_initial[1, 5] then if 3 <= glob_max_terms then temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4); array_x2[5] := temporary; array_x2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 3] := temporary end if end if; kkk := 4; array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1); array_tmp13[3] := array_x2_higher[2, 3]; array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1); array_tmp15[3] := array_tmp12[3] - array_tmp14[3]; array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1); array_tmp17[3] := array_tmp15[3] - array_tmp16[3]; if not array_x1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp17[3]*glob_h*factorial_3(2, 3); array_x1[4] := temporary; array_x1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_x2_higher[2, 4]; array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1); array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1); array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; array_tmp6[4] := array_x1_higher[3, 4]; array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; array_tmp8[4] := array_x1_higher[2, 4]; array_tmp9[4] := array_tmp7[4] - array_tmp8[4]; array_tmp10[4] := array_tmp9[4] + array_x1[4]; if not array_x2_set_initial[1, 6] then if 4 <= glob_max_terms then temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5); array_x2[6] := temporary; array_x2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 4] := temporary end if end if; kkk := 5; array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1); array_tmp13[4] := array_x2_higher[2, 4]; array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1); array_tmp15[4] := array_tmp12[4] - array_tmp14[4]; array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1); array_tmp17[4] := array_tmp15[4] - array_tmp16[4]; if not array_x1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp17[4]*glob_h*factorial_3(3, 4); array_x1[5] := temporary; array_x1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_x2_higher[2, 5]; array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1); array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1); array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; array_tmp6[5] := array_x1_higher[3, 5]; array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; array_tmp8[5] := array_x1_higher[2, 5]; array_tmp9[5] := array_tmp7[5] - array_tmp8[5]; array_tmp10[5] := array_tmp9[5] + array_x1[5]; if not array_x2_set_initial[1, 7] then if 5 <= glob_max_terms then temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6); array_x2[7] := temporary; array_x2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 5] := temporary end if end if; kkk := 6; array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1); array_tmp13[5] := array_x2_higher[2, 5]; array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1); array_tmp15[5] := array_tmp12[5] - array_tmp14[5]; array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1); array_tmp17[5] := array_tmp15[5] - array_tmp16[5]; if not array_x1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp17[5]*glob_h*factorial_3(4, 5); array_x1[6] := temporary; array_x1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_x2_higher[2, kkk]; array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1); array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1); array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := array_x1_higher[3, kkk]; array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; array_tmp8[kkk] := array_x1_higher[2, kkk]; array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk]; array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then if not array_x2_set_initial[1, kkk + order_d] then temporary := array_tmp10[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x2[kkk + order_d] := temporary; array_x2_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_x2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1); array_tmp13[kkk] := array_x2_higher[2, kkk]; array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1); array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk]; array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1); array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_x1_set_initial[2, kkk + order_d] then temporary := array_tmp17[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x1[kkk + order_d] := temporary; array_x1_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_x1_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_x1 := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > 1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; 1.0 + 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x1p := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > - 6.0 * c3 * exp(-t); > end; exact_soln_x1p := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; -6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > 1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; 1.0 + c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; 2.0*c2*exp(2.0*t) - c3*exp(-t) 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, > t_start,t_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_optimal_start, > glob_hmin_init, > glob_reached_optimal_h, > glob_max_opt_iter, > glob_log10normmin, > glob_log10relerr, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > glob_last_good_h, > glob_not_yet_start_msg, > glob_subiter_method, > glob_initial_pass, > centuries_in_millinium, > hours_in_day, > glob_small_float, > glob_max_iter, > glob_unchanged_h_cnt, > glob_max_rel_trunc_err, > glob_abserr, > glob_not_yet_finished, > glob_percent_done, > glob_max_sec, > glob_no_eqs, > glob_max_trunc_err, > glob_h, > glob_clock_start_sec, > years_in_century, > glob_current_iter, > glob_relerr, > glob_clock_sec, > djd_debug2, > glob_max_minutes, > glob_start, > glob_warned2, > glob_warned, > glob_look_poles, > glob_almost_1, > glob_orig_start_sec, > glob_optimal_done, > days_in_year, > min_in_hour, > sec_in_min, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_log10_relerr, > glob_large_float, > glob_hmax, > glob_disp_incr, > glob_display_flag, > djd_debug, > glob_dump, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_hmin, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_0D0, > array_const_4D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_m1, > array_x2, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_last_rel_error, > array_pole, > array_x2_init, > array_1st_rel_error, > array_norms, > array_x1_init, > array_t, > array_type_pole, > array_real_pole, > array_x1_higher_work, > array_x2_higher, > array_x2_higher_work2, > array_complex_pole, > array_x1_set_initial, > array_x1_higher, > array_x2_set_initial, > array_poles, > array_x2_higher_work, > array_x1_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_max_terms := 30; > ALWAYS := 1; > INFO := 2; > glob_iolevel := 5; > glob_curr_iter_when_opt := 0; > glob_optimal_start := 0.0; > glob_hmin_init := 0.001; > glob_reached_optimal_h := false; > glob_max_opt_iter := 10; > glob_log10normmin := 0.1; > glob_log10relerr := 0.0; > glob_smallish_float := 0.1e-100; > glob_log10_abserr := 0.1e-10; > glob_dump_analytic := false; > glob_last_good_h := 0.1; > glob_not_yet_start_msg := true; > glob_subiter_method := 3; > glob_initial_pass := true; > centuries_in_millinium := 10.0; > hours_in_day := 24.0; > glob_small_float := 0.1e-50; > glob_max_iter := 1000; > glob_unchanged_h_cnt := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_abserr := 0.1e-10; > glob_not_yet_finished := true; > glob_percent_done := 0.0; > glob_max_sec := 10000.0; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_h := 0.1; > glob_clock_start_sec := 0.0; > years_in_century := 100.0; > glob_current_iter := 0; > glob_relerr := 0.1e-10; > glob_clock_sec := 0.0; > djd_debug2 := true; > glob_max_minutes := 0.0; > glob_start := 0; > glob_warned2 := false; > glob_warned := false; > glob_look_poles := false; > glob_almost_1 := 0.9990; > glob_orig_start_sec := 0.0; > glob_optimal_done := false; > days_in_year := 365.0; > min_in_hour := 60.0; > sec_in_min := 60.0; > glob_optimal_expect_sec := 0.1; > MAX_UNCHANGED := 10; > glob_log10_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmax := 1.0; > glob_disp_incr := 0.1; > glob_display_flag := true; > djd_debug := true; > glob_dump := false; > glob_log10abserr := 0.0; > glob_normmax := 0.0; > glob_iter := 0; > glob_optimal_clock_start_sec := 0.0; > glob_max_hours := 0.0; > glob_hmin := 0.00000000001; > glob_html_log := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest6_revpostode.ode#################"); > omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > 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,"#"); > omniout_str(ALWAYS,"# was complicatedrev.ode"); > omniout_str(ALWAYS,"#"); > omniout_str(ALWAYS,"t_start := 0.5;"); > omniout_str(ALWAYS,"t_end := 5.0;"); > omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,"array_x1_init[1 + 1] := exact_soln_x1p(t_start);"); > omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#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_x1 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x1p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"- 6.0 * c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_m1:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_x1:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_tmp7:= Array(1..(max_terms + 1),[]); > array_tmp8:= Array(1..(max_terms + 1),[]); > array_tmp9:= Array(1..(max_terms + 1),[]); > array_tmp10:= Array(1..(max_terms + 1),[]); > array_tmp11:= Array(1..(max_terms + 1),[]); > array_tmp12:= Array(1..(max_terms + 1),[]); > array_tmp13:= Array(1..(max_terms + 1),[]); > array_tmp14:= Array(1..(max_terms + 1),[]); > array_tmp15:= Array(1..(max_terms + 1),[]); > array_tmp16:= Array(1..(max_terms + 1),[]); > array_tmp17:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_x2_init:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_t:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp17[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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_t[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 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_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_x2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_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_x2_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_x1_higher_work2[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_x1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_t := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > 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 > # > # was complicatedrev.ode > # > t_start := 0.5; > t_end := 5.0; > array_x1_init[0 + 1] := exact_soln_x1(t_start); > array_x1_init[1 + 1] := exact_soln_x1p(t_start); > array_x2_init[0 + 1] := exact_soln_x2(t_start); > array_x2_init[1 + 1] := exact_soln_x2p(t_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #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_x2_set_initial[1,1] := true; > array_x2_set_initial[1,2] := true; > array_x2_set_initial[1,3] := false; > array_x2_set_initial[1,4] := false; > array_x2_set_initial[1,5] := false; > array_x2_set_initial[1,6] := false; > array_x2_set_initial[1,7] := false; > array_x2_set_initial[1,8] := false; > array_x2_set_initial[1,9] := false; > array_x2_set_initial[1,10] := false; > array_x2_set_initial[1,11] := false; > array_x2_set_initial[1,12] := false; > array_x2_set_initial[1,13] := false; > array_x2_set_initial[1,14] := false; > array_x2_set_initial[1,15] := false; > array_x2_set_initial[1,16] := false; > array_x2_set_initial[1,17] := false; > array_x2_set_initial[1,18] := false; > array_x2_set_initial[1,19] := false; > array_x2_set_initial[1,20] := false; > array_x2_set_initial[1,21] := false; > array_x2_set_initial[1,22] := false; > array_x2_set_initial[1,23] := false; > array_x2_set_initial[1,24] := false; > array_x2_set_initial[1,25] := false; > array_x2_set_initial[1,26] := false; > array_x2_set_initial[1,27] := false; > array_x2_set_initial[1,28] := false; > array_x2_set_initial[1,29] := false; > array_x2_set_initial[1,30] := false; > array_x1_set_initial[2,1] := true; > array_x1_set_initial[2,2] := true; > array_x1_set_initial[2,3] := false; > array_x1_set_initial[2,4] := false; > array_x1_set_initial[2,5] := false; > array_x1_set_initial[2,6] := false; > array_x1_set_initial[2,7] := false; > array_x1_set_initial[2,8] := false; > array_x1_set_initial[2,9] := false; > array_x1_set_initial[2,10] := false; > array_x1_set_initial[2,11] := false; > array_x1_set_initial[2,12] := false; > array_x1_set_initial[2,13] := false; > array_x1_set_initial[2,14] := false; > array_x1_set_initial[2,15] := false; > array_x1_set_initial[2,16] := false; > array_x1_set_initial[2,17] := false; > array_x1_set_initial[2,18] := false; > array_x1_set_initial[2,19] := false; > array_x1_set_initial[2,20] := false; > array_x1_set_initial[2,21] := false; > array_x1_set_initial[2,22] := false; > array_x1_set_initial[2,23] := false; > array_x1_set_initial[2,24] := false; > array_x1_set_initial[2,25] := false; > array_x1_set_initial[2,26] := false; > array_x1_set_initial[2,27] := false; > array_x1_set_initial[2,28] := false; > array_x1_set_initial[2,29] := false; > array_x1_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_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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 := 2; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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_x2(); > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x2_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_x1(); > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x1_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_t[1] <= t_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 <= 3 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 3 + 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_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > #Jump Series array_x2 > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[3,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_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_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_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_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x2_higher[ord,term_no] := array_x2_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_x1 > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[3,iii] := array_x1_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_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 := 2; > calc_term := 2; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[2,iii] := array_x1_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 := 2; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_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 := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[2,iii] := array_x1_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_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_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 := 3; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_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 := 3; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_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_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_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_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_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_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_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_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_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_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x1_higher[ord,term_no] := array_x1_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 (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if glob_html_log then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-13T03:00:47-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest6_rev") > ; > logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[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,"mtest6_rev diffeq.mxt") > ; > logitem_str(html_log_file,"mtest6_rev maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") > ; > 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, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init, glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin, glob_log10relerr, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg, glob_subiter_method, glob_initial_pass, centuries_in_millinium, hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished, glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h, glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr, glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2, glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec, glob_optimal_done, days_in_year, min_in_hour, sec_in_min, glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float, glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump, glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec, glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2, array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0, array_m1, array_x2, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_last_rel_error, array_pole, array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t, array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher, array_x2_higher_work2, array_complex_pole, array_x1_set_initial, array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work, array_x1_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; DEBUGL := 3; glob_max_terms := 30; ALWAYS := 1; INFO := 2; glob_iolevel := 5; glob_curr_iter_when_opt := 0; glob_optimal_start := 0.; glob_hmin_init := 0.001; glob_reached_optimal_h := false; glob_max_opt_iter := 10; glob_log10normmin := 0.1; glob_log10relerr := 0.; glob_smallish_float := 0.1*10^(-100); glob_log10_abserr := 0.1*10^(-10); glob_dump_analytic := false; glob_last_good_h := 0.1; glob_not_yet_start_msg := true; glob_subiter_method := 3; glob_initial_pass := true; centuries_in_millinium := 10.0; hours_in_day := 24.0; glob_small_float := 0.1*10^(-50); glob_max_iter := 1000; glob_unchanged_h_cnt := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_not_yet_finished := true; glob_percent_done := 0.; glob_max_sec := 10000.0; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_h := 0.1; glob_clock_start_sec := 0.; years_in_century := 100.0; glob_current_iter := 0; glob_relerr := 0.1*10^(-10); glob_clock_sec := 0.; djd_debug2 := true; glob_max_minutes := 0.; glob_start := 0; glob_warned2 := false; glob_warned := false; glob_look_poles := false; glob_almost_1 := 0.9990; glob_orig_start_sec := 0.; glob_optimal_done := false; days_in_year := 365.0; min_in_hour := 60.0; sec_in_min := 60.0; glob_optimal_expect_sec := 0.1; MAX_UNCHANGED := 10; glob_log10_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmax := 1.0; glob_disp_incr := 0.1; glob_display_flag := true; djd_debug := true; glob_dump := false; glob_log10abserr := 0.; glob_normmax := 0.; glob_iter := 0; glob_optimal_clock_start_sec := 0.; glob_max_hours := 0.; glob_hmin := 0.1*10^(-10); glob_html_log := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest6_revpostode.ode#################"); omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \ diff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); 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, "#"); omniout_str(ALWAYS, "# was complicatedrev.ode"); omniout_str(ALWAYS, "#"); omniout_str(ALWAYS, "t_start := 0.5;"); omniout_str(ALWAYS, "t_end := 5.0;"); omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, "array_x1_init[1 + 1] := exact_soln_x1p(t_start);") ; omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);") ; omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#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_x1 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x1p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "- 6.0 * c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_m1 := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_x1 := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_tmp7 := Array(1 .. max_terms + 1, []); array_tmp8 := Array(1 .. max_terms + 1, []); array_tmp9 := Array(1 .. max_terms + 1, []); array_tmp10 := Array(1 .. max_terms + 1, []); array_tmp11 := Array(1 .. max_terms + 1, []); array_tmp12 := Array(1 .. max_terms + 1, []); array_tmp13 := Array(1 .. max_terms + 1, []); array_tmp14 := Array(1 .. max_terms + 1, []); array_tmp15 := Array(1 .. max_terms + 1, []); array_tmp16 := Array(1 .. max_terms + 1, []); array_tmp17 := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_x2_init := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_t := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_x1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_x1_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_x2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_x1_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_t[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_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_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_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_x2_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_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1 end do; array_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 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_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; 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; t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x1_init[2] := exact_soln_x1p(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; 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_x2_set_initial[1, 1] := true; array_x2_set_initial[1, 2] := true; array_x2_set_initial[1, 3] := false; array_x2_set_initial[1, 4] := false; array_x2_set_initial[1, 5] := false; array_x2_set_initial[1, 6] := false; array_x2_set_initial[1, 7] := false; array_x2_set_initial[1, 8] := false; array_x2_set_initial[1, 9] := false; array_x2_set_initial[1, 10] := false; array_x2_set_initial[1, 11] := false; array_x2_set_initial[1, 12] := false; array_x2_set_initial[1, 13] := false; array_x2_set_initial[1, 14] := false; array_x2_set_initial[1, 15] := false; array_x2_set_initial[1, 16] := false; array_x2_set_initial[1, 17] := false; array_x2_set_initial[1, 18] := false; array_x2_set_initial[1, 19] := false; array_x2_set_initial[1, 20] := false; array_x2_set_initial[1, 21] := false; array_x2_set_initial[1, 22] := false; array_x2_set_initial[1, 23] := false; array_x2_set_initial[1, 24] := false; array_x2_set_initial[1, 25] := false; array_x2_set_initial[1, 26] := false; array_x2_set_initial[1, 27] := false; array_x2_set_initial[1, 28] := false; array_x2_set_initial[1, 29] := false; array_x2_set_initial[1, 30] := false; array_x1_set_initial[2, 1] := true; array_x1_set_initial[2, 2] := true; array_x1_set_initial[2, 3] := false; array_x1_set_initial[2, 4] := false; array_x1_set_initial[2, 5] := false; array_x1_set_initial[2, 6] := false; array_x1_set_initial[2, 7] := false; array_x1_set_initial[2, 8] := false; array_x1_set_initial[2, 9] := false; array_x1_set_initial[2, 10] := false; array_x1_set_initial[2, 11] := false; array_x1_set_initial[2, 12] := false; array_x1_set_initial[2, 13] := false; array_x1_set_initial[2, 14] := false; array_x1_set_initial[2, 15] := false; array_x1_set_initial[2, 16] := false; array_x1_set_initial[2, 17] := false; array_x1_set_initial[2, 18] := false; array_x1_set_initial[2, 19] := false; array_x1_set_initial[2, 20] := false; array_x1_set_initial[2, 21] := false; array_x1_set_initial[2, 22] := false; array_x1_set_initial[2, 23] := false; array_x1_set_initial[2, 24] := false; array_x1_set_initial[2, 25] := false; array_x1_set_initial[2, 26] := false; array_x1_set_initial[2, 27] := false; array_x1_set_initial[2, 28] := false; array_x1_set_initial[2, 29] := false; array_x1_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_t[1] := t_start; array_t[2] := glob_h; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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 := 2; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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_x2(); if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_x1(); if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_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_t[1] <= t_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 <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 2; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[3, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_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_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[3, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[2, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[2, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_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_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_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 (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\ ff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(INFO, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-13T03:00:47-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest6_rev"); logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \ 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[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, "mtest6_rev diffeq.mxt"); logitem_str(html_log_file, "mtest6_rev maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; 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/mtest6_revpostode.ode################# diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # # was complicatedrev.ode # t_start := 0.5; t_end := 5.0; array_x1_init[0 + 1] := exact_soln_x1(t_start); array_x1_init[1 + 1] := exact_soln_x1p(t_start); array_x2_init[0 + 1] := exact_soln_x2(t_start); array_x2_init[1 + 1] := exact_soln_x2p(t_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #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_x1 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; 1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t); end; exact_soln_x1p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; - 6.0 * c3 * exp(-t); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; 1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion t[1] = 0.5 x2[1] (analytic) = 2.0007256155636055990741531973548 x2[1] (numeric) = 2.0007256155636055990741531973548 absolute error = 0 relative error = 0 % h = 0.0001 x1[1] (analytic) = 3.001091755187482740162486839163 x1[1] (numeric) = 3.001091755187482740162486839163 absolute error = 0 relative error = 0 % h = 0.0001 t[1] = 0.5 x2[1] (analytic) = 2.0007256155636055990741531973548 x2[1] (numeric) = 2.0007256155636055990741531973548 absolute error = 0 relative error = 0 % h = 0.0001 x1[1] (analytic) = 3.001091755187482740162486839163 x1[1] (numeric) = 3.001091755187482740162486839163 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.21 NO POLE NO POLE t[1] = 0.5001 x2[1] (analytic) = 2.0007257061107425639459896605159 x2[1] (numeric) = 2.0007257011153643353864612335881 absolute error = 4.9953782285595284269278e-09 relative error = 2.4967831488855915461522379994911e-07 % h = 0.0001 x1[1] (analytic) = 3.0010916460174225858712352664712 x1[1] (numeric) = 3.0010916560067727215008266624966 absolute error = 9.9893501356295913960254e-09 relative error = 3.3285721710251293877171755932824e-07 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.4MB, time=0.48 memory used=11.4MB, alloc=4.5MB, time=0.77 NO POLE NO POLE t[1] = 0.5002 x2[1] (analytic) = 2.0007257966814495432344339416603 x2[1] (numeric) = 2.0007257766964922309278518366111 absolute error = 1.99849573123065821050492e-08 relative error = 9.9888537177133903968906655509262e-07 % h = 0.0001 x1[1] (analytic) = 3.0010915368582788917633066026401 x1[1] (numeric) = 3.0010915768291406277631439384486 absolute error = 3.99708617359998373358085e-08 relative error = 1.3318774600871958952379931288251e-06 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.5MB, time=1.04 NO POLE NO POLE t[1] = 0.5003 x2[1] (analytic) = 2.0007258872757307055634980331085 x2[1] (numeric) = 2.0007258423019961384481191417913 absolute error = 4.49737345671153788913172e-08 relative error = 2.2478708779218843915256838296736e-06 % h = 0.0001 x1[1] (analytic) = 3.0010914277100505662472629969306 x1[1] (numeric) = 3.0010915176565853304214059875617 absolute error = 8.99465347641741429906311e-08 relative error = 2.9971274428252539409122863375084e-06 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.6MB, time=1.31 memory used=22.8MB, alloc=4.6MB, time=1.60 NO POLE NO POLE t[1] = 0.5004 x2[1] (analytic) = 2.0007259778935902204455844087623 x2[1] (numeric) = 2.0007258979268816125707643515641 absolute error = 7.99667086078748200571982e-08 relative error = 3.9968846054603433631685930316760e-06 % h = 0.0001 x1[1] (analytic) = 3.001091318572736517840820284614 x1[1] (numeric) = 3.0010914784911059004451523859818 absolute error = 1.599183693826043321013678e-07 relative error = 5.3286738858269247387356422877830e-06 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.6MB, time=1.88 NO POLE NO POLE t[1] = 0.5005 x2[1] (analytic) = 2.0007260685350322582816582620126 x2[1] (numeric) = 2.0007259435661529095035171680427 absolute error = 1.249688793487781410939699e-07 relative error = 6.2461763913678902738712398140542e-06 % h = 0.0001 x1[1] (analytic) = 3.001091209446335655170837072148 x1[1] (numeric) = 3.0010914593347016083213566057672 absolute error = 2.498883659531505195336192e-07 relative error = 8.3265835162421419242860776700606e-06 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.6MB, time=2.15 NO POLE NO POLE t[1] = 0.5006 x2[1] (analytic) = 2.0007261592000609903614197786446 x2[1] (numeric) = 2.0007259792148129867487963653838 absolute error = 1.799852480036126234132608e-07 relative error = 8.9959961375011513730950786241284e-06 % h = 0.0001 x1[1] (analytic) = 3.0010911003308468869733038234462 x1[1] (numeric) = 3.0010914601893719240742896227248 absolute error = 3.598585250371009857992786e-07 relative error = 1.1990923067861198552416354341961e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.6MB, time=2.42 memory used=38.1MB, alloc=4.6MB, time=2.72 NO POLE NO POLE t[1] = 0.5007 x2[1] (analytic) = 2.0007262498886805888634764447463 x2[1] (numeric) = 2.0007260048678635028141094894452 absolute error = 2.450208170860493669553011e-07 relative error = 1.2246593810606633619644383900098e-05 % h = 0.0001 x1[1] (analytic) = 3.0010909912262691220933319472376 x1[1] (numeric) = 3.0010914810571165172853854919654 absolute error = 4.898308473951920535447278e-07 relative error = 1.6321759281115410609326674455606e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.6MB, time=2.99 NO POLE NO POLE t[1] = 0.5008 x2[1] (analytic) = 2.0007263406008952268555153896278 x2[1] (numeric) = 2.0007260205203048169223916722684 absolute error = 3.200805904099331237173594e-07 relative error = 1.5998219442335156476547231962628e-05 % h = 0.0001 x1[1] (analytic) = 3.0010908821326012694851428855176 x1[1] (numeric) = 3.0010915219399352571131088913724 absolute error = 6.398073339876279660058548e-07 relative error = 2.1319158903077780590078737915743e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.6MB, time=3.27 memory used=49.5MB, alloc=4.6MB, time=3.55 NO POLE NO POLE t[1] = 0.5009 x2[1] (analytic) = 2.0007264313367090782944757637584 x2[1] (numeric) = 2.000726026167135988722283548917 absolute error = 4.051695730895721922148414e-07 relative error = 2.0251123129256286722292177246485e-05 % h = 0.0001 x1[1] (analytic) = 3.0010907730498422382120572030903 x1[1] (numeric) = 3.0010915828398282123128246331756 absolute error = 8.097899859741007674300853e-07 relative error = 2.6983188687463661141557572960993e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.6MB, time=3.83 NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 2.0007265220961263180267211517279 x2[1] (numeric) = 2.0007260218033547779983482641991 absolute error = 5.002927715400283728875288e-07 relative error = 2.5005555032872776279030240107841e-05 % h = 0.0001 x1[1] (analytic) = 3.001090663977990937446483678202 x1[1] (numeric) = 3.001091663758795651256669143824 absolute error = 9.997808047138101854656220e-07 relative error = 3.3313915394631418770887620633644e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.6MB, time=4.10 NO POLE NO POLE t[1] = 0.5011 x2[1] (analytic) = 2.0007266128791511217882120202398 x2[1] (numeric) = 2.0007260074239576443812275567997 absolute error = 6.054551934774069844634401e-07 relative error = 3.0261765379635003058351992003446e-05 % h = 0.0001 x1[1] (analytic) = 3.0010905549170462764699083942649 x1[1] (numeric) = 3.0010917646988380419534239123498 absolute error = 1.2097817917654835155180849e-06 relative error = 4.0311405791583097619309527245136e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.6MB, time=4.38 memory used=64.8MB, alloc=4.6MB, time=4.67 NO POLE NO POLE t[1] = 0.5012 x2[1] (analytic) = 2.000726703685787666204678201143 x2[1] (numeric) = 2.0007259830239397470577369083458 absolute error = 7.206618479191469412927972e-07 relative error = 3.6020004460955414825249627419352e-05 % h = 0.0001 x1[1] (analytic) = 3.0010904458670071646728838326719 x1[1] (numeric) = 3.0010918856619560520683909074176 absolute error = 1.4397949488873955070747457e-06 relative error = 4.7975726651965083301524095610830e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.6MB, time=4.95 NO POLE NO POLE t[1] = 0.5013 x2[1] (analytic) = 2.0007267945160401287917914095088 x2[1] (numeric) = 2.0007259485982949444808997449253 absolute error = 8.459177451843108916645835e-07 relative error = 4.2280522633222976080873995512731e-05 % h = 0.0001 x1[1] (analytic) = 3.0010903368278725115550179667025 x1[1] (numeric) = 3.0010920266501505489432699632507 absolute error = 1.6898222780373882519965482e-06 relative error = 5.6306944756068766810509805840835e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.6MB, time=5.22 memory used=76.2MB, alloc=4.6MB, time=5.51 NO POLE NO POLE t[1] = 0.5014 x2[1] (analytic) = 2.0007268853699126879553377967599 x2[1] (numeric) = 2.0007259041420157940799206785779 absolute error = 9.812278968938754171181820e-07 relative error = 4.9043570317817617964696697995377e-05 % h = 0.0001 x1[1] (analytic) = 3.0010902277996412267249633565185 x1[1] (numeric) = 3.0010921876654225996160381346285 absolute error = 1.9598657813728910747781100e-06 relative error = 6.5305126890831208487820429764471e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.6MB, time=5.79 NO POLE NO POLE t[1] = 0.5015 x2[1] (analytic) = 2.0007269762474095229913905388596 x2[1] (numeric) = 2.0007258496500935519700977762729 absolute error = 1.1265973159710212927625867e-06 relative error = 5.6309398001124691176687593313273e-05 % h = 0.0001 x1[1] (analytic) = 3.001090118782312219900406245251 x1[1] (numeric) = 3.0010923687097734708408310211475 absolute error = 2.2499274612509404247758965e-06 relative error = 7.4970339849835802059369119783263e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.6MB, time=6.06 NO POLE NO POLE memory used=87.7MB, alloc=4.6MB, time=6.34 t[1] = 0.5016 x2[1] (analytic) = 2.0007270671485348140864824595667 x2[1] (numeric) = 2.0007257851175181726626738438882 absolute error = 1.2820310166414238086156785e-06 relative error = 6.4078256234549421920117935825066e-05 % h = 0.0001 x1[1] (analytic) = 3.0010900097758844009080556561764 x1[1] (numeric) = 3.0010925697852046291078260609394 absolute error = 2.5600093202281997704047630e-06 relative error = 8.5302650433312938736705512887943e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.6MB, time=6.64 NO POLE NO POLE t[1] = 0.5017 x2[1] (analytic) = 2.000727158073292742317778688764 x2[1] (numeric) = 2.0007257105392783087746267126998 absolute error = 1.4475340144335431519760642e-06 relative error = 7.2350395634531370865599742155319e-05 % h = 0.0001 x1[1] (analytic) = 3.0010899007803566796836324909845 x1[1] (numeric) = 3.001092790893717740663127794039 absolute error = 2.8901133610609794953030545e-06 relative error = 9.6302125448140671383792183981859e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.6MB, time=6.91 NO POLE NO POLE t[1] = 0.5018 x2[1] (analytic) = 2.0007272490216874896532493558668 x2[1] (numeric) = 2.000725625910361310738398515891 absolute error = 1.6231113261789148508399758e-06 relative error = 8.1126066882558895136971900528569e-05 % h = 0.0001 x1[1] (analytic) = 3.0010897917957279662718586291348 x1[1] (numeric) = 3.0010930320373146715286550955952 absolute error = 3.2402415867052567964664604e-06 relative error = 0.00010796883170784537874928703589327 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.6MB, time=7.19 memory used=102.9MB, alloc=4.6MB, time=7.48 NO POLE NO POLE t[1] = 0.5019 x2[1] (analytic) = 2.0007273399937232389518423183184 x2[1] (numeric) = 2.0007255312257532265115639425858 absolute error = 1.8087679700124402783757326e-06 relative error = 9.0405520725183613319643797395834e-05 % h = 0.0001 x1[1] (analytic) = 3.0010896828219971708264460283046 x1[1] (numeric) = 3.0010932932179974875220303791187 absolute error = 3.6103960003166955843508141e-06 relative error = 0.00012030283603260242976433797354466 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.6MB, time=7.76 NO POLE NO POLE t[1] = 0.502 x2[1] (analytic) = 2.0007274309894041739636559251805 x2[1] (numeric) = 2.0007254264804388012864374569104 absolute error = 2.0045089653726772184682701e-06 relative error = 0.00010018900797403487349200730423701 % h = 0.0001 x1[1] (analytic) = 3.0010895738591632036100858259251 x1[1] (numeric) = 3.0010935744377684542764707699585 absolute error = 4.0005786052506663849440334e-06 relative error = 0.00013330420524923684790589640634121 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.6MB, time=8.04 memory used=114.4MB, alloc=4.6MB, time=8.32 NO POLE NO POLE t[1] = 0.5021 x2[1] (analytic) = 2.0007275220087344793301118158238 x2[1] (numeric) = 2.0007253116694014771996194695823 absolute error = 2.2103393330021304923462415e-06 relative error = 0.0001104767795058342242805280509864 % h = 0.0001 x1[1] (analytic) = 3.0010894649072249749944374418092 x1[1] (numeric) = 3.0010938756986300372606812492015 absolute error = 4.4107914050622662438073923e-06 relative error = 0.00014697300619122397562555594623657 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.6MB, time=8.60 NO POLE NO POLE t[1] = 0.5022 x2[1] (analytic) = 2.0007276130517183405841277537279 x2[1] (numeric) = 2.0007251867876233930414814495262 absolute error = 2.4262640949475426463042017e-06 relative error = 0.00012126908626240988893912711104737 % h = 0.0001 x1[1] (analytic) = 3.0010893559661813954601176818676 x1[1] (numeric) = 3.0010941970025849017987497681878 absolute error = 4.8410364035063386320863202e-06 relative error = 0.00016130930569869013884392284886742 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.6MB, time=8.88 NO POLE NO POLE t[1] = 0.5023 x2[1] (analytic) = 2.0007277041183599441502904953943 x2[1] (numeric) = 2.0007250518300853839655899630107 absolute error = 2.6522882745601847005323836e-06 relative error = 0.00013256617925071124245346421145519 % h = 0.0001 x1[1] (analytic) = 3.001089247036031375596689842915 x1[1] (numeric) = 3.0010945383516359130900443338351 absolute error = 5.2913156045374933544909201e-06 relative error = 0.00017631317061841331151052459853348 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.6MB, time=9.15 memory used=129.7MB, alloc=4.6MB, time=9.44 NO POLE NO POLE t[1] = 0.5024 x2[1] (analytic) = 2.0007277952086634773450286943839 x2[1] (numeric) = 2.0007249067917669811980696277997 absolute error = 2.8884168964961469590665842e-06 relative error = 0.00014436830954282329167073396019443 % h = 0.0001 x1[1] (analytic) = 3.001089138116773826102652818566 x1[1] (numeric) = 3.0010948997477861362291120649652 absolute error = 5.7616310123101264592463992e-06 relative error = 0.00019198466780382378022926309777651 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.6MB, time=9.73 NO POLE NO POLE t[1] = 0.5025 x2[1] (analytic) = 2.0007278863226331283767858404813 x2[1] (numeric) = 2.0007247516676464117469049698087 absolute error = 3.1346549867166298808706726e-06 relative error = 0.00015667572827598115845558630636137 % h = 0.0001 x1[1] (analytic) = 3.0010890292084076577854302062196 x1[1] (numeric) = 3.0010952811930388362255802198265 absolute error = 6.2519846311784401500136069e-06 relative error = 0.0002083238641150048089494189756244 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.6MB, time=10.00 memory used=141.1MB, alloc=4.6MB, time=10.28 NO POLE NO POLE t[1] = 0.5026 x2[1] (analytic) = 2.0007279774602730863461932339965 x2[1] (numeric) = 2.0007245864527005981111811697531 absolute error = 3.3910075724882350120642434e-06 relative error = 0.00016948868665258456587278301223639 % h = 0.0001 x1[1] (analytic) = 3.0010889203109317815613594151339 x1[1] (numeric) = 3.0010956826893974780240591950046 absolute error = 6.7623784656964626997798707e-06 relative error = 0.00022533082641869330372221337861953 % h = 0.0001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.6MB, time=10.56 NO POLE NO POLE t[1] = 0.5027 x2[1] (analytic) = 2.000728068621587541246242995209 x2[1] (numeric) = 2.0007244111419051579902636872749 absolute error = 3.6574796823832559793079341e-06 relative error = 0.00018280743594021232739720166500053 % h = 0.0001 x1[1] (analytic) = 3.0010888114243451084556807755893 x1[1] (numeric) = 3.0010961042388657265240474959158 absolute error = 7.2928145206180683667203265e-06 relative error = 0.00024300562158828047752293380867672 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.6MB, time=10.84 NO POLE NO POLE t[1] = 0.5028 x2[1] (analytic) = 2.0007281598065806839624611089617 x2[1] (numeric) = 2.0007242257302344039929167500296 absolute error = 3.9340763462799695443589321e-06 relative error = 0.00019663222747163683915179909927934 % h = 0.0001 x1[1] (analytic) = 3.0010887025486465496025266491408 x1[1] (numeric) = 3.0010965458434474465998386790756 absolute error = 7.8432948008969973120299348e-06 relative error = 0.00026134831650381251513863040520838 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.6MB, time=11.11 memory used=156.4MB, alloc=4.7MB, time=11.40 NO POLE NO POLE t[1] = 0.5029 x2[1] (analytic) = 2.0007282510152567062730805044118 x2[1] (numeric) = 2.0007240302126613433463606952141 absolute error = 4.2208025953629267198091977e-06 relative error = 0.00021096331264483857517414613525726 % h = 0.0001 x1[1] (analytic) = 3.0010885936838350162449105399592 x1[1] (numeric) = 3.001097007505146703120430266336 absolute error = 8.4138213116868755197263768e-06 relative error = 0.00028035897805199123812138915225629 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.7MB, time=11.68 NO POLE NO POLE t[1] = 0.503 x2[1] (analytic) = 2.0007283422476198008492141699459 x2[1] (numeric) = 2.0007238245841576776052681510129 absolute error = 4.5176634621232439460189330e-06 relative error = 0.00022580094292302058571214570561259 % h = 0.0001 x1[1] (analytic) = 3.0010884848299094197347162072617 x1[1] (numeric) = 3.001097489225967760969434631285 absolute error = 9.0043960583412347184240233e-06 relative error = 0.00030003767312617476980718845471468 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.7MB, time=11.95 memory used=167.8MB, alloc=4.7MB, time=12.23 NO POLE NO POLE t[1] = 0.5031 x2[1] (analytic) = 2.0007284335036741612550283032656 x2[1] (numeric) = 2.0007236088396938023606990454384 absolute error = 4.8246639803588943292578272e-06 relative error = 0.00024114536983462299854954646808129 % h = 0.0001 x1[1] (analytic) = 3.0010883759868686715326867788304 x1[1] (numeric) = 3.0010979910079150850649918580018 absolute error = 9.6150210464135323050791714e-06 relative error = 0.00032038446862637820040034559770259 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.7MB, time=12.51 NO POLE NO POLE t[1] = 0.5032 x2[1] (analytic) = 2.0007285247834239819479154966509 x2[1] (numeric) = 2.000723382974238806948974430037 absolute error = 5.1418091851749989410666139e-06 relative error = 0.00025699684497333752336186424893023 % h = 0.0001 x1[1] (analytic) = 3.0010882671547116832084138656195 x1[1] (numeric) = 3.0010985128529933403796845723605 absolute error = 1.02456982816571712707067410e-05 relative error = 0.00034139943145927425212355950317828 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.7MB, time=12.79 NO POLE NO POLE t[1] = 0.5033 x2[1] (analytic) = 2.0007286160868734582786679574086 x2[1] (numeric) = 2.0007231469827604741604891059317 absolute error = 5.4691041129841181788514769e-06 relative error = 0.00027335561999812195910332370116704 % h = 0.0001 x1[1] (analytic) = 3.0010881583334373664403266774516 x1[1] (numeric) = 3.0010990547632073919604547460762 absolute error = 1.08964297700255201280686246e-05 relative error = 0.00036308262853819394443355624786891 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.7MB, time=13.06 memory used=183.1MB, alloc=4.7MB, time=13.36 NO POLE NO POLE t[1] = 0.5034 x2[1] (analytic) = 2.0007287074140267864916507635123 x2[1] (numeric) = 2.000722900860225279948463039669 absolute error = 5.8065538015065431877238433e-06 relative error = 0.00029022194663321470442543266983201 % h = 0.0001 x1[1] (analytic) = 3.0010880495230446330156811398021 x1[1] (numeric) = 3.0010996167405623049485224736871 absolute error = 1.15672175176719328413338850e-05 relative error = 0.00038543412678312725930234384324101 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.7MB, time=13.63 NO POLE NO POLE t[1] = 0.5035 x2[1] (analytic) = 2.0007287987648881637249751544417 x2[1] (numeric) = 2.0007226446015983931376315563345 absolute error = 6.1541632897705873435981072e-06 relative error = 0.0003075960766681492711278019751926 % h = 0.0001 x1[1] (analytic) = 3.0010879407235323948305490116711 x1[1] (numeric) = 3.0011001987870633445993067226653 absolute error = 1.22580635309497687577109942e-05 relative error = 0.00040845399312072380656408273491791 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.7MB, time=13.91 memory used=194.5MB, alloc=4.7MB, time=14.20 NO POLE NO POLE t[1] = 0.5036 x2[1] (analytic) = 2.0007288901394617880106718572265 x2[1] (numeric) = 2.0007223782018436751328742973996 absolute error = 6.5119376181128777975598269e-06 relative error = 0.00032547826195776880064182329822305 % h = 0.0001 x1[1] (analytic) = 3.0010878319348995638898070045447 x1[1] (numeric) = 3.0011008009047159763023480568508 absolute error = 1.29689698164124125410523061e-05 relative error = 0.00043214229448429348932757845562427 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.7MB, time=14.47 NO POLE NO POLE t[1] = 0.5037 x2[1] (analytic) = 2.0007289815377518582748644477049 x2[1] (numeric) = 2.0007221016559236796277829307605 absolute error = 6.8798818281786470815169444e-06 relative error = 0.00034386875442224058354781814119526 % h = 0.0001 x1[1] (analytic) = 3.0010877231571450523071259024436 x1[1] (numeric) = 3.001101423095525865601233333401 absolute error = 1.36999383808132941074309574e-05 relative error = 0.0004564990978138071694544029257146 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.7MB, time=14.75 NO POLE NO POLE t[1] = 0.5038 x2[1] (analytic) = 2.0007290729597625743379427469999 x2[1] (numeric) = 2.0007218149587996523131676004251 absolute error = 7.2580009629220247751465748e-06 relative error = 0.00036276780604707058212627076977874 % h = 0.0001 x1[1] (analytic) = 3.0010876143902677723049596830596 x1[1] (numeric) = 3.0011020653614988782135223734502 absolute error = 1.44509712311059085626903906e-05 relative error = 0.00048152447005589733310265087868094 % h = 0.0001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.7MB, time=15.02 memory used=209.8MB, alloc=4.7MB, time=15.31 NO POLE NO POLE t[1] = 0.5039 x2[1] (analytic) = 2.0007291644054981369147362532235 x2[1] (numeric) = 2.0007215181054315305855021033043 absolute error = 7.6463000666063292341499192e-06 relative error = 0.00038217566888311795594375833648284 % h = 0.0001 x1[1] (analytic) = 3.0010875056342666362145346399805 x1[1] (numeric) = 3.001102727704641080050676606672 absolute error = 1.52220703744438361419666915e-05 relative error = 0.00050721847816385875633633783905114 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.7MB, time=15.58 NO POLE NO POLE t[1] = 0.504 x2[1] (analytic) = 2.0007292558749627476146876084142 x2[1] (numeric) = 2.0007212110907779432553077805589 absolute error = 8.0447841848043593798278553e-06 relative error = 0.00040209259504660959047419140880803 % h = 0.0001 x1[1] (analytic) = 3.0010873968891405564758385060019 x1[1] (numeric) = 3.0011034101269587372379896899386 absolute error = 1.60132378181807621511839367e-05 relative error = 0.00053358118909764917080044618338419 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.7MB, time=15.86 memory used=221.2MB, alloc=4.7MB, time=16.14 NO POLE NO POLE t[1] = 0.5041 x2[1] (analytic) = 2.0007293473681606089420261007159 x2[1] (numeric) = 2.0007208939097962102554761109527 absolute error = 8.4534583643986865499897632e-06 relative error = 0.00042251883671915462875597828395208 % h = 0.0001 x1[1] (analytic) = 3.0010872881548884456376095775276 x1[1] (numeric) = 3.0011041126304583161345201002703 absolute error = 1.68244755698704969105227427e-05 relative error = 0.00056061266982388992946162568511453 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.7MB, time=16.42 NO POLE NO POLE t[1] = 0.5042 x2[1] (analytic) = 2.0007294388850959242959412018029 x2[1] (numeric) = 2.0007205665574423423495299936585 absolute error = 8.8723276535819464112081444e-06 relative error = 0.00044345464614775900608572649044672 % h = 0.0001 x1[1] (analytic) = 3.0010871794315092163573258400565 x1[1] (numeric) = 3.0011048352171464833530257022683 absolute error = 1.76557856372669956998622118e-05 relative error = 0.0005883129873158666724145550639524 % h = 0.0001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.7MB, time=16.70 NO POLE NO POLE memory used=232.7MB, alloc=4.7MB, time=16.98 t[1] = 0.5043 x2[1] (analytic) = 2.0007295304257728979707561395621 x2[1] (numeric) = 2.0007202290286710408398237079618 absolute error = 9.3013971018571309324316003e-06 relative error = 0.00046490027564483998774909528548233 % h = 0.0001 x1[1] (analytic) = 3.0010870707190017814011940947576 x1[1] (numeric) = 3.0011055778890301057799002902256 absolute error = 1.85071700283243787061954680e-05 relative error = 0.00061668220855352999275397099390363 % h = 0.0001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.7MB, time=17.26 NO POLE NO POLE t[1] = 0.5044 x2[1] (analytic) = 2.000729621990195735156101506034 x2[1] (numeric) = 2.0007198813184356972756815373051 absolute error = 9.7406717600378804199687289e-06 relative error = 0.00048685597758824070978941257035049 % h = 0.0001 x1[1] (analytic) = 3.001086962017365053644139086132 x1[1] (numeric) = 3.0011063406481162505951121051085 absolute error = 1.93786307511969509730189765e-05 relative error = 0.00064572040052349610251237103729905 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.7MB, time=17.54 NO POLE NO POLE t[1] = 0.5045 x2[1] (analytic) = 2.0007297135783686419370889006249 x2[1] (numeric) = 2.0007195234216883931614750451113 absolute error = 1.01901566802487756138555136e-05 relative error = 0.00050932200442124472281467039968436 % h = 0.0001 x1[1] (analytic) = 3.0010868533265979460697926307621 x1[1] (numeric) = 3.0011071234964121852921443266027 absolute error = 2.02701698142392223516958406e-05 relative error = 0.000675427630219047498663396978887 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.7MB, time=17.82 memory used=247.9MB, alloc=4.7MB, time=18.10 NO POLE NO POLE t[1] = 0.5046 x2[1] (analytic) = 2.0007298051902958252944846085935 x2[1] (numeric) = 2.0007191553333798996646389898241 absolute error = 1.06498569159256298456187694e-05 relative error = 0.00053229860865259053884351282386162 % h = 0.0001 x1[1] (analytic) = 3.0010867446466993717704827471482 x1[1] (numeric) = 3.0011079264359253776979375404177 absolute error = 2.11817892260059274547932695e-05 relative error = 0.00070580396464013362919090502404427 % h = 0.0001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.7MB, time=18.38 NO POLE NO POLE t[1] = 0.5047 x2[1] (analytic) = 2.0007298968259814931048833148203 x2[1] (numeric) = 2.0007187770484596773236258665998 absolute error = 1.11197775218157812574482205e-05 relative error = 0.00055578604285648618119083023229862 % h = 0.0001 x1[1] (analytic) = 3.0010866359776682439472227866313 x1[1] (numeric) = 3.0011087494686634959928341810434 absolute error = 2.21134909952520456113944121e-05 relative error = 0.0007368494707933715592237293784739 % h = 0.0001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.7MB, time=18.66 NO POLE NO POLE memory used=259.4MB, alloc=4.7MB, time=18.94 t[1] = 0.5048 x2[1] (analytic) = 2.0007299884854298541408818528671 x2[1] (numeric) = 2.0007183885618758757557990630827 absolute error = 1.15999235539783850827897844e-05 relative error = 0.00057978455967262373739357441386523 % h = 0.0001 x1[1] (analytic) = 3.0010865273195034759097005654036 x1[1] (numeric) = 3.0011095925966344087305249501521 absolute error = 2.30652771309328208243847485e-05 relative error = 0.000768564215692046637236145613464 % h = 0.0001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.7MB, time=19.23 NO POLE NO POLE t[1] = 0.5049 x2[1] (analytic) = 2.0007300801686451180712529893331 x2[1] (numeric) = 2.0007179898685753333652646166927 absolute error = 1.20903000697847059883726404e-05 relative error = 0.00060429441180619391517740868411672 % h = 0.0001 x1[1] (analytic) = 3.0010864186722039810762674976051 x1[1] (numeric) = 3.0011104558218461848579972108397 absolute error = 2.40371496422037817297132346e-05 relative error = 0.00080094826635611316131404034406985 % h = 0.0001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.7MB, time=19.52 NO POLE NO POLE t[1] = 0.505 x2[1] (analytic) = 2.0007301718756314954611192435145 x2[1] (numeric) = 2.0007175809635035770506415608534 absolute error = 1.25909121279184104776826611e-05 relative error = 0.00062931585202790060146480745754155 % h = 0.0001 x1[1] (analytic) = 3.0010863100357686729739277295073 x1[1] (numeric) = 3.0011113391463070937354853579002 absolute error = 2.50291105384207615576283929e-05 relative error = 0.00083400168981219504548679367094041 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.7MB, time=19.79 memory used=274.6MB, alloc=4.7MB, time=20.07 NO POLE NO POLE t[1] = 0.5051 x2[1] (analytic) = 2.0007302636063931977721267423749 x2[1] (numeric) = 2.0007171618416048219127708475841 absolute error = 1.31017647883758593558947908e-05 relative error = 0.00065484913317397542442521990143891 % h = 0.0001 x1[1] (analytic) = 3.0010862014101964652383272747832 x1[1] (numeric) = 3.0011122425720256051564231643269 absolute error = 2.60411618291399180958895437e-05 relative error = 0.00086772455309358648612488087316308 % h = 0.0001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.7MB, time=20.35 NO POLE NO POLE t[1] = 0.5052 x2[1] (analytic) = 2.0007303553609344373626191108334 x2[1] (numeric) = 2.0007167324978219709623628338777 absolute error = 1.36228631124664002562769557e-05 relative error = 0.00068089450814619231856791235153157 % h = 0.0001 x1[1] (analytic) = 3.0010860927954862716137431508637 x1[1] (numeric) = 3.0011131661010103893673981042343 absolute error = 2.70733055241177536549533706e-05 relative error = 0.00090211692324025262840319982950248 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.7MB, time=20.62 memory used=286.1MB, alloc=4.7MB, time=20.91 NO POLE NO POLE t[1] = 0.5053 x2[1] (analytic) = 2.0007304471392594274878113973781 x2[1] (numeric) = 2.0007162929270966148275833192844 absolute error = 1.41542121628126602280780937e-05 relative error = 0.00070745222991188209287810430787265 % h = 0.0001 x1[1] (analytic) = 3.0010859841916370059530725163803 x1[1] (numeric) = 3.0011141097352703170881076523941 absolute error = 2.81255436333111350351360138e-05 relative error = 0.00093717886729883023283013063207923 % h = 0.0001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.7MB, time=21.18 NO POLE NO POLE t[1] = 0.5054 x2[1] (analytic) = 2.0007305389413723822999640350102 x2[1] (numeric) = 2.0007158431243690314615781221169 absolute error = 1.46958170033508383859128933e-05 relative error = 0.00073452255150394700199701290807868 % h = 0.0001 x1[1] (analytic) = 3.0010858755986475822178218096944 x1[1] (numeric) = 3.0011150734768144595313175605793 absolute error = 2.91978781668773134957508849e-05 relative error = 0.0009729104523226283418423338631974 % h = 0.0001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.7MB, time=21.47 NO POLE NO POLE t[1] = 0.5055 x2[1] (analytic) = 2.000730630767277516848556837528 x2[1] (numeric) = 2.0007153830845781858499361816928 absolute error = 1.52476826993309986206558352e-05 relative error = 0.00076210572602087532044642097334608 % h = 0.0001 x1[1] (analytic) = 3.0010857670165169144780958885117 x1[1] (numeric) = 3.0011160573276520884228221109106 absolute error = 3.02903111351739447262223989e-05 relative error = 0.0010093117453716289464652940726711 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.7MB, time=21.75 memory used=301.3MB, alloc=4.7MB, time=22.03 NO POLE NO POLE t[1] = 0.5056 x2[1] (analytic) = 2.0007307226169790470804630311551 x2[1] (numeric) = 2.0007149128026617297180911740239 absolute error = 1.58098143173173623718571312e-05 relative error = 0.00079020200662675591989838376618953 % h = 0.0001 x1[1] (analytic) = 3.001085658445243916912587170584 x1[1] (numeric) = 3.0011170612897926760214063463982 absolute error = 3.14028445487591088191758142e-05 relative error = 0.0010463828135124876530396148297237 % h = 0.0001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.7MB, time=22.32 NO POLE NO POLE t[1] = 0.5057 x2[1] (analytic) = 2.0007308144904811898401233215242 x2[1] (numeric) = 2.0007144322735560012386616283639 absolute error = 1.63822169251886014616931603e-05 relative error = 0.00081881164655129284949068985723696 % h = 0.0001 x1[1] (analytic) = 3.0010855498848275038085647754956 x1[1] (numeric) = 3.0011180853652458951388102788737 absolute error = 3.25354804183913302455033781e-05 relative error = 0.0010841237238185343500130719467869 % h = 0.0001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.7MB, time=22.59 memory used=312.8MB, alloc=4.7MB, time=22.88 NO POLE NO POLE t[1] = 0.5058 x2[1] (analytic) = 2.0007309063877881628697199960171 x2[1] (numeric) = 2.0007139414921960247387295320188 absolute error = 1.69648955921381309904639983e-05 relative error = 0.0008479348990898199191886913119778 % h = 0.0001 x1[1] (analytic) = 3.001085441335266589561863667536 x1[1] (numeric) = 3.0011191295560216191596950745048 absolute error = 3.36882207550295978314069688e-05 relative error = 0.0011225345433697738747984312559335 % h = 0.0001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.7MB, time=23.16 NO POLE NO POLE t[1] = 0.5059 x2[1] (analytic) = 2.0007309983089041848093510614748 x2[1] (numeric) = 2.0007134404535155104070574108255 absolute error = 1.75578553886744022936506493e-05 relative error = 0.00087757201760331528619411900662502 % h = 0.0001 x1[1] (analytic) = 3.0010853327965600886768737996586 x1[1] (numeric) = 3.001120193864129922061611217088 absolute error = 3.48610675698333847374174294e-05 relative error = 0.0011616153392528866806970374686261 % h = 0.0001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.7MB, time=23.44 NO POLE NO POLE t[1] = 0.506 x2[1] (analytic) = 2.0007310902538334751972044172794 x2[1] (numeric) = 2.0007129291524468540012438726996 absolute error = 1.81611013866211959605445798e-05 relative error = 0.00090772325551841604440149849088332 % h = 0.0001 x1[1] (analytic) = 3.0010852242687069157665292585244 x1[1] (numeric) = 3.0011212782915810784349686493126 absolute error = 3.60540228741626684393907882e-05 relative error = 0.0012013661785612295038881806094736 % h = 0.0001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.7MB, time=23.73 memory used=328.0MB, alloc=4.7MB, time=24.01 NO POLE NO POLE t[1] = 0.5061 x2[1] (analytic) = 2.0007311822225802544697320638176 x2[1] (numeric) = 2.0007124075839211365548176016517 absolute error = 1.87746386591179149144621659e-05 relative error = 0.00093838886632743281690278229871783 % h = 0.0001 x1[1] (analytic) = 3.001085115751705985552297410631 x1[1] (numeric) = 3.0011223828403855635030088921895 absolute error = 3.72670886795779507114815585e-05 relative error = 0.0012417871283948360304842464780357 % h = 0.0001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.7MB, time=24.29 NO POLE NO POLE t[1] = 0.5062 x2[1] (analytic) = 2.0007312742151487439618243463322 x2[1] (numeric) = 2.0007118757428681240842697896674 absolute error = 1.93984722806198775545566648e-05 relative error = 0.00096956910358836435154081463668729 % h = 0.0001 x1[1] (analytic) = 3.0010850072455562128641680495278 x1[1] (numeric) = 3.0011235075125540531417791428395 absolute error = 3.85002669978402776110933117e-05 relative error = 0.0012828782558604175636516576127038 % h = 0.0001 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.7MB, time=24.57 memory used=339.5MB, alloc=4.7MB, time=24.85 NO POLE NO POLE t[1] = 0.5063 x2[1] (analytic) = 2.0007313662315431659069842341678 x2[1] (numeric) = 2.0007113336242162672960249938469 absolute error = 2.00326073268986109592403209e-05 relative error = 0.0010012642209249121195122443279005 % h = 0.0001 x1[1] (analytic) = 3.0010848987502565126406425441156 x1[1] (numeric) = 3.0011246523100974239001083508346 absolute error = 3.97535598409112594658067190e-05 relative error = 0.0013246396280713636907976112806705 % h = 0.0001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.7MB, time=25.14 NO POLE NO POLE t[1] = 0.5064 x2[1] (analytic) = 2.0007314582717677434375016354202 x2[1] (numeric) = 2.0007107812228927012933504061931 absolute error = 2.06770488750421441512292271e-05 relative error = 0.0010334744720264949170205023979404 % h = 0.0001 x1[1] (analytic) = 3.0010847902658057999287229880316 x1[1] (numeric) = 3.0011258172350267530195852732868 absolute error = 4.10269692209530908622852552e-05 relative error = 0.0013670713121477429508226209580169 % h = 0.0001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.7MB, time=25.43 NO POLE NO POLE t[1] = 0.5065 x2[1] (analytic) = 2.0007315503358267005846277469922 x2[1] (numeric) = 2.0007102185338232452832035234391 absolute error = 2.13318020034553014242235531e-05 relative error = 0.0010662001106482634699794602427373 % h = 0.0001 x1[1] (analytic) = 3.0010846817922029898839013501196 x1[1] (numeric) = 3.0011270022893533184545385088774 absolute error = 4.23204971503285706371587578e-05 relative error = 0.0014101733752163035014388677539528 % h = 0.0001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.7MB, time=25.71 memory used=354.7MB, alloc=4.7MB, time=25.99 NO POLE NO POLE t[1] = 0.5066 x2[1] (analytic) = 2.0007316424237242622787494400674 x2[1] (numeric) = 2.0007096455519324022830182043 absolute error = 2.19968717918599957312357674e-05 relative error = 0.0010994413906111150417683850565651 % h = 0.0001 x1[1] (analytic) = 3.0010845733294469977701486259847 x1[1] (numeric) = 3.0011282074750885988920185110219 absolute error = 4.36341456416011218698850372e-05 relative error = 0.0014539458844104737865543683198753 % h = 0.0001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.7MB, time=26.27 NO POLE NO POLE t[1] = 0.5067 x2[1] (analytic) = 2.0007317345354646543495636810068 x2[1] (numeric) = 2.0007090622721433588274291015325 absolute error = 2.26722633212955221345794743e-05 relative error = 0.0011331985658017080440388089219044 % h = 0.0001 x1[1] (analytic) = 3.0010844648775367389599039906329 x1[1] (numeric) = 3.001129432794244273771781580364 absolute error = 4.49679167075348118775897311e-05 relative error = 0.0014983889068703632037229656939455 % h = 0.0001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.7MB, time=26.54 memory used=366.2MB, alloc=4.7MB, time=26.83 NO POLE NO POLE t[1] = 0.5068 x2[1] (analytic) = 2.0007318266710521035262519876743 x2[1] (numeric) = 2.0007084686893779846749344561848 absolute error = 2.33579816741188513175314895e-05 relative error = 0.001167471890172476650573928071336 % h = 0.0001 x1[1] (analytic) = 3.0010843564364711289340639521961 x1[1] (numeric) = 3.0011306782488322233062758367929 absolute error = 4.63218123610943722118845968e-05 relative error = 0.0015435025097427627716601495518716 % h = 0.0001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.7MB, time=27.10 NO POLE NO POLE t[1] = 0.5069 x2[1] (analytic) = 2.0007319188304908374376549212004 x2[1] (numeric) = 2.0007078647985568325144972414135 absolute error = 2.40540319340049231576797869e-05 relative error = 0.0012022616177416454142011492749264 % h = 0.0001 x1[1] (analytic) = 3.0010842480062490832819715067401 x1[1] (numeric) = 3.0011319438408645285006291711778 absolute error = 4.76958346154452186576644377e-05 relative error = 0.0015892867601811457978247124212235 % h = 0.0001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.7MB, time=27.39 NO POLE NO POLE t[1] = 0.507 x2[1] (analytic) = 2.00073201101378508461244661319 x2[1] (numeric) = 2.000707250594599137672084643245 absolute error = 2.47604191859469403619699450e-05 relative error = 0.0012375680025932438867584000900998 % h = 0.0001 x1[1] (analytic) = 3.0010841395868695177014052941589 x1[1] (numeric) = 3.0011332295723534711726391770138 absolute error = 4.90899854839534712338828549e-05 relative error = 0.0016357417253456685460662482366656 % h = 0.0001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.7MB, time=27.66 memory used=381.4MB, alloc=4.7MB, time=27.94 NO POLE NO POLE t[1] = 0.5071 x2[1] (analytic) = 2.0007321032209390744793093283805 x2[1] (numeric) = 2.0007066260724228178171458656538 absolute error = 2.54771485162566621634627267e-05 relative error = 0.0012733912988771212421148199743517 % h = 0.0001 x1[1] (analytic) = 3.0010840311783313479985687551521 x1[1] (numeric) = 3.0011345354453115339727650621734 absolute error = 5.05042669801859741963070213e-05 relative error = 0.0016828674724031709043384998300817 % h = 0.0001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.7MB, time=28.22 NO POLE NO POLE t[1] = 0.5072 x2[1] (analytic) = 2.0007321954519570373671080627591 x2[1] (numeric) = 2.0007059912269444726690282473293 absolute error = 2.62042250125646980798154298e-05 relative error = 0.0013097317608089609022464494295436 % h = 0.0001 x1[1] (analytic) = 3.0010839227806334900880792892867 x1[1] (numeric) = 3.0011358614617514004041215409578 absolute error = 5.19386811179103160422516711e-05 relative error = 0.001730664068527177052478561799621 % h = 0.0001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.7MB, time=28.50 memory used=392.9MB, alloc=4.7MB, time=28.79 NO POLE NO POLE t[1] = 0.5073 x2[1] (analytic) = 2.0007322877068432045050651771445 x2[1] (numeric) = 2.0007053460530793837033316774986 absolute error = 2.69416537638208017334996459e-05 relative error = 0.0013465896426702951663675343599645 % h = 0.0001 x1[1] (analytic) = 3.0010838143937748599929574141438 x1[1] (numeric) = 3.0011372076236859548424747066418 absolute error = 5.33932299110948495172924980e-05 relative error = 0.001779131580897896130051945215017 % h = 0.0001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.7MB, time=29.07 NO POLE NO POLE t[1] = 0.5074 x2[1] (analytic) = 2.0007323799856018080229350662418 x2[1] (numeric) = 2.0007046905457415138582012981723 absolute error = 2.76894398602941647337680695e-05 relative error = 0.001383965198808519843118063024714 % h = 0.0001 x1[1] (analytic) = 3.0010837060177543738446159255482 x1[1] (numeric) = 3.0011385739331282825562398847069 absolute error = 5.48679153739087116239591587e-05 relative error = 0.0018282700767022229042635107264958 % h = 0.0001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.7MB, time=29.35 NO POLE NO POLE t[1] = 0.5075 memory used=404.3MB, alloc=4.7MB, time=29.65 x2[1] (analytic) = 2.0007324722882370809511788631756 x2[1] (numeric) = 2.0007040246998435072405584801751 absolute error = 2.84475883935737106203830005e-05 relative error = 0.0014218586836369088858081530283827 % h = 0.0001 x1[1] (analytic) = 3.001083597652570947882849058883 x1[1] (numeric) = 3.0011399603920916697264814669562 absolute error = 5.63627395207218436324080732e-05 relative error = 0.0018780796231337384379342764746436 % h = 0.0001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.7MB, time=29.95 NO POLE NO POLE t[1] = 0.5076 x2[1] (analytic) = 2.0007325646147532572211391795107 x2[1] (numeric) = 2.0007033485102966888322700603227 absolute error = 2.92161044565683888691191880e-05 relative error = 0.0014602703516346290307199060223593 % h = 0.0001 x1[1] (analytic) = 3.0010834892982234984558216514875 x1[1] (numeric) = 3.0011413670025896034669147267061 absolute error = 5.78777043661050110930752186e-05 relative error = 0.0019285602873927107575441073718794 % h = 0.0001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.7MB, time=30.25 NO POLE NO POLE t[1] = 0.5077 x2[1] (analytic) = 2.0007326569651545716652148807651 x2[1] (numeric) = 2.0007026619720110641962558271033 absolute error = 2.99949931435074689590536618e-05 relative error = 0.0014992004573467544384673477075599 % h = 0.0001 x1[1] (analytic) = 3.0010833809547109420200583061384 x1[1] (numeric) = 3.0011427937666357718439096152485 absolute error = 5.94128119248298238513091101e-05 relative error = 0.0019797121366860955213402922262079 % h = 0.0001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.7MB, time=30.55 memory used=419.6MB, alloc=4.8MB, time=30.84 NO POLE NO POLE t[1] = 0.5078 x2[1] (analytic) = 2.0007327493394452600170358974238 x2[1] (numeric) = 2.0007019650798953191825342422182 absolute error = 3.07842595499408345016552056e-05 relative error = 0.0015386492553842813384150711026736 % h = 0.0001 x1[1] (analytic) = 3.0010832726220321951404325556154 x1[1] (numeric) = 3.0011442406862440638964965397776 absolute error = 6.09680642118687560639841622e-05 relative error = 0.0020315352382275366875120151546054 % h = 0.0001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.8MB, time=31.13 NO POLE NO POLE t[1] = 0.5079 x2[1] (analytic) = 2.0007328417376295589116380714609 x2[1] (numeric) = 2.0007012578288568196342063853357 absolute error = 3.15839087727392774316861252e-05 relative error = 0.0015786170004241426761562010004593 % h = 0.0001 x1[1] (analytic) = 3.0010831643001861744901560283501 x1[1] (numeric) = 3.0011457077634285696563741229762 absolute error = 6.25434632423951662180946261e-05 relative error = 0.0020840296592373671824307278333515 % h = 0.0001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.8MB, time=31.41 NO POLE NO POLE memory used=431.0MB, alloc=4.8MB, time=31.69 t[1] = 0.508 x2[1] (analytic) = 2.0007329341597117058856380383748 x2[1] (numeric) = 2.000700540213801611093378109408 absolute error = 3.23939459100947922599289668e-05 relative error = 0.0016191039472092227640502976180315 % h = 0.0001 x1[1] (analytic) = 3.0010830559891717968507676151575 x1[1] (numeric) = 3.0011471950002035801679189444551 absolute error = 6.41390110317833171513292976e-05 relative error = 0.0021371954669426095689564290759732 % h = 0.0001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.8MB, time=31.98 NO POLE NO POLE t[1] = 0.5081 x2[1] (analytic) = 2.0007330266056959393774081447462 x2[1] (numeric) = 2.0006998122296344185070203938991 absolute error = 3.32143760615208703877508471e-05 relative error = 0.0016601103505483719348218177703747 % h = 0.0001 x1[1] (analytic) = 3.0010829476889879791121226370521 x1[1] (numeric) = 3.0011487023985835875081972642403 absolute error = 6.57547095956083960746271882e-05 relative error = 0.0021910327285769767148098581761518 % h = 0.0001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.8MB, time=32.28 NO POLE NO POLE t[1] = 0.5082 x2[1] (analytic) = 2.0007331190755864987272514013242 x2[1] (numeric) = 2.0006990738712586459327678832688 absolute error = 3.40452043278527944835180554e-05 relative error = 0.0017016364653164211982197518147786 % h = 0.0001 x1[1] (analytic) = 3.0010828393996336382723820141458 x1[1] (numeric) = 3.0011502299605832848069787285022 absolute error = 6.73905609496465345967143564e-05 relative error = 0.0022455415113808724610106085962242 % h = 0.0001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.8MB, time=32.59 memory used=446.3MB, alloc=4.8MB, time=32.88 NO POLE NO POLE t[1] = 0.5083 x2[1] (analytic) = 2.0007332115693876241775764716484 x2[1] (numeric) = 2.0006983251335763762446555980564 absolute error = 3.48864358112479329208735920e-05 relative error = 0.0017436825464541969007390548122339 % h = 0.0001 x1[1] (analytic) = 3.00108273112110769143800143563 x1[1] (numeric) = 3.0011517776882175662667520577212 absolute error = 6.90465671098748287506220912e-05 relative error = 0.0023007218826013922903811684153008 % h = 0.0001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.8MB, time=33.18 NO POLE NO POLE t[1] = 0.5084 x2[1] (analytic) = 2.0007333040871035568730726962129 x2[1] (numeric) = 2.0006975660114883708387938059029 absolute error = 3.57380756151860342788903100e-05 relative error = 0.0017862488489685353884044904851956 % h = 0.0001 x1[1] (analytic) = 3.0010826228534090558237205308397 x1[1] (numeric) = 3.0011533455835015271827427174839 absolute error = 7.07227300924713590221866442e-05 relative error = 0.0023565739094923239961168940976361 % h = 0.0001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.8MB, time=33.48 memory used=457.7MB, alloc=4.8MB, time=33.97 NO POLE NO POLE t[1] = 0.5085 x2[1] (analytic) = 2.0007333966287385388608851521817 x2[1] (numeric) = 2.000696796499894069338981039851 absolute error = 3.66001288444695219041123307e-05 relative error = 0.0018293356279322976726175066994752 % h = 0.0001 x1[1] (analytic) = 3.0010825145965366487525520414014 x1[1] (numeric) = 3.0011549336484504639629325721046 absolute error = 7.24190519138152103805307032e-05 relative error = 0.0024130976593141483504219240252608 % h = 0.0001 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.8MB, time=34.69 NO POLE NO POLE t[1] = 0.5086 x2[1] (analytic) = 2.0007334891942968130907897486592 x2[1] (numeric) = 2.0006960165936915893022552512561 absolute error = 3.74726006052237885344974031e-05 relative error = 0.0018729431384843840990667612064385 % h = 0.0001 x1[1] (analytic) = 3.0010824063504893876557709944627 x1[1] (numeric) = 3.0011565418850798741480815212659 absolute error = 7.41355345904864923105268032e-05 relative error = 0.0024702931993340397732110383388492 % h = 0.0001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.8MB, time=35.40 NO POLE NO POLE t[1] = 0.5087 x2[1] (analytic) = 2.0007335817837826234153683575261 x2[1] (numeric) = 2.0006952262877777259243830846427 absolute error = 3.83554960048974909852728834e-05 relative error = 0.0019170716358297490197029166449879 % h = 0.0001 x1[1] (analytic) = 3.0010822981152661900729038770055 x1[1] (numeric) = 3.0011581702954054564317511198736 absolute error = 7.58721801392663588472428681e-05 relative error = 0.0025281605968258670008774715441546 % h = 0.0001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.8MB, time=36.10 memory used=473.0MB, alloc=4.8MB, time=36.82 NO POLE NO POLE t[1] = 0.5088 x2[1] (analytic) = 2.0007336743972002145901839798449 x2[1] (numeric) = 2.0006944255770479517452872618344 absolute error = 3.92488201522628448967180105e-05 relative error = 0.0019617213752394154677783238012207 % h = 0.0001 x1[1] (analytic) = 3.0010821898908659736517178112409 x1[1] (numeric) = 3.0011598188814431106803301813197 absolute error = 7.76289905771370286123700788e-05 relative error = 0.00258669991907019375512668442132 % h = 0.0001 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.8MB, time=37.51 NO POLE NO POLE t[1] = 0.5089 x2[1] (analytic) = 2.000733767034553832273955947845 x2[1] (numeric) = 2.0006936144563964163544120626864 absolute error = 4.01525781574159195438851586e-05 relative error = 0.0020068926120504898359522123719589 % h = 0.0001 x1[1] (analytic) = 3.0010820816772876561482097310871 x1[1] (numeric) = 3.0011614876452089379530623643481 absolute error = 7.94059679212818048526332610e-05 relative error = 0.002645911233354279411876101694396 % h = 0.0001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.8MB, time=38.20 memory used=484.4MB, alloc=4.8MB, time=38.92 NO POLE NO POLE t[1] = 0.509 x2[1] (analytic) = 2.0007338596958477230287351624915 x2[1] (numeric) = 2.0006927929207159460960268897442 absolute error = 4.10667751317769327082727473e-05 relative error = 0.0020525856016661765574620084367665 % h = 0.0001 x1[1] (analytic) = 3.0010819734745301554265955597291 x1[1] (numeric) = 3.0011631765887192405220757437177 absolute error = 8.12031141890850954801839886e-05 relative error = 0.0027057946069720796702208220050324 % h = 0.0001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.8MB, time=39.64 NO POLE NO POLE t[1] = 0.5091 x2[1] (analytic) = 2.000733952381086134320079366647 x2[1] (numeric) = 2.0006919609648980437744679041512 absolute error = 4.19914161880905456114624958e-05 relative error = 0.0020988005995557927903613981463498 % h = 0.0001 x1[1] (analytic) = 3.0010818652825923894592993882611 x1[1] (numeric) = 3.0011648857139905218924143648572 absolute error = 8.30204313981324331149765961e-05 relative error = 0.0027663501072242472214653066510051 % h = 0.0001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.8MB, time=40.36 NO POLE NO POLE t[1] = 0.5092 x2[1] (analytic) = 2.0007340450902733145172284538324 x2[1] (numeric) = 2.0006911185838328883593177201251 absolute error = 4.29265064404261579107337073e-05 relative error = 0.0021455378612547831048257571036437 % h = 0.0001 x1[1] (analytic) = 3.0010817571014732763269426554107 x1[1] (numeric) = 3.001166615023039486822071782706 absolute error = 8.48579215662104951291272953e-05 relative error = 0.0028275778014181324182210536135505 % h = 0.0001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.8MB, time=41.08 memory used=499.7MB, alloc=4.8MB, time=41.82 NO POLE NO POLE t[1] = 0.5093 x2[1] (analytic) = 2.0007341378234135128932798125935 x2[1] (numeric) = 2.0006902657724093346905231453197 absolute error = 4.38720510041782027566672738e-05 relative error = 0.0021927976423647341735255651122045 % h = 0.0001 x1[1] (analytic) = 3.001081648931171734218333328345 x1[1] (numeric) = 3.001168364517883041342026584936 absolute error = 8.67155867113071236932565910e-05 relative error = 0.0028894777568677839435702633774836 % h = 0.0001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.8MB, time=42.55 NO POLE NO POLE t[1] = 0.5094 x2[1] (analytic) = 2.000734230580510979625363706482 x2[1] (numeric) = 2.0006894025255149131834509543871 absolute error = 4.48280549960664419127520949e-05 relative error = 0.002240580198553389465068426129855 % h = 0.0001 x1[1] (analytic) = 3.0010815407716866814304550845588 x1[1] (numeric) = 3.0011701342005382927762798997486 absolute error = 8.85934288516113458248151898e-05 relative error = 0.0029520500408939494802955030280831 % h = 0.0001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.8MB, time=43.31 memory used=511.1MB, alloc=4.8MB, time=44.04 NO POLE NO POLE t[1] = 0.5095 x2[1] (analytic) = 2.0007343233615699657948186896566 x2[1] (numeric) = 2.0006885288380358295338816830522 absolute error = 4.57945235341362609370066044e-05 relative error = 0.0022888857855546639405103132689121 % h = 0.0001 x1[1] (analytic) = 3.0010814326230170363684564948442 x1[1] (numeric) = 3.0011719240730225497618948884415 absolute error = 9.04914500055133934383935973e-05 relative error = 0.0030152947208240763801753751487102 % h = 0.0001 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.8MB, time=44.76 NO POLE NO POLE t[1] = 0.5096 x2[1] (analytic) = 2.0007344161665947233873670581104 x2[1] (numeric) = 2.0006876447048569644229414300086 absolute error = 4.67714617377589644256281018e-05 relative error = 0.0023377146591686587529366588426543 % h = 0.0001 x1[1] (analytic) = 3.0010813244851617175456402073423 x1[1] (numeric) = 3.0011737341373533222690382229401 absolute error = 9.24096521916047233980155978e-05 relative error = 0.0030792118639923123333461980031414 % h = 0.0001 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.8MB, time=45.48 NO POLE NO POLE t[1] = 0.5097 x2[1] (analytic) = 2.0007345089955895052932903365348 x2[1] (numeric) = 2.0006867501208618732219716539434 absolute error = 4.77588747276320713186825914e-05 relative error = 0.0023870670752616759501139097309562 % h = 0.0001 x1[1] (analytic) = 3.0010812163581196435834521326761 x1[1] (numeric) = 3.0011755643955483216210235484878 absolute error = 9.43480374286780375714158117e-05 relative error = 0.0031438015377395060377297035232476 % h = 0.0001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.8MB, time=46.21 memory used=526.4MB, alloc=4.8MB, time=46.94 NO POLE NO POLE t[1] = 0.5098 x2[1] (analytic) = 2.0007346018485585653076048008237 x2[1] (numeric) = 2.0006858450809327856973369529947 absolute error = 4.87567676257796102678478290e-05 relative error = 0.0024369432897662331802121681964536 % h = 0.0001 x1[1] (analytic) = 3.0010811082418897332114706301652 x1[1] (numeric) = 3.0011774148496254605143569316901 absolute error = 9.63066077357273028863015249e-05 relative error = 0.0032090638094132078685267595926606 % h = 0.0001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.8MB, time=47.67 NO POLE NO POLE t[1] = 0.5099 x2[1] (analytic) = 2.0007346947255061581302370362269 x2[1] (numeric) = 2.0006849295799506057151708139434 absolute error = 4.97651455555524150662222835e-05 relative error = 0.0024873435586810784005995386408407 % h = 0.0001 x1[1] (analytic) = 3.001081000136470905267395695121 x1[1] (numeric) = 3.0011792855016028530387842941068 absolute error = 9.82853651319477713885989858e-05 relative error = 0.0032749987463676705477771231603871 % h = 0.0001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.8MB, time=48.40 memory used=537.8MB, alloc=4.8MB, time=49.14 NO POLE NO POLE t[1] = 0.51 x2[1] (analytic) = 2.0007347876264365393661995311595 x2[1] (numeric) = 2.0006840036127949109460593184389 absolute error = 5.07840136416284201402127206e-05 relative error = 0.0025382681380712045897088007792725 % h = 0.0001 x1[1] (analytic) = 3.0010808920418620786970381472244 x1[1] (numeric) = 3.0011811763534988146973408315873 absolute error = 0.0001002843116367360003026843629 relative error = 0.0033416064159638498139852306316874 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; Iterations = 100 Total Elapsed Time = 49 Seconds Elapsed Time(since restart) = 49 Seconds Expected Time Remaining = 6 Hours 4 Minutes 29 Seconds Optimized Time Remaining = 6 Hours 4 Minutes 21 Seconds Time to Timeout = 14 Minutes 10 Seconds Percent Done = 0.2244 % > quit memory used=538.5MB, alloc=4.8MB, time=49.25