|\^/| 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 > INFO, > ALWAYS, > DEBUGMASSIVE, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_max_iter, > glob_hmin_init, > sec_in_min, > glob_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_warned2, > glob_max_trunc_err, > glob_max_order, > glob_max_rel_trunc_err, > glob_dump, > glob_html_log, > glob_log10abserr, > glob_relerr, > glob_hmax, > years_in_century, > days_in_year, > glob_normmax, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_log10_relerr, > glob_log10_abserr, > glob_not_yet_start_msg, > centuries_in_millinium, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_last_good_h, > glob_clock_sec, > djd_debug, > glob_percent_done, > glob_smallish_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_disp_incr, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > glob_look_poles, > glob_log10normmin, > glob_max_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > min_in_hour, > glob_current_iter, > glob_no_eqs, > glob_almost_1, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_t, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1_init, > array_1st_rel_error, > array_x2_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_x2, > array_x1, > array_last_rel_error, > array_x1_higher, > array_x2_higher, > array_poles, > array_real_pole, > array_x1_higher_work2, > array_x1_higher_work, > array_x2_higher_work2, > array_x2_higher_work, > array_complex_pole, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order, glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr, glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr, glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium, glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h, glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass, glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin, glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour, glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init, array_1st_rel_error, array_x2_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1, array_last_rel_error, array_x1_higher, array_x2_higher, array_poles, array_real_pole, array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2, array_x2_higher_work, array_complex_pole, glob_last; if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > INFO, > ALWAYS, > DEBUGMASSIVE, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_max_iter, > glob_hmin_init, > sec_in_min, > glob_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_warned2, > glob_max_trunc_err, > glob_max_order, > glob_max_rel_trunc_err, > glob_dump, > glob_html_log, > glob_log10abserr, > glob_relerr, > glob_hmax, > years_in_century, > days_in_year, > glob_normmax, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_log10_relerr, > glob_log10_abserr, > glob_not_yet_start_msg, > centuries_in_millinium, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_last_good_h, > glob_clock_sec, > djd_debug, > glob_percent_done, > glob_smallish_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_disp_incr, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > glob_look_poles, > glob_log10normmin, > glob_max_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > min_in_hour, > glob_current_iter, > glob_no_eqs, > glob_almost_1, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_t, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1_init, > array_1st_rel_error, > array_x2_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_x2, > array_x1, > array_last_rel_error, > array_x1_higher, > array_x2_higher, > array_poles, > array_real_pole, > array_x1_higher_work2, > array_x1_higher_work, > array_x2_higher_work2, > array_x2_higher_work, > array_complex_pole, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_x1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_t[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order, glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr, glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr, glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium, glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h, glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass, glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin, glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour, glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init, array_1st_rel_error, array_x2_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1, array_last_rel_error, array_x1_higher, array_x2_higher, array_poles, array_real_pole, array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2, array_x2_higher_work, array_complex_pole, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_t[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(t_start,t_end) > global > INFO, > ALWAYS, > DEBUGMASSIVE, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_max_iter, > glob_hmin_init, > sec_in_min, > glob_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_warned2, > glob_max_trunc_err, > glob_max_order, > glob_max_rel_trunc_err, > glob_dump, > glob_html_log, > glob_log10abserr, > glob_relerr, > glob_hmax, > years_in_century, > days_in_year, > glob_normmax, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_log10_relerr, > glob_log10_abserr, > glob_not_yet_start_msg, > centuries_in_millinium, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_last_good_h, > glob_clock_sec, > djd_debug, > glob_percent_done, > glob_smallish_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_disp_incr, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > glob_look_poles, > glob_log10normmin, > glob_max_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > min_in_hour, > glob_current_iter, > glob_no_eqs, > glob_almost_1, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_t, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1_init, > array_1st_rel_error, > array_x2_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_x2, > array_x1, > array_last_rel_error, > array_x1_higher, > array_x2_higher, > array_poles, > array_real_pole, > array_x1_higher_work2, > array_x1_higher_work, > array_x2_higher_work2, > array_x2_higher_work, > array_complex_pole, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order, glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr, glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr, glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium, glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h, glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass, glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin, glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour, glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init, array_1st_rel_error, array_x2_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1, array_last_rel_error, array_x1_higher, array_x2_higher, array_poles, array_real_pole, array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2, array_x2_higher_work, array_complex_pole, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > ALWAYS, > DEBUGMASSIVE, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_max_iter, > glob_hmin_init, > sec_in_min, > glob_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_warned2, > glob_max_trunc_err, > glob_max_order, > glob_max_rel_trunc_err, > glob_dump, > glob_html_log, > glob_log10abserr, > glob_relerr, > glob_hmax, > years_in_century, > days_in_year, > glob_normmax, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_log10_relerr, > glob_log10_abserr, > glob_not_yet_start_msg, > centuries_in_millinium, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_last_good_h, > glob_clock_sec, > djd_debug, > glob_percent_done, > glob_smallish_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_disp_incr, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > glob_look_poles, > glob_log10normmin, > glob_max_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > min_in_hour, > glob_current_iter, > glob_no_eqs, > glob_almost_1, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_t, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1_init, > array_1st_rel_error, > array_x2_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_x2, > array_x1, > array_last_rel_error, > array_x1_higher, > array_x2_higher, > array_poles, > array_real_pole, > array_x1_higher_work2, > array_x1_higher_work, > array_x2_higher_work2, > array_x2_higher_work, > array_complex_pole, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1]; > rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1]; > rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order, glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr, glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr, glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium, glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h, glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass, glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin, glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour, glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init, array_1st_rel_error, array_x2_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1, array_last_rel_error, array_x1_higher, array_x2_higher, array_poles, array_real_pole, array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2, array_x2_higher_work, array_complex_pole, glob_last; n := glob_max_terms; m := n - 3; while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or abs(array_x2_higher[1, m - 1]) < glob_small_float or abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or abs(array_x1_higher[1, m - 1]) < glob_small_float or abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_x2_higher[1, m]) or glob_large_float <= abs(array_x2_higher[1, m - 1]) or glob_large_float <= abs(array_x2_higher[1, m - 2]) or glob_large_float <= abs(array_x2_higher[1, m - 3]) or glob_large_float <= abs(array_x2_higher[1, m - 4]) or glob_large_float <= abs(array_x2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_x1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_x1_higher[1, m]) or glob_large_float <= abs(array_x1_higher[1, m - 1]) or glob_large_float <= abs(array_x1_higher[1, m - 2]) or glob_large_float <= abs(array_x1_higher[1, m - 3]) or glob_large_float <= abs(array_x1_higher[1, m - 4]) or glob_large_float <= abs(array_x1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > INFO, > ALWAYS, > DEBUGMASSIVE, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_max_iter, > glob_hmin_init, > sec_in_min, > glob_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_warned2, > glob_max_trunc_err, > glob_max_order, > glob_max_rel_trunc_err, > glob_dump, > glob_html_log, > glob_log10abserr, > glob_relerr, > glob_hmax, > years_in_century, > days_in_year, > glob_normmax, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_log10_relerr, > glob_log10_abserr, > glob_not_yet_start_msg, > centuries_in_millinium, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_last_good_h, > glob_clock_sec, > djd_debug, > glob_percent_done, > glob_smallish_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_disp_incr, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > glob_look_poles, > glob_log10normmin, > glob_max_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > min_in_hour, > glob_current_iter, > glob_no_eqs, > glob_almost_1, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_t, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1_init, > array_1st_rel_error, > array_x2_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_x2, > array_x1, > array_last_rel_error, > array_x1_higher, > array_x2_higher, > array_poles, > array_real_pole, > array_x1_higher_work2, > array_x1_higher_work, > array_x2_higher_work2, > array_x2_higher_work, > array_complex_pole, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_x1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order, glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr, glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr, glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium, glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h, glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass, glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin, glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour, glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init, array_1st_rel_error, array_x2_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1, array_last_rel_error, array_x1_higher, array_x2_higher, array_poles, array_real_pole, array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2, array_x2_higher_work, array_complex_pole, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x2[iii]) then array_norms[iii] := abs(array_x2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x1[iii]) then array_norms[iii] := abs(array_x1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > INFO, > ALWAYS, > DEBUGMASSIVE, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_max_iter, > glob_hmin_init, > sec_in_min, > glob_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_warned2, > glob_max_trunc_err, > glob_max_order, > glob_max_rel_trunc_err, > glob_dump, > glob_html_log, > glob_log10abserr, > glob_relerr, > glob_hmax, > years_in_century, > days_in_year, > glob_normmax, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_log10_relerr, > glob_log10_abserr, > glob_not_yet_start_msg, > centuries_in_millinium, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_last_good_h, > glob_clock_sec, > djd_debug, > glob_percent_done, > glob_smallish_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_disp_incr, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > glob_look_poles, > glob_log10normmin, > glob_max_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > min_in_hour, > glob_current_iter, > glob_no_eqs, > glob_almost_1, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_t, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1_init, > array_1st_rel_error, > array_x2_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_x2, > array_x1, > array_last_rel_error, > array_x1_higher, > array_x2_higher, > array_poles, > array_real_pole, > array_x1_higher_work2, > array_x1_higher_work, > array_x2_higher_work2, > array_x2_higher_work, > array_complex_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp4[1] := (array_const_2D0[1] * (array_x2[1])); > #emit pre sub $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp6[1] := array_x1_higher[3,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1])); > #emit pre diff $eq_no = 1 i = 1 > array_tmp8[1] := array_x1_higher[2,1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp10[1] := array_tmp9[1] + array_x1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2); > array_x2[3] := temporary; > array_x2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,2] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,1] := temporary > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult $eq_no = 2 i = 1 > array_tmp12[1] := (array_const_4D0[1] * (array_x2[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp13[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1])); > # emit pre mult $eq_no = 2 i = 1 > array_tmp16[1] := (array_const_2D0[1] * (array_x1[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_x1[2] := temporary; > array_x1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,1] := temporary > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp4[2] := ats(2,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp6[2] := array_x1_higher[3,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2])); > #emit pre diff $eq_no = 1 i = 2 > array_tmp8[2] := array_x1_higher[2,2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2])); > #emit pre add $eq_no = 1 i = 2 > array_tmp10[2] := array_tmp9[2] + array_x1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3); > array_x2[4] := temporary; > array_x2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,2] := temporary > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult $eq_no = 2 i = 2 > array_tmp12[2] := ats(2,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 2 > array_tmp13[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2])); > # emit pre mult $eq_no = 2 i = 2 > array_tmp16[2] := ats(2,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2])); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_x1[3] := temporary; > array_x1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,2] := temporary > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp4[3] := ats(3,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp6[3] := array_x1_higher[3,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3])); > #emit pre diff $eq_no = 1 i = 3 > array_tmp8[3] := array_x1_higher[2,3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3])); > #emit pre add $eq_no = 1 i = 3 > array_tmp10[3] := array_tmp9[3] + array_x1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4); > array_x2[5] := temporary; > array_x2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,3] := temporary > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult $eq_no = 2 i = 3 > array_tmp12[3] := ats(3,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 3 > array_tmp13[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3])); > # emit pre mult $eq_no = 2 i = 3 > array_tmp16[3] := ats(3,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3])); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_x1[4] := temporary; > array_x1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,3] := temporary > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp4[4] := ats(4,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp6[4] := array_x1_higher[3,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4])); > #emit pre diff $eq_no = 1 i = 4 > array_tmp8[4] := array_x1_higher[2,4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4])); > #emit pre add $eq_no = 1 i = 4 > array_tmp10[4] := array_tmp9[4] + array_x1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5); > array_x2[6] := temporary; > array_x2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,4] := temporary > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult $eq_no = 2 i = 4 > array_tmp12[4] := ats(4,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 4 > array_tmp13[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4])); > # emit pre mult $eq_no = 2 i = 4 > array_tmp16[4] := ats(4,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4])); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_x1[5] := temporary; > array_x1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,4] := temporary > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp4[5] := ats(5,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp6[5] := array_x1_higher[3,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5])); > #emit pre diff $eq_no = 1 i = 5 > array_tmp8[5] := array_x1_higher[2,5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5])); > #emit pre add $eq_no = 1 i = 5 > array_tmp10[5] := array_tmp9[5] + array_x1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6); > array_x2[7] := temporary; > array_x2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_x2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_x2_higher[3,5] := temporary > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult $eq_no = 2 i = 5 > array_tmp12[5] := ats(5,array_const_4D0,array_x2,1); > #emit pre diff $eq_no = 2 i = 5 > array_tmp13[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5])); > # emit pre mult $eq_no = 2 i = 5 > array_tmp16[5] := ats(5,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5])); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_x1[6] := temporary; > array_x1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_x1_higher[2,5] := temporary > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 1 > array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1); > #emit add $eq_no = 1 > array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; > #emit mult $eq_no = 1 > array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1); > #emit sub $eq_no = 1 > array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk])); > #emit diff $eq_no = 1 > array_tmp6[kkk] := array_x1_higher[3,kkk]; > #emit sub $eq_no = 1 > array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk])); > #emit diff $eq_no = 1 > array_tmp8[kkk] := array_x1_higher[2,kkk]; > #emit sub $eq_no = 1 > array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk])); > #emit add $eq_no = 1 > array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x2[kkk + order_d] := temporary; > array_x2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_x2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 1 > ; > #emit mult $eq_no = 2 > array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1); > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 2 > array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1); > #emit sub $eq_no = 2 > array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk])); > #emit mult $eq_no = 2 > array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1); > #emit sub $eq_no = 2 > array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk])); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_x1[kkk + order_d] := temporary; > array_x1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_x1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order, glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr, glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr, glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium, glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h, glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass, glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin, glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour, glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init, array_1st_rel_error, array_x2_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1, array_last_rel_error, array_x1_higher, array_x2_higher, array_poles, array_real_pole, array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2, array_x2_higher_work, array_complex_pole, glob_last; array_tmp1[1] := array_x2_higher[2, 1]; array_tmp2[1] := array_const_3D0[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; array_tmp4[1] := array_const_2D0[1]*array_x2[1]; array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; array_tmp6[1] := array_x1_higher[3, 1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; array_tmp8[1] := array_x1_higher[2, 1]; array_tmp9[1] := array_tmp7[1] - array_tmp8[1]; array_tmp10[1] := array_tmp9[1] + array_x1[1]; if 1 <= glob_max_terms then temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2); array_x2[3] := temporary; array_x2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 2] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 1] := temporary end if; kkk := 2; array_tmp12[1] := array_const_4D0[1]*array_x2[1]; array_tmp13[1] := array_x2_higher[2, 1]; array_tmp14[1] := array_const_2D0[1]*array_tmp13[1]; array_tmp15[1] := array_tmp12[1] - array_tmp14[1]; array_tmp16[1] := array_const_2D0[1]*array_x1[1]; array_tmp17[1] := array_tmp15[1] - array_tmp16[1]; if 1 <= glob_max_terms then temporary := array_tmp17[1]*glob_h*factorial_3(0, 1); array_x1[2] := temporary; array_x1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 1] := temporary end if; kkk := 2; array_tmp1[2] := array_x2_higher[2, 2]; array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1); array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1); array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; array_tmp6[2] := array_x1_higher[3, 2]; array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; array_tmp8[2] := array_x1_higher[2, 2]; array_tmp9[2] := array_tmp7[2] - array_tmp8[2]; array_tmp10[2] := array_tmp9[2] + array_x1[2]; if 2 <= glob_max_terms then temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3); array_x2[4] := temporary; array_x2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 2] := temporary end if; kkk := 3; array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1); array_tmp13[2] := array_x2_higher[2, 2]; array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1); array_tmp15[2] := array_tmp12[2] - array_tmp14[2]; array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1); array_tmp17[2] := array_tmp15[2] - array_tmp16[2]; if 2 <= glob_max_terms then temporary := array_tmp17[2]*glob_h*factorial_3(1, 2); array_x1[3] := temporary; array_x1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 2] := temporary end if; kkk := 3; array_tmp1[3] := array_x2_higher[2, 3]; array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1); array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1); array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; array_tmp6[3] := array_x1_higher[3, 3]; array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; array_tmp8[3] := array_x1_higher[2, 3]; array_tmp9[3] := array_tmp7[3] - array_tmp8[3]; array_tmp10[3] := array_tmp9[3] + array_x1[3]; if 3 <= glob_max_terms then temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4); array_x2[5] := temporary; array_x2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 3] := temporary end if; kkk := 4; array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1); array_tmp13[3] := array_x2_higher[2, 3]; array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1); array_tmp15[3] := array_tmp12[3] - array_tmp14[3]; array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1); array_tmp17[3] := array_tmp15[3] - array_tmp16[3]; if 3 <= glob_max_terms then temporary := array_tmp17[3]*glob_h*factorial_3(2, 3); array_x1[4] := temporary; array_x1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 3] := temporary end if; kkk := 4; array_tmp1[4] := array_x2_higher[2, 4]; array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1); array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1); array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; array_tmp6[4] := array_x1_higher[3, 4]; array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; array_tmp8[4] := array_x1_higher[2, 4]; array_tmp9[4] := array_tmp7[4] - array_tmp8[4]; array_tmp10[4] := array_tmp9[4] + array_x1[4]; if 4 <= glob_max_terms then temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5); array_x2[6] := temporary; array_x2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 4] := temporary end if; kkk := 5; array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1); array_tmp13[4] := array_x2_higher[2, 4]; array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1); array_tmp15[4] := array_tmp12[4] - array_tmp14[4]; array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1); array_tmp17[4] := array_tmp15[4] - array_tmp16[4]; if 4 <= glob_max_terms then temporary := array_tmp17[4]*glob_h*factorial_3(3, 4); array_x1[5] := temporary; array_x1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 4] := temporary end if; kkk := 5; array_tmp1[5] := array_x2_higher[2, 5]; array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1); array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1); array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; array_tmp6[5] := array_x1_higher[3, 5]; array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; array_tmp8[5] := array_x1_higher[2, 5]; array_tmp9[5] := array_tmp7[5] - array_tmp8[5]; array_tmp10[5] := array_tmp9[5] + array_x1[5]; if 5 <= glob_max_terms then temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6); array_x2[7] := temporary; array_x2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_x2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_x2_higher[3, 5] := temporary end if; kkk := 6; array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1); array_tmp13[5] := array_x2_higher[2, 5]; array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1); array_tmp15[5] := array_tmp12[5] - array_tmp14[5]; array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1); array_tmp17[5] := array_tmp15[5] - array_tmp16[5]; if 5 <= glob_max_terms then temporary := array_tmp17[5]*glob_h*factorial_3(4, 5); array_x1[6] := temporary; array_x1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_x1_higher[2, 5] := temporary end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_x2_higher[2, kkk]; array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1); array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1); array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := array_x1_higher[3, kkk]; array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; array_tmp8[kkk] := array_x1_higher[2, kkk]; array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk]; array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp10[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x2[kkk + order_d] := temporary; array_x2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_x2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1); array_tmp13[kkk] := array_x2_higher[2, kkk]; array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1); array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk]; array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1); array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp17[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_x1[kkk + order_d] := temporary; array_x1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_x1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_x1 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c1 + 6.0 * c3 * exp(-t); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > c1 + c2 * exp(2.0 * t) + c3 * exp(-t); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 0.0001; > c2 := 0.0002; > c3 := 0.0003; > 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c2*exp(2.0*t) - c3*exp(-t) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > t_start,t_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > INFO, > ALWAYS, > DEBUGMASSIVE, > glob_iolevel, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_start, > glob_max_iter, > glob_hmin_init, > sec_in_min, > glob_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_h, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_warned2, > glob_max_trunc_err, > glob_max_order, > glob_max_rel_trunc_err, > glob_dump, > glob_html_log, > glob_log10abserr, > glob_relerr, > glob_hmax, > years_in_century, > days_in_year, > glob_normmax, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_log10_relerr, > glob_log10_abserr, > glob_not_yet_start_msg, > centuries_in_millinium, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_last_good_h, > glob_clock_sec, > djd_debug, > glob_percent_done, > glob_smallish_float, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_disp_incr, > glob_initial_pass, > glob_max_minutes, > glob_log10relerr, > glob_look_poles, > glob_log10normmin, > glob_max_sec, > glob_reached_optimal_h, > glob_not_yet_finished, > min_in_hour, > glob_current_iter, > glob_no_eqs, > glob_almost_1, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_1, > array_const_2, > array_const_4D0, > array_const_0D0, > #END CONST > array_t, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1_init, > array_1st_rel_error, > array_x2_init, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_x2, > array_x1, > array_last_rel_error, > array_x1_higher, > array_x2_higher, > array_poles, > array_real_pole, > array_x1_higher_work2, > array_x1_higher_work, > array_x2_higher_work2, > array_x2_higher_work, > array_complex_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > ALWAYS := 1; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGL := 3; > glob_start := 0; > glob_max_iter := 1000; > glob_hmin_init := 0.001; > sec_in_min := 60.0; > glob_iter := 0; > glob_unchanged_h_cnt := 0; > glob_dump_analytic := false; > glob_hmin := 0.00000000001; > glob_optimal_done := false; > glob_max_opt_iter := 10; > glob_optimal_expect_sec := 0.1; > glob_h := 0.1; > glob_clock_start_sec := 0.0; > hours_in_day := 24.0; > djd_debug2 := true; > glob_warned2 := false; > glob_max_trunc_err := 0.1e-10; > glob_max_order := 30; > glob_max_rel_trunc_err := 0.1e-10; > glob_dump := false; > glob_html_log := true; > glob_log10abserr := 0.0; > glob_relerr := 0.1e-10; > glob_hmax := 1.0; > years_in_century := 100.0; > days_in_year := 365.0; > glob_normmax := 0.0; > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_log10_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_not_yet_start_msg := true; > centuries_in_millinium := 10.0; > glob_orig_start_sec := 0.0; > glob_warned := false; > glob_small_float := 0.1e-50; > glob_last_good_h := 0.1; > glob_clock_sec := 0.0; > djd_debug := true; > glob_percent_done := 0.0; > glob_smallish_float := 0.1e-100; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_hours := 0.0; > glob_abserr := 0.1e-10; > glob_large_float := 9.0e100; > glob_disp_incr := 0.1; > glob_initial_pass := true; > glob_max_minutes := 0.0; > glob_log10relerr := 0.0; > glob_look_poles := false; > glob_log10normmin := 0.1; > glob_max_sec := 10000.0; > glob_reached_optimal_h := false; > glob_not_yet_finished := true; > min_in_hour := 60.0; > glob_current_iter := 0; > glob_no_eqs := 0; > glob_almost_1 := 0.9990; > glob_display_flag := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_max_order := 2; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/complicatedrev2postode.ode#################"); > omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"t_start := 0.5;"); > omniout_str(ALWAYS,"t_end := 5.0;"); > omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.00005 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_x1 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_t:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_tmp10:= Array(1..(max_terms + 1),[]); > array_tmp11:= Array(1..(max_terms + 1),[]); > array_tmp12:= Array(1..(max_terms + 1),[]); > array_tmp13:= Array(1..(max_terms + 1),[]); > array_tmp14:= Array(1..(max_terms + 1),[]); > array_tmp15:= Array(1..(max_terms + 1),[]); > array_tmp16:= Array(1..(max_terms + 1),[]); > array_tmp17:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_x2_init:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_tmp7:= Array(1..(max_terms + 1),[]); > array_tmp8:= Array(1..(max_terms + 1),[]); > array_tmp9:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_x1:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher_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_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_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_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > t_start := 0.5; > t_end := 5.0; > array_x1_init[1] := exact_soln_x1(t_start); > array_x2_init[1] := exact_soln_x2(t_start); > array_x2_init[2] := exact_soln_x2p(t_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00005 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_x2(); > if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_x1(); > if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_x1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > sub_iter := 1; > while sub_iter <= 3 do # do number 3 > atomall() > ; > sub_iter := sub_iter + 1; > od;# end do number 3 > ; > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3 > ;#was right paren 0004C > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > order_diff := 2; > #Jump Series array_x2 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > order_diff := 2; > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 3; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > order_diff := 2; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > order_diff := 2; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > order_diff := 1; > #Jump Series array_x1 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > order_diff := 1; > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > order_diff := 1; > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > order_diff := 1; > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_x1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 3 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 3 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if glob_html_log then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-02T02:11:49-05:00") > ; > 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 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 4 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 4 > ; > log_revs(html_log_file," 076 ") > ; > logitem_str(html_log_file,"complicatedrev2 diffeq.mxt") > ; > logitem_str(html_log_file,"complicatedrev2 maple results") > ; > logitem_str(html_log_file,"sub iter tot order eqs reversed") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 4 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 4 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 3 > ; > if glob_html_log then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp; global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL, glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec, hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order, glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr, glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr, glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium, glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h, glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass, glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin, glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour, glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag, array_const_2D0, array_const_3D0, array_const_1, array_const_2, array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init, array_1st_rel_error, array_x2_init, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1, array_last_rel_error, array_x1_higher, array_x2_higher, array_poles, array_real_pole, array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2, array_x2_higher_work, array_complex_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; ALWAYS := 1; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_max_terms := 30; DEBUGL := 3; glob_start := 0; glob_max_iter := 1000; glob_hmin_init := 0.001; sec_in_min := 60.0; glob_iter := 0; glob_unchanged_h_cnt := 0; glob_dump_analytic := false; glob_hmin := 0.1*10^(-10); glob_optimal_done := false; glob_max_opt_iter := 10; glob_optimal_expect_sec := 0.1; glob_h := 0.1; glob_clock_start_sec := 0.; hours_in_day := 24.0; djd_debug2 := true; glob_warned2 := false; glob_max_trunc_err := 0.1*10^(-10); glob_max_order := 30; glob_max_rel_trunc_err := 0.1*10^(-10); glob_dump := false; glob_html_log := true; glob_log10abserr := 0.; glob_relerr := 0.1*10^(-10); glob_hmax := 1.0; years_in_century := 100.0; days_in_year := 365.0; glob_normmax := 0.; MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_log10_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_not_yet_start_msg := true; centuries_in_millinium := 10.0; glob_orig_start_sec := 0.; glob_warned := false; glob_small_float := 0.1*10^(-50); glob_last_good_h := 0.1; glob_clock_sec := 0.; djd_debug := true; glob_percent_done := 0.; glob_smallish_float := 0.1*10^(-100); glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_max_hours := 0.; glob_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_disp_incr := 0.1; glob_initial_pass := true; glob_max_minutes := 0.; glob_log10relerr := 0.; glob_look_poles := false; glob_log10normmin := 0.1; glob_max_sec := 10000.0; glob_reached_optimal_h := false; glob_not_yet_finished := true; min_in_hour := 60.0; glob_current_iter := 0; glob_no_eqs := 0; glob_almost_1 := 0.9990; glob_display_flag := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_max_order := 2; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/complicatedrev2postode.ode#################"); omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \ diff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "t_start := 0.5;"); omniout_str(ALWAYS, "t_end := 5.0;"); omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.00005 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_x1 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_t := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_tmp10 := Array(1 .. max_terms + 1, []); array_tmp11 := Array(1 .. max_terms + 1, []); array_tmp12 := Array(1 .. max_terms + 1, []); array_tmp13 := Array(1 .. max_terms + 1, []); array_tmp14 := Array(1 .. max_terms + 1, []); array_tmp15 := Array(1 .. max_terms + 1, []); array_tmp16 := Array(1 .. max_terms + 1, []); array_tmp17 := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_x2_init := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_tmp7 := Array(1 .. max_terms + 1, []); array_tmp8 := Array(1 .. max_terms + 1, []); array_tmp9 := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_x1 := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); term := 1; while term <= max_terms do array_t[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_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_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 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_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1 end do; array_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1 end do; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.00005; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_t[1] := t_start; array_t[2] := glob_h; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x2_higher[r_order, term_no] := array_x2_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_x1_higher[r_order, term_no] := array_x1_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_x2(); if glob_small_float < abs(array_x2_higher[1, 1]) then tmp := abs(array_x2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_x1(); if glob_small_float < abs(array_x1_higher[1, 1]) then tmp := abs(array_x1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_t[1] <= t_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; sub_iter := 1; while sub_iter <= 3 do atomall(); sub_iter := sub_iter + 1 end do; if glob_look_poles then check_for_pole() end if; array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 2; order_diff := 2; order_diff := 2; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 2; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 2; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x2_higher_work[ord, iii]; iii := iii - 1 end do; array_x2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; order_diff := 1; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; order_diff := 1; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; order_diff := 1; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_x1_higher_work[ord, iii]; iii := iii - 1 end do; array_x1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\ ff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(INFO, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-02T02:11:49-05:00"); 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 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 076 "); logitem_str(html_log_file, "complicatedrev2 diffeq.mxt"); logitem_str(html_log_file, "complicatedrev2 maple results"); logitem_str(html_log_file, "sub iter tot order eqs reversed"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/complicatedrev2postode.ode################# diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; #END FIRST INPUT BLOCK ! #BEGIN SECOND INPUT BLOCK t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00005 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c1 + 6.0 * c3 * exp(-t); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2 * exp(2.0 * t) + c3 * exp(-t); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 5e-05 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 5e-05 t[1] = 0.5 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 5e-05 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50005 x2[1] (analytic) = 0.00082566083422809021229815693339498 x2[1] (numeric) = 0.00082566083695768288479862473217238 absolute error = 2.72959267250046779877740e-12 relative error = 3.3059490765991852437183619152925e-07 % h = 5e-05 x1[1] (analytic) = 0.0012917006010880372652167092040327 x1[1] (numeric) = 0.0012917005956294101955839744243888 absolute error = 5.4586270696327347796439e-12 relative error = 4.2259228377185651630693344462209e-07 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5001 x2[1] (analytic) = 0.00082570611074256394598966051590164 x2[1] (numeric) = 0.0008257061216619581905866203014748 absolute error = 1.091939424459695978557316e-11 relative error = 1.3224310808087714609409672985013e-06 % h = 5e-05 x1[1] (analytic) = 0.001291646017422585871235266471237 x1[1] (numeric) = 0.0012916459955876806696845089414704 absolute error = 2.18349052015507575297666e-11 relative error = 1.6904712984073766292123104322750e-06 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50015 x2[1] (analytic) = 0.00082575139314954126995470805844824 x2[1] (numeric) = 0.00082575141772058388848201984275335 absolute error = 2.457104261852731178430511e-11 relative error = 2.9755980822278267259784906914217e-06 % h = 5e-05 x1[1] (analytic) = 0.0012915914364862495213788540506512 x1[1] (numeric) = 0.0012915913873563234520967973558018 absolute error = 4.91299260692820566948494e-11 relative error = 3.8038287248899006888429764192898e-06 % h = 5e-05 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.19 NO POLE NO POLE t[1] = 0.5002 x2[1] (analytic) = 0.0008257966814495432344339416603249 x2[1] (numeric) = 0.00082579672513571924184372022173345 absolute error = 4.368617600740977856140855e-11 relative error = 5.2901854643840724902673898864862e-06 % h = 5e-05 x1[1] (analytic) = 0.0012915368582788917633066026400632 x1[1] (numeric) = 0.0012915367709341102289641324488217 absolute error = 8.73447815343424701912415e-11 relative error = 6.7628562804423984205663586989851e-06 % h = 5e-05 TOP MAIN SOLVE Loop Real estimate of pole used Real estimate of pole used Radius of convergence = 9.350e-05 Order of pole = 16.66 t[1] = 0.50025 x2[1] (analytic) = 0.00082584197564309094518702663178858 x2[1] (numeric) = 0.00082584204390952388351643390389363 absolute error = 6.826643293832940727210505e-11 relative error = 8.2662827697962060206482364727461e-06 % h = 5e-05 x1[1] (analytic) = 0.0012914822828003761515000894181426 x1[1] (numeric) = 0.0012914821463198125022053129662058 absolute error = 1.364805636492947764519368e-10 relative error = 1.0567745718768835573366335286247e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003 x2[1] (analytic) = 0.00082588727573070556349803310856235 x2[1] (numeric) = 0.00082588737404415781589066880464538 absolute error = 9.831345225239263569608303e-11 relative error = 1.1903979531033408280222606045950e-05 % h = 5e-05 x1[1] (analytic) = 0.0012914277100505662472629969306448 x1[1] (numeric) = 0.0012914275135122015894870119253148 absolute error = 1.965383646577759850053300e-10 relative error = 1.5218688830060837488250530272266e-05 % h = 5e-05 TOP MAIN SOLVE Loop Real estimate of pole used NO POLE Radius of convergence = 2.209e-05 Order of pole = 14.49 t[1] = 0.50035 x2[1] (analytic) = 0.00082593258171290830618081821305085 x2[1] (numeric) = 0.00082593271554178141096271953900157 absolute error = 1.3382887310478190132595072e-10 relative error = 1.6203365270714119513613392729942e-05 % h = 5e-05 x1[1] (analytic) = 0.0012913731400293256187207719936699 x1[1] (numeric) = 0.0012913728725100486241959736067518 absolute error = 2.675192769945247983869181e-10 relative error = 2.0715877441004366805546748571025e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5004 x2[1] (analytic) = 0.00082597789359022044558440876232671 x2[1] (numeric) = 0.00082597806840455541039472407880014 absolute error = 1.7481433496481031531647343e-10 relative error = 2.1164529501504822355681136962805e-05 % h = 5e-05 x1[1] (analytic) = 0.0012913185727365178408202846139762 x1[1] (numeric) = 0.0012913182233121245554096702686067 absolute error = 3.494243932854106143453695e-10 relative error = 2.7059503414786521327758974520177e-05 % h = 5e-05 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.43 NO POLE NO POLE t[1] = 0.50045 x2[1] (analytic) = 0.00082602321136316330959838452294175 x2[1] (numeric) = 0.00082602343263464092557510775552467 absolute error = 2.2127147761597672323258292e-10 relative error = 2.6787561726118871435357218524860e-05 % h = 5e-05 x1[1] (analytic) = 0.0012912640081720064953294869263476 x1[1] (numeric) = 0.0012912635659172001478721065182233 absolute error = 4.422548063474573804081243e-10 relative error = 3.4249758651101934136272782037769e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005 x2[1] (analytic) = 0.00082606853503225828165826201261726 x2[1] (numeric) = 0.00082606880823419943767817763089351 absolute error = 2.7320194115601991561827625e-10 relative error = 3.3072551437315219714070518961689e-05 % h = 5e-05 x1[1] (analytic) = 0.0012912094463356551708370721480129 x1[1] (numeric) = 0.0012912089003240459819675880018586 absolute error = 5.460116091888694841461543e-10 relative error = 4.2286835086159332170507930775301e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50055 x2[1] (analytic) = 0.00082611386459802680075087884886784 x2[1] (numeric) = 0.00082611419520539279772344960351137 absolute error = 3.3060736599697257075464353e-10 relative error = 4.0019588117897112093437107681065e-05 % h = 5e-05 x1[1] (analytic) = 0.0012911548872273274627521335501181 x1[1] (numeric) = 0.0012911542265314324536875837108666 absolute error = 6.606958950090645498392515e-10 relative error = 5.1170924692688630552235011916403e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006 x2[1] (analytic) = 0.00082615920006099036141977864461309 x2[1] (numeric) = 0.00082615959355038322663631031313428 absolute error = 3.9348939286521653166852119e-10 relative error = 4.7628761240710940221696755323917e-05 % h = 5e-05 x1[1] (analytic) = 0.0012911003308468869733038234462486 x1[1] (numeric) = 0.0012910995445381297746055627577284 absolute error = 7.863087571986982606885202e-10 relative error = 6.0902219479947410241924577104276e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50065 x2[1] (analytic) = 0.0008262045414216705137705964508309 x2[1] (numeric) = 0.00082620500327133331530806540102026 absolute error = 4.6184966280153746895018936e-10 relative error = 5.5900160268645022606672778380011e-05 % h = 5e-05 x1[1] (analytic) = 0.0012910457771941973115410121980021 x1[1] (numeric) = 0.0012910448543429079718493443012584 absolute error = 9.228512893396916678967437e-10 relative error = 7.1480911493727589142713592393058e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=4.4MB, time=0.68 t[1] = 0.5007 x2[1] (analytic) = 0.00082624988868058886347644474630742 x2[1] (numeric) = 0.00082625042437040602465599500090491 absolute error = 5.3568981716117955025459749e-10 relative error = 6.4833874654628385207710841664897e-05 % h = 5e-05 x1[1] (analytic) = 0.0012909912262691220933319472376107 x1[1] (numeric) = 0.001290990155944536888073434395288 absolute error = 1.0703245852052585128423227e-09 relative error = 8.2907192816362095090813207966641e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50075 x2[1] (analytic) = 0.00082629524183826707178329997453724 x2[1] (numeric) = 0.00082629585684976468568341869391415 absolute error = 6.1501149761390011871937691e-10 relative error = 7.4429993841629542776787993177462e-05 % h = 5e-05 x1[1] (analytic) = 0.0012909366780715249413639121076118 x1[1] (numeric) = 0.0012909354493417861814313586884613 absolute error = 1.2287297387599325534191505e-09 relative error = 9.5181255566731540041161526063086e-05 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5008 x2[1] (analytic) = 0.00082634060089522685551538962782877 x2[1] (numeric) = 0.00082634130071157299953976992887908 absolute error = 6.9981634614402438030105031e-10 relative error = 8.4688607262655280948776273498662e-05 % h = 5e-05 x1[1] (analytic) = 0.0012908821326012694851428855175656 x1[1] (numeric) = 0.0012908807345334253255479909745209 absolute error = 1.3980678441595948945430447e-09 relative error = 0.00010830329190027089544853111764657 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50085 x2[1] (analytic) = 0.00082638596585198998708057987866837 x2[1] (numeric) = 0.00082638675595799503758067990951836 absolute error = 7.9010600505050010003084999e-10 relative error = 9.5609804340749439080845370351817e-05 % h = 5e-05 x1[1] (analytic) = 0.0012908275898582193609932004178204 x1[1] (numeric) = 0.0012908260115182236094918775924611 absolute error = 1.5783399957515013228253593e-09 relative error = 0.00012227349400897616884430139243105 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5009 x2[1] (analytic) = 0.00082643133670907829447576375839823 x2[1] (numeric) = 0.00082643222259119524142807094995361 absolute error = 8.8588211694695230719155538e-10 relative error = 0.00010719367448899169384098852769017 % h = 5e-05 x1[1] (analytic) = 0.0012907730498422382120572030903234 x1[1] (numeric) = 0.0012907712802949501377475576759261 absolute error = 1.7695472880743096454143973e-09 relative error = 0.00013709205412141108160910566126488 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50095 x2[1] (analytic) = 0.00082647671346701366129224988326191 x2[1] (numeric) = 0.00082647770061333842303025930002354 absolute error = 9.8714632476173800941676163e-10 relative error = 0.00011944030711049634354565597816647 % h = 5e-05 x1[1] (analytic) = 0.0012907185125531896882949122564762 x1[1] (numeric) = 0.0012907165408623738301878792512308 absolute error = 1.9716908158581070330052454e-09 relative error = 0.0001527591645027137479415628748044 % h = 5e-05 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.5MB, time=0.94 NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652319002658976472206744186286 absolute error = 1.09390027173800091571399100e-09 relative error = 0.00013234979159841109324648006152025 % h = 5e-05 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906617932192634220463111833818 absolute error = 2.1847716740244373670186533e-09 relative error = 0.00016927501745460335502330412088217 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50105 x2[1] (analytic) = 0.0008265674846875133855587774461534 x2[1] (numeric) = 0.0008265686908331148192849458592121 absolute error = 1.20614560143372616841305870e-09 relative error = 0.00014592221733591584056607608391875 % h = 5e-05 x1[1] (analytic) = 0.0012906094461553451502178419190542 x1[1] (numeric) = 0.0012906070373643874638892509694754 absolute error = 2.4087909576863285909495788e-09 relative error = 0.00018663980531538684438050389101978 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5011 x2[1] (analytic) = 0.00082661287915112178821202023981947 x2[1] (numeric) = 0.00082661420303507951000710428092484 absolute error = 1.32388395772179508404110537e-09 relative error = 0.00016015767369622146228290294082126 % h = 5e-05 x1[1] (analytic) = 0.0012905549170462764699083942648711 x1[1] (numeric) = 0.0012905522732965143215883283788502 absolute error = 2.6437497621483200658860209e-09 relative error = 0.000204853720459965594442126232761 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50115 x2[1] (analytic) = 0.00082665827951766534070374927443031 x2[1] (numeric) = 0.00082665972663465013074365240013893 absolute error = 1.44711698479003990312570862e-09 relative error = 0.00017505625004256860166516745596366 % h = 5e-05 x1[1] (analytic) = 0.0012905003906635950827826351381346 x1[1] (numeric) = 0.0012904975010144121762927049393711 absolute error = 2.8896491829064899301987635e-09 relative error = 0.00022391695529984210429509596426505 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5012 x2[1] (analytic) = 0.00082670368578766620467820114309252 x2[1] (numeric) = 0.00082670526163399334597675007057864 absolute error = 1.57584632714129854892748612e-09 relative error = 0.00019061803572822645655375629974239 % h = 5e-05 x1[1] (analytic) = 0.0012904458670071646728838326718726 x1[1] (numeric) = 0.0012904427205168490244013692692221 absolute error = 3.1464903156484824634026505e-09 relative error = 0.000243829702283126678636605016894 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50125 x2[1] (analytic) = 0.00082674909796164659740637187785192 x2[1] (numeric) = 0.00082675080803527619087576698145478 absolute error = 1.71007362959346939510360286e-09 relative error = 0.00020684312009649156819417926823876 % h = 5e-05 x1[1] (analytic) = 0.0012903913460768489310708824436005 x1[1] (numeric) = 0.0012903879318025926775354282535843 absolute error = 3.4142742562535354541900162e-09 relative error = 0.00026459215389454411392376424050123 % h = 5e-05 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.5MB, time=1.19 NO POLE NO POLE t[1] = 0.5013 x2[1] (analytic) = 0.00082679451604012879179140950883443 x2[1] (numeric) = 0.00082679636584066607135745181243016 absolute error = 1.84980053727956604230359573e-09 relative error = 0.0002237315924806866108175076704816 % h = 5e-05 x1[1] (analytic) = 0.0012903368278725115550179667024679 x1[1] (numeric) = 0.0012903331348704107625103940655763 absolute error = 3.6930021007925075726368916e-09 relative error = 0.00028620450265544038572081077920033 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50135 x2[1] (analytic) = 0.00082683994002363511637400717118929 x2[1] (numeric) = 0.00082684193505233076414611087011793 absolute error = 1.99502869564777210369892864e-09 relative error = 0.00024128354220415918197029148226361 % h = 5e-05 x1[1] (analytic) = 0.0012902823123940162492142136134444 x1[1] (numeric) = 0.001290278329719070721308467030834 absolute error = 3.9826749455279057465826104e-09 relative error = 0.00030866694112378933724408140213576 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5014 x2[1] (analytic) = 0.00082688536991268795533779675988916 x2[1] (numeric) = 0.00082688751567243841683379620758055 absolute error = 2.14575975046149599944769139e-09 relative error = 0.00025949905858028059359343882588919 % h = 5e-05 x1[1] (analytic) = 0.0012902277996412267249633565185424 x1[1] (numeric) = 0.0012902235163473398110508143351055 absolute error = 4.2832938869139125421834369e-09 relative error = 0.00033197966189419936910496207858925 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50145 x2[1] (analytic) = 0.00082693080570780974851474313244131 x2[1] (numeric) = 0.00082693310770315754794050322829742 absolute error = 2.30199534779942576009585611e-09 relative error = 0.00027837823091244466385004131129571 % h = 5e-05 x1[1] (analytic) = 0.0012901732896140067003833932150759 x1[1] (numeric) = 0.0012901686947539851039698445742384 absolute error = 4.5948600215964135486408375e-09 relative error = 0.00035614285759792013025102407678215 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5015 x2[1] (analytic) = 0.00082697624740952299139053885956424 x2[1] (numeric) = 0.00082697871114665704697437777606938 absolute error = 2.46373713405558383891650514e-09 relative error = 0.00029792114849406650970212868232588 % h = 5e-05 x1[1] (analytic) = 0.0012901187823122199004062452509559 x1[1] (numeric) = 0.0012901138649377734873814781459362 absolute error = 4.9173744464130247671050197e-09 relative error = 0.00038115672090284921010555706503082 % h = 5e-05 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.6MB, time=1.46 NO POLE NO POLE t[1] = 0.50155 x2[1] (analytic) = 0.00082702169501835023510999952388432 x2[1] (numeric) = 0.00082702432600510617449193271232851 absolute error = 2.63098675593938193318844419e-09 relative error = 0.0003181279006085813402363361106129 % h = 5e-05 x1[1] (analytic) = 0.0012900642777357300567774172370197 x1[1] (numeric) = 0.0012900590268974716636574134826591 absolute error = 5.2508382583931200037543606e-09 relative error = 0.00040702144451353883190570957546355 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5016 x2[1] (analytic) = 0.00082706714853481408648245956670656 x2[1] (numeric) = 0.00082706995228067456215827398232196 absolute error = 2.80374586047567581441561540e-09 relative error = 0.0003389985765294432507384674761872 % h = 5e-05 x1[1] (analytic) = 0.001290009775884400908055656176395 x1[1] (numeric) = 0.0012900041806318461501973891250464 absolute error = 5.5952525547578582670513486e-09 relative error = 0.00043373722117120254723944735107061 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50165 x2[1] (analytic) = 0.00082711260795943720798716868291399 x2[1] (numeric) = 0.00082711558997553221280733617163863 absolute error = 2.98201609500482016748872464e-09 relative error = 0.00036053326552012401751693784238226 % h = 5e-05 x1[1] (analytic) = 0.0012899552767580961996126108108966 x1[1] (numeric) = 0.0012899493261396632794014416352363 absolute error = 5.9506184329202111691756603e-09 relative error = 0.00046130424365372193178153999390187 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5017 x2[1] (analytic) = 0.00082715807329274231777868876405026 x2[1] (numeric) = 0.00082716123909184950050212755454788 absolute error = 3.16579910718272343879049762e-09 relative error = 0.00038273205683411189347507826278361 % h = 5e-05 x1[1] (analytic) = 0.0012899007803566796836324909844552 x1[1] (numeric) = 0.0012898944634196891986421593494593 absolute error = 6.3169369904849903316349959e-09 relative error = 0.00048972270477565328222878646179523 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50175 x2[1] (analytic) = 0.0008272035445352521896922913896394 x2[1] (numeric) = 0.00082720689963179717059498463561962 absolute error = 3.35509654498090269324598022e-09 relative error = 0.00040559503971491040443228606188571 % h = 5e-05 x1[1] (analytic) = 0.0012898462866800151191117270235781 x1[1] (numeric) = 0.0012898395924706898702369319692811 absolute error = 6.6942093252488747950542970e-09 relative error = 0.00051899279738823431443469003635923 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5018 x2[1] (analytic) = 0.00082724902168748965324935586679766 x2[1] (numeric) = 0.00082725257159754633978783618609529 absolute error = 3.54991005668653848031929763e-09 relative error = 0.00042912230339603714619400353435105 % h = 5e-05 x1[1] (analytic) = 0.0012897917957279662718586291348401 x1[1] (numeric) = 0.0012897847132914310714201959908708 absolute error = 7.0824365352004384331439693e-09 relative error = 0.00054911471437939086274379330522984 % h = 5e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.6MB, time=1.72 NO POLE NO POLE t[1] = 0.50185 x2[1] (analytic) = 0.00082729450474997759366276781819127 x2[1] (numeric) = 0.00082729825499126849619247677647961 absolute error = 3.75024129090252970895828834e-09 relative error = 0.00045331393710102258237050808545802 % h = 5e-05 x1[1] (analytic) = 0.0012897373075003969144930468194044 x1[1] (numeric) = 0.0012897298258806783943156759716703 absolute error = 7.4816197185201773708477341e-09 relative error = 0.00058008864867374358052588383897648 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5019 x2[1] (analytic) = 0.00082733999372323895184231831839524 x2[1] (numeric) = 0.00082734394981513549939084980682307 absolute error = 3.95609189654754853148842783e-09 relative error = 0.00047817003004340884294449659385864 % h = 5e-05 x1[1] (analytic) = 0.0012896828219971708264460283045716 x1[1] (numeric) = 0.0012896749302371972459086216338408 absolute error = 7.8917599735805374066707308e-09 relative error = 0.00061191479323261464191028114006243 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50195 x2[1] (analytic) = 0.00082738548860779672440010357870682 x2[1] (numeric) = 0.00082738965607131958049534003616543 absolute error = 4.16746352285609523645745861e-09 relative error = 0.0005036906714267485235874468977786 % h = 5e-05 x1[1] (analytic) = 0.0012896283392181517939594799923581 x1[1] (numeric) = 0.0012896200263597528480180408038615 absolute error = 8.3128583989459414391884966e-09 relative error = 0.00064459334105403444472041578023347 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.502 x2[1] (analytic) = 0.0008274309894041739636559251804687 x2[1] (numeric) = 0.00082743537376199334220907561261066 absolute error = 4.38435781937855315043214196e-09 relative error = 0.00052987595044460348572473905106498 % h = 5e-05 x1[1] (analytic) = 0.0012895738591632036100858259251 x1[1] (numeric) = 0.0012895651142471102372689281876565 absolute error = 8.7449160933728168977374435e-09 relative error = 0.0006781244851727483146089111985958 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50205 x2[1] (analytic) = 0.00082747649611289377764269085695601 x2[1] (numeric) = 0.00082748110288932975888623960550411 absolute error = 4.60677643598124354874854810e-09 relative error = 0.00055672595628054365734951906474069 % h = 5e-05 x1[1] (analytic) = 0.0012895193818321900746876672680847 x1[1] (numeric) = 0.0012895101938980342650644899806252 absolute error = 9.1879341558096231772874595e-09 relative error = 0.00071250841866022321039337918872178 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=30.5MB, alloc=4.6MB, time=1.98 t[1] = 0.5021 x2[1] (analytic) = 0.00082752200873447933011181582388164 x2[1] (numeric) = 0.00082752684345550217659239104118273 absolute error = 4.83472102284648057521730109e-09 relative error = 0.00058424077810814583458528770019382 % h = 5e-05 x1[1] (analytic) = 0.0012894649072249749944374418092067 x1[1] (numeric) = 0.0012894552653112895975583643119514 absolute error = 9.6419136853968790774972553e-09 relative error = 0.00074774533462465443059313969776857 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50215 x2[1] (analytic) = 0.00082756752726945384053862465857453 x2[1] (numeric) = 0.00082757259546268431316479544376956 absolute error = 5.06819323047262617078519503e-09 relative error = 0.00061242050509099248399719681523601 % h = 5e-05 x1[1] (analytic) = 0.0012894104353414221828170834756492 x1[1] (numeric) = 0.0012894003284856407156268375225664 absolute error = 1.01068557814671902459530828e-08 relative error = 0.00078383542621097232116707597715393 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5022 x2[1] (analytic) = 0.0008276130517183405841277537278848 x2[1] (numeric) = 0.00082761835891305025827276488248383 absolute error = 5.30719470967414501115459903e-09 relative error = 0.00064126522638267054565203577550089 % h = 5e-05 x1[1] (analytic) = 0.0012893559661813954601176818675888 x1[1] (numeric) = 0.001289345383419851914841056276141 absolute error = 1.05827615435452766255914478e-08 relative error = 0.00082077888660084898445283585078009 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50225 x2[1] (analytic) = 0.00082765858208166289181855416487103 x2[1] (numeric) = 0.00082766413380877447347800752693827 absolute error = 5.55172711158165945336206724e-09 relative error = 0.00067077503112677023692689020354951 % h = 5e-05 x1[1] (analytic) = 0.0012893014997447586534391418089226 x1[1] (numeric) = 0.0012892904301126873054392355024821 absolute error = 1.10696320713479999063064405e-08 relative error = 0.00085857590901270498930758998869022 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5023 x2[1] (analytic) = 0.00082770411835994415029049539432325 x2[1] (numeric) = 0.00082770992015203179229498671189548 absolute error = 5.80179208764200449131757223e-09 relative error = 0.00070095000845688385706645548223783 % h = 5e-05 x1[1] (analytic) = 0.0012892470360313755966898429150187 x1[1] (numeric) = 0.0012892354685629108122988621727082 absolute error = 1.15674684647843909807423105e-08 relative error = 0.00089722668670171608245055834334565 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50235 x2[1] (analytic) = 0.00082774966055370780196856920717682 x2[1] (numeric) = 0.00082775571794499742025128951295537 absolute error = 6.05739128961828272030577855e-09 relative error = 0.00073179024749660459248898715499189 % h = 5e-05 x1[1] (analytic) = 0.0012891925750411101305862991774863 x1[1] (numeric) = 0.001289180498769286174908894905579 absolute error = 1.20762718239556774042719073e-08 relative error = 0.00093673141295981990100751549251598 % h = 5e-05 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.6MB, time=2.24 NO POLE NO POLE t[1] = 0.5024 x2[1] (analytic) = 0.00082779520866347734502869438387111 x2[1] (numeric) = 0.00082780152718984693494800483464597 absolute error = 6.31852636958991931045077486e-09 relative error = 0.00076329583735952532284087045666596 % h = 5e-05 x1[1] (analytic) = 0.0012891381167738261026528185659675 x1[1] (numeric) = 0.0012891255207305769473419594043536 absolute error = 1.25960432491553108591616139e-08 relative error = 0.00097709028111572268625748617353088 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50245 x2[1] (analytic) = 0.00082784076268977633340312186670805 x2[1] (numeric) = 0.00082784734788875628612011101239014 absolute error = 6.58519897995271698914568209e-09 relative error = 0.00079546686714923742779979099883499 % h = 5e-05 x1[1] (analytic) = 0.0012890836612293873672211626469477 x1[1] (numeric) = 0.0012890705344455464982265397235523 absolute error = 1.31267838408689946229233954e-08 relative error = 0.0010183034845349059985818418804371 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5025 x2[1] (analytic) = 0.00082788632263312837678584048126422 x2[1] (numeric) = 0.00082789318004390179569687292982079 absolute error = 6.85741077341891103244855657e-09 relative error = 0.0008283034259593295946264887147353 % h = 5e-05 x1[1] (analytic) = 0.0012890292084076577854302062195851 x1[1] (numeric) = 0.0012890155399129580107191653649962 absolute error = 1.36684946997747110408545889e-08 relative error = 0.0010603712166196334336160097657627 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50255 x2[1] (analytic) = 0.00082793188849405714063798320691191 x2[1] (numeric) = 0.00082793902365746015786224865291776 absolute error = 7.13516340301722426544600585e-09 relative error = 0.00086180560287338662646507692424887 % h = 5e-05 x1[1] (analytic) = 0.0012889747583085012252255969685576 x1[1] (numeric) = 0.0012889605371315744824765942024995 absolute error = 1.42211769267427490027660581e-08 relative error = 0.0011032936708089573396040048925428 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5026 x2[1] (analytic) = 0.00082797746027308634619323399650282 x2[1] (numeric) = 0.0008279848787316084391153055824393 absolute error = 7.41845852209292207158593648e-09 relative error = 0.00089597348696498825139190846916007 % h = 5e-05 x1[1] (analytic) = 0.001288920310931781561359415133927 x1[1] (numeric) = 0.0012889055261001587256279912345886 absolute error = 1.47848316228357314238993384e-08 relative error = 0.0011470710405787255359559970973248 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50265 x2[1] (analytic) = 0.00082802303797073977046323514526932 x2[1] (numeric) = 0.00082803074526852407833064612612176 absolute error = 7.70729778430786741098085244e-09 relative error = 0.00093080716729770793221297070143657 % h = 5e-05 x1[1] (analytic) = 0.0012888658662773626753898331980192 x1[1] (numeric) = 0.0012888505068174733667471031646224 absolute error = 1.53594598893086427300333968e-08 relative error = 0.0011917035194415880330091236374181 % h = 5e-05 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.6MB, time=2.49 NO POLE NO POLE t[1] = 0.5027 x2[1] (analytic) = 0.00082806862158754124624299520899781 x2[1] (numeric) = 0.00082807662327038488681884289212098 absolute error = 8.00168284364057584768312317e-09 relative error = 0.00096630673292511167700979104131201 % h = 5e-05 x1[1] (analytic) = 0.0012888114243451084556807755893193 x1[1] (numeric) = 0.0012887954792822808468244288076879 absolute error = 1.59450628276088563467816314e-08 relative error = 0.0012371913009470037529917588633377 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50275 x2[1] (analytic) = 0.00082811421112401466211629747152829 x2[1] (numeric) = 0.00082812251273936904838688340516931 absolute error = 8.30161535438627058593364102e-09 relative error = 0.0010024722728907568504338348296439 % h = 5e-05 x1[1] (analytic) = 0.0012887569851348827974015784033818 x1[1] (numeric) = 0.0012887404434933434212393853236452 absolute error = 1.65416415393761621930797366e-08 relative error = 0.0012835345786812472521914522871693 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5028 x2[1] (analytic) = 0.00082815980658068396246110896163522 x2[1] (numeric) = 0.00082816841367765511939862434692228 absolute error = 8.60709697115693751538528706e-09 relative error = 0.0010393038762281909857493769953758 % h = 5e-05 x1[1] (analytic) = 0.0012887025486465496025266491407532 x1[1] (numeric) = 0.0012886853994494231597324702756963 absolute error = 1.71491971264427941788650569e-08 relative error = 0.0013307335462674154443267461982148 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50285 x2[1] (analytic) = 0.0008282054079580731474549900193436 x2[1] (numeric) = 0.0008282143260874220288352553219693 absolute error = 8.91812934888138026530262570e-09 relative error = 0.0010768016319609505976248291439456 % h = 5e-05 x1[1] (analytic) = 0.0012886481148799727798351264619085 x1[1] (numeric) = 0.0012886303471492819463774195138511 absolute error = 1.77677306908334577069480574e-08 relative error = 0.0013787883973654343251230844096569 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5029 x2[1] (analytic) = 0.0008282510152567062730805044117353 x2[1] (numeric) = 0.00082826024997084907835577215098285 absolute error = 9.23471414280527526773924755e-09 relative error = 0.001114965629102559995672503451959 % h = 5e-05 x1[1] (analytic) = 0.0012885936838350162449105399591989 x1[1] (numeric) = 0.0012885752865916814795533608826647 absolute error = 1.83972433347653571790765342e-08 relative error = 0.0014276993256720656980930233687258 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=41.9MB, alloc=4.6MB, time=2.76 t[1] = 0.50295 x2[1] (analytic) = 0.00082829662847710745113062999829971 x2[1] (numeric) = 0.00082830618533011594235745969248093 absolute error = 9.55685300849122682969418122e-09 relative error = 0.0011537959566565300987367948094926 % h = 5e-05 x1[1] (analytic) = 0.0012885392555115439201404699458103 x1[1] (numeric) = 0.0012885202177753832719169637526194 absolute error = 1.90377361606482235061931909e-08 relative error = 0.0014774665249209139015209571245397 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.503 x2[1] (analytic) = 0.0008283422476198008492141699458837 x2[1] (numeric) = 0.00082835213216740266803638419467778 absolute error = 9.88454760181882221424879408e-09 relative error = 0.0011932927036163572499307624719625 % h = 5e-05 x1[1] (analytic) = 0.0012884848299094197347162072617323 x1[1] (numeric) = 0.0012884651406991486503745843745259 absolute error = 1.96892102710843416228872064e-08 relative error = 0.001528090188882432536652567599137 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50305 x2[1] (analytic) = 0.00082838787268531069076116449329504 x2[1] (numeric) = 0.00082839809048488967544789517889809 absolute error = 1.021779957898468673068560305e-08 relative error = 0.0012334559589655220324210925129811 % h = 5e-05 x1[1] (analytic) = 0.0012884304070285076246324130967366 x1[1] (numeric) = 0.001288410055361738756054407056316 absolute error = 2.03516667688685780060404206e-08 relative error = 0.0015795705113639311970892117448033 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5031 x2[1] (analytic) = 0.00082843350367416125502830326561401 x2[1] (numeric) = 0.00082844406028475775756713685603004 absolute error = 1.055661059650253883359041603e-08 relative error = 0.0012742858116774880859614222167988 % h = 5e-05 x1[1] (analytic) = 0.0012883759868686715326867788303632 x1[1] (numeric) = 0.0012883549617619145442785811616016 absolute error = 2.10251067569884081976687616e-08 relative error = 0.0016319076862095821993874569669156 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50315 x2[1] (analytic) = 0.0008284791405868768771043381382677 x2[1] (numeric) = 0.00082849004156918808034956907749296 absolute error = 1.090098231120324523093922526e-08 relative error = 0.001315782350715700924174007533751 % h = 5e-05 x1[1] (analytic) = 0.0012883215694297754084796858889148 x1[1] (numeric) = 0.0012882998598984367845353539293719 absolute error = 2.17095313386239443319595429e-08 relative error = 0.0016851019073004273148639766007555 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5032 x2[1] (analytic) = 0.00082852478342398194791549665092172 x2[1] (numeric) = 0.00082853603434036218279149782219539 absolute error = 1.125091638023487600117127367e-08 relative error = 0.0013579456650335867525797145971141 % h = 5e-05 x1[1] (analytic) = 0.0012882671547116832084138656194575 x1[1] (numeric) = 0.0012882447497700660604511991142034 absolute error = 2.24049416171479626665052541e-08 relative error = 0.0017391533685543845026060168716461 % h = 5e-05 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.6MB, time=3.01 NO POLE NO POLE t[1] = 0.50325 x2[1] (analytic) = 0.00082857043218600091423089597124342 x2[1] (numeric) = 0.00082858203860046197699061522095972 absolute error = 1.160641446106275971924971630e-08 relative error = 0.001400775843574551287376316325649 % h = 5e-05 x1[1] (analytic) = 0.0012882127427142588956940591808277 x1[1] (numeric) = 0.0012881896313755627697629414463551 absolute error = 2.31113386961259311177344726e-08 relative error = 0.0017940622639262546436876471071705 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5033 x2[1] (analytic) = 0.00082861608687345827866795740859187 x2[1] (numeric) = 0.00082862805435166974820654911988968 absolute error = 1.196747821146953859171129781e-08 relative error = 0.0014442729752719785749650749109355 % h = 5e-05 x1[1] (analytic) = 0.0012881583334373664403266774516441 x1[1] (numeric) = 0.0012881345047136871242898769111221 absolute error = 2.38287236793160368005405220e-08 relative error = 0.0018498287874077282765920048594922 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50335 x2[1] (analytic) = 0.0008286617474868785996978214776885 x2[1] (numeric) = 0.00082867408159616815492142218415731 absolute error = 1.233410928955522360070646881e-08 relative error = 0.0014884371490492298122255910977855 % h = 5e-05 x1[1] (analytic) = 0.0012881039268808698191194609553229 x1[1] (numeric) = 0.0012880793697831991499058888468208 absolute error = 2.45570976706692135721085021e-08 relative error = 0.0019064531330273923338397475626503 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5034 x2[1] (analytic) = 0.00082870741402678649165076351232339 x2[1] (numeric) = 0.00082872012033614022890042054368619 absolute error = 1.270630935373724965703136280e-08 relative error = 0.0015332684538196421675389009553542 % h = 5e-05 x1[1] (analytic) = 0.0012880495230446330156811398020981 x1[1] (numeric) = 0.0012880242265828586865115598607782 absolute error = 2.52964617743291695799413199e-08 relative error = 0.0019639354948507368798239227279972 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50345 x2[1] (analytic) = 0.00082875308649370662472160982915166 x2[1] (numeric) = 0.00082876617057376937525237198220787 absolute error = 1.308408006275053076215305621e-08 relative error = 0.0015787669784865276025588008238704 % h = 5e-05 x1[1] (analytic) = 0.0012879951219285200204210936480425 x1[1] (numeric) = 0.0012879690751114253880062795626987 absolute error = 2.60468170946324148140853438e-08 relative error = 0.0020222760669801618498514681510032 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5035 x2[1] (analytic) = 0.00082879876488816372497515444163463 x2[1] (numeric) = 0.00082881223231123937249033367116884 absolute error = 1.346742307564751517922953421e-08 relative error = 0.0016249328119431716947313810464512 % h = 5e-05 x1[1] (analytic) = 0.0012879407235323948305490116710912 x1[1] (numeric) = 0.0012879139153676587222603481147803 absolute error = 2.68081647361082886635563109e-08 relative error = 0.0020814750435549837903915542293673 % h = 5e-05 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.6MB, time=3.27 NO POLE NO POLE t[1] = 0.50355 x2[1] (analytic) = 0.00082884444921068257435157632418004 x2[1] (numeric) = 0.00082885830555073437259218944996547 absolute error = 1.385634005179824061312578543e-08 relative error = 0.0016717660430728324605627490550104 % h = 5e-05 x1[1] (analytic) = 0.0012878863278561214500745525640661 x1[1] (numeric) = 0.0012878587473503179710870755979535 absolute error = 2.75805058034789874769661126e-08 relative error = 0.0021415326187514426005309801565139 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5036 x2[1] (analytic) = 0.00082889013946178801067185722653652 x2[1] (numeric) = 0.00082890439029443890106125665398459 absolute error = 1.425083265089038939942744807e-08 relative error = 0.0017192667607487391796349222024878 % h = 5e-05 x1[1] (analytic) = 0.0012878319348995638898070045446997 x1[1] (numeric) = 0.001287803571058162230214877193615 absolute error = 2.83638414016595921273510847e-08 relative error = 0.0022024489867827082746368358611554 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50365 x2[1] (analytic) = 0.00082893583564200492764320003849618 x2[1] (numeric) = 0.00082895048654453785698690249192763 absolute error = 1.465090253292934370245343145e-08 relative error = 0.0017674350538340912193698708259265 % h = 5e-05 x1[1] (analytic) = 0.0012877775446625861673549453826583 x1[1] (numeric) = 0.0012877483864899504092593641802288 absolute error = 2.91581726357580955812024295e-08 relative error = 0.0022642243418988876462266416935311 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5037 x2[1] (analytic) = 0.00082898153775185827486444770496057 x2[1] (numeric) = 0.00082899659430321651310516997389653 absolute error = 1.505655135823824072226893596e-08 relative error = 0.00181627101118205686054169179628 % h = 5e-05 x1[1] (analytic) = 0.0012877231571450523071259024435631 x1[1] (numeric) = 0.0012876931936444412316954307441673 absolute error = 2.99635006110754304716993958e-08 relative error = 0.0023268588783870311330461777637003 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50375 x2[1] (analytic) = 0.00082902724579187305783150269142413 x2[1] (numeric) = 0.00082904271357266051585941339171972 absolute error = 1.546778078745802791070029559e-08 relative error = 0.0018657747216357721235368928609194 % h = 5e-05 x1[1] (analytic) = 0.0012876687723468263403260127500097 x1[1] (numeric) = 0.0012876379925203932348293366041635 absolute error = 3.07798264331054966761458462e-08 relative error = 0.0023903527905711394833552151380518 % h = 5e-05 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.6MB, time=3.54 NO POLE NO POLE t[1] = 0.5038 x2[1] (analytic) = 0.0008290729597625743379427469999303 x2[1] (numeric) = 0.00082908884435505588546094335299682 absolute error = 1.588459248154751819635306652e-08 relative error = 0.0019159462740283395953627679032619 % h = 5e-05 x1[1] (analytic) = 0.0012876143902677723049596830595824 x1[1] (numeric) = 0.0012875827831165647697707854487481 absolute error = 3.16071512075351888976108343e-08 relative error = 0.0024547062728121705234213606011611 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50385 x2[1] (analytic) = 0.00082911867966448723250446273555416 x2[1] (numeric) = 0.00082913498665258901594968137034082 absolute error = 1.630698810178344521863478666e-08 relative error = 0.0019667857571828272574038433169543 % h = 5e-05 x1[1] (analytic) = 0.0012875600109077542458292499598661 x1[1] (numeric) = 0.0012875275654317140014049991860422 absolute error = 3.24454760402444242507738239e-08 relative error = 0.0025199195195080459062222274568422 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5039 x2[1] (analytic) = 0.00082916440549813691473625322346704 x2[1] (numeric) = 0.00082918114046744667525482400729687 absolute error = 1.673496930976051857078382983e-08 relative error = 0.0020182932599122673139263754502166 % h = 5e-05 x1[1] (analytic) = 0.0012875056342666362145346399804511 x1[1] (numeric) = 0.001287472339464598908364788005278 absolute error = 3.32948020373061698519751731e-08 relative error = 0.0025859927250936578613561441568386 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50395 x2[1] (analytic) = 0.00082921013726404861377646467663714 x2[1] (numeric) = 0.00082922730580181600525551658241691 absolute error = 1.716853776739147905190577977e-08 relative error = 0.002070468871019655021330879159833 % h = 5e-05 x1[1] (analytic) = 0.0012874512603442822694730297219339 x1[1] (numeric) = 0.0012874171052139772830026162494197 absolute error = 3.41551303049864704134725142e-08 relative error = 0.0026529260840408759461616131958758 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.504 x2[1] (analytic) = 0.00082925587496274761468760841422102 x2[1] (numeric) = 0.00082927348265788452184153643296966 absolute error = 1.760769513690715392801874864e-08 relative error = 0.0021233126792979475181526673533022 % h = 5e-05 x1[1] (analytic) = 0.0012873968891405564758385060019091 x1[1] (numeric) = 0.0012873618626786067313626640982556 absolute error = 3.50264619497444758419036535e-08 relative error = 0.0027207197908585537980457322127342 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50405 x2[1] (analytic) = 0.00082930161859475925846178363070083 x2[1] (numeric) = 0.0008293196710378401149739857397657 absolute error = 1.805244308085651220210906487e-08 relative error = 0.0021768247735300626558103813247552 % h = 5e-05 x1[1] (analytic) = 0.0012873425206553229056217260179551 x1[1] (numeric) = 0.0012873066118572446731528850613339 absolute error = 3.59087980782324688409566212e-08 relative error = 0.002789374040092535888021789739774 % h = 5e-05 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.6MB, time=3.81 NO POLE NO POLE t[1] = 0.5041 x2[1] (analytic) = 0.00082934736816060894202610071582133 x2[1] (numeric) = 0.00082936587094387104874599391457756 absolute error = 1.850278326210671989319875623e-08 relative error = 0.0022310052424888778301024917150396 % h = 5e-05 x1[1] (analytic) = 0.0012872881548884456376095775276106 x1[1] (numeric) = 0.001287251352748648341717059280113 absolute error = 3.68021397972958925182474976e-08 relative error = 0.0028588890263256642754562477617295 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50415 x2[1] (analytic) = 0.00082939312366082211824810512538206 x2[1] (numeric) = 0.0008294120823781659614434295516351 absolute error = 1.895871734384319532442625304e-08 relative error = 0.0022858541749372288134517497147927 % h = 5e-05 x1[1] (analytic) = 0.0012872337918397887573848390453416 x1[1] (numeric) = 0.0012871960853515747840068426386986 absolute error = 3.77064882139733779964066430e-08 relative error = 0.0029292649441777853640253233668121 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5042 x2[1] (analytic) = 0.00082943888509592429594120180293885 x2[1] (numeric) = 0.00082945830534291386560562194467646 absolute error = 1.942024698956966442014173761e-08 relative error = 0.0023413716596279085878975681734402 % h = 5e-05 x1[1] (analytic) = 0.0012871794315092163573258400564985 x1[1] (numeric) = 0.0012871408096647808605538116825378 absolute error = 3.86218444354967720283739607e-08 relative error = 0.003000501988305756658881381957573 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50425 x2[1] (analytic) = 0.00082948465246644103987008015246953 x2[1] (numeric) = 0.00082950453984030414808609217103536 absolute error = 1.988737386310821601201856583e-08 relative error = 0.0023975577853036661788363121595683 % h = 5e-05 x1[1] (analytic) = 0.0012871250738965925366061212482615 x1[1] (numeric) = 0.001287085525687023245441504344443 absolute error = 3.95482095692911646169038185e-08 relative error = 0.0030726003534034535250293542073064 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5043 x2[1] (analytic) = 0.00082953042577289797075613956205843 x2[1] (numeric) = 0.00082955078587252657011329374424548 absolute error = 2.036009962859935715418218705e-08 relative error = 0.0024544126406972054895094784476866 % h = 5e-05 x1[1] (analytic) = 0.0012870707190017814011940947575749 x1[1] (numeric) = 0.0012870302334170584262774564773152 absolute error = 4.04855847229749166382802597e-08 relative error = 0.0031455602342017759469133894118461 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50435 x2[1] (analytic) = 0.00082957620501582076528291547865441 x2[1] (numeric) = 0.00082959704344177126735136283664308 absolute error = 2.083842595050206844735798867e-08 relative error = 0.0025119363145311841362397433432096 % h = 5e-05 x1[1] (analytic) = 0.0012870163668246470638527044360674 x1[1] (numeric) = 0.0012869749328536427041652341929395 absolute error = 4.14339710043596874702431279e-08 relative error = 0.0032193818254686552892139573951761 % h = 5e-05 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.6MB, time=4.07 NO POLE NO POLE t[1] = 0.5044 x2[1] (analytic) = 0.00082962199019573515610150603395714 x2[1] (numeric) = 0.00082964331255022874996087807344922 absolute error = 2.132235449359385937203949208e-08 relative error = 0.0025701288955182122844148581870717 % h = 5e-05 x1[1] (analytic) = 0.00128696201736505364413908613196 x1[1] (numeric) = 0.0012869196239955321936764620062218 absolute error = 4.23933695214504626241257382e-08 relative error = 0.0032940653220090610588556118011558 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50445 x2[1] (analytic) = 0.00082966778131316693183599922148616 x2[1] (numeric) = 0.00082968959320008990265962989981299 absolute error = 2.181188692297082363067832683e-08 relative error = 0.0026289904723608514852193718134016 % h = 5e-05 x1[1] (analytic) = 0.0012869076706228652684042279889585 x1[1] (numeric) = 0.0012868643068414828228228467842397 absolute error = 4.33637813824455813812047188e-08 relative error = 0.0033696109186650076682256269645856 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5045 x2[1] (analytic) = 0.00082971357836864193708890062488759 x2[1] (numeric) = 0.00082973588539354598478339952229767 absolute error = 2.230702490404769449889741008e-08 relative error = 0.0026885211337516135131141591572655 % h = 5e-05 x1[1] (analytic) = 0.0012868533265979460697926307621308 x1[1] (numeric) = 0.0012868089813902503330281974994768 absolute error = 4.43452076957367644332626540e-08 relative error = 0.003446018810315561199603721127757 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50455 x2[1] (analytic) = 0.00082975938136268607244656169753319 x2[1] (numeric) = 0.00082978218913278863034674742629174 absolute error = 2.280777010255790018572875855e-08 relative error = 0.0027487209683729592040637351330894 % h = 5e-05 x1[1] (analytic) = 0.0012867989852901601882419681507683 x1[1] (numeric) = 0.0012867536476405902791004407866119 absolute error = 4.53376495699091415273641564e-08 relative error = 0.0035232891918768461708030785490962 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5046 x2[1] (analytic) = 0.00082980519029582529448460859346626 x2[1] (numeric) = 0.00082982850442000984810381147082694 absolute error = 2.331412418455361920287736068e-08 relative error = 0.002809590064897297294511332866548 % h = 5e-05 x1[1] (analytic) = 0.0012867446466993717704827471482299 x1[1] (numeric) = 0.0012866983055912580292036323022335 absolute error = 4.63411081137412791148459964e-08 relative error = 0.0036014222583020523020228831028955 % h = 5e-05 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.6MB, time=4.34 NO POLE NO POLE t[1] = 0.50465 x2[1] (analytic) = 0.00082985100516858561577337154974936 x2[1] (numeric) = 0.00082987483125740202160911456228591 absolute error = 2.382608881640583574301253655e-08 relative error = 0.002871128511986983261101725246555 % h = 5e-05 x1[1] (analytic) = 0.001286690310825444970037968408768 x1[1] (numeric) = 0.0012866429552410087648299638868505 absolute error = 4.73555844362052080045219175e-08 relative error = 0.0036804182045814412839125760292819 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5047 x2[1] (analytic) = 0.00082989682598149310488331482026843 x2[1] (numeric) = 0.000829921169647157909278381908482 absolute error = 2.434366566480439506708821357e-08 relative error = 0.0029333363982943181611517687225775 % h = 5e-05 x1[1] (analytic) = 0.0012866359776682439472227866313365 x1[1] (numeric) = 0.0012865875965885974807717665285687 absolute error = 4.83810796464664510201027678e-08 relative error = 0.0037602772257423535468480506703337 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50475 x2[1] (analytic) = 0.00082994265273507388639046716104801 x2[1] (numeric) = 0.00082996751959147064444936785459426 absolute error = 2.486685639675805890069354625e-08 relative error = 0.0029962138124615474738686482118107 % h = 5e-05 x1[1] (analytic) = 0.001286581647227632869144170960378 x1[1] (numeric) = 0.0012865322296327789850935091278043 absolute error = 4.94175948538840506618325737e-08 relative error = 0.0038409995168492150314199967154081 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5048 x2[1] (analytic) = 0.00082998848542985414088185286713247 x2[1] (numeric) = 0.00083001388109253373544269230244063 absolute error = 2.539566267959456083943530816e-08 relative error = 0.0030597608431208599423158018598169 % h = 5e-05 x1[1] (analytic) = 0.0012865273195034759097005654035915 x1[1] (numeric) = 0.0012864768543723078991037930624043 absolute error = 5.04651311680105967723411872e-08 relative error = 0.0039225852730035439601346069274927 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50485 x2[1] (analytic) = 0.00083003432406636010496092336108762 x2[1] (numeric) = 0.00083006025415254106562268671457279 absolute error = 2.593008618096066176335348517e-08 relative error = 0.0031239775788943864161265044195161 % h = 5e-05 x1[1] (analytic) = 0.0012864729944956372495815492666783 x1[1] (numeric) = 0.0012864214708059386573273425525437 absolute error = 5.15236896985922542067141346e-08 relative error = 0.0040050346893439576103268590717388 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5049 x2[1] (analytic) = 0.00083008016864511807125298933317795 x2[1] (numeric) = 0.00083010663877368689345824970467616 absolute error = 2.647012856882220526037149821e-08 relative error = 0.0031888641083941986949650878141877 % h = 5e-05 x1[1] (analytic) = 0.001286418672203981076267497605066 x1[1] (numeric) = 0.0012863660789324255074769908247704 absolute error = 5.25932715555687905067802956e-08 relative error = 0.0040883479610461790882865858896879 % h = 5e-05 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.6MB, time=4.61 NO POLE NO POLE t[1] = 0.50495 x2[1] (analytic) = 0.00083012601916665438841065343327373 x2[1] (numeric) = 0.00083015303495816585258371221575895 absolute error = 2.701579151146417305878248522e-08 relative error = 0.0032544205202223083727357775256635 % h = 5e-05 x1[1] (analytic) = 0.0012863643526283715840292416926091 x1[1] (numeric) = 0.0012863106787505225104256620745665 absolute error = 5.36738778490736035796180426e-08 relative error = 0.0041725252833230441045975460540075 % h = 5e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.505 x2[1] (analytic) = 0.00083017187563149546111924351454314 x2[1] (numeric) = 0.00083019944270817295185971228761426 absolute error = 2.756707667749074046877307112e-08 relative error = 0.0033206469029706656825391232509064 % h = 5e-05 x1[1] (analytic) = 0.0012863100357686729739277295072664 x1[1] (numeric) = 0.0012862552702589835401783492267968 absolute error = 5.47655096894337493802804696e-08 relative error = 0.0042575668514245077506897090365854 % h = 5e-05 Finished! Maximum Iterations Reached before Solution Completed! diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; Iterations = 100 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Expected Time Remaining = 1 Hours 8 Minutes 50 Seconds Optimized Time Remaining = 1 Hours 8 Minutes 41 Seconds Time to Timeout = 14 Minutes 55 Seconds Percent Done = 0.1122 % > quit memory used=69.9MB, alloc=4.6MB, time=4.69