|\^/| 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 > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > #Top Generate Globals Decl > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_hmin_init, > glob_hmin, > days_in_year, > sec_in_min, > glob_current_iter, > glob_optimal_clock_start_sec, > glob_abserr, > glob_last_good_h, > glob_reached_optimal_h, > glob_log10relerr, > glob_look_poles, > glob_clock_start_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_order, > glob_log10_abserr, > glob_initial_pass, > glob_not_yet_finished, > glob_max_minutes, > glob_iter, > glob_start, > hours_in_day, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmax, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_log10_relerr, > glob_h, > glob_log10normmin, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_disp_incr, > glob_not_yet_start_msg, > glob_almost_1, > years_in_century, > MAX_UNCHANGED, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_optimal_done, > glob_clock_sec, > djd_debug2, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > #END CONST > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_type_pole, > array_pole, > array_x1_init, > array_t, > array_x2, > array_x1, > array_last_rel_error, > array_1st_rel_error, > array_x2_init, > array_norms, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_poles, > array_x2_higher_work, > array_real_pole, > 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 DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin, days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec, glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr, glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter, glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin, centuries_in_millinium, glob_percent_done, glob_normmax, glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED, glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic, glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2, glob_display_flag, array_const_1, array_const_2, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1, array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms, array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole, array_x1_higher_work, array_x2_higher_work2, array_poles, array_x2_higher_work, array_real_pole, 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 > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > #Top Generate Globals Decl > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_hmin_init, > glob_hmin, > days_in_year, > sec_in_min, > glob_current_iter, > glob_optimal_clock_start_sec, > glob_abserr, > glob_last_good_h, > glob_reached_optimal_h, > glob_log10relerr, > glob_look_poles, > glob_clock_start_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_order, > glob_log10_abserr, > glob_initial_pass, > glob_not_yet_finished, > glob_max_minutes, > glob_iter, > glob_start, > hours_in_day, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmax, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_log10_relerr, > glob_h, > glob_log10normmin, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_disp_incr, > glob_not_yet_start_msg, > glob_almost_1, > years_in_century, > MAX_UNCHANGED, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_optimal_done, > glob_clock_sec, > djd_debug2, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > #END CONST > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_type_pole, > array_pole, > array_x1_init, > array_t, > array_x2, > array_x1, > array_last_rel_error, > array_1st_rel_error, > array_x2_init, > array_norms, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_poles, > array_x2_higher_work, > array_real_pole, > 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 DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin, days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec, glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr, glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter, glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin, centuries_in_millinium, glob_percent_done, glob_normmax, glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED, glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic, glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2, glob_display_flag, array_const_1, array_const_2, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1, array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms, array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole, array_x1_higher_work, array_x2_higher_work2, array_poles, array_x2_higher_work, array_real_pole, 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 > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > #Top Generate Globals Decl > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_hmin_init, > glob_hmin, > days_in_year, > sec_in_min, > glob_current_iter, > glob_optimal_clock_start_sec, > glob_abserr, > glob_last_good_h, > glob_reached_optimal_h, > glob_log10relerr, > glob_look_poles, > glob_clock_start_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_order, > glob_log10_abserr, > glob_initial_pass, > glob_not_yet_finished, > glob_max_minutes, > glob_iter, > glob_start, > hours_in_day, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmax, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_log10_relerr, > glob_h, > glob_log10normmin, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_disp_incr, > glob_not_yet_start_msg, > glob_almost_1, > years_in_century, > MAX_UNCHANGED, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_optimal_done, > glob_clock_sec, > djd_debug2, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > #END CONST > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_type_pole, > array_pole, > array_x1_init, > array_t, > array_x2, > array_x1, > array_last_rel_error, > array_1st_rel_error, > array_x2_init, > array_norms, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_poles, > array_x2_higher_work, > array_real_pole, > 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 DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin, days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec, glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr, glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter, glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin, centuries_in_millinium, glob_percent_done, glob_normmax, glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED, glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic, glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2, glob_display_flag, array_const_1, array_const_2, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1, array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms, array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole, array_x1_higher_work, array_x2_higher_work2, array_poles, array_x2_higher_work, array_real_pole, 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 > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > #Top Generate Globals Decl > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_hmin_init, > glob_hmin, > days_in_year, > sec_in_min, > glob_current_iter, > glob_optimal_clock_start_sec, > glob_abserr, > glob_last_good_h, > glob_reached_optimal_h, > glob_log10relerr, > glob_look_poles, > glob_clock_start_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_order, > glob_log10_abserr, > glob_initial_pass, > glob_not_yet_finished, > glob_max_minutes, > glob_iter, > glob_start, > hours_in_day, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmax, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_log10_relerr, > glob_h, > glob_log10normmin, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_disp_incr, > glob_not_yet_start_msg, > glob_almost_1, > years_in_century, > MAX_UNCHANGED, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_optimal_done, > glob_clock_sec, > djd_debug2, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > #END CONST > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_type_pole, > array_pole, > array_x1_init, > array_t, > array_x2, > array_x1, > array_last_rel_error, > array_1st_rel_error, > array_x2_init, > array_norms, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_poles, > array_x2_higher_work, > array_real_pole, > 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 DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin, days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec, glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr, glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter, glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin, centuries_in_millinium, glob_percent_done, glob_normmax, glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED, glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic, glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2, glob_display_flag, array_const_1, array_const_2, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1, array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms, array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole, array_x1_higher_work, array_x2_higher_work2, array_poles, array_x2_higher_work, array_real_pole, 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 > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > #Top Generate Globals Decl > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_hmin_init, > glob_hmin, > days_in_year, > sec_in_min, > glob_current_iter, > glob_optimal_clock_start_sec, > glob_abserr, > glob_last_good_h, > glob_reached_optimal_h, > glob_log10relerr, > glob_look_poles, > glob_clock_start_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_order, > glob_log10_abserr, > glob_initial_pass, > glob_not_yet_finished, > glob_max_minutes, > glob_iter, > glob_start, > hours_in_day, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmax, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_log10_relerr, > glob_h, > glob_log10normmin, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_disp_incr, > glob_not_yet_start_msg, > glob_almost_1, > years_in_century, > MAX_UNCHANGED, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_optimal_done, > glob_clock_sec, > djd_debug2, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > #END CONST > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_type_pole, > array_pole, > array_x1_init, > array_t, > array_x2, > array_x1, > array_last_rel_error, > array_1st_rel_error, > array_x2_init, > array_norms, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_poles, > array_x2_higher_work, > array_real_pole, > 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 DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin, days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec, glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr, glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter, glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin, centuries_in_millinium, glob_percent_done, glob_normmax, glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED, glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic, glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2, glob_display_flag, array_const_1, array_const_2, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1, array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms, array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole, array_x1_higher_work, array_x2_higher_work2, array_poles, array_x2_higher_work, array_real_pole, 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 > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > #Top Generate Globals Decl > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_hmin_init, > glob_hmin, > days_in_year, > sec_in_min, > glob_current_iter, > glob_optimal_clock_start_sec, > glob_abserr, > glob_last_good_h, > glob_reached_optimal_h, > glob_log10relerr, > glob_look_poles, > glob_clock_start_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_order, > glob_log10_abserr, > glob_initial_pass, > glob_not_yet_finished, > glob_max_minutes, > glob_iter, > glob_start, > hours_in_day, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmax, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_log10_relerr, > glob_h, > glob_log10normmin, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_disp_incr, > glob_not_yet_start_msg, > glob_almost_1, > years_in_century, > MAX_UNCHANGED, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_optimal_done, > glob_clock_sec, > djd_debug2, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > #END CONST > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_type_pole, > array_pole, > array_x1_init, > array_t, > array_x2, > array_x1, > array_last_rel_error, > array_1st_rel_error, > array_x2_init, > array_norms, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_poles, > array_x2_higher_work, > array_real_pole, > 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 DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin, days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec, glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr, glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter, glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin, centuries_in_millinium, glob_percent_done, glob_normmax, glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED, glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic, glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2, glob_display_flag, array_const_1, array_const_2, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1, array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms, array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole, array_x1_higher_work, array_x2_higher_work2, array_poles, array_x2_higher_work, array_real_pole, 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 > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > #Top Generate Globals Decl > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_hmin_init, > glob_hmin, > days_in_year, > sec_in_min, > glob_current_iter, > glob_optimal_clock_start_sec, > glob_abserr, > glob_last_good_h, > glob_reached_optimal_h, > glob_log10relerr, > glob_look_poles, > glob_clock_start_sec, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_order, > glob_log10_abserr, > glob_initial_pass, > glob_not_yet_finished, > glob_max_minutes, > glob_iter, > glob_start, > hours_in_day, > glob_dump, > glob_max_opt_iter, > glob_html_log, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_warned2, > glob_max_rel_trunc_err, > glob_hmax, > min_in_hour, > djd_debug, > glob_optimal_expect_sec, > glob_log10_relerr, > glob_h, > glob_log10normmin, > centuries_in_millinium, > glob_percent_done, > glob_normmax, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_disp_incr, > glob_not_yet_start_msg, > glob_almost_1, > years_in_century, > MAX_UNCHANGED, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_optimal_done, > glob_clock_sec, > djd_debug2, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > #END CONST > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_type_pole, > array_pole, > array_x1_init, > array_t, > array_x2, > array_x1, > array_last_rel_error, > array_1st_rel_error, > array_x2_init, > array_norms, > array_x1_higher_work2, > array_x1_higher, > array_x2_higher, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work2, > array_poles, > array_x2_higher_work, > array_real_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > glob_max_terms := 30; > glob_max_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_relerr := 0.1e-10; > glob_hmin_init := 0.001; > glob_hmin := 0.00000000001; > days_in_year := 365.0; > sec_in_min := 60.0; > glob_current_iter := 0; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_last_good_h := 0.1; > glob_reached_optimal_h := false; > glob_log10relerr := 0.0; > glob_look_poles := false; > glob_clock_start_sec := 0.0; > glob_unchanged_h_cnt := 0; > glob_optimal_start := 0.0; > glob_no_eqs := 0; > glob_max_order := 30; > glob_log10_abserr := 0.1e-10; > glob_initial_pass := true; > glob_not_yet_finished := true; > glob_max_minutes := 0.0; > glob_iter := 0; > glob_start := 0; > hours_in_day := 24.0; > glob_dump := false; > glob_max_opt_iter := 10; > glob_html_log := true; > glob_log10abserr := 0.0; > glob_curr_iter_when_opt := 0; > glob_warned2 := false; > glob_max_rel_trunc_err := 0.1e-10; > glob_hmax := 1.0; > min_in_hour := 60.0; > djd_debug := true; > glob_optimal_expect_sec := 0.1; > glob_log10_relerr := 0.1e-10; > glob_h := 0.1; > glob_log10normmin := 0.1; > centuries_in_millinium := 10.0; > glob_percent_done := 0.0; > glob_normmax := 0.0; > glob_orig_start_sec := 0.0; > glob_warned := false; > glob_small_float := 0.1e-50; > glob_disp_incr := 0.1; > glob_not_yet_start_msg := true; > glob_almost_1 := 0.9990; > years_in_century := 100.0; > MAX_UNCHANGED := 10; > glob_max_sec := 10000.0; > glob_smallish_float := 0.1e-100; > glob_max_iter := 1000; > glob_dump_analytic := false; > glob_large_float := 9.0e100; > glob_optimal_done := false; > glob_clock_sec := 0.0; > djd_debug2 := true; > glob_display_flag := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_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/complicatedrev3postode.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 := 0.00005 ;"); > 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_m1:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_tmp7:= Array(1..(max_terms + 1),[]); > array_tmp8:= Array(1..(max_terms + 1),[]); > array_tmp9:= Array(1..(max_terms + 1),[]); > array_tmp10:= Array(1..(max_terms + 1),[]); > array_tmp11:= Array(1..(max_terms + 1),[]); > array_tmp12:= Array(1..(max_terms + 1),[]); > array_tmp13:= Array(1..(max_terms + 1),[]); > array_tmp14:= Array(1..(max_terms + 1),[]); > array_tmp15:= Array(1..(max_terms + 1),[]); > array_tmp16:= Array(1..(max_terms + 1),[]); > array_tmp17:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_t:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_x1:= 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_init:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 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 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_t[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_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_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 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[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > 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_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_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_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 := 0.00005 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_x2(); > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_x1(); > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > sub_iter := 1; > while sub_iter <= 3 + glob_max_terms do # do number 3 > atomall() > ; > sub_iter := sub_iter + 1; > od;# end do number 3 > ; > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3 > ;#was right paren 0004C > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > order_diff := 2; > #Jump Series array_x2 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > order_diff := 2; > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 3; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > order_diff := 1; > #Jump Series array_x1 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > order_diff := 1; > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 3 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 3 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if glob_html_log then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-02T02:12:37-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"complicatedrev3") > ; > 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,"complicatedrev3 diffeq.mxt") > ; > logitem_str(html_log_file,"complicatedrev3 maple results") > ; > logitem_str(html_log_file,"sub iter tot order + max terms 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 DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin, days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec, glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr, glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr, glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter, glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log, glob_log10abserr, glob_curr_iter_when_opt, glob_warned2, glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug, glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin, centuries_in_millinium, glob_percent_done, glob_normmax, glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED, glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic, glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2, glob_display_flag, array_const_1, array_const_2, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1, array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms, array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole, array_x1_higher_work, array_x2_higher_work2, array_poles, array_x2_higher_work, array_real_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; ALWAYS := 1; INFO := 2; glob_max_terms := 30; glob_max_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_relerr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_hmin := 0.1*10^(-10); days_in_year := 365.0; sec_in_min := 60.0; glob_current_iter := 0; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_reached_optimal_h := false; glob_log10relerr := 0.; glob_look_poles := false; glob_clock_start_sec := 0.; glob_unchanged_h_cnt := 0; glob_optimal_start := 0.; glob_no_eqs := 0; glob_max_order := 30; glob_log10_abserr := 0.1*10^(-10); glob_initial_pass := true; glob_not_yet_finished := true; glob_max_minutes := 0.; glob_iter := 0; glob_start := 0; hours_in_day := 24.0; glob_dump := false; glob_max_opt_iter := 10; glob_html_log := true; glob_log10abserr := 0.; glob_curr_iter_when_opt := 0; glob_warned2 := false; glob_max_rel_trunc_err := 0.1*10^(-10); glob_hmax := 1.0; min_in_hour := 60.0; djd_debug := true; glob_optimal_expect_sec := 0.1; glob_log10_relerr := 0.1*10^(-10); glob_h := 0.1; glob_log10normmin := 0.1; centuries_in_millinium := 10.0; glob_percent_done := 0.; glob_normmax := 0.; glob_orig_start_sec := 0.; glob_warned := false; glob_small_float := 0.1*10^(-50); glob_disp_incr := 0.1; glob_not_yet_start_msg := true; glob_almost_1 := 0.9990; years_in_century := 100.0; MAX_UNCHANGED := 10; glob_max_sec := 10000.0; glob_smallish_float := 0.1*10^(-100); glob_max_iter := 1000; glob_dump_analytic := false; glob_large_float := 0.90*10^101; glob_optimal_done := false; glob_clock_sec := 0.; djd_debug2 := true; glob_display_flag := true; 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/complicatedrev3postode.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 := 0.00005 ;"); 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_m1 := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_tmp7 := Array(1 .. max_terms + 1, []); array_tmp8 := Array(1 .. max_terms + 1, []); array_tmp9 := Array(1 .. max_terms + 1, []); array_tmp10 := Array(1 .. max_terms + 1, []); array_tmp11 := Array(1 .. max_terms + 1, []); array_tmp12 := Array(1 .. max_terms + 1, []); array_tmp13 := Array(1 .. max_terms + 1, []); array_tmp14 := Array(1 .. max_terms + 1, []); array_tmp15 := Array(1 .. max_terms + 1, []); array_tmp16 := Array(1 .. max_terms + 1, []); array_tmp17 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_t := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_x1 := 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_init := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_t[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_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_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 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[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 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_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_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_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 := 0.00005; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_t[1] := t_start; array_t[2] := glob_h; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x2_higher[r_order, term_no] := array_x2_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x1_higher[r_order, term_no] := array_x1_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_x2(); if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_x1(); if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_t[1] <= t_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; sub_iter := 1; while sub_iter <= 3 + glob_max_terms do atomall(); sub_iter := sub_iter + 1 end do; if glob_look_poles then check_for_pole() end if; array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 2; order_diff := 2; order_diff := 2; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; order_diff := 1; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\ ff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(INFO, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-02T02:12:37-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "complicatedrev3"); 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, "complicatedrev3 diffeq.mxt"); logitem_str(html_log_file, "complicatedrev3 maple results"); logitem_str(html_log_file, "sub iter tot order + max terms 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/complicatedrev3postode.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 := 0.00005 ; 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 = 5e-05 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 5e-05 t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 5e-05 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 5e-05 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.20 NO POLE NO POLE t[1] = 0.50005 x2[1] (analytic) = 0.00082566083422809021229815693339498 x2[1] (numeric) = 0.00082566083695768288580953900132404 absolute error = 2.72959267351138206792906e-12 relative error = 3.3059490778235551390117036491830e-07 % h = 5e-05 x1[1] (analytic) = 0.0012917006010880372652167092040327 x1[1] (numeric) = 0.0012917005956294101945681497523304 absolute error = 5.4586270706485594517023e-12 relative error = 4.2259228385049894096809262604668e-07 % h = 5e-05 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.4MB, time=0.48 memory used=11.4MB, alloc=4.5MB, time=0.76 NO POLE NO POLE t[1] = 0.5001 x2[1] (analytic) = 0.00082570611074256394598966051590164 x2[1] (numeric) = 0.00082570612166195819564280058730035 absolute error = 1.091939424965314007139871e-11 relative error = 1.3224310814211176964894105127815e-06 % h = 5e-05 x1[1] (analytic) = 0.001291646017422585871235266471237 x1[1] (numeric) = 0.0012916459955876806646200645590095 absolute error = 2.18349052066152019122275e-11 relative error = 1.6904712987994689141068004837108e-06 % h = 5e-05 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.5MB, time=1.03 NO POLE NO POLE t[1] = 0.50015 x2[1] (analytic) = 0.00082575139314954126995470805844824 x2[1] (numeric) = 0.00082575141772058389758603430137354 absolute error = 2.457104262763132624292530e-11 relative error = 2.9755980833303394839523035700290e-06 % h = 5e-05 x1[1] (analytic) = 0.0012915914364862495213788540506512 x1[1] (numeric) = 0.0012915913873563234429827445767725 absolute error = 4.91299260783961094738787e-11 relative error = 3.8038287255955458736565201710781e-06 % h = 5e-05 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.6MB, time=1.30 memory used=22.8MB, alloc=4.6MB, time=1.57 NO POLE NO POLE t[1] = 0.5002 x2[1] (analytic) = 0.0008257966814495432344339416603249 x2[1] (numeric) = 0.00082579672513571925499813755054128 absolute error = 4.368617602056419589021638e-11 relative error = 5.2901854659770090598013732063872e-06 % h = 5e-05 x1[1] (analytic) = 0.0012915368582788917633066026400632 x1[1] (numeric) = 0.0012915367709341102157994826101921 absolute error = 8.73447815475071200298711e-11 relative error = 6.7628562814616995542694166023323e-06 % h = 5e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.6MB, time=1.84 NO POLE NO POLE t[1] = 0.50025 x2[1] (analytic) = 0.00082584197564309094518702663178858 x2[1] (numeric) = 0.0008258420439095239007238233415556 absolute error = 6.826643295553679670976702e-11 relative error = 8.2662827718798237035908373678726e-06 % h = 5e-05 x1[1] (analytic) = 0.0012914822828003761515000894181426 x1[1] (numeric) = 0.0012914821463198124849890774353521 absolute error = 1.364805636665110119827905e-10 relative error = 1.0567745720101895713651264456650e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.6MB, time=2.12 memory used=34.3MB, alloc=4.6MB, time=2.39 NO POLE NO POLE t[1] = 0.5003 x2[1] (analytic) = 0.00082588727573070556349803310856235 x2[1] (numeric) = 0.00082588737404415783715360011311766 absolute error = 9.831345227365556700455531e-11 relative error = 1.1903979533607964388943357952219e-05 % h = 5e-05 x1[1] (analytic) = 0.0012914277100505662472629969306448 x1[1] (numeric) = 0.0012914275135122015682182038172444 absolute error = 1.965383646790447931134004e-10 relative error = 1.5218688831707759568560980890415e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.6MB, time=2.67 NO POLE NO POLE t[1] = 0.50035 x2[1] (analytic) = 0.00082593258171290830618081821305085 x2[1] (numeric) = 0.00082593271554178143628376102029713 absolute error = 1.3382887313010294280724628e-10 relative error = 1.6203365273779871130867920442261e-05 % h = 5e-05 x1[1] (analytic) = 0.0012913731400293256187207719936699 x1[1] (numeric) = 0.0012913728725100485988737783832529 absolute error = 2.675192770198469936104170e-10 relative error = 2.0715877442965240424377310718147e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.6MB, time=2.94 NO POLE NO POLE t[1] = 0.5004 x2[1] (analytic) = 0.00082597789359022044558440876232671 x2[1] (numeric) = 0.00082597806840455543977638267263934 absolute error = 1.7481433499419197391031263e-10 relative error = 2.1164529505062019082354776596102e-05 % h = 5e-05 x1[1] (analytic) = 0.0012913185727365178408202846139762 x1[1] (numeric) = 0.0012913182233121245260353213521031 absolute error = 3.494243933147849632618731e-10 relative error = 2.7059503417061277498442285575952e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.6MB, time=3.21 memory used=49.5MB, alloc=4.6MB, time=3.49 NO POLE NO POLE t[1] = 0.50045 x2[1] (analytic) = 0.00082602321136316330959838452294175 x2[1] (numeric) = 0.00082602343263464095901933332742376 absolute error = 2.2127147764942094880448201e-10 relative error = 2.6787561730167695380232448787849e-05 % h = 5e-05 x1[1] (analytic) = 0.0012912640081720064953294869263476 x1[1] (numeric) = 0.0012912635659172001144473141176543 absolute error = 4.422548063808821728086933e-10 relative error = 3.4249758653690466937391215708875e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.6MB, time=3.76 NO POLE NO POLE t[1] = 0.5005 x2[1] (analytic) = 0.00082606853503225828165826201261726 x2[1] (numeric) = 0.00082606880823419947518629053953756 absolute error = 2.7320194119352802852692030e-10 relative error = 3.3072551441855776740271661500744e-05 % h = 5e-05 x1[1] (analytic) = 0.0012912094463356551708370721480129 x1[1] (numeric) = 0.0012912089003240459444915526869146 absolute error = 5.460116092263455194610983e-10 relative error = 4.2286835089061730028678645513922e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.6MB, time=4.04 memory used=61.0MB, alloc=4.6MB, time=4.32 NO POLE NO POLE t[1] = 0.50055 x2[1] (analytic) = 0.00082611386459802680075087884886784 x2[1] (numeric) = 0.00082611419520539283929676826942815 absolute error = 3.3060736603854588942056031e-10 relative error = 4.0019588122929507801520963897019e-05 % h = 5e-05 x1[1] (analytic) = 0.0012911548872273274627521335501181 x1[1] (numeric) = 0.0012911542265314324121594969716558 absolute error = 6.606958950505926365784623e-10 relative error = 5.1170924695904982606510212787934e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.6MB, time=4.60 NO POLE NO POLE t[1] = 0.5006 x2[1] (analytic) = 0.00082615920006099036141977864461309 x2[1] (numeric) = 0.00082615959355038327227615345059897 absolute error = 3.9348939291085637480598588e-10 relative error = 4.7628761246235280219858777252507e-05 % h = 5e-05 x1[1] (analytic) = 0.0012911003308468869733038234462486 x1[1] (numeric) = 0.0012910995445381297290246159330063 absolute error = 7.863087572442792075132423e-10 relative error = 6.0902219483477805652389977664018e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.6MB, time=4.90 memory used=72.4MB, alloc=4.6MB, time=5.19 NO POLE NO POLE t[1] = 0.50065 x2[1] (analytic) = 0.0008262045414216705137705964508309 x2[1] (numeric) = 0.00082620500327133336501575201811287 absolute error = 4.6184966285124515556728197e-10 relative error = 5.5900160274661412510746576950557e-05 % h = 5e-05 x1[1] (analytic) = 0.0012910457771941973115410121980021 x1[1] (numeric) = 0.0012910448543429079222147285784005 absolute error = 9.228512893893262836196016e-10 relative error = 7.1480911497572117090493086975919e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.6MB, time=5.48 NO POLE NO POLE t[1] = 0.5007 x2[1] (analytic) = 0.00082624988868058886347644474630742 x2[1] (numeric) = 0.00082625042437040607843284439956772 absolute error = 5.3568981721495639965326030e-10 relative error = 6.4833874661136930641167696137183e-05 % h = 5e-05 x1[1] (analytic) = 0.0012909912262691220933319472376107 x1[1] (numeric) = 0.0012909901559445368343843408102628 absolute error = 1.0703245852589476064273479e-09 relative error = 8.2907192820520844778073521367501e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.6MB, time=5.76 NO POLE NO POLE memory used=83.9MB, alloc=4.6MB, time=6.03 t[1] = 0.50075 x2[1] (analytic) = 0.00082629524183826707178329997453724 x2[1] (numeric) = 0.00082629585684976474353075047000912 absolute error = 6.1501149767174745049547188e-10 relative error = 7.4429993848630349370736355705148e-05 % h = 5e-05 x1[1] (analytic) = 0.0012909366780715249413639121076118 x1[1] (numeric) = 0.0012909354493417861236869781258031 absolute error = 1.2287297388176769339818087e-09 relative error = 9.5181255571204600691116879333554e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.6MB, time=6.32 NO POLE NO POLE t[1] = 0.5008 x2[1] (analytic) = 0.00082634060089522685551538962782877 x2[1] (numeric) = 0.00082634130071157306145890397224534 absolute error = 6.9981634620594351434441657e-10 relative error = 8.4688607270148454341961282132375e-05 % h = 5e-05 x1[1] (analytic) = 0.0012908821326012694851428855175656 x1[1] (numeric) = 0.0012908807345334252637475141673024 absolute error = 1.3980678442213953713502632e-09 relative error = 0.0001083032919050583563054479100121 % h = 5e-05 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.6MB, time=6.59 NO POLE NO POLE t[1] = 0.50085 x2[1] (analytic) = 0.00082638596585198998708057987866837 x2[1] (numeric) = 0.00082638675595799510357293640402965 absolute error = 7.9010600511649235652536128e-10 relative error = 9.5609804348735084919648354747817e-05 % h = 5e-05 x1[1] (analytic) = 0.0012908275898582193609932004178204 x1[1] (numeric) = 0.0012908260115182235436344951222662 absolute error = 1.5783399958173587052955542e-09 relative error = 0.00012227349401407811917350286834454 % h = 5e-05 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.6MB, time=6.88 memory used=99.1MB, alloc=4.7MB, time=7.18 NO POLE NO POLE t[1] = 0.5009 x2[1] (analytic) = 0.00082643133670907829447576375839823 x2[1] (numeric) = 0.00082643222259119531149477037357576 absolute error = 8.8588211701701900661517753e-10 relative error = 0.00010719367449746991777942651841703 % h = 5e-05 x1[1] (analytic) = 0.0012907730498422382120572030903234 x1[1] (numeric) = 0.0012907712802949500678324599728227 absolute error = 1.7695472881442247431175007e-09 relative error = 0.00013709205412682761069697657808744 % h = 5e-05 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.7MB, time=7.47 NO POLE NO POLE t[1] = 0.50095 x2[1] (analytic) = 0.00082647671346701366129224988326191 x2[1] (numeric) = 0.00082647770061333849717272242487194 absolute error = 9.8714632483588047254161003e-10 relative error = 0.00011944030711946725124538121355859 % h = 5e-05 x1[1] (analytic) = 0.0012907185125531896882949122564762 x1[1] (numeric) = 0.0012907165408623737562142565937436 absolute error = 1.9716908159320806556627326e-09 relative error = 0.00015275916450844494509555417111334 % h = 5e-05 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.7MB, time=7.76 memory used=110.6MB, alloc=4.7MB, time=8.05 NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652319002658984294161533425997 absolute error = 1.09390027181622046360638811e-09 relative error = 0.00013234979160787479037677949812843 % h = 5e-05 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906617932192633440133536984651 absolute error = 2.1847716741024703245035700e-09 relative error = 0.00016927501746064930957193758540632 % h = 5e-05 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.7MB, time=8.35 NO POLE NO POLE t[1] = 0.50105 x2[1] (analytic) = 0.0008265674846875133855587774461534 x2[1] (numeric) = 0.00082656869083311490158289987974494 absolute error = 1.20614560151602412243359154e-09 relative error = 0.0001459222173458724328038709032973 % h = 5e-05 x1[1] (analytic) = 0.0012906094461553451502178419190542 x1[1] (numeric) = 0.0012906070373643873817961486324857 absolute error = 2.4087909577684216932865685e-09 relative error = 0.00018663980532174764567337684769861 % h = 5e-05 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.7MB, time=8.65 NO POLE NO POLE memory used=122.0MB, alloc=4.7MB, time=8.93 t[1] = 0.5011 x2[1] (analytic) = 0.00082661287915112178821202023981947 x2[1] (numeric) = 0.00082661420303507959638478608450251 absolute error = 1.32388395780817276584468304e-09 relative error = 0.0001601576737066710553127480587017 % h = 5e-05 x1[1] (analytic) = 0.0012905549170462764699083942648711 x1[1] (numeric) = 0.0012905522732965142354342710135191 absolute error = 2.6437497622344741232513520e-09 relative error = 0.00020485372046664133184991620318868 % h = 5e-05 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.7MB, time=9.22 NO POLE NO POLE t[1] = 0.50115 x2[1] (analytic) = 0.00082665827951766534070374927443031 x2[1] (numeric) = 0.00082665972663465022120238393605014 absolute error = 1.44711698488049863466161983e-09 relative error = 0.0001750562500535113011792510313945 % h = 5e-05 x1[1] (analytic) = 0.0012905003906635950827826351381346 x1[1] (numeric) = 0.001290497501014412086076882217778 absolute error = 2.8896491829967057529203566e-09 relative error = 0.00022391695530683286720956534625808 % h = 5e-05 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.7MB, time=9.50 NO POLE NO POLE t[1] = 0.5012 x2[1] (analytic) = 0.00082670368578766620467820114309252 x2[1] (numeric) = 0.00082670526163399344051785358254924 absolute error = 1.57584632723583965243945672e-09 relative error = 0.00019061803573966236825189924298533 % h = 5e-05 x1[1] (analytic) = 0.0012904458670071646728838326718726 x1[1] (numeric) = 0.0012904427205168489301229707117668 absolute error = 3.1464903157427608619601058e-09 relative error = 0.00024382970229043255647060577143722 % h = 5e-05 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.7MB, time=9.78 memory used=137.3MB, alloc=4.7MB, time=10.07 NO POLE NO POLE t[1] = 0.50125 x2[1] (analytic) = 0.00082674909796164659740637187785192 x2[1] (numeric) = 0.0008267508080352762895005650077053 absolute error = 1.71007362969209419312985338e-09 relative error = 0.00020684312010842079778383474863105 % h = 5e-05 x1[1] (analytic) = 0.0012903913460768489310708824436005 x1[1] (numeric) = 0.0012903879318025925791936432289599 absolute error = 3.4142742563518772392146406e-09 relative error = 0.00026459215390216519611124255607596 % h = 5e-05 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.7MB, time=10.35 NO POLE NO POLE t[1] = 0.5013 x2[1] (analytic) = 0.00082679451604012879179140950883443 x2[1] (numeric) = 0.00082679636584066617406726718573338 absolute error = 1.84980053738227585767689895e-09 relative error = 0.00022373159249310926401376062668334 % h = 5e-05 x1[1] (analytic) = 0.0012903368278725115550179667024679 x1[1] (numeric) = 0.0012903331348704106601044117907419 absolute error = 3.6930021008949135549117260e-09 relative error = 0.00028620450266337676171681175223814 % h = 5e-05 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.7MB, time=10.64 memory used=148.7MB, alloc=4.7MB, time=10.94 NO POLE NO POLE t[1] = 0.50135 x2[1] (analytic) = 0.00082683994002363511637400717118929 x2[1] (numeric) = 0.00082684193505233087094226671785644 absolute error = 1.99502869575456825954666715e-09 relative error = 0.00024128354221707536449585813005146 % h = 5e-05 x1[1] (analytic) = 0.0012902823123940162492142136134444 x1[1] (numeric) = 0.0012902783297190706148374765709874 absolute error = 3.9826749456343767370424570e-09 relative error = 0.00030866694113204109652475371810161 % h = 5e-05 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.7MB, time=11.23 NO POLE NO POLE t[1] = 0.5014 x2[1] (analytic) = 0.00082688536991268795533779675988916 x2[1] (numeric) = 0.00082688751567243852771761595180433 absolute error = 2.14575975057237981919191517e-09 relative error = 0.00025949905859369041117866616712503 % h = 5e-05 x1[1] (analytic) = 0.0012902277996412267249633565185424 x1[1] (numeric) = 0.0012902235163473397005140046036559 absolute error = 4.2832938870244493519148865e-09 relative error = 0.00033197966190276660116756269369389 % h = 5e-05 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.7MB, time=11.51 memory used=160.2MB, alloc=4.7MB, time=11.79 NO POLE NO POLE t[1] = 0.50145 x2[1] (analytic) = 0.00082693080570780974851474313244131 x2[1] (numeric) = 0.00082693310770315766291331058578142 absolute error = 2.30199534791439856745334011e-09 relative error = 0.00027837823092634822223290664165133 % h = 5e-05 x1[1] (analytic) = 0.0012901732896140067003833932150759 x1[1] (numeric) = 0.0012901686947539849893664043327792 absolute error = 4.5948600217110169888822967e-09 relative error = 0.00035614285760680292461392289257297 % h = 5e-05 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.7MB, time=12.07 NO POLE NO POLE t[1] = 0.5015 x2[1] (analytic) = 0.00082697624740952299139053885956424 x2[1] (numeric) = 0.00082697871114665716603749675837113 absolute error = 2.46373713417464695789880689e-09 relative error = 0.0002979211485084639146282391013914 % h = 5e-05 x1[1] (analytic) = 0.0012901187823122199004062452509559 x1[1] (numeric) = 0.0012901138649377733687105960042176 absolute error = 4.9173744465316956492467383e-09 relative error = 0.00038115672091204765630824161911299 % h = 5e-05 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.7MB, time=12.35 NO POLE NO POLE t[1] = 0.50155 x2[1] (analytic) = 0.00082702169501835023510999952388432 x2[1] (numeric) = 0.00082702432600510629764668762584572 absolute error = 2.63098675606253668810196140e-09 relative error = 0.00031812790062347269745892802955144 % h = 5e-05 x1[1] (analytic) = 0.0012900642777357300567774172370197 x1[1] (numeric) = 0.0012900590268974715409182778985608 absolute error = 5.2508382585158591393384589e-09 relative error = 0.00040702144452305301950878972510061 % h = 5e-05 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.7MB, time=12.62 memory used=175.4MB, alloc=4.7MB, time=12.90 NO POLE NO POLE t[1] = 0.5016 x2[1] (analytic) = 0.00082706714853481408648245956670656 x2[1] (numeric) = 0.00082706995228067468940598942835014 absolute error = 2.80374586060292352986164358e-09 relative error = 0.00033899857654482866601840612656375 % h = 5e-05 x1[1] (analytic) = 0.001290009775884400908055656176395 x1[1] (numeric) = 0.0012900041806318460233891884045503 absolute error = 5.5952525548846664677718447e-09 relative error = 0.00043373722118103256582465995741464 % h = 5e-05 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.7MB, time=13.19 NO POLE NO POLE t[1] = 0.50165 x2[1] (analytic) = 0.00082711260795943720798716868291399 x2[1] (numeric) = 0.00082711558997553234414933704642873 absolute error = 2.98201609513616216836351474e-09 relative error = 0.00036053326553600359662271678616608 % h = 5e-05 x1[1] (analytic) = 0.0012899552767580961996126108108966 x1[1] (numeric) = 0.0012899493261396631485233639323994 absolute error = 5.9506184330510892468784972e-09 relative error = 0.00046130424366386787095175359134877 % h = 5e-05 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.7MB, time=13.46 memory used=186.9MB, alloc=4.7MB, time=13.74 NO POLE NO POLE t[1] = 0.5017 x2[1] (analytic) = 0.00082715807329274231777868876405026 x2[1] (numeric) = 0.00082716123909184963593973904936392 absolute error = 3.16579910731816105028531366e-09 relative error = 0.0003827320568504857421828188998968 % h = 5e-05 x1[1] (analytic) = 0.0012899007803566796836324909844552 x1[1] (numeric) = 0.0012898944634196890636933926663862 absolute error = 6.3169369906199390983180690e-09 relative error = 0.00048972270478611523160800595897644 % h = 5e-05 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.7MB, time=14.02 NO POLE NO POLE t[1] = 0.50175 x2[1] (analytic) = 0.0008272035445352521896922913896394 x2[1] (numeric) = 0.00082720689963179731012953223679634 absolute error = 3.35509654512043724084715694e-09 relative error = 0.00040559503973177862852573713892529 % h = 5e-05 x1[1] (analytic) = 0.0012898462866800151191117270235781 x1[1] (numeric) = 0.0012898395924706897312166641560967 absolute error = 6.6942093253878950628674814e-09 relative error = 0.00051899279739901236366806140226071 % h = 5e-05 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.7MB, time=14.29 memory used=198.3MB, alloc=4.7MB, time=14.57 NO POLE NO POLE t[1] = 0.5018 x2[1] (analytic) = 0.00082724902168748965324935586679766 x2[1] (numeric) = 0.00082725257159754648342064567509583 absolute error = 3.54991005683017128980829817e-09 relative error = 0.00042912230341339985146454065569276 % h = 5e-05 x1[1] (analytic) = 0.0012897917957279662718586291348401 x1[1] (numeric) = 0.001289784713291430928327614745693 absolute error = 7.0824365353435310143891471e-09 relative error = 0.00054911471439048510149760825594077 % h = 5e-05 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.7MB, time=14.84 NO POLE NO POLE t[1] = 0.50185 x2[1] (analytic) = 0.00082729450474997759366276781819127 x2[1] (numeric) = 0.00082729825499126864392487422995316 absolute error = 3.75024129105026210641176189e-09 relative error = 0.00045331393711887987461713321948834 % h = 5e-05 x1[1] (analytic) = 0.0012897373075003969144930468194044 x1[1] (numeric) = 0.0012897298258806782471499688405826 absolute error = 7.4816197186673430779788218e-09 relative error = 0.00058008864868515409848758453282111 % h = 5e-05 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.7MB, time=15.11 NO POLE NO POLE t[1] = 0.5019 x2[1] (analytic) = 0.00082733999372323895184231831839524 x2[1] (numeric) = 0.00082734394981513565122416159666257 absolute error = 3.95609189669938184327826733e-09 relative error = 0.00047817003006176082797383758400603 % h = 5e-05 x1[1] (analytic) = 0.0012896828219971708264460283045716 x1[1] (numeric) = 0.0012896749302371970946689760108651 absolute error = 7.8917599737317770522937065e-09 relative error = 0.00061191479324434152878846485785581 % h = 5e-05 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.7MB, time=15.39 memory used=213.6MB, alloc=4.7MB, time=15.66 NO POLE NO POLE t[1] = 0.50195 x2[1] (analytic) = 0.00082738548860779672440010357870682 x2[1] (numeric) = 0.00082738965607131973643089282956524 absolute error = 4.16746352301203078925085842e-09 relative error = 0.00050369067144559530721375696867321 % h = 5e-05 x1[1] (analytic) = 0.0012896283392181517939594799923581 x1[1] (numeric) = 0.0012896200263597526927036439309307 absolute error = 8.3128583991012558360614274e-09 relative error = 0.0006445933410660777902448396216737 % h = 5e-05 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.7MB, time=15.94 NO POLE NO POLE t[1] = 0.502 x2[1] (analytic) = 0.0008274309894041739636559251804687 x2[1] (numeric) = 0.0008274353737619935022481963721243 absolute error = 4.38435781953859227119165560e-09 relative error = 0.00052987595046394517376989632191381 % h = 5e-05 x1[1] (analytic) = 0.0012895738591632036100858259251 x1[1] (numeric) = 0.0012895651142471100778789671545872 absolute error = 8.7449160935322068587705128e-09 relative error = 0.00067812448518510820853049677153328 % h = 5e-05 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.7MB, time=16.22 memory used=225.0MB, alloc=4.7MB, time=16.49 NO POLE NO POLE t[1] = 0.50205 x2[1] (analytic) = 0.00082747649611289377764269085695601 x2[1] (numeric) = 0.00082748110288932992303025558910194 absolute error = 4.60677643614538756473214593e-09 relative error = 0.0005567259563003803556430260542053 % h = 5e-05 x1[1] (analytic) = 0.0012895193818321900746876672680847 x1[1] (numeric) = 0.0012895101938980341015981517250904 absolute error = 9.1879341559730895155429943e-09 relative error = 0.00071250841867289974248421729905844 % h = 5e-05 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.7MB, time=16.76 NO POLE NO POLE t[1] = 0.5021 x2[1] (analytic) = 0.00082752200873447933011181582388164 x2[1] (numeric) = 0.0008275268434555023448426298023097 absolute error = 4.83472102301473081397842806e-09 relative error = 0.00058424077812847764896427083848272 % h = 5e-05 x1[1] (analytic) = 0.0012894649072249749944374418092067 x1[1] (numeric) = 0.0012894552653112894300148356194531 absolute error = 9.6419136855644226061897536e-09 relative error = 0.00074774533463764769064649504774226 % h = 5e-05 TOP MAIN SOLVE Loop memory used=232.6MB, alloc=4.7MB, time=17.04 memory used=236.5MB, alloc=4.7MB, time=17.31 NO POLE NO POLE t[1] = 0.50215 x2[1] (analytic) = 0.00082756752726945384053862465857453 x2[1] (numeric) = 0.00082757259546268448552258483140294 absolute error = 5.06819323064498396017282841e-09 relative error = 0.00061242050511181952030640595253393 % h = 5e-05 x1[1] (analytic) = 0.0012894104353414221828170834756492 x1[1] (numeric) = 0.0012894003284856405440053050264081 absolute error = 1.01068557816388117784492411e-08 relative error = 0.00078383542622428239899739187200994 % h = 5e-05 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.7MB, time=17.59 NO POLE NO POLE t[1] = 0.5022 x2[1] (analytic) = 0.0008276130517183405841277537278848 x2[1] (numeric) = 0.00082761835891305043473943304119095 absolute error = 5.30719470985061167931330615e-09 relative error = 0.00064126522640399290974384369036098 % h = 5e-05 x1[1] (analytic) = 0.0012893559661813954601176818675888 x1[1] (numeric) = 0.0012893453834198517391407064574005 absolute error = 1.05827615437209769754101883e-08 relative error = 0.0008207788866144759698957388828087 % h = 5e-05 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.7MB, time=17.86 NO POLE NO POLE t[1] = 0.50225 x2[1] (analytic) = 0.00082765858208166289181855416487103 x2[1] (numeric) = 0.00082766413380877465405488289693428 absolute error = 5.55172711176223632873206325e-09 relative error = 0.00067077503114858803466129211245632 % h = 5e-05 x1[1] (analytic) = 0.0012893014997447586534391418089226 x1[1] (numeric) = 0.0012892904301126871256592546899842 absolute error = 1.10696320715277798871189384e-08 relative error = 0.00085857590902664897221989472964876 % h = 5e-05 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.7MB, time=18.14 memory used=251.7MB, alloc=4.7MB, time=18.43 NO POLE NO POLE t[1] = 0.5023 x2[1] (analytic) = 0.00082770411835994415029049539432325 x2[1] (numeric) = 0.00082770992015203197698339802910111 absolute error = 5.80179208782669290263477786e-09 relative error = 0.00070095000847919719431106854792435 % h = 5e-05 x1[1] (analytic) = 0.0012892470360313755966898429150187 x1[1] (numeric) = 0.0012892354685629106284384365429973 absolute error = 1.15674684649682514063720214e-08 relative error = 0.00089722668671597715271027204526737 % h = 5e-05 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.7MB, time=18.70 NO POLE NO POLE t[1] = 0.50235 x2[1] (analytic) = 0.00082774966055370780196856920717682 x2[1] (numeric) = 0.00082775571794499760905256580905472 absolute error = 6.05739128980708399660187790e-09 relative error = 0.00073179024751941357511904999713522 % h = 5e-05 x1[1] (analytic) = 0.0012891925750411101305862991774863 x1[1] (numeric) = 0.0012891804987692859869672104828916 absolute error = 1.20762718241436190886945947e-08 relative error = 0.00093673141297439814851384279690749 % h = 5e-05 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.7MB, time=18.98 memory used=263.2MB, alloc=4.8MB, time=19.26 NO POLE NO POLE t[1] = 0.5024 x2[1] (analytic) = 0.00082779520866347734502869438387111 x2[1] (numeric) = 0.00082780152718984712786347543714429 absolute error = 6.31852636978283478105327318e-09 relative error = 0.00076329583738283005673924266012828 % h = 5e-05 x1[1] (analytic) = 0.0012891381167738261026528185659675 x1[1] (numeric) = 0.001289125520730576755318202060591 absolute error = 1.25960432493473346165053765e-08 relative error = 0.00097709028113061820093083380568895 % h = 5e-05 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.8MB, time=19.53 NO POLE NO POLE t[1] = 0.50245 x2[1] (analytic) = 0.00082784076268977633340312186670805 x2[1] (numeric) = 0.00082784734788875648315110554467163 absolute error = 6.58519898014974798367796358e-09 relative error = 0.00079546686717303801885695262307471 % h = 5e-05 x1[1] (analytic) = 0.0012890836612293873672211626469477 x1[1] (numeric) = 0.0012890705344455463021198951782532 absolute error = 1.31267838410651012674686945e-08 relative error = 0.0010183034845501188703638233521533 % h = 5e-05 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.8MB, time=19.80 memory used=274.6MB, alloc=4.8MB, time=20.09 NO POLE NO POLE t[1] = 0.5025 x2[1] (analytic) = 0.00082788632263312837678584048126422 x2[1] (numeric) = 0.00082789318004390199684472131120643 absolute error = 6.85741077362005888082994221e-09 relative error = 0.00082830342598362614874053980559543 % h = 5e-05 x1[1] (analytic) = 0.0012890292084076577854302062195851 x1[1] (numeric) = 0.0012890155399129578105288191853093 absolute error = 1.36684946999749013870342758e-08 relative error = 0.0010603712166351637524694500786599 % h = 5e-05 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.8MB, time=20.36 NO POLE NO POLE t[1] = 0.50255 x2[1] (analytic) = 0.00082793188849405714063798320691191 x2[1] (numeric) = 0.0008279390236574603631282810987231 absolute error = 7.13516340322249029789181119e-09 relative error = 0.00086180560289817924954173701966705 % h = 5e-05 x1[1] (analytic) = 0.0012889747583085012252255969685576 x1[1] (numeric) = 0.0012889605371315742782017318031562 absolute error = 1.42211769269470238651654014e-08 relative error = 0.001103293670824805195512945234286 % h = 5e-05 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.8MB, time=20.64 NO POLE NO POLE t[1] = 0.5026 x2[1] (analytic) = 0.00082797746027308634619323399650282 x2[1] (numeric) = 0.00082798487873160864850085260403231 absolute error = 7.41845852230230761860752949e-09 relative error = 0.00089597348699027704934451611087957 % h = 5e-05 x1[1] (analytic) = 0.001288920310931781561359415133927 x1[1] (numeric) = 0.0012889055261001585172677978778756 absolute error = 1.47848316230440916172560514e-08 relative error = 0.0011470710405948910189256995462205 % h = 5e-05 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.8MB, time=20.92 memory used=289.9MB, alloc=4.8MB, time=21.20 NO POLE NO POLE t[1] = 0.50265 x2[1] (analytic) = 0.00082802303797073977046323514526932 x2[1] (numeric) = 0.00082803074526852429183703853098066 absolute error = 7.70729778452137380338571134e-09 relative error = 0.0009308071673234930109624829430547 % h = 5e-05 x1[1] (analytic) = 0.0012888658662773626753898331980192 x1[1] (numeric) = 0.0012888505068174731543007639603542 absolute error = 1.53594598895210890692376650e-08 relative error = 0.0011917035194580712330660758754047 % h = 5e-05 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.8MB, time=21.46 NO POLE NO POLE t[1] = 0.5027 x2[1] (analytic) = 0.00082806862158754124624299520899781 x2[1] (numeric) = 0.0008280766232703851044474117838921 absolute error = 8.00168284385820441657489429e-09 relative error = 0.00096630673295139314248478295870496 % h = 5e-05 x1[1] (analytic) = 0.0012888114243451084556807755893193 x1[1] (numeric) = 0.0012887954792822806302911287131794 absolute error = 1.59450628278253896468761399e-08 relative error = 0.0012371913009638047601836788818509 % h = 5e-05 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.8MB, time=21.73 memory used=301.3MB, alloc=4.8MB, time=22.03 NO POLE NO POLE t[1] = 0.50275 x2[1] (analytic) = 0.00082811421112401466211629747152829 x2[1] (numeric) = 0.00082812251273936927013896018372495 absolute error = 8.30161535460802266271219666e-09 relative error = 0.0010024722729175348085704990301445 % h = 5e-05 x1[1] (analytic) = 0.0012887569851348827974015784033818 x1[1] (numeric) = 0.0012887404434933432006183091436844 absolute error = 1.65416415395967832692596974e-08 relative error = 0.0012835345786983661565872930858802 % h = 5e-05 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.8MB, time=22.30 NO POLE NO POLE t[1] = 0.5028 x2[1] (analytic) = 0.00082815980658068396246110896163522 x2[1] (numeric) = 0.00082816841367765534527554070841859 absolute error = 8.60709697138281443174678337e-09 relative error = 0.0010393038762554655424915231281195 % h = 5e-05 x1[1] (analytic) = 0.0012887025486465496025266491407532 x1[1] (numeric) = 0.0012886853994494229350228026625168 absolute error = 1.71491971266675038464782364e-08 relative error = 0.001330733546284852336016700499918 % h = 5e-05 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.8MB, time=22.58 memory used=312.8MB, alloc=4.8MB, time=22.86 NO POLE NO POLE t[1] = 0.50285 x2[1] (analytic) = 0.0008282054079580731474549900193436 x2[1] (numeric) = 0.00082821432608742225883834325890416 absolute error = 8.91812934911138335323956056e-09 relative error = 0.0010768016319887218589238834089685 % h = 5e-05 x1[1] (analytic) = 0.0012886481148799727798351264619085 x1[1] (numeric) = 0.0012886303471492817175783449671047 absolute error = 1.77677306910622567814948038e-08 relative error = 0.0013787883973831892942185893680331 % h = 5e-05 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.8MB, time=23.14 NO POLE NO POLE t[1] = 0.5029 x2[1] (analytic) = 0.0008282510152567062730805044117353 x2[1] (numeric) = 0.00082826024997084931248636395225375 absolute error = 9.23471414303940585954051845e-09 relative error = 0.0011149656291308280674875081080501 % h = 5e-05 x1[1] (analytic) = 0.0012885936838350162449105399591989 x1[1] (numeric) = 0.0012885752865916812466640637493939 absolute error = 1.83972433349982464762098050e-08 relative error = 0.0014276993256901388347267652844964 % h = 5e-05 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.8MB, time=23.41 NO POLE NO POLE memory used=324.2MB, alloc=4.8MB, time=23.69 t[1] = 0.50295 x2[1] (analytic) = 0.00082829662847710745113062999829971 x2[1] (numeric) = 0.00082830618533011618061688794344289 absolute error = 9.55685300872948625794514318e-09 relative error = 0.0011537959566852950870344076856271 % h = 5e-05 x1[1] (analytic) = 0.0012885392555115439201404699458103 x1[1] (numeric) = 0.0012885202177753830349366282272301 absolute error = 1.90377361608852038417185802e-08 relative error = 0.0014774665249393052958468761467348 % h = 5e-05 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.8MB, time=23.97 NO POLE NO POLE t[1] = 0.503 x2[1] (analytic) = 0.0008283422476198008492141699458837 x2[1] (numeric) = 0.00082835213216740291042598177720128 absolute error = 9.88454760206121181183131758e-09 relative error = 0.0011932927036456192606852564786948 % h = 5e-05 x1[1] (analytic) = 0.0012884848299094197347162072617323 x1[1] (numeric) = 0.0012884651406991484093023944987599 absolute error = 1.96892102713254138127629724e-08 relative error = 0.0015280901889011422788458624425162 % h = 5e-05 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.8MB, time=24.24 NO POLE NO POLE t[1] = 0.50305 x2[1] (analytic) = 0.00082838787268531069076116449329504 x2[1] (numeric) = 0.00082839809048488992196899527142696 absolute error = 1.021779957923120783077813192e-08 relative error = 0.0012334559589952811716143551477617 % h = 5e-05 x1[1] (analytic) = 0.0012884304070285076246324130967366 x1[1] (numeric) = 0.0012884100553617385108895467192237 absolute error = 2.03516667691137428663775129e-08 relative error = 0.0015795705113829593773463443923874 % h = 5e-05 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.8MB, time=24.51 memory used=339.5MB, alloc=4.8MB, time=24.80 NO POLE NO POLE t[1] = 0.5031 x2[1] (analytic) = 0.00082843350367416125502830326561401 x2[1] (numeric) = 0.00082844406028475800822107293363943 absolute error = 1.055661059675319276966802542e-08 relative error = 0.0012742858117077444595829550777008 % h = 5e-05 x1[1] (analytic) = 0.0012883759868686715326867788303632 x1[1] (numeric) = 0.0012883549617619142950202340995143 absolute error = 2.10251067572376665447308489e-08 relative error = 0.0016319076862289289079261574041971 % h = 5e-05 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.8MB, time=25.07 NO POLE NO POLE t[1] = 0.50315 x2[1] (analytic) = 0.0008284791405868768771043381382677 x2[1] (numeric) = 0.00082849004156918833513767491194727 absolute error = 1.090098231145803333677367957e-08 relative error = 0.0013157823507464546382209258271202 % h = 5e-05 x1[1] (analytic) = 0.0012883215694297754084796858889148 x1[1] (numeric) = 0.0012882998598984365311827037258745 absolute error = 2.17095313388772969821630403e-08 relative error = 0.0016851019073200926419232475194978 % h = 5e-05 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.8MB, time=25.34 memory used=350.9MB, alloc=4.8MB, time=25.62 NO POLE NO POLE t[1] = 0.5032 x2[1] (analytic) = 0.00082852478342398194791549665092172 x2[1] (numeric) = 0.00082853603434036244171510748200624 absolute error = 1.125091638049379961083108452e-08 relative error = 0.0013579456650648379130567466487991 % h = 5e-05 x1[1] (analytic) = 0.0012882671547116832084138656194575 x1[1] (numeric) = 0.001288244749770065803003429200107 absolute error = 2.24049416174054104364193505e-08 relative error = 0.0017391533685743685384461383820764 % h = 5e-05 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.8MB, time=25.90 NO POLE NO POLE t[1] = 0.50325 x2[1] (analytic) = 0.00082857043218600091423089597124342 x2[1] (numeric) = 0.0008285820386004622400510630714439 absolute error = 1.160641446132582016710020048e-08 relative error = 0.0014007758436063000002958030885695 % h = 5e-05 x1[1] (analytic) = 0.0012882127427142588956940591808277 x1[1] (numeric) = 0.0012881896313755625082192350996694 absolute error = 2.31113386963874748240811583e-08 relative error = 0.0017940622639465574785901814663308 % h = 5e-05 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.8MB, time=26.17 NO POLE NO POLE memory used=362.4MB, alloc=4.8MB, time=26.45 t[1] = 0.5033 x2[1] (analytic) = 0.00082861608687345827866795740859187 x2[1] (numeric) = 0.00082862805435167001540516982322714 absolute error = 1.196747821173673721241463527e-08 relative error = 0.0014442729753042249463469694762306 % h = 5e-05 x1[1] (analytic) = 0.0012881583334373664403266774516441 x1[1] (numeric) = 0.001288134504713686858649417257028 absolute error = 2.38287236795816772601946161e-08 relative error = 0.0018498287874283500008598011847003 % h = 5e-05 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.8MB, time=26.72 NO POLE NO POLE t[1] = 0.50335 x2[1] (analytic) = 0.0008286617474868785996978214776885 x2[1] (numeric) = 0.00082867408159616842625955069944916 absolute error = 1.233410928982656172922176066e-08 relative error = 0.0014884371490819739480974582059198 % h = 5e-05 x1[1] (analytic) = 0.0012881039268808698191194609553229 x1[1] (numeric) = 0.001288079369783198880167858857643 absolute error = 2.45570976709389516020976799e-08 relative error = 0.001906453133048333037796946545594 % h = 5e-05 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.8MB, time=27.00 NO POLE NO POLE t[1] = 0.5034 x2[1] (analytic) = 0.00082870741402678649165076351232339 x2[1] (numeric) = 0.00082872012033614050437939212701268 absolute error = 1.270630935401272862861468929e-08 relative error = 0.0015332684538528841739359165035621 % h = 5e-05 x1[1] (analytic) = 0.0012880495230446330156811398020981 x1[1] (numeric) = 0.0012880242265828584126751423559577 absolute error = 2.52964617746030059974461404e-08 relative error = 0.0019639354948719966538159613572247 % h = 5e-05 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.8MB, time=27.27 memory used=377.6MB, alloc=4.8MB, time=27.55 NO POLE NO POLE t[1] = 0.50345 x2[1] (analytic) = 0.00082875308649370662472160982915166 x2[1] (numeric) = 0.00082876617057376965487352218668642 absolute error = 1.308408006303015191235753476e-08 relative error = 0.001578766978520267585523751378386 % h = 5e-05 x1[1] (analytic) = 0.0012879951219285200204210936480425 x1[1] (numeric) = 0.0012879690751114251100706572087652 absolute error = 2.60468170949103504364392773e-08 relative error = 0.0020222760670017407842450844428122 % h = 5e-05 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.8MB, time=27.82 NO POLE NO POLE t[1] = 0.5035 x2[1] (analytic) = 0.00082879876488816372497515444163463 x2[1] (numeric) = 0.00082881223231123965625499834701206 absolute error = 1.346742307593127984390537743e-08 relative error = 0.0016249328119774097603146633522819 % h = 5e-05 x1[1] (analytic) = 0.0012879407235323948305490116710912 x1[1] (numeric) = 0.0012879139153676584402247034253248 absolute error = 2.68081647363903243082457664e-08 relative error = 0.0020814750435768819755747919438021 % h = 5e-05 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.8MB, time=28.09 memory used=389.1MB, alloc=4.8MB, time=28.38 NO POLE NO POLE t[1] = 0.50355 x2[1] (analytic) = 0.00082884444921068257435157632418004 x2[1] (numeric) = 0.00082885830555073466050170474453918 absolute error = 1.385634005208615012842035914e-08 relative error = 0.0016717660431075687148223695444627 % h = 5e-05 x1[1] (analytic) = 0.0012878863278561214500745525640661 x1[1] (numeric) = 0.0012878587473503176849505909336008 absolute error = 2.75805058037651239616304653e-08 relative error = 0.0021415326187736601269131935217596 % h = 5e-05 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.8MB, time=28.65 NO POLE NO POLE t[1] = 0.5036 x2[1] (analytic) = 0.00082889013946178801067185722653652 x2[1] (numeric) = 0.00082890439029443919311695901186586 absolute error = 1.425083265118244510178532934e-08 relative error = 0.001719266760783973728636496504857 % h = 5e-05 x1[1] (analytic) = 0.0012878319348995638898070045446997 x1[1] (numeric) = 0.0012878035710581619399767347619963 absolute error = 2.83638414019498302697827034e-08 relative error = 0.0022024489868052452326486942908023 % h = 5e-05 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.8MB, time=28.93 NO POLE NO POLE memory used=400.5MB, alloc=4.8MB, time=29.21 t[1] = 0.50365 x2[1] (analytic) = 0.00082893583564200492764320003849618 x2[1] (numeric) = 0.00082895048654453815319012865496285 absolute error = 1.465090253322554692861646667e-08 relative error = 0.0017674350538698241691866232795569 % h = 5e-05 x1[1] (analytic) = 0.0012877775446625861673549453826583 x1[1] (numeric) = 0.0012877483864899501149187460359543 absolute error = 2.91581726360524361993467040e-08 relative error = 0.0022642243419217441263201345044724 % h = 5e-05 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.8MB, time=29.48 NO POLE NO POLE t[1] = 0.5037 x2[1] (analytic) = 0.00082898153775185827486444770496057 x2[1] (numeric) = 0.00082899659430321681345725698125947 absolute error = 1.505655135853859280927629890e-08 relative error = 0.0018162710112182883172544549581695 % h = 5e-05 x1[1] (analytic) = 0.0012877231571450523071259024435631 x1[1] (numeric) = 0.0012876931936444409332515187887983 absolute error = 2.99635006113738743836547648e-08 relative error = 0.0023268588784102072256946189334907 % h = 5e-05 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.8MB, time=29.77 NO POLE NO POLE t[1] = 0.50375 x2[1] (analytic) = 0.00082902724579187305783150269142413 x2[1] (numeric) = 0.0008290427135726608203616985799696 absolute error = 1.546778078776253019588854547e-08 relative error = 0.0018657747216725021932341070162811 % h = 5e-05 x1[1] (analytic) = 0.0012876687723468263403260127500097 x1[1] (numeric) = 0.0012876379925203929322813125861852 absolute error = 3.07798264334080447001638245e-08 relative error = 0.0023903527905946352790532480085461 % h = 5e-05 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.8MB, time=30.05 memory used=415.8MB, alloc=4.8MB, time=30.33 NO POLE NO POLE t[1] = 0.5038 x2[1] (analytic) = 0.0008290729597625743379427469999303 x2[1] (numeric) = 0.0008290888443550561941147643561364 absolute error = 1.588459248185617201735620610e-08 relative error = 0.0019159462740655683841404805762492 % h = 5e-05 x1[1] (analytic) = 0.0012876143902677723049596830595824 x1[1] (numeric) = 0.0012875827831165644631178309635421 absolute error = 3.16071512078418418520960403e-08 relative error = 0.0024547062728359861126849626060819 % h = 5e-05 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.8MB, time=30.60 NO POLE NO POLE t[1] = 0.50385 x2[1] (analytic) = 0.00082911867966448723250446273555416 x2[1] (numeric) = 0.00082913498665258932875637611987449 absolute error = 1.630698810209625191338432033e-08 relative error = 0.0019667857572205548713657087801367 % h = 5e-05 x1[1] (analytic) = 0.0012875600109077542458292499598661 x1[1] (numeric) = 0.0012875275654317136906462956758588 absolute error = 3.24454760405551829542840073e-08 relative error = 0.0025199195195321813795887148655157 % h = 5e-05 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.8MB, time=30.89 memory used=427.2MB, alloc=4.8MB, time=31.17 NO POLE NO POLE t[1] = 0.5039 x2[1] (analytic) = 0.00082916440549813691473625322346704 x2[1] (numeric) = 0.00082918114046744699221573073228877 absolute error = 1.673496931007747947750882173e-08 relative error = 0.0020182932599504938591836542364237 % h = 5e-05 x1[1] (analytic) = 0.0012875056342666362145346399804511 x1[1] (numeric) = 0.0012874723394645985934995167592088 absolute error = 3.32948020376210351232212423e-08 relative error = 0.0025859927251181133093841767952675 % h = 5e-05 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.8MB, time=31.45 NO POLE NO POLE t[1] = 0.50395 x2[1] (analytic) = 0.00082921013726404861377646467663714 x2[1] (numeric) = 0.00082922730580181632637197380954903 absolute error = 1.716853776771259550913291189e-08 relative error = 0.0020704688710583806040024375703374 % h = 5e-05 x1[1] (analytic) = 0.0012874512603442822694730297219339 x1[1] (numeric) = 0.00128741710521397696402995840337 absolute error = 3.41551303053054430713185639e-08 relative error = 0.0026529260840656514594311991839808 % h = 5e-05 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.8MB, time=31.72 memory used=438.6MB, alloc=4.8MB, time=32.01 NO POLE NO POLE t[1] = 0.504 x2[1] (analytic) = 0.00082925587496274761468760841422102 x2[1] (numeric) = 0.00082927348265788484711488298659999 absolute error = 1.760769513723242727457237897e-08 relative error = 0.0021233126793371722443649769707826 % h = 5e-05 x1[1] (analytic) = 0.0012873968891405564758385060019091 x1[1] (numeric) = 0.001287361862678606408281800634917 absolute error = 3.50264619500675567053669921e-08 relative error = 0.002720719790883649467158232686697 % h = 5e-05 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.8MB, time=32.28 NO POLE NO POLE t[1] = 0.50405 x2[1] (analytic) = 0.00082930161859475925846178363070083 x2[1] (numeric) = 0.00082931967103784044440556074198634 absolute error = 1.805244308118594377711128551e-08 relative error = 0.0021768247735697866316975185201854 % h = 5e-05 x1[1] (analytic) = 0.0012873425206553229056217260179551 x1[1] (numeric) = 0.0012873066118572443459629968101567 absolute error = 3.59087980785596587292077984e-08 relative error = 0.0027893740401179518035999235905492 % h = 5e-05 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.8MB, time=32.55 NO POLE NO POLE t[1] = 0.5041 x2[1] (analytic) = 0.00082934736816060894202610071582133 x2[1] (numeric) = 0.00082936587094387138233713678527289 absolute error = 1.850278326244031103606945156e-08 relative error = 0.0022310052425291011618061371605633 % h = 5e-05 x1[1] (analytic) = 0.0012872881548884456376095775276106 x1[1] (numeric) = 0.0012872513527486480104173269172787 absolute error = 3.68021397976271922506103319e-08 relative error = 0.0028588890263514005281440963664259 % h = 5e-05 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.8MB, time=32.84 memory used=453.9MB, alloc=4.8MB, time=33.11 NO POLE NO POLE t[1] = 0.50415 x2[1] (analytic) = 0.00082939312366082211824810512538206 x2[1] (numeric) = 0.00082941208237816629919548000853992 absolute error = 1.895871734418094737488315786e-08 relative error = 0.0022858541749779516071211878917311 % h = 5e-05 x1[1] (analytic) = 0.0012872337918397887573848390453416 x1[1] (numeric) = 0.0012871960853515744485964466870922 absolute error = 3.77064882143087883923582494e-08 relative error = 0.0029292649442038420444883353362457 % h = 5e-05 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.8MB, time=33.38 NO POLE NO POLE t[1] = 0.5042 x2[1] (analytic) = 0.00082943888509592429594120180293885 x2[1] (numeric) = 0.0008294583053429142075199200034342 absolute error = 1.942024698991157871820049535e-08 relative error = 0.0023413716596691309496896868874888 % h = 5e-05 x1[1] (analytic) = 0.0012871794315092163573258400564985 x1[1] (numeric) = 0.0012871408096647805210319325117205 absolute error = 3.86218444358362939075447780e-08 relative error = 0.0030005019883321338578063778533837 % h = 5e-05 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.8MB, time=33.65 memory used=465.4MB, alloc=4.8MB, time=33.93 NO POLE NO POLE t[1] = 0.50425 x2[1] (analytic) = 0.00082948465246644103987008015246953 x2[1] (numeric) = 0.00082950453984030449416397814525622 absolute error = 1.988737386345429389799278669e-08 relative error = 0.0023975577853453882149156020463035 % h = 5e-05 x1[1] (analytic) = 0.0012871250738965925366061212482615 x1[1] (numeric) = 0.0012870855256870229018073221706243 absolute error = 3.95482095696347987990776372e-08 relative error = 0.0030726003534301513331245313063218 % h = 5e-05 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.8MB, time=34.20 NO POLE NO POLE t[1] = 0.5043 x2[1] (analytic) = 0.00082953042577289797075613956205843 x2[1] (numeric) = 0.00082955078587252692035610824556464 absolute error = 2.036009962894959996868350621e-08 relative error = 0.0024544126407394273060480324852624 % h = 5e-05 x1[1] (analytic) = 0.0012870707190017814011940947575749 x1[1] (numeric) = 0.0012870302334170580785301513633258 absolute error = 4.04855847233226639433942491e-08 relative error = 0.0031455602342287944549083264089309 % h = 5e-05 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.8MB, time=34.48 memory used=476.8MB, alloc=4.8MB, time=34.76 NO POLE NO POLE t[1] = 0.50435 x2[1] (analytic) = 0.00082957620501582076528291547865441 x2[1] (numeric) = 0.00082959704344177162176044677477891 absolute error = 2.083842595085647753129612450e-08 relative error = 0.0025119363145739058394172563638025 % h = 5e-05 x1[1] (analytic) = 0.0012870163668246470638527044360674 x1[1] (numeric) = 0.0012869749328536423523039860482033 absolute error = 4.14339710047115487183878641e-08 relative error = 0.0032193818254959945878596191766395 % h = 5e-05 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.8MB, time=35.03 NO POLE NO POLE t[1] = 0.5044 x2[1] (analytic) = 0.00082962199019573515610150603395714 x2[1] (numeric) = 0.00082964331255022910853757265626147 absolute error = 2.132235449395243606662230433e-08 relative error = 0.0025701288955614339804186263846646 % h = 5e-05 x1[1] (analytic) = 0.00128696201736505364413908613196 x1[1] (numeric) = 0.0012869196239955318377004505867286 absolute error = 4.23933695218064386355452314e-08 relative error = 0.0032940653220367212389243541644111 % h = 5e-05 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.8MB, time=35.30 NO POLE NO POLE t[1] = 0.50445 x2[1] (analytic) = 0.00082966778131316693183599922148616 x2[1] (numeric) = 0.00082968959320009026540527663336103 absolute error = 2.181188692333356927741187487e-08 relative error = 0.0026289904724045732802442922563442 % h = 5e-05 x1[1] (analytic) = 0.0012869076706228652684042279889585 x1[1] (numeric) = 0.0012868643068414824627312516925175 absolute error = 4.33637813828056729762964410e-08 relative error = 0.0033696109186929888205112013695244 % h = 5e-05 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.8MB, time=35.57 memory used=492.1MB, alloc=4.8MB, time=35.86 NO POLE NO POLE t[1] = 0.5045 x2[1] (analytic) = 0.00082971357836864193708890062488759 x2[1] (numeric) = 0.00082973588539354635169934021089874 absolute error = 2.230702490441461043958601115e-08 relative error = 0.0026885211337958355133627293007885 % h = 5e-05 x1[1] (analytic) = 0.0012868533265979460697926307621308 x1[1] (numeric) = 0.0012868089813902499688201981845643 absolute error = 4.43452076961009724325775665e-08 relative error = 0.0034460188103438634149212794332203 % h = 5e-05 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.8MB, time=36.13 NO POLE NO POLE t[1] = 0.50455 x2[1] (analytic) = 0.00082975938136268607244656169753319 x2[1] (numeric) = 0.00082978218913278900143432417257916 absolute error = 2.280777010292898776247504597e-08 relative error = 0.0027487209684176815157460523257469 % h = 5e-05 x1[1] (analytic) = 0.0012867989852901601882419681507683 x1[1] (numeric) = 0.0012867536476405899107752165440308 absolute error = 4.53376495702774667516067375e-08 relative error = 0.0035232891919054695399891777655242 % h = 5e-05 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.8MB, time=36.40 memory used=503.5MB, alloc=4.8MB, time=36.67 NO POLE NO POLE t[1] = 0.5046 x2[1] (analytic) = 0.00082980519029582529448460859346626 x2[1] (numeric) = 0.00082982850442001022336436667580839 absolute error = 2.331412418492887975808234213e-08 relative error = 0.002809590064942520023845093863846 % h = 5e-05 x1[1] (analytic) = 0.0012867446466993717704827471482299 x1[1] (numeric) = 0.0012866983055912576567603622739612 absolute error = 4.63411081141137223848742687e-08 relative error = 0.0036014222583309969159354901145294 % h = 5e-05 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.8MB, time=36.94 NO POLE NO POLE t[1] = 0.50465 x2[1] (analytic) = 0.00082985100516858561577337154974936 x2[1] (numeric) = 0.00082987483125740240104399092540168 absolute error = 2.382608881678527061937565232e-08 relative error = 0.002871128512032706514312225719712 % h = 5e-05 x1[1] (analytic) = 0.001286690310825444970037968408768 x1[1] (numeric) = 0.0012866429552410083882678270612921 absolute error = 4.73555844365817701413474759e-08 relative error = 0.0036804182046107072334310723714021 % h = 5e-05 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.8MB, time=37.21 memory used=514.9MB, alloc=4.8MB, time=37.49 NO POLE NO POLE t[1] = 0.5047 x2[1] (analytic) = 0.00082989682598149310488331482026843 x2[1] (numeric) = 0.00082992116964715829288892242766328 absolute error = 2.434366566518800560760739485e-08 relative error = 0.0029333363983405420444719027708556 % h = 5e-05 x1[1] (analytic) = 0.0012866359776682439472227866313365 x1[1] (numeric) = 0.0012865875965885971000899417405297 absolute error = 4.83810796468471328448908068e-08 relative error = 0.0037602772257719409228732372527364 % h = 5e-05 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.8MB, time=37.77 NO POLE NO POLE t[1] = 0.50475 x2[1] (analytic) = 0.00082994265273507388639046716104801 x2[1] (numeric) = 0.00082996751959147103223691582632143 absolute error = 2.486685639714584644866527342e-08 relative error = 0.0029962138125082720935389078735937 % h = 5e-05 x1[1] (analytic) = 0.001286581647227632869144170960378 x1[1] (numeric) = 0.0012865322296327786002911750584629 absolute error = 4.94175948542688529959019151e-08 relative error = 0.0038409995168791239248740985776043 % h = 5e-05 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.8MB, time=38.04 NO POLE NO POLE t[1] = 0.5048 x2[1] (analytic) = 0.00082998848542985414088185286713247 x2[1] (numeric) = 0.00083001388109253412740859132180156 absolute error = 2.539566267998652673845466909e-08 relative error = 0.0030597608431680854045842766236431 % h = 5e-05 x1[1] (analytic) = 0.0012865273195034759097005654035915 x1[1] (numeric) = 0.0012864768543723075101801282392837 absolute error = 5.04651311683995204371643078e-08 relative error = 0.0039225852730337744619612779945469 % h = 5e-05 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.8MB, time=38.31 memory used=530.2MB, alloc=4.8MB, time=38.59 NO POLE NO POLE t[1] = 0.50485 x2[1] (analytic) = 0.00083003432406636010496092336108762 x2[1] (numeric) = 0.00083006025415254146176828067532113 absolute error = 2.593008618135680735731423351e-08 relative error = 0.0031239775789421128272488807326534 % h = 5e-05 x1[1] (analytic) = 0.0012864729944956372495815492666783 x1[1] (numeric) = 0.0012864214708059382642815253494848 absolute error = 5.15236896989853000239171935e-08 relative error = 0.0040050346893745098114911868796541 % h = 5e-05 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.8MB, time=38.87 NO POLE NO POLE t[1] = 0.5049 x2[1] (analytic) = 0.00083008016864511807125298933317795 x2[1] (numeric) = 0.00083010663877368729378488279928968 absolute error = 2.647012856922253189346611173e-08 relative error = 0.0031888641084424261612046485959821 % h = 5e-05 x1[1] (analytic) = 0.001286418672203981076267497605066 x1[1] (numeric) = 0.0012863660789324251103081994619038 absolute error = 5.25932715559659592981431622e-08 relative error = 0.0040883479610770530797750963658383 % h = 5e-05 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.8MB, time=39.14 memory used=541.6MB, alloc=4.8MB, time=39.41 NO POLE NO POLE t[1] = 0.50495 x2[1] (analytic) = 0.00083012601916665438841065343327373 x2[1] (numeric) = 0.00083015303495816625709272893549786 absolute error = 2.701579151186868207550222413e-08 relative error = 0.0032544205202710370003634016772257 % h = 5e-05 x1[1] (analytic) = 0.0012863643526283715840292416926091 x1[1] (numeric) = 0.001286310678750522109133074618285 absolute error = 5.36738778494748961670743241e-08 relative error = 0.0041725252833542399774182082593455 % h = 5e-05 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.8MB, time=39.70 NO POLE NO POLE t[1] = 0.505 x2[1] (analytic) = 0.00083017187563149546111924351454314 x2[1] (numeric) = 0.00083019944270817336055245742257955 absolute error = 2.756707667789943321390803641e-08 relative error = 0.0033206469030198955778332851659561 % h = 5e-05 x1[1] (analytic) = 0.0012863100357686729739277295072664 x1[1] (numeric) = 0.0012862552702589831347611435897279 absolute error = 5.47655096898391665859175385e-08 relative error = 0.0042575668514560255958719399084856 % h = 5e-05 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 = 39 Seconds Elapsed Time(since restart) = 39 Seconds Expected Time Remaining = 9 Hours 51 Minutes 3 Seconds Optimized Time Remaining = 9 Hours 50 Minutes 54 Seconds Time to Timeout = 14 Minutes 20 Seconds Percent Done = 0.1122 % > quit memory used=548.1MB, alloc=4.8MB, time=39.88