|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGL, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_max_minutes, > glob_iter, > MAX_UNCHANGED, > years_in_century, > days_in_year, > hours_in_day, > glob_max_order, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_warned2, > glob_abserr, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_max_opt_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_iter, > glob_large_float, > glob_hmax, > glob_reached_optimal_h, > glob_clock_sec, > glob_html_log, > glob_max_sec, > glob_h, > glob_optimal_done, > glob_current_iter, > glob_max_trunc_err, > glob_almost_1, > djd_debug2, > glob_log10abserr, > glob_max_hours, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin_init, > glob_disp_incr, > glob_percent_done, > glob_optimal_clock_start_sec, > glob_dump_analytic, > sec_in_min, > glob_optimal_expect_sec, > glob_smallish_float, > glob_optimal_start, > glob_look_poles, > glob_not_yet_start_msg, > glob_no_eqs, > glob_last_good_h, > glob_hmin, > djd_debug, > glob_log10normmin, > glob_log10relerr, > glob_normmax, > glob_curr_iter_when_opt, > glob_start, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_finished, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0, > array_const_1, > array_const_2, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_2D0, > #END CONST > array_tmp20, > array_tmp21, > array_m1, > array_pole, > array_last_rel_error, > array_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_x1_init, > array_norms, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > array_tmp19, > array_type_pole, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_complex_pole, > array_poles, > array_x1_higher_work2, > array_x1_higher, > array_x1_higher_work, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGL, glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_max_minutes, glob_iter, MAX_UNCHANGED, years_in_century, days_in_year, hours_in_day, glob_max_order, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_warned2, glob_abserr, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_max_opt_iter, glob_unchanged_h_cnt, glob_small_float, glob_max_iter, glob_large_float, glob_hmax, glob_reached_optimal_h, glob_clock_sec, glob_html_log, glob_max_sec, glob_h, glob_optimal_done, glob_current_iter, glob_max_trunc_err, glob_almost_1, djd_debug2, glob_log10abserr, glob_max_hours, glob_log10_relerr, glob_log10_abserr, glob_hmin_init, glob_disp_incr, glob_percent_done, glob_optimal_clock_start_sec, glob_dump_analytic, sec_in_min, glob_optimal_expect_sec, glob_smallish_float, glob_optimal_start, glob_look_poles, glob_not_yet_start_msg, glob_no_eqs, glob_last_good_h, glob_hmin, djd_debug, glob_log10normmin, glob_log10relerr, glob_normmax, glob_curr_iter_when_opt, glob_start, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_finished, array_const_0, array_const_1, array_const_2, array_const_3D0, array_const_0D0, array_const_4D0, array_const_2D0, array_tmp20, array_tmp21, array_m1, array_pole, array_last_rel_error, array_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_x1_init, array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_tmp19, array_type_pole, array_x2_higher_work, array_x2_higher_work2, array_x2_higher, array_real_pole, array_complex_pole, array_poles, array_x1_higher_work2, array_x1_higher, array_x1_higher_work, glob_last; if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGL, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_max_minutes, > glob_iter, > MAX_UNCHANGED, > years_in_century, > days_in_year, > hours_in_day, > glob_max_order, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_warned2, > glob_abserr, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_max_opt_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_iter, > glob_large_float, > glob_hmax, > glob_reached_optimal_h, > glob_clock_sec, > glob_html_log, > glob_max_sec, > glob_h, > glob_optimal_done, > glob_current_iter, > glob_max_trunc_err, > glob_almost_1, > djd_debug2, > glob_log10abserr, > glob_max_hours, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin_init, > glob_disp_incr, > glob_percent_done, > glob_optimal_clock_start_sec, > glob_dump_analytic, > sec_in_min, > glob_optimal_expect_sec, > glob_smallish_float, > glob_optimal_start, > glob_look_poles, > glob_not_yet_start_msg, > glob_no_eqs, > glob_last_good_h, > glob_hmin, > djd_debug, > glob_log10normmin, > glob_log10relerr, > glob_normmax, > glob_curr_iter_when_opt, > glob_start, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_finished, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0, > array_const_1, > array_const_2, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_2D0, > #END CONST > array_tmp20, > array_tmp21, > array_m1, > array_pole, > array_last_rel_error, > array_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_x1_init, > array_norms, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > array_tmp19, > array_type_pole, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_complex_pole, > array_poles, > array_x1_higher_work2, > array_x1_higher, > array_x1_higher_work, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_t[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGL, glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_max_minutes, glob_iter, MAX_UNCHANGED, years_in_century, days_in_year, hours_in_day, glob_max_order, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_warned2, glob_abserr, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_max_opt_iter, glob_unchanged_h_cnt, glob_small_float, glob_max_iter, glob_large_float, glob_hmax, glob_reached_optimal_h, glob_clock_sec, glob_html_log, glob_max_sec, glob_h, glob_optimal_done, glob_current_iter, glob_max_trunc_err, glob_almost_1, djd_debug2, glob_log10abserr, glob_max_hours, glob_log10_relerr, glob_log10_abserr, glob_hmin_init, glob_disp_incr, glob_percent_done, glob_optimal_clock_start_sec, glob_dump_analytic, sec_in_min, glob_optimal_expect_sec, glob_smallish_float, glob_optimal_start, glob_look_poles, glob_not_yet_start_msg, glob_no_eqs, glob_last_good_h, glob_hmin, djd_debug, glob_log10normmin, glob_log10relerr, glob_normmax, glob_curr_iter_when_opt, glob_start, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_finished, array_const_0, array_const_1, array_const_2, array_const_3D0, array_const_0D0, array_const_4D0, array_const_2D0, array_tmp20, array_tmp21, array_m1, array_pole, array_last_rel_error, array_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_x1_init, array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_tmp19, array_type_pole, array_x2_higher_work, array_x2_higher_work2, array_x2_higher, array_real_pole, array_complex_pole, array_poles, array_x1_higher_work2, array_x1_higher, array_x1_higher_work, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_t[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(t_start,t_end) > global > DEBUGL, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_max_minutes, > glob_iter, > MAX_UNCHANGED, > years_in_century, > days_in_year, > hours_in_day, > glob_max_order, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_warned2, > glob_abserr, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_max_opt_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_iter, > glob_large_float, > glob_hmax, > glob_reached_optimal_h, > glob_clock_sec, > glob_html_log, > glob_max_sec, > glob_h, > glob_optimal_done, > glob_current_iter, > glob_max_trunc_err, > glob_almost_1, > djd_debug2, > glob_log10abserr, > glob_max_hours, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin_init, > glob_disp_incr, > glob_percent_done, > glob_optimal_clock_start_sec, > glob_dump_analytic, > sec_in_min, > glob_optimal_expect_sec, > glob_smallish_float, > glob_optimal_start, > glob_look_poles, > glob_not_yet_start_msg, > glob_no_eqs, > glob_last_good_h, > glob_hmin, > djd_debug, > glob_log10normmin, > glob_log10relerr, > glob_normmax, > glob_curr_iter_when_opt, > glob_start, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_finished, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0, > array_const_1, > array_const_2, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_2D0, > #END CONST > array_tmp20, > array_tmp21, > array_m1, > array_pole, > array_last_rel_error, > array_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_x1_init, > array_norms, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > array_tmp19, > array_type_pole, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_complex_pole, > array_poles, > array_x1_higher_work2, > array_x1_higher, > array_x1_higher_work, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGL, glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_max_minutes, glob_iter, MAX_UNCHANGED, years_in_century, days_in_year, hours_in_day, glob_max_order, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_warned2, glob_abserr, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_max_opt_iter, glob_unchanged_h_cnt, glob_small_float, glob_max_iter, glob_large_float, glob_hmax, glob_reached_optimal_h, glob_clock_sec, glob_html_log, glob_max_sec, glob_h, glob_optimal_done, glob_current_iter, glob_max_trunc_err, glob_almost_1, djd_debug2, glob_log10abserr, glob_max_hours, glob_log10_relerr, glob_log10_abserr, glob_hmin_init, glob_disp_incr, glob_percent_done, glob_optimal_clock_start_sec, glob_dump_analytic, sec_in_min, glob_optimal_expect_sec, glob_smallish_float, glob_optimal_start, glob_look_poles, glob_not_yet_start_msg, glob_no_eqs, glob_last_good_h, glob_hmin, djd_debug, glob_log10normmin, glob_log10relerr, glob_normmax, glob_curr_iter_when_opt, glob_start, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_finished, array_const_0, array_const_1, array_const_2, array_const_3D0, array_const_0D0, array_const_4D0, array_const_2D0, array_tmp20, array_tmp21, array_m1, array_pole, array_last_rel_error, array_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_x1_init, array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_tmp19, array_type_pole, array_x2_higher_work, array_x2_higher_work2, array_x2_higher, array_real_pole, array_complex_pole, array_poles, array_x1_higher_work2, array_x1_higher, array_x1_higher_work, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGL, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_max_minutes, > glob_iter, > MAX_UNCHANGED, > years_in_century, > days_in_year, > hours_in_day, > glob_max_order, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_warned2, > glob_abserr, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_max_opt_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_iter, > glob_large_float, > glob_hmax, > glob_reached_optimal_h, > glob_clock_sec, > glob_html_log, > glob_max_sec, > glob_h, > glob_optimal_done, > glob_current_iter, > glob_max_trunc_err, > glob_almost_1, > djd_debug2, > glob_log10abserr, > glob_max_hours, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin_init, > glob_disp_incr, > glob_percent_done, > glob_optimal_clock_start_sec, > glob_dump_analytic, > sec_in_min, > glob_optimal_expect_sec, > glob_smallish_float, > glob_optimal_start, > glob_look_poles, > glob_not_yet_start_msg, > glob_no_eqs, > glob_last_good_h, > glob_hmin, > djd_debug, > glob_log10normmin, > glob_log10relerr, > glob_normmax, > glob_curr_iter_when_opt, > glob_start, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_finished, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0, > array_const_1, > array_const_2, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_2D0, > #END CONST > array_tmp20, > array_tmp21, > array_m1, > array_pole, > array_last_rel_error, > array_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_x1_init, > array_norms, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > array_tmp19, > array_type_pole, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_complex_pole, > array_poles, > array_x1_higher_work2, > array_x1_higher, > array_x1_higher_work, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1]; > rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1]; > rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGL, glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_max_minutes, glob_iter, MAX_UNCHANGED, years_in_century, days_in_year, hours_in_day, glob_max_order, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_warned2, glob_abserr, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_max_opt_iter, glob_unchanged_h_cnt, glob_small_float, glob_max_iter, glob_large_float, glob_hmax, glob_reached_optimal_h, glob_clock_sec, glob_html_log, glob_max_sec, glob_h, glob_optimal_done, glob_current_iter, glob_max_trunc_err, glob_almost_1, djd_debug2, glob_log10abserr, glob_max_hours, glob_log10_relerr, glob_log10_abserr, glob_hmin_init, glob_disp_incr, glob_percent_done, glob_optimal_clock_start_sec, glob_dump_analytic, sec_in_min, glob_optimal_expect_sec, glob_smallish_float, glob_optimal_start, glob_look_poles, glob_not_yet_start_msg, glob_no_eqs, glob_last_good_h, glob_hmin, djd_debug, glob_log10normmin, glob_log10relerr, glob_normmax, glob_curr_iter_when_opt, glob_start, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_finished, array_const_0, array_const_1, array_const_2, array_const_3D0, array_const_0D0, array_const_4D0, array_const_2D0, array_tmp20, array_tmp21, array_m1, array_pole, array_last_rel_error, array_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_x1_init, array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_tmp19, array_type_pole, array_x2_higher_work, array_x2_higher_work2, array_x2_higher, array_real_pole, array_complex_pole, array_poles, array_x1_higher_work2, array_x1_higher, array_x1_higher_work, glob_last; n := glob_max_terms; m := n - 3; while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or abs(array_x2_higher[1, m - 1]) < glob_small_float or abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or abs(array_x1_higher[1, m - 1]) < glob_small_float or abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_x2_higher[1, m]) or glob_large_float <= abs(array_x2_higher[1, m - 1]) or glob_large_float <= abs(array_x2_higher[1, m - 2]) or glob_large_float <= abs(array_x2_higher[1, m - 3]) or glob_large_float <= abs(array_x2_higher[1, m - 4]) or glob_large_float <= abs(array_x2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_x1_higher[1, m]) or glob_large_float <= abs(array_x1_higher[1, m - 1]) or glob_large_float <= abs(array_x1_higher[1, m - 2]) or glob_large_float <= abs(array_x1_higher[1, m - 3]) or glob_large_float <= abs(array_x1_higher[1, m - 4]) or glob_large_float <= abs(array_x1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGL, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_max_minutes, > glob_iter, > MAX_UNCHANGED, > years_in_century, > days_in_year, > hours_in_day, > glob_max_order, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_warned2, > glob_abserr, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_max_opt_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_iter, > glob_large_float, > glob_hmax, > glob_reached_optimal_h, > glob_clock_sec, > glob_html_log, > glob_max_sec, > glob_h, > glob_optimal_done, > glob_current_iter, > glob_max_trunc_err, > glob_almost_1, > djd_debug2, > glob_log10abserr, > glob_max_hours, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin_init, > glob_disp_incr, > glob_percent_done, > glob_optimal_clock_start_sec, > glob_dump_analytic, > sec_in_min, > glob_optimal_expect_sec, > glob_smallish_float, > glob_optimal_start, > glob_look_poles, > glob_not_yet_start_msg, > glob_no_eqs, > glob_last_good_h, > glob_hmin, > djd_debug, > glob_log10normmin, > glob_log10relerr, > glob_normmax, > glob_curr_iter_when_opt, > glob_start, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_finished, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0, > array_const_1, > array_const_2, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_2D0, > #END CONST > array_tmp20, > array_tmp21, > array_m1, > array_pole, > array_last_rel_error, > array_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_x1_init, > array_norms, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > array_tmp19, > array_type_pole, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_complex_pole, > array_poles, > array_x1_higher_work2, > array_x1_higher, > array_x1_higher_work, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGL, glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_max_minutes, glob_iter, MAX_UNCHANGED, years_in_century, days_in_year, hours_in_day, glob_max_order, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_warned2, glob_abserr, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_max_opt_iter, glob_unchanged_h_cnt, glob_small_float, glob_max_iter, glob_large_float, glob_hmax, glob_reached_optimal_h, glob_clock_sec, glob_html_log, glob_max_sec, glob_h, glob_optimal_done, glob_current_iter, glob_max_trunc_err, glob_almost_1, djd_debug2, glob_log10abserr, glob_max_hours, glob_log10_relerr, glob_log10_abserr, glob_hmin_init, glob_disp_incr, glob_percent_done, glob_optimal_clock_start_sec, glob_dump_analytic, sec_in_min, glob_optimal_expect_sec, glob_smallish_float, glob_optimal_start, glob_look_poles, glob_not_yet_start_msg, glob_no_eqs, glob_last_good_h, glob_hmin, djd_debug, glob_log10normmin, glob_log10relerr, glob_normmax, glob_curr_iter_when_opt, glob_start, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_finished, array_const_0, array_const_1, array_const_2, array_const_3D0, array_const_0D0, array_const_4D0, array_const_2D0, array_tmp20, array_tmp21, array_m1, array_pole, array_last_rel_error, array_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_x1_init, array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_tmp19, array_type_pole, array_x2_higher_work, array_x2_higher_work2, array_x2_higher, array_real_pole, array_complex_pole, array_poles, array_x1_higher_work2, array_x1_higher, array_x1_higher_work, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x2[iii]) then array_norms[iii] := abs(array_x2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x1[iii]) then array_norms[iii] := abs(array_x1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGL, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_max_minutes, > glob_iter, > MAX_UNCHANGED, > years_in_century, > days_in_year, > hours_in_day, > glob_max_order, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_warned2, > glob_abserr, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_max_opt_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_iter, > glob_large_float, > glob_hmax, > glob_reached_optimal_h, > glob_clock_sec, > glob_html_log, > glob_max_sec, > glob_h, > glob_optimal_done, > glob_current_iter, > glob_max_trunc_err, > glob_almost_1, > djd_debug2, > glob_log10abserr, > glob_max_hours, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin_init, > glob_disp_incr, > glob_percent_done, > glob_optimal_clock_start_sec, > glob_dump_analytic, > sec_in_min, > glob_optimal_expect_sec, > glob_smallish_float, > glob_optimal_start, > glob_look_poles, > glob_not_yet_start_msg, > glob_no_eqs, > glob_last_good_h, > glob_hmin, > djd_debug, > glob_log10normmin, > glob_log10relerr, > glob_normmax, > glob_curr_iter_when_opt, > glob_start, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_finished, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0, > array_const_1, > array_const_2, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_2D0, > #END CONST > array_tmp20, > array_tmp21, > array_m1, > array_pole, > array_last_rel_error, > array_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_x1_init, > array_norms, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > array_tmp19, > array_type_pole, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_complex_pole, > array_poles, > array_x1_higher_work2, > array_x1_higher, > array_x1_higher_work, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre diff $eq_no = 1 i = 1 > array_tmp4[1] := array_x2_higher[1,1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp5[1] := (array_const_2D0[1] * (array_tmp4[1])); > #emit pre sub $eq_no = 1 i = 1 > array_tmp6[1] := (array_tmp3[1] - (array_tmp5[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp7[1] := array_x1_higher[3,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp8[1] := (array_tmp6[1] - (array_tmp7[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp9[1] := array_x1_higher[2,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp10[1] := (array_tmp8[1] - (array_tmp9[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp11[1] := array_x1_higher[1,1]; > #emit pre add $eq_no = 1 i = 1 > array_tmp12[1] := array_tmp10[1] + array_tmp11[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp12[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 diff $eq_no = 2 i = 1 > array_tmp14[1] := array_x2_higher[1,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp15[1] := (array_const_4D0[1] * (array_tmp14[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp16[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp17[1] := (array_const_2D0[1] * (array_tmp16[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp18[1] := (array_tmp15[1] - (array_tmp17[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp19[1] := array_x1_higher[1,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp20[1] := (array_const_2D0[1] * (array_tmp19[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp21[1] := (array_tmp18[1] - (array_tmp20[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp21[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 diff $eq_no = 1 i = 2 > array_tmp4[2] := array_x2_higher[1,2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp5[2] := ats(2,array_const_2D0,array_tmp4,1); > #emit pre sub $eq_no = 1 i = 2 > array_tmp6[2] := (array_tmp3[2] - (array_tmp5[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp7[2] := array_x1_higher[3,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp8[2] := (array_tmp6[2] - (array_tmp7[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp9[2] := array_x1_higher[2,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp10[2] := (array_tmp8[2] - (array_tmp9[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp11[2] := array_x1_higher[1,2]; > #emit pre add $eq_no = 1 i = 2 > array_tmp12[2] := array_tmp10[2] + array_tmp11[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp12[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 diff $eq_no = 2 i = 2 > array_tmp14[2] := array_x2_higher[1,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp15[2] := ats(2,array_const_4D0,array_tmp14,1); > #emit pre diff $eq_no = 2 i = 2 > array_tmp16[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp17[2] := ats(2,array_const_2D0,array_tmp16,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp18[2] := (array_tmp15[2] - (array_tmp17[2])); > #emit pre diff $eq_no = 2 i = 2 > array_tmp19[2] := array_x1_higher[1,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp20[2] := ats(2,array_const_2D0,array_tmp19,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp21[2] := (array_tmp18[2] - (array_tmp20[2])); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp21[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 diff $eq_no = 1 i = 3 > array_tmp4[3] := array_x2_higher[1,3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp5[3] := ats(3,array_const_2D0,array_tmp4,1); > #emit pre sub $eq_no = 1 i = 3 > array_tmp6[3] := (array_tmp3[3] - (array_tmp5[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp7[3] := array_x1_higher[3,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp8[3] := (array_tmp6[3] - (array_tmp7[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp9[3] := array_x1_higher[2,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp10[3] := (array_tmp8[3] - (array_tmp9[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp11[3] := array_x1_higher[1,3]; > #emit pre add $eq_no = 1 i = 3 > array_tmp12[3] := array_tmp10[3] + array_tmp11[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp12[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 diff $eq_no = 2 i = 3 > array_tmp14[3] := array_x2_higher[1,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp15[3] := ats(3,array_const_4D0,array_tmp14,1); > #emit pre diff $eq_no = 2 i = 3 > array_tmp16[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp17[3] := ats(3,array_const_2D0,array_tmp16,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp18[3] := (array_tmp15[3] - (array_tmp17[3])); > #emit pre diff $eq_no = 2 i = 3 > array_tmp19[3] := array_x1_higher[1,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp20[3] := ats(3,array_const_2D0,array_tmp19,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp21[3] := (array_tmp18[3] - (array_tmp20[3])); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp21[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 diff $eq_no = 1 i = 4 > array_tmp4[4] := array_x2_higher[1,4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp5[4] := ats(4,array_const_2D0,array_tmp4,1); > #emit pre sub $eq_no = 1 i = 4 > array_tmp6[4] := (array_tmp3[4] - (array_tmp5[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp7[4] := array_x1_higher[3,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp8[4] := (array_tmp6[4] - (array_tmp7[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp9[4] := array_x1_higher[2,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp10[4] := (array_tmp8[4] - (array_tmp9[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp11[4] := array_x1_higher[1,4]; > #emit pre add $eq_no = 1 i = 4 > array_tmp12[4] := array_tmp10[4] + array_tmp11[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp12[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 diff $eq_no = 2 i = 4 > array_tmp14[4] := array_x2_higher[1,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp15[4] := ats(4,array_const_4D0,array_tmp14,1); > #emit pre diff $eq_no = 2 i = 4 > array_tmp16[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp17[4] := ats(4,array_const_2D0,array_tmp16,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp18[4] := (array_tmp15[4] - (array_tmp17[4])); > #emit pre diff $eq_no = 2 i = 4 > array_tmp19[4] := array_x1_higher[1,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp20[4] := ats(4,array_const_2D0,array_tmp19,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp21[4] := (array_tmp18[4] - (array_tmp20[4])); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp21[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 diff $eq_no = 1 i = 5 > array_tmp4[5] := array_x2_higher[1,5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp5[5] := ats(5,array_const_2D0,array_tmp4,1); > #emit pre sub $eq_no = 1 i = 5 > array_tmp6[5] := (array_tmp3[5] - (array_tmp5[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp7[5] := array_x1_higher[3,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp8[5] := (array_tmp6[5] - (array_tmp7[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp9[5] := array_x1_higher[2,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp10[5] := (array_tmp8[5] - (array_tmp9[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp11[5] := array_x1_higher[1,5]; > #emit pre add $eq_no = 1 i = 5 > array_tmp12[5] := array_tmp10[5] + array_tmp11[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp12[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 diff $eq_no = 2 i = 5 > array_tmp14[5] := array_x2_higher[1,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp15[5] := ats(5,array_const_4D0,array_tmp14,1); > #emit pre diff $eq_no = 2 i = 5 > array_tmp16[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp17[5] := ats(5,array_const_2D0,array_tmp16,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp18[5] := (array_tmp15[5] - (array_tmp17[5])); > #emit pre diff $eq_no = 2 i = 5 > array_tmp19[5] := array_x1_higher[1,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp20[5] := ats(5,array_const_2D0,array_tmp19,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp21[5] := (array_tmp18[5] - (array_tmp20[5])); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp21[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 diff $eq_no = 1 > array_tmp4[kkk] := array_x2_higher[1,kkk]; > #emit mult $eq_no = 1 > array_tmp5[kkk] := ats(kkk,array_const_2D0,array_tmp4,1); > #emit sub $eq_no = 1 > array_tmp6[kkk] := (array_tmp3[kkk] - (array_tmp5[kkk])); > #emit diff $eq_no = 1 > array_tmp7[kkk] := array_x1_higher[3,kkk]; > #emit sub $eq_no = 1 > array_tmp8[kkk] := (array_tmp6[kkk] - (array_tmp7[kkk])); > #emit diff $eq_no = 1 > array_tmp9[kkk] := array_x1_higher[2,kkk]; > #emit sub $eq_no = 1 > array_tmp10[kkk] := (array_tmp8[kkk] - (array_tmp9[kkk])); > #emit diff $eq_no = 1 > array_tmp11[kkk] := array_x1_higher[1,kkk]; > #emit add $eq_no = 1 > array_tmp12[kkk] := array_tmp10[kkk] + array_tmp11[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp12[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 diff $eq_no = 2 > array_tmp14[kkk] := array_x2_higher[1,kkk]; > #emit mult $eq_no = 2 > array_tmp15[kkk] := ats(kkk,array_const_4D0,array_tmp14,1); > #emit diff $eq_no = 2 > array_tmp16[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 2 > array_tmp17[kkk] := ats(kkk,array_const_2D0,array_tmp16,1); > #emit sub $eq_no = 2 > array_tmp18[kkk] := (array_tmp15[kkk] - (array_tmp17[kkk])); > #emit diff $eq_no = 2 > array_tmp19[kkk] := array_x1_higher[1,kkk]; > #emit mult $eq_no = 2 > array_tmp20[kkk] := ats(kkk,array_const_2D0,array_tmp19,1); > #emit sub $eq_no = 2 > array_tmp21[kkk] := (array_tmp18[kkk] - (array_tmp20[kkk])); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp21[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x1[kkk + order_d] := temporary; > array_x1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_x1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGL, glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_max_minutes, glob_iter, MAX_UNCHANGED, years_in_century, days_in_year, hours_in_day, glob_max_order, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_warned2, glob_abserr, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_max_opt_iter, glob_unchanged_h_cnt, glob_small_float, glob_max_iter, glob_large_float, glob_hmax, glob_reached_optimal_h, glob_clock_sec, glob_html_log, glob_max_sec, glob_h, glob_optimal_done, glob_current_iter, glob_max_trunc_err, glob_almost_1, djd_debug2, glob_log10abserr, glob_max_hours, glob_log10_relerr, glob_log10_abserr, glob_hmin_init, glob_disp_incr, glob_percent_done, glob_optimal_clock_start_sec, glob_dump_analytic, sec_in_min, glob_optimal_expect_sec, glob_smallish_float, glob_optimal_start, glob_look_poles, glob_not_yet_start_msg, glob_no_eqs, glob_last_good_h, glob_hmin, djd_debug, glob_log10normmin, glob_log10relerr, glob_normmax, glob_curr_iter_when_opt, glob_start, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_finished, array_const_0, array_const_1, array_const_2, array_const_3D0, array_const_0D0, array_const_4D0, array_const_2D0, array_tmp20, array_tmp21, array_m1, array_pole, array_last_rel_error, array_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_x1_init, array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_tmp19, array_type_pole, array_x2_higher_work, array_x2_higher_work2, array_x2_higher, array_real_pole, array_complex_pole, array_poles, array_x1_higher_work2, array_x1_higher, array_x1_higher_work, glob_last; array_tmp1[1] := array_x2_higher[2, 1]; array_tmp2[1] := array_const_3D0[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; array_tmp4[1] := array_x2_higher[1, 1]; array_tmp5[1] := array_const_2D0[1]*array_tmp4[1]; array_tmp6[1] := array_tmp3[1] - array_tmp5[1]; array_tmp7[1] := array_x1_higher[3, 1]; array_tmp8[1] := array_tmp6[1] - array_tmp7[1]; array_tmp9[1] := array_x1_higher[2, 1]; array_tmp10[1] := array_tmp8[1] - array_tmp9[1]; array_tmp11[1] := array_x1_higher[1, 1]; array_tmp12[1] := array_tmp10[1] + array_tmp11[1]; if 1 <= glob_max_terms then temporary := array_tmp12[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_tmp14[1] := array_x2_higher[1, 1]; array_tmp15[1] := array_const_4D0[1]*array_tmp14[1]; array_tmp16[1] := array_x2_higher[2, 1]; array_tmp17[1] := array_const_2D0[1]*array_tmp16[1]; array_tmp18[1] := array_tmp15[1] - array_tmp17[1]; array_tmp19[1] := array_x1_higher[1, 1]; array_tmp20[1] := array_const_2D0[1]*array_tmp19[1]; array_tmp21[1] := array_tmp18[1] - array_tmp20[1]; if 1 <= glob_max_terms then temporary := array_tmp21[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] := array_x2_higher[1, 2]; array_tmp5[2] := ats(2, array_const_2D0, array_tmp4, 1); array_tmp6[2] := array_tmp3[2] - array_tmp5[2]; array_tmp7[2] := array_x1_higher[3, 2]; array_tmp8[2] := array_tmp6[2] - array_tmp7[2]; array_tmp9[2] := array_x1_higher[2, 2]; array_tmp10[2] := array_tmp8[2] - array_tmp9[2]; array_tmp11[2] := array_x1_higher[1, 2]; array_tmp12[2] := array_tmp10[2] + array_tmp11[2]; if 2 <= glob_max_terms then temporary := array_tmp12[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_tmp14[2] := array_x2_higher[1, 2]; array_tmp15[2] := ats(2, array_const_4D0, array_tmp14, 1); array_tmp16[2] := array_x2_higher[2, 2]; array_tmp17[2] := ats(2, array_const_2D0, array_tmp16, 1); array_tmp18[2] := array_tmp15[2] - array_tmp17[2]; array_tmp19[2] := array_x1_higher[1, 2]; array_tmp20[2] := ats(2, array_const_2D0, array_tmp19, 1); array_tmp21[2] := array_tmp18[2] - array_tmp20[2]; if 2 <= glob_max_terms then temporary := array_tmp21[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] := array_x2_higher[1, 3]; array_tmp5[3] := ats(3, array_const_2D0, array_tmp4, 1); array_tmp6[3] := array_tmp3[3] - array_tmp5[3]; array_tmp7[3] := array_x1_higher[3, 3]; array_tmp8[3] := array_tmp6[3] - array_tmp7[3]; array_tmp9[3] := array_x1_higher[2, 3]; array_tmp10[3] := array_tmp8[3] - array_tmp9[3]; array_tmp11[3] := array_x1_higher[1, 3]; array_tmp12[3] := array_tmp10[3] + array_tmp11[3]; if 3 <= glob_max_terms then temporary := array_tmp12[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_tmp14[3] := array_x2_higher[1, 3]; array_tmp15[3] := ats(3, array_const_4D0, array_tmp14, 1); array_tmp16[3] := array_x2_higher[2, 3]; array_tmp17[3] := ats(3, array_const_2D0, array_tmp16, 1); array_tmp18[3] := array_tmp15[3] - array_tmp17[3]; array_tmp19[3] := array_x1_higher[1, 3]; array_tmp20[3] := ats(3, array_const_2D0, array_tmp19, 1); array_tmp21[3] := array_tmp18[3] - array_tmp20[3]; if 3 <= glob_max_terms then temporary := array_tmp21[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] := array_x2_higher[1, 4]; array_tmp5[4] := ats(4, array_const_2D0, array_tmp4, 1); array_tmp6[4] := array_tmp3[4] - array_tmp5[4]; array_tmp7[4] := array_x1_higher[3, 4]; array_tmp8[4] := array_tmp6[4] - array_tmp7[4]; array_tmp9[4] := array_x1_higher[2, 4]; array_tmp10[4] := array_tmp8[4] - array_tmp9[4]; array_tmp11[4] := array_x1_higher[1, 4]; array_tmp12[4] := array_tmp10[4] + array_tmp11[4]; if 4 <= glob_max_terms then temporary := array_tmp12[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_tmp14[4] := array_x2_higher[1, 4]; array_tmp15[4] := ats(4, array_const_4D0, array_tmp14, 1); array_tmp16[4] := array_x2_higher[2, 4]; array_tmp17[4] := ats(4, array_const_2D0, array_tmp16, 1); array_tmp18[4] := array_tmp15[4] - array_tmp17[4]; array_tmp19[4] := array_x1_higher[1, 4]; array_tmp20[4] := ats(4, array_const_2D0, array_tmp19, 1); array_tmp21[4] := array_tmp18[4] - array_tmp20[4]; if 4 <= glob_max_terms then temporary := array_tmp21[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] := array_x2_higher[1, 5]; array_tmp5[5] := ats(5, array_const_2D0, array_tmp4, 1); array_tmp6[5] := array_tmp3[5] - array_tmp5[5]; array_tmp7[5] := array_x1_higher[3, 5]; array_tmp8[5] := array_tmp6[5] - array_tmp7[5]; array_tmp9[5] := array_x1_higher[2, 5]; array_tmp10[5] := array_tmp8[5] - array_tmp9[5]; array_tmp11[5] := array_x1_higher[1, 5]; array_tmp12[5] := array_tmp10[5] + array_tmp11[5]; if 5 <= glob_max_terms then temporary := array_tmp12[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_tmp14[5] := array_x2_higher[1, 5]; array_tmp15[5] := ats(5, array_const_4D0, array_tmp14, 1); array_tmp16[5] := array_x2_higher[2, 5]; array_tmp17[5] := ats(5, array_const_2D0, array_tmp16, 1); array_tmp18[5] := array_tmp15[5] - array_tmp17[5]; array_tmp19[5] := array_x1_higher[1, 5]; array_tmp20[5] := ats(5, array_const_2D0, array_tmp19, 1); array_tmp21[5] := array_tmp18[5] - array_tmp20[5]; if 5 <= glob_max_terms then temporary := array_tmp21[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] := array_x2_higher[1, kkk]; array_tmp5[kkk] := ats(kkk, array_const_2D0, array_tmp4, 1); array_tmp6[kkk] := array_tmp3[kkk] - array_tmp5[kkk]; array_tmp7[kkk] := array_x1_higher[3, kkk]; array_tmp8[kkk] := array_tmp6[kkk] - array_tmp7[kkk]; array_tmp9[kkk] := array_x1_higher[2, kkk]; array_tmp10[kkk] := array_tmp8[kkk] - array_tmp9[kkk]; array_tmp11[kkk] := array_x1_higher[1, kkk]; array_tmp12[kkk] := array_tmp10[kkk] + array_tmp11[kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp12[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_tmp14[kkk] := array_x2_higher[1, kkk]; array_tmp15[kkk] := ats(kkk, array_const_4D0, array_tmp14, 1); array_tmp16[kkk] := array_x2_higher[2, kkk]; array_tmp17[kkk] := ats(kkk, array_const_2D0, array_tmp16, 1); array_tmp18[kkk] := array_tmp15[kkk] - array_tmp17[kkk]; array_tmp19[kkk] := array_x1_higher[1, kkk]; array_tmp20[kkk] := ats(kkk, array_const_2D0, array_tmp19, 1); array_tmp21[kkk] := array_tmp18[kkk] - array_tmp20[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp21[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x1[kkk + order_d] := temporary; array_x1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_x1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_x1 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c1 + 6.0 * c3 * exp(-t); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > c1 + c2 * exp(2.0 * t) + c3 * exp(-t); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c2*exp(2.0*t) - c3*exp(-t) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > t_start,t_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGL, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_max_minutes, > glob_iter, > MAX_UNCHANGED, > years_in_century, > days_in_year, > hours_in_day, > glob_max_order, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_warned2, > glob_abserr, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > min_in_hour, > glob_max_opt_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_max_iter, > glob_large_float, > glob_hmax, > glob_reached_optimal_h, > glob_clock_sec, > glob_html_log, > glob_max_sec, > glob_h, > glob_optimal_done, > glob_current_iter, > glob_max_trunc_err, > glob_almost_1, > djd_debug2, > glob_log10abserr, > glob_max_hours, > glob_log10_relerr, > glob_log10_abserr, > glob_hmin_init, > glob_disp_incr, > glob_percent_done, > glob_optimal_clock_start_sec, > glob_dump_analytic, > sec_in_min, > glob_optimal_expect_sec, > glob_smallish_float, > glob_optimal_start, > glob_look_poles, > glob_not_yet_start_msg, > glob_no_eqs, > glob_last_good_h, > glob_hmin, > djd_debug, > glob_log10normmin, > glob_log10relerr, > glob_normmax, > glob_curr_iter_when_opt, > glob_start, > glob_orig_start_sec, > glob_warned, > glob_relerr, > glob_not_yet_finished, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0, > array_const_1, > array_const_2, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_2D0, > #END CONST > array_tmp20, > array_tmp21, > array_m1, > array_pole, > array_last_rel_error, > array_x2, > array_t, > array_x1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_x1_init, > array_norms, > array_x2_init, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_tmp18, > array_tmp19, > array_type_pole, > array_x2_higher_work, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_complex_pole, > array_poles, > array_x1_higher_work2, > array_x1_higher, > array_x1_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > glob_iolevel := 5; > ALWAYS := 1; > DEBUGMASSIVE := 4; > glob_max_terms := 30; > INFO := 2; > glob_max_minutes := 0.0; > glob_iter := 0; > MAX_UNCHANGED := 10; > years_in_century := 100.0; > days_in_year := 365.0; > hours_in_day := 24.0; > glob_max_order := 30; > glob_max_rel_trunc_err := 0.1e-10; > glob_display_flag := true; > glob_dump := false; > glob_warned2 := false; > glob_abserr := 0.1e-10; > glob_initial_pass := true; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > min_in_hour := 60.0; > glob_max_opt_iter := 10; > glob_unchanged_h_cnt := 0; > glob_small_float := 0.1e-50; > glob_max_iter := 1000; > glob_large_float := 9.0e100; > glob_hmax := 1.0; > glob_reached_optimal_h := false; > glob_clock_sec := 0.0; > glob_html_log := true; > glob_max_sec := 10000.0; > glob_h := 0.1; > glob_optimal_done := false; > glob_current_iter := 0; > glob_max_trunc_err := 0.1e-10; > glob_almost_1 := 0.9990; > djd_debug2 := true; > glob_log10abserr := 0.0; > glob_max_hours := 0.0; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_hmin_init := 0.001; > glob_disp_incr := 0.1; > glob_percent_done := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_dump_analytic := false; > sec_in_min := 60.0; > glob_optimal_expect_sec := 0.1; > glob_smallish_float := 0.1e-100; > glob_optimal_start := 0.0; > glob_look_poles := false; > glob_not_yet_start_msg := true; > glob_no_eqs := 0; > glob_last_good_h := 0.1; > glob_hmin := 0.00000000001; > djd_debug := true; > glob_log10normmin := 0.1; > glob_log10relerr := 0.0; > glob_normmax := 0.0; > glob_curr_iter_when_opt := 0; > glob_start := 0; > glob_orig_start_sec := 0.0; > glob_warned := false; > glob_relerr := 0.1e-10; > glob_not_yet_finished := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_max_order := 2; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/complicatedrev2postode.ode#################"); > omniout_str(ALWAYS,"diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );"); > omniout_str(ALWAYS,"diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );"); > 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 := 0.0001 ;"); > 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_tmp20:= Array(1..(max_terms + 1),[]); > array_tmp21:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_t:= Array(1..(max_terms + 1),[]); > array_x1:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_tmp7:= Array(1..(max_terms + 1),[]); > array_tmp8:= Array(1..(max_terms + 1),[]); > array_tmp9:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_x2_init:= Array(1..(max_terms + 1),[]); > array_tmp10:= Array(1..(max_terms + 1),[]); > array_tmp11:= Array(1..(max_terms + 1),[]); > array_tmp12:= Array(1..(max_terms + 1),[]); > array_tmp13:= Array(1..(max_terms + 1),[]); > array_tmp14:= Array(1..(max_terms + 1),[]); > array_tmp15:= Array(1..(max_terms + 1),[]); > array_tmp16:= Array(1..(max_terms + 1),[]); > array_tmp17:= Array(1..(max_terms + 1),[]); > array_tmp18:= Array(1..(max_terms + 1),[]); > array_tmp19:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_tmp20[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp21[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_pole[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_x2[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_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_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_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_tmp18[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp19[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 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp21 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp21[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp20 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp20[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_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_tmp19 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp19[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp18 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp18[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0[1] := 0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_const_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_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 := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_x2(); > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_x1(); > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > sub_iter := 1; > while sub_iter <= 3 do # do number 3 > atomall() > ; > sub_iter := sub_iter + 1; > od;# end do number 3 > ; > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3 > ;#was right paren 0004C > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > order_diff := 2; > #Jump Series array_x2 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > order_diff := 2; > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 3; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > order_diff := 1; > #Jump Series array_x1 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > order_diff := 1; > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 3 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 3 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );"); > omniout_str(INFO,"diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );"); > 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,"2012-06-01T22:21:19-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"complicatedrev2") > ; > logitem_str(html_log_file,"diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 4 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 4 > ; > log_revs(html_log_file," 076 ") > ; > logitem_str(html_log_file,"complicatedrev2 diffeq.mxt") > ; > logitem_str(html_log_file,"complicatedrev2 maple results") > ; > logitem_str(html_log_file,"tot order sub iterationsd 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 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 4 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 4 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 3 > ; > if glob_html_log then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp; global DEBUGL, glob_iolevel, ALWAYS, DEBUGMASSIVE, glob_max_terms, INFO, glob_max_minutes, glob_iter, MAX_UNCHANGED, years_in_century, days_in_year, hours_in_day, glob_max_order, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_warned2, glob_abserr, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, min_in_hour, glob_max_opt_iter, glob_unchanged_h_cnt, glob_small_float, glob_max_iter, glob_large_float, glob_hmax, glob_reached_optimal_h, glob_clock_sec, glob_html_log, glob_max_sec, glob_h, glob_optimal_done, glob_current_iter, glob_max_trunc_err, glob_almost_1, djd_debug2, glob_log10abserr, glob_max_hours, glob_log10_relerr, glob_log10_abserr, glob_hmin_init, glob_disp_incr, glob_percent_done, glob_optimal_clock_start_sec, glob_dump_analytic, sec_in_min, glob_optimal_expect_sec, glob_smallish_float, glob_optimal_start, glob_look_poles, glob_not_yet_start_msg, glob_no_eqs, glob_last_good_h, glob_hmin, djd_debug, glob_log10normmin, glob_log10relerr, glob_normmax, glob_curr_iter_when_opt, glob_start, glob_orig_start_sec, glob_warned, glob_relerr, glob_not_yet_finished, array_const_0, array_const_1, array_const_2, array_const_3D0, array_const_0D0, array_const_4D0, array_const_2D0, array_tmp20, array_tmp21, array_m1, array_pole, array_last_rel_error, array_x2, array_t, array_x1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_x1_init, array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_tmp19, array_type_pole, array_x2_higher_work, array_x2_higher_work2, array_x2_higher, array_real_pole, array_complex_pole, array_poles, array_x1_higher_work2, array_x1_higher, array_x1_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; glob_iolevel := 5; ALWAYS := 1; DEBUGMASSIVE := 4; glob_max_terms := 30; INFO := 2; glob_max_minutes := 0.; glob_iter := 0; MAX_UNCHANGED := 10; years_in_century := 100.0; days_in_year := 365.0; hours_in_day := 24.0; glob_max_order := 30; glob_max_rel_trunc_err := 0.1*10^(-10); glob_display_flag := true; glob_dump := false; glob_warned2 := false; glob_abserr := 0.1*10^(-10); glob_initial_pass := true; glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; min_in_hour := 60.0; glob_max_opt_iter := 10; glob_unchanged_h_cnt := 0; glob_small_float := 0.1*10^(-50); glob_max_iter := 1000; glob_large_float := 0.90*10^101; glob_hmax := 1.0; glob_reached_optimal_h := false; glob_clock_sec := 0.; glob_html_log := true; glob_max_sec := 10000.0; glob_h := 0.1; glob_optimal_done := false; glob_current_iter := 0; glob_max_trunc_err := 0.1*10^(-10); glob_almost_1 := 0.9990; djd_debug2 := true; glob_log10abserr := 0.; glob_max_hours := 0.; glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_disp_incr := 0.1; glob_percent_done := 0.; glob_optimal_clock_start_sec := 0.; glob_dump_analytic := false; sec_in_min := 60.0; glob_optimal_expect_sec := 0.1; glob_smallish_float := 0.1*10^(-100); glob_optimal_start := 0.; glob_look_poles := false; glob_not_yet_start_msg := true; glob_no_eqs := 0; glob_last_good_h := 0.1; glob_hmin := 0.1*10^(-10); djd_debug := true; glob_log10normmin := 0.1; glob_log10relerr := 0.; glob_normmax := 0.; glob_curr_iter_when_opt := 0; glob_start := 0; glob_orig_start_sec := 0.; glob_warned := false; glob_relerr := 0.1*10^(-10); glob_not_yet_finished := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_max_order := 2; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/complicatedrev2postode.ode#################"); omniout_str(ALWAYS, "diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - \ 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t ,\ 1 ) + diff ( x1 , t , 0 );"); omniout_str(ALWAYS, "diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) \ - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );"); 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 := 0.0001 ;"); 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_tmp20 := Array(1 .. max_terms + 1, []); array_tmp21 := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_t := Array(1 .. max_terms + 1, []); array_x1 := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_tmp7 := Array(1 .. max_terms + 1, []); array_tmp8 := Array(1 .. max_terms + 1, []); array_tmp9 := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_x2_init := Array(1 .. max_terms + 1, []); array_tmp10 := Array(1 .. max_terms + 1, []); array_tmp11 := Array(1 .. max_terms + 1, []); array_tmp12 := Array(1 .. max_terms + 1, []); array_tmp13 := Array(1 .. max_terms + 1, []); array_tmp14 := Array(1 .. max_terms + 1, []); array_tmp15 := Array(1 .. max_terms + 1, []); array_tmp16 := Array(1 .. max_terms + 1, []); array_tmp17 := Array(1 .. max_terms + 1, []); array_tmp18 := Array(1 .. max_terms + 1, []); array_tmp19 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_tmp20[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp21[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_pole[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_x2[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_x1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_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_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_tmp18[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp19[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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; array_tmp21 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp21[term] := 0.; term := term + 1 end do; array_tmp20 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp20[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1 end do; array_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[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_tmp19 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp19[term] := 0.; term := term + 1 end do; array_tmp18 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp18[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_const_0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0[term] := 0.; term := term + 1 end do; array_const_0[1] := 0; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_const_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_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 := 0.0001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_t[1] := t_start; array_t[2] := glob_h; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x2_higher[r_order, term_no] := array_x2_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x1_higher[r_order, term_no] := array_x1_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_x2(); if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_x1(); if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_t[1] <= t_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; sub_iter := 1; while sub_iter <= 3 do atomall(); sub_iter := sub_iter + 1 end do; if glob_look_poles then check_for_pole() end if; array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 2; order_diff := 2; order_diff := 2; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; order_diff := 1; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.\ 0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1\ ) + diff ( x1 , t , 0 );"); omniout_str(INFO, "diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - \ 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 );"); 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, "2012-06-01T22:21:19-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "complicatedrev2"); logitem_str(html_log_file, "diff ( x2 , t , 2 ) = 3.0 * diff (x2 \ , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - \ diff ( x1 , t , 1 ) + diff ( x1 , t , 0 );"); logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 076 "); logitem_str(html_log_file, "complicatedrev2 diffeq.mxt"); logitem_str(html_log_file, "complicatedrev2 maple results"); logitem_str(html_log_file, "tot order sub iterationsd 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 * diff ( x2\ , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t\ , 0 );"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/complicatedrev2postode.ode################# diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 ); diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 ); ! #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 := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c1 + 6.0 * c3 * exp(-t); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2 * exp(2.0 * t) + c3 * exp(-t); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 0.0001 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.0001 t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 0.0001 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001 x2[1] (analytic) = 0.00082570611074256394598966051590164 x2[1] (numeric) = 0.00082570612166175344873238013284757 absolute error = 1.091918950274271961694593e-11 relative error = 1.3224062848369872576388138559004e-06 % h = 0.0001 x1[1] (analytic) = 0.001291646017422585871235266471237 x1[1] (numeric) = 0.0012916459955886731368688976978373 absolute error = 2.18339127343663687733997e-11 relative error = 1.6903944610099007190317782129499e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002 x2[1] (analytic) = 0.0008257966814495432344339416603249 x2[1] (numeric) = 0.00082579672513448995494907004693409 absolute error = 4.368494672051512838660919e-11 relative error = 5.2900366036629937406787825061754e-06 % h = 0.0001 x1[1] (analytic) = 0.0012915368582788917633066026400632 x1[1] (numeric) = 0.0012915367709400662091462400606959 absolute error = 8.73388255541603625793673e-11 relative error = 6.7623951259547096541965245002863e-06 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003 x2[1] (analytic) = 0.00082588727573070556349803310856235 x2[1] (numeric) = 0.00082588737404108259020305742704614 absolute error = 9.831037702670502431848379e-11 relative error = 1.1903607176866201797354402820400e-05 % h = 0.0001 x1[1] (analytic) = 0.0012914277100505662472629969306448 x1[1] (numeric) = 0.0012914275135270950535250596079249 absolute error = 1.965234711937379373227199e-10 relative error = 1.5217535574332921868067101846963e-05 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.20 NO POLE NO POLE t[1] = 0.5004 x2[1] (analytic) = 0.00082597789359022044558440876232671 x2[1] (numeric) = 0.00082597806839881121490639659787472 absolute error = 1.7480859076932198783554801e-10 relative error = 2.1163834059709962739351790559512e-05 % h = 0.0001 x1[1] (analytic) = 0.0012913185727365178408202846139762 x1[1] (numeric) = 0.0012913182233399324461462470223398 absolute error = 3.493965853946740375916364e-10 relative error = 2.7057349965488750659944092361416e-05 % h = 0.0001 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] = 0.5005 x2[1] (analytic) = 0.00082606853503225828165826201261726 x2[1] (numeric) = 0.00082606880822496160289996026168012 absolute error = 2.7319270332124169824906286e-10 relative error = 3.3071433148167714945794793009397e-05 % h = 0.0001 x1[1] (analytic) = 0.0012912094463356551708370721480129 x1[1] (numeric) = 0.0012912089003687482154163477083865 absolute error = 5.459669069554207244396264e-10 relative error = 4.2283373042601982050385666536194e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006 x2[1] (analytic) = 0.00082615920006099036141977864461309 x2[1] (numeric) = 0.00082615959353682544570143671508893 absolute error = 3.9347583508428165807047584e-10 relative error = 4.7627120179165674768176686601620e-05 % h = 0.0001 x1[1] (analytic) = 0.0012911003308468869733038234462486 x1[1] (numeric) = 0.0012910995446037089939407851805827 absolute error = 7.862431779793630382656659e-10 relative error = 6.0897140152046362748851057228284e-05 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 2.209e-05 Order of pole = 14.48 t[1] = 0.5007 x2[1] (analytic) = 0.00082624988868058886347644474630742 x2[1] (numeric) = 0.0008262504243517007440749921376385 absolute error = 5.3567111188059854739133108e-10 relative error = 6.4831610777702377664454728111586e-05 % h = 0.0001 x1[1] (analytic) = 0.0012909912262691220933319472376107 x1[1] (numeric) = 0.0012909901560349418312735224681438 absolute error = 1.0702341802620584247694669e-09 relative error = 8.2900190062093861039005776377149e-05 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5008 x2[1] (analytic) = 0.00082634060089522685551538962782877 x2[1] (numeric) = 0.000826341300686904797698571054708 absolute error = 6.9979167794218318142687923e-10 relative error = 8.4685622028501897433996777816451e-05 % h = 0.0001 x1[1] (analytic) = 0.0012908821326012694851428855175656 x1[1] (numeric) = 0.0012908807346521060641935087506295 absolute error = 1.3979491634209493767669361e-09 relative error = 0.0001082940981299298060545915079463 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.45 NO POLE NO POLE t[1] = 0.5009 x2[1] (analytic) = 0.00082643133670907829447576375839823 x2[1] (numeric) = 0.00082643222255988278464140025172629 absolute error = 8.8585080449016563649332806e-10 relative error = 0.00010718988561320784957949268432768 % h = 0.0001 x1[1] (analytic) = 0.0012907730498422382120572030903234 x1[1] (numeric) = 0.0012907712804451935376400477576047 absolute error = 1.7693970446744171553327187e-09 relative error = 0.00013708041432153217545762686134307 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652318998811513995001086021368 absolute error = 1.09386179711322885913234182e-09 relative error = 0.00013234513659584644596398736231146 % h = 0.0001 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906617934050166328715852920601 absolute error = 2.1845859208136120929099750e-09 relative error = 0.00016926062538865955920154170699227 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5011 x2[1] (analytic) = 0.00082661287915112178821202023981947 x2[1] (numeric) = 0.00082661420298892388219290528870462 absolute error = 1.32383780209398088504888515e-09 relative error = 0.00016015208999084034145514485076069 % h = 0.0001 x1[1] (analytic) = 0.0012905549170462764699083942648711 x1[1] (numeric) = 0.0012905522735217299599278473520282 absolute error = 2.6435245465099805469128429e-09 relative error = 0.00020483626939024630071956776389601 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5012 x2[1] (analytic) = 0.00082670368578766620467820114309252 x2[1] (numeric) = 0.00082670526157963635782447462890289 absolute error = 1.57579197015314627348581037e-09 relative error = 0.0001906114605805542304131949522664 % h = 0.0001 x1[1] (analytic) = 0.0012904458670071646728838326718726 x1[1] (numeric) = 0.0012904427207854827787693857825297 absolute error = 3.1462216818941144468893429e-09 relative error = 0.00024380888515617574044322028399468 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5013 x2[1] (analytic) = 0.00082679451604012879179140950883443 x2[1] (numeric) = 0.0008267963657775858421183730437273 absolute error = 1.84973745705032696353489287e-09 relative error = 0.00022372396298774546301418022720761 % h = 0.0001 x1[1] (analytic) = 0.0012903368278725115550179667024679 x1[1] (numeric) = 0.0012903331351864213948949885266703 absolute error = 3.6926860901601229781757976e-09 relative error = 0.00028618001210184550552515386625851 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=4.4MB, time=0.70 t[1] = 0.5014 x2[1] (analytic) = 0.00082688536991268795533779675988916 x2[1] (numeric) = 0.00082688751560011154109210629229005 absolute error = 2.14568742358575430953240089e-09 relative error = 0.00025949031167552530362904182619953 % h = 0.0001 x1[1] (analytic) = 0.0012902277996412267249633565185424 x1[1] (numeric) = 0.001290223516714689158455590024069 absolute error = 4.2829265375665077664944734e-09 relative error = 0.00033195119022838136980151533649844 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5015 x2[1] (analytic) = 0.00082697624740952299139053885956424 x2[1] (numeric) = 0.00082697871106455859343222635883307 absolute error = 2.46365503560204168749926883e-09 relative error = 0.00029791122094732023709354802979059 % h = 0.0001 x1[1] (analytic) = 0.0012901187823122199004062452509559 x1[1] (numeric) = 0.0012901138653604264633679493764703 absolute error = 4.9169517934370382958744856e-09 relative error = 0.00038112396012285118775633651353075 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5016 x2[1] (analytic) = 0.00082706714853481408648245956670656 x2[1] (numeric) = 0.00082706995218827807242012091049951 absolute error = 2.80365346398593766134379295e-09 relative error = 0.00033898740494683332148102567008036 % h = 0.0001 x1[1] (analytic) = 0.001290009775884400908055656176395 x1[1] (numeric) = 0.0012900041811137707464284413187226 absolute error = 5.5947706301616272148576724e-09 relative error = 0.00043369986295847887576020490224855 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5017 x2[1] (analytic) = 0.00082715807329274231777868876405026 x2[1] (numeric) = 0.00082716123898862698785831201000862 absolute error = 3.16569588467007962324595836e-09 relative error = 0.00038271957765800557700862869397785 % h = 0.0001 x1[1] (analytic) = 0.0012899007803566796836324909844552 x1[1] (numeric) = 0.0012898944639648564864260100854435 absolute error = 6.3163918231972064808990117e-09 relative error = 0.00048968044049485851422864959282994 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5018 x2[1] (analytic) = 0.00082724902168748965324935586679766 x2[1] (numeric) = 0.0008272525714829682879974113440187 absolute error = 3.54979547863474805547722104e-09 relative error = 0.00042910845290497742886263460350964 % h = 0.0001 x1[1] (analytic) = 0.0012897917957279662718586291348401 x1[1] (numeric) = 0.0012897847139038152032542060560984 absolute error = 7.0818241510686044230787417e-09 relative error = 0.00054906723507816857695880618661999 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5019 x2[1] (analytic) = 0.00082733999372323895184231831839524 x2[1] (numeric) = 0.00082734394968867086146387719629344 absolute error = 3.95596543190962155887789820e-09 relative error = 0.00047815474435205022146703035414794 % h = 0.0001 x1[1] (analytic) = 0.0012896828219971708264460283045716 x1[1] (numeric) = 0.0012896749309207754570240934022767 absolute error = 7.8910763953694219349022949e-09 relative error = 0.00061186178964138614903887484077145 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=0.95 NO POLE NO POLE t[1] = 0.502 x2[1] (analytic) = 0.0008274309894041739636559251804687 x2[1] (numeric) = 0.00082743537362310953918829340129057 absolute error = 4.38421893557553236822082187e-09 relative error = 0.00052985916550364777034118552689246 % h = 0.0001 x1[1] (analytic) = 0.0012895738591632036100858259251 x1[1] (numeric) = 0.0012895651150058628471767586330421 absolute error = 8.7441573407629090672920579e-09 relative error = 0.00067806564770450123178919631328366 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5021 x2[1] (analytic) = 0.00082752200873447933011181582388164 x2[1] (numeric) = 0.0008275268433036650963342073951073 absolute error = 4.83456918576622239157122566e-09 relative error = 0.00058422242970427795601494997632118 % h = 0.0001 x1[1] (analytic) = 0.0012894649072249749944374418092067 x1[1] (numeric) = 0.0012894552661492000115953588502093 absolute error = 9.6410757749828420829589974e-09 relative error = 0.00074768035337473113950702892269502 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5022 x2[1] (analytic) = 0.0008276130517183405841277537278848 x2[1] (numeric) = 0.00082761835874772425422757604445839 absolute error = 5.30702938367009982231657359e-09 relative error = 0.00064124525013849436586280194384198 % h = 0.0001 x1[1] (analytic) = 0.0012893559661813954601176818675888 x1[1] (numeric) = 0.0012893453843409066257169035248855 absolute error = 1.05818404888344007783427033e-08 relative error = 0.00082070745134673497301304559555098 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5023 x2[1] (analytic) = 0.00082770411835994415029049539432325 x2[1] (numeric) = 0.00082770991997267968228681948473313 absolute error = 5.80161273553199632409040988e-09 relative error = 0.00070092833983085798385999477745415 % h = 0.0001 x1[1] (analytic) = 0.0012892470360313755966898429150187 x1[1] (numeric) = 0.0012892354695710994016437698893244 absolute error = 1.15664602761950460730256943e-08 relative error = 0.00089714848690282817001303036128957 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5024 x2[1] (analytic) = 0.00082779520866347734502869438387111 x2[1] (numeric) = 0.00082780152699592999995348315486407 absolute error = 6.31833245265492478877099296e-09 relative error = 0.00076327241164589892825838823092436 % h = 0.0001 x1[1] (analytic) = 0.0012891381167738261026528185659675 x1[1] (numeric) = 0.001289125521829892087254951862258 absolute error = 1.25949439340153978667037095e-08 relative error = 0.00097700500591319713230189499404261 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=19.0MB, alloc=4.4MB, time=1.20 t[1] = 0.5025 x2[1] (analytic) = 0.00082788632263312837678584048126422 x2[1] (numeric) = 0.00082789317983487977862350821728348 absolute error = 6.85720175140183766773601926e-09 relative error = 0.000828278178288078237179690920521 % h = 0.0001 x1[1] (analytic) = 0.0012890292084076577854302062195851 x1[1] (numeric) = 0.0012890155411073954653170424277919 absolute error = 1.36673002623201131637917932e-08 relative error = 0.0010602785548361139298369953216543 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5026 x2[1] (analytic) = 0.00082797746027308634619323399650282 x2[1] (numeric) = 0.00082798487850693954357911055130097 absolute error = 7.41823385319738587655479815e-09 relative error = 0.00089594635230174970212382231411593 % h = 0.0001 x1[1] (analytic) = 0.001288920310931781561359415133927 x1[1] (numeric) = 0.0012889055273937173525949493879249 absolute error = 1.47835380642087644657460021e-08 relative error = 0.0011469706807181510817077358127997 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5027 x2[1] (analytic) = 0.00082806862158754124624299520899781 x2[1] (numeric) = 0.00082807662302952577592126850829325 absolute error = 8.00144198452967827329929544e-09 relative error = 0.00096627764607112174939008445797475 % h = 0.0001 x1[1] (analytic) = 0.0012888114243451084556807755893193 x1[1] (numeric) = 0.0012887954806789625989623444087289 absolute error = 1.59436661458567184311805904e-08 relative error = 0.001237082931194396414028460479705 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5028 x2[1] (analytic) = 0.00082815980658068396246110896163522 x2[1] (numeric) = 0.00082816841342006091450281961715487 absolute error = 8.60683937695204171065551965e-09 relative error = 0.0010392727718202193694088155748925 % h = 0.0001 x1[1] (analytic) = 0.0012887025486465496025266491407532 x1[1] (numeric) = 0.0012886854009532330865118452802011 absolute error = 1.71476933165160148038605521e-08 relative error = 0.0013306168544886679947816373692586 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5029 x2[1] (analytic) = 0.0008282510152567062730805044117353 x2[1] (numeric) = 0.00082826024969597335786216642851648 absolute error = 9.23443926708478166201678118e-09 relative error = 0.0011149324416128460939811794953911 % h = 0.0001 x1[1] (analytic) = 0.0012885936838350162449105399591989 x1[1] (numeric) = 0.0012885752882066277286649313097781 absolute error = 1.83956283885162456086494208e-08 relative error = 0.0014275739994137291456383529357998 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.503 x2[1] (analytic) = 0.0008283422476198008492141699458837 x2[1] (numeric) = 0.00082835213187469746615759168629496 absolute error = 9.88425489661694342174041126e-09 relative error = 0.0011932573673525460214247268180421 % h = 0.0001 x1[1] (analytic) = 0.0012884848299094197347162072617323 x1[1] (numeric) = 0.0012884651424292424692815917694756 absolute error = 1.96874801772654346154922567e-08 relative error = 0.0015279559153715035307831422636481 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.5MB, time=1.46 NO POLE NO POLE t[1] = 0.5031 x2[1] (analytic) = 0.00082843350367416125502830326561401 x2[1] (numeric) = 0.0008284440599736735631021830151972 absolute error = 1.055629951230807387974958319e-08 relative error = 0.0012742482607825658896223455001299 % h = 0.0001 x1[1] (analytic) = 0.0012883759868686715326867788303632 x1[1] (numeric) = 0.0012883549636111702817697073165949 absolute error = 2.10232575012509170715137683e-08 relative error = 0.0016317641523532903227701898846915 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5032 x2[1] (analytic) = 0.00082852478342398194791549665092172 x2[1] (numeric) = 0.00082853603401034793789936731285738 absolute error = 1.125058636598998387066193566e-08 relative error = 0.0013579058334858171969722005903091 % h = 0.0001 x1[1] (analytic) = 0.0012882671547116832084138656194575 x1[1] (numeric) = 0.001288244751742501168194164307913 absolute error = 2.24029691820402197013115445e-08 relative error = 0.0017390002609399794454379455230495 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5033 x2[1] (analytic) = 0.00082861608687345827866795740859187 x2[1] (numeric) = 0.00082862805400217284717905503534514 absolute error = 1.196712871456851109762675327e-08 relative error = 0.0014442307968848383712362445959755 % h = 0.0001 x1[1] (analytic) = 0.0012881583334373664403266774516441 x1[1] (numeric) = 0.001288134506813322158385701927248 absolute error = 2.38266240442819409755243961e-08 relative error = 0.0018496657923022668939092083079033 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5034 x2[1] (analytic) = 0.00082870741402678649165076351232339 x2[1] (numeric) = 0.00082872011996660651693439456483988 absolute error = 1.270593982002528363105251649e-08 relative error = 0.0015332238622417569862848619813268 % h = 0.0001 x1[1] (analytic) = 0.0012880495230446330156811398020981 x1[1] (numeric) = 0.0012880242288137173090494920462695 absolute error = 2.52942309157066316477558286e-08 relative error = 0.0019637622982008701317037421760952 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5035 x2[1] (analytic) = 0.00082879876488816372497515444163463 x2[1] (numeric) = 0.00082881223192111314445913684832421 absolute error = 1.346703294941948398240668958e-08 relative error = 0.0016248857406582520267351931999897 % h = 0.0001 x1[1] (analytic) = 0.0012879407235323948305490116710912 x1[1] (numeric) = 0.0012879139177337677028734517383973 absolute error = 2.68057986271276755599326939e-08 relative error = 0.0020812913309867435649904945864583 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5036 x2[1] (analytic) = 0.00082889013946178801067185722653652 x2[1] (numeric) = 0.00082890438988316290028561049620747 absolute error = 1.425042137488961375326967095e-08 relative error = 0.001719217143075516200480665541488 % h = 0.0001 x1[1] (analytic) = 0.0012878319348995638898070045446997 x1[1] (numeric) = 0.0012878035735635514476362883656101 absolute error = 2.83613360124421707161790896e-08 relative error = 0.0022022544436012940940064997136431 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.5MB, time=1.71 NO POLE NO POLE t[1] = 0.5037 x2[1] (analytic) = 0.00082898153775185827486444770496057 x2[1] (numeric) = 0.00082899659387023193012330752984796 absolute error = 1.505611837365525885982488739e-08 relative error = 0.0018162187802742182991092400717945 % h = 0.0001 x1[1] (analytic) = 0.0012877231571450523071259024435631 x1[1] (numeric) = 0.0012876931962931436753152771579597 absolute error = 2.99608519086318106252856034e-08 relative error = 0.0023266531895765967416695569353037 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5038 x2[1] (analytic) = 0.0008290729597625743379427469999303 x2[1] (numeric) = 0.00082908884389980235679807996700038 absolute error = 1.588413722801885533296707008e-08 relative error = 0.001915891362874465606207865898536 % h = 0.0001 x1[1] (analytic) = 0.0012876143902677723049596830595824 x1[1] (numeric) = 0.0012875827859126165411937712055635 absolute error = 3.16043551557637659118540189e-08 relative error = 0.0024544891230356103594117842987973 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5039 x2[1] (analytic) = 0.00082916440549813691473625322346704 x2[1] (numeric) = 0.00082918113998936228219194743427298 absolute error = 1.673449122536745569421080594e-08 relative error = 0.0020182356013357663535506148477489 % h = 0.0001 x1[1] (analytic) = 0.0012875056342666362145346399804511 x1[1] (numeric) = 0.0012874723424120392229684437828236 absolute error = 3.32918545969915661961976275e-08 relative error = 0.0025857637986923934102611562736706 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.504 x2[1] (analytic) = 0.00082925587496274761468760841422102 x2[1] (numeric) = 0.00082927348215640578918351599573659 absolute error = 1.760719365817449590758151557e-08 relative error = 0.0021232522059569922251679517476335 % h = 0.0001 x1[1] (analytic) = 0.0012873968891405564758385060019091 x1[1] (numeric) = 0.0012873618657814779198562629245967 absolute error = 3.50233590785559822430773124e-08 relative error = 0.0027204787718523198291981441676226 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5041 x2[1] (analytic) = 0.00082934736816060894202610071582133 x2[1] (numeric) = 0.00082936587041843294358900838688586 absolute error = 1.850225782400156290767106453e-08 relative error = 0.0022309418868763409092945773652273 % h = 0.0001 x1[1] (analytic) = 0.0012872881548884456376095775276106 x1[1] (numeric) = 0.0012872513560109958517011981740149 absolute error = 3.67988774497859083793535957e-08 relative error = 0.0028586355984122949608145869448336 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.6MB, time=1.97 NO POLE NO POLE t[1] = 0.5042 x2[1] (analytic) = 0.00082943888509592429594120180293885 x2[1] (numeric) = 0.00082945830479294979610390584321073 absolute error = 1.941969702550016270404027188e-08 relative error = 0.0023413053540712986981932630999801 % h = 0.0001 x1[1] (analytic) = 0.0012871794315092163573258400564985 x1[1] (numeric) = 0.0012871408130906532580806594216339 absolute error = 3.86184185630992451806348646e-08 relative error = 0.0030002358348609715743019295493337 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5043 x2[1] (analytic) = 0.00082953042577289797075613956205843 x2[1] (numeric) = 0.00082955078529746838424520171269417 absolute error = 2.035952457041348906215063574e-08 relative error = 0.0024543433173586031358520784420122 % h = 0.0001 x1[1] (analytic) = 0.0012870707190017814011940947575749 x1[1] (numeric) = 0.0012870302370105073974116677555596 absolute error = 4.04819912740037824270020153e-08 relative error = 0.0031452810382789659557959750159911 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5044 x2[1] (analytic) = 0.00082962199019573515610150603395714 x2[1] (numeric) = 0.00082964331194950673429426704161032 absolute error = 2.132175377157819276100765318e-08 relative error = 0.0025700564863942057135523943189862 % h = 0.0001 x1[1] (analytic) = 0.00128696201736505364413908613196 x1[1] (numeric) = 0.0012869196277606125460567582421827 absolute error = 4.23896044410980823278897773e-08 relative error = 0.0032937727663390740781053059505923 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5045 x2[1] (analytic) = 0.00082971357836864193708890062488759 x2[1] (numeric) = 0.00082973588476658886324032832305484 absolute error = 2.230639794692615142769816725e-08 relative error = 0.0026884455706732346133050273306322 % h = 0.0001 x1[1] (analytic) = 0.0012868533265979460697926307621308 x1[1] (numeric) = 0.0012868089853310199974296145571232 absolute error = 4.43412669260723630162050076e-08 relative error = 0.0034457125773064878478505404717331 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5046 x2[1] (analytic) = 0.00082980519029582529448460859346626 x2[1] (numeric) = 0.00082982850376624478072455759769763 absolute error = 2.331347041948623994900423137e-08 relative error = 0.0028095112795299574991518719815494 % h = 0.0001 x1[1] (analytic) = 0.0012867446466993717704827471482299 x1[1] (numeric) = 0.0012866983097117780611004353859659 absolute error = 4.63369875937093823117622640e-08 relative error = 0.0036011020300390114300415966693949 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5047 x2[1] (analytic) = 0.00082989682598149310488331482026843 x2[1] (numeric) = 0.00082992116896601049098477509630575 absolute error = 2.434298451738610146027603732e-08 relative error = 0.0029332543221377443563303499730658 % h = 0.0001 x1[1] (analytic) = 0.0012866359776682439472227866313365 x1[1] (numeric) = 0.0012865876008929320619010325143419 absolute error = 4.83767753118853217541169946e-08 relative error = 0.0037599426839872776501201492368303 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.6MB, time=2.22 NO POLE NO POLE t[1] = 0.5048 x2[1] (analytic) = 0.00082998848542985414088185286713247 x2[1] (numeric) = 0.00083001388038342799480076461364266 absolute error = 2.539495357385391891174651019e-08 relative error = 0.0030596754075090303782979877038852 % h = 0.0001 x1[1] (analytic) = 0.0012865273195034759097005654035915 x1[1] (numeric) = 0.0012864768588645243390296605268875 absolute error = 5.04606389515706709048767040e-08 relative error = 0.0039222360991949644734944711871066 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5049 x2[1] (analytic) = 0.00083008016864511807125298933317795 x2[1] (numeric) = 0.00083010663803604529144020180340773 absolute error = 2.646939092722018721247022978e-08 relative error = 0.0031887752444952789016144151050532 % h = 0.0001 x1[1] (analytic) = 0.001286418672203981076267497605066 x1[1] (numeric) = 0.0012863660836165942451555780345881 absolute error = 5.25885873868311119195704779e-08 relative error = 0.0040879838362990115625938626518686 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.505 x2[1] (analytic) = 0.00083017187563149546111924351454314 x2[1] (numeric) = 0.0008301994419414163806051955839383 absolute error = 2.756630992091948595206939516e-08 relative error = 0.003320554541786944388678061048136 % h = 0.0001 x1[1] (analytic) = 0.0012863100357686729739277295072664 x1[1] (numeric) = 0.0012862552751391781455233403499901 absolute error = 5.47606294948284043891572763e-08 relative error = 0.0042571874565298369114698784159514 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5051 x2[1] (analytic) = 0.00083026360639319777212674237484908 x2[1] (numeric) = 0.00083029229211710126437944284445429 absolute error = 2.868572390349225270046960521e-08 relative error = 0.0034550140079134354583148025513057 % h = 0.0001 x1[1] (analytic) = 0.0012862014101964652383272747831672 x1[1] (numeric) = 0.0012861444334223094170568235297397 absolute error = 5.69767741558212704512534275e-08 relative error = 0.0044298485217115535579715749949898 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5052 x2[1] (analytic) = 0.0008303553609344373626191108333988 x2[1] (numeric) = 0.00083038518858066594917599664168379 absolute error = 2.982764622858655688580828499e-08 relative error = 0.0035921543512430779642158071109008 % h = 0.0001 x1[1] (analytic) = 0.0012860927954862716137431508636619 x1[1] (numeric) = 0.001286033558456018447462979703884 absolute error = 5.92370302531662801711597779e-08 relative error = 0.0046059685942621863735220072812983 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=38.1MB, alloc=4.6MB, time=2.47 t[1] = 0.5053 x2[1] (analytic) = 0.00083044713925942748781139737812144 x2[1] (numeric) = 0.00083047813134968244768564807676604 absolute error = 3.099209025495987425069864460e-08 relative error = 0.0037319762799830781212217895685918 % h = 0.0001 x1[1] (analytic) = 0.0012859841916370059530725163803239 x1[1] (numeric) = 0.0012859226502303326343353236113443 absolute error = 6.15414066733187371927689796e-08 relative error = 0.0047855492371938889305232143304729 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5054 x2[1] (analytic) = 0.00083053894137238229996403501027281 x2[1] (numeric) = 0.00083057112044172878082592204238625 absolute error = 3.217906934648086188703211344e-08 relative error = 0.0038744805021794856794508869456226 % h = 0.0001 x1[1] (analytic) = 0.0012858755986475822178218096943695 x1[1] (numeric) = 0.001285811708735276384257150260949 absolute error = 6.38899123058335646594334205e-08 relative error = 0.0049685920141131604474169430766505 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5055 x2[1] (analytic) = 0.0008306307672775168485568375279051 x2[1] (numeric) = 0.00083066415587438897969068703015502 absolute error = 3.338859687213113384950224992e-08 relative error = 0.0040196677257171571462673368103868 % h = 0.0001 x1[1] (analytic) = 0.0012857670165169144780958885117126 x1[1] (numeric) = 0.0012857007339608711119044836373876 absolute error = 6.62825560433661914048743250e-08 relative error = 0.0051550984892210628114283680367501 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5056 x2[1] (analytic) = 0.0008307226169790470804630311551197 x2[1] (numeric) = 0.00083075723766525308750037918830325 absolute error = 3.462068620600703734803318355e-08 relative error = 0.0041675386583197190560881268552688 % h = 0.0001 x1[1] (analytic) = 0.001285658445243916912587170584005 x1[1] (numeric) = 0.0012855897258971352391487563714249 absolute error = 6.87193467816734384142125801e-08 relative error = 0.0053450702273134376790200745955584 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5057 x2[1] (analytic) = 0.00083081449048118984012332152411889 x2[1] (numeric) = 0.00083085036583191716155284081982151 absolute error = 3.587535072732142951929570262e-08 relative error = 0.0043180940075495312880247654023712 % h = 0.0001 x1[1] (analytic) = 0.0012855498848275038085647754955507 x1[1] (numeric) = 0.0012854786845340841941592202936889 absolute error = 7.12002934196144055552018618e-08 relative error = 0.0055385087937811236540835824843864 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5058 x2[1] (analytic) = 0.00083090638778816286971999601707344 x2[1] (numeric) = 0.00083094354039198327517477351123115 absolute error = 3.715260382040545477749415771e-08 relative error = 0.0044713344808076504313573046980173 % h = 0.0001 x1[1] (analytic) = 0.0012854413352665895618636675359888 x1[1] (numeric) = 0.0012853676098617304105050877913217 absolute error = 7.37254048591513585797446671e-08 relative error = 0.0057354157546101735438956958904262 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.6MB, time=2.72 NO POLE NO POLE t[1] = 0.5059 x2[1] (analytic) = 0.0008309983089041848093510614748241 x2[1] (numeric) = 0.00083103676136305951967380608223267 absolute error = 3.845245887471032274460740857e-08 relative error = 0.0046272607853337931988377310349089 % h = 0.0001 x1[1] (analytic) = 0.0012853327965600886768737996586336 x1[1] (numeric) = 0.0012852565018700833262574038867601 absolute error = 7.62946900053506163957718735e-08 relative error = 0.0059357926763820716928669753876432 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.506 x2[1] (analytic) = 0.00083109025383347519720441727943742 x2[1] (numeric) = 0.00083113002876276000629117754653499 absolute error = 3.977492928480908676026709757e-08 relative error = 0.0047858736282062998878198177286879 % h = 0.0001 x1[1] (analytic) = 0.0012852242687069157665292585243653 x1[1] (numeric) = 0.0012851453605491493830906489578866 absolute error = 7.89081577663834386095664787e-08 relative error = 0.006139641126273951394109636740661 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5061 x2[1] (analytic) = 0.00083118222258025446973206381763632 x2[1] (numeric) = 0.00083122334260870486815503527422761 absolute error = 4.112002845039842297145659129e-08 relative error = 0.0049471737163420978892125192959836 % h = 0.0001 x1[1] (analytic) = 0.0012851157517059855522974106309618 x1[1] (numeric) = 0.0012850341858889320253840720187679 absolute error = 8.15658170535269133386121939e-08 relative error = 0.0063469626720588123788521907107678 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5062 x2[1] (analytic) = 0.00083127421514874396182434633212867 x2[1] (numeric) = 0.00083131670291852026223434854611594 absolute error = 4.248776977630041000221398727e-08 relative error = 0.005111161756496665244253967156186 % h = 0.0001 x1[1] (analytic) = 0.001285007245556212864168049527763 x1[1] (numeric) = 0.0012849229778794316993227544801739 absolute error = 8.42676767811648452950475891e-08 relative error = 0.006557758882105738383728147407784 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5063 x2[1] (analytic) = 0.00083136623154316590698423416785765 x2[1] (numeric) = 0.00083141010970983837129343769049827 absolute error = 4.387816667246430920352264062e-08 relative error = 0.0052778384552639942491031094290421 % h = 0.0001 x1[1] (analytic) = 0.0012848987502565126406425441155605 x1[1] (numeric) = 0.0012848117365106458519984043090462 absolute error = 8.70137458667886441398065143e-08 relative error = 0.0067720313253801147959661181876543 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=45.7MB, alloc=4.6MB, time=2.98 t[1] = 0.5064 x2[1] (analytic) = 0.00083145827176774343750163542019918 x2[1] (numeric) = 0.00083150356300029740584711899292126 absolute error = 4.529123255396834548357272208e-08 relative error = 0.0054472045190765551072460195612212 % h = 0.0001 x1[1] (analytic) = 0.0012847902658057999287229880316013 x1[1] (numeric) = 0.0012847004617725689305098805060603 absolute error = 8.98040332309982131075255410e-08 relative error = 0.0069897815714438463765086571652261 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5065 x2[1] (analytic) = 0.00083155033582670058462774699213345 x2[1] (numeric) = 0.00083159706280754160611646556950911 absolute error = 4.672698084102148871857737566e-08 relative error = 0.0056192606542052596297138806402534 % h = 0.0001 x1[1] (analytic) = 0.0012846817922029898839013501196003 x1[1] (numeric) = 0.0012845891536551923810634478204016 absolute error = 9.26385477975028379022991987e-08 relative error = 0.0072110111904555750610871942463834 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5066 x2[1] (analytic) = 0.00083164242372426227874944006741881 x2[1] (numeric) = 0.00083169060914922124398518439451994 absolute error = 4.818542495896523574432710113e-08 relative error = 0.0057940075667594249831096344580123 % h = 0.0001 x1[1] (analytic) = 0.0012845733294469977701486259846507 x1[1] (numeric) = 0.0012844778121485046480727616208515 absolute error = 9.55172984931220758643637992e-08 relative error = 0.0074357217531708978392804204716523 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5067 x2[1] (analytic) = 0.00083173453546465434956368100679754 x2[1] (numeric) = 0.00083178420204299262495660967284123 absolute error = 4.966657833827539292866604369e-08 relative error = 0.0059714459626867374854402665863628 % h = 0.0001 x1[1] (analytic) = 0.001284464877536738959903990632925 x1[1] (numeric) = 0.0012843664372424911732585828422547 absolute error = 9.84402942477866454077906703e-08 relative error = 0.0076639148309425847115834961865043 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5068 x2[1] (analytic) = 0.00083182667105210352625198767426466 x2[1] (numeric) = 0.00083187784150651809011131274819462 absolute error = 5.117045441456385932507392996e-08 relative error = 0.006151576547773216449751680904293 % h = 0.0001 x1[1] (analytic) = 0.0012843564364711289340639521960578 x1[1] (numeric) = 0.0012842550289271343947482229264159 absolute error = 1.014075439945393157292696419e-07 relative error = 0.0078955919957207967245154617033784 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5069 x2[1] (analytic) = 0.00083191883049083743765492120043225 x2[1] (numeric) = 0.00083197152755746601806532873787865 absolute error = 5.269706662858041040753744640e-08 relative error = 0.0063344000276431780755630992181459 % h = 0.0001 x1[1] (analytic) = 0.0012842480062490832819715067401017 x1[1] (numeric) = 0.0012841435871924137461747186764485 absolute error = 1.044190566695357967880636532e-07 relative error = 0.0081307548200533040837922396074346 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.6MB, time=3.23 NO POLE NO POLE t[1] = 0.507 x2[1] (analytic) = 0.00083201101378508461244661319002326 x2[1] (numeric) = 0.00083206526021351082692900008493661 absolute error = 5.424642842621448238689491335e-08 relative error = 0.0065199171077591993880979038384207 % h = 0.0001 x1[1] (analytic) = 0.001284139586869517701405294158948 x1[1] (numeric) = 0.001284032112028305655775736943574 absolute error = 1.074748412120456295572153740e-07 relative error = 0.0083694048770857043455926272386566 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5071 x2[1] (analytic) = 0.00083210322093907447930932838052986 x2[1] (numeric) = 0.00083215903949233297626643721869494 absolute error = 5.581855325849695710883816508e-08 relative error = 0.0067081284934220822253078232192365 % h = 0.0001 x1[1] (analytic) = 0.0012840311783313479985687551521049 x1[1] (numeric) = 0.0012839206034247835454922090653471 absolute error = 1.105749065644530765460867578e-07 relative error = 0.0086115437405616406859446872972237 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5072 x2[1] (analytic) = 0.00083219545195703736710806275907346 x2[1] (numeric) = 0.00083225286541161896905559651467615 absolute error = 5.741345458160194753375560269e-08 relative error = 0.0068990348897708172726873429253779 % h = 0.0001 x1[1] (analytic) = 0.0012839227806334900880792892867217 x1[1] (numeric) = 0.0012838090613718178300666949742568 absolute error = 1.137192616722580125943124649e-07 relative error = 0.0088571729848230202482599536088663 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5073 x2[1] (analytic) = 0.00083228770684320450506517714450406 x2[1] (numeric) = 0.00083234673798906135364897574494872 absolute error = 5.903114585684858379860044466e-08 relative error = 0.0070926370017825481458752065385411 % h = 0.0001 x1[1] (analytic) = 0.0012838143937748599929574141437547 x1[1] (numeric) = 0.0012836974858593759161414768956289 absolute error = 1.169079154840768159372481258e-07 relative error = 0.0091062941848102325690428790825254 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5074 x2[1] (analytic) = 0.00083237998560180802293506624177892 x2[1] (numeric) = 0.00083244065724235872573492721003484 absolute error = 6.067164055070279986096825592e-08 relative error = 0.0072889355342725355210398532402929 % h = 0.0001 x1[1] (analytic) = 0.0012837060177543738446159255481629 x1[1] (numeric) = 0.0012835858768774222013563825537319 absolute error = 1.201408769516432595429944310e-07 relative error = 0.0093589089160623680818029616215899 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5075 x2[1] (analytic) = 0.0008324722882370809511788631756612 x2[1] (numeric) = 0.00083253462318921573029958874355545 absolute error = 6.233495213477912072556789425e-08 relative error = 0.0074879311918941213130456211662856 % h = 0.0001 x1[1] (analytic) = 0.0012835976525709478828490588830272 x1[1] (numeric) = 0.0012834742344159180734463378049638 absolute error = 1.234181550298094027210780634e-07 relative error = 0.0096150187547174366991969935949668 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.6MB, time=3.48 NO POLE NO POLE t[1] = 0.5076 x2[1] (analytic) = 0.00083256461475325722113917951078113 x2[1] (numeric) = 0.00083262863584734306358943278085052 absolute error = 6.402109408584245025327006939e-08 relative error = 0.0076896246791386929013965278250327 % h = 0.0001 x1[1] (analytic) = 0.0012834892982234984558216514874832 x1[1] (numeric) = 0.0012833625584648219093386486169724 absolute error = 1.267397586765464830028705108e-07 relative error = 0.009874625277512586473428889636544 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5077 x2[1] (analytic) = 0.00083265696515457166521488076510333 x2[1] (numeric) = 0.00083272269523445747507443368287104 absolute error = 6.573007988580985955291776771e-08 relative error = 0.0078940167003356474039544211878553 % h = 0.0001 x1[1] (analytic) = 0.0012833809547109420200583061383613 x1[1] (numeric) = 0.0012832508490140890742500123125379 absolute error = 1.301056968529458082938258234e-07 relative error = 0.010137730061784322334934557181545 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5078 x2[1] (analytic) = 0.00083274933944526001703589742384568 x2[1] (numeric) = 0.00083281680136828176941185350669774 absolute error = 6.746192302175237595608285206e-08 relative error = 0.0081011079596523559984282772922171 % h = 0.0001 x1[1] (analytic) = 0.001283272622032195140432555615423 x1[1] (numeric) = 0.001283139106053671920783257997022 absolute error = 1.335159785232196492976184010e-07 relative error = 0.010404334685468724909379283198782 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5079 x2[1] (analytic) = 0.00083284173762955891163807146089618 x2[1] (numeric) = 0.00083291095426654480841064641410022 absolute error = 6.921663698589677257495320404e-08 relative error = 0.0083108991610941282916314025447863 % h = 0.0001 x1[1] (analytic) = 0.0012831643001861744901560283500877 x1[1] (numeric) = 0.001283027329573519788023816088164 absolute error = 1.369706126547021322122619237e-07 relative error = 0.010674440727101669412995120355303 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.508 x2[1] (analytic) = 0.00083293415971170588563803837477598 x2[1] (numeric) = 0.00083300515394698151299648190960864 absolute error = 7.099423527562735844353483266e-08 relative error = 0.0085233910085041767365032811541882 % h = 0.0001 x1[1] (analytic) = 0.0012830559891717968507676151575396 x1[1] (numeric) = 0.0012829155195635790006359168669783 absolute error = 1.404696082178501316982905613e-07 relative error = 0.010948049765819044626285765030207 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.6MB, time=3.74 NO POLE NO POLE t[1] = 0.5081 x2[1] (analytic) = 0.00083302660569593937740814474619785 x2[1] (numeric) = 0.00083309940042733286517738709962882 absolute error = 7.279473139348776924235343097e-08 relative error = 0.0087385842055635810968927904791602 % h = 0.0001 x1[1] (analytic) = 0.0012829476889879791121226370521077 x1[1] (numeric) = 0.0012828036760137928679585179684863 absolute error = 1.440129741862441641190836214e-07 relative error = 0.011225163381356971946126429042008 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5082 x2[1] (analytic) = 0.0008331190755864987272514013242712 x2[1] (numeric) = 0.00083319369372534591001000816419018 absolute error = 7.461813884718275860683991898e-08 relative error = 0.0089564794557912529600994893355106 % h = 0.0001 x1[1] (analytic) = 0.0012828393996336382723820141458102 x1[1] (numeric) = 0.0012826917989141016831009607309874 absolute error = 1.476007195365892810534148228e-07 relative error = 0.011505783154052024516286216544497 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5083 x2[1] (analytic) = 0.00083321156938762417757647164840573 x2[1] (numeric) = 0.00083328803385877375756649123297466 absolute error = 7.646447114957999001958456893e-08 relative error = 0.0091770774625439002971696666894934 % h = 0.0001 x1[1] (analytic) = 0.0012827311211076914380014356299545 x1[1] (numeric) = 0.0012825798882544427220383553225537 absolute error = 1.512328532487159630803074008e-07 relative error = 0.011789910664841446436400526624748 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5084 x2[1] (analytic) = 0.00083330408710355687307269621296731 x2[1] (numeric) = 0.00083338242084537558490198285733336 absolute error = 7.833374181871182928664436605e-08 relative error = 0.0094003789290159920709438204765976 % h = 0.0001 x1[1] (analytic) = 0.0012826228534090558237205308396847 x1[1] (numeric) = 0.001282467944024750242706694563405 absolute error = 1.549093843055810138362762797e-07 relative error = 0.012077547495263372049421011896219 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5085 x2[1] (analytic) = 0.00083339662873853886088515218174166 x2[1] (numeric) = 0.00083347685470291663802275027005631 absolute error = 8.022596437777713759808831465e-08 relative error = 0.0096263845582397228918522185570031 % h = 0.0001 x1[1] (analytic) = 0.0012825145965366487525520414013697 x1[1] (numeric) = 0.0012823559662149554840976963627982 absolute error = 1.586303216932684543450385715e-07 relative error = 0.012368695227457045307570632752163 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5086 x2[1] (analytic) = 0.00083348919429681309078974865926187 x2[1] (numeric) = 0.00083357133544916823385492162471963 absolute error = 8.214115235514306517296545776e-08 relative error = 0.0098550950530849777214551762993121 % h = 0.0001 x1[1] (analytic) = 0.0012824063504893876557709944627208 x1[1] (numeric) = 0.0012822439548149866653533746890409 absolute error = 1.623956744009904176197736799e-07 relative error = 0.012663355444163039216831356038659 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.6MB, time=3.99 NO POLE NO POLE t[1] = 0.5087 x2[1] (analytic) = 0.00083358178378262341536835752605775 x2[1] (numeric) = 0.00083366586310190776221384640649278 absolute error = 8.407931928434684548888043503e-08 relative error = 0.010086511116259296623724667544112 % h = 0.0001 x1[1] (analytic) = 0.0012822981152661900729038770055334 x1[1] (numeric) = 0.0012821319098147689848603389912134 absolute error = 1.662054514210880435380143200e-07 relative error = 0.012961529728723475359992056876339 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5088 x2[1] (analytic) = 0.00083367439720021459018397984488692 x2[1] (numeric) = 0.00083376043767891868777407620634766 absolute error = 8.604047870409759009636146074e-08 relative error = 0.010320633450307839564063868043404 % h = 0.0001 x1[1] (analytic) = 0.0012821898908659736517178112409428 x1[1] (numeric) = 0.0012820198312042246193438219911596 absolute error = 1.700596617490323739892497832e-07 relative error = 0.013263219665082243498284191381224 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5089 x2[1] (analytic) = 0.0008337670345538322739559478450075 x2[1] (numeric) = 0.00083385505919799055203996605066985 absolute error = 8.802464415827808401820566235e-08 relative error = 0.010557462757613351256061212995645 % h = 0.0001 x1[1] (analytic) = 0.0012820816772876561482097310870861 x1[1] (numeric) = 0.0012819077189732727229614357642837 absolute error = 1.739583143834252482953228024e-07 relative error = 0.013568426837785221251632817565562 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.509 x2[1] (analytic) = 0.00083385969584772302873516249155556 x2[1] (numeric) = 0.00083394972767691897531689647833109 absolute error = 9.003182919594658173398677553e-08 relative error = 0.010796999740396126055975532457993 % h = 0.0001 x1[1] (analytic) = 0.001281973474530155426595559729063 x1[1] (numeric) = 0.0012817955731118294263966560276631 absolute error = 1.779014183260001989037013999e-07 relative error = 0.013877152831980493857550551365371 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5091 x2[1] (analytic) = 0.00083395238108613432007936664709021 x2[1] (numeric) = 0.00083404444313350565868311655734097 absolute error = 9.206204737133860374991025076e-08 relative error = 0.01103924510071397290494881102244 % h = 0.0001 x1[1] (analytic) = 0.0012818652825923894592993882610856 x1[1] (numeric) = 0.0012816833936098078359520345539655 absolute error = 1.818889825816233473537071201e-07 relative error = 0.014189399233418574008702053816987 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=64.8MB, alloc=4.6MB, time=4.26 t[1] = 0.5092 x2[1] (analytic) = 0.00083404509027331451722845383237174 x2[1] (numeric) = 0.00083413920558555838596220803325458 absolute error = 9.411531224386873375420088284e-08 relative error = 0.011284199540462180318943100406113 % h = 0.0001 x1[1] (analytic) = 0.0012817571014732763269426554107106 x1[1] (numeric) = 0.0012815711804571180326421396296326 absolute error = 1.859210161582943005157810780e-07 relative error = 0.014505167628452621769166655200607 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5093 x2[1] (analytic) = 0.00083413782341351289327981259343914 x2[1] (numeric) = 0.00083423401505089102569617080157157 absolute error = 9.619163737813241635820813243e-08 relative error = 0.011531863761373481426398096059758 % h = 0.0001 x1[1] (analytic) = 0.0012816489311717342183333283450442 x1[1] (numeric) = 0.0012814589336436670712862244757688 absolute error = 1.899975280671470471038692754e-07 relative error = 0.01482445960403866456942673114313 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5094 x2[1] (analytic) = 0.00083423058051097962536370648205495 x2[1] (numeric) = 0.00083432887154732353311912989642112 absolute error = 9.829103634390775542341436617e-08 relative error = 0.011782238465018019053605871316659 % h = 0.0001 x1[1] (analytic) = 0.0012815407716866814304550845588136 x1[1] (numeric) = 0.0012813466531593589796006235501486 absolute error = 1.941185273224508544610086650e-07 relative error = 0.015147276747735817280109455426686 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5095 x2[1] (analytic) = 0.00083432336156996579481868965658664 x2[1] (numeric) = 0.00083442377509268195213166418788603 absolute error = 1.0041352271615731297453129939e-07 relative error = 0.012035324352803310857799245032527 % h = 0.0001 x1[1] (analytic) = 0.0012814326230170363684564948441937 x1[1] (numeric) = 0.001281234338994094757290876648732 absolute error = 1.982840229416111656181954617e-07 relative error = 0.015473620647706502364509563288243 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5096 x2[1] (analytic) = 0.0008344161665947233873670581103952 x2[1] (numeric) = 0.0008345187257047984172757569803781 absolute error = 1.0255911007502990869886998290e-07 relative error = 0.012291122125974214507950241104234 % h = 0.0001 x1[1] (analytic) = 0.0012813244851617175456402073422847 x1[1] (numeric) = 0.0012811219911377723751435807250531 absolute error = 2.024940239451704966266172316e-07 relative error = 0.015803492892716670109920768981159 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5097 x2[1] (analytic) = 0.00083450899558950529329033653480331 x2[1] (numeric) = 0.0008346137234015111557103687045358 absolute error = 1.0472781200586242003216973249e-07 relative error = 0.012549632485612892913275080658243 % h = 0.0001 x1[1] (analytic) = 0.0012812163581196435834521326761291 x1[1] (numeric) = 0.0012810096095802867741179693458218 absolute error = 2.067485393568093341633303073e-07 relative error = 0.016136895072136018937803490335663 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.6MB, time=4.51 NO POLE NO POLE t[1] = 0.5098 x2[1] (analytic) = 0.00083460184855856530760480082371625 x2[1] (numeric) = 0.0008347087682006644891876318951742 absolute error = 1.0691964209918158283107145795e-07 relative error = 0.012810856132638779499442130233887 % h = 0.0001 x1[1] (analytic) = 0.0012811082418897332114706301651619 x1[1] (numeric) = 0.0012808971943115298644372197010548 absolute error = 2.110475782033470334104641071e-07 relative error = 0.016473828775938215792816542874286 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5099 x2[1] (analytic) = 0.00083469472550615813023703622697089 x2[1] (numeric) = 0.00083480386012010883602966864787603 absolute error = 1.0913461395070579263242090514e-07 relative error = 0.013074793767808543532479211652419 % h = 0.0001 x1[1] (analytic) = 0.0012810001364709052673956951209852 x1[1] (numeric) = 0.0012807847453213905246794870870271 absolute error = 2.153911495147427162080339581e-07 relative error = 0.016814295594701116610740475344957 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.51 x2[1] (analytic) = 0.00083478762643653936619953115948893 x2[1] (numeric) = 0.00083489899917770071310603074687174 absolute error = 1.1137274116134690649958738281e-07 relative error = 0.013341446091716055490376661808917 % h = 0.0001 x1[1] (analytic) = 0.0012808920418620786970381472243591 x1[1] (numeric) = 0.0012806722625997546008686667803114 absolute error = 2.197792623240961694804440477e-07 relative error = 0.017158297119606986865320228007574 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( x2 , t , 2 ) = 3.0 * diff (x2 , t , 1) - 2.0 * diff ( x2 , t , 0 ) - diff (x1 ,t , 2 ) - diff ( x1 , t , 1 ) + diff ( x1 , t , 0 ); diff ( x1 , t , 1 ) = 4.0 * diff ( x2 , t , 0 ) - 2.0 * diff ( x2 , t , 1 )- 2.0 * diff ( x1 , t , 0 ); Iterations = 100 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Expected Time Remaining = 33 Minutes 53 Seconds Optimized Time Remaining = 33 Minutes 48 Seconds Time to Timeout = 14 Minutes 55 Seconds Percent Done = 0.2244 % > quit memory used=70.4MB, alloc=4.6MB, time=4.62