|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGMASSIVE, > INFO, > glob_iolevel, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_clock_start_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_look_poles, > glob_clock_sec, > years_in_century, > sec_in_min, > djd_debug2, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin_init, > glob_hmax, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > djd_debug, > glob_iter, > glob_warned, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin, > glob_start, > glob_not_yet_start_msg, > glob_initial_pass, > days_in_year, > glob_smallish_float, > glob_max_order, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_unchanged_h_cnt, > glob_percent_done, > glob_max_sec, > glob_warned2, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_last_good_h, > glob_reached_optimal_h, > min_in_hour, > glob_max_minutes, > glob_orig_start_sec, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > centuries_in_millinium, > glob_log10normmin, > glob_log10_abserr, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_h, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_4D0, > array_const_0D0, > array_const_1, > array_const_2, > #END CONST > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_norms, > array_t, > array_last_rel_error, > array_1st_rel_error, > array_x2, > array_x1, > array_m1, > array_x1_init, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_higher, > array_x1_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > array_x2_higher_work2, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float, glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2, glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax, glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter, glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start, glob_not_yet_start_msg, glob_initial_pass, days_in_year, glob_smallish_float, glob_max_order, glob_display_flag, glob_dump, glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done, glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr, glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes, glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_dump_analytic, glob_large_float, centuries_in_millinium, glob_log10normmin, glob_log10_abserr, glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h, hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0, array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t, array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1, array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole, array_real_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, array_x2_higher_work2, glob_last; if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGMASSIVE, > INFO, > glob_iolevel, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_clock_start_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_look_poles, > glob_clock_sec, > years_in_century, > sec_in_min, > djd_debug2, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin_init, > glob_hmax, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > djd_debug, > glob_iter, > glob_warned, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin, > glob_start, > glob_not_yet_start_msg, > glob_initial_pass, > days_in_year, > glob_smallish_float, > glob_max_order, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_unchanged_h_cnt, > glob_percent_done, > glob_max_sec, > glob_warned2, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_last_good_h, > glob_reached_optimal_h, > min_in_hour, > glob_max_minutes, > glob_orig_start_sec, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > centuries_in_millinium, > glob_log10normmin, > glob_log10_abserr, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_h, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_4D0, > array_const_0D0, > array_const_1, > array_const_2, > #END CONST > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_norms, > array_t, > array_last_rel_error, > array_1st_rel_error, > array_x2, > array_x1, > array_m1, > array_x1_init, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_higher, > array_x1_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > array_x2_higher_work2, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_t[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float, glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2, glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax, glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter, glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start, glob_not_yet_start_msg, glob_initial_pass, days_in_year, glob_smallish_float, glob_max_order, glob_display_flag, glob_dump, glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done, glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr, glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes, glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_dump_analytic, glob_large_float, centuries_in_millinium, glob_log10normmin, glob_log10_abserr, glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h, hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0, array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t, array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1, array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole, array_real_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, array_x2_higher_work2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_t[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(t_start,t_end) > global > DEBUGMASSIVE, > INFO, > glob_iolevel, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_clock_start_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_look_poles, > glob_clock_sec, > years_in_century, > sec_in_min, > djd_debug2, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin_init, > glob_hmax, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > djd_debug, > glob_iter, > glob_warned, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin, > glob_start, > glob_not_yet_start_msg, > glob_initial_pass, > days_in_year, > glob_smallish_float, > glob_max_order, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_unchanged_h_cnt, > glob_percent_done, > glob_max_sec, > glob_warned2, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_last_good_h, > glob_reached_optimal_h, > min_in_hour, > glob_max_minutes, > glob_orig_start_sec, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > centuries_in_millinium, > glob_log10normmin, > glob_log10_abserr, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_h, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_4D0, > array_const_0D0, > array_const_1, > array_const_2, > #END CONST > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_norms, > array_t, > array_last_rel_error, > array_1st_rel_error, > array_x2, > array_x1, > array_m1, > array_x1_init, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_higher, > array_x1_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > array_x2_higher_work2, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float, glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2, glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax, glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter, glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start, glob_not_yet_start_msg, glob_initial_pass, days_in_year, glob_smallish_float, glob_max_order, glob_display_flag, glob_dump, glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done, glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr, glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes, glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_dump_analytic, glob_large_float, centuries_in_millinium, glob_log10normmin, glob_log10_abserr, glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h, hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0, array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t, array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1, array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole, array_real_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, array_x2_higher_work2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGMASSIVE, > INFO, > glob_iolevel, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_clock_start_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_look_poles, > glob_clock_sec, > years_in_century, > sec_in_min, > djd_debug2, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin_init, > glob_hmax, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > djd_debug, > glob_iter, > glob_warned, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin, > glob_start, > glob_not_yet_start_msg, > glob_initial_pass, > days_in_year, > glob_smallish_float, > glob_max_order, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_unchanged_h_cnt, > glob_percent_done, > glob_max_sec, > glob_warned2, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_last_good_h, > glob_reached_optimal_h, > min_in_hour, > glob_max_minutes, > glob_orig_start_sec, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > centuries_in_millinium, > glob_log10normmin, > glob_log10_abserr, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_h, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_4D0, > array_const_0D0, > array_const_1, > array_const_2, > #END CONST > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_norms, > array_t, > array_last_rel_error, > array_1st_rel_error, > array_x2, > array_x1, > array_m1, > array_x1_init, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_higher, > array_x1_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > array_x2_higher_work2, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1]; > rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1]; > rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float, glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2, glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax, glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter, glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start, glob_not_yet_start_msg, glob_initial_pass, days_in_year, glob_smallish_float, glob_max_order, glob_display_flag, glob_dump, glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done, glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr, glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes, glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_dump_analytic, glob_large_float, centuries_in_millinium, glob_log10normmin, glob_log10_abserr, glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h, hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0, array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t, array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1, array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole, array_real_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, array_x2_higher_work2, glob_last; n := glob_max_terms; m := n - 3; while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or abs(array_x2_higher[1, m - 1]) < glob_small_float or abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or abs(array_x1_higher[1, m - 1]) < glob_small_float or abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_x2_higher[1, m]) or glob_large_float <= abs(array_x2_higher[1, m - 1]) or glob_large_float <= abs(array_x2_higher[1, m - 2]) or glob_large_float <= abs(array_x2_higher[1, m - 3]) or glob_large_float <= abs(array_x2_higher[1, m - 4]) or glob_large_float <= abs(array_x2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_x1_higher[1, m]) or glob_large_float <= abs(array_x1_higher[1, m - 1]) or glob_large_float <= abs(array_x1_higher[1, m - 2]) or glob_large_float <= abs(array_x1_higher[1, m - 3]) or glob_large_float <= abs(array_x1_higher[1, m - 4]) or glob_large_float <= abs(array_x1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGMASSIVE, > INFO, > glob_iolevel, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_clock_start_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_look_poles, > glob_clock_sec, > years_in_century, > sec_in_min, > djd_debug2, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin_init, > glob_hmax, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > djd_debug, > glob_iter, > glob_warned, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin, > glob_start, > glob_not_yet_start_msg, > glob_initial_pass, > days_in_year, > glob_smallish_float, > glob_max_order, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_unchanged_h_cnt, > glob_percent_done, > glob_max_sec, > glob_warned2, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_last_good_h, > glob_reached_optimal_h, > min_in_hour, > glob_max_minutes, > glob_orig_start_sec, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > centuries_in_millinium, > glob_log10normmin, > glob_log10_abserr, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_h, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_4D0, > array_const_0D0, > array_const_1, > array_const_2, > #END CONST > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_norms, > array_t, > array_last_rel_error, > array_1st_rel_error, > array_x2, > array_x1, > array_m1, > array_x1_init, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_higher, > array_x1_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > array_x2_higher_work2, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float, glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2, glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax, glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter, glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start, glob_not_yet_start_msg, glob_initial_pass, days_in_year, glob_smallish_float, glob_max_order, glob_display_flag, glob_dump, glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done, glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr, glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes, glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_dump_analytic, glob_large_float, centuries_in_millinium, glob_log10normmin, glob_log10_abserr, glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h, hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0, array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t, array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1, array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole, array_real_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, array_x2_higher_work2, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x2[iii]) then array_norms[iii] := abs(array_x2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x1[iii]) then array_norms[iii] := abs(array_x1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGMASSIVE, > INFO, > glob_iolevel, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_clock_start_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_look_poles, > glob_clock_sec, > years_in_century, > sec_in_min, > djd_debug2, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin_init, > glob_hmax, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > djd_debug, > glob_iter, > glob_warned, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin, > glob_start, > glob_not_yet_start_msg, > glob_initial_pass, > days_in_year, > glob_smallish_float, > glob_max_order, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_unchanged_h_cnt, > glob_percent_done, > glob_max_sec, > glob_warned2, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_last_good_h, > glob_reached_optimal_h, > min_in_hour, > glob_max_minutes, > glob_orig_start_sec, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > centuries_in_millinium, > glob_log10normmin, > glob_log10_abserr, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_h, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_4D0, > array_const_0D0, > array_const_1, > array_const_2, > #END CONST > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_norms, > array_t, > array_last_rel_error, > array_1st_rel_error, > array_x2, > array_x1, > array_m1, > array_x1_init, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_higher, > array_x1_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > array_x2_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp4[1] := (array_const_2D0[1] * (array_x2[1])); > #emit pre sub $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp6[1] := array_x1_higher[3,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp8[1] := array_x1_higher[2,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp10[1] := array_tmp9[1] + array_x1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2); > array_x2[3] := temporary; > array_x2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,2] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,1] := temporary > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult $eq_no = 2 i = 1 > array_tmp12[1] := (array_const_4D0[1] * (array_x2[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp13[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1])); > # emit pre mult $eq_no = 2 i = 1 > array_tmp16[1] := (array_const_2D0[1] * (array_x1[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_x1[2] := temporary; > array_x1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,1] := temporary > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp4[2] := ats(2,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp6[2] := array_x1_higher[3,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp8[2] := array_x1_higher[2,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2])); > #emit pre add $eq_no = 1 i = 2 > array_tmp10[2] := array_tmp9[2] + array_x1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3); > array_x2[4] := temporary; > array_x2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,2] := temporary > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult $eq_no = 2 i = 2 > array_tmp12[2] := ats(2,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 2 > array_tmp13[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2])); > # emit pre mult $eq_no = 2 i = 2 > array_tmp16[2] := ats(2,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2])); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_x1[3] := temporary; > array_x1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,2] := temporary > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp4[3] := ats(3,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp6[3] := array_x1_higher[3,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp8[3] := array_x1_higher[2,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3])); > #emit pre add $eq_no = 1 i = 3 > array_tmp10[3] := array_tmp9[3] + array_x1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4); > array_x2[5] := temporary; > array_x2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,3] := temporary > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult $eq_no = 2 i = 3 > array_tmp12[3] := ats(3,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 3 > array_tmp13[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3])); > # emit pre mult $eq_no = 2 i = 3 > array_tmp16[3] := ats(3,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3])); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_x1[4] := temporary; > array_x1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,3] := temporary > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp4[4] := ats(4,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp6[4] := array_x1_higher[3,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp8[4] := array_x1_higher[2,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4])); > #emit pre add $eq_no = 1 i = 4 > array_tmp10[4] := array_tmp9[4] + array_x1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5); > array_x2[6] := temporary; > array_x2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,4] := temporary > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult $eq_no = 2 i = 4 > array_tmp12[4] := ats(4,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 4 > array_tmp13[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4])); > # emit pre mult $eq_no = 2 i = 4 > array_tmp16[4] := ats(4,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4])); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_x1[5] := temporary; > array_x1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,4] := temporary > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp4[5] := ats(5,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp6[5] := array_x1_higher[3,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp8[5] := array_x1_higher[2,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5])); > #emit pre add $eq_no = 1 i = 5 > array_tmp10[5] := array_tmp9[5] + array_x1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6); > array_x2[7] := temporary; > array_x2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,5] := temporary > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult $eq_no = 2 i = 5 > array_tmp12[5] := ats(5,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 5 > array_tmp13[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5])); > # emit pre mult $eq_no = 2 i = 5 > array_tmp16[5] := ats(5,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5])); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_x1[6] := temporary; > array_x1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,5] := temporary > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 1 > array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1); > #emit add $eq_no = 1 > array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; > #emit mult $eq_no = 1 > array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1); > #emit sub $eq_no = 1 > array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk])); > #emit diff $eq_no = 1 > array_tmp6[kkk] := array_x1_higher[3,kkk]; > #emit sub $eq_no = 1 > array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk])); > #emit diff $eq_no = 1 > array_tmp8[kkk] := array_x1_higher[2,kkk]; > #emit sub $eq_no = 1 > array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk])); > #emit add $eq_no = 1 > array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x2[kkk + order_d] := temporary; > array_x2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_x2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 1 > ; > #emit mult $eq_no = 2 > array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1); > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 2 > array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1); > #emit sub $eq_no = 2 > array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk])); > #emit mult $eq_no = 2 > array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1); > #emit sub $eq_no = 2 > array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk])); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x1[kkk + order_d] := temporary; > array_x1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_x1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float, glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2, glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax, glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter, glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start, glob_not_yet_start_msg, glob_initial_pass, days_in_year, glob_smallish_float, glob_max_order, glob_display_flag, glob_dump, glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done, glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr, glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes, glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_dump_analytic, glob_large_float, centuries_in_millinium, glob_log10normmin, glob_log10_abserr, glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h, hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0, array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t, array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1, array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole, array_real_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, array_x2_higher_work2, glob_last; array_tmp1[1] := array_x2_higher[2, 1]; array_tmp2[1] := array_const_3D0[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; array_tmp4[1] := array_const_2D0[1]*array_x2[1]; array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; array_tmp6[1] := array_x1_higher[3, 1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; array_tmp8[1] := array_x1_higher[2, 1]; array_tmp9[1] := array_tmp7[1] - array_tmp8[1]; array_tmp10[1] := array_tmp9[1] + array_x1[1]; if 1 <= glob_max_terms then temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2); array_x2[3] := temporary; array_x2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 2] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 1] := temporary end if; kkk := 2; array_tmp12[1] := array_const_4D0[1]*array_x2[1]; array_tmp13[1] := array_x2_higher[2, 1]; array_tmp14[1] := array_const_2D0[1]*array_tmp13[1]; array_tmp15[1] := array_tmp12[1] - array_tmp14[1]; array_tmp16[1] := array_const_2D0[1]*array_x1[1]; array_tmp17[1] := array_tmp15[1] - array_tmp16[1]; if 1 <= glob_max_terms then temporary := array_tmp17[1]*glob_h*factorial_3(0, 1); array_x1[2] := temporary; array_x1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 1] := temporary end if; kkk := 2; array_tmp1[2] := array_x2_higher[2, 2]; array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1); array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1); array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; array_tmp6[2] := array_x1_higher[3, 2]; array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; array_tmp8[2] := array_x1_higher[2, 2]; array_tmp9[2] := array_tmp7[2] - array_tmp8[2]; array_tmp10[2] := array_tmp9[2] + array_x1[2]; if 2 <= glob_max_terms then temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3); array_x2[4] := temporary; array_x2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 2] := temporary end if; kkk := 3; array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1); array_tmp13[2] := array_x2_higher[2, 2]; array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1); array_tmp15[2] := array_tmp12[2] - array_tmp14[2]; array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1); array_tmp17[2] := array_tmp15[2] - array_tmp16[2]; if 2 <= glob_max_terms then temporary := array_tmp17[2]*glob_h*factorial_3(1, 2); array_x1[3] := temporary; array_x1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 2] := temporary end if; kkk := 3; array_tmp1[3] := array_x2_higher[2, 3]; array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1); array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1); array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; array_tmp6[3] := array_x1_higher[3, 3]; array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; array_tmp8[3] := array_x1_higher[2, 3]; array_tmp9[3] := array_tmp7[3] - array_tmp8[3]; array_tmp10[3] := array_tmp9[3] + array_x1[3]; if 3 <= glob_max_terms then temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4); array_x2[5] := temporary; array_x2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 3] := temporary end if; kkk := 4; array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1); array_tmp13[3] := array_x2_higher[2, 3]; array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1); array_tmp15[3] := array_tmp12[3] - array_tmp14[3]; array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1); array_tmp17[3] := array_tmp15[3] - array_tmp16[3]; if 3 <= glob_max_terms then temporary := array_tmp17[3]*glob_h*factorial_3(2, 3); array_x1[4] := temporary; array_x1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 3] := temporary end if; kkk := 4; array_tmp1[4] := array_x2_higher[2, 4]; array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1); array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1); array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; array_tmp6[4] := array_x1_higher[3, 4]; array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; array_tmp8[4] := array_x1_higher[2, 4]; array_tmp9[4] := array_tmp7[4] - array_tmp8[4]; array_tmp10[4] := array_tmp9[4] + array_x1[4]; if 4 <= glob_max_terms then temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5); array_x2[6] := temporary; array_x2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 4] := temporary end if; kkk := 5; array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1); array_tmp13[4] := array_x2_higher[2, 4]; array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1); array_tmp15[4] := array_tmp12[4] - array_tmp14[4]; array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1); array_tmp17[4] := array_tmp15[4] - array_tmp16[4]; if 4 <= glob_max_terms then temporary := array_tmp17[4]*glob_h*factorial_3(3, 4); array_x1[5] := temporary; array_x1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 4] := temporary end if; kkk := 5; array_tmp1[5] := array_x2_higher[2, 5]; array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1); array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1); array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; array_tmp6[5] := array_x1_higher[3, 5]; array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; array_tmp8[5] := array_x1_higher[2, 5]; array_tmp9[5] := array_tmp7[5] - array_tmp8[5]; array_tmp10[5] := array_tmp9[5] + array_x1[5]; if 5 <= glob_max_terms then temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6); array_x2[7] := temporary; array_x2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 5] := temporary end if; kkk := 6; array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1); array_tmp13[5] := array_x2_higher[2, 5]; array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1); array_tmp15[5] := array_tmp12[5] - array_tmp14[5]; array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1); array_tmp17[5] := array_tmp15[5] - array_tmp16[5]; if 5 <= glob_max_terms then temporary := array_tmp17[5]*glob_h*factorial_3(4, 5); array_x1[6] := temporary; array_x1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 5] := temporary end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_x2_higher[2, kkk]; array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1); array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1); array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := array_x1_higher[3, kkk]; array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; array_tmp8[kkk] := array_x1_higher[2, kkk]; array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk]; array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp10[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x2[kkk + order_d] := temporary; array_x2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_x2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1); array_tmp13[kkk] := array_x2_higher[2, kkk]; array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1); array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk]; array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1); array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp17[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x1[kkk + order_d] := temporary; array_x1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_x1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_x1 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c1 + 6.0 * c3 * exp(-t); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > c1 + c2 * exp(2.0 * t) + c3 * exp(-t); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c2*exp(2.0*t) - c3*exp(-t) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > t_start,t_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > INFO, > glob_iolevel, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_clock_start_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_look_poles, > glob_clock_sec, > years_in_century, > sec_in_min, > djd_debug2, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin_init, > glob_hmax, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > djd_debug, > glob_iter, > glob_warned, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin, > glob_start, > glob_not_yet_start_msg, > glob_initial_pass, > days_in_year, > glob_smallish_float, > glob_max_order, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_unchanged_h_cnt, > glob_percent_done, > glob_max_sec, > glob_warned2, > glob_optimal_clock_start_sec, > glob_log10_relerr, > glob_last_good_h, > glob_reached_optimal_h, > min_in_hour, > glob_max_minutes, > glob_orig_start_sec, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > centuries_in_millinium, > glob_log10normmin, > glob_log10_abserr, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_h, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_4D0, > array_const_0D0, > array_const_1, > array_const_2, > #END CONST > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_norms, > array_t, > array_last_rel_error, > array_1st_rel_error, > array_x2, > array_x1, > array_m1, > array_x1_init, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_higher, > array_x1_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher_work, > array_x2_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > INFO := 2; > glob_iolevel := 5; > DEBUGL := 3; > ALWAYS := 1; > glob_max_terms := 30; > glob_clock_start_sec := 0.0; > glob_html_log := true; > glob_current_iter := 0; > glob_small_float := 0.1e-50; > glob_look_poles := false; > glob_clock_sec := 0.0; > years_in_century := 100.0; > sec_in_min := 60.0; > djd_debug2 := true; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_hmin_init := 0.001; > glob_hmax := 1.0; > glob_disp_incr := 0.1; > glob_optimal_done := false; > glob_almost_1 := 0.9990; > djd_debug := true; > glob_iter := 0; > glob_warned := false; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_hmin := 0.00000000001; > glob_start := 0; > glob_not_yet_start_msg := true; > glob_initial_pass := true; > days_in_year := 365.0; > glob_smallish_float := 0.1e-100; > glob_max_order := 30; > glob_display_flag := true; > glob_dump := false; > glob_max_opt_iter := 10; > glob_normmax := 0.0; > glob_unchanged_h_cnt := 0; > glob_percent_done := 0.0; > glob_max_sec := 10000.0; > glob_warned2 := false; > glob_optimal_clock_start_sec := 0.0; > glob_log10_relerr := 0.1e-10; > glob_last_good_h := 0.1; > glob_reached_optimal_h := false; > min_in_hour := 60.0; > glob_max_minutes := 0.0; > glob_orig_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_dump_analytic := false; > glob_large_float := 9.0e100; > centuries_in_millinium := 10.0; > glob_log10normmin := 0.1; > glob_log10_abserr := 0.1e-10; > glob_not_yet_finished := true; > glob_optimal_expect_sec := 0.1; > glob_log10relerr := 0.0; > glob_log10abserr := 0.0; > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_h := 0.1; > hours_in_day := 24.0; > #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 := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_x1 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_pole:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_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_type_pole:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_t:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_x1:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_x2_init:= Array(1..(max_terms + 1),[]); > array_tmp10:= Array(1..(max_terms + 1),[]); > array_tmp11:= Array(1..(max_terms + 1),[]); > array_tmp12:= Array(1..(max_terms + 1),[]); > array_tmp13:= Array(1..(max_terms + 1),[]); > array_tmp14:= Array(1..(max_terms + 1),[]); > array_tmp15:= Array(1..(max_terms + 1),[]); > array_tmp16:= Array(1..(max_terms + 1),[]); > array_tmp17:= Array(1..(max_terms + 1),[]); > array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_real_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),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > 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_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_type_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_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_m1[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_init[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 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_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_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_x1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_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_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > t_start := 0.5; > t_end := 5.0; > array_x1_init[1] := exact_soln_x1(t_start); > array_x2_init[1] := exact_soln_x2(t_start); > array_x2_init[2] := exact_soln_x2p(t_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_x2(); > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_x1(); > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > 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,"2012-06-02T01:53:37-05:00") > ; > 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 DEBUGMASSIVE, INFO, glob_iolevel, DEBUGL, ALWAYS, glob_max_terms, glob_clock_start_sec, glob_html_log, glob_current_iter, glob_small_float, glob_look_poles, glob_clock_sec, years_in_century, sec_in_min, djd_debug2, glob_max_iter, glob_relerr, glob_abserr, glob_hmin_init, glob_hmax, glob_disp_incr, glob_optimal_done, glob_almost_1, djd_debug, glob_iter, glob_warned, glob_no_eqs, glob_max_trunc_err, glob_hmin, glob_start, glob_not_yet_start_msg, glob_initial_pass, days_in_year, glob_smallish_float, glob_max_order, glob_display_flag, glob_dump, glob_max_opt_iter, glob_normmax, glob_unchanged_h_cnt, glob_percent_done, glob_max_sec, glob_warned2, glob_optimal_clock_start_sec, glob_log10_relerr, glob_last_good_h, glob_reached_optimal_h, min_in_hour, glob_max_minutes, glob_orig_start_sec, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_dump_analytic, glob_large_float, centuries_in_millinium, glob_log10normmin, glob_log10_abserr, glob_not_yet_finished, glob_optimal_expect_sec, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_h, hours_in_day, array_const_2D0, array_const_3D0, array_const_4D0, array_const_0D0, array_const_1, array_const_2, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_norms, array_t, array_last_rel_error, array_1st_rel_error, array_x2, array_x1, array_m1, array_x1_init, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_higher, array_x1_higher_work, array_poles, array_complex_pole, array_real_pole, array_x1_higher_work2, array_x1_higher, array_x2_higher_work, array_x2_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; INFO := 2; glob_iolevel := 5; DEBUGL := 3; ALWAYS := 1; glob_max_terms := 30; glob_clock_start_sec := 0.; glob_html_log := true; glob_current_iter := 0; glob_small_float := 0.1*10^(-50); glob_look_poles := false; glob_clock_sec := 0.; years_in_century := 100.0; sec_in_min := 60.0; djd_debug2 := true; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_hmax := 1.0; glob_disp_incr := 0.1; glob_optimal_done := false; glob_almost_1 := 0.9990; djd_debug := true; glob_iter := 0; glob_warned := false; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_start := 0; glob_not_yet_start_msg := true; glob_initial_pass := true; days_in_year := 365.0; glob_smallish_float := 0.1*10^(-100); glob_max_order := 30; glob_display_flag := true; glob_dump := false; glob_max_opt_iter := 10; glob_normmax := 0.; glob_unchanged_h_cnt := 0; glob_percent_done := 0.; glob_max_sec := 10000.0; glob_warned2 := false; glob_optimal_clock_start_sec := 0.; glob_log10_relerr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_reached_optimal_h := false; min_in_hour := 60.0; glob_max_minutes := 0.; glob_orig_start_sec := 0.; glob_optimal_start := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_dump_analytic := false; glob_large_float := 0.90*10^101; centuries_in_millinium := 10.0; glob_log10normmin := 0.1; glob_log10_abserr := 0.1*10^(-10); glob_not_yet_finished := true; glob_optimal_expect_sec := 0.1; glob_log10relerr := 0.; glob_log10abserr := 0.; MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_h := 0.1; hours_in_day := 24.0; 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 := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_x1 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_pole := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_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_type_pole := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_t := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_x1 := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_x2_init := Array(1 .. max_terms + 1, []); array_tmp10 := Array(1 .. max_terms + 1, []); array_tmp11 := Array(1 .. max_terms + 1, []); array_tmp12 := Array(1 .. max_terms + 1, []); array_tmp13 := Array(1 .. max_terms + 1, []); array_tmp14 := Array(1 .. max_terms + 1, []); array_tmp15 := Array(1 .. max_terms + 1, []); array_tmp16 := Array(1 .. max_terms + 1, []); array_tmp17 := Array(1 .. max_terms + 1, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_real_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, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_type_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_t[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_m1[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_init[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; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_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_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1 end do; array_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1 end do; array_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_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_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_t[1] := t_start; array_t[2] := glob_h; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x2_higher[r_order, term_no] := array_x2_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x1_higher[r_order, term_no] := array_x1_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_x2(); if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_x1(); if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_t[1] <= t_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; 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, "2012-06-02T01:53:37-05:00"); 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 := 0.001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c1 + 6.0 * c3 * exp(-t); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2 * exp(2.0 * t) + c3 * exp(-t); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 0.001 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.001 t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 0.001 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652209612614425075269168613102 absolute error = 1.7377596846004174084e-16 relative error = 2.1024963431042189816430962969600e-11 % h = 0.001 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906639784542818918618739547211 absolute error = 4.633444453781957526860e-13 relative error = 3.5899696069572120796765728479236e-08 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.502 x2[1] (analytic) = 0.0008274309894041739636559251804687 x2[1] (numeric) = 0.00082743208206711503358407744411689 absolute error = 1.09266294106992815226364819e-09 relative error = 0.00013205487286096759163327430459812 % h = 0.001 x1[1] (analytic) = 0.0012895738591632036100858259251 x1[1] (numeric) = 0.0012895716796697751322509839346479 absolute error = 2.1794934284778348419904521e-09 relative error = 0.00016900880961499130103998997246766 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.503 x2[1] (analytic) = 0.0008283422476198008492141699458837 x2[1] (numeric) = 0.00082834662209419532515247999857985 absolute error = 4.37447439447593831005269615e-09 relative error = 0.00052809987744145214230170552587512 % h = 0.001 x1[1] (analytic) = 0.0012884848299094197347162072617323 x1[1] (numeric) = 0.0012884761133078092129236615748211 absolute error = 8.7166016105217925456869112e-09 relative error = 0.00067650013474621724202878276122865 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.504 x2[1] (analytic) = 0.00082925587496274761468760841422102 x2[1] (numeric) = 0.00082926573062464187676195249676034 absolute error = 9.85566189426207434408253932e-09 relative error = 0.0011884946723717594353916049289451 % h = 0.001 x1[1] (analytic) = 0.0012873968891405564758385060019091 x1[1] (numeric) = 0.0012873772731260255561388750919475 absolute error = 1.96160145309196996309099616e-08 relative error = 0.0015236959710237459080535094232935 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.505 x2[1] (analytic) = 0.00083017187563149546111924351454314 x2[1] (numeric) = 0.0008301894292660833587342720599604 absolute error = 1.755363458789761502854541726e-08 relative error = 0.0021144578735029911161583922341777 % h = 0.001 x1[1] (analytic) = 0.0012863100357686729739277295072664 x1[1] (numeric) = 0.0012862747677288049168478543730644 absolute error = 3.52680398680570798751342020e-08 relative error = 0.0027417993242182557854751824962821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=2.9MB, time=0.17 t[1] = 0.506 x2[1] (analytic) = 0.00083109025383347519720441727943742 x2[1] (numeric) = 0.00083111813963898378021103730559235 absolute error = 2.788580550858300662002615493e-08 relative error = 0.0033553281824636172738729172433782 % h = 0.001 x1[1] (analytic) = 0.0012852242687069157665292585243653 x1[1] (numeric) = 0.0012851346937267006448141946499636 absolute error = 8.95749802151217150638744017e-08 relative error = 0.0069695991895052295674023577236862 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.507 x2[1] (analytic) = 0.00083201101378508461244661319002326 x2[1] (numeric) = 0.00083208182025711992659294685537073 absolute error = 7.080647203531414633366534747e-08 relative error = 0.0085102806167424183765694805023606 % h = 0.001 x1[1] (analytic) = 0.001284139586869517701405294158948 x1[1] (numeric) = 0.0012816032012667107580533020335611 absolute error = 2.5363856028069433519921253869e-06 relative error = 0.19751634703437167860653061977856 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.508 x2[1] (analytic) = 0.00083293415971170588563803837477598 x2[1] (numeric) = 0.00083486689850480914716087654457917 absolute error = 1.93273879310326152283816980319e-06 relative error = 0.23203980417518458136622086027346 % h = 0.001 x1[1] (analytic) = 0.0012830559891717968507676151575396 x1[1] (numeric) = 0.0011445592494289191531884065137392 absolute error = 0.0001384967397428776975792086438004 relative error = 10.794286524649350533293680493259 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.509 x2[1] (analytic) = 0.00083385969584772302873516249155556 x2[1] (numeric) = 0.00092687683083470305397401705731068 absolute error = 9.301713498698002523885456575512e-05 relative error = 11.155010303312049881472952177155 % h = 0.001 x1[1] (analytic) = 0.001281973474530155426595559729063 x1[1] (numeric) = -0.0050876137298401921977037822387805 absolute error = 0.0063695872043703476242993419678435 relative error = 496.85795618390682919220616232654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.51 x2[1] (analytic) = 0.00083478762643653936619953115948893 x2[1] (numeric) = 0.0046589937378618315002240136718923 absolute error = 0.0038242061114252921340244825124034 relative error = 458.10527016909595292703358234922 % h = 0.001 x1[1] (analytic) = 0.0012808920418620786970381472243591 x1[1] (numeric) = -0.24131402437289095671277172187697 absolute error = 0.24259491641475303540980986910133 relative error = 18939.528741398385565485550762183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.511 x2[1] (analytic) = 0.00083571795573059504987431312643056 x2[1] (numeric) = 0.13285816078867771248944683425825 absolute error = 0.13202244283294711743957252113182 relative error = 15797.487887828310799736820128395 % h = 0.001 x1[1] (analytic) = 0.0012798116900861339038992560756415 x1[1] (numeric) = -7.7093942279778686438373784130089 absolute error = 7.7106740396679547777412776690845 relative error = 602485.0452138791518531421981286 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.512 x2[1] (analytic) = 0.00083665068799138460946718195917937 x2[1] (numeric) = 3.848764768360869453897499526031 absolute error = 3.8479281176728780692880323440718 relative error = 459920.51078221333123823971899632 % h = 0.001 x1[1] (analytic) = 0.0012787324181219691812047754809758 x1[1] (numeric) = -205.62452745932470778191386248986 absolute error = 205.62580619174282975109506726534 relative error = 16080440.542341020722247847680653 % h = 0.001 TOP MAIN SOLVE Loop Complex estimate of poles used NO POLE Radius of convergence = 9.530e-05 Order of pole = 1.449 t[1] = 0.513 x2[1] (analytic) = 0.00083758582748947453871027492802935 x2[1] (numeric) = 95.03997140458233662383395828203 absolute error = 95.039133818754847149295248007102 relative error = 11346793.45084180635823719951838 % h = 0.001 x1[1] (analytic) = 0.0012776542248903124748506494008434 x1[1] (numeric) = -4614.1765933388366477251758552195 absolute error = 4614.1778709930615380376507058689 relative error = 361144492.86067143827350427059414 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 6.634e-05 Order of pole = 0.2405 t[1] = 0.514 x2[1] (analytic) = 0.0008385233785045209172681139251402 x2[1] (numeric) = 1992.6637388793779558995202832394 absolute error = 1992.6629003559994513786030151255 relative error = 237639516.25413816240454496582944 % h = 0.001 x1[1] (analytic) = 0.0012765771093129704633307325147448 x1[1] (numeric) = -87182.96718468238078720867603815 absolute error = 87182.968461259490100179139368883 relative error = 6829432223.5011488387443148255895 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 9.347e-05 Order of pole = 16.65 t[1] = 0.515 x2[1] (analytic) = 0.00083946334532528706846451570820467 x2[1] (numeric) = 35463.481349374228164985292732259 absolute error = 35463.480509910882839698224267743 relative error = 4224541870.3980451264878519214906 % h = 0.001 x1[1] (analytic) = 0.0012755010703128274795433788656077 x1[1] (numeric) = -1385013.8243610767550654844287504 absolute error = 1385013.8256365778253783119082938 relative error = 108585861499.66078912881341962994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0003875 Order of pole = 180.9 memory used=7.6MB, alloc=4.1MB, time=0.38 t[1] = 0.516 x2[1] (analytic) = 0.00084040573224966125289966149752755 x2[1] (numeric) = 534723.84790466957895035491098952 absolute error = 534723.84706426384670069365808986 relative error = 63626868135.80802784577150418021 % h = 0.001 x1[1] (analytic) = 0.0012744261068138444336756849984992 x1[1] (numeric) = -18432473.242678055858975289924739 absolute error = 18432473.243952481965789134358415 relative error = 1446335189259.0282151448527669851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.517 x2[1] (analytic) = 0.0008413505435846743980286389764889 x2[1] (numeric) = 6805672.8427367871910800556581839 absolute error = 6805672.8418954366474953812601553 relative error = 808898608765.26629591003009895997 % h = 0.001 x1[1] (analytic) = 0.0012733522177410577371643104777951 x1[1] (numeric) = -204280317.45416562057307061203871 absolute error = 204280317.45543897279081166977587 relative error = 16042718943689.808866691108116321 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.518 x2[1] (analytic) = 0.00084229778364651786377291305301299 x2[1] (numeric) = 72704196.59553744274731642534695 absolute error = 72704196.594695144963669907483177 relative error = 8631649994369.0325267923053004535 % h = 0.001 x1[1] (analytic) = 0.0012722794020205782277317997435378 x1[1] (numeric) = -1869185610.9990685417338471914189 absolute error = 1869185611.0003408211358677696466 relative error = 146916283328314.70722635113676919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.519 x2[1] (analytic) = 0.00084324745676056124423632533367627 x2[1] (numeric) = 646913806.76858365663383533572403 absolute error = 646913806.76774040917707477447979 relative error = 76716959129997.179650868112208331 % h = 0.001 x1[1] (analytic) = 0.0012712076585795900954973303432135 x1[1] (numeric) = -13958789929.958012959304013896182 absolute error = 13958789929.959284166962593486277 relative error = 1098073146094511.7253913579901584 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.52 x2[1] (analytic) = 0.00084419956726137020559736614303792 x2[1] (numeric) = 4747258637.5844548551973869526829 absolute error = 4747258637.5836106556301255824773 relative error = 562338435328032.51616216893304551 % h = 0.001 x1[1] (analytic) = 0.00127013698634634981016081364961 x1[1] (numeric) = -83835909426.063292532867110345569 absolute error = 83835909426.064562669853456695379 relative error = 6600540754838203.1208627605382563 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 3.560e-05 Order of pole = 38.68 t[1] = 0.521 x2[1] (analytic) = 0.00084515411949272436024960708923766 x2[1] (numeric) = 28393092936.383396962744004738756 absolute error = 28393092936.382551808624512014396 relative error = 3359516599578850.9120275925160686 % h = 0.001 x1[1] (analytic) = 0.0012690673842501850492592752487639 x1[1] (numeric) = -398022389772.65971946563416331421 absolute error = 398022389772.66098853301841349926 relative error = 31363377131296166.698088651723839 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0001169 Order of pole = 228.7 t[1] = 0.522 x2[1] (analytic) = 0.00084611111780763517726232663345645 x2[1] (numeric) = 136671615850.64154313074210004024 absolute error = 136671615850.64069701962429240506 relative error = 16152915731065151.271615074867864 % h = 0.001 x1[1] (analytic) = 0.0012679988512214936274944432542899 x1[1] (numeric) = -1469402384393.40254974984770924 absolute error = 1469402384393.4038177486989307336 relative error = 115883573788564031.31663473669231 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.523 x2[1] (analytic) = 0.00084707056656836392923350586605222 x2[1] (numeric) = 524315431733.21614790863155058981 absolute error = 524315431733.21530083806498222588 relative error = 61897491475510941.811060006420899 % h = 0.001 x1[1] (analytic) = 0.0012669313861917424271304738755899 x1[1] (numeric) = -4198510280127.8065888182437736909 absolute error = 4198510280127.8078557496299654333 relative error = 331392080572577166.94861286814447 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.524 x2[1] (analytic) = 0.00084803247014643967560751672664236 x2[1] (numeric) = 1605595799032.6572100156258602256 absolute error = 1605595799032.6563619831557137859 relative error = 189331877676263902.31171389903844 % h = 0.001 x1[1] (analytic) = 0.0012658649880934663294607446375807 x1[1] (numeric) = -9556189501036.6680043320599734608 absolute error = 9556189501036.6692701970480669271 relative error = 754913801307464477.36671125618277 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 0.001167 Order of pole = 280.4 t[1] = 0.525 x2[1] (analytic) = 0.00084899683292267728252997022968994 x2[1] (numeric) = 4020473916672.2860943242908248939 absolute error = 4020473916672.2852453274579022166 relative error = 473555820324061382.49275585960482 % h = 0.001 x1[1] (analytic) = 0.0012647996558602671473426467186411 x1[1] (numeric) = -18097458069571.86542017725871785 absolute error = 18097458069571.866684976914578117 relative error = 1430855707915471016.1510171161615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0001137 Order of pole = 11.65 memory used=11.4MB, alloc=4.2MB, time=0.62 t[1] = 0.526 x2[1] (analytic) = 0.00084996365928719547931233787183942 x2[1] (numeric) = 8416124951971.5064426398063244774 absolute error = 8416124951971.5055926761470372819 relative error = 990174681001010735.15966424812374 % h = 0.001 x1[1] (analytic) = 0.0012637353884268125587993089414852 x1[1] (numeric) = -18080977850166.451559871822635303 absolute error = 18080977850166.452823607211062116 relative error = 1430756629572187294.2232910188971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.527 x2[1] (analytic) = 0.00085093295363943495157910530292247 x2[1] (numeric) = 10619053727748.775740450074613078 absolute error = 10619053727748.774889517120973643 relative error = 1247930719139639395.2845057128129 % h = 0.001 x1[1] (analytic) = 0.0012626721847288350416871870185942 x1[1] (numeric) = 208388532861669.09174743790579605 absolute error = 208388532861669.09048476572106721 relative error = 16503771555435153245.503965934719 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.528 x2[1] (analytic) = 0.00085190472038817647117036353980059 x2[1] (numeric) = -76377295454035.304669209461938995 absolute error = 76377295454035.305521114182327171 relative error = 8965473911123939455.2496080780862 % h = 0.001 x1[1] (analytic) = 0.0012616100437031308094284527197097 x1[1] (numeric) = 4028911219777281.6723537642880636 absolute error = 4028911219777281.6710921542443605 relative error = 319346793399920325283.54610079869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.529 x2[1] (analytic) = 0.00085287896395155906287288949160932 x2[1] (numeric) = -1584199293909485.2191174470730754 absolute error = 1584199293909485.219970326037027 relative error = 185747258505424098216.8567063679 % h = 0.001 x1[1] (analytic) = 0.001260548964287558747807118693686 x1[1] (numeric) = 59645665455178133.700293949005246 absolute error = 59645665455178133.699033400040958 relative error = 4731721428123093107440.8879292078 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.53 x2[1] (analytic) = 0.00085385568875709820805291434710783 x2[1] (numeric) = -23044614641880801.120824519976832 absolute error = 23044614641880801.121678375665589 relative error = 2698888693407352834375.9881218953 % h = 0.001 x1[1] (analytic) = 0.0012594889454210393528278357407412 x1[1] (numeric) = 789441831498582105.60231663497849 absolute error = 789441831498582105.60105714603307 relative error = 62679536360255753682248.344868604 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.531 x2[1] (analytic) = 0.00085483489924170408526392545030159 x2[1] (numeric) = -297700552474111974.70144902897774 absolute error = 297700552474111974.70230386387698 relative error = 34825502882274967990297.17199346 % h = 0.001 x1[1] (analytic) = 0.0012584299860435536696363003938124 x1[1] (numeric) = 9419807278531444728.2307140802689 absolute error = 9419807278531444728.2294556502829 relative error = 748536460748753139692563.58284364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.532 x2[1] (analytic) = 0.00085581659985169984790299465988337 x2[1] (numeric) = -3471766895682267226.6209457098289 absolute error = 3471766895682267226.6218015264288 relative error = 405667160029832588191634.20157905 % h = 0.001 x1[1] (analytic) = 0.001257372085096142232500211729337 x1[1] (numeric) = 101081058865388804662.54687367722 absolute error = 101081058865388804662.54561630513 relative error = 8039072925470574645346776.8560099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.533 x2[1] (analytic) = 0.0008568007950428399389892738519192 x2[1] (numeric) = -36500192779859514087.336456621742 absolute error = 36500192779859514087.337313422537 relative error = 4260055895260287280767385.65163 % h = 0.001 x1[1] (analytic) = 0.0012563152415209040058497173883259 x1[1] (numeric) = 971671203008010545373.90298913125 absolute error = 971671203008010545373.90173281601 relative error = 77342944739864701520548792.014237 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.534 x2[1] (analytic) = 0.00085778748928032844313844618417794 x2[1] (numeric) = -344763967424345606117.35198703553 absolute error = 344763967424345606117.35284482302 relative error = 40192235458411464216896436.725986 % h = 0.001 x1[1] (analytic) = 0.0012552594542609953263762898480893 x1[1] (numeric) = 8331108755382093997844.817964788 absolute error = 8331108755382093997844.8167095285 relative error = 663696156766796838428306550.02122 % h = 0.001 TOP MAIN SOLVE Loop Complex estimate of poles used NO POLE Radius of convergence = 0.0003058 Order of pole = 310.8 t[1] = 0.535 x2[1] (analytic) = 0.00085877668703883747580706999516187 x2[1] (numeric) = -2914574886945155522813.1246417025 absolute error = 2914574886945155522813.1255004792 relative error = 339386819755779682547215014.86589 % h = 0.001 x1[1] (analytic) = 0.0012542047222606288461889750434006 x1[1] (numeric) = 63444812881827322429418.049838158 absolute error = 63444812881827322429418.048583953 relative error = 5058569127970739060693491388.9891 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.536 x2[1] (analytic) = 0.00085976839280252560988090076182799 x2[1] (numeric) = -21977161734593959798322.193332718 absolute error = 21977161734593959798322.194192486 relative error = 2556172327172504643561522940.6447 % h = 0.001 x1[1] (analytic) = 0.0012531510444650724770269564932605 x1[1] (numeric) = 428038360735937613695808.71233172 absolute error = 428038360735937613695808.71107857 relative error = 34156964767056681443137624102.043 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=0.85 NO POLE NO POLE t[1] = 0.537 x2[1] (analytic) = 0.00086076261106505633968142538779503 x2[1] (numeric) = -147594906722031812720483.02090421 absolute error = 147594906722031812720483.02176497 relative error = 17146993238868341895702273750.884 % h = 0.001 x1[1] (analytic) = 0.0012520984198206483355273791457368 x1[1] (numeric) = 2565132925887698907547833.2990847 absolute error = 2565132925887698907547833.2978326 relative error = 204866716967435417287671514248.52 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.538 x2[1] (analytic) = 0.0008617593463296165824649922390997 x2[1] (numeric) = -886284898338716046806321.12008458 absolute error = 886284898338716046806321.12094634 relative error = 102845986192497716400303751820.17 % h = 0.001 x1[1] (analytic) = 0.0012510468472747316895473782086164 x1[1] (numeric) = 13867043360108630895489782.873343 absolute error = 13867043360108630895489782.872092 relative error = 1108435178931665394371383900078.4 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.539 x2[1] (analytic) = 0.00086275860310893521748906978789598 x2[1] (numeric) = -4835122702791031967582892.6683127 absolute error = 4835122702791031967582892.6691755 relative error = 560425904229497528400235909032.57 % h = 0.001 x1[1] (analytic) = 0.0012499963257757499055392592878095 x1[1] (numeric) = 70350186225748130153879863.743503 absolute error = 70350186225748130153879863.742253 relative error = 5628031440979531005162062267178.4 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 4.342e-05 Order of pole = 7.198 t[1] = 0.54 x2[1] (analytic) = 0.0008637603859253016627203164664802 x2[1] (numeric) = -24858034430362983879728442.259866 absolute error = 24858034430362983879728442.26073 relative error = 2877885445479635188585245344284.6 % h = 0.001 x1[1] (analytic) = 0.0012489468542731813969777772086 x1[1] (numeric) = 356950605722257851507598948.66393 absolute error = 356950605722257851507598948.66268 relative error = 28580127689258926579437053952018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 9.568e-05 Order of pole = 61.16 t[1] = 0.541 x2[1] (analytic) = 0.00086476469931058448925929437526969 x2[1] (numeric) = -127200742934307154159662141.92313 absolute error = 127200742934307154159662141.92399 relative error = 14709289479058902074523271982624 % h = 0.001 x1[1] (analytic) = 0.0012478984317175545738384619469313 x1[1] (numeric) = 1895145680929461501567251596.5581 absolute error = 1895145680929461501567251596.5569 relative error = 1.5186698153960039952798340153173e+32 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.542 x2[1] (analytic) = 0.00086577154780625007355680982946525 x2[1] (numeric) = -672065666098214441207771350.90056 absolute error = 672065666098214441207771350.90143 relative error = 77626213035198423021416083240120 % h = 0.001 x1[1] (analytic) = 0.001246851057060446793125941148968 x1[1] (numeric) = 10211682922641022570422368549.784 absolute error = 10211682922641022570422368549.783 relative error = 8.1899781572274551595030358583525e+32 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.543 x2[1] (analytic) = 0.00086678093596338128749701437068642 x2[1] (numeric) = -3571921968778738599744148503.7726 absolute error = 3571921968778738599744148503.7735 relative error = 4.1209050875221843116265932774054e+32 % h = 0.001 x1[1] (analytic) = 0.0012458047292544833104512097671668 x1[1] (numeric) = 50989848709111945273759000647.705 absolute error = 50989848709111945273759000647.704 relative error = 4.0929246383279811068905285829752e+33 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.544 x2[1] (analytic) = 0.00086779286834269622642255081248739 x2[1] (numeric) = -17635360651247484324761069901.842 absolute error = 17635360651247484324761069901.843 relative error = 2.0322085251665357540110571666253e+33 % h = 0.001 x1[1] (analytic) = 0.00124475944725333623265679839004 x1[1] (numeric) = 209308394696559569053895112815.48 absolute error = 209308394696559569053895112815.48 relative error = 1.6815168196426683189508152492371e+34 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.545 x2[1] (analytic) = 0.00086880734951456697517718013294248 x2[1] (numeric) = -72091855217655734366068732132.198 absolute error = 72091855217655734366068732132.199 relative error = 8.2977952773921598355168830041327e+33 % h = 0.001 x1[1] (analytic) = 0.0012437152100117234714887928906918 x1[1] (numeric) = 507695167407203124076201562387.98 absolute error = 507695167407203124076201562387.98 relative error = 4.0820853787131661992055669161699e+34 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0002099 Order of pole = 72.05 t[1] = 0.546 x2[1] (analytic) = 0.00086982438405903841224147657403825 x2[1] (numeric) = -173674618527119777865356493368.03 absolute error = 173674618527119777865356493368.03 relative error = 1.9966630242838972469166590487744e+34 % h = 0.001 x1[1] (analytic) = 0.0012426720164854076983146590660609 x1[1] (numeric) = -2038824696603027221866061391504.1 absolute error = 2038824696603027221866061391504.1 relative error = 1.6406780466251599147448345103381e+35 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.09 NO POLE NO POLE t[1] = 0.547 x2[1] (analytic) = 0.00087084397656584705203733015703041 x2[1] (numeric) = 742895166451449508478869070552.21 absolute error = 742895166451449508478869070552.21 relative error = 8.5307493241331162725508940022443e+34 % h = 0.001 x1[1] (analytic) = 0.0012416298656311952998858269846059 x1[1] (numeric) = -46426739093838342823868197241364 absolute error = 46426739093838342823868197241364 relative error = 3.7391770590373833326580896636108e+36 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.548 x2[1] (analytic) = 0.0008718661316344399254771479758239 x2[1] (numeric) = 16613889867063091210172183428212 absolute error = 16613889867063091210172183428212 relative error = 1.9055551379106718177226399005637e+36 % h = 0.001 x1[1] (analytic) = 0.0012405887564069353351439908049313 x1[1] (numeric) = -5.2078761025166113535027250827395e+32 absolute error = 5.2078761025166113535027250827395e+32 relative error = 4.1979069015585489488458050722047e+37 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.549 x2[1] (analytic) = 0.00087289085387399349883379808742284 x2[1] (numeric) = 1.8555396819436862183297832333337e+32 absolute error = 1.8555396819436862183297832333337e+32 relative error = 2.1257407769924272525656712605514e+37 % h = 0.001 x1[1] (analytic) = 0.0012395486877715184930700808715671 x1[1] (numeric) = -4.8658790120476665950009646954474e+33 absolute error = 4.8658790120476665950009646954474e+33 relative error = 3.9255247172223834404821535533903e+38 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.55 x2[1] (analytic) = 0.00087391814790343263100749258018221 x2[1] (numeric) = 1.7226529906994720272543097480685e+33 absolute error = 1.7226529906994720272543097480685e+33 relative error = 1.9711834510270680715072698198015e+38 % h = 0.001 x1[1] (analytic) = 0.0012385096586848760515748659367868 x1[1] (numeric) = -4.0997660674376877732734577125954e+34 absolute error = 4.0997660674376877732734577125954e+34 relative error = 3.3102414976650772686936356475767e+39 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.551 x2[1] (analytic) = 0.0008749480183514495692659594675856 x2[1] (numeric) = 1.4413463999623131253119244409390e+34 absolute error = 1.4413463999623131253119244409390e+34 relative error = 1.6473508936885806663947198962633e+39 % h = 0.001 x1[1] (analytic) = 0.0012374716681079788374301443989802 x1[1] (numeric) = -3.1723244358050155898812802891035e+35 absolute error = 3.1723244358050155898812802891035e+35 relative error = 2.5635531847410393377204969442104e+40 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.552 x2[1] (analytic) = 0.00087598046985652298353440642818536 x2[1] (numeric) = 1.1089522158592725949721176493768e+35 absolute error = 1.1089522158592725949721176493768e+35 relative error = 1.2659554111302368423117445991817e+40 % h = 0.001 x1[1] (analytic) = 0.0012364347150028361872394844886841 x1[1] (numeric) = -2.2685791336849822624297430149174e+36 absolute error = 2.2685791336849822624297430149174e+36 relative error = 1.8347747003203307000623688539782e+41 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.553 x2[1] (analytic) = 0.00087701550706693703931193309178555 x2[1] (numeric) = 7.9040722915796569740431090377779e+35 absolute error = 7.9040722915796569740431090377779e+35 relative error = 9.0124658320053959939259204755806e+40 % h = 0.001 x1[1] (analytic) = 0.0012353987983324949094474743729255 x1[1] (numeric) = -1.5095292224034438926228771451801e+37 absolute error = 1.5095292224034438926228771451801e+37 relative error = 1.2218963013732587366039930575378e+42 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.554 x2[1] (analytic) = 0.00087805313464080050929120255853851 x2[1] (numeric) = 5.2571558079547644152423193008139e+36 absolute error = 5.2571558079547644152423193008139e+36 relative error = 5.9872866465027708481374516468066e+41 % h = 0.001 x1[1] (analytic) = 0.0012343639170610382473864441870416 x1[1] (numeric) = -9.4570451831048801319996977359934e+37 absolute error = 9.4570451831048801319996977359934e+37 relative error = 7.6614724818120532271767784660222e+42 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.555 x2[1] (analytic) = 0.00087909335724606592375833713197844 x2[1] (numeric) = 3.3009832203067912539813012769618e+37 absolute error = 3.3009832203067912539813012769618e+37 relative error = 3.7549859671875750089028344566231e+42 % h = 0.001 x1[1] (analytic) = 0.0012333300701535848433596230406101 x1[1] (numeric) = -5.6798572535330703244873441964760e+38 absolute error = 5.6798572535330703244873441964760e+38 relative error = 4.6053018498330830134198770581258e+43 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.556 x2[1] (analytic) = 0.00088013617956054875985015784974602 x2[1] (numeric) = 1.9899010927491380458888180533748e+38 absolute error = 1.9899010927491380458888180533748e+38 relative error = 2.2609013684026646377494039278007e+43 % h = 0.001 x1[1] (analytic) = 0.0012322972565762877037596950805625 x1[1] (numeric) = -3.3387962804542805611859924924515e+39 absolute error = 3.3387962804542805611859924924515e+39 relative error = 2.7094081907887344483128857061890e+44 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=1.33 NO POLE NO POLE t[1] = 0.557 x2[1] (analytic) = 0.00088118160627194666974604230748542 x2[1] (numeric) = 1.1730599093150617765957628371400e+39 absolute error = 1.1730599093150617765957628371400e+39 relative error = 1.3312351290195188398087848025415e+44 % h = 0.001 x1[1] (analytic) = 0.0012312654752963331652217197299492 x1[1] (numeric) = -1.9465631240143861855132373507554e+40 absolute error = 1.9465631240143861855132373507554e+40 relative error = 1.5809451032856254813892425039252e+45 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 7.409e-05 Order of pole = 35.39 t[1] = 0.558 x2[1] (analytic) = 0.00088222964207785874787183049273793 x2[1] (numeric) = 6.8380483340048683774335473601477e+39 absolute error = 6.8380483340048683774335473601477e+39 relative error = 7.7508712106970842973023269982535e+44 % h = 0.001 x1[1] (analytic) = 0.0012302347252819398618093822551908 x1[1] (numeric) = -1.1199027394228693951106010691967e+41 absolute error = 1.1199027394228693951106010691967e+41 relative error = 9.1031631314602580379885164670517e+45 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.559 x2[1] (analytic) = 0.00088328029168580483719336387723487 x2[1] (numeric) = 3.9211576234463187242686762218825e+40 absolute error = 3.9211576234463187242686762218825e+40 relative error = 4.4393129342470706619072172274257e+45 % h = 0.001 x1[1] (analytic) = 0.00122920500550235769323354184798 x1[1] (numeric) = -6.2047025932490207049817642871715e+41 absolute error = 6.2047025932490207049817642871715e+41 relative error = 5.0477361916641818389650003332843e+46 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.56 x2[1] (analytic) = 0.00088433355981324487467739885842914 x2[1] (numeric) = 2.1630544115884961953541852346008e+41 absolute error = 2.1630544115884961953541852346008e+41 relative error = 2.4459711921882664408741618447104e+46 % h = 0.001 x1[1] (analytic) = 0.0012281763149278667941020454402963 x1[1] (numeric) = -3.1914625948378813318380404820238e+42 absolute error = 3.1914625948378813318380404820238e+42 relative error = 2.5985378125658791872284847789117e+47 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.561 x2[1] (analytic) = 0.00088538945118759827599779179502061 x2[1] (numeric) = 1.1093427606551960601998447075342e+42 absolute error = 1.1093427606551960601998447075342e+42 relative error = 1.2529432772970163402770215044478e+47 % h = 0.001 x1[1] (analytic) = 0.0012271486525297765041997765022611 x1[1] (numeric) = -1.4490982384840528134570113217892e+43 absolute error = 1.4490982384840528134570113217892e+43 relative error = 1.1808660959670415717553623979297e+48 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.562 x2[1] (analytic) = 0.00088644797054626335956500934725191 x2[1] (numeric) = 5.0344038888645337075486087438096e+42 absolute error = 5.0344038888645337075486087438096e+42 relative error = 5.6792999207411352669319834782364e+47 % h = 0.001 x1[1] (analytic) = 0.0012261220172804243397979091027969 x1[1] (numeric) = -5.1886925824970336226824803564450e+43 absolute error = 5.1886925824970336226824803564450e+43 relative error = 4.2317913791367277266872373848867e+48 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 0.0001112 Order of pole = 20.75 t[1] = 0.563 x2[1] (analytic) = 0.00088750912263663680995717461150232 x2[1] (numeric) = 1.8023253611685577571600748147999e+43 absolute error = 1.8023253611685577571600748147999e+43 relative error = 2.0307682650226280459050907171822e+48 % h = 0.001 x1[1] (analytic) = 0.0012250964081531749659913385422579 x1[1] (numeric) = -7.1710464586995159459036459624407e+43 absolute error = 7.1710464586995159459036459624407e+43 relative error = 5.8534548064750453541367282842641e+48 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 7.221e-05 Order of pole = 10.86 t[1] = 0.564 x2[1] (analytic) = 0.00088857291221613318083101663081396 x2[1] (numeric) = 2.4259668645623557801352660236288e+43 absolute error = 2.4259668645623557801352660236288e+43 relative error = 2.7301832311227067814793039364087e+48 % h = 0.001 x1[1] (analytic) = 0.0012240718241224191700632608943781 x1[1] (numeric) = 1.1574263562365199010318002425107e+45 absolute error = 1.1574263562365199010318002425107e+45 relative error = 9.4555428319438707252964415819686e+49 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.565 x2[1] (analytic) = 0.00088963934405220443739124826907637 x2[1] (numeric) = -4.1413018969797786111451927000158e+44 absolute error = 4.1413018969797786111451927000158e+44 relative error = 4.6550345650369135997211770405507e+49 % h = 0.001 x1[1] (analytic) = 0.00122304826416357283587587482203 x1[1] (numeric) = 1.7557792400527687448103988235585e+46 absolute error = 1.7557792400527687448103988235585e+46 relative error = 1.4355764130481995760484465983179e+51 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.566 x2[1] (analytic) = 0.00089070842292235953849705515730068 x2[1] (numeric) = -6.2242725438754744400350241917297e+45 absolute error = 6.2242725438754744400350241917297e+45 relative error = 6.9880023402653128011532026095229e+50 % h = 0.001 x1[1] (analytic) = 0.001222025727253075919286180057411 x1[1] (numeric) = 1.7620043161420033069605273349766e+47 absolute error = 1.7620043161420033069605273349766e+47 relative error = 1.4418717027363371542977335928792e+52 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=26.7MB, alloc=4.3MB, time=1.56 t[1] = 0.567 x2[1] (analytic) = 0.00089178015361418405848453645636232 x2[1] (numeric) = -6.2141071752097569666088393566103e+46 absolute error = 6.2141071752097569666088393566103e+46 relative error = 6.9682052802199965166189847573389e+51 % h = 0.001 x1[1] (analytic) = 0.0012210042123683914245858479623694 x1[1] (numeric) = 1.5111828972596486947701778356762e+48 absolute error = 1.5111828972596486947701778356762e+48 relative error = 1.2376557606860302345494036962019e+53 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.568 x2[1] (analytic) = 0.00089285454092535984878409653241629 x2[1] (numeric) = -5.3060398252158809707396469081545e+47 absolute error = 5.3060398252158809707396469081545e+47 relative error = 5.9427819224805299075885320262646e+52 % h = 0.001 x1[1] (analytic) = 0.0012199837184880043819641406086574 x1[1] (numeric) = 1.1763192844019761307956268538499e+49 absolute error = 1.1763192844019761307956268538499e+49 relative error = 9.6420900260853965953780541957631e+53 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.569 x2[1] (analytic) = 0.00089393158966368473941194530952011 x2[1] (numeric) = -4.1179096084541391241054471485886e+48 absolute error = 4.1179096084541391241054471485886e+48 relative error = 4.6065153710513581263231385534888e+53 % h = 0.001 x1[1] (analytic) = 0.0012189642445914208259928558409419 x1[1] (numeric) = 8.5177628724472357333257217805781e+49 absolute error = 8.5177628724472357333257217805781e+49 relative error = 6.9877052671895774757523014343295e+54 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.57 x2[1] (analytic) = 0.00089501130464709228041502404947533 x2[1] (numeric) = -2.9781501641580982926819264023201e+49 absolute error = 2.9781501641580982926819264023201e+49 relative error = 3.3275000535690426262334893649923e+54 % h = 0.001 x1[1] (analytic) = 0.0012179457896591667751322768074366 x1[1] (numeric) = 5.8321391716182165243656133848141e+50 absolute error = 5.8321391716182165243656133848141e+50 relative error = 4.7885047274971885513334860490382e+55 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.571 x2[1] (analytic) = 0.00089609369070367152334883261215016 x2[1] (numeric) = -2.0397258833796450993649500299965e+50 absolute error = 2.0397258833796450993649500299965e+50 relative error = 2.2762417641596366889588345449381e+55 % h = 0.001 x1[1] (analytic) = 0.0012169283526727872122571054640167 x1[1] (numeric) = 3.8298145741817899014545709204468e+51 absolute error = 3.8298145741817899014545709204468e+51 relative error = 3.1471159051970633723447357469897e+56 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.572 x2[1] (analytic) = 0.00089717875267168684286779387121317 x2[1] (numeric) = -1.3408563099943228462922517660030e+51 absolute error = 1.3408563099943228462922517660030e+51 relative error = 1.4945252615506323223481151456817e+56 % h = 0.001 x1[1] (analytic) = 0.0012159119326148450662013605776668 x1[1] (numeric) = 2.4406515362741576292103795590223e+52 absolute error = 2.4406515362741576292103795590223e+52 relative error = 2.0072601237044227357479230161324e+57 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.573 x2[1] (analytic) = 0.00089826649539959779850795090092798 x2[1] (numeric) = -8.5528634610705944862683893186664e+51 absolute error = 8.5528634610705944862683893186664e+51 relative error = 9.5215211798207118750045392232150e+56 % h = 0.001 x1[1] (analytic) = 0.0012148965284689201943212217740738 x1[1] (numeric) = 1.5202235678608787521377880015141e+53 absolute error = 1.5202235678608787521377880015141e+53 relative error = 1.2513193776072013158575006432788e+58 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.574 x2[1] (analytic) = 0.00089935692374607903674195281006981 x2[1] (numeric) = -5.3276543688642093012574115002706e+52 absolute error = 5.3276543688642093012574115002706e+52 relative error = 5.9238487281256520092105665062035e+57 % h = 0.001 x1[1] (analytic) = 0.0012138821392196083660748021921261 x1[1] (numeric) = 9.2570621658676472834064895360310e+53 absolute error = 9.2570621658676472834064895360310e+53 relative error = 7.6259975056712770625052448494990e+58 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.575 x2[1] (analytic) = 0.00090045004258004023338644567976864 x2[1] (numeric) = -3.2408818039140228044448331934073e+53 absolute error = 3.2408818039140228044448331934073e+53 relative error = 3.5991800218344079821589597192459e+58 % h = 0.001 x1[1] (analytic) = 0.0012128687638525202476178333250037 x1[1] (numeric) = 5.4726711960066224015198422044698e+54 absolute error = 5.4726711960066224015198422044698e+54 relative error = 4.5121709447140781136913519544988e+59 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 8.287e-05 Order of pole = 44.99 t[1] = 0.576 x2[1] (analytic) = 0.00090154585678064607644214596380192 x2[1] (numeric) = -1.9128471401725350634317086798115e+54 absolute error = 1.9128471401725350634317086798115e+54 relative error = 2.1217413687676092969344047917474e+59 % h = 0.001 x1[1] (analytic) = 0.0012118564013542803874142466434628 x1[1] (numeric) = 3.1031377015220580801033398774309e+55 absolute error = 3.1031377015220580801033398774309e+55 relative error = 2.5606480256689015958235101457987e+60 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.577 memory used=30.5MB, alloc=4.3MB, time=1.79 x2[1] (analytic) = 0.00090264437123733628944703493319481 x2[1] (numeric) = -1.0830031259993200683646363988051e+55 absolute error = 1.0830031259993200683646363988051e+55 relative error = 1.1998115321039998501240429761896e+60 % h = 0.001 x1[1] (analytic) = 0.0012108450507125262028606376118103 x1[1] (numeric) = 1.6610425221115017734463373981237e+56 absolute error = 1.6610425221115017734463373981237e+56 relative error = 1.3718043618661654688336698857089e+61 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.578 x2[1] (analytic) = 0.00090374559084984569542327429258224 x2[1] (numeric) = -5.7923535769912255219744191938231e+55 absolute error = 5.7923535769912255219744191938231e+55 relative error = 6.4092745078228610451255820554276e+60 % h = 0.001 x1[1] (analytic) = 0.0012098347109159069679235987209479 x1[1] (numeric) = 8.2060930899503125274936483247462e+56 absolute error = 8.2060930899503125274936483247462e+56 relative error = 6.7828216663893523943154890279843e+61 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.579 x2[1] (analytic) = 0.00090484952052822432149860496429206 x2[1] (numeric) = -2.8609726586177813939954436750353e+56 absolute error = 2.8609726586177813939954436750353e+56 relative error = 3.1618214893318729760650217704806e+61 % h = 0.001 x1[1] (analytic) = 0.0012088253809540828017889091757341 x1[1] (numeric) = 3.5737760382361641920914785963704e+57 absolute error = 3.5737760382361641920914785963704e+57 relative error = 2.9564038731677772198661007769200e+62 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.58 x2[1] (analytic) = 0.00090595616519285754428315322816622 x2[1] (numeric) = -1.2449978815061120073683373794633e+57 absolute error = 1.2449978815061120073683373794633e+57 relative error = 1.3742363365241630230990374100745e+62 % h = 0.001 x1[1] (analytic) = 0.0012078170598177236585215698857712 x1[1] (numeric) = 1.1834306117011450248147940616412e+58 absolute error = 1.1834306117011450248147940616412e+58 relative error = 9.7980948528723473498446437501943e+62 % h = 0.001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 7.054e-05 Order of pole = 5.63 t[1] = 0.581 x2[1] (analytic) = 0.00090706552977448627608273092139788 x2[1] (numeric) = -4.1009381579274677288208541912904e+57 absolute error = 4.1009381579274677288208541912904e+57 relative error = 4.5211046206849452961255053807970e+62 % h = 0.001 x1[1] (analytic) = 0.0012068097464985083177356734195659 x1[1] (numeric) = 4.9158190708782411993261744499246e+57 absolute error = 4.9158190708782411993261744499246e+57 relative error = 4.0734002067361637919702258649170e+62 % h = 0.001 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 5.144e-05 Order of pole = 1.61 t[1] = 0.582 x2[1] (analytic) = 0.00090817761921422719202987924377588 x2[1] (numeric) = -1.3764404433401996478927625577277e+57 absolute error = 1.3764404433401996478927625577277e+57 relative error = 1.5156070951529531093604096058848e+62 % h = 0.001 x1[1] (analytic) = 0.0012058034399891233762730995918507 x1[1] (numeric) = -4.1783158310013619174562996225764e+59 absolute error = 4.1783158310013619174562996225764e+59 relative error = 3.4651715963250621387003757068289e+64 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.583 x2[1] (analytic) = 0.00090929243846359299821406888034318 x2[1] (numeric) = 1.4880362600581185880347151894486e+59 absolute error = 1.4880362600581185880347151894486e+59 relative error = 1.6364771080384364298545807586215e+64 % h = 0.001 x1[1] (analytic) = 0.0012047981392832622408900283626774 x1[1] (numeric) = -5.4711006233959855894363711515958e+60 absolute error = 5.4711006233959855894363711515958e+60 relative error = 4.5410931881508038724405194768252e+65 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.584 x2[1] (analytic) = 0.00091040999248451274089263264624774 x2[1] (numeric) = 1.9300132430361618402214430292855e+60 absolute error = 1.9300132430361618402214430292855e+60 relative error = 2.1199385540234982404362204221787e+65 % h = 0.001 x1[1] (analytic) = 0.0012037938433756241219502627347115 x1[1] (numeric) = -5.1739401427306391912768564985913e+61 absolute error = 5.1739401427306391912768564985913e+61 relative error = 4.2980284134217789335943795406151e+66 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.585 x2[1] (analytic) = 0.00091153028624935215686417067814311 x2[1] (numeric) = 1.8177609467006611604627154451172e+61 absolute error = 1.8177609467006611604627154451172e+61 relative error = 1.9941860123816078855848369973268e+66 % h = 0.001 x1[1] (analytic) = 0.0012027905512619130281243553419666 x1[1] (numeric) = -4.2510572335481436371702240130992e+62 absolute error = 4.2510572335481436371702240130992e+62 relative error = 3.5343287566468892971290472412034e+67 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.586 x2[1] (analytic) = 0.0009126533247409340650863323435399 x2[1] (numeric) = 1.4903756675927179844930831829429e+62 absolute error = 1.4903756675927179844930831829429e+62 relative error = 1.6330140122107989759349129747956e+67 % h = 0.001 x1[1] (analytic) = 0.0012017882619388367620935334290215 x1[1] (numeric) = -3.2095476108022800455768938587771e+63 absolute error = 3.2095476108022800455768938587771e+63 relative error = 2.6706431677276818243777301664304e+68 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.587 x2[1] (analytic) = 0.00091377911295255879962004351467114 x2[1] (numeric) = 1.1243462369502534914511383972012e+63 absolute error = 1.1243462369502534914511383972012e+63 relative error = 1.2304354750649972750890661739801e+68 % h = 0.001 x1[1] (analytic) = 0.0012007869744041059172574179245617 x1[1] (numeric) = -2.2870791849151302458501096617625e+64 absolute error = 2.2870791849151302458501096617625e+64 relative error = 1.9046502282805824460053098896670e+69 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.03 NO POLE NO POLE t[1] = 0.588 x2[1] (analytic) = 0.00091490765588802468398241265737402 x2[1] (numeric) = 8.0118923017946421777450514613766e+63 absolute error = 8.0118923017946421777450514613766e+63 relative error = 8.7570502336852405190101976323188e+68 % h = 0.001 x1[1] (analytic) = 0.0011997866876564328754445333168804 x1[1] (numeric) = -1.5629565678008495831816850257672e+65 absolute error = 1.5629565678008495831816850257672e+65 relative error = 1.3026953740033602431499287891374e+70 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.589 x2[1] (analytic) = 0.00091603895856164854699071431886538 x2[1] (numeric) = 5.4762562415555361135822530536608e+64 absolute error = 5.4762562415555361135822530536608e+64 relative error = 5.9781914190137463449025339654806e+69 % h = 0.001 x1[1] (analytic) = 0.0011987874006955308056246060417651 x1[1] (numeric) = -1.0341097134354206938215479800156e+66 absolute error = 1.0341097134354206938215479800156e+66 relative error = 8.6262978142365786209645964569143e+70 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.59 x2[1] (analytic) = 0.00091717302599828628018001406175885 x2[1] (numeric) = 3.6230418852219134339158494260653e+65 absolute error = 3.6230418852219134339158494260653e+65 relative error = 3.9502272554063130686279994019155e+70 % h = 0.001 x1[1] (analytic) = 0.0011977891125221126636216500949856 x1[1] (numeric) = -6.6516002029969479587038167170453e+66 absolute error = 6.6516002029969479587038167170453e+66 relative error = 5.5532314774435313787592546101951e+71 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.591 x2[1] (analytic) = 0.00091830986323335343687716468589885 x2[1] (numeric) = 2.3292514846201026170126830694318e+66 absolute error = 2.3292514846201026170126830694318e+66 relative error = 2.5364548262814554631612768957381e+71 % h = 0.001 x1[1] (analytic) = 0.0011967918221378901928268395823847 x1[1] (numeric) = -4.1578916226152450201242728216474e+67 absolute error = 4.1578916226152450201242728216474e+67 relative error = 3.4741978894773791353878735820395e+72 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.592 x2[1] (analytic) = 0.00091944947531284587301406970523356 x2[1] (numeric) = 1.4548366059964883097726377014911e+67 absolute error = 1.4548366059964883097726377014911e+67 relative error = 1.5822909741739480666894786112207e+72 % h = 0.001 x1[1] (analytic) = 0.0011957955285455729259101689203614 x1[1] (numeric) = -2.5170844193402301366549004981790e+68 absolute error = 2.5170844193402301366549004981790e+68 relative error = 2.1049455021810625638570947561428e+73 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.593 x2[1] (analytic) = 0.00092059186729336042976327650467993 x2[1] (numeric) = 8.7998648046171344928540264292756e+67 absolute error = 8.7998648046171344928540264292756e+67 relative error = 9.5589208608693100273025295188011e+72 % h = 0.001 x1[1] (analytic) = 0.001194800230748867187529902398324 x1[1] (numeric) = -1.4677151183780838290829407608899e+69 absolute error = 1.4677151183780838290829407608899e+69 relative error = 1.2284188440925904945620816109595e+74 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.594 x2[1] (analytic) = 0.00092173704424211565807912839241284 x2[1] (numeric) = 5.1279543047820128922466442898460e+68 absolute error = 5.1279543047820128922466442898460e+68 relative error = 5.5633592430891130681035339330519e+73 % h = 0.001 x1[1] (analytic) = 0.0011938059277524750980388158124784 x1[1] (numeric) = -8.1831317210789717805782561923994e+69 absolute error = 8.1831317210789717805782561923994e+69 relative error = 6.8546583082268547809552551361832e+74 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.595 x2[1] (analytic) = 0.00092288501123697258522787188690669 x2[1] (numeric) = 2.8579102890795473554490271730013e+69 absolute error = 2.8579102890795473554490271730013e+69 relative error = 3.0967133004457379782201978888659e+74 % h = 0.001 x1[1] (analytic) = 0.0011928126185620935781862338771108 x1[1] (numeric) = -4.3124854774878951646519863228473e+70 absolute error = 4.3124854774878951646519863228473e+70 relative error = 3.6153922337663487119714040838299e+75 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.596 x2[1] (analytic) = 0.00092403577336645552339028303603533 x2[1] (numeric) = 1.5055052064378101951615934808220e+70 absolute error = 1.5055052064378101951615934808220e+70 relative error = 1.6292715605078144877306596721691e+75 % h = 0.001 x1[1] (analytic) = 0.0011918203021844133548148681153206 x1[1] (numeric) = -2.0994896005525668548011801626882e+71 absolute error = 2.0994896005525668548011801626882e+71 relative error = 1.7615823431641018858190686179219e+76 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.597 x2[1] (analytic) = 0.00092518933572977292042054435826881 x2[1] (numeric) = 7.3224242801927720218823847443467e+70 absolute error = 7.3224242801927720218823847443467e+70 relative error = 7.9145143565851564492655003774011e+75 % h = 0.001 x1[1] (analytic) = 0.0011908289776271179675514609259555 x1[1] (numeric) = -8.9217291718118612335310348792867e+71 absolute error = 8.9217291718118612335310348792867e+71 relative error = 7.4920323064270488949435598672783e+76 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=38.1MB, alloc=4.4MB, time=2.27 t[1] = 0.598 x2[1] (analytic) = 0.00092634570343683825284527212416087 x2[1] (numeric) = 3.1035207533019070951412139108633e+71 absolute error = 3.1035207533019070951412139108633e+71 relative error = 3.3502835299905040865330934159545e+76 % h = 0.001 x1[1] (analytic) = 0.0011898386438988827764902425173134 x1[1] (numeric) = -2.7112285306233839106350033281485e+72 absolute error = 2.7112285306233839106350033281485e+72 relative error = 2.2786522731680539549209282557749e+77 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.599 x2[1] (analytic) = 0.0009275048816082909611867621605716 x2[1] (numeric) = 9.3472236197729701929881478446902e+71 absolute error = 9.3472236197729701929881478446902e+71 relative error = 1.0077816090374543006540576385845e+77 % h = 0.001 x1[1] (analytic) = 0.001188849300009373970868208390983 x1[1] (numeric) = 2.0946281308220220861936040218879e+72 absolute error = 2.0946281308220220861936040218879e+72 relative error = 1.7618954150080301430134911247571e+77 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.6 x2[1] (analytic) = 0.00092866687537551742769469116109009 x2[1] (numeric) = -8.2971446950140066344438697293588e+71 absolute error = 8.2971446950140066344438697293588e+71 relative error = 8.9344682307732340583419286343589e+76 % h = 0.001 x1[1] (analytic) = 0.0011878609449692475787312260510186 x1[1] (numeric) = 1.3603092904579727828001945828630e+74 absolute error = 1.3603092904579727828001945828630e+74 relative error = 1.1451755327246571804827170807987e+79 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; Iterations = 100 Total Elapsed Time = 2 Seconds Elapsed Time(since restart) = 2 Seconds Expected Time Remaining = 1 Minutes 39 Seconds Optimized Time Remaining = 1 Minutes 38 Seconds Time to Timeout = 14 Minutes 57 Seconds Percent Done = 2.244 % > quit memory used=39.1MB, alloc=4.4MB, time=2.33