|\^/| 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, > INFO, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_unchanged_h_cnt, > glob_h, > glob_reached_optimal_h, > glob_current_iter, > glob_start, > glob_max_trunc_err, > glob_max_order, > glob_log10_abserr, > glob_large_float, > sec_in_min, > glob_html_log, > glob_orig_start_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmin, > glob_almost_1, > centuries_in_millinium, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > min_in_hour, > djd_debug2, > glob_normmax, > glob_relerr, > glob_look_poles, > days_in_year, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_not_yet_finished, > glob_percent_done, > glob_log10relerr, > hours_in_day, > glob_iter, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_not_yet_start_msg, > glob_display_flag, > MAX_UNCHANGED, > glob_abserr, > glob_last_good_h, > years_in_century, > glob_optimal_expect_sec, > glob_small_float, > glob_initial_pass, > djd_debug, > glob_dump, > glob_dump_analytic, > glob_hmax, > glob_max_opt_iter, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_t, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_last_rel_error, > array_pole, > array_x1_init, > array_x2, > array_x1, > array_norms, > array_m1, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_poles, > array_x2_higher, > array_x1_higher, > array_x2_higher_work, > array_real_pole, > array_complex_pole, > array_x1_higher_work, > array_x1_higher_work2, > array_x2_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, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h, glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order, glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log, glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr, glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr, glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day, glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter, glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr, glob_last_good_h, years_in_century, glob_optimal_expect_sec, glob_small_float, glob_initial_pass, djd_debug, glob_dump, glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_last_rel_error, array_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles, array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole, array_complex_pole, array_x1_higher_work, array_x1_higher_work2, array_x2_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, > INFO, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_unchanged_h_cnt, > glob_h, > glob_reached_optimal_h, > glob_current_iter, > glob_start, > glob_max_trunc_err, > glob_max_order, > glob_log10_abserr, > glob_large_float, > sec_in_min, > glob_html_log, > glob_orig_start_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmin, > glob_almost_1, > centuries_in_millinium, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > min_in_hour, > djd_debug2, > glob_normmax, > glob_relerr, > glob_look_poles, > days_in_year, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_not_yet_finished, > glob_percent_done, > glob_log10relerr, > hours_in_day, > glob_iter, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_not_yet_start_msg, > glob_display_flag, > MAX_UNCHANGED, > glob_abserr, > glob_last_good_h, > years_in_century, > glob_optimal_expect_sec, > glob_small_float, > glob_initial_pass, > djd_debug, > glob_dump, > glob_dump_analytic, > glob_hmax, > glob_max_opt_iter, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_t, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_last_rel_error, > array_pole, > array_x1_init, > array_x2, > array_x1, > array_norms, > array_m1, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_poles, > array_x2_higher, > array_x1_higher, > array_x2_higher_work, > array_real_pole, > array_complex_pole, > array_x1_higher_work, > array_x1_higher_work2, > array_x2_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, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h, glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order, glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log, glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr, glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr, glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day, glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter, glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr, glob_last_good_h, years_in_century, glob_optimal_expect_sec, glob_small_float, glob_initial_pass, djd_debug, glob_dump, glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_last_rel_error, array_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles, array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole, array_complex_pole, array_x1_higher_work, array_x1_higher_work2, array_x2_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, > INFO, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_unchanged_h_cnt, > glob_h, > glob_reached_optimal_h, > glob_current_iter, > glob_start, > glob_max_trunc_err, > glob_max_order, > glob_log10_abserr, > glob_large_float, > sec_in_min, > glob_html_log, > glob_orig_start_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmin, > glob_almost_1, > centuries_in_millinium, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > min_in_hour, > djd_debug2, > glob_normmax, > glob_relerr, > glob_look_poles, > days_in_year, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_not_yet_finished, > glob_percent_done, > glob_log10relerr, > hours_in_day, > glob_iter, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_not_yet_start_msg, > glob_display_flag, > MAX_UNCHANGED, > glob_abserr, > glob_last_good_h, > years_in_century, > glob_optimal_expect_sec, > glob_small_float, > glob_initial_pass, > djd_debug, > glob_dump, > glob_dump_analytic, > glob_hmax, > glob_max_opt_iter, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_t, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_last_rel_error, > array_pole, > array_x1_init, > array_x2, > array_x1, > array_norms, > array_m1, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_poles, > array_x2_higher, > array_x1_higher, > array_x2_higher_work, > array_real_pole, > array_complex_pole, > array_x1_higher_work, > array_x1_higher_work2, > array_x2_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, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h, glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order, glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log, glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr, glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr, glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day, glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter, glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr, glob_last_good_h, years_in_century, glob_optimal_expect_sec, glob_small_float, glob_initial_pass, djd_debug, glob_dump, glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_last_rel_error, array_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles, array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole, array_complex_pole, array_x1_higher_work, array_x1_higher_work2, array_x2_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, > INFO, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_unchanged_h_cnt, > glob_h, > glob_reached_optimal_h, > glob_current_iter, > glob_start, > glob_max_trunc_err, > glob_max_order, > glob_log10_abserr, > glob_large_float, > sec_in_min, > glob_html_log, > glob_orig_start_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmin, > glob_almost_1, > centuries_in_millinium, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > min_in_hour, > djd_debug2, > glob_normmax, > glob_relerr, > glob_look_poles, > days_in_year, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_not_yet_finished, > glob_percent_done, > glob_log10relerr, > hours_in_day, > glob_iter, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_not_yet_start_msg, > glob_display_flag, > MAX_UNCHANGED, > glob_abserr, > glob_last_good_h, > years_in_century, > glob_optimal_expect_sec, > glob_small_float, > glob_initial_pass, > djd_debug, > glob_dump, > glob_dump_analytic, > glob_hmax, > glob_max_opt_iter, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_t, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_last_rel_error, > array_pole, > array_x1_init, > array_x2, > array_x1, > array_norms, > array_m1, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_poles, > array_x2_higher, > array_x1_higher, > array_x2_higher_work, > array_real_pole, > array_complex_pole, > array_x1_higher_work, > array_x1_higher_work2, > array_x2_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, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h, glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order, glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log, glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr, glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr, glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day, glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter, glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr, glob_last_good_h, years_in_century, glob_optimal_expect_sec, glob_small_float, glob_initial_pass, djd_debug, glob_dump, glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_last_rel_error, array_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles, array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole, array_complex_pole, array_x1_higher_work, array_x1_higher_work2, array_x2_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, > INFO, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_unchanged_h_cnt, > glob_h, > glob_reached_optimal_h, > glob_current_iter, > glob_start, > glob_max_trunc_err, > glob_max_order, > glob_log10_abserr, > glob_large_float, > sec_in_min, > glob_html_log, > glob_orig_start_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmin, > glob_almost_1, > centuries_in_millinium, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > min_in_hour, > djd_debug2, > glob_normmax, > glob_relerr, > glob_look_poles, > days_in_year, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_not_yet_finished, > glob_percent_done, > glob_log10relerr, > hours_in_day, > glob_iter, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_not_yet_start_msg, > glob_display_flag, > MAX_UNCHANGED, > glob_abserr, > glob_last_good_h, > years_in_century, > glob_optimal_expect_sec, > glob_small_float, > glob_initial_pass, > djd_debug, > glob_dump, > glob_dump_analytic, > glob_hmax, > glob_max_opt_iter, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_t, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_last_rel_error, > array_pole, > array_x1_init, > array_x2, > array_x1, > array_norms, > array_m1, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_poles, > array_x2_higher, > array_x1_higher, > array_x2_higher_work, > array_real_pole, > array_complex_pole, > array_x1_higher_work, > array_x1_higher_work2, > array_x2_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, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h, glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order, glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log, glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr, glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr, glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day, glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter, glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr, glob_last_good_h, years_in_century, glob_optimal_expect_sec, glob_small_float, glob_initial_pass, djd_debug, glob_dump, glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_last_rel_error, array_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles, array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole, array_complex_pole, array_x1_higher_work, array_x1_higher_work2, array_x2_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, > INFO, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_unchanged_h_cnt, > glob_h, > glob_reached_optimal_h, > glob_current_iter, > glob_start, > glob_max_trunc_err, > glob_max_order, > glob_log10_abserr, > glob_large_float, > sec_in_min, > glob_html_log, > glob_orig_start_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmin, > glob_almost_1, > centuries_in_millinium, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > min_in_hour, > djd_debug2, > glob_normmax, > glob_relerr, > glob_look_poles, > days_in_year, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_not_yet_finished, > glob_percent_done, > glob_log10relerr, > hours_in_day, > glob_iter, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_not_yet_start_msg, > glob_display_flag, > MAX_UNCHANGED, > glob_abserr, > glob_last_good_h, > years_in_century, > glob_optimal_expect_sec, > glob_small_float, > glob_initial_pass, > djd_debug, > glob_dump, > glob_dump_analytic, > glob_hmax, > glob_max_opt_iter, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_t, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_last_rel_error, > array_pole, > array_x1_init, > array_x2, > array_x1, > array_norms, > array_m1, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_poles, > array_x2_higher, > array_x1_higher, > array_x2_higher_work, > array_real_pole, > array_complex_pole, > array_x1_higher_work, > array_x1_higher_work2, > array_x2_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 (1 <= glob_max_terms) then # if number 1 > 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 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 (1 <= glob_max_terms) then # if number 1 > 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 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 (2 <= glob_max_terms) then # if number 1 > 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 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 (2 <= glob_max_terms) then # if number 1 > 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 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 (3 <= glob_max_terms) then # if number 1 > 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 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 (3 <= glob_max_terms) then # if number 1 > 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 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 (4 <= glob_max_terms) then # if number 1 > 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 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 (4 <= glob_max_terms) then # if number 1 > 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 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 (5 <= glob_max_terms) then # if number 1 > 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 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 (5 <= glob_max_terms) then # if number 1 > 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 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 > 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 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 > 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 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, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h, glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order, glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log, glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr, glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr, glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day, glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter, glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr, glob_last_good_h, years_in_century, glob_optimal_expect_sec, glob_small_float, glob_initial_pass, djd_debug, glob_dump, glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_last_rel_error, array_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles, array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole, array_complex_pole, array_x1_higher_work, array_x1_higher_work2, array_x2_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 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; 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 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; 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 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; 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 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; 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 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; 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 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; 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 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; 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 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; 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 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; 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 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; 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 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; 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 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; 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 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c1 + 6.0 * c3 * exp(-t); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > c1 + c2 * exp(2.0 * t) + c3 * exp(-t); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 0.0001; > 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 := 0.0001; 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, > INFO, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_unchanged_h_cnt, > glob_h, > glob_reached_optimal_h, > glob_current_iter, > glob_start, > glob_max_trunc_err, > glob_max_order, > glob_log10_abserr, > glob_large_float, > sec_in_min, > glob_html_log, > glob_orig_start_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmin, > glob_almost_1, > centuries_in_millinium, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > min_in_hour, > djd_debug2, > glob_normmax, > glob_relerr, > glob_look_poles, > days_in_year, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_not_yet_finished, > glob_percent_done, > glob_log10relerr, > hours_in_day, > glob_iter, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_not_yet_start_msg, > glob_display_flag, > MAX_UNCHANGED, > glob_abserr, > glob_last_good_h, > years_in_century, > glob_optimal_expect_sec, > glob_small_float, > glob_initial_pass, > djd_debug, > glob_dump, > glob_dump_analytic, > glob_hmax, > glob_max_opt_iter, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_t, > array_type_pole, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_last_rel_error, > array_pole, > array_x1_init, > array_x2, > array_x1, > array_norms, > array_m1, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_poles, > array_x2_higher, > array_x1_higher, > array_x2_higher_work, > array_real_pole, > array_complex_pole, > array_x1_higher_work, > array_x1_higher_work2, > array_x2_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > INFO := 2; > ALWAYS := 1; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGL := 3; > glob_max_minutes := 0.0; > glob_unchanged_h_cnt := 0; > glob_h := 0.1; > glob_reached_optimal_h := false; > glob_current_iter := 0; > glob_start := 0; > glob_max_trunc_err := 0.1e-10; > glob_max_order := 30; > glob_log10_abserr := 0.1e-10; > glob_large_float := 9.0e100; > sec_in_min := 60.0; > glob_html_log := true; > glob_orig_start_sec := 0.0; > glob_no_eqs := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_hmin_init := 0.001; > glob_hmin := 0.00000000001; > glob_almost_1 := 0.9990; > centuries_in_millinium := 10.0; > glob_log10abserr := 0.0; > glob_curr_iter_when_opt := 0; > glob_warned2 := false; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_done := false; > glob_clock_start_sec := 0.0; > glob_clock_sec := 0.0; > min_in_hour := 60.0; > djd_debug2 := true; > glob_normmax := 0.0; > glob_relerr := 0.1e-10; > glob_look_poles := false; > days_in_year := 365.0; > glob_warned := false; > glob_max_hours := 0.0; > glob_disp_incr := 0.1; > glob_not_yet_finished := true; > glob_percent_done := 0.0; > glob_log10relerr := 0.0; > hours_in_day := 24.0; > glob_iter := 0; > glob_max_sec := 10000.0; > glob_smallish_float := 0.1e-100; > glob_max_iter := 1000; > glob_not_yet_start_msg := true; > glob_display_flag := true; > MAX_UNCHANGED := 10; > glob_abserr := 0.1e-10; > glob_last_good_h := 0.1; > years_in_century := 100.0; > glob_optimal_expect_sec := 0.1; > glob_small_float := 0.1e-50; > glob_initial_pass := true; > djd_debug := true; > glob_dump := false; > glob_dump_analytic := false; > glob_hmax := 1.0; > glob_max_opt_iter := 10; > glob_log10normmin := 0.1; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_max_order := 2; > 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/complicatedrev2postode.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,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"t_start := 0.5;"); > omniout_str(ALWAYS,"t_end := 5.0;"); > omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[2] := 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 := 0.001 ;"); > 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 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c1 + 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 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"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 := 0.0001;"); > 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 > #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_t:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_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_last_rel_error:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_x1:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_m1:= 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_x2_init:= Array(1..(max_terms + 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > 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 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_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_x1_init[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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_x2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_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 <=2 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_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 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 <=2 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 > ; > 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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > 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_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_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_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_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_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_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_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 > #BEGIN SECOND INPUT BLOCK > t_start := 0.5; > t_end := 5.0; > array_x1_init[1] := exact_soln_x1(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; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > 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 > 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 := 1; > #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; > sub_iter := 1; > while sub_iter <= 3 do # do number 3 > atomall() > ; > sub_iter := sub_iter + 1; > od;# end do number 3 > ; > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3 > ;#was right paren 0004C > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > order_diff := 2; > #Jump Series array_x2 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > order_diff := 2; > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 2; > 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 > order_diff := 1; > #Jump Series array_x1 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > order_diff := 1; > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > 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 > order_diff := 1; > 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 > order_diff := 1; > 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 > order_diff := 1; > 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 > order_diff := 1; > 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 > order_diff := 1; > 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 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 3 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 3 > ; > 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 3 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-02T01:53:47-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"complicatedrev2") > ; > 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 4 > 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 4 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 4 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 4 > ; > log_revs(html_log_file," 076 ") > ; > logitem_str(html_log_file,"complicatedrev2 diffeq.mxt") > ; > logitem_str(html_log_file,"complicatedrev2 maple results") > ; > logitem_str(html_log_file,"sub iter tot order eqs reversed") > ; > 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 4 > 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 4 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 4 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 4 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 3 > ; > if glob_html_log then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; 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; global DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, glob_max_minutes, glob_unchanged_h_cnt, glob_h, glob_reached_optimal_h, glob_current_iter, glob_start, glob_max_trunc_err, glob_max_order, glob_log10_abserr, glob_large_float, sec_in_min, glob_html_log, glob_orig_start_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmin, glob_almost_1, centuries_in_millinium, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, min_in_hour, djd_debug2, glob_normmax, glob_relerr, glob_look_poles, days_in_year, glob_warned, glob_max_hours, glob_disp_incr, glob_not_yet_finished, glob_percent_done, glob_log10relerr, hours_in_day, glob_iter, glob_max_sec, glob_smallish_float, glob_max_iter, glob_not_yet_start_msg, glob_display_flag, MAX_UNCHANGED, glob_abserr, glob_last_good_h, years_in_century, glob_optimal_expect_sec, glob_small_float, glob_initial_pass, djd_debug, glob_dump, glob_dump_analytic, glob_hmax, glob_max_opt_iter, glob_log10normmin, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_t, array_type_pole, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_last_rel_error, array_pole, array_x1_init, array_x2, array_x1, array_norms, array_m1, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_poles, array_x2_higher, array_x1_higher, array_x2_higher_work, array_real_pole, array_complex_pole, array_x1_higher_work, array_x1_higher_work2, array_x2_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; INFO := 2; ALWAYS := 1; glob_iolevel := 5; glob_max_terms := 30; DEBUGL := 3; glob_max_minutes := 0.; glob_unchanged_h_cnt := 0; glob_h := 0.1; glob_reached_optimal_h := false; glob_current_iter := 0; glob_start := 0; glob_max_trunc_err := 0.1*10^(-10); glob_max_order := 30; glob_log10_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; sec_in_min := 60.0; glob_html_log := true; glob_orig_start_sec := 0.; glob_no_eqs := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_hmin := 0.1*10^(-10); glob_almost_1 := 0.9990; centuries_in_millinium := 10.0; glob_log10abserr := 0.; glob_curr_iter_when_opt := 0; glob_warned2 := false; glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_optimal_done := false; glob_clock_start_sec := 0.; glob_clock_sec := 0.; min_in_hour := 60.0; djd_debug2 := true; glob_normmax := 0.; glob_relerr := 0.1*10^(-10); glob_look_poles := false; days_in_year := 365.0; glob_warned := false; glob_max_hours := 0.; glob_disp_incr := 0.1; glob_not_yet_finished := true; glob_percent_done := 0.; glob_log10relerr := 0.; hours_in_day := 24.0; glob_iter := 0; glob_max_sec := 10000.0; glob_smallish_float := 0.1*10^(-100); glob_max_iter := 1000; glob_not_yet_start_msg := true; glob_display_flag := true; MAX_UNCHANGED := 10; glob_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; years_in_century := 100.0; glob_optimal_expect_sec := 0.1; glob_small_float := 0.1*10^(-50); glob_initial_pass := true; djd_debug := true; glob_dump := false; glob_dump_analytic := false; glob_hmax := 1.0; glob_max_opt_iter := 10; glob_log10normmin := 0.1; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_max_order := 2; 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/complicatedrev2postode.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, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "t_start := 0.5;"); omniout_str(ALWAYS, "t_end := 5.0;"); omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[2] := 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 := 0.001 ;"); 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 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c1 + 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 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "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 := 0.0001;"); 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_t := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_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_last_rel_error := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_x1 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_m1 := 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_x2_init := Array(1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); 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; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_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_x1_init[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_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_x2_init[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_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_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 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 <= 2 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; 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; 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_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_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_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_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_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_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_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_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 := 0.001; 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(); 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 := 1; 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; sub_iter := 1; while sub_iter <= 3 do atomall(); sub_iter := sub_iter + 1 end do; 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; order_diff := 2; 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; order_diff := 2; 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)!; order_diff := 2; 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; order_diff := 2; 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)!; order_diff := 2; 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; order_diff := 2; 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)!; order_diff := 2; 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; order_diff := 2; 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)!; order_diff := 2; 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; order_diff := 2; 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)!; order_diff := 2; 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; order_diff := 2; 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 := 1; order_diff := 1; order_diff := 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; order_diff := 1; 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)!; order_diff := 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; order_diff := 1; 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)!; order_diff := 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; order_diff := 1; 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, "2012-06-02T01:53:47-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "complicatedrev2"); 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, " 076 "); logitem_str(html_log_file, "complicatedrev2 diffeq.mxt"); logitem_str(html_log_file, "complicatedrev2 maple results"); logitem_str(html_log_file, "sub iter tot order eqs reversed"); 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/complicatedrev2postode.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 t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(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; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; 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 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c1 + 6.0 * c3 * exp(-t); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2 * exp(2.0 * t) + c3 * exp(-t); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 0.0001; 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) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 0.001 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.001 t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 0.001 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652318951926688082885102467593 absolute error = 1.09339294885410769929680407e-09 relative error = 0.0001322884111602750894560937083493 % h = 0.001 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906617956534023791764003418242 absolute error = 2.1823375350673072778602109e-09 relative error = 0.00016908642158467607169130706620805 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.502 x2[1] (analytic) = 0.0008274309894041739636559251804687 x2[1] (numeric) = 0.00082743568533374563170506053559616 absolute error = 4.69592957166804913535512746e-09 relative error = 0.00056753126626905141469010651621218 % h = 0.001 x1[1] (analytic) = 0.0012895738591632036100858259251 x1[1] (numeric) = 0.0012895304745981906282540724479938 absolute error = 4.33845650129818317534771062e-08 relative error = 0.0033642559287867236943712535472889 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.503 x2[1] (analytic) = 0.0008283422476198008492141699458837 x2[1] (numeric) = 0.00088459482297093295741378802757285 absolute error = 5.625257535113210819961808168915e-05 relative error = 6.7909822917726351684230091751351 % h = 0.001 x1[1] (analytic) = 0.0012884848299094197347162072617323 x1[1] (numeric) = -0.0049375841560521641729929436123067 absolute error = 0.006226068985961583907709150874039 relative error = 483.20855949846732016059948848008 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.21 NO POLE NO POLE t[1] = 0.504 x2[1] (analytic) = 0.00082925587496274761468760841422102 x2[1] (numeric) = 1.7819047752952228731507051795107 absolute error = 1.7810755194202601255360175710965 relative error = 214779.96999421569217487929557044 % h = 0.001 x1[1] (analytic) = 0.0012873968891405564758385060019091 x1[1] (numeric) = -197.64342496743666735511188153441 absolute error = 197.64471236432580791158772004041 relative error = 15352275.124438893298867121912277 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 9.350e-05 Order of pole = 16.66 t[1] = 0.505 x2[1] (analytic) = 0.00083017187563149546111924351454314 x2[1] (numeric) = 11677.969939701327108178176973385 absolute error = 11677.969109529451476682715854141 relative error = 1406692933.3936119493830013257466 % h = 0.001 x1[1] (analytic) = 0.0012863100357686729739277295072664 x1[1] (numeric) = -1294945.8027578425187564318752508 absolute error = 1294945.8040441525545251048491785 relative error = 100671359783.82684539822304607948 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.506 x2[1] (analytic) = 0.00083109025383347519720441727943742 x2[1] (numeric) = 15190133.655680629788756958255439 absolute error = 15190133.654849539534923483058235 relative error = 1827735746482.8570691407040050704 % h = 0.001 x1[1] (analytic) = 0.0012852242687069157665292585243653 x1[1] (numeric) = -1659087026.1911173902717090267217 absolute error = 1659087026.1924026145404159424882 relative error = 129089301111753.51631930131951026 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 2.520e-05 Order of pole = 20.05 t[1] = 0.507 x2[1] (analytic) = 0.00083201101378508461244661319002326 x2[1] (numeric) = 3215149058.4717771689039053206405 absolute error = 3215149058.4709451578901202360281 relative error = 386431069445126.95939080587236139 % h = 0.001 x1[1] (analytic) = 0.001284139586869517701405294158948 x1[1] (numeric) = -312994174290.25798705079183120614 absolute error = 312994174290.25927119037870072384 relative error = 24373843582945537.100187866500004 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.508 x2[1] (analytic) = 0.00083293415971170588563803837477598 x2[1] (numeric) = 128346839526.98656082162642607918 absolute error = 128346839526.98572788746671437329 relative error = 15409001783695481.178463189885481 % h = 0.001 x1[1] (analytic) = 0.0012830559891717968507676151575396 x1[1] (numeric) = -5559642573677.7251265512441919115 absolute error = 5559642573677.7264096072333637084 relative error = 433312546030546536.15320769871422 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.46 NO POLE NO POLE t[1] = 0.509 x2[1] (analytic) = 0.00083385969584772302873516249155556 x2[1] (numeric) = 909476508149.17723083576601216928 absolute error = 909476508149.17639697607016444625 relative error = 109068289626899329.72012517147899 % h = 0.001 x1[1] (analytic) = 0.001281973474530155426595559729063 x1[1] (numeric) = 61759254276919.802741728478002898 absolute error = 61759254276919.801459755003472743 relative error = 4817514207893781151.6366857226152 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.51 x2[1] (analytic) = 0.00083478762643653936619953115948893 x2[1] (numeric) = -2196897453344137.6268061971997727 absolute error = 2196897453344137.6276409848262092 relative error = 263168425569751299909.84169222196 % h = 0.001 x1[1] (analytic) = 0.0012808920418620786970381472243591 x1[1] (numeric) = 243216278518670872.10312222635347 absolute error = 243216278518670872.10184133431161 relative error = 18988038848699430259156.093445197 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 4.676e-05 Order of pole = 3.406 t[1] = 0.511 x2[1] (analytic) = 0.00083571795573059504987431312643056 x2[1] (numeric) = -2648710503393110060.2732435025041 absolute error = 2648710503393110060.2740792204598 relative error = 316938326528783785134818.35325885 % h = 0.001 x1[1] (analytic) = 0.0012798116900861339038992560756415 x1[1] (numeric) = 288665208555132940889.01693243517 absolute error = 288665208555132940889.01565262348 relative error = 22555287687339782860414540.038094 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.512 x2[1] (analytic) = 0.00083665068799138460946718195917937 x2[1] (numeric) = -1148725493627825941390.7844176365 absolute error = 1148725493627825941390.7852542872 relative error = 137300489931546547034197921.18023 % h = 0.001 x1[1] (analytic) = 0.0012787324181219691812047754809758 x1[1] (numeric) = 120225511498815605700958.09076191 absolute error = 120225511498815605700958.08948318 relative error = 9401928800349546634057085224.7283 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 4.048e-05 Order of pole = 13.91 t[1] = 0.513 x2[1] (analytic) = 0.00083758582748947453871027492802935 x2[1] (numeric) = -210096106696411492766220.73373276 absolute error = 210096106696411492766220.73457035 relative error = 25083531717118464517858851807.898 % h = 0.001 x1[1] (analytic) = 0.0012776542248903124748506494008434 x1[1] (numeric) = 20099948297333144918671865.063741 absolute error = 20099948297333144918671865.062463 relative error = 1573191549463137398941932217045.3 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=4.4MB, time=0.72 t[1] = 0.514 x2[1] (analytic) = 0.0008385233785045209172681139251402 x2[1] (numeric) = -25923957869351262233340807.929845 absolute error = 25923957869351262233340807.930684 relative error = 3091620166343578295757211096374.1 % h = 0.001 x1[1] (analytic) = 0.0012765771093129704633307325147448 x1[1] (numeric) = 2330446577219046110200347818.4663 absolute error = 2330446577219046110200347818.465 relative error = 1.8255431342280985782980557794469e+32 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.515 x2[1] (analytic) = 0.00083946334532528706846451570820467 x2[1] (numeric) = -2554553462863983425926148214.0911 absolute error = 2554553462863983425926148214.0919 relative error = 3.0430792208969042085516096172102e+32 % h = 0.001 x1[1] (analytic) = 0.0012755010703128274795433788656077 x1[1] (numeric) = 220162432703007731265300266763.32 absolute error = 220162432703007731265300266763.32 relative error = 1.7260858326760245149315535526630e+34 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.516 x2[1] (analytic) = 0.00084040573224966125289966149752755 x2[1] (numeric) = 382905437799974922008629669691.49 absolute error = 382905437799974922008629669691.49 relative error = 4.5561973592800807775907727531295e+34 % h = 0.001 x1[1] (analytic) = 0.0012744261068138444336756849984992 x1[1] (numeric) = -48890300214412641155527495449107 absolute error = 48890300214412641155527495449107 relative error = 3.8362600980171267683128998828691e+36 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.517 x2[1] (analytic) = 0.0008413505435846743980286389764889 x2[1] (numeric) = 2.8381007123517247585891510895531e+32 absolute error = 2.8381007123517247585891510895531e+32 relative error = 3.3732678180246463901030732139499e+37 % h = 0.001 x1[1] (analytic) = 0.0012733522177410577371643104777951 x1[1] (numeric) = -3.0319464357000671925991849933332e+34 absolute error = 3.0319464357000671925991849933332e+34 relative error = 2.3810744532873841505443331732903e+39 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.518 x2[1] (analytic) = 0.00084229778364651786377291305301299 x2[1] (numeric) = 8.9157816957575197449331205416986e+34 absolute error = 8.9157816957575197449331205416986e+34 relative error = 1.0585070825140806962302190866050e+40 % h = 0.001 x1[1] (analytic) = 0.0012722794020205782277317997435378 x1[1] (numeric) = -9.1081973266512989405817711648826e+36 absolute error = 9.1081973266512989405817711648826e+36 relative error = 7.1589599833071731453862167182889e+41 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.519 x2[1] (analytic) = 0.00084324745676056124423632533367627 x2[1] (numeric) = 1.8009848306206213036086093015404e+37 absolute error = 1.8009848306206213036086093015404e+37 relative error = 2.1357726206958582532697140156487e+42 % h = 0.001 x1[1] (analytic) = 0.0012712076585795900954973303432135 x1[1] (numeric) = -1.7559642038875284665895426053970e+39 absolute error = 1.7559642038875284665895426053970e+39 relative error = 1.3813354506136243877587970009341e+44 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=0.98 NO POLE NO POLE t[1] = 0.52 x2[1] (analytic) = 0.00084419956726137020559736614303792 x2[1] (numeric) = 2.9381939395914476076660439601372e+39 absolute error = 2.9381939395914476076660439601372e+39 relative error = 3.4804494737223216476110748347130e+44 % h = 0.001 x1[1] (analytic) = 0.00127013698634634981016081364961 x1[1] (numeric) = -2.7892033589816468170502798269432e+41 absolute error = 2.7892033589816468170502798269432e+41 relative error = 2.1959862510617948384657702762582e+46 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.521 x2[1] (analytic) = 0.00084515411949272436024960708923766 x2[1] (numeric) = 2.8828164769390235485375509891162e+41 absolute error = 2.8828164769390235485375509891162e+41 relative error = 3.4109950013251289835990483116487e+46 % h = 0.001 x1[1] (analytic) = 0.0012690673842501850492592752487639 x1[1] (numeric) = -2.4393714556513207592439195132267e+43 absolute error = 2.4393714556513207592439195132267e+43 relative error = 1.9221764627515011025020683649732e+48 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.522 x2[1] (analytic) = 0.00084611111780763517726232663345645 x2[1] (numeric) = -3.0835833708071225386080135199334e+43 absolute error = 3.0835833708071225386080135199334e+43 relative error = 3.6444189254917467461904399926535e+48 % h = 0.001 x1[1] (analytic) = 0.0012679988512214936274944432542899 x1[1] (numeric) = 4.1253436949404049769512496557223e+45 absolute error = 4.1253436949404049769512496557223e+45 relative error = 3.2534285744552234457829858504083e+50 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.523 x2[1] (analytic) = 0.00084707056656836392923350586605222 x2[1] (numeric) = -2.4179029109238865073572390611867e+46 absolute error = 2.4179029109238865073572390611867e+46 relative error = 2.8544291424494284036261216292873e+51 % h = 0.001 x1[1] (analytic) = 0.0012669313861917424271304738755899 x1[1] (numeric) = 2.5842606842144773750490515703002e+48 absolute error = 2.5842606842144773750490515703002e+48 relative error = 2.0397795116454436788853390183402e+53 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.524 x2[1] (analytic) = 0.00084803247014643967560751672664236 x2[1] (numeric) = -7.5370057230450261713434077256891e+48 absolute error = 7.5370057230450261713434077256891e+48 relative error = 8.8876381369495478465011152451617e+53 % h = 0.001 x1[1] (analytic) = 0.0012658649880934663294607446375807 x1[1] (numeric) = 7.6927800284125934656558547695650e+50 absolute error = 7.6927800284125934656558547695650e+50 relative error = 6.0770936085362286931950614293304e+55 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.525 memory used=19.0MB, alloc=4.4MB, time=1.24 x2[1] (analytic) = 0.00084899683292267728252997022968994 x2[1] (numeric) = -1.6630429620249270359034525997113e+51 absolute error = 1.6630429620249270359034525997113e+51 relative error = 1.9588329396941217116064425131979e+56 % h = 0.001 x1[1] (analytic) = 0.0012647996558602671473426467186411 x1[1] (numeric) = 1.6416074541388392284185299124989e+53 absolute error = 1.6416074541388392284185299124989e+53 relative error = 1.2979189601552209366185063099501e+58 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0001646 Order of pole = 132 t[1] = 0.526 x2[1] (analytic) = 0.00084996365928719547931233787183942 x2[1] (numeric) = -2.8630998538135398916237853552101e+53 absolute error = 2.8630998538135398916237853552101e+53 relative error = 3.3684967851621087282827986521779e+58 % h = 0.001 x1[1] (analytic) = 0.0012637353884268125587993089414852 x1[1] (numeric) = 2.7376577430826790481709854581064e+55 absolute error = 2.7376577430826790481709854581064e+55 relative error = 2.1663219754340420691398793662625e+60 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.527 x2[1] (analytic) = 0.00085093295363943495157910530292247 x2[1] (numeric) = -2.9880365775222779343038163266641e+55 absolute error = 2.9880365775222779343038163266641e+55 relative error = 3.5114829725919816267282456525505e+60 % h = 0.001 x1[1] (analytic) = 0.0012626721847288350416871870185942 x1[1] (numeric) = 2.5706771161701424940197997037491e+57 absolute error = 2.5706771161701424940197997037491e+57 relative error = 2.0359022296212281236273554486349e+62 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.528 x2[1] (analytic) = 0.00085190472038817647117036353980059 x2[1] (numeric) = 1.7868398786828264852282109970259e+57 absolute error = 1.7868398786828264852282109970259e+57 relative error = 2.0974644651207474595896184122519e+62 % h = 0.001 x1[1] (analytic) = 0.0012616100437031308094284527197097 x1[1] (numeric) = -2.7141382543996044438799734441813e+59 absolute error = 2.7141382543996044438799734441813e+59 relative error = 2.1513289846939960936290617329388e+64 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.529 x2[1] (analytic) = 0.00085287896395155906287288949160932 x2[1] (numeric) = 1.9955262286732546922595035794772e+60 absolute error = 1.9955262286732546922595035794772e+60 relative error = 2.3397531338181703901278884762703e+65 % h = 0.001 x1[1] (analytic) = 0.001260548964287558747807118693686 x1[1] (numeric) = -2.1521239883380276264544158041182e+62 absolute error = 2.1521239883380276264544158041182e+62 relative error = 1.7072910686610037502739798855189e+67 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.53 x2[1] (analytic) = 0.00085385568875709820805291434710783 x2[1] (numeric) = 6.5614045677978813135363625682398e+62 absolute error = 6.5614045677978813135363625682398e+62 relative error = 7.6844420599327365493580244109066e+67 % h = 0.001 x1[1] (analytic) = 0.0012594889454210393528278357407412 x1[1] (numeric) = -6.7241226907398039841891773599469e+64 absolute error = 6.7241226907398039841891773599469e+64 relative error = 5.3387707094896108197039126570093e+69 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.51 NO POLE NO POLE t[1] = 0.531 x2[1] (analytic) = 0.00085483489924170408526392545030159 x2[1] (numeric) = 1.5232678875418984436709413809022e+65 absolute error = 1.5232678875418984436709413809022e+65 relative error = 1.7819439623875198247497978244760e+70 % h = 0.001 x1[1] (analytic) = 0.0012584299860435536696363003938124 x1[1] (numeric) = -1.5126890724578338356993707388052e+67 absolute error = 1.5126890724578338356993707388052e+67 relative error = 1.2020446820515292288412036371000e+72 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 4.471e-05 Order of pole = 16.11 t[1] = 0.532 x2[1] (analytic) = 0.00085581659985169984790299465988337 x2[1] (numeric) = 2.7031305542048032948968587726712e+67 absolute error = 2.7031305542048032948968587726712e+67 relative error = 3.1585395219877894240565682962974e+72 % h = 0.001 x1[1] (analytic) = 0.001257372085096142232500211729337 x1[1] (numeric) = -2.5950937522616787181116193549241e+69 absolute error = 2.5950937522616787181116193549241e+69 relative error = 2.0639027882213962912884316359254e+74 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.533 x2[1] (analytic) = 0.0008568007950428399389892738519192 x2[1] (numeric) = 3.0917676683037028372394862651691e+69 absolute error = 3.0917676683037028372394862651691e+69 relative error = 3.6085023335548081715159309117171e+74 % h = 0.001 x1[1] (analytic) = 0.0012563152415209040058497173883259 x1[1] (numeric) = -2.7262425864120028721874692454044e+71 absolute error = 2.7262425864120028721874692454044e+71 relative error = 2.1700306549744589233989780426184e+76 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.534 x2[1] (analytic) = 0.00085778748928032844313844618417794 x2[1] (numeric) = -6.4053877518790548671826806180032e+70 absolute error = 6.4053877518790548671826806180032e+70 relative error = 7.4673364113215086500356853463122e+75 % h = 0.001 x1[1] (analytic) = 0.0012552594542609953263762898480893 x1[1] (numeric) = 1.4776029553879756872485320604502e+73 absolute error = 1.4776029553879756872485320604502e+73 relative error = 1.1771295172262852239891540744593e+78 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.535 x2[1] (analytic) = 0.00085877668703883747580706999516187 x2[1] (numeric) = -1.6296499950062552754683335399836e+74 absolute error = 1.6296499950062552754683335399836e+74 relative error = 1.8976411674907934273434809597401e+79 % h = 0.001 x1[1] (analytic) = 0.0012542047222606288461889750434006 x1[1] (numeric) = 1.7782087202786389312292695741353e+76 absolute error = 1.7782087202786389312292695741353e+76 relative error = 1.4177978193811328366492309253926e+81 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.536 x2[1] (analytic) = 0.00085976839280252560988090076182799 x2[1] (numeric) = -5.7198816544976968685684836788736e+76 absolute error = 5.7198816544976968685684836788736e+76 relative error = 6.6528168543774995686085248483473e+81 % h = 0.001 x1[1] (analytic) = 0.0012531510444650724770269564932605 x1[1] (numeric) = 5.8890705981453487160301290157988e+78 absolute error = 5.8890705981453487160301290157988e+78 relative error = 4.6994100385234826080938635211753e+83 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.76 NO POLE NO POLE t[1] = 0.537 x2[1] (analytic) = 0.00086076261106505633968142538779503 x2[1] (numeric) = -1.3811599191741633169149401593430e+79 absolute error = 1.3811599191741633169149401593430e+79 relative error = 1.6045770360136790470038428720869e+84 % h = 0.001 x1[1] (analytic) = 0.0012520984198206483355273791457368 x1[1] (numeric) = 1.3773922897840372633500847906328e+81 absolute error = 1.3773922897840372633500847906328e+81 relative error = 1.1000671097255566623196829994334e+86 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 2.915e-05 Order of pole = 0.8698 t[1] = 0.538 x2[1] (analytic) = 0.0008617593463296165824649922390997 x2[1] (numeric) = -2.5354217358792180589193414722630e+81 absolute error = 2.5354217358792180589193414722630e+81 relative error = 2.9421459096185282092403628724800e+86 % h = 0.001 x1[1] (analytic) = 0.0012510468472747316895473782086164 x1[1] (numeric) = 2.4456562024293990765632852230001e+83 absolute error = 2.4456562024293990765632852230001e+83 relative error = 1.9548877867819201274284123246376e+88 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.539 x2[1] (analytic) = 0.00086275860310893521748906978789598 x2[1] (numeric) = -3.1512144899275561941372511125483e+83 absolute error = 3.1512144899275561941372511125483e+83 relative error = 3.6524868932888192133632734783326e+88 % h = 0.001 x1[1] (analytic) = 0.0012499963257757499055392592878095 x1[1] (numeric) = 2.8344150891632112552218853228415e+85 absolute error = 2.8344150891632112552218853228415e+85 relative error = 2.2675387364872199080947802956975e+90 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 8.426e-05 Order of pole = 12.51 t[1] = 0.54 x2[1] (analytic) = 0.0008637603859253016627203164664802 x2[1] (numeric) = -2.8973468742378521291582873570235e+84 absolute error = 2.8973468742378521291582873570235e+84 relative error = 3.3543409971667950795739810691033e+89 % h = 0.001 x1[1] (analytic) = 0.0012489468542731813969777772086 x1[1] (numeric) = -4.6915647451505550827772955634034e+86 absolute error = 4.6915647451505550827772955634034e+86 relative error = 3.7564166394260135088088623972110e+91 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.541 x2[1] (analytic) = 0.00086476469931058448925929437526969 x2[1] (numeric) = 1.3109067108457221718202132694702e+88 absolute error = 1.3109067108457221718202132694702e+88 relative error = 1.5159114518559962491984230035665e+93 % h = 0.001 x1[1] (analytic) = 0.0012478984317175545738384619469313 x1[1] (numeric) = -1.4505335378807750092412584872553e+90 absolute error = 1.4505335378807750092412584872553e+90 relative error = 1.1623810888874361781826351735272e+95 % h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.5MB, time=2.02 NO POLE NO POLE t[1] = 0.542 x2[1] (analytic) = 0.00086577154780625007355680982946525 x2[1] (numeric) = 4.9620873081344920758850029649559e+90 absolute error = 4.9620873081344920758850029649559e+90 relative error = 5.7314049193551823181722389315928e+95 % h = 0.001 x1[1] (analytic) = 0.001246851057060446793125941148968 x1[1] (numeric) = -5.1346054806778018480955532204282e+92 absolute error = 5.1346054806778018480955532204282e+92 relative error = 4.1180584093043588151265370917093e+97 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.543 x2[1] (analytic) = 0.00086678093596338128749701437068642 x2[1] (numeric) = 1.2446130856122418838612558386458e+93 absolute error = 1.2446130856122418838612558386458e+93 relative error = 1.4359026992545931951455850020606e+98 % h = 0.001 x1[1] (analytic) = 0.0012458047292544833104512097671668 x1[1] (numeric) = -1.2460386419338376224795093569785e+95 absolute error = 1.2460386419338376224795093569785e+95 relative error = 1.0001877603077444492214746155896e+100 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.544 x2[1] (analytic) = 0.00086779286834269622642255081248739 x2[1] (numeric) = 2.3677701091072226257633632203015e+95 absolute error = 2.3677701091072226257633632203015e+95 relative error = 2.7284968515922131903449811568090e+100 % h = 0.001 x1[1] (analytic) = 0.00124475944725333623265679839004 x1[1] (numeric) = -2.2951946086995204474539512870810e+97 absolute error = 2.2951946086995204474539512870810e+97 relative error = 1.8438860727380342559779410628511e+102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.545 x2[1] (analytic) = 0.00086880734951456697517718013294248 x2[1] (numeric) = 3.1567592003226709419783231221908e+97 absolute error = 3.1567592003226709419783231221908e+97 relative error = 3.6334397977715803319598945328408e+102 % h = 0.001 x1[1] (analytic) = 0.0012437152100117234714887928906918 x1[1] (numeric) = -2.8826980634783566466984404195411e+99 absolute error = 2.8826980634783566466984404195411e+99 relative error = 2.3178120202061240720559913973579e+104 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.546 x2[1] (analytic) = 0.00086982438405903841224147657403825 x2[1] (numeric) = 1.0394559714278914022168365891816e+99 absolute error = 1.0394559714278914022168365891816e+99 relative error = 1.1950182019240097837675458929898e+104 % h = 0.001 x1[1] (analytic) = 0.0012426720164854076983146590660609 x1[1] (numeric) = -3.5440795930613496206992793798774e+100 absolute error = 3.5440795930613496206992793798774e+100 relative error = 2.8519831025767422344893318367091e+105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.547 x2[1] (analytic) = 0.00087084397656584705203733015703041 x2[1] (numeric) = -1.0336800401868840538674860002611e+102 absolute error = 1.0336800401868840538674860002611e+102 relative error = 1.1869864958625277834792693845628e+107 % h = 0.001 x1[1] (analytic) = 0.0012416298656311952998858269846059 x1[1] (numeric) = 1.1640364577113484320860326422200e+104 absolute error = 1.1640364577113484320860326422200e+104 relative error = 9.3750681256333870350735344143879e+108 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.5MB, time=2.28 NO POLE NO POLE t[1] = 0.548 x2[1] (analytic) = 0.0008718661316344399254771479758239 x2[1] (numeric) = -4.2786480111082964303931894852392e+104 absolute error = 4.2786480111082964303931894852392e+104 relative error = 4.9074598219423297986534585238744e+109 % h = 0.001 x1[1] (analytic) = 0.0012405887564069353351439908049313 x1[1] (numeric) = 4.4516532312116311948088458634225e+106 absolute error = 4.4516532312116311948088458634225e+106 relative error = 3.5883391722046279703323742247368e+111 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.549 x2[1] (analytic) = 0.00087289085387399349883379808742284 x2[1] (numeric) = -1.1162439060400833274411264756040e+107 absolute error = 1.1162439060400833274411264756040e+107 relative error = 1.2787897834947634286776322150299e+112 % h = 0.001 x1[1] (analytic) = 0.0012395486877715184930700808715671 x1[1] (numeric) = 1.1218122900984245712270368944498e+109 absolute error = 1.1218122900984245712270368944498e+109 relative error = 9.0501672194517635248696773917288e+113 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.55 x2[1] (analytic) = 0.00087391814790343263100749258018221 x2[1] (numeric) = -2.2005067776163207475233403666272e+109 absolute error = 2.2005067776163207475233403666272e+109 relative error = 2.5179781228887757003432797034187e+114 % h = 0.001 x1[1] (analytic) = 0.0012385096586848760515748659367868 x1[1] (numeric) = 2.1431805553893224350187082181441e+111 absolute error = 2.1431805553893224350187082181441e+111 relative error = 1.7304512244701266858919527471475e+116 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.551 x2[1] (analytic) = 0.0008749480183514495692659594675856 x2[1] (numeric) = -3.1170281801300013059078417600079e+111 absolute error = 3.1170281801300013059078417600079e+111 relative error = 3.5625295614738472680677707043461e+116 % h = 0.001 x1[1] (analytic) = 0.0012374716681079788374301443989802 x1[1] (numeric) = 2.8808558122645671707565555799648e+113 absolute error = 2.8808558122645671707565555799648e+113 relative error = 2.3280175914404777610762139153184e+118 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.552 x2[1] (analytic) = 0.00087598046985652298353440642818536 x2[1] (numeric) = -1.6365027091050105676264309846931e+113 absolute error = 1.6365027091050105676264309846931e+113 relative error = 1.8681954283444854356855231685604e+118 % h = 0.001 x1[1] (analytic) = 0.0012364347150028361872394844886841 x1[1] (numeric) = 1.0215280512870817284279412689250e+115 absolute error = 1.0215280512870817284279412689250e+115 relative error = 8.2618842619987299803058620601827e+119 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.553 x2[1] (analytic) = 0.00087701550706693703931193309178555 x2[1] (numeric) = 7.9417437826979721212764438461717e+115 absolute error = 7.9417437826979721212764438461717e+115 relative error = 9.0554200224555768490502515799165e+120 % h = 0.001 x1[1] (analytic) = 0.0012353987983324949094474743729255 x1[1] (numeric) = -9.1527953728361935997546199878268e+117 absolute error = 9.1527953728361935997546199878268e+117 relative error = 7.4087779470000849451614746147866e+122 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.5MB, time=2.57 NO POLE NO POLE t[1] = 0.554 x2[1] (analytic) = 0.00087805313464080050929120255853851 x2[1] (numeric) = 3.6645166167290946724325100483841e+118 absolute error = 3.6645166167290946724325100483841e+118 relative error = 4.1734565622024664191546045743876e+123 % h = 0.001 x1[1] (analytic) = 0.0012343639170610382473864441870416 x1[1] (numeric) = -3.8355325698308304158095289245187e+120 absolute error = 3.8355325698308304158095289245187e+120 relative error = 3.1072947911204752007073680062923e+125 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.555 x2[1] (analytic) = 0.00087909335724606592375833713197844 x2[1] (numeric) = 9.9664217254733075966557119725876e+120 absolute error = 9.9664217254733075966557119725876e+120 relative error = 1.1337159635348739119396953800022e+126 % h = 0.001 x1[1] (analytic) = 0.0012333300701535848433596230406101 x1[1] (numeric) = -1.0055051605594930505268745833023e+123 absolute error = 1.0055051605594930505268745833023e+123 relative error = 8.1527661158401734244749180927461e+127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.556 x2[1] (analytic) = 0.00088013617956054875985015784974602 x2[1] (numeric) = 2.0349015806649733577525019467788e+123 absolute error = 2.0349015806649733577525019467788e+123 relative error = 2.3120303743007110251995925703477e+128 % h = 0.001 x1[1] (analytic) = 0.0012322972565762877037596950805625 x1[1] (numeric) = -1.9908053728133400234494710353380e+125 absolute error = 1.9908053728133400234494710353380e+125 relative error = 1.6155236589136197862999057404919e+130 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.557 x2[1] (analytic) = 0.00088118160627194666974604230748542 x2[1] (numeric) = 3.0419166594856722537739586191418e+125 absolute error = 3.0419166594856722537739586191418e+125 relative error = 3.4520882390580544568160687826249e+130 % h = 0.001 x1[1] (analytic) = 0.0012312654752963331652217197299492 x1[1] (numeric) = -2.8396072241410448439552316261581e+127 absolute error = 2.8396072241410448439552316261581e+127 relative error = 2.3062509922627581087841975403014e+132 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.558 x2[1] (analytic) = 0.00088222964207785874787183049273793 x2[1] (numeric) = 2.1011642309653974303792993030826e+127 absolute error = 2.1011642309653974303792993030826e+127 relative error = 2.3816522714161592029807769241411e+132 % h = 0.001 x1[1] (analytic) = 0.0012302347252819398618093822551908 x1[1] (numeric) = -1.5518635561074817518517493781388e+129 absolute error = 1.5518635561074817518517493781388e+129 relative error = 1.2614369633826035829986926599933e+134 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=41.9MB, alloc=4.6MB, time=2.85 t[1] = 0.559 x2[1] (analytic) = 0.00088328029168580483719336387723487 x2[1] (numeric) = -5.8864760083894036921995792288383e+129 absolute error = 5.8864760083894036921995792288383e+129 relative error = 6.6643352781647998095723131308019e+134 % h = 0.001 x1[1] (analytic) = 0.00122920500550235769323354184798 x1[1] (numeric) = 7.0063582995167713224599649802118e+131 absolute error = 7.0063582995167713224599649802118e+131 relative error = 5.6999103226506773954561936142385e+136 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.56 x2[1] (analytic) = 0.00088433355981324487467739885842914 x2[1] (numeric) = -3.1150418412916309484379017667828e+132 absolute error = 3.1150418412916309484379017667828e+132 relative error = 3.5224738524561603137609496909233e+137 % h = 0.001 x1[1] (analytic) = 0.0012281763149278667941020454402963 x1[1] (numeric) = 3.2820619556199126748136745143039e+134 absolute error = 3.2820619556199126748136745143039e+134 relative error = 2.6723052022157540272931241106321e+139 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.561 x2[1] (analytic) = 0.00088538945118759827599779179502061 x2[1] (numeric) = -8.8585161934434118012299808277280e+134 absolute error = 8.8585161934434118012299808277280e+134 relative error = 1.0005219941982852683813228783520e+140 % h = 0.001 x1[1] (analytic) = 0.0012271486525297765041997765022611 x1[1] (numeric) = 8.9728370843019973267850755624201e+136 absolute error = 8.9728370843019973267850755624201e+136 relative error = 7.3119398092516532509873580393713e+141 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.562 x2[1] (analytic) = 0.00088644797054626335956500934725191 x2[1] (numeric) = -1.8726427819414007399244281419497e+137 absolute error = 1.8726427819414007399244281419497e+137 relative error = 2.1125241911123178251793611149196e+142 % h = 0.001 x1[1] (analytic) = 0.0012261220172804243397979091027969 x1[1] (numeric) = 1.8399057373849162928251911630766e+139 absolute error = 1.8399057373849162928251911630766e+139 relative error = 1.5005894286654135605363417501609e+144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.563 x2[1] (analytic) = 0.00088750912263663680995717461150232 x2[1] (numeric) = -2.9395178941495789436746070558382e+139 absolute error = 2.9395178941495789436746070558382e+139 relative error = 3.3120987933248250417749318243079e+144 % h = 0.001 x1[1] (analytic) = 0.0012250964081531749659913385422579 x1[1] (numeric) = 2.7674779169372311921723813704946e+141 absolute error = 2.7674779169372311921723813704946e+141 relative error = 2.2589878629300583200250662679777e+146 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.564 x2[1] (analytic) = 0.00088857291221613318083101663081396 x2[1] (numeric) = -2.4512183399346446864644012444757e+141 absolute error = 2.4512183399346446864644012444757e+141 relative error = 2.7586012427738956611579485597826e+146 % h = 0.001 x1[1] (analytic) = 0.0012240718241224191700632608943781 x1[1] (numeric) = 1.9628765041616965203023004407598e+143 absolute error = 1.9628765041616965203023004407598e+143 relative error = 1.6035631778134855973372754296046e+148 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.6MB, time=3.12 NO POLE NO POLE t[1] = 0.565 x2[1] (analytic) = 0.00088963934405220443739124826907637 x2[1] (numeric) = 4.1349561252277888163910844011948e+143 absolute error = 4.1349561252277888163910844011948e+143 relative error = 4.6479015939128111769200036786600e+148 % h = 0.001 x1[1] (analytic) = 0.00122304826416357283587587482203 x1[1] (numeric) = -5.1656956429018182233333412262481e+145 absolute error = 5.1656956429018182233333412262481e+145 relative error = 4.2236237066527965865814509389766e+150 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.566 x2[1] (analytic) = 0.00089070842292235953849705515730068 x2[1] (numeric) = 2.6256741133277481488811813978577e+146 absolute error = 2.6256741133277481488811813978577e+146 relative error = 2.9478492015524821430040564240975e+151 % h = 0.001 x1[1] (analytic) = 0.001222025727253075919286180057411 x1[1] (numeric) = -2.7871501762237413458207269548624e+148 absolute error = 2.7871501762237413458207269548624e+148 relative error = 2.2807622737115544677300702103725e+153 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.567 x2[1] (analytic) = 0.00089178015361418405848453645636232 x2[1] (numeric) = 7.8372906747422933163871804716262e+148 absolute error = 7.8372906747422933163871804716262e+148 relative error = 8.7883663288306202269755423316535e+153 % h = 0.001 x1[1] (analytic) = 0.0012210042123683914245858479623694 x1[1] (numeric) = -7.9710262956275324452157288421030e+150 absolute error = 7.9710262956275324452157288421030e+150 relative error = 6.5282545423541744950989911622369e+155 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.568 x2[1] (analytic) = 0.00089285454092535984878409653241629 x2[1] (numeric) = 1.7152628492274580523953085865779e+151 absolute error = 1.7152628492274580523953085865779e+151 relative error = 1.9210999895344086580784130411093e+156 % h = 0.001 x1[1] (analytic) = 0.0012199837184880043819641406086574 x1[1] (numeric) = -1.6922048878529728536450440697855e+153 absolute error = 1.6922048878529728536450440697855e+153 relative error = 1.3870716979323455093485261321511e+158 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 2.892e-05 Order of pole = 2.819 t[1] = 0.569 x2[1] (analytic) = 0.00089393158966368473941194530952011 x2[1] (numeric) = 2.8164341883122487568130440727767e+153 absolute error = 2.8164341883122487568130440727767e+153 relative error = 3.1506149026144703408439097857569e+158 % h = 0.001 x1[1] (analytic) = 0.0012189642445914208259928558409419 x1[1] (numeric) = -2.6713586668953363351519572787877e+155 absolute error = 2.6713586668953363351519572787877e+155 relative error = 2.1914987898523119523882924836857e+160 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.57 x2[1] (analytic) = 0.00089501130464709228041502404947533 x2[1] (numeric) = 2.7030001957150697518182953492705e+155 absolute error = 2.7030001957150697518182953492705e+155 relative error = 3.0200738042977871783098319226694e+160 % h = 0.001 x1[1] (analytic) = 0.0012179457896591667751322768074366 x1[1] (numeric) = -2.2708764354108825201033201999193e+157 absolute error = 2.2708764354108825201033201999193e+157 relative error = 1.8645135560970826856238613084162e+162 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.6MB, time=3.39 NO POLE NO POLE t[1] = 0.571 x2[1] (analytic) = 0.00089609369070367152334883261215016 x2[1] (numeric) = -2.6538851007375019792137286905298e+157 absolute error = 2.6538851007375019792137286905298e+157 relative error = 2.9616156527711933573089614836187e+162 % h = 0.001 x1[1] (analytic) = 0.0012169283526727872122571054640167 x1[1] (numeric) = 3.5981871445297746493732663902938e+159 absolute error = 3.5981871445297746493732663902938e+159 relative error = 2.9567781345770569498149087675934e+164 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.572 x2[1] (analytic) = 0.00089717875267168684286779387121317 x2[1] (numeric) = -2.1918964291886309942617622092065e+160 absolute error = 2.1918964291886309942617622092065e+160 relative error = 2.4430989060557172036542352122001e+165 % h = 0.001 x1[1] (analytic) = 0.0012159119326148450662013605776668 x1[1] (numeric) = 2.3466663967973498245221392136330e+162 absolute error = 2.3466663967973498245221392136330e+162 relative error = 1.9299641148769653742853155644113e+167 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.573 x2[1] (analytic) = 0.00089826649539959779850795090092798 x2[1] (numeric) = -6.9003364019415514610655524615401e+162 absolute error = 6.9003364019415514610655524615401e+162 relative error = 7.6818365566133093771297524541791e+167 % h = 0.001 x1[1] (analytic) = 0.0012148965284689201943212217740738 x1[1] (numeric) = 7.0480849882964382110846393523429e+164 absolute error = 7.0480849882964382110846393523429e+164 relative error = 5.8013870507793982829626987112047e+169 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.574 x2[1] (analytic) = 0.00089935692374607903674195281006981 x2[1] (numeric) = -1.5639852269764528298734051521815e+165 absolute error = 1.5639852269764528298734051521815e+165 relative error = 1.7390039323453547831740155317034e+170 % h = 0.001 x1[1] (analytic) = 0.0012138821392196083660748021921261 x1[1] (numeric) = 1.5491116635582366716679371800497e+167 absolute error = 1.5491116635582366716679371800497e+167 relative error = 1.2761631574496546454379933787072e+172 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0003571 Order of pole = 314 t[1] = 0.575 x2[1] (analytic) = 0.00090045004258004023338644567976864 x2[1] (numeric) = -2.6782002001458911257312341891187e+167 absolute error = 2.6782002001458911257312341891187e+167 relative error = 2.9742907140879258749288119698960e+172 % h = 0.001 x1[1] (analytic) = 0.0012128687638525202476178333250037 x1[1] (numeric) = 2.5570352931855616862860262283403e+169 absolute error = 2.5570352931855616862860262283403e+169 relative error = 2.1082538930786467581879319872561e+174 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.576 x2[1] (analytic) = 0.00090154585678064607644214596380192 x2[1] (numeric) = -2.8713355555072083205406238430460e+169 absolute error = 2.8713355555072083205406238430460e+169 relative error = 3.1849023917214109679098760653181e+174 % h = 0.001 x1[1] (analytic) = 0.0012118564013542803874142466434628 x1[1] (numeric) = 2.4907978629577821573397962173010e+171 absolute error = 2.4907978629577821573397962173010e+171 relative error = 2.0553572685462172906116081806172e+176 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.6MB, time=3.67 NO POLE NO POLE t[1] = 0.577 x2[1] (analytic) = 0.00090264437123733628944703493319481 x2[1] (numeric) = 1.4127678586122844730489323127047e+171 absolute error = 1.4127678586122844730489323127047e+171 relative error = 1.5651433760958103307263050730186e+176 % h = 0.001 x1[1] (analytic) = 0.0012108450507125262028606376118103 x1[1] (numeric) = -2.2739598558636747847222978225459e+173 absolute error = 2.2739598558636747847222978225459e+173 relative error = 1.8779940955496781217593351145454e+178 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.578 x2[1] (analytic) = 0.00090374559084984569542327429258224 x2[1] (numeric) = 1.8092509461861444618720258007312e+174 absolute error = 1.8092509461861444618720258007312e+174 relative error = 2.0019471901210585822973972742013e+179 % h = 0.001 x1[1] (analytic) = 0.0012098347109159069679235987209479 x1[1] (numeric) = -1.9564689662597984057374685306933e+176 absolute error = 1.9564689662597984057374685306933e+176 relative error = 1.6171374061326534327740329796935e+181 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.579 x2[1] (analytic) = 0.00090484952052822432149860496429206 x2[1] (numeric) = 6.0445820046076656227896265059928e+176 absolute error = 6.0445820046076656227896265059928e+176 relative error = 6.6802068934943103788166796719799e+181 % h = 0.001 x1[1] (analytic) = 0.0012088253809540828017889091757341 x1[1] (numeric) = -6.2017419422196130223538839343644e+178 absolute error = 6.2017419422196130223538839343644e+178 relative error = 5.1303869358904419100617446987211e+183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.58 x2[1] (analytic) = 0.00090595616519285754428315322816622 x2[1] (numeric) = 1.4197258370614728926162059243511e+179 absolute error = 1.4197258370614728926162059243511e+179 relative error = 1.5671021309946551597136936817075e+184 % h = 0.001 x1[1] (analytic) = 0.0012078170598177236585215698857712 x1[1] (numeric) = -1.4117122440387761132198090843311e+181 absolute error = 1.4117122440387761132198090843311e+181 relative error = 1.1688129692851192755413152833199e+186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 4.543e-05 Order of pole = 16.38 t[1] = 0.581 x2[1] (analytic) = 0.00090706552977448627608273092139788 x2[1] (numeric) = 2.5295011941253122571812011998517e+181 absolute error = 2.5295011941253122571812011998517e+181 relative error = 2.7886642266674981152595006544294e+186 % h = 0.001 x1[1] (analytic) = 0.0012068097464985083177356734195659 x1[1] (numeric) = -2.4294352403996662732452371324061e+183 absolute error = 2.4294352403996662732452371324061e+183 relative error = 2.0131054190178179729301728345114e+188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=57.2MB, alloc=4.6MB, time=3.94 t[1] = 0.582 x2[1] (analytic) = 0.00090817761921422719202987924377588 x2[1] (numeric) = 2.9694828921665853778348993531584e+183 absolute error = 2.9694828921665853778348993531584e+183 relative error = 3.2697159997576677789409880436311e+188 % h = 0.001 x1[1] (analytic) = 0.0012058034399891233762730995918507 x1[1] (numeric) = -2.6360659723035981709490424352775e+185 absolute error = 2.6360659723035981709490424352775e+185 relative error = 2.1861489898613791406356479389839e+190 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.583 x2[1] (analytic) = 0.00090929243846359299821406888034318 x2[1] (numeric) = -3.8366778695190664222424782899994e+184 absolute error = 3.8366778695190664222424782899994e+184 relative error = 4.2194102878517256031573963250417e+189 % h = 0.001 x1[1] (analytic) = 0.0012047981392832622408900283626774 x1[1] (numeric) = 1.1655761457764713502850485830256e+187 absolute error = 1.1655761457764713502850485830256e+187 relative error = 9.6744517423464468207740085193811e+191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.584 x2[1] (analytic) = 0.00091040999248451274089263264624774 x2[1] (numeric) = -1.4733987039421769273307992841632e+188 absolute error = 1.4733987039421769273307992841632e+188 relative error = 1.6183903033854731743799274789541e+193 % h = 0.001 x1[1] (analytic) = 0.0012037938433756241219502627347115 x1[1] (numeric) = 1.6124807536506692665198483295023e+190 absolute error = 1.6124807536506692665198483295023e+190 relative error = 1.3394990865952793366000938922985e+195 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.585 x2[1] (analytic) = 0.00091153028624935215686417067814311 x2[1] (numeric) = -5.2664589954474224991124817367288e+190 absolute error = 5.2664589954474224991124817367288e+190 relative error = 5.7776017702244125284113421428549e+195 % h = 0.001 x1[1] (analytic) = 0.0012027905512619130281243553419666 x1[1] (numeric) = 5.4291529538277003792731555963132e+192 absolute error = 5.4291529538277003792731555963132e+192 relative error = 4.5137974754887129256537002721267e+197 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.586 x2[1] (analytic) = 0.0009126533247409340650863323435399 x2[1] (numeric) = -1.2831318889292172269235434114965e+193 absolute error = 1.2831318889292172269235434114965e+193 relative error = 1.4059356977562616921285736018315e+198 % h = 0.001 x1[1] (analytic) = 0.0012017882619388367620935334290215 x1[1] (numeric) = 1.2808088115399740649047412076587e+195 absolute error = 1.2808088115399740649047412076587e+195 relative error = 1.0657524724643707136885686081884e+200 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.587 x2[1] (analytic) = 0.00091377911295255879962004351467114 x2[1] (numeric) = -2.3742916492168930889440382274940e+195 absolute error = 2.3742916492168930889440382274940e+195 relative error = 2.5983212086619018244682270807470e+200 % h = 0.001 x1[1] (analytic) = 0.0012007869744041059172574179245617 x1[1] (numeric) = 2.2927493987497574454898435346131e+197 absolute error = 2.2927493987497574454898435346131e+197 relative error = 1.9093723096784432614117627729653e+202 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=61.0MB, alloc=4.6MB, time=4.23 t[1] = 0.588 x2[1] (analytic) = 0.00091490765588802468398241265737402 x2[1] (numeric) = -3.0091915857827392239367176414397e+197 absolute error = 3.0091915857827392239367176414397e+197 relative error = 3.2890659143757710768370917202902e+202 % h = 0.001 x1[1] (analytic) = 0.0011997866876564328754445333168804 x1[1] (numeric) = 2.7186271433845339062407741966360e+199 absolute error = 2.7186271433845339062407741966360e+199 relative error = 2.2659254110369254106675790938986e+204 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 0.0001471 Order of pole = 39.06 t[1] = 0.589 x2[1] (analytic) = 0.00091603895856164854699071431886538 x2[1] (numeric) = -4.5898139861683876751375097944701e+198 absolute error = 4.5898139861683876751375097944701e+198 relative error = 5.0105008561811048538043315377767e+203 % h = 0.001 x1[1] (analytic) = 0.0011987874006955308056246060417651 x1[1] (numeric) = -2.4783165100148222787352781290296e+200 absolute error = 2.4783165100148222787352781290296e+200 relative error = 2.0673528171691783783340570732511e+205 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.59 x2[1] (analytic) = 0.00091717302599828628018001406175885 x2[1] (numeric) = 1.1801684404947794720107940027144e+202 absolute error = 1.1801684404947794720107940027144e+202 relative error = 1.2867456925155849422106091161703e+207 % h = 0.001 x1[1] (analytic) = 0.0011977891125221126636216500949856 x1[1] (numeric) = -1.3107493537648024229749383625332e+204 absolute error = 1.3107493537648024229749383625332e+204 relative error = 1.0943072867016098996686990278039e+209 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.591 x2[1] (analytic) = 0.00091830986323335343687716468589885 x2[1] (numeric) = 4.5620276768210643342320348024697e+204 absolute error = 4.5620276768210643342320348024697e+204 relative error = 4.9678522026957680066158500559386e+209 % h = 0.001 x1[1] (analytic) = 0.0011967918221378901928268395823847 x1[1] (numeric) = -4.7270245616492396206363960899312e+206 absolute error = 4.7270245616492396206363960899312e+206 relative error = 3.9497467096701202936719332178263e+211 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.592 x2[1] (analytic) = 0.00091944947531284587301406970523356 x2[1] (numeric) = 1.1546241315300502182029383014614e+207 absolute error = 1.1546241315300502182029383014614e+207 relative error = 1.2557776827673813753887796796214e+212 % h = 0.001 x1[1] (analytic) = 0.0011957955285455729259101689203614 x1[1] (numeric) = -1.1569632544000763301742833938770e+209 absolute error = 1.1569632544000763301742833938770e+209 relative error = 9.6752599151066598075759997234429e+213 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.593 x2[1] (analytic) = 0.00092059186729336042976327650467993 x2[1] (numeric) = 2.2158805456087614183084294385969e+209 absolute error = 2.2158805456087614183084294385969e+209 relative error = 2.4070172943453103419516198869611e+214 % h = 0.001 x1[1] (analytic) = 0.001194800230748867187529902398324 x1[1] (numeric) = -2.1505151539601950370129241070135e+211 absolute error = 2.1505151539601950370129241070135e+211 relative error = 1.7998951612290136651335197835988e+216 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.6MB, time=4.50 NO POLE NO POLE t[1] = 0.594 x2[1] (analytic) = 0.00092173704424211565807912839241284 x2[1] (numeric) = 3.0008114069978380073892632354590e+211 absolute error = 3.0008114069978380073892632354590e+211 relative error = 3.2556046496592851976029892119345e+216 % h = 0.001 x1[1] (analytic) = 0.0011938059277524750980388158124784 x1[1] (numeric) = -2.7490478408081023007321961445957e+213 absolute error = 2.7490478408081023007321961445957e+213 relative error = 2.3027594158320284361799657222464e+218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.595 x2[1] (analytic) = 0.00092288501123697258522787188690669 x2[1] (numeric) = 1.1385024083145948641889069070784e+213 absolute error = 1.1385024083145948641889069070784e+213 relative error = 1.2336340870772441284659533213559e+218 % h = 0.001 x1[1] (analytic) = 0.0011928126185620935781862338771108 x1[1] (numeric) = -5.0235883460945186497752823044904e+214 absolute error = 5.0235883460945186497752823044904e+214 relative error = 4.2115486271014901455900635936752e+219 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.596 x2[1] (analytic) = 0.00092403577336645552339028303603533 x2[1] (numeric) = -9.2558760489434365197517798347519e+215 absolute error = 9.2558760489434365197517798347519e+215 relative error = 1.0016794063310281612429230785660e+221 % h = 0.001 x1[1] (analytic) = 0.0011918203021844133548148681153206 x1[1] (numeric) = 1.0474849429570159560407055964507e+218 absolute error = 1.0474849429570159560407055964507e+218 relative error = 8.7889503227721990475737144936004e+222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.597 x2[1] (analytic) = 0.00092518933572977292042054435826881 x2[1] (numeric) = -3.9270899892546612945045755317726e+218 absolute error = 3.9270899892546612945045755317726e+218 relative error = 4.2446338685443692886289033802130e+223 % h = 0.001 x1[1] (analytic) = 0.0011908289776271179675514609259555 x1[1] (numeric) = 4.0917294079122404325505014929161e+220 absolute error = 4.0917294079122404325505014929161e+220 relative error = 3.4360344640466718194587393897644e+225 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.598 x2[1] (analytic) = 0.00092634570343683825284527212416087 x2[1] (numeric) = -1.0344346851258801577952942167435e+221 absolute error = 1.0344346851258801577952942167435e+221 relative error = 1.1166832007618976556021230829249e+226 % h = 0.001 x1[1] (analytic) = 0.0011898386438988827764902425173134 x1[1] (numeric) = 1.0405361849240302137470330637133e+223 absolute error = 1.0405361849240302137470330637133e+223 relative error = 8.7451873433391285959119138794376e+227 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.599 x2[1] (analytic) = 0.0009275048816082909611867621605716 x2[1] (numeric) = -2.0570055645524882828405890256035e+223 absolute error = 2.0570055645524882828405890256035e+223 relative error = 2.2177840843119296430848455793513e+228 % h = 0.001 x1[1] (analytic) = 0.001188849300009373970868208390983 x1[1] (numeric) = 2.0056883236338192325676605111160e+225 absolute error = 2.0056883236338192325676605111160e+225 relative error = 1.6870837402335220778062311367829e+230 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.6MB, time=4.78 NO POLE NO POLE t[1] = 0.6 x2[1] (analytic) = 0.00092866687537551742769469116109009 x2[1] (numeric) = -2.9534126619800315371630880515661e+225 absolute error = 2.9534126619800315371630880515661e+225 relative error = 3.1802713548771557277829127172104e+230 % h = 0.001 x1[1] (analytic) = 0.0011878609449692475787312260510186 x1[1] (numeric) = 2.7366286163010312725677402019894e+227 absolute error = 2.7366286163010312725677402019894e+227 relative error = 2.3038291038113721263050781320324e+232 % h = 0.001 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 = 4 Seconds Elapsed Time(since restart) = 4 Seconds Expected Time Remaining = 3 Minutes 27 Seconds Optimized Time Remaining = 3 Minutes 27 Seconds Time to Timeout = 14 Minutes 55 Seconds Percent Done = 2.244 % > quit memory used=69.2MB, alloc=4.6MB, time=4.82