|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_hmax, > glob_clock_sec, > glob_iter, > glob_no_eqs, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_order, > glob_max_iter, > glob_relerr, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > hours_in_day, > glob_log10normmin, > glob_orig_start_sec, > glob_max_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_last_good_h, > glob_not_yet_finished, > glob_clock_start_sec, > sec_in_min, > min_in_hour, > djd_debug2, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_hours, > centuries_in_millinium, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_max_trunc_err, > glob_almost_1, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_max_minutes, > glob_warned, > glob_disp_incr, > days_in_year, > glob_html_log, > glob_current_iter, > glob_optimal_start, > glob_large_float, > glob_h, > years_in_century, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_norms, > array_x1_init, > array_x2, > array_x1, > array_x2_init, > array_m1, > array_t, > array_type_pole, > array_1st_rel_error, > array_last_rel_error, > array_poles, > array_x2_higher, > array_real_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_complex_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, DEBUGL, glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs, glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump, glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr, glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin, glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr, glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min, min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_small_float, glob_max_hours, centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_look_poles, glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass, glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log, glob_current_iter, glob_optimal_start, glob_large_float, glob_h, years_in_century, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms, array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t, array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles, array_x2_higher, array_real_pole, array_x1_higher_work, array_x2_higher_work2, array_complex_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, 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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_hmax, > glob_clock_sec, > glob_iter, > glob_no_eqs, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_order, > glob_max_iter, > glob_relerr, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > hours_in_day, > glob_log10normmin, > glob_orig_start_sec, > glob_max_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_last_good_h, > glob_not_yet_finished, > glob_clock_start_sec, > sec_in_min, > min_in_hour, > djd_debug2, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_hours, > centuries_in_millinium, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_max_trunc_err, > glob_almost_1, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_max_minutes, > glob_warned, > glob_disp_incr, > days_in_year, > glob_html_log, > glob_current_iter, > glob_optimal_start, > glob_large_float, > glob_h, > years_in_century, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_norms, > array_x1_init, > array_x2, > array_x1, > array_x2_init, > array_m1, > array_t, > array_type_pole, > array_1st_rel_error, > array_last_rel_error, > array_poles, > array_x2_higher, > array_real_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_complex_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > 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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, DEBUGL, glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs, glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump, glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr, glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin, glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr, glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min, min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_small_float, glob_max_hours, centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_look_poles, glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass, glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log, glob_current_iter, glob_optimal_start, glob_large_float, glob_h, years_in_century, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms, array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t, array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles, array_x2_higher, array_real_pole, array_x1_higher_work, array_x2_higher_work2, array_complex_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, 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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_hmax, > glob_clock_sec, > glob_iter, > glob_no_eqs, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_order, > glob_max_iter, > glob_relerr, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > hours_in_day, > glob_log10normmin, > glob_orig_start_sec, > glob_max_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_last_good_h, > glob_not_yet_finished, > glob_clock_start_sec, > sec_in_min, > min_in_hour, > djd_debug2, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_hours, > centuries_in_millinium, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_max_trunc_err, > glob_almost_1, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_max_minutes, > glob_warned, > glob_disp_incr, > days_in_year, > glob_html_log, > glob_current_iter, > glob_optimal_start, > glob_large_float, > glob_h, > years_in_century, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_norms, > array_x1_init, > array_x2, > array_x1, > array_x2_init, > array_m1, > array_t, > array_type_pole, > array_1st_rel_error, > array_last_rel_error, > array_poles, > array_x2_higher, > array_real_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_complex_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, DEBUGL, glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs, glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump, glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr, glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin, glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr, glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min, min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_small_float, glob_max_hours, centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_look_poles, glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass, glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log, glob_current_iter, glob_optimal_start, glob_large_float, glob_h, years_in_century, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms, array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t, array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles, array_x2_higher, array_real_pole, array_x1_higher_work, array_x2_higher_work2, array_complex_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_hmax, > glob_clock_sec, > glob_iter, > glob_no_eqs, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_order, > glob_max_iter, > glob_relerr, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > hours_in_day, > glob_log10normmin, > glob_orig_start_sec, > glob_max_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_last_good_h, > glob_not_yet_finished, > glob_clock_start_sec, > sec_in_min, > min_in_hour, > djd_debug2, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_hours, > centuries_in_millinium, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_max_trunc_err, > glob_almost_1, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_max_minutes, > glob_warned, > glob_disp_incr, > days_in_year, > glob_html_log, > glob_current_iter, > glob_optimal_start, > glob_large_float, > glob_h, > years_in_century, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_norms, > array_x1_init, > array_x2, > array_x1, > array_x2_init, > array_m1, > array_t, > array_type_pole, > array_1st_rel_error, > array_last_rel_error, > array_poles, > array_x2_higher, > array_real_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_complex_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, DEBUGL, glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs, glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump, glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr, glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin, glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr, glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min, min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_small_float, glob_max_hours, centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_look_poles, glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass, glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log, glob_current_iter, glob_optimal_start, glob_large_float, glob_h, years_in_century, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms, array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t, array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles, array_x2_higher, array_real_pole, array_x1_higher_work, array_x2_higher_work2, array_complex_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, 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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_hmax, > glob_clock_sec, > glob_iter, > glob_no_eqs, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_order, > glob_max_iter, > glob_relerr, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > hours_in_day, > glob_log10normmin, > glob_orig_start_sec, > glob_max_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_last_good_h, > glob_not_yet_finished, > glob_clock_start_sec, > sec_in_min, > min_in_hour, > djd_debug2, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_hours, > centuries_in_millinium, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_max_trunc_err, > glob_almost_1, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_max_minutes, > glob_warned, > glob_disp_incr, > days_in_year, > glob_html_log, > glob_current_iter, > glob_optimal_start, > glob_large_float, > glob_h, > years_in_century, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_norms, > array_x1_init, > array_x2, > array_x1, > array_x2_init, > array_m1, > array_t, > array_type_pole, > array_1st_rel_error, > array_last_rel_error, > array_poles, > array_x2_higher, > array_real_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_complex_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, DEBUGL, glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs, glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump, glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr, glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin, glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr, glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min, min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_small_float, glob_max_hours, centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_look_poles, glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass, glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log, glob_current_iter, glob_optimal_start, glob_large_float, glob_h, years_in_century, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms, array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t, array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles, array_x2_higher, array_real_pole, array_x1_higher_work, array_x2_higher_work2, array_complex_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_hmax, > glob_clock_sec, > glob_iter, > glob_no_eqs, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_order, > glob_max_iter, > glob_relerr, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > hours_in_day, > glob_log10normmin, > glob_orig_start_sec, > glob_max_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_last_good_h, > glob_not_yet_finished, > glob_clock_start_sec, > sec_in_min, > min_in_hour, > djd_debug2, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_hours, > centuries_in_millinium, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_max_trunc_err, > glob_almost_1, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_max_minutes, > glob_warned, > glob_disp_incr, > days_in_year, > glob_html_log, > glob_current_iter, > glob_optimal_start, > glob_large_float, > glob_h, > years_in_century, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_norms, > array_x1_init, > array_x2, > array_x1, > array_x2_init, > array_m1, > array_t, > array_type_pole, > array_1st_rel_error, > array_last_rel_error, > array_poles, > array_x2_higher, > array_real_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_complex_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > 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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, DEBUGL, glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs, glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump, glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr, glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin, glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr, glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min, min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_small_float, glob_max_hours, centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_look_poles, glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass, glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log, glob_current_iter, glob_optimal_start, glob_large_float, glob_h, years_in_century, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms, array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t, array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles, array_x2_higher, array_real_pole, array_x1_higher_work, array_x2_higher_work2, array_complex_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, 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 > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_hmax, > glob_clock_sec, > glob_iter, > glob_no_eqs, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_order, > glob_max_iter, > glob_relerr, > glob_max_opt_iter, > MAX_UNCHANGED, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > hours_in_day, > glob_log10normmin, > glob_orig_start_sec, > glob_max_sec, > glob_max_rel_trunc_err, > glob_abserr, > glob_last_good_h, > glob_not_yet_finished, > glob_clock_start_sec, > sec_in_min, > min_in_hour, > djd_debug2, > glob_percent_done, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_hours, > centuries_in_millinium, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_max_trunc_err, > glob_almost_1, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_look_poles, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_max_minutes, > glob_warned, > glob_disp_incr, > days_in_year, > glob_html_log, > glob_current_iter, > glob_optimal_start, > glob_large_float, > glob_h, > years_in_century, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_norms, > array_x1_init, > array_x2, > array_x1, > array_x2_init, > array_m1, > array_t, > array_type_pole, > array_1st_rel_error, > array_last_rel_error, > array_poles, > array_x2_higher, > array_real_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_complex_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > DEBUGMASSIVE := 4; > glob_max_terms := 30; > INFO := 2; > glob_iolevel := 5; > DEBUGL := 3; > glob_start := 0; > glob_hmax := 1.0; > glob_clock_sec := 0.0; > glob_iter := 0; > glob_no_eqs := 0; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_dump := false; > glob_optimal_clock_start_sec := 0.0; > glob_max_order := 30; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_max_opt_iter := 10; > MAX_UNCHANGED := 10; > glob_warned2 := false; > glob_dump_analytic := false; > glob_hmin_init := 0.001; > glob_optimal_done := false; > hours_in_day := 24.0; > glob_log10normmin := 0.1; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_abserr := 0.1e-10; > glob_last_good_h := 0.1; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > sec_in_min := 60.0; > min_in_hour := 60.0; > djd_debug2 := true; > glob_percent_done := 0.0; > glob_log10relerr := 0.0; > glob_unchanged_h_cnt := 0; > glob_small_float := 0.1e-50; > glob_max_hours := 0.0; > centuries_in_millinium := 10.0; > djd_debug := true; > glob_normmax := 0.0; > glob_curr_iter_when_opt := 0; > glob_smallish_float := 0.1e-100; > glob_max_trunc_err := 0.1e-10; > glob_almost_1 := 0.9990; > glob_display_flag := true; > glob_optimal_expect_sec := 0.1; > glob_log10abserr := 0.0; > glob_look_poles := false; > glob_reached_optimal_h := false; > glob_not_yet_start_msg := true; > glob_initial_pass := true; > glob_max_minutes := 0.0; > glob_warned := false; > glob_disp_incr := 0.1; > days_in_year := 365.0; > glob_html_log := true; > glob_current_iter := 0; > glob_optimal_start := 0.0; > glob_large_float := 9.0e100; > glob_h := 0.1; > years_in_century := 100.0; > #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/complicatedrevpostode.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 := 0.0002 ;"); > 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_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_tmp7:= Array(1..(max_terms + 1),[]); > array_tmp8:= Array(1..(max_terms + 1),[]); > array_tmp9:= Array(1..(max_terms + 1),[]); > array_tmp10:= Array(1..(max_terms + 1),[]); > array_tmp11:= Array(1..(max_terms + 1),[]); > array_tmp12:= Array(1..(max_terms + 1),[]); > array_tmp13:= Array(1..(max_terms + 1),[]); > array_tmp14:= Array(1..(max_terms + 1),[]); > array_tmp15:= Array(1..(max_terms + 1),[]); > array_tmp16:= Array(1..(max_terms + 1),[]); > array_tmp17:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_norms:= 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_x2_init:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > 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_last_rel_error:= 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_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work2 := Array(1..(2+ 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),[]); > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_x2_init[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_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_last_rel_error[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 <= 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 <= max_terms do # do number 3 > array_x1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 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 <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_t := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_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_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_const_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_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #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 := 0.0002 ; > 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; > atomall(); > 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,"2012-06-02T02:04:44-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"complicatedrev") > ; > 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,"complicatedrev diffeq.mxt") > ; > logitem_str(html_log_file,"complicatedrev maple results") > ; > logitem_str(html_log_file,"sub iter once 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 ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_iolevel, DEBUGL, glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs, glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump, glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr, glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin, glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr, glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min, min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr, glob_unchanged_h_cnt, glob_small_float, glob_max_hours, centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_look_poles, glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass, glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log, glob_current_iter, glob_optimal_start, glob_large_float, glob_h, years_in_century, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms, array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t, array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles, array_x2_higher, array_real_pole, array_x1_higher_work, array_x2_higher_work2, array_complex_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; DEBUGMASSIVE := 4; glob_max_terms := 30; INFO := 2; glob_iolevel := 5; DEBUGL := 3; glob_start := 0; glob_hmax := 1.0; glob_clock_sec := 0.; glob_iter := 0; glob_no_eqs := 0; glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_dump := false; glob_optimal_clock_start_sec := 0.; glob_max_order := 30; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_max_opt_iter := 10; MAX_UNCHANGED := 10; glob_warned2 := false; glob_dump_analytic := false; glob_hmin_init := 0.001; glob_optimal_done := false; hours_in_day := 24.0; glob_log10normmin := 0.1; glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_not_yet_finished := true; glob_clock_start_sec := 0.; sec_in_min := 60.0; min_in_hour := 60.0; djd_debug2 := true; glob_percent_done := 0.; glob_log10relerr := 0.; glob_unchanged_h_cnt := 0; glob_small_float := 0.1*10^(-50); glob_max_hours := 0.; centuries_in_millinium := 10.0; djd_debug := true; glob_normmax := 0.; glob_curr_iter_when_opt := 0; glob_smallish_float := 0.1*10^(-100); glob_max_trunc_err := 0.1*10^(-10); glob_almost_1 := 0.9990; glob_display_flag := true; glob_optimal_expect_sec := 0.1; glob_log10abserr := 0.; glob_look_poles := false; glob_reached_optimal_h := false; glob_not_yet_start_msg := true; glob_initial_pass := true; glob_max_minutes := 0.; glob_warned := false; glob_disp_incr := 0.1; days_in_year := 365.0; glob_html_log := true; glob_current_iter := 0; glob_optimal_start := 0.; glob_large_float := 0.90*10^101; glob_h := 0.1; years_in_century := 100.0; 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/complicatedrevpostode.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 := 0.0002 ;"); 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_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_tmp7 := Array(1 .. max_terms + 1, []); array_tmp8 := Array(1 .. max_terms + 1, []); array_tmp9 := Array(1 .. max_terms + 1, []); array_tmp10 := Array(1 .. max_terms + 1, []); array_tmp11 := Array(1 .. max_terms + 1, []); array_tmp12 := Array(1 .. max_terms + 1, []); array_tmp13 := Array(1 .. max_terms + 1, []); array_tmp14 := Array(1 .. max_terms + 1, []); array_tmp15 := Array(1 .. max_terms + 1, []); array_tmp16 := Array(1 .. max_terms + 1, []); array_tmp17 := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_norms := 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_x2_init := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); 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_last_rel_error := Array(1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work2 := Array(1 .. 3, 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, []); term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_x2_init[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_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_last_rel_error[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 <= 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 <= max_terms do array_x1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_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; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_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_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1 end do; array_const_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_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_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_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; 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 := 0.0002; 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; atomall(); 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, "2012-06-02T02:04:44-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "complicatedrev"); 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, "complicatedrev diffeq.mxt"); logitem_str(html_log_file, "complicatedrev maple results"); logitem_str(html_log_file, "sub iter once 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/complicatedrevpostode.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 := 0.0002 ; 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 = 0.0002 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.0002 t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 0.0002 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002 x2[1] (analytic) = 0.0008257966814495432344339416603249 x2[1] (numeric) = 0.00082579668144954295656970752147277 absolute error = 2.7786423413885213e-19 relative error = 3.3648020194403001202555678944769e-14 % h = 0.0002 x1[1] (analytic) = 0.0012915368582788917633066026400632 x1[1] (numeric) = 0.0012915368582825965220508034624851 absolute error = 3.7047587442008224219e-15 relative error = 2.8684885920621744892044777987859e-10 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004 x2[1] (analytic) = 0.00082597789359022044558440876232671 x2[1] (numeric) = 0.00082597793726770304844334465273524 absolute error = 4.367748260285893589040853e-11 relative error = 5.2879723466943009264497482790105e-06 % h = 0.0002 x1[1] (analytic) = 0.0012913185727365178408202846139762 x1[1] (numeric) = 0.0012913184854282161389109575671542 absolute error = 8.73083017019093270468220e-11 relative error = 6.7611744727630286731394953540443e-06 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006 x2[1] (analytic) = 0.00082615920006099036141977864461309 x2[1] (numeric) = 0.00082615937480149199912013595485247 absolute error = 1.7474050163770035731023938e-10 relative error = 2.1150947859056743272639430613083e-05 % h = 0.0002 x1[1] (analytic) = 0.0012911003308468869733038234462486 x1[1] (numeric) = 0.0012910999816248061854917034942565 absolute error = 3.492220807878121199519921e-10 relative error = 2.7048407660057114151063292779636e-05 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5008 x2[1] (analytic) = 0.00082634060089522685551538962782877 x2[1] (numeric) = 0.00082634099416580736205926833904204 absolute error = 3.9327058050654387871121327e-10 relative error = 4.7591825946890310339890093724049e-05 % h = 0.0002 x1[1] (analytic) = 0.0012908821326012694851428855175656 x1[1] (numeric) = 0.0012908813468481420933054466274498 absolute error = 7.857531273918374388901158e-10 relative error = 6.0869471158335615032526769378067e-05 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652279549888325782994999044965 absolute error = 6.9937256523110879826257779e-10 relative error = 8.4616318003943978658726761330945e-05 % h = 0.0002 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906625810197011896414794514703 absolute error = 1.3969712362568421987505648e-09 relative error = 0.00010823663324294398193566625967614 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=2.9MB, time=0.18 t[1] = 0.5012 x2[1] (analytic) = 0.00082670368578766620467820114309252 x2[1] (numeric) = 0.00082670477893903363437304090801915 absolute error = 1.09315136742969483976492663e-09 relative error = 0.00013223013108840355353924522727657 % h = 0.0002 x1[1] (analytic) = 0.0012904458670071646728838326718726 x1[1] (numeric) = 0.0012904436840609486139626090689805 absolute error = 2.1829462160589212236028921e-09 relative error = 0.0001691621688185701560748882430076 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5014 x2[1] (analytic) = 0.00082688536991268795533779675988916 x2[1] (numeric) = 0.00082688694462466704401939056790316 absolute error = 1.57471197908868159380801400e-09 relative error = 0.00019043896970325617831278847413274 % h = 0.0002 x1[1] (analytic) = 0.0012902277996412267249633565185424 x1[1] (numeric) = 0.0012902246558933024230900683055535 absolute error = 3.1437479243018732882129889e-09 relative error = 0.00024365836212613418916516642007777 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5016 x2[1] (analytic) = 0.00082706714853481408648245956670656 x2[1] (numeric) = 0.00082706929269428669538843927546727 absolute error = 2.14415947260890597970876071e-09 relative error = 0.00025924853579390488513073379773444 % h = 0.0002 x1[1] (analytic) = 0.001290009775884400908055656176395 x1[1] (numeric) = 0.0012900054964381335854790961656122 absolute error = 4.2794462673225765600107828e-09 relative error = 0.00033173750674786065384438730279401 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5018 x2[1] (analytic) = 0.00082724902168748965324935586679766 x2[1] (numeric) = 0.00082725182328649051480899688372647 absolute error = 2.80159900086155964101692881e-09 relative error = 0.0003386645287469341165477264835366 % h = 0.0002 x1[1] (analytic) = 0.0012897917957279662718586291348401 x1[1] (numeric) = 0.0012897862056167659526349170410761 absolute error = 5.5901112003192237120937640e-09 relative error = 0.00043341190561412520235509609670574 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.502 x2[1] (analytic) = 0.0008274309894041739636559251804687 x2[1] (numeric) = 0.00082743453653997120796381016749464 absolute error = 3.54713579724430788498702594e-09 relative error = 0.00042869264538890068428622344893383 % h = 0.0002 x1[1] (analytic) = 0.0012895738591632036100858259251 x1[1] (numeric) = 0.0012895667833504762197049488149959 absolute error = 7.0758127273903808771101041e-09 relative error = 0.00054869387101114405199029797595248 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5022 x2[1] (analytic) = 0.0008276130517183405841277537278848 x2[1] (numeric) = 0.00082761743259351632713996918423416 absolute error = 4.38087517574301221545634936e-09 relative error = 0.00052933857998580043754926160665025 % h = 0.0002 x1[1] (analytic) = 0.0012893559661813954601176818675888 x1[1] (numeric) = 0.0012893472295604935894890206105429 absolute error = 8.7366209018706286612570459e-09 relative error = 0.00067759572461167025606797914501583 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5024 x2[1] (analytic) = 0.00082779520866347734502869438387111 x2[1] (numeric) = 0.00082780051158600847983556373950985 absolute error = 5.30292253113480686935563874e-09 relative error = 0.00064060802425960863474305264850311 % h = 0.0002 x1[1] (analytic) = 0.0012891381167738261026528185659675 x1[1] (numeric) = 0.0012891275441679924852993021722094 absolute error = 1.05726058336173535163937581e-08 relative error = 0.00082012979804492686829285161867557 % h = 0.0002 TOP MAIN SOLVE Loop Complex estimate of poles used NO POLE Radius of convergence = 9.530e-05 Order of pole = 1.45 t[1] = 0.5026 x2[1] (analytic) = 0.00082797746027308634619323399650282 x2[1] (numeric) = 0.00082798377365642862375972228741365 absolute error = 6.31338334227756648829091083e-09 relative error = 0.00076250666777755820669048111618628 % h = 0.0002 x1[1] (analytic) = 0.001288920310931781561359415133927 x1[1] (numeric) = 0.0012889077270939469785959313608432 absolute error = 1.25838378345827634837730838e-08 relative error = 0.00097630844419587906243489232256141 % h = 0.0002 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 6.634e-05 Order of pole = 0.2426 t[1] = 0.5028 x2[1] (analytic) = 0.00082815980658068396246110896163522 x2[1] (numeric) = 0.00082816721894391696070246787596743 absolute error = 7.41236323299824135891433221e-09 relative error = 0.00089504020529594338090610059909377 % h = 0.0002 x1[1] (analytic) = 0.0012887025486465496025266491407532 x1[1] (numeric) = 0.0012886877782566644877809380394351 absolute error = 1.47703898851147457111013181e-08 relative error = 0.0011461442285985419466025077056596 % h = 0.0002 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 9.349e-05 Order of pole = 16.66 t[1] = 0.503 x2[1] (analytic) = 0.0008283422476198008492141699458837 x2[1] (numeric) = 0.00082835084758874686858105083852782 absolute error = 8.59996894601936688089264412e-09 relative error = 0.0010382144543189651989776439971618 % h = 0.0002 x1[1] (analytic) = 0.0012884848299094197347162072617323 x1[1] (numeric) = 0.0012884676975367039718929715909045 absolute error = 1.71323727157628232356708278e-08 relative error = 0.0013296526523301967113966336978683 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0003882 Order of pole = 181.3 t[1] = 0.5032 memory used=7.6MB, alloc=4.2MB, time=0.41 x2[1] (analytic) = 0.00082852478342398194791549665092172 x2[1] (numeric) = 0.00082853465974550381865352070652182 absolute error = 9.87632152187073802405560010e-09 relative error = 0.0011920369456005417477326123678177 % h = 0.0002 x1[1] (analytic) = 0.0012882671547116832084138656194575 x1[1] (numeric) = 0.0012882474843617741076017791778918 absolute error = 1.96703499091008120864415657e-08 relative error = 0.0015268843762071288801236201260203 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5034 x2[1] (analytic) = 0.00082870741402678649165076351232339 x2[1] (numeric) = 0.0008287186557325216145265495880055 absolute error = 1.124170573512287578607568211e-08 relative error = 0.0013565349536935007635837180828972 % h = 0.0002 x1[1] (analytic) = 0.0012880495230446330156811398020981 x1[1] (numeric) = 0.0012880271336733904480463627920345 absolute error = 2.23893712425676347770100636e-08 relative error = 0.00173823838617979959187724820248 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5036 x2[1] (analytic) = 0.00082889013946178801067185722653652 x2[1] (numeric) = 0.00082890283743477308534545606401217 absolute error = 1.269797298507467359883747565e-08 relative error = 0.0015319247244658593879998195377655 % h = 0.0002 x1[1] (analytic) = 0.0012878319348995638898070045446997 x1[1] (numeric) = 0.0012878066043398732527806447122973 absolute error = 2.53305596906370263598324024e-08 relative error = 0.0019669150146220375635676999048347 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5038 x2[1] (analytic) = 0.0008290729597625743379427469999303 x2[1] (numeric) = 0.00082908721902626852438550180001675 absolute error = 1.425926369418644275480008645e-08 relative error = 0.001719904566453347792027238993419 % h = 0.0002 x1[1] (analytic) = 0.0012876143902677723049596830595824 x1[1] (numeric) = 0.0012875856252981118639329826130245 absolute error = 2.87649696604410267004465579e-08 relative error = 0.0022339739193547738499871928868676 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.504 x2[1] (analytic) = 0.00082925587496274761468760841422102 x2[1] (numeric) = 0.00082927189209752282550820286548163 absolute error = 1.601713477521082059445126061e-08 relative error = 0.0019315069399936844586206027276548 % h = 0.0002 x1[1] (analytic) = 0.0012873968891405564758385060019091 x1[1] (numeric) = 0.0012873628044553975085529320253896 absolute error = 3.40846851589672855739765195e-08 relative error = 0.0026475662203690442348998916425004 % h = 0.0002 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 2.209e-05 Order of pole = 14.48 t[1] = 0.5042 x2[1] (analytic) = 0.00082943888509592429594120180293885 x2[1] (numeric) = 0.00082945732877455552349826570664043 absolute error = 1.844367863122755706390370158e-08 relative error = 0.0022236332251404577624032033060365 % h = 0.0002 x1[1] (analytic) = 0.0012871794315092163573258400564985 x1[1] (numeric) = 0.0012871328045902889047442552380465 absolute error = 4.66269189274525815848184520e-08 relative error = 0.0036224101928650751064799278320996 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 2.336e-05 Order of pole = 24.82 t[1] = 0.5044 x2[1] (analytic) = 0.00082962199019573515610150603395714 x2[1] (numeric) = 0.00082964540059568947067070539392613 absolute error = 2.341039995431456919935996899e-08 relative error = 0.0028218152641772772545634247808408 % h = 0.0002 x1[1] (analytic) = 0.00128696201736505364413908613196 x1[1] (numeric) = 0.0012868812757865866748673999294928 absolute error = 8.07415784669692716862024672e-08 relative error = 0.0062738120766206336355349304387263 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 1.142e-05 Order of pole = 2.47 t[1] = 0.5046 x2[1] (analytic) = 0.00082980519029582529448460859346626 x2[1] (numeric) = 0.00082984159662462000902930700677151 absolute error = 3.640632879471454469841330525e-08 relative error = 0.0043873344274619082231034851507026 % h = 0.0002 x1[1] (analytic) = 0.0012867446466993717704827471482299 x1[1] (numeric) = 0.0012865833565601520114967419869926 absolute error = 1.612901392197589860051612373e-07 relative error = 0.012534743364465068029638665685928 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5048 x2[1] (analytic) = 0.00082998848542985414088185286713247 x2[1] (numeric) = 0.00083005745566682691868344013745968 absolute error = 6.897023697277780158727032721e-08 relative error = 0.0083097823865662254218315509719537 % h = 0.0002 x1[1] (analytic) = 0.0012865273195034759097005654035915 x1[1] (numeric) = 0.0012862113920296655478608498354166 absolute error = 3.159274738103618397155681749e-07 relative error = 0.024556608244610873511066851610329 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.505 x2[1] (analytic) = 0.00083017187563149546111924351454314 x2[1] (numeric) = 0.00083031106956566084135863599001952 absolute error = 1.3919393416538023939247547638e-07 relative error = 0.016766881443616497379508623135248 % h = 0.0002 x1[1] (analytic) = 0.0012863100357686729739277295072664 x1[1] (numeric) = 0.0012857330628105319400118571340878 absolute error = 5.769729581410339158723731786e-07 relative error = 0.044854890508278316825100674492429 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5052 x2[1] (analytic) = 0.0008303553609344373626191108333988 x2[1] (numeric) = 0.00083062777471325575779214464934517 absolute error = 2.7241377881839517303381594637e-07 relative error = 0.032806891077554473218718252863392 % h = 0.0002 x1[1] (analytic) = 0.0012860927954862716137431508636619 x1[1] (numeric) = 0.0012851386119041624658586857339937 absolute error = 9.541835821091478844651296682e-07 relative error = 0.074192436615615370558001801295444 % h = 0.0002 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.65 NO POLE NO POLE t[1] = 0.5054 x2[1] (analytic) = 0.00083053894137238229996403501027281 x2[1] (numeric) = 0.00083103320273431695814886333164244 absolute error = 4.9426136193465818482832136963e-07 relative error = 0.059510919634658051941123036976253 % h = 0.0002 x1[1] (analytic) = 0.0012858755986475822178218096943695 x1[1] (numeric) = 0.0012845583321700129924350793014682 absolute error = 1.3172664775692253867303929013e-06 relative error = 0.10244120651754014773680199758567 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5056 x2[1] (analytic) = 0.0008307226169790470804630311551197 x2[1] (numeric) = 0.00083152092578206264159383345207356 absolute error = 7.9830880301556113080229695386e-07 relative error = 0.096098118276668575667459944945737 % h = 0.0002 x1[1] (analytic) = 0.001285658445243916912587170584005 x1[1] (numeric) = 0.0012839655779355721865821109188262 absolute error = 1.6928673083447260050596651788e-06 relative error = 0.13167317607621306133676097434277 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5058 x2[1] (analytic) = 0.00083090638778816286971999601707344 x2[1] (numeric) = 0.0008320911750515030574430212761025 absolute error = 1.18478726334018772302525902906e-06 relative error = 0.14258974064383360327214822294214 % h = 0.0002 x1[1] (analytic) = 0.0012854413352665895618636675359888 x1[1] (numeric) = 0.001283361059320866871333300909334 absolute error = 2.0802759457226905303666266548e-06 relative error = 0.16183359665272153817131774240199 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.506 x2[1] (analytic) = 0.00083109025383347519720441727943742 x2[1] (numeric) = 0.00083274401550308590275221316542373 absolute error = 1.65376166961070554779588598631e-06 relative error = 0.19898701278021102608393159938577 % h = 0.0002 x1[1] (analytic) = 0.0012852242687069157665292585243653 x1[1] (numeric) = 0.0012827448218177086026975699046929 absolute error = 2.4794468892071638316886196724e-06 relative error = 0.19291939543763627474913520719137 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5062 x2[1] (analytic) = 0.00083127421514874396182434633212867 x2[1] (numeric) = 0.00083347951225322660070412206948138 absolute error = 2.20529710448263887977573735271e-06 relative error = 0.26529117158867176949359872698855 % h = 0.0002 x1[1] (analytic) = 0.001285007245556212864168049527763 x1[1] (numeric) = 0.0012821169115012363053973037546034 absolute error = 2.8903340549765587707457731596e-06 relative error = 0.22492745196354775010463932924373 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5064 x2[1] (analytic) = 0.00083145827176774343750163542019918 x2[1] (numeric) = 0.00083429773043718332061567553157015 absolute error = 2.83945866943988311404011137097e-06 relative error = 0.3415034483213424911267994911882 % h = 0.0002 x1[1] (analytic) = 0.0012847902658057999287229880316013 x1[1] (numeric) = 0.001281477374510871079925706995815 absolute error = 3.3128912949288487972810357863e-06 relative error = 0.25785463846513939022724647588433 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5066 x2[1] (analytic) = 0.00083164242372426227874944006741881 x2[1] (numeric) = 0.00083519873520913624525003111987828 absolute error = 3.55631148487396650059105245947e-06 relative error = 0.427625068589946070405989013458 % h = 0.0002 x1[1] (analytic) = 0.0012845733294469977701486259846507 x1[1] (numeric) = 0.0012808262570507201848333718951608 absolute error = 3.7470723962775853152540894899e-06 relative error = 0.29169781984269288569240534387278 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5068 x2[1] (analytic) = 0.00083182667105210352625198767426466 x2[1] (numeric) = 0.00083618259174217138825910156291898 absolute error = 4.35592069006786200711388865432e-06 relative error = 0.52365725236465976613986579025017 % h = 0.0002 x1[1] (analytic) = 0.0012843564364711289340639521960578 x1[1] (numeric) = 0.0012801636053896611817841781060522 absolute error = 4.1928310814677522797740900056e-06 relative error = 0.32645385365046231752288835764108 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.507 x2[1] (analytic) = 0.00083201101378508461244661319002326 x2[1] (numeric) = 0.0008372493652282580480861394259819 absolute error = 5.23835144317343563952623595864e-06 relative error = 0.62960121397221618133236064478381 % h = 0.0002 x1[1] (analytic) = 0.001284139586869517701405294158948 x1[1] (numeric) = 0.0012794894658615471213459103436553 absolute error = 4.6501210079705800593838152927e-06 relative error = 0.36211959007561395458920640471073 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5072 x2[1] (analytic) = 0.00083219545195703736710806275907346 x2[1] (numeric) = 0.00083839912087818472870452239932362 absolute error = 6.20366892114736159645964025016e-06 relative error = 0.74545816208902209309369420678029 % h = 0.0002 x1[1] (analytic) = 0.0012839227806334900880792892867217 x1[1] (numeric) = 0.001278803884866098320204055888511 absolute error = 5.1188957673917678752333982107e-06 relative error = 0.39869187186367192464637598795531 % h = 0.0002 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=0.89 NO POLE NO POLE t[1] = 0.5074 x2[1] (analytic) = 0.00083237998560180802293506624177892 x2[1] (numeric) = 0.00083963192392125826691079800159036 absolute error = 7.25193831945024397573175981144e-06 relative error = 0.87122929970584481941153260854942 % h = 0.0002 x1[1] (analytic) = 0.0012837060177543738446159255481629 x1[1] (numeric) = 0.0012781069088732430783452808302736 absolute error = 5.5991088811307662706447178893e-06 relative error = 0.43616753397522109422576378238981 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5076 x2[1] (analytic) = 0.00083256461475325722113917951078113 x2[1] (numeric) = 0.00084094783960379637195193861328902 absolute error = 8.38322485053915081275910250789e-06 relative error = 1.006915823947627524087941888768 % h = 0.0002 x1[1] (analytic) = 0.0012834892982234984558216514874832 x1[1] (numeric) = 0.0012773985844436609194309269936584 absolute error = 6.0907137798375363907244938248e-06 relative error = 0.47454340197988462036213404923824 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5078 x2[1] (analytic) = 0.00083274933944526001703589742384568 x2[1] (numeric) = 0.00084234693318182678529274153428221 absolute error = 9.59759373656676825684411043653e-06 relative error = 1.1525189251978574424501810983918 % h = 0.0002 x1[1] (analytic) = 0.001283272622032195140432555615423 x1[1] (numeric) = 0.0012766789583291460474048695255201 absolute error = 6.5936637030490930276860899029e-06 relative error = 0.51381628422862660849421164194597 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.508 x2[1] (analytic) = 0.00083293415971170588563803837477598 x2[1] (numeric) = 0.00084382926988491902227837187419271 absolute error = 1.089511017321313664033349941673e-05 relative error = 1.3080397827583561163512406550331 % h = 0.0002 x1[1] (analytic) = 0.0012830559891717968507676151575396 x1[1] (numeric) = 0.0012759480780182114186018061871577 absolute error = 7.1079111535854321658089703819e-06 relative error = 0.55398292931655587630423694022472 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5082 x2[1] (analytic) = 0.0008331190755864987272514013242712 x2[1] (numeric) = 0.00084539491472142113918700078669772 absolute error = 1.227583913492241193559946242652e-05 relative error = 1.4734795414785663356126957974355 % h = 0.0002 x1[1] (analytic) = 0.0012828393996336382723820141458102 x1[1] (numeric) = 0.0012752059948664318989247089416906 absolute error = 7.6334047672063734573052041196e-06 relative error = 0.59503978201685818838402241850154 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5084 x2[1] (analytic) = 0.00083330408710355687307269621296731 x2[1] (numeric) = 0.00084704393138553083933014864282526 absolute error = 1.373984428197396625745242985795e-05 relative error = 1.6488391806323253950381895114145 % h = 0.0002 x1[1] (analytic) = 0.0012826228534090558237205308396847 x1[1] (numeric) = 0.001274452780719718143042146263964 absolute error = 8.1700726893376806783845757207e-06 relative error = 0.63698168698792629353900810405557 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5086 x2[1] (analytic) = 0.00083348919429681309078974865926187 x2[1] (numeric) = 0.00084877637652655955466129731749078 absolute error = 1.528718222974646387154865822891e-05 relative error = 1.834118826536647227816197310866 % h = 0.0002 x1[1] (analytic) = 0.0012824063504893876557709944627208 x1[1] (numeric) = 0.0012736886019331708373343354090548 absolute error = 8.7177485562168184366590536660e-06 relative error = 0.67979611555182802726590380381655 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5088 x2[1] (analytic) = 0.00083367439720021459018397984488692 x2[1] (numeric) = 0.00085059227402459189619813820190909 absolute error = 1.691787682437730601415835702217e-05 relative error = 2.0293146678359995225338698661721 % h = 0.0002 x1[1] (analytic) = 0.0012821898908659736517178112409428 x1[1] (numeric) = 0.0012729139798646284782976159849897 absolute error = 9.2759110013451734201952559531e-06 relative error = 0.72344284317203195332379766197737 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.509 x2[1] (analytic) = 0.00083385969584772302873516249155556 x2[1] (numeric) = 0.00085249152115612474455268274741662 absolute error = 1.863182530840171581752025586106e-05 relative error = 2.2344077068577018979978705303528 % h = 0.0002 x1[1] (analytic) = 0.001281973474530155426595559729063 x1[1] (numeric) = 0.0012721304803064850385707100510401 absolute error = 9.8429942236703880248496780229e-06 relative error = 0.76780014713470224887089684396591 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5092 x2[1] (analytic) = 0.00083404509027331451722845383237174 x2[1] (numeric) = 0.00085447362029999434179426513387781 absolute error = 2.042853002667982456581130150607e-05 relative error = 2.4493316086766299054926213234444 % h = 0.0002 x1[1] (analytic) = 0.0012817571014732763269426554107106 x1[1] (numeric) = 0.0012713419960478300464587754366893 absolute error = 1.04151054254462804838799740213e-05 relative error = 0.81256467496649384555779616031425 % h = 0.0002 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.13 NO POLE NO POLE t[1] = 0.5094 x2[1] (analytic) = 0.00083423058051097962536370648205495 x2[1] (numeric) = 0.00085653709759566161766385226919744 absolute error = 2.230651708468199230014578714249e-05 relative error = 2.6739030677847954724688208683087 % h = 0.0002 x1[1] (analytic) = 0.0012815407716866814304550845588136 x1[1] (numeric) = 0.0012705562222460623663141148707134 absolute error = 1.09845494406190641409696881002e-05 relative error = 0.85713616634778678086589199267414 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5096 x2[1] (analytic) = 0.0008344161665947233873670581103952 x2[1] (numeric) = 0.00085867858043596976258032685952376 absolute error = 2.426241384124637521326874912856e-05 relative error = 2.9077113810320802908721803473739 % h = 0.0002 x1[1] (analytic) = 0.0012813244851617175456402073422847 x1[1] (numeric) = 0.0012697853118504635398182038097477 absolute error = 1.15391733112540058220035325370e-05 relative error = 0.9005660505892566712421513303496 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5098 x2[1] (analytic) = 0.00083460184855856530760480082371625 x2[1] (numeric) = 0.00086089175885086442357440928691679 absolute error = 2.628991029229911596960846320054e-05 relative error = 3.1499942562677312526814644889383 % h = 0.0002 x1[1] (analytic) = 0.0012811082418897332114706301651619 x1[1] (numeric) = 0.0012690448126940856947909379604858 absolute error = 1.20634291956475166796922046761e-05 relative error = 0.94164012073273610242906185226596 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.51 x2[1] (analytic) = 0.00083478762643653936619953115948893 x2[1] (numeric) = 0.0008631666806345237511174038194854 absolute error = 2.837905419798438491787265999647e-05 relative error = 3.3995537666419595983998882402707 % h = 0.0002 x1[1] (analytic) = 0.0012808920418620786970381472243591 x1[1] (numeric) = 0.0012683490861931777715355370827204 absolute error = 1.25429556689009255026101416387e-05 relative error = 0.97923597453746226942078280783063 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5102 x2[1] (analytic) = 0.00083497350026269402464858159959997 x2[1] (numeric) = 0.00086549025486403774521897862137068 absolute error = 3.051675460134372057039702177071e-05 relative error = 3.6548171399143486987323355234757 % h = 0.0002 x1[1] (analytic) = 0.0012806758850701060012077512721846 x1[1] (numeric) = 0.0012677024453783951276695082187267 absolute error = 1.29734396917108735382430534579e-05 relative error = 1.0130150682895609596204172671573 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5104 x2[1] (analytic) = 0.00083515947007109223144473450814446 x2[1] (numeric) = 0.00086784886145172292863590710336164 absolute error = 3.268939138063069719117259521718e-05 relative error = 3.9141496387328327691610094690332 % h = 0.0002 x1[1] (analytic) = 0.0012804597715051688522717135697878 x1[1] (numeric) = 0.0012671004581779165205882805182367 absolute error = 1.33593133272523316834330515511e-05 relative error = 1.0433215962379341279762047420685 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5106 x2[1] (analytic) = 0.00083534553589581142769921939997556 x2[1] (numeric) = 0.00087023040298601898671604976853646 absolute error = 3.488486709020755901683036856090e-05 relative error = 4.1761002592535046784275617847692 % h = 0.0002 x1[1] (analytic) = 0.0012802437011586227076037330176972 x1[1] (numeric) = 0.0012665467601887454651605033307163 absolute error = 1.36969409698772424432296869809e-05 relative error = 1.0698698191197103939749703512904 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5108 x2[1] (analytic) = 0.00083553169777094355276699444660709 x2[1] (numeric) = 0.00087262232144069692530834239082586 absolute error = 3.709062366975337254134794421877e-05 relative error = 4.4391641596249247568613135260625 % h = 0.0002 x1[1] (analytic) = 0.0012800276740218247533131544496155 x1[1] (numeric) = 0.0012660430513527964357579458279371 absolute error = 1.39846226690283175552086216784e-05 relative error = 1.0925250252667487768361854524201 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.511 x2[1] (analytic) = 0.00083571795573059504987431312643056 x2[1] (numeric) = 0.00087501207745645315907868120809912 absolute error = 3.929412172585810920436808166856e-05 relative error = 4.701840071332043881982803132291 % h = 0.0002 x1[1] (analytic) = 0.0012798116900861339038992560756415 x1[1] (numeric) = 0.0012655912074983859605004465574916 absolute error = 1.42204825877479433988095181499e-05 relative error = 1.111138669689044353460475446109 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5112 x2[1] (analytic) = 0.00083590430980888687174857692657073 x2[1] (numeric) = 0.00087738710526159298945474673380613 absolute error = 4.148279545270611770616980723540e-05 relative error = 4.9626249040623256750174551629041 % h = 0.0002 x1[1] (analytic) = 0.0012795957493429108019056060610889 x1[1] (numeric) = 0.001265193093242743534150183948238 absolute error = 1.44026561001672677554221128509e-05 relative error = 1.1255629840567398368905082519731 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=22.8MB, alloc=4.3MB, time=1.37 t[1] = 0.5114 x2[1] (analytic) = 0.00083609076003995448625047500406982 x2[1] (numeric) = 0.00087973481424594513473168630970469 absolute error = 4.364405420599064848121130563487e-05 relative error = 5.2200139377099465529551009744251 % h = 0.0002 x1[1] (analytic) = 0.0012793798517835178175744882270767 x1[1] (numeric) = 0.0012648505684576735519947408813833 absolute error = 1.45292833258442655797473456934e-05 relative error = 1.1356504720306277346569371157669 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5116 x2[1] (analytic) = 0.00083627730645794788200841171445351 x2[1] (numeric) = 0.00088204258891436714183203978670534 absolute error = 4.576528245641925982362807225183e-05 relative error = 5.4725008203628161379143773979468 % h = 0.0002 x1[1] (analytic) = 0.0012791639973993190485013968590695 x1[1] (numeric) = 0.0012645654881736119411207294276581 absolute error = 1.45985092257071073806674314114e-05 relative error = 1.1412539170417147925835138123205 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5118 x2[1] (analytic) = 0.00083646394909703157405522291609771 x2[1] (numeric) = 0.00088429778886016896939526504897476 absolute error = 4.783383976313739534004213287705e-05 relative error = 5.7185775686775676582787661420868 % h = 0.0002 x1[1] (analytic) = 0.0012789481861816803192896006095455 x1[1] (numeric) = 0.0012643397025631196458047636856388 absolute error = 1.46084836185606734848369239067e-05 relative error = 1.1422263838673971850503549323486 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.512 x2[1] (analytic) = 0.00083665068799138460946718195917937 x2[1] (numeric) = 0.00088648774873853070748136315045331 absolute error = 4.983706074714609801418119127394e-05 relative error = 5.9567345682573913045344843082381 % h = 0.0002 x1[1] (analytic) = 0.0012787324181219691812047754809758 x1[1] (numeric) = 0.001264175056923622584519222042895 absolute error = 1.45573611983465966855534380808e-05 relative error = 1.1384212202679977449771002596744 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5122 x2[1] (analytic) = 0.00083683752317520057300529626835942 x2[1] (numeric) = 0.00088859977824011466237291099448442 absolute error = 5.176225506491408936761472612500e-05 relative error = 6.1854605740566352446950222666469 % h = 0.0002 x1[1] (analytic) = 0.0012785166932115549118297068753011 x1[1] (numeric) = 0.0012640733916574052039819916705593 absolute error = 1.44433015541497078477152047418e-05 relative error = 1.1296920588396094417431175982815 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5124 x2[1] (analytic) = 0.00083702445468268759275889542871143 x2[1] (numeric) = 0.00089062116206562851641464031024111 absolute error = 5.359670738294092365574488152968e-05 relative error = 6.403242710902539549241759260689 % h = 0.0002 x1[1] (analytic) = 0.0012783010114418085147190606960915 x1[1] (numeric) = 0.0012640365422395764395854356512425 absolute error = 1.42644692022320751336250448490e-05 relative error = 1.1158928198095562360912347064218 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5126 x2[1] (analytic) = 0.00083721148254806834579151168477479 x2[1] (numeric) = 0.00089253915990469801117723839971887 absolute error = 5.532767735662966538572671494408e-05 relative error = 6.6085664745350690768727344768788 % h = 0.0002 x1[1] (analytic) = 0.0012780853728041027190542234895835 x1[1] (numeric) = 0.0012640663391308226814723067236894 absolute error = 1.40190336732800375819167658941e-05 relative error = 1.096877718154496961532905630532 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5128 x2[1] (analytic) = 0.0008373986068055800637890537629762 x2[1] (numeric) = 0.00089434100643459310259889555909374 absolute error = 5.694239962901303880984179611754e-05 relative error = 6.7999157350202554903779858798814 % h = 0.0002 x1[1] (analytic) = 0.0012778697772898119792982116107845 x1[1] (numeric) = 0.0012641646074257788732714545142486 absolute error = 1.37051698640331060267570965359e-05 relative error = 1.0725012914148347375860101828287 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.513 x2[1] (analytic) = 0.00083758582748947453871027492802935 x2[1] (numeric) = 0.00089601391141295323211990127912323 absolute error = 5.842808392347869340962635109388e-05 relative error = 6.9757727513856394221561295645634 % h = 0.0002 x1[1] (analytic) = 0.0012776542248903124748506494008434 x1[1] (numeric) = 0.0012643331652722698792472913998206 absolute error = 1.33210596180425956033580010228e-05 relative error = 1.0426185237391766194641745362828 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5132 x2[1] (analytic) = 0.00083777314463401812843953618428816 x2[1] (numeric) = 0.00089754506020372379957292688549532 absolute error = 5.977191556970567113339070120716e-05 relative error = 7.1346182379499739740803223782495 % h = 0.0002 x1[1] (analytic) = 0.0012774387155969821097028163618863 x1[1] (numeric) = 0.0012645738171760943554562354832977 absolute error = 1.28648984208877542465808785886e-05 relative error = 1.0070853704223012182408611131002 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=26.7MB, alloc=4.3MB, time=1.60 t[1] = 0.5134 x2[1] (analytic) = 0.00083796055827349176244186553339435 x2[1] (numeric) = 0.00089892161611640263487578831878954 absolute error = 6.096105784291087243392278539519e-05 relative error = 7.2749316469635714830627002759362 % h = 0.0002 x1[1] (analytic) = 0.0012772232494012005120927633155174 x1[1] (numeric) = 0.0012648883293203322373143885567562 absolute error = 1.23349200808682747783747587612e-05 relative error = 0.96576069114395191689112553701488 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5136 x2[1] (analytic) = 0.00083814806844219094742031419992721 x2[1] (numeric) = 0.00090013072929395869062343910277814 absolute error = 6.198266085176774320312490285093e-05 relative error = 7.3951922321995822590153710246215 % h = 0.0002 x1[1] (analytic) = 0.0012770078262943490341604975311922 x1[1] (numeric) = 0.0012652783535275161760101175543782 absolute error = 1.17294727668328581503799768140e-05 relative error = 0.91851220684134055893375703951629 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5138 x2[1] (analytic) = 0.00083833567517442577297561073712817 x2[1] (numeric) = 0.00090115956533272785310857276095478 absolute error = 6.282389015830208013296202382661e-05 relative error = 7.4938824648289979688387105421658 % h = 0.0002 x1[1] (analytic) = 0.0012767924462678107516032368106682 x1[1] (numeric) = 0.0012657452366686092745882304354977 absolute error = 1.10472095992014770150063751705e-05 relative error = 0.86523143456037444374124753504093 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.514 x2[1] (analytic) = 0.0008385233785045209172681139251402 x2[1] (numeric) = 0.0009019953822556114367820102719205 absolute error = 6.347200375109051951389634678030e-05 relative error = 7.5694972111917460161030175911496 % h = 0.0002 x1[1] (analytic) = 0.0012765771093129704633307325147448 x1[1] (numeric) = 0.0012662896414880765961305960896766 absolute error = 1.02874678248938672001364250682e-05 relative error = 0.80586341003955388580626604884747 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5142 x2[1] (analytic) = 0.00083871117846681565268206537456791 x2[1] (numeric) = 0.00090262570141712417338914486419364 absolute error = 6.391452295030852070707948962573e-05 relative error = 7.6205640977798598835382744985896 % h = 0.0002 x1[1] (analytic) = 0.0012763618154212146911206615185049 x1[1] (numeric) = 0.0012669109659642103278669056986766 absolute error = 9.4508494570043632537558198283e-06 relative error = 0.74045222466056536662809461456082 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5144 x2[1] (analytic) = 0.00083889907509566385149214274853093 x2[1] (numeric) = 0.00090303861817626327506093420512186 absolute error = 6.413954308059942356879145659093e-05 relative error = 7.6456805096948367859904107259841 % h = 0.0002 x1[1] (analytic) = 0.0012761465645839316792740870812734 x1[1] (numeric) = 0.0012676067000617396094291125823351 absolute error = 8.5398645221920698449744989383e-06 relative error = 0.66919151445401286972108999975063 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5146 x2[1] (analytic) = 0.00083908706842543399153231451674996 x2[1] (numeric) = 0.0009032232602147844903404763946313 absolute error = 6.413619178935049880816187788134e-05 relative error = 7.6435681352715308198247792380516 % h = 0.0002 x1[1] (analytic) = 0.0012759313567925113942709886175111 x1[1] (numeric) = 0.0012683720404492090461709956051873 absolute error = 7.5593163433023480999930123238e-06 relative error = 0.59245478238776635595642291485278 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5148 x2[1] (analytic) = 0.00083927515849050916186699715557149 x2[1] (numeric) = 0.00090317031987057060594499489675351 absolute error = 6.389516138006144407799774118202e-05 relative error = 7.6131362561690778932920961870563 % h = 0.0002 x1[1] (analytic) = 0.0012757161920383455244258603548666 x1[1] (numeric) = 0.0012692002049355174689778262811008 absolute error = 6.5159871028280554480340737658e-06 relative error = 0.51077090214060696558075513018622 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.515 x2[1] (analytic) = 0.00083946334532528706846451570820467 x2[1] (numeric) = 0.00090287248114552785735904936389313 absolute error = 6.340913582024078889453365568846e-05 relative error = 7.5535324053571540717635681559108 % h = 0.0002 x1[1] (analytic) = 0.0012755010703128274795433788656077 x1[1] (numeric) = 0.001270083651657865274538688087909 absolute error = 5.4174186549622050046907776987e-06 relative error = 0.42472866397779948787269622948099 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5152 x2[1] (analytic) = 0.00083965162896418003987286861981033 x2[1] (numeric) = 0.00090232452712004262633264945288806 absolute error = 6.267289815586258645978083307773e-05 relative error = 7.4641548939978586960662219592683 % h = 0.0002 x1[1] (analytic) = 0.0012752859916073523905741394576611 x1[1] (numeric) = 0.0012710152960964653668616890348754 absolute error = 4.2706955108870237124504227857e-06 relative error = 0.33488139436898382412815102347551 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5154 x2[1] (analytic) = 0.00083984000944161503289779776245017 x2[1] (numeric) = 0.00090152315349317021037604315507385 absolute error = 6.168314405155517747824539262368e-05 relative error = 7.3446303293607658828524819918931 % h = 0.0002 x1[1] (analytic) = 0.0012750709559133171092704614114891 x1[1] (numeric) = 0.0012719881862244786944205641447963 absolute error = 3.0827696888384148498972666928e-06 relative error = 0.24177240290366947686324950585301 % h = 0.0002 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.85 NO POLE NO POLE t[1] = 0.5156 x2[1] (analytic) = 0.0008400284867920336382831645652709 x2[1] (numeric) = 0.0009004668750119155379867514657139 absolute error = 6.043838821988189970358690044300e-05 relative error = 7.1948022204209686658065061111293 % h = 0.0002 x1[1] (analytic) = 0.0012748559632221202078422620490348 x1[1] (numeric) = 0.0012729946504825059142682041912918 absolute error = 1.8613127396142935740578577430e-06 relative error = 0.14600180673822475249130988812576 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5158 x2[1] (analytic) = 0.00084021706104989208639363316566634 x2[1] (numeric) = 0.00089915613592493747530626104884742 absolute error = 5.893907487504538891262788318108e-05 relative error = 7.0147438807536409731806410888166 % h = 0.0002 x1[1] (analytic) = 0.0012746410135251619786129996209726 x1[1] (numeric) = 0.0012740268505618765623236618771576 absolute error = 6.141629632854162893377438150e-07 relative error = 0.048183210548582621784941715933528 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.516 x2[1] (analytic) = 0.00084040573224966125289966149752755 x2[1] (numeric) = 0.00089759328488579639490782545184948 absolute error = 5.718755263613514200816395432193e-05 relative error = 6.8047551845048939953891656197995 % h = 0.0002 x1[1] (analytic) = 0.0012744261068138444336756849984992 x1[1] (numeric) = 0.0012750766378522043380459523718736 absolute error = 6.505310383599043702673733744e-07 relative error = 0.051045018215004874582804309045537 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5162 x2[1] (analytic) = 0.00084059450042582666446480123305994 x2[1] (numeric) = 0.00089578258549417971425425226579706 absolute error = 5.518808506835304978945103273712e-05 relative error = 6.5653635659519519942814882690259 % h = 0.0002 x1[1] (analytic) = 0.0012742112430795713045489621559082 x1[1] (numeric) = 0.0012761355732861470664683905078837 absolute error = 1.9243302065757619194283519755e-06 relative error = 0.15102128607223349636964831683026 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5164 x2[1] (analytic) = 0.00084078336561288850443530749501307 x2[1] (numeric) = 0.00089373022200997225020890279472242 absolute error = 5.294685639708374577359529970935e-05 relative error = 6.2973244431980606769306919604631 % h = 0.0002 x1[1] (analytic) = 0.0012739964223137480418332574301895 x1[1] (numeric) = 0.0012771949262969095020880364139585 absolute error = 3.1985039831614602547789837690e-06 relative error = 0.25106067231747392706331308015118 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5166 x2[1] (analytic) = 0.00084097232784536161853205925653825 x2[1] (numeric) = 0.0008914443054351798800383856571772 absolute error = 5.047197758981826150632640063895e-05 relative error = 6.0016216846434776081345726711176 % h = 0.0002 x1[1] (analytic) = 0.0012737816445077818148669975439001 x1[1] (numeric) = 0.0012782456752694611773127273517463 absolute error = 4.4640307616793624457298078462e-06 relative error = 0.35045494499996232994215302589782 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5168 x2[1] (analytic) = 0.0008411613871577755205447913462566 x2[1] (numeric) = 0.00088893487959205864098220784357596 absolute error = 4.777349243428312043741649731936e-05 relative error = 5.6794680739811836036545802126891 % h = 0.0002 x1[1] (analytic) = 0.0012735669096530815113828963775561 x1[1] (numeric) = 0.0012792785079374966500120678874012 absolute error = 5.7115982844151386291715098451e-06 relative error = 0.44847257267158212363934645928667 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.517 x2[1] (analytic) = 0.0008413505435846743980286389764889 x2[1] (numeric) = 0.00088621392721178277604846034190282 absolute error = 4.486338362710837801982136541392e-05 relative error = 5.3323057754218090908544826783238 % h = 0.0002 x1[1] (analytic) = 0.0012733522177410577371643104777951 x1[1] (numeric) = 0.0012802838217862447343356617766865 absolute error = 6.9316040451869971713512988914e-06 relative error = 0.54435873661756734788147979622852 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5172 x2[1] (analytic) = 0.00084153979716061711800299571296767 x2[1] (numeric) = 0.0008832953760329395298210840181273 absolute error = 4.175557887232241181808830515963e-05 relative error = 4.9618067990613283778615293433214 % h = 0.0002 x1[1] (analytic) = 0.0012731375687631228157016632875658 x1[1] (numeric) = 0.0012812517244650833495064671601028 absolute error = 8.1141557019605338048038725370e-06 relative error = 0.63733534388146202147997420250729 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5174 x2[1] (analytic) = 0.00084172914792017723265268580471965 x2[1] (numeric) = 0.0008801951049080135118955048312484 absolute error = 3.846595698783627924281902652875e-05 relative error = 4.5698734661715764543997717275839 % h = 0.0002 x1[1] (analytic) = 0.0012729229627106907878489380845994 x1[1] (numeric) = 0.0012821720342319846570881188460468 absolute error = 9.2490715212938692391807614474e-06 relative error = 0.72660104281550249570222355900372 % h = 0.0002 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.09 Real estimate of pole used NO POLE Radius of convergence = 1.603e-05 Order of pole = 48.75 t[1] = 0.5176 x2[1] (analytic) = 0.00084191859589794298503145179317699 x2[1] (numeric) = 0.0008769309499099387120677892960702 absolute error = 3.501235401199572703633750289321e-05 relative error = 4.1586388734713147652013600524351 % h = 0.0002 x1[1] (analytic) = 0.0012727083995751774114802396144245 x1[1] (numeric) = 0.0012830342805229329765801344957537 absolute error = 1.03258809477555650998948813292e-05 relative error = 0.81133124847783541863541646982219 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 8.139e-05 Order of pole = 428.6 t[1] = 0.5178 x2[1] (analytic) = 0.00084210814112851731476775831994364 x2[1] (numeric) = 0.00087352271040531001582216768523604 absolute error = 3.141456927679270105440936529240e-05 relative error = 3.7304673524107878901034318558959 % h = 0.0002 x1[1] (analytic) = 0.0012724938793480001611464244041865 x1[1] (numeric) = 0.001283827705012963364257381461179 absolute error = 1.13338256649632031109570569925e-05 relative error = 0.89067820670150677529032973585581 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.518 x2[1] (analytic) = 0.00084229778364651786377291305301299 x2[1] (numeric) = 0.00086999215496209044110130534481862 absolute error = 2.769437131557257732839229180563e-05 relative error = 3.2879549077853101148150655365017 % h = 0.0002 x1[1] (analytic) = 0.0012722794020205782277317997435378 x1[1] (numeric) = 0.001284541264447191387485364700766 absolute error = 1.22618624266131597535649572282e-05 relative error = 0.96377119735959010061524265881789 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5182 x2[1] (analytic) = 0.00084248752348657698195150565160216 x2[1] (numeric) = 0.00086636302662176480081113190475821 absolute error = 2.387550313518781885962625315605e-05 relative error = 2.8339295799159947724282230516694 % h = 0.0002 x1[1] (analytic) = 0.0012720649675843325181108913188656 x1[1] (numeric) = 0.0012851636390486746027952411691412 absolute error = 1.30986714643420846843498502756e-05 relative error = 1.0297171762552841673311315423753 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5184 x2[1] (analytic) = 0.00084267736068334173291416569013793 x2[1] (numeric) = 0.00086266104607997454998877170710713 absolute error = 1.998368539663281707460601696920e-05 relative error = 2.3714515577382663875931555714707 % h = 0.0002 x1[1] (analytic) = 0.0012718505760306856548052794871294 x1[1] (numeric) = 0.0012856832558962353937260702771771 absolute error = 1.38326798655497389207907900477e-05 relative error = 1.0876025946947403782855619874687 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5186 x2[1] (analytic) = 0.00084286729527147389969264046229865 x2[1] (numeric) = 0.00085891390893923946625422027953704 absolute error = 1.604661366776556656157981723839e-05 relative error = 1.9038125880299119075459716094073 % h = 0.0002 x1[1] (analytic) = 0.0012716362273510619756405041755803 x1[1] (numeric) = 0.0012860883458176980934434125224392 absolute error = 1.44521184666361178029083468589e-05 relative error = 1.1364978565246793629355154332623 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5188 x2[1] (analytic) = 0.00084305732728564999045719358638684 x2[1] (numeric) = 0.00085515126861245697724666919161986 absolute error = 1.209394132680698678947560523302e-05 relative error = 1.4345336829875201904171963995833 % h = 0.0002 x1[1] (analytic) = 0.0012714219215368875334030383936394 x1[1] (numeric) = 0.001286367061420974051820072953735 absolute error = 1.49451398840865184170345600956e-05 relative error = 1.175466588307752233972393576781 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.519 x2[1] (analytic) = 0.00084324745676056124423632533367627 x2[1] (numeric) = 0.00085140468985416416828802223392587 absolute error = 8.15723309360292405169690024960e-06 relative error = 0.96735934727155153894137483192576 % h = 0.0002 x1[1] (analytic) = 0.0012712076585795900954973303432135 x1[1] (numeric) = 0.0012865076827205793463406788564452 absolute error = 1.53000241409892508433485132317e-05 relative error = 1.2035818096065473736834134645983 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5192 x2[1] (analytic) = 0.00084343768373091363663881560174858 x2[1] (numeric) = 0.00084770755202168292703219043217149 absolute error = 4.26986829076929039337483042291e-06 relative error = 0.50624585231735139629383971756377 % h = 0.0002 x1[1] (analytic) = 0.0012709934384705991436029141137296 x1[1] (numeric) = 0.0012864989129491383430009961915604 absolute error = 1.55054744785391993980820778308e-05 relative error = 1.2199492152530002943029346438631 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5194 x2[1] (analytic) = 0.00084362800823142788557809045520348 x2[1] (numeric) = 0.00084409488169664841864773302356079 absolute error = 4.6687346522053306964256835731e-07 relative error = 0.055341152814411800542026958154936 % h = 0.0002 x1[1] (analytic) = 0.0012707792612013458733315889481744 x1[1] (numeric) = 0.0012863302176959055404793214346149 absolute error = 1.55509564945596671477324864405e-05 relative error = 1.223733890641116581644189944473 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=38.1MB, alloc=4.4MB, time=2.32 t[1] = 0.5196 x2[1] (analytic) = 0.00084381843029683945699891315649824 x2[1] (numeric) = 0.00084060310721987376438251011868665 absolute error = 3.21532307696569261640303781159e-06 relative error = 0.38104442395677496844968300077217 % h = 0.0002 x1[1] (analytic) = 0.001270565126763263193884667066423 x1[1] (numeric) = 0.0012859921053603116918302687150214 absolute error = 1.54269785970484979456016485984e-05 relative error = 1.2141824352088418890729111391457 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5198 x2[1] (analytic) = 0.00084400894996189857060640061004145 x2[1] (numeric) = 0.00083726975350761275709391412790397 absolute error = 6.73919645428581351248648213748e-06 relative error = 0.79847452501422451975902091941169 % h = 0.0002 x1[1] (analytic) = 0.0012703510351477857277102900321493 x1[1] (numeric) = 0.0012854762406484485449923872756961 absolute error = 1.51252055006628172820972435468e-05 relative error = 1.1906319656679173853141766646753 % h = 0.0002 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.52 x2[1] (analytic) = 0.00084419956726137020559736614303792 x2[1] (numeric) = 0.00083413312094142166334828364587771 absolute error = 1.006644631994854224908249716021e-05 relative error = 1.1924249561753090415329233152338 % h = 0.0002 x1[1] (analytic) = 0.00127013698634634981016081364961 x1[1] (numeric) = 0.0012847753927529076517715166016845 absolute error = 1.46384064065578416107029520745e-05 relative error = 1.1525061126411556113427387816493 % h = 0.0002 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 = 2 Seconds Elapsed Time(since restart) = 2 Seconds Expected Time Remaining = 8 Minutes 38 Seconds Optimized Time Remaining = 8 Minutes 35 Seconds Time to Timeout = 14 Minutes 57 Seconds Percent Done = 0.4489 % > quit memory used=39.1MB, alloc=4.4MB, time=2.38