|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_current_iter, > glob_smallish_float, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_relerr, > glob_clock_start_sec, > djd_debug2, > glob_orig_start_sec, > glob_log10_abserr, > glob_disp_incr, > glob_optimal_done, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_sec, > glob_warned, > glob_max_rel_trunc_err, > glob_reached_optimal_h, > glob_not_yet_start_msg, > days_in_year, > glob_normmax, > glob_unchanged_h_cnt, > glob_hmin_init, > glob_html_log, > glob_log10relerr, > glob_look_poles, > glob_optimal_expect_sec, > glob_max_minutes, > glob_iter, > glob_max_trunc_err, > glob_abserr, > glob_hmin, > glob_display_flag, > djd_debug, > glob_dump, > glob_curr_iter_when_opt, > glob_dump_analytic, > glob_initial_pass, > glob_not_yet_finished, > glob_max_opt_iter, > glob_h, > glob_almost_1, > sec_in_min, > glob_log10abserr, > glob_start, > glob_warned2, > glob_no_eqs, > glob_max_order, > glob_log10_relerr, > glob_hmax, > centuries_in_millinium, > glob_last_good_h, > glob_large_float, > glob_clock_sec, > glob_log10normmin, > glob_max_iter, > years_in_century, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_4D0, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_norms, > array_x2_init, > array_type_pole, > array_m1, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_pole, > array_t, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2, > array_x1, > array_x2_higher, > array_real_pole, > array_x2_higher_work2, > array_x1_higher, > array_x1_higher_work2, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work, > array_poles, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_current_iter, glob_smallish_float, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_relerr, glob_clock_start_sec, djd_debug2, glob_orig_start_sec, glob_log10_abserr, glob_disp_incr, glob_optimal_done, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_sec, glob_warned, glob_max_rel_trunc_err, glob_reached_optimal_h, glob_not_yet_start_msg, days_in_year, glob_normmax, glob_unchanged_h_cnt, glob_hmin_init, glob_html_log, glob_log10relerr, glob_look_poles, glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_trunc_err, glob_abserr, glob_hmin, glob_display_flag, djd_debug, glob_dump, glob_curr_iter_when_opt, glob_dump_analytic, glob_initial_pass, glob_not_yet_finished, glob_max_opt_iter, glob_h, glob_almost_1, sec_in_min, glob_log10abserr, glob_start, glob_warned2, glob_no_eqs, glob_max_order, glob_log10_relerr, glob_hmax, centuries_in_millinium, glob_last_good_h, glob_large_float, glob_clock_sec, glob_log10normmin, glob_max_iter, years_in_century, hours_in_day, array_const_1, array_const_2, array_const_4D0, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_norms, array_x2_init, array_type_pole, array_m1, array_1st_rel_error, array_x1_init, array_last_rel_error, array_pole, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_x2_higher, array_real_pole, array_x2_higher_work2, array_x1_higher, array_x1_higher_work2, array_complex_pole, array_x1_higher_work, array_x2_higher_work, array_poles, glob_last; if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_current_iter, > glob_smallish_float, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_relerr, > glob_clock_start_sec, > djd_debug2, > glob_orig_start_sec, > glob_log10_abserr, > glob_disp_incr, > glob_optimal_done, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_sec, > glob_warned, > glob_max_rel_trunc_err, > glob_reached_optimal_h, > glob_not_yet_start_msg, > days_in_year, > glob_normmax, > glob_unchanged_h_cnt, > glob_hmin_init, > glob_html_log, > glob_log10relerr, > glob_look_poles, > glob_optimal_expect_sec, > glob_max_minutes, > glob_iter, > glob_max_trunc_err, > glob_abserr, > glob_hmin, > glob_display_flag, > djd_debug, > glob_dump, > glob_curr_iter_when_opt, > glob_dump_analytic, > glob_initial_pass, > glob_not_yet_finished, > glob_max_opt_iter, > glob_h, > glob_almost_1, > sec_in_min, > glob_log10abserr, > glob_start, > glob_warned2, > glob_no_eqs, > glob_max_order, > glob_log10_relerr, > glob_hmax, > centuries_in_millinium, > glob_last_good_h, > glob_large_float, > glob_clock_sec, > glob_log10normmin, > glob_max_iter, > years_in_century, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_4D0, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_norms, > array_x2_init, > array_type_pole, > array_m1, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_pole, > array_t, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2, > array_x1, > array_x2_higher, > array_real_pole, > array_x2_higher_work2, > array_x1_higher, > array_x1_higher_work2, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work, > array_poles, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_t[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_current_iter, glob_smallish_float, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_relerr, glob_clock_start_sec, djd_debug2, glob_orig_start_sec, glob_log10_abserr, glob_disp_incr, glob_optimal_done, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_sec, glob_warned, glob_max_rel_trunc_err, glob_reached_optimal_h, glob_not_yet_start_msg, days_in_year, glob_normmax, glob_unchanged_h_cnt, glob_hmin_init, glob_html_log, glob_log10relerr, glob_look_poles, glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_trunc_err, glob_abserr, glob_hmin, glob_display_flag, djd_debug, glob_dump, glob_curr_iter_when_opt, glob_dump_analytic, glob_initial_pass, glob_not_yet_finished, glob_max_opt_iter, glob_h, glob_almost_1, sec_in_min, glob_log10abserr, glob_start, glob_warned2, glob_no_eqs, glob_max_order, glob_log10_relerr, glob_hmax, centuries_in_millinium, glob_last_good_h, glob_large_float, glob_clock_sec, glob_log10normmin, glob_max_iter, years_in_century, hours_in_day, array_const_1, array_const_2, array_const_4D0, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_norms, array_x2_init, array_type_pole, array_m1, array_1st_rel_error, array_x1_init, array_last_rel_error, array_pole, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_x2_higher, array_real_pole, array_x2_higher_work2, array_x1_higher, array_x1_higher_work2, array_complex_pole, array_x1_higher_work, array_x2_higher_work, array_poles, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_t[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(t_start,t_end) > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_current_iter, > glob_smallish_float, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_relerr, > glob_clock_start_sec, > djd_debug2, > glob_orig_start_sec, > glob_log10_abserr, > glob_disp_incr, > glob_optimal_done, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_sec, > glob_warned, > glob_max_rel_trunc_err, > glob_reached_optimal_h, > glob_not_yet_start_msg, > days_in_year, > glob_normmax, > glob_unchanged_h_cnt, > glob_hmin_init, > glob_html_log, > glob_log10relerr, > glob_look_poles, > glob_optimal_expect_sec, > glob_max_minutes, > glob_iter, > glob_max_trunc_err, > glob_abserr, > glob_hmin, > glob_display_flag, > djd_debug, > glob_dump, > glob_curr_iter_when_opt, > glob_dump_analytic, > glob_initial_pass, > glob_not_yet_finished, > glob_max_opt_iter, > glob_h, > glob_almost_1, > sec_in_min, > glob_log10abserr, > glob_start, > glob_warned2, > glob_no_eqs, > glob_max_order, > glob_log10_relerr, > glob_hmax, > centuries_in_millinium, > glob_last_good_h, > glob_large_float, > glob_clock_sec, > glob_log10normmin, > glob_max_iter, > years_in_century, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_4D0, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_norms, > array_x2_init, > array_type_pole, > array_m1, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_pole, > array_t, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2, > array_x1, > array_x2_higher, > array_real_pole, > array_x2_higher_work2, > array_x1_higher, > array_x1_higher_work2, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work, > array_poles, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_current_iter, glob_smallish_float, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_relerr, glob_clock_start_sec, djd_debug2, glob_orig_start_sec, glob_log10_abserr, glob_disp_incr, glob_optimal_done, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_sec, glob_warned, glob_max_rel_trunc_err, glob_reached_optimal_h, glob_not_yet_start_msg, days_in_year, glob_normmax, glob_unchanged_h_cnt, glob_hmin_init, glob_html_log, glob_log10relerr, glob_look_poles, glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_trunc_err, glob_abserr, glob_hmin, glob_display_flag, djd_debug, glob_dump, glob_curr_iter_when_opt, glob_dump_analytic, glob_initial_pass, glob_not_yet_finished, glob_max_opt_iter, glob_h, glob_almost_1, sec_in_min, glob_log10abserr, glob_start, glob_warned2, glob_no_eqs, glob_max_order, glob_log10_relerr, glob_hmax, centuries_in_millinium, glob_last_good_h, glob_large_float, glob_clock_sec, glob_log10normmin, glob_max_iter, years_in_century, hours_in_day, array_const_1, array_const_2, array_const_4D0, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_norms, array_x2_init, array_type_pole, array_m1, array_1st_rel_error, array_x1_init, array_last_rel_error, array_pole, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_x2_higher, array_real_pole, array_x2_higher_work2, array_x1_higher, array_x1_higher_work2, array_complex_pole, array_x1_higher_work, array_x2_higher_work, array_poles, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_current_iter, > glob_smallish_float, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_relerr, > glob_clock_start_sec, > djd_debug2, > glob_orig_start_sec, > glob_log10_abserr, > glob_disp_incr, > glob_optimal_done, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_sec, > glob_warned, > glob_max_rel_trunc_err, > glob_reached_optimal_h, > glob_not_yet_start_msg, > days_in_year, > glob_normmax, > glob_unchanged_h_cnt, > glob_hmin_init, > glob_html_log, > glob_log10relerr, > glob_look_poles, > glob_optimal_expect_sec, > glob_max_minutes, > glob_iter, > glob_max_trunc_err, > glob_abserr, > glob_hmin, > glob_display_flag, > djd_debug, > glob_dump, > glob_curr_iter_when_opt, > glob_dump_analytic, > glob_initial_pass, > glob_not_yet_finished, > glob_max_opt_iter, > glob_h, > glob_almost_1, > sec_in_min, > glob_log10abserr, > glob_start, > glob_warned2, > glob_no_eqs, > glob_max_order, > glob_log10_relerr, > glob_hmax, > centuries_in_millinium, > glob_last_good_h, > glob_large_float, > glob_clock_sec, > glob_log10normmin, > glob_max_iter, > years_in_century, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_4D0, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_norms, > array_x2_init, > array_type_pole, > array_m1, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_pole, > array_t, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2, > array_x1, > array_x2_higher, > array_real_pole, > array_x2_higher_work2, > array_x1_higher, > array_x1_higher_work2, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work, > array_poles, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1]; > rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1]; > rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_current_iter, glob_smallish_float, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_relerr, glob_clock_start_sec, djd_debug2, glob_orig_start_sec, glob_log10_abserr, glob_disp_incr, glob_optimal_done, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_sec, glob_warned, glob_max_rel_trunc_err, glob_reached_optimal_h, glob_not_yet_start_msg, days_in_year, glob_normmax, glob_unchanged_h_cnt, glob_hmin_init, glob_html_log, glob_log10relerr, glob_look_poles, glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_trunc_err, glob_abserr, glob_hmin, glob_display_flag, djd_debug, glob_dump, glob_curr_iter_when_opt, glob_dump_analytic, glob_initial_pass, glob_not_yet_finished, glob_max_opt_iter, glob_h, glob_almost_1, sec_in_min, glob_log10abserr, glob_start, glob_warned2, glob_no_eqs, glob_max_order, glob_log10_relerr, glob_hmax, centuries_in_millinium, glob_last_good_h, glob_large_float, glob_clock_sec, glob_log10normmin, glob_max_iter, years_in_century, hours_in_day, array_const_1, array_const_2, array_const_4D0, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_norms, array_x2_init, array_type_pole, array_m1, array_1st_rel_error, array_x1_init, array_last_rel_error, array_pole, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_x2_higher, array_real_pole, array_x2_higher_work2, array_x1_higher, array_x1_higher_work2, array_complex_pole, array_x1_higher_work, array_x2_higher_work, array_poles, glob_last; n := glob_max_terms; m := n - 3; while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or abs(array_x2_higher[1, m - 1]) < glob_small_float or abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or abs(array_x1_higher[1, m - 1]) < glob_small_float or abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_x2_higher[1, m]) or glob_large_float <= abs(array_x2_higher[1, m - 1]) or glob_large_float <= abs(array_x2_higher[1, m - 2]) or glob_large_float <= abs(array_x2_higher[1, m - 3]) or glob_large_float <= abs(array_x2_higher[1, m - 4]) or glob_large_float <= abs(array_x2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_x1_higher[1, m]) or glob_large_float <= abs(array_x1_higher[1, m - 1]) or glob_large_float <= abs(array_x1_higher[1, m - 2]) or glob_large_float <= abs(array_x1_higher[1, m - 3]) or glob_large_float <= abs(array_x1_higher[1, m - 4]) or glob_large_float <= abs(array_x1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_current_iter, > glob_smallish_float, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_relerr, > glob_clock_start_sec, > djd_debug2, > glob_orig_start_sec, > glob_log10_abserr, > glob_disp_incr, > glob_optimal_done, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_sec, > glob_warned, > glob_max_rel_trunc_err, > glob_reached_optimal_h, > glob_not_yet_start_msg, > days_in_year, > glob_normmax, > glob_unchanged_h_cnt, > glob_hmin_init, > glob_html_log, > glob_log10relerr, > glob_look_poles, > glob_optimal_expect_sec, > glob_max_minutes, > glob_iter, > glob_max_trunc_err, > glob_abserr, > glob_hmin, > glob_display_flag, > djd_debug, > glob_dump, > glob_curr_iter_when_opt, > glob_dump_analytic, > glob_initial_pass, > glob_not_yet_finished, > glob_max_opt_iter, > glob_h, > glob_almost_1, > sec_in_min, > glob_log10abserr, > glob_start, > glob_warned2, > glob_no_eqs, > glob_max_order, > glob_log10_relerr, > glob_hmax, > centuries_in_millinium, > glob_last_good_h, > glob_large_float, > glob_clock_sec, > glob_log10normmin, > glob_max_iter, > years_in_century, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_4D0, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_norms, > array_x2_init, > array_type_pole, > array_m1, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_pole, > array_t, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2, > array_x1, > array_x2_higher, > array_real_pole, > array_x2_higher_work2, > array_x1_higher, > array_x1_higher_work2, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work, > array_poles, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_current_iter, glob_smallish_float, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_relerr, glob_clock_start_sec, djd_debug2, glob_orig_start_sec, glob_log10_abserr, glob_disp_incr, glob_optimal_done, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_sec, glob_warned, glob_max_rel_trunc_err, glob_reached_optimal_h, glob_not_yet_start_msg, days_in_year, glob_normmax, glob_unchanged_h_cnt, glob_hmin_init, glob_html_log, glob_log10relerr, glob_look_poles, glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_trunc_err, glob_abserr, glob_hmin, glob_display_flag, djd_debug, glob_dump, glob_curr_iter_when_opt, glob_dump_analytic, glob_initial_pass, glob_not_yet_finished, glob_max_opt_iter, glob_h, glob_almost_1, sec_in_min, glob_log10abserr, glob_start, glob_warned2, glob_no_eqs, glob_max_order, glob_log10_relerr, glob_hmax, centuries_in_millinium, glob_last_good_h, glob_large_float, glob_clock_sec, glob_log10normmin, glob_max_iter, years_in_century, hours_in_day, array_const_1, array_const_2, array_const_4D0, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_norms, array_x2_init, array_type_pole, array_m1, array_1st_rel_error, array_x1_init, array_last_rel_error, array_pole, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_x2_higher, array_real_pole, array_x2_higher_work2, array_x1_higher, array_x1_higher_work2, array_complex_pole, array_x1_higher_work, array_x2_higher_work, array_poles, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x2[iii]) then array_norms[iii] := abs(array_x2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x1[iii]) then array_norms[iii] := abs(array_x1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_current_iter, > glob_smallish_float, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_relerr, > glob_clock_start_sec, > djd_debug2, > glob_orig_start_sec, > glob_log10_abserr, > glob_disp_incr, > glob_optimal_done, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_sec, > glob_warned, > glob_max_rel_trunc_err, > glob_reached_optimal_h, > glob_not_yet_start_msg, > days_in_year, > glob_normmax, > glob_unchanged_h_cnt, > glob_hmin_init, > glob_html_log, > glob_log10relerr, > glob_look_poles, > glob_optimal_expect_sec, > glob_max_minutes, > glob_iter, > glob_max_trunc_err, > glob_abserr, > glob_hmin, > glob_display_flag, > djd_debug, > glob_dump, > glob_curr_iter_when_opt, > glob_dump_analytic, > glob_initial_pass, > glob_not_yet_finished, > glob_max_opt_iter, > glob_h, > glob_almost_1, > sec_in_min, > glob_log10abserr, > glob_start, > glob_warned2, > glob_no_eqs, > glob_max_order, > glob_log10_relerr, > glob_hmax, > centuries_in_millinium, > glob_last_good_h, > glob_large_float, > glob_clock_sec, > glob_log10normmin, > glob_max_iter, > years_in_century, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_4D0, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_norms, > array_x2_init, > array_type_pole, > array_m1, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_pole, > array_t, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2, > array_x1, > array_x2_higher, > array_real_pole, > array_x2_higher_work2, > array_x1_higher, > array_x1_higher_work2, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work, > array_poles, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp4[1] := (array_const_2D0[1] * (array_x2[1])); > #emit pre sub $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp6[1] := array_x1_higher[3,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp8[1] := array_x1_higher[2,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp10[1] := array_tmp9[1] + array_x1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2); > array_x2[3] := temporary; > array_x2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,2] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,1] := temporary > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult $eq_no = 2 i = 1 > array_tmp12[1] := (array_const_4D0[1] * (array_x2[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp13[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1])); > # emit pre mult $eq_no = 2 i = 1 > array_tmp16[1] := (array_const_2D0[1] * (array_x1[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_x1[2] := temporary; > array_x1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,1] := temporary > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp4[2] := ats(2,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp6[2] := array_x1_higher[3,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp8[2] := array_x1_higher[2,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2])); > #emit pre add $eq_no = 1 i = 2 > array_tmp10[2] := array_tmp9[2] + array_x1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3); > array_x2[4] := temporary; > array_x2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,2] := temporary > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult $eq_no = 2 i = 2 > array_tmp12[2] := ats(2,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 2 > array_tmp13[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2])); > # emit pre mult $eq_no = 2 i = 2 > array_tmp16[2] := ats(2,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2])); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_x1[3] := temporary; > array_x1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,2] := temporary > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp4[3] := ats(3,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp6[3] := array_x1_higher[3,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp8[3] := array_x1_higher[2,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3])); > #emit pre add $eq_no = 1 i = 3 > array_tmp10[3] := array_tmp9[3] + array_x1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4); > array_x2[5] := temporary; > array_x2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,3] := temporary > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult $eq_no = 2 i = 3 > array_tmp12[3] := ats(3,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 3 > array_tmp13[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3])); > # emit pre mult $eq_no = 2 i = 3 > array_tmp16[3] := ats(3,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3])); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_x1[4] := temporary; > array_x1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,3] := temporary > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp4[4] := ats(4,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp6[4] := array_x1_higher[3,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp8[4] := array_x1_higher[2,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4])); > #emit pre add $eq_no = 1 i = 4 > array_tmp10[4] := array_tmp9[4] + array_x1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5); > array_x2[6] := temporary; > array_x2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,4] := temporary > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult $eq_no = 2 i = 4 > array_tmp12[4] := ats(4,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 4 > array_tmp13[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4])); > # emit pre mult $eq_no = 2 i = 4 > array_tmp16[4] := ats(4,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4])); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_x1[5] := temporary; > array_x1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,4] := temporary > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp4[5] := ats(5,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp6[5] := array_x1_higher[3,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp8[5] := array_x1_higher[2,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5])); > #emit pre add $eq_no = 1 i = 5 > array_tmp10[5] := array_tmp9[5] + array_x1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6); > array_x2[7] := temporary; > array_x2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,5] := temporary > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult $eq_no = 2 i = 5 > array_tmp12[5] := ats(5,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 5 > array_tmp13[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5])); > # emit pre mult $eq_no = 2 i = 5 > array_tmp16[5] := ats(5,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5])); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_x1[6] := temporary; > array_x1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,5] := temporary > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 1 > array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1); > #emit add $eq_no = 1 > array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; > #emit mult $eq_no = 1 > array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1); > #emit sub $eq_no = 1 > array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk])); > #emit diff $eq_no = 1 > array_tmp6[kkk] := array_x1_higher[3,kkk]; > #emit sub $eq_no = 1 > array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk])); > #emit diff $eq_no = 1 > array_tmp8[kkk] := array_x1_higher[2,kkk]; > #emit sub $eq_no = 1 > array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk])); > #emit add $eq_no = 1 > array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x2[kkk + order_d] := temporary; > array_x2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_x2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 1 > ; > #emit mult $eq_no = 2 > array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1); > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 2 > array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1); > #emit sub $eq_no = 2 > array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk])); > #emit mult $eq_no = 2 > array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1); > #emit sub $eq_no = 2 > array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk])); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x1[kkk + order_d] := temporary; > array_x1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_x1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_current_iter, glob_smallish_float, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_relerr, glob_clock_start_sec, djd_debug2, glob_orig_start_sec, glob_log10_abserr, glob_disp_incr, glob_optimal_done, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_sec, glob_warned, glob_max_rel_trunc_err, glob_reached_optimal_h, glob_not_yet_start_msg, days_in_year, glob_normmax, glob_unchanged_h_cnt, glob_hmin_init, glob_html_log, glob_log10relerr, glob_look_poles, glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_trunc_err, glob_abserr, glob_hmin, glob_display_flag, djd_debug, glob_dump, glob_curr_iter_when_opt, glob_dump_analytic, glob_initial_pass, glob_not_yet_finished, glob_max_opt_iter, glob_h, glob_almost_1, sec_in_min, glob_log10abserr, glob_start, glob_warned2, glob_no_eqs, glob_max_order, glob_log10_relerr, glob_hmax, centuries_in_millinium, glob_last_good_h, glob_large_float, glob_clock_sec, glob_log10normmin, glob_max_iter, years_in_century, hours_in_day, array_const_1, array_const_2, array_const_4D0, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_norms, array_x2_init, array_type_pole, array_m1, array_1st_rel_error, array_x1_init, array_last_rel_error, array_pole, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_x2_higher, array_real_pole, array_x2_higher_work2, array_x1_higher, array_x1_higher_work2, array_complex_pole, array_x1_higher_work, array_x2_higher_work, array_poles, glob_last; array_tmp1[1] := array_x2_higher[2, 1]; array_tmp2[1] := array_const_3D0[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; array_tmp4[1] := array_const_2D0[1]*array_x2[1]; array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; array_tmp6[1] := array_x1_higher[3, 1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; array_tmp8[1] := array_x1_higher[2, 1]; array_tmp9[1] := array_tmp7[1] - array_tmp8[1]; array_tmp10[1] := array_tmp9[1] + array_x1[1]; if 1 <= glob_max_terms then temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2); array_x2[3] := temporary; array_x2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 2] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 1] := temporary end if; kkk := 2; array_tmp12[1] := array_const_4D0[1]*array_x2[1]; array_tmp13[1] := array_x2_higher[2, 1]; array_tmp14[1] := array_const_2D0[1]*array_tmp13[1]; array_tmp15[1] := array_tmp12[1] - array_tmp14[1]; array_tmp16[1] := array_const_2D0[1]*array_x1[1]; array_tmp17[1] := array_tmp15[1] - array_tmp16[1]; if 1 <= glob_max_terms then temporary := array_tmp17[1]*glob_h*factorial_3(0, 1); array_x1[2] := temporary; array_x1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 1] := temporary end if; kkk := 2; array_tmp1[2] := array_x2_higher[2, 2]; array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1); array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1); array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; array_tmp6[2] := array_x1_higher[3, 2]; array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; array_tmp8[2] := array_x1_higher[2, 2]; array_tmp9[2] := array_tmp7[2] - array_tmp8[2]; array_tmp10[2] := array_tmp9[2] + array_x1[2]; if 2 <= glob_max_terms then temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3); array_x2[4] := temporary; array_x2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 2] := temporary end if; kkk := 3; array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1); array_tmp13[2] := array_x2_higher[2, 2]; array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1); array_tmp15[2] := array_tmp12[2] - array_tmp14[2]; array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1); array_tmp17[2] := array_tmp15[2] - array_tmp16[2]; if 2 <= glob_max_terms then temporary := array_tmp17[2]*glob_h*factorial_3(1, 2); array_x1[3] := temporary; array_x1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 2] := temporary end if; kkk := 3; array_tmp1[3] := array_x2_higher[2, 3]; array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1); array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1); array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; array_tmp6[3] := array_x1_higher[3, 3]; array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; array_tmp8[3] := array_x1_higher[2, 3]; array_tmp9[3] := array_tmp7[3] - array_tmp8[3]; array_tmp10[3] := array_tmp9[3] + array_x1[3]; if 3 <= glob_max_terms then temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4); array_x2[5] := temporary; array_x2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 3] := temporary end if; kkk := 4; array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1); array_tmp13[3] := array_x2_higher[2, 3]; array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1); array_tmp15[3] := array_tmp12[3] - array_tmp14[3]; array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1); array_tmp17[3] := array_tmp15[3] - array_tmp16[3]; if 3 <= glob_max_terms then temporary := array_tmp17[3]*glob_h*factorial_3(2, 3); array_x1[4] := temporary; array_x1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 3] := temporary end if; kkk := 4; array_tmp1[4] := array_x2_higher[2, 4]; array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1); array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1); array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; array_tmp6[4] := array_x1_higher[3, 4]; array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; array_tmp8[4] := array_x1_higher[2, 4]; array_tmp9[4] := array_tmp7[4] - array_tmp8[4]; array_tmp10[4] := array_tmp9[4] + array_x1[4]; if 4 <= glob_max_terms then temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5); array_x2[6] := temporary; array_x2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 4] := temporary end if; kkk := 5; array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1); array_tmp13[4] := array_x2_higher[2, 4]; array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1); array_tmp15[4] := array_tmp12[4] - array_tmp14[4]; array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1); array_tmp17[4] := array_tmp15[4] - array_tmp16[4]; if 4 <= glob_max_terms then temporary := array_tmp17[4]*glob_h*factorial_3(3, 4); array_x1[5] := temporary; array_x1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 4] := temporary end if; kkk := 5; array_tmp1[5] := array_x2_higher[2, 5]; array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1); array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1); array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; array_tmp6[5] := array_x1_higher[3, 5]; array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; array_tmp8[5] := array_x1_higher[2, 5]; array_tmp9[5] := array_tmp7[5] - array_tmp8[5]; array_tmp10[5] := array_tmp9[5] + array_x1[5]; if 5 <= glob_max_terms then temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6); array_x2[7] := temporary; array_x2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 5] := temporary end if; kkk := 6; array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1); array_tmp13[5] := array_x2_higher[2, 5]; array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1); array_tmp15[5] := array_tmp12[5] - array_tmp14[5]; array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1); array_tmp17[5] := array_tmp15[5] - array_tmp16[5]; if 5 <= glob_max_terms then temporary := array_tmp17[5]*glob_h*factorial_3(4, 5); array_x1[6] := temporary; array_x1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 5] := temporary end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_x2_higher[2, kkk]; array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1); array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1); array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := array_x1_higher[3, kkk]; array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; array_tmp8[kkk] := array_x1_higher[2, kkk]; array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk]; array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp10[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x2[kkk + order_d] := temporary; array_x2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_x2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1); array_tmp13[kkk] := array_x2_higher[2, kkk]; array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1); array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk]; array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1); array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp17[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x1[kkk + order_d] := temporary; array_x1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_x1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_x1 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c1 + 6.0 * c3 * exp(-t); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > c1 + c2 * exp(2.0 * t) + c3 * exp(-t); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c2*exp(2.0*t) - c3*exp(-t) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > t_start,t_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_current_iter, > glob_smallish_float, > glob_small_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_relerr, > glob_clock_start_sec, > djd_debug2, > glob_orig_start_sec, > glob_log10_abserr, > glob_disp_incr, > glob_optimal_done, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_sec, > glob_warned, > glob_max_rel_trunc_err, > glob_reached_optimal_h, > glob_not_yet_start_msg, > days_in_year, > glob_normmax, > glob_unchanged_h_cnt, > glob_hmin_init, > glob_html_log, > glob_log10relerr, > glob_look_poles, > glob_optimal_expect_sec, > glob_max_minutes, > glob_iter, > glob_max_trunc_err, > glob_abserr, > glob_hmin, > glob_display_flag, > djd_debug, > glob_dump, > glob_curr_iter_when_opt, > glob_dump_analytic, > glob_initial_pass, > glob_not_yet_finished, > glob_max_opt_iter, > glob_h, > glob_almost_1, > sec_in_min, > glob_log10abserr, > glob_start, > glob_warned2, > glob_no_eqs, > glob_max_order, > glob_log10_relerr, > glob_hmax, > centuries_in_millinium, > glob_last_good_h, > glob_large_float, > glob_clock_sec, > glob_log10normmin, > glob_max_iter, > years_in_century, > hours_in_day, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_2, > array_const_4D0, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_norms, > array_x2_init, > array_type_pole, > array_m1, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_pole, > array_t, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2, > array_x1, > array_x2_higher, > array_real_pole, > array_x2_higher_work2, > array_x1_higher, > array_x1_higher_work2, > array_complex_pole, > array_x1_higher_work, > array_x2_higher_work, > array_poles, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > DEBUGL := 3; > glob_max_terms := 30; > ALWAYS := 1; > INFO := 2; > glob_current_iter := 0; > glob_smallish_float := 0.1e-100; > glob_small_float := 0.1e-50; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_hours := 0.0; > glob_relerr := 0.1e-10; > glob_clock_start_sec := 0.0; > djd_debug2 := true; > glob_orig_start_sec := 0.0; > glob_log10_abserr := 0.1e-10; > glob_disp_incr := 0.1; > glob_optimal_done := false; > min_in_hour := 60.0; > glob_percent_done := 0.0; > MAX_UNCHANGED := 10; > glob_max_sec := 10000.0; > glob_warned := false; > glob_max_rel_trunc_err := 0.1e-10; > glob_reached_optimal_h := false; > glob_not_yet_start_msg := true; > days_in_year := 365.0; > glob_normmax := 0.0; > glob_unchanged_h_cnt := 0; > glob_hmin_init := 0.001; > glob_html_log := true; > glob_log10relerr := 0.0; > glob_look_poles := false; > glob_optimal_expect_sec := 0.1; > glob_max_minutes := 0.0; > glob_iter := 0; > glob_max_trunc_err := 0.1e-10; > glob_abserr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_display_flag := true; > djd_debug := true; > glob_dump := false; > glob_curr_iter_when_opt := 0; > glob_dump_analytic := false; > glob_initial_pass := true; > glob_not_yet_finished := true; > glob_max_opt_iter := 10; > glob_h := 0.1; > glob_almost_1 := 0.9990; > sec_in_min := 60.0; > glob_log10abserr := 0.0; > glob_start := 0; > glob_warned2 := false; > glob_no_eqs := 0; > glob_max_order := 30; > glob_log10_relerr := 0.1e-10; > glob_hmax := 1.0; > centuries_in_millinium := 10.0; > glob_last_good_h := 0.1; > glob_large_float := 9.0e100; > glob_clock_sec := 0.0; > glob_log10normmin := 0.1; > glob_max_iter := 1000; > years_in_century := 100.0; > hours_in_day := 24.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_max_order := 2; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/complicatedrevpostode.ode#################"); > omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"t_start := 0.5;"); > omniout_str(ALWAYS,"t_end := 5.0;"); > omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_x1 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_tmp7:= Array(1..(max_terms + 1),[]); > array_tmp8:= Array(1..(max_terms + 1),[]); > array_tmp9:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_x2_init:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_t:= Array(1..(max_terms + 1),[]); > array_tmp10:= Array(1..(max_terms + 1),[]); > array_tmp11:= Array(1..(max_terms + 1),[]); > array_tmp12:= Array(1..(max_terms + 1),[]); > array_tmp13:= Array(1..(max_terms + 1),[]); > array_tmp14:= Array(1..(max_terms + 1),[]); > array_tmp15:= Array(1..(max_terms + 1),[]); > array_tmp16:= Array(1..(max_terms + 1),[]); > array_tmp17:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_x1:= Array(1..(max_terms + 1),[]); > array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher_work2 := Array(1..(2+ 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_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_x1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x2[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 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <= 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 <=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 <= 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_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > t_start := 0.5; > t_end := 5.0; > array_x1_init[1] := exact_soln_x1(t_start); > array_x2_init[1] := exact_soln_x2(t_start); > array_x2_init[2] := exact_soln_x2p(t_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_x2(); > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_x1(); > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3 > ;#was right paren 0004C > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > order_diff := 2; > #Jump Series array_x2 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > order_diff := 2; > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 3; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > order_diff := 1; > #Jump Series array_x1 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > order_diff := 1; > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 3 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 3 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if glob_html_log then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-02T02:14:30-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"complicatedrev") > ; > logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 4 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 4 > ; > log_revs(html_log_file," 076 ") > ; > logitem_str(html_log_file,"complicatedrev diffeq.mxt") > ; > logitem_str(html_log_file,"complicatedrev maple results") > ; > logitem_str(html_log_file,"sub iter once eqs reversed") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 4 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 4 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 3 > ; > if glob_html_log then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_current_iter, glob_smallish_float, glob_small_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_relerr, glob_clock_start_sec, djd_debug2, glob_orig_start_sec, glob_log10_abserr, glob_disp_incr, glob_optimal_done, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_sec, glob_warned, glob_max_rel_trunc_err, glob_reached_optimal_h, glob_not_yet_start_msg, days_in_year, glob_normmax, glob_unchanged_h_cnt, glob_hmin_init, glob_html_log, glob_log10relerr, glob_look_poles, glob_optimal_expect_sec, glob_max_minutes, glob_iter, glob_max_trunc_err, glob_abserr, glob_hmin, glob_display_flag, djd_debug, glob_dump, glob_curr_iter_when_opt, glob_dump_analytic, glob_initial_pass, glob_not_yet_finished, glob_max_opt_iter, glob_h, glob_almost_1, sec_in_min, glob_log10abserr, glob_start, glob_warned2, glob_no_eqs, glob_max_order, glob_log10_relerr, glob_hmax, centuries_in_millinium, glob_last_good_h, glob_large_float, glob_clock_sec, glob_log10normmin, glob_max_iter, years_in_century, hours_in_day, array_const_1, array_const_2, array_const_4D0, array_const_2D0, array_const_3D0, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_norms, array_x2_init, array_type_pole, array_m1, array_1st_rel_error, array_x1_init, array_last_rel_error, array_pole, array_t, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2, array_x1, array_x2_higher, array_real_pole, array_x2_higher_work2, array_x1_higher, array_x1_higher_work2, array_complex_pole, array_x1_higher_work, array_x2_higher_work, array_poles, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; glob_iolevel := 5; DEBUGL := 3; glob_max_terms := 30; ALWAYS := 1; INFO := 2; glob_current_iter := 0; glob_smallish_float := 0.1*10^(-100); glob_small_float := 0.1*10^(-50); glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_max_hours := 0.; glob_relerr := 0.1*10^(-10); glob_clock_start_sec := 0.; djd_debug2 := true; glob_orig_start_sec := 0.; glob_log10_abserr := 0.1*10^(-10); glob_disp_incr := 0.1; glob_optimal_done := false; min_in_hour := 60.0; glob_percent_done := 0.; MAX_UNCHANGED := 10; glob_max_sec := 10000.0; glob_warned := false; glob_max_rel_trunc_err := 0.1*10^(-10); glob_reached_optimal_h := false; glob_not_yet_start_msg := true; days_in_year := 365.0; glob_normmax := 0.; glob_unchanged_h_cnt := 0; glob_hmin_init := 0.001; glob_html_log := true; glob_log10relerr := 0.; glob_look_poles := false; glob_optimal_expect_sec := 0.1; glob_max_minutes := 0.; glob_iter := 0; glob_max_trunc_err := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_display_flag := true; djd_debug := true; glob_dump := false; glob_curr_iter_when_opt := 0; glob_dump_analytic := false; glob_initial_pass := true; glob_not_yet_finished := true; glob_max_opt_iter := 10; glob_h := 0.1; glob_almost_1 := 0.9990; sec_in_min := 60.0; glob_log10abserr := 0.; glob_start := 0; glob_warned2 := false; glob_no_eqs := 0; glob_max_order := 30; glob_log10_relerr := 0.1*10^(-10); glob_hmax := 1.0; centuries_in_millinium := 10.0; glob_last_good_h := 0.1; glob_large_float := 0.90*10^101; glob_clock_sec := 0.; glob_log10normmin := 0.1; glob_max_iter := 1000; years_in_century := 100.0; hours_in_day := 24.0; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_max_order := 2; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/complicatedrevpostode.ode#################"); omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \ diff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "t_start := 0.5;"); omniout_str(ALWAYS, "t_end := 5.0;"); omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_x1 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_tmp7 := Array(1 .. max_terms + 1, []); array_tmp8 := Array(1 .. max_terms + 1, []); array_tmp9 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_x2_init := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_t := Array(1 .. max_terms + 1, []); array_tmp10 := Array(1 .. max_terms + 1, []); array_tmp11 := Array(1 .. max_terms + 1, []); array_tmp12 := Array(1 .. max_terms + 1, []); array_tmp13 := Array(1 .. max_terms + 1, []); array_tmp14 := Array(1 .. max_terms + 1, []); array_tmp15 := Array(1 .. max_terms + 1, []); array_tmp16 := Array(1 .. max_terms + 1, []); array_tmp17 := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_x1 := Array(1 .. max_terms + 1, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_x1_higher_work2 := Array(1 .. 3, 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_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); 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_norms[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_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_t[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_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 <= max_terms do array_x1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_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_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1 end do; array_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_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_t[1] := t_start; array_t[2] := glob_h; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x2_higher[r_order, term_no] := array_x2_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x1_higher[r_order, term_no] := array_x1_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_x2(); if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_x1(); if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_t[1] <= t_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 2; order_diff := 2; order_diff := 2; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; order_diff := 1; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\ ff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(INFO, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-02T02:14:30-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "complicatedrev"); logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \ 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 076 "); logitem_str(html_log_file, "complicatedrev diffeq.mxt"); logitem_str(html_log_file, "complicatedrev maple results"); logitem_str(html_log_file, "sub iter once eqs reversed"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/complicatedrevpostode.ode################# diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; #END FIRST INPUT BLOCK ! #BEGIN SECOND INPUT BLOCK t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00001 ; 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 = 1e-05 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 1e-05 t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 1e-05 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50001 x2[1] (analytic) = 0.00082562461725876370002024077185103 x2[1] (numeric) = 0.00082562461725876370001850438630327 absolute error = 1.73638554776e-24 relative error = 2.1031174597544607182379664103030e-19 % h = 1e-05 x1[1] (analytic) = 0.0012917442699854529125006082860118 x1[1] (numeric) = 0.0012917442699854533755361438697077 absolute error = 4.630355355836959e-19 relative error = 3.5845758819499962937733300874971e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50002 x2[1] (analytic) = 0.00082563367114759095929891755098496 x2[1] (numeric) = 0.00082563367125676738782278565937351 absolute error = 1.0917642852386810838855e-13 relative error = 1.3223349814708760775039866741433e-08 % h = 1e-05 x1[1] (analytic) = 0.0012917333525973400895138324871812 x1[1] (numeric) = 0.0012917333523789930655009089285212 absolute error = 2.183470240129235586600e-13 relative error = 1.6903413043712499578921990894768e-08 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50003 x2[1] (analytic) = 0.00082564272527208501941416438049361 x2[1] (numeric) = 0.00082564272570879455466581711189685 absolute error = 4.3670953525165273140324e-13 relative error = 5.2893282031612164295245176770861e-08 % h = 1e-05 x1[1] (analytic) = 0.0012917224353184006017877004750958 x1[1] (numeric) = 0.0012917224344450138963419301919134 absolute error = 8.733867054457702831824e-13 relative error = 6.7614115971476993897360275399639e-08 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50004 x2[1] (analytic) = 0.00082565177963225004787972600227534 x2[1] (numeric) = 0.00082565178061485955781373035006816 absolute error = 9.8260950993400434779282e-13 relative error = 1.1901016072074163721437244438536e-07 % h = 1e-05 x1[1] (analytic) = 0.0012917115181486333575943182918853 x1[1] (numeric) = 0.0012917115161835128356349680207825 absolute error = 1.9651205219593502711028e-12 relative error = 1.5213308036270291783122833102169e-07 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50005 x2[1] (analytic) = 0.00082566083422809021229815693339498 x2[1] (numeric) = 0.00082566083597497966616595569491602 absolute error = 1.74688945386779876152104e-12 relative error = 2.1157470252309649622630824800761e-07 % h = 1e-05 x1[1] (analytic) = 0.0012917006010880372652167092040327 x1[1] (numeric) = 0.0012917005975944800581063618292001 absolute error = 3.4935572071103473748326e-12 relative error = 2.7046183954452152243310747632178e-07 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=2.9MB, time=0.18 t[1] = 0.50006 x2[1] (analytic) = 0.00082566988905960968036082318771056 x2[1] (numeric) = 0.00082566989178917214912074789050692 absolute error = 2.72956246875992470279636e-12 relative error = 3.3058762405260275596487976833741e-07 % h = 1e-05 x1[1] (analytic) = 0.0012916896841366112329488135932026 x1[1] (numeric) = 0.0012916896786779057384060406140816 absolute error = 5.4587054945427729791210e-12 relative error = 4.2260192688551744107118307424308e-07 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50007 x2[1] (analytic) = 0.00082567894412681261984790399753532 x2[1] (numeric) = 0.00082567894805745427666738695047968 absolute error = 3.93064165681948295294436e-12 relative error = 4.7604964190727769488393004963567e-07 % h = 1e-05 x1[1] (analytic) = 0.0012916787672943541690954888470709 x1[1] (numeric) = 0.0012916787594337800508891848391061 absolute error = 7.8605741182063040079648e-12 relative error = 6.0855487581263286027031522090687e-07 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50008 x2[1] (analytic) = 0.00082568799942970319862839353533439 x2[1] (numeric) = 0.00082568800477984331938619437797027 absolute error = 5.35014012075780084263588e-12 relative error = 6.4796147266922910292856982375231e-07 % h = 1e-05 x1[1] (analytic) = 0.0012916678505612649819725092501548 x1[1] (numeric) = 0.0012916678398620931696162246387965 absolute error = 1.06991718123562846113583e-11 relative error = 8.2832221981116910618011072053618e-07 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50009 x2[1] (analytic) = 0.00082569705496828558466010263545667 x2[1] (numeric) = 0.00082569706195635654844855235532287 absolute error = 6.98807096378844971986620e-12 relative error = 8.4632383290465488887496652259715e-07 % h = 1e-05 x1[1] (analytic) = 0.0012916569339373425799065658746448 x1[1] (numeric) = 0.0012916569199628352683528309763718 absolute error = 1.39745073115537348982730e-11 relative error = 1.0819054924247887765897703160457e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001 x2[1] (analytic) = 0.00082570611074256394598966051590164 x2[1] (numeric) = 0.00082570611958701123561692293431001 absolute error = 8.84444728962726241840837e-12 relative error = 1.0711374391638426877064940718591e-06 % h = 1e-05 x1[1] (analytic) = 0.001291646017422585871235266471237 x1[1] (numeric) = 0.0012916459997359965205699068015618 absolute error = 1.76865893506653596696752e-11 relative error = 1.3693062272555178730016330751030e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50011 x2[1] (analytic) = 0.00082571516675254245075251650012108 x2[1] (numeric) = 0.0008257151776718246532448672269575 absolute error = 1.091928220249235072683642e-11 relative error = 1.3224030079811694680378355692477e-06 % h = 1e-05 x1[1] (analytic) = 0.0012916351010169937643071353599673 x1[1] (numeric) = 0.0012916350791815670994435782081568 absolute error = 2.18354266648635571518105e-11 relative error = 1.6905259579637479327811484185126e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50012 x2[1] (analytic) = 0.00082572422299822526717294173885586 x2[1] (numeric) = 0.00082572423621081407427706459697429 absolute error = 1.321258880710412285811843e-11 relative error = 1.6001212558751011395870340520451e-06 % h = 1e-05 x1[1] (analytic) = 0.0012916241847205651674816133210459 x1[1] (numeric) = 0.0012916241582995371778551855912916 absolute error = 2.64210279896264277297543e-11 relative error = 2.0455662182682381613832081814347e-06 % h = 1e-05 TOP MAIN SOLVE Loop Complex estimate of poles used NO POLE Radius of convergence = 9.530e-05 Order of pole = 1.45 t[1] = 0.50013 x2[1] (analytic) = 0.00082573327947961656356403093200764 x2[1] (numeric) = 0.0008257332952039967722493318517872 absolute error = 1.572438020868530091977956e-11 relative error = 1.9042928993481921606955010914472e-06 % h = 1e-05 x1[1] (analytic) = 0.0012916132685332989891290574856932 x1[1] (numeric) = 0.0012916132370898969283912748044647 absolute error = 3.14434020607377826812285e-11 relative error = 2.4344285419461175646548562580817e-06 % h = 1e-05 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 6.634e-05 Order of pole = 0.2431 t[1] = 0.50014 x2[1] (analytic) = 0.00082574233619672050832770405054562 x2[1] (numeric) = 0.00082574235465139002128864243518058 absolute error = 1.845466951296093838463496e-11 relative error = 2.2349186548870851458959711514823e-06 % h = 1e-05 x1[1] (analytic) = 0.0012916023524551941376307412269771 x1[1] (numeric) = 0.001291602315552636523343588316292 absolute error = 3.69025576142871529106851e-11 relative error = 2.8571144628328870812144320932198e-06 % h = 1e-05 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 9.350e-05 Order of pole = 16.66 t[1] = 0.50015 x2[1] (analytic) = 0.00082575139314954126995470805844824 x2[1] (numeric) = 0.0008257514145530110961131456205409 absolute error = 2.140346982615843756209266e-11 relative error = 2.5919992389625104735284114494174e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915914364862495213788540506512 x1[1] (numeric) = 0.0012915913936877461347090563669952 absolute error = 4.27985033866697976836560e-11 relative error = 3.3136255148224217149070958940880e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 0.0003884 Order of pole = 181.4 t[1] = 0.50016 x2[1] (analytic) = 0.00082576045033808301702461863467988 x2[1] (numeric) = 0.00082576047490887727203218570470628 absolute error = 2.457079425500756707002640e-11 relative error = 2.9755353680292858934038800993677e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915805206264640487765014859936 x1[1] (numeric) = 0.0012915804714952159341897881246249 absolute error = 4.91312481145867133613687e-11 relative error = 3.8039632318669726673367144025253e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.2MB, time=0.41 NO POLE NO POLE t[1] = 0.50017 x2[1] (analytic) = 0.00082576950776234991820584189520253 x2[1] (numeric) = 0.00082576953571900582494632120242102 absolute error = 2.795665590674047930721849e-11 relative error = 3.3855277585263161345163410640853e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915696048758366282377049766475 x1[1] (numeric) = 0.0012915695489750360931930628410185 absolute error = 5.59008005350446421356290e-11 relative error = 4.3281291479771694704741944607951e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50018 x2[1] (analytic) = 0.00082577856542234614225561611502238 x2[1] (numeric) = 0.0008257785969834140313473440413951 absolute error = 3.156106788909172792637272e-11 relative error = 3.8219771268765925128024359620369e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915586892343661681874017714626 x1[1] (numeric) = 0.0012915586261271967828313210074928 absolute error = 6.31071693853560807639698e-11 relative error = 4.8861247972220221193421967587350e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50019 x2[1] (analytic) = 0.0008257876233180758580200134502716 x2[1] (numeric) = 0.0008257876587021191683182987579687 absolute error = 3.538404331029828530769710e-11 relative error = 4.2848841894871925389491837134457e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915477737020515770614448153374 x1[1] (numeric) = 0.0012915477029516881739221555102713 absolute error = 7.07503634031392893050661e-11 relative error = 5.4779517137289232047762395716644e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002 x2[1] (analytic) = 0.0008257966814495432344339416603249 x2[1] (numeric) = 0.00082579672087513851353350169338175 absolute error = 3.942559527909956003305685e-11 relative error = 4.7742496627492795262496565121709e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915368582788917633066026400632 x1[1] (numeric) = 0.0012915367794485004369883027856458 absolute error = 7.88303913263182998544174e-11 relative error = 6.1036114316836500462622874688790e-06 % h = 1e-05 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 2.210e-05 Order of pole = 14.49 t[1] = 0.50021 x2[1] (analytic) = 0.0008258057398167524405211458299511 x2[1] (numeric) = 0.00082580578350248934525856019064851 absolute error = 4.368573690473741436069741e-11 relative error = 5.2900742630381021985066018947665e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915259429648856353805592551682 x1[1] (numeric) = 0.0012915258556176237422576339748735 absolute error = 8.73472618931229252802947e-11 relative error = 6.7631054853303668248506102677261e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 2.337e-05 Order of pole = 24.84 t[1] = 0.50022 x2[1] (analytic) = 0.00082581479841970764539421009149987 x2[1] (numeric) = 0.00082581484658418894235039179203724 absolute error = 4.816448129695618170053737e-11 relative error = 5.8323587067129942979839964224779e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915150277600321017519140387637 x1[1] (numeric) = 0.0012915149314590482596631460788077 absolute error = 9.63009838420887679599560e-11 relative error = 7.4564354089716267161462162641946e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE Real estimate of pole used Radius of convergence = 1.141e-05 Order of pole = 2.458 t[1] = 0.50023 x2[1] (analytic) = 0.00082582385725841301825455934712328 x2[1] (numeric) = 0.00082582391012025458425724343715494 absolute error = 5.286184156600268409003166e-11 relative error = 6.4011037101173741934065697730631e-06 % h = 1e-05 x1[1] (analytic) = 0.0012915041126643300709001816283908 x1[1] (numeric) = 0.0012915040069727641588429531122643 absolute error = 1.056915659120572285161265e-10 relative error = 8.1836027369683740233755675873505e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50024 x2[1] (analytic) = 0.0008258329163328727283924609910323 x2[1] (numeric) = 0.0008258329741107035510187106616372 absolute error = 5.777783082262624967060490e-11 relative error = 6.9963099895787444880072847561126e-06 % h = 1e-05 x1[1] (analytic) = 0.0012914931976777784513157918118686 x1[1] (numeric) = 0.0012914930821587616091402772581219 absolute error = 1.155190168421755145537467e-10 relative error = 8.9446090037399463105298275133529e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50025 x2[1] (analytic) = 0.00082584197564309094518702663178858 x2[1] (numeric) = 0.00082584203855555312326575679644316 absolute error = 6.291246217807873016465458e-11 relative error = 7.6179782614086916276227309161763e-06 % h = 1e-05 x1[1] (analytic) = 0.0012914822828003761515000894181426 x1[1] (numeric) = 0.0012914821570170307796034400211573 absolute error = 1.257833453718966493969853e-10 relative error = 9.7394557437640765355844017800122e-06 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50026 x2[1] (analytic) = 0.00082585103518907183810621381463082 x2[1] (numeric) = 0.00082585110345482058222073216775562 absolute error = 6.826574874411451835312480e-11 relative error = 8.2661092419028855088365177439090e-06 % h = 1e-05 x1[1] (analytic) = 0.0012914713680321220799653342081357 x1[1] (numeric) = 0.0012914712315475618389858533816152 absolute error = 1.364845602409794808265205e-10 relative error = 1.0568144491576895183795054714749e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=4.3MB, time=0.64 t[1] = 0.50027 x2[1] (analytic) = 0.00082586009497081957670682774383651 x2[1] (numeric) = 0.00082586016880852320969739329748633 absolute error = 7.383770363299056555364982e-11 relative error = 8.9407036473410790871705743005057e-06 % h = 1e-05 x1[1] (analytic) = 0.0012914604533730151452347007655986 x1[1] (numeric) = 0.0012914603057503449557460109485126 absolute error = 1.476226701894886898170860e-10 relative error = 1.1430676781772932401070315756194e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50028 x2[1] (analytic) = 0.00082586915498833833063452300511837 x2[1] (numeric) = 0.00082586923461667828810092210438643 absolute error = 7.962833995746639909926806e-11 relative error = 9.6417621939871079853244303761579e-06 % h = 1e-05 x1[1] (analytic) = 0.0012914495388230542558422783879629 x1[1] (numeric) = 0.0012914493796253702980474791126781 absolute error = 1.591976839577947992752848e-10 relative error = 1.2327054149005120127420418470416e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50029 x2[1] (analytic) = 0.00082587821524163226962380528805599 x2[1] (numeric) = 0.00082587830087930310042794510576207 absolute error = 8.563767083080413981770608e-11 relative error = 1.0369285598088890101462419894005e-05 % h = 1e-05 x1[1] (analytic) = 0.0012914386243822383203330709771937 x1[1] (numeric) = 0.0012914384531726280337588881995255 absolute error = 1.712096102865741827776682e-10 relative error = 1.3257278127984794230482572810814e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003 x2[1] (analytic) = 0.00082588727573070556349803310856235 x2[1] (numeric) = 0.00082588736759641493026655261979532 absolute error = 9.186570936676851951123297e-11 relative error = 1.1123274575878425217548856249711e-05 % h = 1e-05 x1[1] (analytic) = 0.0012914277100505662472629969306448 x1[1] (numeric) = 0.001291427526392108330453923621562 absolute error = 1.836584579168090733090828e-10 relative error = 1.4221350253481696639122789498978e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50031 x2[1] (analytic) = 0.00082589633645556238216941953138531 x2[1] (numeric) = 0.00082589643476803106179631796847022 absolute error = 9.831246867962689843708491e-11 relative error = 1.1903729843571794607731148148176e-05 % h = 1e-05 x1[1] (analytic) = 0.001291416795828036945198889031914 x1[1] (numeric) = 0.0012914165992838013554113170306312 absolute error = 1.965442355897875720012828e-10 relative error = 1.5219272060323977477114049529678e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50032 x2[1] (analytic) = 0.0008259053974162068956390338926443 x2[1] (numeric) = 0.00082590550239416877978831668110416 absolute error = 1.0497796188414928278845986e-10 relative error = 1.2710652117369160646770848717243e-05 % h = 1e-05 x1[1] (analytic) = 0.0012914058817146493227184943416995 x1[1] (numeric) = 0.0012914056718476972756148374698906 absolute error = 2.098669520471036568718089e-10 relative error = 1.6251045083398197196890921529027e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50033 x2[1] (analytic) = 0.00082591445861264327399680352240172 x2[1] (numeric) = 0.00082591457047484536960514569848449 absolute error = 1.1186220209560834217608277e-10 relative error = 1.3544042113454766418522682742111e-05 % h = 1e-05 x1[1] (analytic) = 0.0012913949677104022884104740886584 x1[1] (numeric) = 0.0012913947440837862577532825255235 absolute error = 2.236266160306571915631349e-10 relative error = 1.7316670857649328713380714214491e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50034 x2[1] (analytic) = 0.00082592352004487568742151546726956 x2[1] (numeric) = 0.00082592363901007811720094257761044 absolute error = 1.1896520242977942711034088e-10 relative error = 1.4403900547996935324461497577193e-05 % h = 1e-05 x1[1] (analytic) = 0.0012913840538152947508744035602647 x1[1] (numeric) = 0.0012913838159920584682204694781858 absolute error = 2.378232362826539340820789e-10 relative error = 1.8416150918080759537910925978878e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50035 x2[1] (analytic) = 0.00082593258171290830618081821305085 x2[1] (numeric) = 0.00082593270799988430912140469704034 absolute error = 1.2628697600294058648398949e-10 relative error = 1.5290228137148070692257181367586e-05 % h = 1e-05 x1[1] (analytic) = 0.0012913731400293256187207719936699 x1[1] (numeric) = 0.0012913728875725040731152264541871 absolute error = 2.524568215456055455394828e-10 relative error = 1.9549486799754293912193280175387e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50036 x2[1] (analytic) = 0.00082594164361674530063122340741629 x2[1] (numeric) = 0.00082594177744428123250380846284417 absolute error = 1.3382753593187258505542788e-10 relative error = 1.6203025597044655384397507456508e-05 % h = 1e-05 x1[1] (analytic) = 0.001291362226352493800570982466564 x1[1] (numeric) = 0.0012913619588251132382413835764063 absolute error = 2.675273805623295988901577e-10 relative error = 2.0716680037790154942384162330899e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50037 x2[1] (analytic) = 0.00082595070575639084121810758261578 x2[1] (numeric) = 0.00082595084734328617507702851516146 absolute error = 1.4158689533385892093254568e-10 relative error = 1.7142293643807251406858938923391e-05 % h = 1e-05 x1[1] (analytic) = 0.001291351312784798205057351788037 x1[1] (numeric) = 0.0012913510297498761291077641149422 absolute error = 2.830349220759495876730948e-10 relative error = 2.1917732167366986733221430378656e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=15.2MB, alloc=4.4MB, time=0.88 t[1] = 0.50038 x2[1] (analytic) = 0.00082595976813184909847571387822485 x2[1] (numeric) = 0.00082595991769691642516155693536455 absolute error = 1.4956506732668584305713970e-10 relative error = 1.8108032993540499517825392083413e-05 % h = 1e-05 x1[1] (analytic) = 0.0012913403993262377408231103894432 x1[1] (numeric) = 0.0012913401003467829109281756374981 absolute error = 2.989794548298949347519451e-10 relative error = 2.3152644723721856522237855523328e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50039 x2[1] (analytic) = 0.00082596883074312424302715376392631 x2[1] (numeric) = 0.00082596898850518927166952245382725 absolute error = 1.5776206502864236868990094e-10 relative error = 1.9100244362333118836454922668790e-05 % h = 1e-05 x1[1] (analytic) = 0.0012913294859768113165224022152644 x1[1] (numeric) = 0.0012913291706158237486214011595011 absolute error = 3.153609875679010010557633e-10 relative error = 2.4421419242150256814050839596317e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004 x2[1] (analytic) = 0.00082597789359022044558440876232671 x2[1] (numeric) = 0.00082597805976812200410470965829888 absolute error = 1.6617790155852030089597217e-10 relative error = 2.0118928466257906451694379531060e-05 % h = 1e-05 x1[1] (analytic) = 0.0012913185727365178408202846139762 x1[1] (numeric) = 0.0012913182405569888068111902939561 absolute error = 3.321795290340090943200201e-10 relative error = 2.5724057258006107514728736208914e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50041 x2[1] (analytic) = 0.00082598695667314187694833217180798 x2[1] (numeric) = 0.00082598713148573191256257820288376 absolute error = 1.7481259003561424603107578e-10 relative error = 2.1164086021371737031141987162930e-05 % h = 1e-05 x1[1] (analytic) = 0.001291307659605356222392728228914 x1[1] (numeric) = 0.0012913073101702682498262504010342 absolute error = 3.494350879725664778278798e-10 relative error = 2.7060560306701758066233537714652e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50042 x2[1] (analytic) = 0.00082599601999189270800865078941384 x2[1] (numeric) = 0.0008259962036580362877302820176261 absolute error = 1.8366614357972163122821226e-10 relative error = 2.2235717743715562429957898244955e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912967465833253699266168891408 x1[1] (numeric) = 0.0012912963794556522417002377373955 absolute error = 3.671276731282263791517453e-10 relative error = 2.8430929923707989580940092671901e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50043 x2[1] (analytic) = 0.00082600508354647710974396663377145 x2[1] (numeric) = 0.00082600527628505242088668851870041 absolute error = 1.9273857531114272188492896e-10 relative error = 2.3333824349314411299822671462498e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912858336704241921197475003156 x1[1] (numeric) = 0.0012912854484131309461717486052465 absolute error = 3.852572932459479988950691e-10 relative error = 2.9835167644554016976231747461155e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50044 x2[1] (analytic) = 0.00082601414733689925322175866804788 x2[1] (numeric) = 0.00082601434936679760390239781920733 absolute error = 2.0202989835068063915115945e-10 relative error = 2.4458406554177388697943710954559e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912749208666515976808299355639 x1[1] (numeric) = 0.001291274517042694526684310501132 absolute error = 4.038239570709965194344319e-10 relative error = 3.1273275004827491109172538032663e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50045 x2[1] (analytic) = 0.00082602321136316330959838452294175 x2[1] (numeric) = 0.00082602342290328912923976194057498 absolute error = 2.1154012581964137741763323e-10 relative error = 2.5609465074297675696109634747195e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912640081720064953294869263476 x1[1] (numeric) = 0.0012912635853443331463863732644615 absolute error = 4.228276733489431136618861e-10 relative error = 3.2745253540174500911255724761482e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50046 x2[1] (analytic) = 0.00082603227562527345011908221970975 x2[1] (numeric) = 0.00082603249689454428995290402456583 absolute error = 2.2126927083983382180485608e-10 relative error = 2.6787000625652528989792604899679e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912530955864877937962539533377 x1[1] (numeric) = 0.00129125265331803696813130022577 absolute error = 4.422684508256649537275677e-10 relative error = 3.4251104786299575523228943526575e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50047 x2[1] (analytic) = 0.00082604134012323384611797189322822 x2[1] (numeric) = 0.00082604157134058037968773754588912 absolute error = 2.3121734653356976565266090e-10 relative error = 2.7991013924203280507298598822249e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912421831100944018225791372872 x1[1] (numeric) = 0.0012912417209637961544773593547132 absolute error = 4.621462982473452197825740e-10 relative error = 3.5790830278965686429995773735709e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50048 x2[1] (analytic) = 0.00082605040485704866901805751508965 x2[1] (numeric) = 0.00082605064624141469268198552541879 absolute error = 2.4138436602366392801032914e-10 relative error = 2.9221505685895337018965631490356e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912312707428252281608231299048 x1[1] (numeric) = 0.0012912307882816008676877144077975 absolute error = 4.824612243604731087221073e-10 relative error = 3.7364431553994249595593740851580e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=19.0MB, alloc=4.4MB, time=1.11 t[1] = 0.50049 x2[1] (analytic) = 0.00082605946982672209033122861673442 x2[1] (numeric) = 0.00082605972159706452376519974401701 absolute error = 2.5177034243343397112728259e-10 relative error = 3.0478476626658179746409898330494e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912203584846791815742590047308 x1[1] (numeric) = 0.001291219855271441269730416075844 absolute error = 5.032132379118438429288868e-10 relative error = 3.8971910147265127598248925867844e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005 x2[1] (analytic) = 0.00082606853503225828165826201261726 x2[1] (numeric) = 0.00082606879740754716835877995696331 absolute error = 2.6237528888670051794434605e-10 relative error = 3.1761927462405363971819899346588e-05 % h = 1e-05 x1[1] (analytic) = 0.0012912094463356551708370721480129 x1[1] (numeric) = 0.0012912089219333075222783931311872 absolute error = 5.244023476485586790168257e-10 relative error = 4.0613267594716631765506951472216e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50051 x2[1] (analytic) = 0.00082607760047366141468882352340884 x2[1] (numeric) = 0.0008260778736728799224759931089893 absolute error = 2.7319921850778716958558046e-10 relative error = 3.3071858909034518647298491259550e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911985342957521047343601495841 x1[1] (numeric) = 0.0012911979882671897867094435746081 absolute error = 5.460285623180249165749760e-10 relative error = 4.2288505432345524309440540578800e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50052 x2[1] (analytic) = 0.00082608666615093566120146969923256 x2[1] (numeric) = 0.00082608695039308008272199254991903 absolute error = 2.8424214442152052285068647e-10 relative error = 3.4408271682427346004252862858098e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911876223649688920621326937406 x1[1] (numeric) = 0.0012911870542730782241062257820018 absolute error = 5.680918906679559069117388e-10 relative error = 4.3997625196207020461933478919113e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50053 x2[1] (analytic) = 0.00082609573206408519306364954293594 x2[1] (numeric) = 0.00082609602756816494629383725091498 absolute error = 2.9550407975323018770797904e-10 relative error = 3.5771166498449621162832502600427e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911767105433044416273114501219 x1[1] (numeric) = 0.0012911761199509629952562496507792 absolute error = 5.905923414463710617993427e-10 relative error = 4.5740628422414790610041185123551e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50054 x2[1] (analytic) = 0.0008261047982131141822317062333974 x2[1] (numeric) = 0.00082610510519815181098051102132975 absolute error = 3.0698503762874880478793235e-10 relative error = 3.7160544072951191741415068924417e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911657988307576622477299645915 x1[1] (numeric) = 0.0012911651853008342606518677460035 absolute error = 6.135299234015958622185880e-10 relative error = 4.7517516647140962431427712236818e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50055 x2[1] (analytic) = 0.00082611386459802680075087884886784 x2[1] (numeric) = 0.00082611418328305797516294172616339 absolute error = 3.1868503117441206287729555e-10 relative error = 3.8576405121765977466140225042587e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911548872273274627521335501181 x1[1] (numeric) = 0.0012911542503226821804902664462609 absolute error = 6.369046452822618671038572e-10 relative error = 4.9328291406616123029879221458904e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50056 x2[1] (analytic) = 0.0008261229312188272207553040903474 x2[1] (numeric) = 0.00082612326182290073781402050412647 absolute error = 3.3060407351705871641377907e-10 relative error = 4.0018750360711969780491401943876e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911439757330127519801791776594 x1[1] (numeric) = 0.0012911433150164969146734570892658 absolute error = 6.607165158373067220883936e-10 relative error = 5.1172954237129321070894069591666e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50057 x2[1] (analytic) = 0.00082613199807551961446801800499697 x2[1] (numeric) = 0.00082613234081769739849862098630887 absolute error = 3.4274217778403060298131190e-10 relative error = 4.1487580505591231454925536849090e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911330643478124387824353670451 x1[1] (numeric) = 0.0012911323793822686228082671172003 absolute error = 6.849655438159741682498448e-10 relative error = 5.3051506675028068917349264423960e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50058 x2[1] (analytic) = 0.00082614106516810815420095770958501 x2[1] (numeric) = 0.00082614142026746525737361851545427 absolute error = 3.5509935710317266080586926e-10 relative error = 4.2982896272189896196550714528102e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911221530717254320203820778627 x1[1] (numeric) = 0.001291121443419987464206331221788 absolute error = 7.096517379678140508560747e-10 relative error = 5.4963950256718344765243568944955e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50059 x2[1] (analytic) = 0.00082615013249659701235496311396918 x2[1] (numeric) = 0.00082615050017222161518790936584045 absolute error = 3.6767562460283294625187127e-10 relative error = 4.4504698376278168258851782934676e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911112419047506405664106003432 x1[1] (numeric) = 0.0012911105071296435978840824891024 absolute error = 7.347751070426823281112408e-10 relative error = 5.6910286518664594779517008616263e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.34 NO POLE NO POLE t[1] = 0.5006 x2[1] (analytic) = 0.00082615920006099036141977864461309 x2[1] (numeric) = 0.00082615958053198377328242996376535 absolute error = 3.8047099341186265131915226e-10 relative error = 4.6052987533610322051463897197432e-05 % h = 1e-05 x1[1] (analytic) = 0.0012911003308468869733038234462486 x1[1] (numeric) = 0.0012910995705112271825627435441094 absolute error = 7.603356597907410799021392e-10 relative error = 5.8890516997389735229946969655201e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50061 x2[1] (analytic) = 0.00082616826786129237397405496813805 x2[1] (numeric) = 0.00082616866134676903359017610863892 absolute error = 3.9348547665961612114050087e-10 relative error = 4.7627764459924701749994007739990e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910894198981333391268342397601 x1[1] (numeric) = 0.0012910886335647283766683176949444 absolute error = 7.863334049624585165448157e-10 relative error = 6.0904643229475154627120766478323e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50062 x2[1] (analytic) = 0.00082617733589750722268535071490973 x2[1] (numeric) = 0.00082617774261659469863622219468078 absolute error = 4.0671908747595087147977105e-10 relative error = 4.9229029870943720905890303460149e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910785090584886469405676083676 x1[1] (numeric) = 0.0012910776962901373383315800769236 absolute error = 8.127683513086089875314440e-10 relative error = 6.2952666751560715858484757827975e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50063 x2[1] (analytic) = 0.00082618640416963908031013420266005 x2[1] (numeric) = 0.00082618682434147807153774043322374 absolute error = 4.2017183899122760623056369e-10 relative error = 5.0856784482373862056359574902200e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910675983279518056610590737599 x1[1] (numeric) = 0.0012910667586874442253880687962897 absolute error = 8.396405075802729902774702e-10 relative error = 6.5034589100344758324469951690455e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50064 x2[1] (analytic) = 0.0008261954726776921196937851601439 x2[1] (numeric) = 0.00082619590652143645600402007562316 absolute error = 4.3384374433631023491547926e-10 relative error = 5.2511029009905676334332541033219e-05 % h = 1e-05 x1[1] (analytic) = 0.001291056687706521724215254942717 x1[1] (numeric) = 0.0012910558207566391953780760736918 absolute error = 8.669498825288371788690252e-10 relative error = 6.7150411812584100074694225004311e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50065 x2[1] (analytic) = 0.0008262045414216705137705964508309 x2[1] (numeric) = 0.00082620498915648715633648663677218 absolute error = 4.4773481664256589018594128e-10 relative error = 5.4191764169213783078477115450236e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910457771941973115410121980021 x1[1] (numeric) = 0.0012910448824977124055466393873997 absolute error = 8.946964849059943728106024e-10 relative error = 6.9300136425094039944240958848291e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50066 x2[1] (analytic) = 0.00082621361040157843556377579663232 x2[1] (numeric) = 0.00082621407224664747742872111922283 absolute error = 4.6184506904186494532259051e-10 relative error = 5.5898990675956869443259596319403e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910348667909774765870983892555 x1[1] (numeric) = 0.0012910339439106540128435326162528 absolute error = 9.228803234637435657730027e-10 relative error = 7.1483764474748359690014246087919e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50067 x2[1] (analytic) = 0.00082622267961742005818544750166287 x2[1] (numeric) = 0.00082622315579193472476647923791306 absolute error = 4.7617451466658103173625019e-10 relative error = 5.7632709245777690009053817603828e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910239564968611283131915238901 x1[1] (numeric) = 0.0012910230049954541739232571823428 absolute error = 9.515014069543899343415473e-10 relative error = 7.3701297498479326127170712283473e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50068 x2[1] (analytic) = 0.00082623174906919955483665417603757 x2[1] (numeric) = 0.00082623223979236620442771064549973 absolute error = 4.9072316664959105646946216e-10 relative error = 5.9392920594303066392298238617467e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910130463118471756898799579863 x1[1] (numeric) = 0.001291012065752103045145033193431 absolute error = 9.805597441305448467645553e-10 relative error = 7.5952737033277693265627719559958e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50069 x2[1] (analytic) = 0.00082624081875692109880735845970363 x2[1] (numeric) = 0.00082624132424795922308257815829749 absolute error = 5.0549103812427521969859386e-10 relative error = 6.1179625437143886855700969519298e-05 % h = 1e-05 x1[1] (analytic) = 0.0012910021362359345276986622871902 x1[1] (numeric) = 0.0012910011261805907825727905850999 absolute error = 1.0100553437451258717020903e-09 relative error = 7.8238084616192704446648280829955e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5007 x2[1] (analytic) = 0.00082624988868058886347644474630742 x2[1] (numeric) = 0.00082625040915873108799347698282367 absolute error = 5.2047814222451703223651625e-10 relative error = 6.2992824489895105918492735203121e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909912262691220933319472376107 x1[1] (numeric) = 0.001290990186280907541975160262639 absolute error = 1.0399882145513567869749717e-09 relative error = 8.0557341784332094479502353373882e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.57 NO POLE NO POLE t[1] = 0.50071 x2[1] (analytic) = 0.00082625895884020702231172090709628 x2[1] (numeric) = 0.00082625949452469910701505394294912 absolute error = 5.3568449208470333303585284e-10 relative error = 6.4832518468135743966727798191977e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909803164114087815930535567197 x1[1] (numeric) = 0.0012909792460530434788254652426647 absolute error = 1.0703583653027675883140550e-09 relative error = 8.2910510074862091778204846919662e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50072 x2[1] (analytic) = 0.00082626802923577974886992001485561 x2[1] (numeric) = 0.00082626858034588058859422670765508 absolute error = 5.5111010083972430669279947e-10 relative error = 6.6698708087428886863632794579670e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909694066627935014962099042517 x1[1] (numeric) = 0.001290968305496988748301711794475 absolute error = 1.1011658047531944981097767e-09 relative error = 8.5297591025007420498330007474641e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50073 x2[1] (analytic) = 0.00082627709986731121679670206788081 x2[1] (numeric) = 0.00082627766662229284177020301939608 absolute error = 5.6675498162497350095151527e-10 relative error = 6.8591394063321685560003532675311e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909584970232751620665547431055 x1[1] (numeric) = 0.0012909573646127335052865805811378 absolute error = 1.1324105416567799741619677e-09 relative error = 8.7718586172051302673902481072322e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50074 x2[1] (analytic) = 0.00082628617073480559982665571398422 x2[1] (numeric) = 0.00082628675335395317617449992306885 absolute error = 5.8261914757634784420908463e-10 relative error = 7.0510577111345355704649731388047e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909475874928526723401362302469 x1[1] (numeric) = 0.001290946423400267904367417800314 absolute error = 1.1640925847679727184299329e-09 relative error = 9.0173497053335460354364881349826e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50075 x2[1] (analytic) = 0.00082629524183826707178329997453724 x2[1] (numeric) = 0.00082629584054087890203096299558729 absolute error = 5.9870261183024766302105005e-10 relative error = 7.2456257947015177254887680231767e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909366780715249413639121076118 x1[1] (numeric) = 0.0012909354818595820998362263248145 absolute error = 1.1962119428415276857827973e-09 relative error = 9.2662325206260117741621886264089e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50076 x2[1] (analytic) = 0.00082630431317769980657908596854734 x2[1] (numeric) = 0.00082630492818308733015578557606357 absolute error = 6.1500538752357669960751623e-10 relative error = 7.4428437285830494087080862131130e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909257687592908781957495930115 x1[1] (numeric) = 0.0012909245399906662456896568428915 absolute error = 1.2287686246325060927501200e-09 relative error = 9.5185072168284003327160974466390e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50077 x2[1] (analytic) = 0.00082631338475310797821539863677017 x2[1] (numeric) = 0.00082631401628059577195752799659527 absolute error = 6.3152748779374212935982510e-10 relative error = 7.6427115843274713607228500333493e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909148595561493919044252710381 x1[1] (numeric) = 0.0012909135977935104956289989982643 absolute error = 1.2617626388962754262727738e-09 relative error = 9.7741739476924352029249625244038e-05 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50078 x2[1] (analytic) = 0.00082632245656449576078255846585668 x2[1] (numeric) = 0.00082632310483342153943713681365865 absolute error = 6.4826892577865457834780197e-10 relative error = 7.8452294334815306361602048823159e-05 % h = 1e-05 x1[1] (analytic) = 0.0012909039504620993915696249839714 x1[1] (numeric) = 0.0012909026552681050030601725298787 absolute error = 1.2951939943885094524540927e-09 relative error = 0.0001003323286697569073302091622652 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50079 x2[1] (analytic) = 0.00082633152861186732845982321253521 x2[1] (numeric) = 0.00082633219384158194518796404010808 absolute error = 6.6522971461672814082757287e-10 relative error = 8.0503973475903805647429632320572e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908930414771397862819437226871 x1[1] (numeric) = 0.0012908917124144399210937184114014 absolute error = 1.3290626998651882253112857e-09 relative error = 0.00010295684128441592341376511925865 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5008 x2[1] (analytic) = 0.00082634060089522685551538962782877 x2[1] (numeric) = 0.0008263412833050943023957863777816 absolute error = 6.8240986744688039674995283e-10 relative error = 8.2582153981975807123628403223270e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908821326012694851428855175656 x1[1] (numeric) = 0.0012908807692325054025447899904479 absolute error = 1.3633687640825980955271177e-09 relative error = 0.0001056152788585941673024741916712 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50081 x2[1] (analytic) = 0.0008263496734145785163063951813071 x2[1] (numeric) = 0.00082635037322397592483882445071264 absolute error = 6.9980939740853242926940554e-10 relative error = 8.4686836568450968421584866347858e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908712238344873972648633294021 x1[1] (numeric) = 0.0012908698257222915999331441275452 absolute error = 1.3981121957973317192018569e-09 relative error = 0.00010830764293004292099522772989593 % h = 1e-05 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.79 NO POLE NO POLE t[1] = 0.50082 x2[1] (analytic) = 0.00082635874616992648527891978537406 x2[1] (numeric) = 0.00082635946359824412688776203894798 absolute error = 7.1742831764160884225357392e-10 relative error = 8.6818021950733008755983112205752e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908603151767924317711989403184 x1[1] (numeric) = 0.0012908588818837886654831323348281 absolute error = 1.4332930037662880666054903e-09 relative error = 0.00011103393503657198360483190009015 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50083 x2[1] (analytic) = 0.00082636781916127493696798751958978 x2[1] (numeric) = 0.00082636855442791622350576531297187 absolute error = 7.3526664128653777779338209e-10 relative error = 8.8975710844209708535681015721530e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908494066281834977961228446744 x1[1] (numeric) = 0.0012908479377169867511236919144702 absolute error = 1.4689111967466724309302042e-09 relative error = 0.00011379415671604967349566427450924 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50084 x2[1] (analytic) = 0.00082637689238862804599756835502798 x2[1] (numeric) = 0.0008263776457130095302485020687364 absolute error = 7.5332438148425093371370842e-10 relative error = 9.1159903964252908974634359279127e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908384981886595044847741399822 x1[1] (numeric) = 0.0012908369932218760084883370968486 absolute error = 1.5049667834959964370431336e-09 relative error = 0.00011658830950640283042140715554918 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50085 x2[1] (analytic) = 0.00082638596585198998708057987866837 x2[1] (numeric) = 0.00082638673745354136326416096329812 absolute error = 7.7160155137618358108462975e-10 relative error = 9.3370602026218511702868888598136e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908275898582193609932004178204 x1[1] (numeric) = 0.0012908260483984465889151501784432 absolute error = 1.5414597727720780502393772e-09 relative error = 0.00011941639494561681766285737992973 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50086 x2[1] (analytic) = 0.0008263950395513649350188890178239 x2[1] (numeric) = 0.00082639582964952903929347075106092 absolute error = 7.9009816410427458173323702e-10 relative error = 9.5607805745446478377500328092581e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908166816368619764883576547494 x1[1] (numeric) = 0.0012908151032466886434467726594698 absolute error = 1.5783901733330415849952796e-09 relative error = 0.00012227841457173552416581272903742 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50087 x2[1] (analytic) = 0.00082640411348675706470331376460328 x2[1] (numeric) = 0.00082640492230098987566971952062519 absolute error = 8.0881423281096640575602191e-10 relative error = 9.7871515837260830293802304917925e-05 % h = 1e-05 x1[1] (analytic) = 0.0012908057735245862601481101032286 x1[1] (numeric) = 0.0012908041577665923228303963812478 absolute error = 1.6157579939373177137219808e-09 relative error = 0.00012517436992286136667903495524923 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50088 x2[1] (analytic) = 0.00082641318765817055111362490040834 x2[1] (numeric) = 0.0008264140154079411903187739322433 absolute error = 8.2774977063920514903183496e-10 relative error = 0.00010016173301696964799632223619056 % h = 1e-05 x1[1] (analytic) = 0.0012907948655213911211612301825339 x1[1] (numeric) = 0.0012907932119581477775177546633013 absolute error = 1.6535632433436434755192326e-09 relative error = 0.00012810426253715529189228939532306 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50089 x2[1] (analytic) = 0.00082642226206560956931854772046646 x2[1] (numeric) = 0.0008264231089704003017590984558814 absolute error = 8.4690479073244055073541494e-10 relative error = 0.00010247845799986507089004514915642 % h = 1e-05 x1[1] (analytic) = 0.0012907839576272754687273983696766 x1[1] (numeric) = 0.0012907822658213451576651134401951 absolute error = 1.6918059303110622849294815e-09 relative error = 0.00013106809395283677857446114193855 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5009 x2[1] (analytic) = 0.00082643133670907829447576375839823 x2[1] (numeric) = 0.00082643220298838452910177460988753 absolute error = 8.6627930623462601085148930e-10 relative error = 0.00010482169150122329685160541134796 % h = 1e-05 x1[1] (analytic) = 0.0012907730498422382120572030903234 x1[1] (numeric) = 0.0012907713193561746131332623981045 absolute error = 1.7304860635989239406922189e-09 relative error = 0.0001340658657081838397117478374376 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50091 x2[1] (analytic) = 0.00082644041158858090183191251081983 x2[1] (numeric) = 0.00082644129746191119205052020026614 absolute error = 8.8587333029021860768944631e-10 relative error = 0.00010719143423630458184054644215112 % h = 1e-05 x1[1] (analytic) = 0.0012907621421662782603721406097174 x1[1] (numeric) = 0.0012907603725626262934875061111189 absolute error = 1.7696036519668846344985985e-09 relative error = 0.00013709757934153302464592908409178 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50092 x2[1] (analytic) = 0.00082644948670412156672259316198068 x2[1] (numeric) = 0.00082645039239099761090170856055894 absolute error = 9.0568687604417911539857826e-10 relative error = 0.00010958768692035323951062832715789 % h = 1e-05 x1[1] (analytic) = 0.0012907512345993945229046149236005 x1[1] (numeric) = 0.0012907494254406903479976551772802 absolute error = 1.8091587041749069597463203e-09 relative error = 0.0001401632363912794212127124264861 % h = 1e-05 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.5MB, time=2.02 NO POLE NO POLE t[1] = 0.50093 x2[1] (analytic) = 0.00082645856205570446457236630843608 x2[1] (numeric) = 0.00082645948777566110654438779233221 absolute error = 9.2571995664197202148389613e-10 relative error = 0.00011201045026859764082118338252498 % h = 1e-05 x1[1] (analytic) = 0.0012907403271415859088979376491362 x1[1] (numeric) = 0.0012907384779903569256380173543546 absolute error = 1.8491512289832599202947816e-09 relative error = 0.00014326283839587665788015593908089 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50094 x2[1] (analytic) = 0.00082646763764333377089475568375482 x2[1] (numeric) = 0.00082646858361591900046030000627043 absolute error = 9.4597258522956554432251561e-10 relative error = 0.00011445972499625021364851965242625 % h = 1e-05 x1[1] (analytic) = 0.0012907294197928513276063279158343 x1[1] (numeric) = 0.0012907275302116161750873886953391 absolute error = 1.8895812351525189392204952e-09 relative error = 0.00014639638689383690588716743651969 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50095 x2[1] (analytic) = 0.00082647671346701366129224988326191 x2[1] (numeric) = 0.00082647767991178861472390056387647 absolute error = 9.6644477495343165068061456e-10 relative error = 0.00011693551181850744239737234809679 % h = 1e-05 x1[1] (analytic) = 0.0012907185125531896882949122564762 x1[1] (numeric) = 0.0012907165821044582447290446837016 absolute error = 1.9304487314435658675727746e-09 relative error = 0.00014956388342373088138208029326262 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50096 x2[1] (analytic) = 0.00082648578952674831145630408881634 x2[1] (numeric) = 0.0008264867766632872720023773197781 absolute error = 9.8713653896054607323096176e-10 relative error = 0.00011943781145054986761240320792707 % h = 1e-05 x1[1] (analytic) = 0.0012907076054225999002397244980414 x1[1] (numeric) = 0.0012907056336688732826507313683553 absolute error = 1.9717537266175889931296861e-09 relative error = 0.00015276532952418784756130586687065 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50097 x2[1] (analytic) = 0.00082649486582254189716734179362378 x2[1] (numeric) = 0.00082649587387043229555566986464109 absolute error = 1.00804789039838832807101731e-09 relative error = 0.00012196662460754208558974781977334 % h = 1e-05 x1[1] (analytic) = 0.0012906966984010808727277056526351 x1[1] (numeric) = 0.0012906946849048514366446564983672 absolute error = 2.0134962294360830491542679e-09 relative error = 0.00015600072673389561680806253476152 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50098 x2[1] (analytic) = 0.00082650394235439859429475652708451 x2[1] (numeric) = 0.00082650497153324100923648876868873 absolute error = 1.02917884241494173224160422e-09 relative error = 0.00012452195200463274798861084743358 % h = 1e-05 x1[1] (analytic) = 0.0012906857914886315150567038084169 x1[1] (numeric) = 0.0012906837358123828542074806574005 absolute error = 2.0556762486608492231510164e-09 relative error = 0.00015927007659160055283118136200638 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50099 x2[1] (analytic) = 0.00082651301912232257879691357967621 x2[1] (numeric) = 0.00082651406965173073749033482582789 absolute error = 1.05052940815869342124615168e-09 relative error = 0.00012710379435695456144290921818379 % h = 1e-05 x1[1] (analytic) = 0.0012906748846852507365354740205306 x1[1] (numeric) = 0.0012906727863914576825403083978912 absolute error = 2.0982937930539951656226394e-09 relative error = 0.00016257338063610757280398837899787 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652316822591880535551829838159 absolute error = 1.07209960077863436657050973e-09 relative error = 0.0001297121523796242871729632351028 % h = 1e-05 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906618366420660685486793749587 absolute error = 2.1413488713779349988270764e-09 relative error = 0.00016591064040628014950326348655854 % h = 1e-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 = 2 Seconds Elapsed Time(since restart) = 2 Seconds Expected Time Remaining = 2 Hours 39 Minutes 14 Seconds Optimized Time Remaining = 2 Hours 38 Minutes 25 Seconds Time to Timeout = 14 Minutes 57 Seconds Percent Done = 0.02244 % > quit memory used=37.1MB, alloc=4.5MB, time=2.19