|\^/| 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 > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_trunc_err, > glob_hmin, > glob_optimal_done, > glob_clock_start_sec, > min_in_hour, > glob_normmax, > glob_iter, > hours_in_day, > glob_percent_done, > glob_start, > glob_orig_start_sec, > glob_smallish_float, > glob_last_good_h, > glob_disp_incr, > years_in_century, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_order, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmax, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_dump_analytic, > glob_clock_sec, > sec_in_min, > glob_warned, > glob_look_poles, > glob_large_float, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_warned2, > glob_max_iter, > glob_log10_abserr, > centuries_in_millinium, > days_in_year, > djd_debug2, > glob_reached_optimal_h, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > djd_debug, > glob_current_iter, > glob_almost_1, > glob_html_log, > glob_unchanged_h_cnt, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > #END CONST > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1, > array_x2, > array_x1_init, > array_m1, > array_1st_rel_error, > array_x2_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_last_rel_error, > array_t, > array_norms, > array_x1_higher, > array_poles, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_x2_higher_work, > array_x1_higher_work, > array_complex_pole, > array_x1_higher_work2, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_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[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_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[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 glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_max_trunc_err, glob_hmin, glob_optimal_done, glob_clock_start_sec, min_in_hour, glob_normmax, glob_iter, hours_in_day, glob_percent_done, glob_start, glob_orig_start_sec, glob_smallish_float, glob_last_good_h, glob_disp_incr, years_in_century, glob_display_flag, glob_dump, glob_max_opt_iter, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_order, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmax, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_dump_analytic, glob_clock_sec, sec_in_min, glob_warned, glob_look_poles, glob_large_float, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_optimal_expect_sec, glob_warned2, glob_max_iter, glob_log10_abserr, centuries_in_millinium, days_in_year, djd_debug2, glob_reached_optimal_h, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, djd_debug, glob_current_iter, glob_almost_1, glob_html_log, glob_unchanged_h_cnt, glob_max_hours, array_const_0D0, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1, array_x2, array_x1_init, array_m1, array_1st_rel_error, array_x2_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_last_rel_error, array_t, array_norms, array_x1_higher, array_poles, array_x2_higher_work2, array_x2_higher, array_real_pole, array_x2_higher_work, array_x1_higher_work, array_complex_pole, array_x1_higher_work2, glob_last; if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_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[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_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[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 > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_trunc_err, > glob_hmin, > glob_optimal_done, > glob_clock_start_sec, > min_in_hour, > glob_normmax, > glob_iter, > hours_in_day, > glob_percent_done, > glob_start, > glob_orig_start_sec, > glob_smallish_float, > glob_last_good_h, > glob_disp_incr, > years_in_century, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_order, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmax, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_dump_analytic, > glob_clock_sec, > sec_in_min, > glob_warned, > glob_look_poles, > glob_large_float, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_warned2, > glob_max_iter, > glob_log10_abserr, > centuries_in_millinium, > days_in_year, > djd_debug2, > glob_reached_optimal_h, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > djd_debug, > glob_current_iter, > glob_almost_1, > glob_html_log, > glob_unchanged_h_cnt, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > #END CONST > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1, > array_x2, > array_x1_init, > array_m1, > array_1st_rel_error, > array_x2_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_last_rel_error, > array_t, > array_norms, > array_x1_higher, > array_poles, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_x2_higher_work, > array_x1_higher_work, > array_complex_pole, > array_x1_higher_work2, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > 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 (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 (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 glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_max_trunc_err, glob_hmin, glob_optimal_done, glob_clock_start_sec, min_in_hour, glob_normmax, glob_iter, hours_in_day, glob_percent_done, glob_start, glob_orig_start_sec, glob_smallish_float, glob_last_good_h, glob_disp_incr, years_in_century, glob_display_flag, glob_dump, glob_max_opt_iter, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_order, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmax, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_dump_analytic, glob_clock_sec, sec_in_min, glob_warned, glob_look_poles, glob_large_float, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_optimal_expect_sec, glob_warned2, glob_max_iter, glob_log10_abserr, centuries_in_millinium, days_in_year, djd_debug2, glob_reached_optimal_h, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, djd_debug, glob_current_iter, glob_almost_1, glob_html_log, glob_unchanged_h_cnt, glob_max_hours, array_const_0D0, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1, array_x2, array_x1_init, array_m1, array_1st_rel_error, array_x2_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_last_rel_error, array_t, array_norms, array_x1_higher, array_poles, array_x2_higher_work2, array_x2_higher, array_real_pole, array_x2_higher_work, array_x1_higher_work, array_complex_pole, array_x1_higher_work2, glob_last; hnew := h_param; glob_normmax := glob_small_float; 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_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_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 > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_trunc_err, > glob_hmin, > glob_optimal_done, > glob_clock_start_sec, > min_in_hour, > glob_normmax, > glob_iter, > hours_in_day, > glob_percent_done, > glob_start, > glob_orig_start_sec, > glob_smallish_float, > glob_last_good_h, > glob_disp_incr, > years_in_century, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_order, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmax, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_dump_analytic, > glob_clock_sec, > sec_in_min, > glob_warned, > glob_look_poles, > glob_large_float, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_warned2, > glob_max_iter, > glob_log10_abserr, > centuries_in_millinium, > days_in_year, > djd_debug2, > glob_reached_optimal_h, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > djd_debug, > glob_current_iter, > glob_almost_1, > glob_html_log, > glob_unchanged_h_cnt, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > #END CONST > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1, > array_x2, > array_x1_init, > array_m1, > array_1st_rel_error, > array_x2_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_last_rel_error, > array_t, > array_norms, > array_x1_higher, > array_poles, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_x2_higher_work, > array_x1_higher_work, > array_complex_pole, > array_x1_higher_work2, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_max_trunc_err, glob_hmin, glob_optimal_done, glob_clock_start_sec, min_in_hour, glob_normmax, glob_iter, hours_in_day, glob_percent_done, glob_start, glob_orig_start_sec, glob_smallish_float, glob_last_good_h, glob_disp_incr, years_in_century, glob_display_flag, glob_dump, glob_max_opt_iter, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_order, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmax, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_dump_analytic, glob_clock_sec, sec_in_min, glob_warned, glob_look_poles, glob_large_float, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_optimal_expect_sec, glob_warned2, glob_max_iter, glob_log10_abserr, centuries_in_millinium, days_in_year, djd_debug2, glob_reached_optimal_h, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, djd_debug, glob_current_iter, glob_almost_1, glob_html_log, glob_unchanged_h_cnt, glob_max_hours, array_const_0D0, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1, array_x2, array_x1_init, array_m1, array_1st_rel_error, array_x2_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_last_rel_error, array_t, array_norms, array_x1_higher, array_poles, array_x2_higher_work2, array_x2_higher, array_real_pole, array_x2_higher_work, array_x1_higher_work, array_complex_pole, array_x1_higher_work2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_trunc_err, > glob_hmin, > glob_optimal_done, > glob_clock_start_sec, > min_in_hour, > glob_normmax, > glob_iter, > hours_in_day, > glob_percent_done, > glob_start, > glob_orig_start_sec, > glob_smallish_float, > glob_last_good_h, > glob_disp_incr, > years_in_century, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_order, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmax, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_dump_analytic, > glob_clock_sec, > sec_in_min, > glob_warned, > glob_look_poles, > glob_large_float, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_warned2, > glob_max_iter, > glob_log10_abserr, > centuries_in_millinium, > days_in_year, > djd_debug2, > glob_reached_optimal_h, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > djd_debug, > glob_current_iter, > glob_almost_1, > glob_html_log, > glob_unchanged_h_cnt, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > #END CONST > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1, > array_x2, > array_x1_init, > array_m1, > array_1st_rel_error, > array_x2_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_last_rel_error, > array_t, > array_norms, > array_x1_higher, > array_poles, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_x2_higher_work, > array_x1_higher_work, > array_complex_pole, > array_x1_higher_work2, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 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[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 - 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[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 - 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 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_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 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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 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 - 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 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_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 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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 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 glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_max_trunc_err, glob_hmin, glob_optimal_done, glob_clock_start_sec, min_in_hour, glob_normmax, glob_iter, hours_in_day, glob_percent_done, glob_start, glob_orig_start_sec, glob_smallish_float, glob_last_good_h, glob_disp_incr, years_in_century, glob_display_flag, glob_dump, glob_max_opt_iter, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_order, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmax, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_dump_analytic, glob_clock_sec, sec_in_min, glob_warned, glob_look_poles, glob_large_float, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_optimal_expect_sec, glob_warned2, glob_max_iter, glob_log10_abserr, centuries_in_millinium, days_in_year, djd_debug2, glob_reached_optimal_h, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, djd_debug, glob_current_iter, glob_almost_1, glob_html_log, glob_unchanged_h_cnt, glob_max_hours, array_const_0D0, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1, array_x2, array_x1_init, array_m1, array_1st_rel_error, array_x2_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_last_rel_error, array_t, array_norms, array_x1_higher, array_poles, array_x2_higher_work2, array_x2_higher, array_real_pole, array_x2_higher_work, array_x1_higher_work, array_complex_pole, array_x1_higher_work2, glob_last; 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[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 - 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[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 - 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[1, 1] := glob_large_float; array_complex_pole[1, 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[1, 1] := glob_large_float; array_complex_pole[1, 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[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 - 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[2, 1] := glob_large_float; array_complex_pole[2, 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[2, 1] := glob_large_float; array_complex_pole[2, 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[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 > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_trunc_err, > glob_hmin, > glob_optimal_done, > glob_clock_start_sec, > min_in_hour, > glob_normmax, > glob_iter, > hours_in_day, > glob_percent_done, > glob_start, > glob_orig_start_sec, > glob_smallish_float, > glob_last_good_h, > glob_disp_incr, > years_in_century, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_order, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmax, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_dump_analytic, > glob_clock_sec, > sec_in_min, > glob_warned, > glob_look_poles, > glob_large_float, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_warned2, > glob_max_iter, > glob_log10_abserr, > centuries_in_millinium, > days_in_year, > djd_debug2, > glob_reached_optimal_h, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > djd_debug, > glob_current_iter, > glob_almost_1, > glob_html_log, > glob_unchanged_h_cnt, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > #END CONST > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1, > array_x2, > array_x1_init, > array_m1, > array_1st_rel_error, > array_x2_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_last_rel_error, > array_t, > array_norms, > array_x1_higher, > array_poles, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_x2_higher_work, > array_x1_higher_work, > array_complex_pole, > array_x1_higher_work2, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_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 > ; > 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 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_max_trunc_err, glob_hmin, glob_optimal_done, glob_clock_start_sec, min_in_hour, glob_normmax, glob_iter, hours_in_day, glob_percent_done, glob_start, glob_orig_start_sec, glob_smallish_float, glob_last_good_h, glob_disp_incr, years_in_century, glob_display_flag, glob_dump, glob_max_opt_iter, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_order, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmax, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_dump_analytic, glob_clock_sec, sec_in_min, glob_warned, glob_look_poles, glob_large_float, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_optimal_expect_sec, glob_warned2, glob_max_iter, glob_log10_abserr, centuries_in_millinium, days_in_year, djd_debug2, glob_reached_optimal_h, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, djd_debug, glob_current_iter, glob_almost_1, glob_html_log, glob_unchanged_h_cnt, glob_max_hours, array_const_0D0, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1, array_x2, array_x1_init, array_m1, array_1st_rel_error, array_x2_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_last_rel_error, array_t, array_norms, array_x1_higher, array_poles, array_x2_higher_work2, array_x2_higher, array_real_pole, array_x2_higher_work, array_x1_higher_work, array_complex_pole, array_x1_higher_work2, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_x1[iii]) then array_norms[iii] := abs(array_x1[iii]) end if; iii := iii + 1 end do; 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 end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_trunc_err, > glob_hmin, > glob_optimal_done, > glob_clock_start_sec, > min_in_hour, > glob_normmax, > glob_iter, > hours_in_day, > glob_percent_done, > glob_start, > glob_orig_start_sec, > glob_smallish_float, > glob_last_good_h, > glob_disp_incr, > years_in_century, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_order, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmax, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_dump_analytic, > glob_clock_sec, > sec_in_min, > glob_warned, > glob_look_poles, > glob_large_float, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_warned2, > glob_max_iter, > glob_log10_abserr, > centuries_in_millinium, > days_in_year, > djd_debug2, > glob_reached_optimal_h, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > djd_debug, > glob_current_iter, > glob_almost_1, > glob_html_log, > glob_unchanged_h_cnt, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > #END CONST > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1, > array_x2, > array_x1_init, > array_m1, > array_1st_rel_error, > array_x2_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_last_rel_error, > array_t, > array_norms, > array_x1_higher, > array_poles, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_x2_higher_work, > array_x1_higher_work, > array_complex_pole, > array_x1_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult $eq_no = 1 i = 1 > array_tmp1[1] := (array_const_4D0[1] * (array_x2[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre diff $eq_no = 1 i = 1 > array_tmp3[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 1 i = 1 > array_tmp4[1] := (array_const_2D0[1] * (array_tmp3[1])); > #emit pre sub $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp2[1] - (array_tmp4[1])); > # emit pre mult $eq_no = 1 i = 1 > array_tmp6[1] := (array_const_2D0[1] * (array_x1[1])); > #emit pre sub $eq_no = 1 i = 1 > array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1])); > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if (1 <= glob_max_terms) then # if number 1 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 1 > array_tmp9[1] := array_x2_higher[2,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp10[1] := (array_const_3D0[1] * (array_tmp9[1])); > # emit pre mult $eq_no = 2 i = 1 > array_tmp11[1] := (array_const_2D0[1] * (array_x2[1])); > #emit pre sub $eq_no = 2 i = 1 > array_tmp12[1] := (array_tmp10[1] - (array_tmp11[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp13[1] := array_x1_higher[3,1]; > #emit pre sub $eq_no = 2 i = 1 > array_tmp14[1] := (array_tmp12[1] - (array_tmp13[1])); > #emit pre diff $eq_no = 2 i = 1 > array_tmp15[1] := array_x1_higher[2,1]; > #emit pre sub $eq_no = 2 i = 1 > array_tmp16[1] := (array_tmp14[1] - (array_tmp15[1])); > #emit pre add $eq_no = 2 i = 1 > array_tmp17[1] := array_tmp16[1] + array_x1[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 ^ (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; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_const_4D0,array_x2,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre diff $eq_no = 1 i = 2 > array_tmp3[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 1 i = 2 > array_tmp4[2] := ats(2,array_const_2D0,array_tmp3,1); > #emit pre sub $eq_no = 1 i = 2 > array_tmp5[2] := (array_tmp2[2] - (array_tmp4[2])); > # emit pre mult $eq_no = 1 i = 2 > array_tmp6[2] := ats(2,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 1 i = 2 > array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2])); > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if (2 <= glob_max_terms) then # if number 1 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 2 > array_tmp9[2] := array_x2_higher[2,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp10[2] := ats(2,array_const_3D0,array_tmp9,1); > # emit pre mult $eq_no = 2 i = 2 > array_tmp11[2] := ats(2,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 2 i = 2 > array_tmp12[2] := (array_tmp10[2] - (array_tmp11[2])); > #emit pre diff $eq_no = 2 i = 2 > array_tmp13[2] := array_x1_higher[3,2]; > #emit pre sub $eq_no = 2 i = 2 > array_tmp14[2] := (array_tmp12[2] - (array_tmp13[2])); > #emit pre diff $eq_no = 2 i = 2 > array_tmp15[2] := array_x1_higher[2,2]; > #emit pre sub $eq_no = 2 i = 2 > array_tmp16[2] := (array_tmp14[2] - (array_tmp15[2])); > #emit pre add $eq_no = 2 i = 2 > array_tmp17[2] := array_tmp16[2] + array_x1[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 ^ (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; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_const_4D0,array_x2,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre diff $eq_no = 1 i = 3 > array_tmp3[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 1 i = 3 > array_tmp4[3] := ats(3,array_const_2D0,array_tmp3,1); > #emit pre sub $eq_no = 1 i = 3 > array_tmp5[3] := (array_tmp2[3] - (array_tmp4[3])); > # emit pre mult $eq_no = 1 i = 3 > array_tmp6[3] := ats(3,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 1 i = 3 > array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3])); > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if (3 <= glob_max_terms) then # if number 1 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 3 > array_tmp9[3] := array_x2_higher[2,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp10[3] := ats(3,array_const_3D0,array_tmp9,1); > # emit pre mult $eq_no = 2 i = 3 > array_tmp11[3] := ats(3,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 2 i = 3 > array_tmp12[3] := (array_tmp10[3] - (array_tmp11[3])); > #emit pre diff $eq_no = 2 i = 3 > array_tmp13[3] := array_x1_higher[3,3]; > #emit pre sub $eq_no = 2 i = 3 > array_tmp14[3] := (array_tmp12[3] - (array_tmp13[3])); > #emit pre diff $eq_no = 2 i = 3 > array_tmp15[3] := array_x1_higher[2,3]; > #emit pre sub $eq_no = 2 i = 3 > array_tmp16[3] := (array_tmp14[3] - (array_tmp15[3])); > #emit pre add $eq_no = 2 i = 3 > array_tmp17[3] := array_tmp16[3] + array_x1[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 ^ (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; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_const_4D0,array_x2,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre diff $eq_no = 1 i = 4 > array_tmp3[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 1 i = 4 > array_tmp4[4] := ats(4,array_const_2D0,array_tmp3,1); > #emit pre sub $eq_no = 1 i = 4 > array_tmp5[4] := (array_tmp2[4] - (array_tmp4[4])); > # emit pre mult $eq_no = 1 i = 4 > array_tmp6[4] := ats(4,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 1 i = 4 > array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4])); > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if (4 <= glob_max_terms) then # if number 1 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 4 > array_tmp9[4] := array_x2_higher[2,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp10[4] := ats(4,array_const_3D0,array_tmp9,1); > # emit pre mult $eq_no = 2 i = 4 > array_tmp11[4] := ats(4,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 2 i = 4 > array_tmp12[4] := (array_tmp10[4] - (array_tmp11[4])); > #emit pre diff $eq_no = 2 i = 4 > array_tmp13[4] := array_x1_higher[3,4]; > #emit pre sub $eq_no = 2 i = 4 > array_tmp14[4] := (array_tmp12[4] - (array_tmp13[4])); > #emit pre diff $eq_no = 2 i = 4 > array_tmp15[4] := array_x1_higher[2,4]; > #emit pre sub $eq_no = 2 i = 4 > array_tmp16[4] := (array_tmp14[4] - (array_tmp15[4])); > #emit pre add $eq_no = 2 i = 4 > array_tmp17[4] := array_tmp16[4] + array_x1[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 ^ (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; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_const_4D0,array_x2,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre diff $eq_no = 1 i = 5 > array_tmp3[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 1 i = 5 > array_tmp4[5] := ats(5,array_const_2D0,array_tmp3,1); > #emit pre sub $eq_no = 1 i = 5 > array_tmp5[5] := (array_tmp2[5] - (array_tmp4[5])); > # emit pre mult $eq_no = 1 i = 5 > array_tmp6[5] := ats(5,array_const_2D0,array_x1,1); > #emit pre sub $eq_no = 1 i = 5 > array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5])); > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if (5 <= glob_max_terms) then # if number 1 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 5 > array_tmp9[5] := array_x2_higher[2,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp10[5] := ats(5,array_const_3D0,array_tmp9,1); > # emit pre mult $eq_no = 2 i = 5 > array_tmp11[5] := ats(5,array_const_2D0,array_x2,1); > #emit pre sub $eq_no = 2 i = 5 > array_tmp12[5] := (array_tmp10[5] - (array_tmp11[5])); > #emit pre diff $eq_no = 2 i = 5 > array_tmp13[5] := array_x1_higher[3,5]; > #emit pre sub $eq_no = 2 i = 5 > array_tmp14[5] := (array_tmp12[5] - (array_tmp13[5])); > #emit pre diff $eq_no = 2 i = 5 > array_tmp15[5] := array_x1_higher[2,5]; > #emit pre sub $eq_no = 2 i = 5 > array_tmp16[5] := (array_tmp14[5] - (array_tmp15[5])); > #emit pre add $eq_no = 2 i = 5 > array_tmp17[5] := array_tmp16[5] + array_x1[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 ^ (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; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_const_4D0,array_x2,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit diff $eq_no = 1 > array_tmp3[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 1 > array_tmp4[kkk] := ats(kkk,array_const_2D0,array_tmp3,1); > #emit sub $eq_no = 1 > array_tmp5[kkk] := (array_tmp2[kkk] - (array_tmp4[kkk])); > #emit mult $eq_no = 1 > array_tmp6[kkk] := ats(kkk,array_const_2D0,array_x1,1); > #emit sub $eq_no = 1 > array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk])); > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > temporary := array_tmp7[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 > ; > #emit diff $eq_no = 2 > array_tmp9[kkk] := array_x2_higher[2,kkk]; > #emit mult $eq_no = 2 > array_tmp10[kkk] := ats(kkk,array_const_3D0,array_tmp9,1); > #emit mult $eq_no = 2 > array_tmp11[kkk] := ats(kkk,array_const_2D0,array_x2,1); > #emit sub $eq_no = 2 > array_tmp12[kkk] := (array_tmp10[kkk] - (array_tmp11[kkk])); > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x1_higher[3,kkk]; > #emit sub $eq_no = 2 > array_tmp14[kkk] := (array_tmp12[kkk] - (array_tmp13[kkk])); > #emit diff $eq_no = 2 > array_tmp15[kkk] := array_x1_higher[2,kkk]; > #emit sub $eq_no = 2 > array_tmp16[kkk] := (array_tmp14[kkk] - (array_tmp15[kkk])); > #emit add $eq_no = 2 > array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk]; > #emit assign $eq_no = 2 > order_d := 2; > 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_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 > ; > 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 glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_max_trunc_err, glob_hmin, glob_optimal_done, glob_clock_start_sec, min_in_hour, glob_normmax, glob_iter, hours_in_day, glob_percent_done, glob_start, glob_orig_start_sec, glob_smallish_float, glob_last_good_h, glob_disp_incr, years_in_century, glob_display_flag, glob_dump, glob_max_opt_iter, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_order, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmax, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_dump_analytic, glob_clock_sec, sec_in_min, glob_warned, glob_look_poles, glob_large_float, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_optimal_expect_sec, glob_warned2, glob_max_iter, glob_log10_abserr, centuries_in_millinium, days_in_year, djd_debug2, glob_reached_optimal_h, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, djd_debug, glob_current_iter, glob_almost_1, glob_html_log, glob_unchanged_h_cnt, glob_max_hours, array_const_0D0, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1, array_x2, array_x1_init, array_m1, array_1st_rel_error, array_x2_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_last_rel_error, array_t, array_norms, array_x1_higher, array_poles, array_x2_higher_work2, array_x2_higher, array_real_pole, array_x2_higher_work, array_x1_higher_work, array_complex_pole, array_x1_higher_work2, glob_last; array_tmp1[1] := array_const_4D0[1]*array_x2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_x2_higher[2, 1]; array_tmp4[1] := array_const_2D0[1]*array_tmp3[1]; array_tmp5[1] := array_tmp2[1] - array_tmp4[1]; array_tmp6[1] := array_const_2D0[1]*array_x1[1]; array_tmp7[1] := array_tmp5[1] - array_tmp6[1]; if 1 <= glob_max_terms then temporary := array_tmp7[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_tmp9[1] := array_x2_higher[2, 1]; array_tmp10[1] := array_const_3D0[1]*array_tmp9[1]; array_tmp11[1] := array_const_2D0[1]*array_x2[1]; array_tmp12[1] := array_tmp10[1] - array_tmp11[1]; array_tmp13[1] := array_x1_higher[3, 1]; array_tmp14[1] := array_tmp12[1] - array_tmp13[1]; array_tmp15[1] := array_x1_higher[2, 1]; array_tmp16[1] := array_tmp14[1] - array_tmp15[1]; array_tmp17[1] := array_tmp16[1] + array_x1[1]; if 1 <= glob_max_terms then temporary := array_tmp17[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_tmp1[2] := ats(2, array_const_4D0, array_x2, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; array_tmp3[2] := array_x2_higher[2, 2]; array_tmp4[2] := ats(2, array_const_2D0, array_tmp3, 1); array_tmp5[2] := array_tmp2[2] - array_tmp4[2]; array_tmp6[2] := ats(2, array_const_2D0, array_x1, 1); array_tmp7[2] := array_tmp5[2] - array_tmp6[2]; if 2 <= glob_max_terms then temporary := array_tmp7[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_tmp9[2] := array_x2_higher[2, 2]; array_tmp10[2] := ats(2, array_const_3D0, array_tmp9, 1); array_tmp11[2] := ats(2, array_const_2D0, array_x2, 1); array_tmp12[2] := array_tmp10[2] - array_tmp11[2]; array_tmp13[2] := array_x1_higher[3, 2]; array_tmp14[2] := array_tmp12[2] - array_tmp13[2]; array_tmp15[2] := array_x1_higher[2, 2]; array_tmp16[2] := array_tmp14[2] - array_tmp15[2]; array_tmp17[2] := array_tmp16[2] + array_x1[2]; if 2 <= glob_max_terms then temporary := array_tmp17[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_tmp1[3] := ats(3, array_const_4D0, array_x2, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; array_tmp3[3] := array_x2_higher[2, 3]; array_tmp4[3] := ats(3, array_const_2D0, array_tmp3, 1); array_tmp5[3] := array_tmp2[3] - array_tmp4[3]; array_tmp6[3] := ats(3, array_const_2D0, array_x1, 1); array_tmp7[3] := array_tmp5[3] - array_tmp6[3]; if 3 <= glob_max_terms then temporary := array_tmp7[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_tmp9[3] := array_x2_higher[2, 3]; array_tmp10[3] := ats(3, array_const_3D0, array_tmp9, 1); array_tmp11[3] := ats(3, array_const_2D0, array_x2, 1); array_tmp12[3] := array_tmp10[3] - array_tmp11[3]; array_tmp13[3] := array_x1_higher[3, 3]; array_tmp14[3] := array_tmp12[3] - array_tmp13[3]; array_tmp15[3] := array_x1_higher[2, 3]; array_tmp16[3] := array_tmp14[3] - array_tmp15[3]; array_tmp17[3] := array_tmp16[3] + array_x1[3]; if 3 <= glob_max_terms then temporary := array_tmp17[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_tmp1[4] := ats(4, array_const_4D0, array_x2, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; array_tmp3[4] := array_x2_higher[2, 4]; array_tmp4[4] := ats(4, array_const_2D0, array_tmp3, 1); array_tmp5[4] := array_tmp2[4] - array_tmp4[4]; array_tmp6[4] := ats(4, array_const_2D0, array_x1, 1); array_tmp7[4] := array_tmp5[4] - array_tmp6[4]; if 4 <= glob_max_terms then temporary := array_tmp7[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_tmp9[4] := array_x2_higher[2, 4]; array_tmp10[4] := ats(4, array_const_3D0, array_tmp9, 1); array_tmp11[4] := ats(4, array_const_2D0, array_x2, 1); array_tmp12[4] := array_tmp10[4] - array_tmp11[4]; array_tmp13[4] := array_x1_higher[3, 4]; array_tmp14[4] := array_tmp12[4] - array_tmp13[4]; array_tmp15[4] := array_x1_higher[2, 4]; array_tmp16[4] := array_tmp14[4] - array_tmp15[4]; array_tmp17[4] := array_tmp16[4] + array_x1[4]; if 4 <= glob_max_terms then temporary := array_tmp17[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_tmp1[5] := ats(5, array_const_4D0, array_x2, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; array_tmp3[5] := array_x2_higher[2, 5]; array_tmp4[5] := ats(5, array_const_2D0, array_tmp3, 1); array_tmp5[5] := array_tmp2[5] - array_tmp4[5]; array_tmp6[5] := ats(5, array_const_2D0, array_x1, 1); array_tmp7[5] := array_tmp5[5] - array_tmp6[5]; if 5 <= glob_max_terms then temporary := array_tmp7[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; array_tmp9[5] := array_x2_higher[2, 5]; array_tmp10[5] := ats(5, array_const_3D0, array_tmp9, 1); array_tmp11[5] := ats(5, array_const_2D0, array_x2, 1); array_tmp12[5] := array_tmp10[5] - array_tmp11[5]; array_tmp13[5] := array_x1_higher[3, 5]; array_tmp14[5] := array_tmp12[5] - array_tmp13[5]; array_tmp15[5] := array_x1_higher[2, 5]; array_tmp16[5] := array_tmp14[5] - array_tmp15[5]; array_tmp17[5] := array_tmp16[5] + array_x1[5]; if 5 <= glob_max_terms then temporary := array_tmp17[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; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_const_4D0, array_x2, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; array_tmp3[kkk] := array_x2_higher[2, kkk]; array_tmp4[kkk] := ats(kkk, array_const_2D0, array_tmp3, 1); array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk]; array_tmp6[kkk] := ats(kkk, array_const_2D0, array_x1, 1); array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then temporary := array_tmp7[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; array_tmp9[kkk] := array_x2_higher[2, kkk]; array_tmp10[kkk] := ats(kkk, array_const_3D0, array_tmp9, 1); array_tmp11[kkk] := ats(kkk, array_const_2D0, array_x2, 1); array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk]; array_tmp13[kkk] := array_x1_higher[3, kkk]; array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk]; array_tmp15[kkk] := array_x1_higher[2, kkk]; array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk]; array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk]; order_d := 2; 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_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; 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 > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_max_trunc_err, > glob_hmin, > glob_optimal_done, > glob_clock_start_sec, > min_in_hour, > glob_normmax, > glob_iter, > hours_in_day, > glob_percent_done, > glob_start, > glob_orig_start_sec, > glob_smallish_float, > glob_last_good_h, > glob_disp_incr, > years_in_century, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_order, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_hmin_init, > glob_hmax, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_dump_analytic, > glob_clock_sec, > sec_in_min, > glob_warned, > glob_look_poles, > glob_large_float, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_optimal_expect_sec, > glob_warned2, > glob_max_iter, > glob_log10_abserr, > centuries_in_millinium, > days_in_year, > djd_debug2, > glob_reached_optimal_h, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > djd_debug, > glob_current_iter, > glob_almost_1, > glob_html_log, > glob_unchanged_h_cnt, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > #END CONST > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_pole, > array_x1, > array_x2, > array_x1_init, > array_m1, > array_1st_rel_error, > array_x2_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_type_pole, > array_last_rel_error, > array_t, > array_norms, > array_x1_higher, > array_poles, > array_x2_higher_work2, > array_x2_higher, > array_real_pole, > array_x2_higher_work, > array_x1_higher_work, > array_complex_pole, > array_x1_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > ALWAYS := 1; > INFO := 2; > glob_curr_iter_when_opt := 0; > glob_max_sec := 10000.0; > glob_max_trunc_err := 0.1e-10; > glob_hmin := 0.00000000001; > glob_optimal_done := false; > glob_clock_start_sec := 0.0; > min_in_hour := 60.0; > glob_normmax := 0.0; > glob_iter := 0; > hours_in_day := 24.0; > glob_percent_done := 0.0; > glob_start := 0; > glob_orig_start_sec := 0.0; > glob_smallish_float := 0.1e-100; > glob_last_good_h := 0.1; > glob_disp_incr := 0.1; > years_in_century := 100.0; > glob_display_flag := true; > glob_dump := false; > glob_max_opt_iter := 10; > glob_log10normmin := 0.1; > glob_max_minutes := 0.0; > glob_log10relerr := 0.0; > glob_small_float := 0.1e-50; > glob_optimal_start := 0.0; > glob_max_order := 30; > glob_max_rel_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_hmin_init := 0.001; > glob_hmax := 1.0; > MAX_UNCHANGED := 10; > glob_no_eqs := 0; > glob_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_clock_sec := 0.0; > sec_in_min := 60.0; > glob_warned := false; > glob_look_poles := false; > glob_large_float := 9.0e100; > glob_h := 0.1; > glob_not_yet_start_msg := true; > glob_initial_pass := true; > glob_not_yet_finished := true; > glob_optimal_expect_sec := 0.1; > glob_warned2 := false; > glob_max_iter := 1000; > glob_log10_abserr := 0.1e-10; > centuries_in_millinium := 10.0; > days_in_year := 365.0; > djd_debug2 := true; > glob_reached_optimal_h := false; > glob_log10abserr := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > djd_debug := true; > glob_current_iter := 0; > glob_almost_1 := 0.9990; > glob_html_log := true; > glob_unchanged_h_cnt := 0; > glob_max_hours := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_max_order := 2; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/complicated3postode.ode#################"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > 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,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"t_start := 0.5;"); > omniout_str(ALWAYS,"t_end := 5.0;"); > omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_x1 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2 := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x2p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 0.0001;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_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:= Array(1..(max_terms + 1),[]); > array_x2:= Array(1..(max_terms + 1),[]); > array_x1_init:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_x2_init:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_tmp7:= Array(1..(max_terms + 1),[]); > array_tmp8:= Array(1..(max_terms + 1),[]); > array_tmp9:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_t:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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[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_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_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_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <= max_terms do # do number 3 > array_x1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_x1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_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_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_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_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_t := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_const_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_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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > t_start := 0.5; > t_end := 5.0; > array_x1_init[1] := exact_soln_x1(t_start); > array_x2_init[1] := exact_soln_x2(t_start); > array_x2_init[2] := exact_soln_x2p(t_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 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 > ; > 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 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > 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) > ; > 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) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > sub_iter := 1; > while sub_iter <= 3 + glob_max_terms do # do number 3 > atomall() > ; > sub_iter := sub_iter + 1; > od;# end do number 3 > ; > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3 > ;#was right paren 0004C > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > order_diff := 1; > #Jump Series array_x1 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x1 > order_diff := 1; > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =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_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 > order_diff := 2; > #Jump Series array_x2 > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x2 > order_diff := 2; > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =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_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 > 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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > 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_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if glob_html_log then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-02T02:14:46-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"complicated3") > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * 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,"complicated3 diffeq.mxt") > ; > logitem_str(html_log_file,"complicated3 maple results") > ; > logitem_str(html_log_file,"sub iter tot order + max terms") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > 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;") > ; > 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 glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_max_trunc_err, glob_hmin, glob_optimal_done, glob_clock_start_sec, min_in_hour, glob_normmax, glob_iter, hours_in_day, glob_percent_done, glob_start, glob_orig_start_sec, glob_smallish_float, glob_last_good_h, glob_disp_incr, years_in_century, glob_display_flag, glob_dump, glob_max_opt_iter, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_order, glob_max_rel_trunc_err, glob_log10_relerr, glob_hmin_init, glob_hmax, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_dump_analytic, glob_clock_sec, sec_in_min, glob_warned, glob_look_poles, glob_large_float, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_optimal_expect_sec, glob_warned2, glob_max_iter, glob_log10_abserr, centuries_in_millinium, days_in_year, djd_debug2, glob_reached_optimal_h, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, djd_debug, glob_current_iter, glob_almost_1, glob_html_log, glob_unchanged_h_cnt, glob_max_hours, array_const_0D0, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1, array_x2, array_x1_init, array_m1, array_1st_rel_error, array_x2_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_type_pole, array_last_rel_error, array_t, array_norms, array_x1_higher, array_poles, array_x2_higher_work2, array_x2_higher, array_real_pole, array_x2_higher_work, array_x1_higher_work, array_complex_pole, array_x1_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_iolevel := 5; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; ALWAYS := 1; INFO := 2; glob_curr_iter_when_opt := 0; glob_max_sec := 10000.0; glob_max_trunc_err := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_optimal_done := false; glob_clock_start_sec := 0.; min_in_hour := 60.0; glob_normmax := 0.; glob_iter := 0; hours_in_day := 24.0; glob_percent_done := 0.; glob_start := 0; glob_orig_start_sec := 0.; glob_smallish_float := 0.1*10^(-100); glob_last_good_h := 0.1; glob_disp_incr := 0.1; years_in_century := 100.0; glob_display_flag := true; glob_dump := false; glob_max_opt_iter := 10; glob_log10normmin := 0.1; glob_max_minutes := 0.; glob_log10relerr := 0.; glob_small_float := 0.1*10^(-50); glob_optimal_start := 0.; glob_max_order := 30; glob_max_rel_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_hmax := 1.0; MAX_UNCHANGED := 10; glob_no_eqs := 0; glob_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_clock_sec := 0.; sec_in_min := 60.0; glob_warned := false; glob_look_poles := false; glob_large_float := 0.90*10^101; glob_h := 0.1; glob_not_yet_start_msg := true; glob_initial_pass := true; glob_not_yet_finished := true; glob_optimal_expect_sec := 0.1; glob_warned2 := false; glob_max_iter := 1000; glob_log10_abserr := 0.1*10^(-10); centuries_in_millinium := 10.0; days_in_year := 365.0; djd_debug2 := true; glob_reached_optimal_h := false; glob_log10abserr := 0.; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); djd_debug := true; glob_current_iter := 0; glob_almost_1 := 0.9990; glob_html_log := true; glob_unchanged_h_cnt := 0; glob_max_hours := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_max_order := 2; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/complicated3postode.ode#################"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); 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, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "t_start := 0.5;"); omniout_str(ALWAYS, "t_end := 5.0;"); omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_x1 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2 := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x2p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 0.0001;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_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 := Array(1 .. max_terms + 1, []); array_x2 := Array(1 .. max_terms + 1, []); array_x1_init := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_x2_init := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_tmp7 := Array(1 .. max_terms + 1, []); array_tmp8 := Array(1 .. max_terms + 1, []); array_tmp9 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_t := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []); array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []); array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); 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[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_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_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_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_t[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_norms[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 <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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 <= max_terms do array_x1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[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_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_const_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_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_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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_t[1] := t_start; array_t[2] := glob_h; order_diff := 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; 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; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); 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); 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); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_t[1] <= t_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; sub_iter := 1; while sub_iter <= 3 + glob_max_terms do atomall(); sub_iter := sub_iter + 1 end do; if glob_look_poles then check_for_pole() end if; array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 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; 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; 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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); 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_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-02T02:14:46-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "complicated3"); logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * 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, "complicated3 diffeq.mxt"); logitem_str(html_log_file, "complicated3 maple results"); logitem_str(html_log_file, "sub iter tot order + max terms"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); 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;"); 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/complicated3postode.ode################# diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; #END FIRST INPUT BLOCK ! #BEGIN SECOND INPUT BLOCK t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x2_init[1] := exact_soln_x2(t_start); array_x2_init[2] := exact_soln_x2p(t_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c1 + 6.0 * c3 * exp(-t); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; c1 + c2 * exp(2.0 * t) + c3 * exp(-t); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion t[1] = 0.5 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 1e-05 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 1e-05 t[1] = 0.5 x1[1] (analytic) = 0.0012917551874827401624868391629841 x1[1] (numeric) = 0.0012917551874827401624868391629841 absolute error = 0 relative error = 0 % h = 1e-05 x2[1] (analytic) = 0.00082561556360559907415319735476789 x2[1] (numeric) = 0.00082561556360559907415319735476789 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.22 NO POLE NO POLE t[1] = 0.50001 x1[1] (analytic) = 0.0012917442699854529125006082860118 x1[1] (numeric) = 0.0012917442697671030658862571704784 absolute error = 2.183498466143511155334e-13 relative error = 1.6903488692603999770323183885140e-08 % h = 1e-05 x2[1] (analytic) = 0.00082562461725876370002024077185103 x2[1] (numeric) = 0.00082562461736794085640242707234942 absolute error = 1.0917715638218630049839e-13 relative error = 1.3223582981897506563710554495991e-08 % h = 1e-05 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.4MB, time=0.51 memory used=11.4MB, alloc=4.4MB, time=0.80 NO POLE NO POLE t[1] = 0.50002 x1[1] (analytic) = 0.0012917333525973400895138324871812 x1[1] (numeric) = 0.0012917333517239375270567373402211 absolute error = 8.734025624570951469601e-13 relative error = 6.7614772096803846154192825553072e-08 % h = 1e-05 x2[1] (analytic) = 0.00082563367114759095929891755098496 x2[1] (numeric) = 0.00082563367158430777304776304159268 absolute error = 4.3671681374884549060772e-13 relative error = 5.2894743638765385460225858394580e-08 % h = 1e-05 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=1.09 NO POLE NO POLE t[1] = 0.50003 x1[1] (analytic) = 0.0012917224353184006017877004750958 x1[1] (numeric) = 0.0012917224333532337203534283257063 absolute error = 1.9651668814342721493895e-12 relative error = 1.5213538355473961963192059508182e-07 % h = 1e-05 x2[1] (analytic) = 0.00082564272527208501941416438049361 x2[1] (numeric) = 0.00082564272625471709300268377174234 absolute error = 9.8263207358851939124873e-13 relative error = 1.1901419869771148115142049428319e-07 % h = 1e-05 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=1.37 NO POLE NO POLE memory used=22.8MB, alloc=4.4MB, time=1.66 t[1] = 0.50004 x1[1] (analytic) = 0.0012917115181486333575943182918853 x1[1] (numeric) = 0.0012917115146549818198367166601437 absolute error = 3.4936515377576016317416e-12 relative error = 2.7046685646690948387092007323119e-07 % h = 1e-05 x2[1] (analytic) = 0.00082565177963225004787972600227534 x2[1] (numeric) = 0.00082565178137918608577169364126929 absolute error = 1.74693603789196763899395e-12 relative error = 2.1158266486993618396219531053189e-07 % h = 1e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.96 NO POLE NO POLE t[1] = 0.50005 x1[1] (analytic) = 0.0012917006010880372652167092040327 x1[1] (numeric) = 0.0012917005956291719992722179138311 absolute error = 5.4588652659444912902016e-12 relative error = 4.2261072429217181776493150255711e-07 % h = 1e-05 x2[1] (analytic) = 0.00082566083422809021229815693339498 x2[1] (numeric) = 0.00082566083695773202145034208764513 absolute error = 2.72964180915218515425015e-12 relative error = 3.3060085885073203719845879843143e-07 % h = 1e-05 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=2.25 NO POLE NO POLE t[1] = 0.50006 x1[1] (analytic) = 0.0012916896841366112329488135932026 x1[1] (numeric) = 0.0012916896762757944321307678512614 absolute error = 7.8608168008180457419412e-12 relative error = 6.0856852054774734754965871147703e-07 % h = 1e-05 x2[1] (analytic) = 0.00082566988905960968036082318771056 x2[1] (numeric) = 0.00082566989299037217072524279772148 absolute error = 3.93076249036441961001092e-12 relative error = 4.7606949731948334431309245247962e-07 % h = 1e-05 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.54 memory used=38.1MB, alloc=4.5MB, time=2.84 NO POLE NO POLE t[1] = 0.50007 x1[1] (analytic) = 0.0012916787672943541690954888470709 x1[1] (numeric) = 0.0012916787565948392915884135879652 absolute error = 1.06995148775070752591057e-11 relative error = 8.2834177880922127899475060384362e-07 % h = 1e-05 x2[1] (analytic) = 0.00082567894412681261984790399753532 x2[1] (numeric) = 0.0008256789494771238048740928987142 absolute error = 5.35031118502618890117888e-12 relative error = 6.4798929693966577611983718299874e-07 % h = 1e-05 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.5MB, time=3.13 NO POLE NO POLE t[1] = 0.50008 x1[1] (analytic) = 0.0012916678505612649819725092501548 x1[1] (numeric) = 0.0012916678365862967505264047470872 absolute error = 1.39749682314461045030676e-11 relative error = 1.0819320327105454296721834727601e-06 % h = 1e-05 x2[1] (analytic) = 0.00082568799942970319862839353533439 x2[1] (numeric) = 0.00082568800641800419576569214979255 absolute error = 6.98830099713729861445816e-12 relative error = 8.4636097435884597805517592219944e-07 % h = 1e-05 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.5MB, time=3.42 NO POLE NO POLE memory used=49.5MB, alloc=4.5MB, time=3.71 t[1] = 0.50009 x1[1] (analytic) = 0.0012916569339373425799065658746448 x1[1] (numeric) = 0.0012916569162501569815311846156977 absolute error = 1.76871855983753812589471e-11 relative error = 1.3693408159440403613010771750836e-06 % h = 1e-05 x2[1] (analytic) = 0.00082569705496828558466010263545667 x2[1] (numeric) = 0.00082569706381303061585996213427319 absolute error = 8.84474503119985949881652e-12 relative error = 1.0711852462086811774881337485085e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.5MB, time=3.99 NO POLE NO POLE t[1] = 0.5001 x1[1] (analytic) = 0.001291646017422585871235266471237 x1[1] (numeric) = 0.0012916459955864101568943813008389 absolute error = 2.18361757143408851703981e-11 relative error = 1.6905696622603975121688388481235e-06 % h = 1e-05 x2[1] (analytic) = 0.00082570611074256394598966051590164 x2[1] (numeric) = 0.0008257061216622203382079654524192 absolute error = 1.091965639221830493651756e-11 relative error = 1.3224628291049187910780476577553e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.5MB, time=4.28 NO POLE NO POLE t[1] = 0.50011 x1[1] (analytic) = 0.0012916351010169937643071353599673 x1[1] (numeric) = 0.0012916350745950464486127988853056 absolute error = 2.64219473156943364746617e-11 relative error = 2.0456201054686813296287910749830e-06 % h = 1e-05 x2[1] (analytic) = 0.00082571516675254245075251650012108 x2[1] (numeric) = 0.00082571517996559063645192491484405 absolute error = 1.321304818569940841472297e-11 relative error = 1.6001944396473960321802975514030e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.5MB, time=4.56 memory used=64.8MB, alloc=4.5MB, time=4.85 NO POLE NO POLE t[1] = 0.50012 x1[1] (analytic) = 0.0012916241847205651674816133210459 x1[1] (numeric) = 0.001291624153276056028388408583161 absolute error = 3.14445091390932047378849e-11 relative error = 2.4344936794363314026741085013210e-06 % h = 1e-05 x2[1] (analytic) = 0.00082572422299822526717294173885586 x2[1] (numeric) = 0.00082572423872315878482524273652049 absolute error = 1.572493351765230099766463e-11 relative error = 1.9043807944200395182999730576679e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=5.13 NO POLE NO POLE t[1] = 0.50013 x1[1] (analytic) = 0.0012916132685332989891290574856932 x1[1] (numeric) = 0.0012916132316294290676283398949865 absolute error = 3.69038699215007175907067e-11 relative error = 2.8571919180891645945882352957991e-06 % h = 1e-05 x2[1] (analytic) = 0.00082573327947961656356403093200764 x2[1] (numeric) = 0.00082573329793494205815251973139452 absolute error = 1.845532549458848879938688e-11 relative error = 2.2350226099908648785935125666169e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=5.41 NO POLE NO POLE memory used=76.2MB, alloc=4.5MB, time=5.68 t[1] = 0.50014 x1[1] (analytic) = 0.0012916023524551941376307412269771 x1[1] (numeric) = 0.0012916023096551557374448717628669 absolute error = 4.28000384001858694641102e-11 relative error = 3.3137163554113771756716771344749e-06 % h = 1e-05 x2[1] (analytic) = 0.00082574233619672050832770405054562 x2[1] (numeric) = 0.00082574235760095773184957450760433 absolute error = 2.140423722352187045705871e-11 relative error = 2.5921206029119763614182818280748e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=5.96 NO POLE NO POLE t[1] = 0.50015 x1[1] (analytic) = 0.0012915914364862495213788540506512 x1[1] (numeric) = 0.0012915913873532262086554237251098 absolute error = 4.91330233127234303255414e-11 relative error = 3.8040685254455469560452239722192e-06 % h = 1e-05 x2[1] (analytic) = 0.00082575139314954126995470805844824 x2[1] (numeric) = 0.00082575141772122308192346266330426 absolute error = 2.457168181196875460485602e-11 relative error = 2.9756754897195664419301079045007e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=6.24 NO POLE NO POLE t[1] = 0.50016 x1[1] (analytic) = 0.0012915805206264640487765014859936 x1[1] (numeric) = 0.0012915804647236306517825470706999 absolute error = 5.59028333969939544152937e-11 relative error = 4.3282499622926354185295282462512e-06 % h = 1e-05 x2[1] (analytic) = 0.00082576045033808301702461863467988 x2[1] (numeric) = 0.00082576047829575538497249598309387 absolute error = 2.795767236794787734841399e-11 relative error = 3.3856879869339154297287709482866e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=6.52 memory used=91.5MB, alloc=4.5MB, time=6.80 NO POLE NO POLE t[1] = 0.50017 x1[1] (analytic) = 0.0012915696048758366282377049766475 x1[1] (numeric) = 0.0012915695417663592370539159934876 absolute error = 6.31094773911837889831599e-11 relative error = 4.8862622001119898516011799421630e-06 % h = 1e-05 x2[1] (analytic) = 0.00082576950776234991820584189520253 x2[1] (numeric) = 0.00082576953932457191818626163505205 absolute error = 3.156222199998041973984952e-11 relative error = 3.8221588110593910765514465845099e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=7.08 NO POLE NO POLE t[1] = 0.50018 x1[1] (analytic) = 0.0012915586892343661681874017714626 x1[1] (numeric) = 0.0012915586184814021344023187461127 absolute error = 7.07529640337850830253499e-11 relative error = 5.4781067731213454824251412292854e-06 % h = 1e-05 x2[1] (analytic) = 0.00082577856542234614225561611502238 x2[1] (numeric) = 0.0008257786008076899593456413683762 absolute error = 3.538534381709002525335382e-11 relative error = 4.2850886785844481840141062122829e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=7.36 NO POLE NO POLE t[1] = 0.50019 x1[1] (analytic) = 0.0012915477737020515770614448153374 x1[1] (numeric) = 0.0012915476948687495134656487936624 absolute error = 7.88333020635957960216750e-11 relative error = 6.1037852155968276099636124143558e-06 % h = 1e-05 x2[1] (analytic) = 0.0008257876233180758580200134502716 x2[1] (numeric) = 0.00082578766274512678682283071162659 absolute error = 3.942705092880281726135499e-11 relative error = 4.7744783059816282114008534737655e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=7.65 memory used=106.8MB, alloc=4.5MB, time=7.93 NO POLE NO POLE t[1] = 0.5002 x1[1] (analytic) = 0.0012915368582788917633066026400632 x1[1] (numeric) = 0.0012915367709283915435868959670638 absolute error = 8.73505002197197066729994e-11 relative error = 6.7632990618729537381613777390467e-06 % h = 1e-05 x2[1] (analytic) = 0.0008257966814495432344339416603249 x2[1] (numeric) = 0.00082579672513689967958135817157577 absolute error = 4.368735644514741651125087e-11 relative error = 5.2903284097075588835012284234319e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=8.22 NO POLE NO POLE t[1] = 0.50021 x1[1] (analytic) = 0.0012915259429648856353805592551682 x1[1] (numeric) = 0.0012915258466603183938141376162115 absolute error = 9.63045672415664216389567e-11 relative error = 7.4566498463426357092074627522840e-06 % h = 1e-05 x2[1] (analytic) = 0.0008258057398167524405211458299511 x2[1] (numeric) = 0.00082580578798302591717610443266318 absolute error = 4.816627347665495860271208e-11 relative error = 5.8326397062029537984954673333612e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.5MB, time=8.52 memory used=118.2MB, alloc=4.5MB, time=8.81 NO POLE NO POLE t[1] = 0.50022 x1[1] (analytic) = 0.0012915150277600321017519140387637 x1[1] (numeric) = 0.0012915149220645202329005297628293 absolute error = 1.056955118688513842759344e-10 relative error = 8.1838391034571818368733376046962e-06 % h = 1e-05 x2[1] (analytic) = 0.00082581479841970764539421009149987 x2[1] (numeric) = 0.00082581485128352277975332155705491 absolute error = 5.286381513435911146555504e-11 relative error = 6.4014129118926120358876903290770e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.5MB, time=9.11 NO POLE NO POLE t[1] = 0.50023 x1[1] (analytic) = 0.0012915041126643300709001816283908 x1[1] (numeric) = 0.0012915039971409872293042982530669 absolute error = 1.155233428415958833753239e-10 relative error = 8.9448683677262990399274747682436e-06 % h = 1e-05 x2[1] (analytic) = 0.00082582385725841301825455934712328 x2[1] (numeric) = 0.00082582391503840754805065218530864 absolute error = 5.777999452979609283818536e-11 relative error = 6.9966487431854177644870617073634e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=9.41 NO POLE NO POLE t[1] = 0.50024 x1[1] (analytic) = 0.0012914931976777784513157918118686 x1[1] (numeric) = 0.0012914930718897095511887299098308 absolute error = 1.257880689001270619020378e-10 relative error = 9.7397391737180949756264026189470e-06 % h = 1e-05 x2[1] (analytic) = 0.0008258329163328727283924609910323 x2[1] (numeric) = 0.00082583297924769750339714873764382 absolute error = 6.291482477500468774661152e-11 relative error = 7.6183479164743398504369108710334e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=9.69 memory used=133.5MB, alloc=4.5MB, time=9.99 NO POLE NO POLE t[1] = 0.50025 x1[1] (analytic) = 0.0012914822828003761515000894181426 x1[1] (numeric) = 0.0012914821463106773664221636848499 absolute error = 1.364896987850779257332927e-10 relative error = 1.0568453056059080173282117580639e-05 % h = 1e-05 x2[1] (analytic) = 0.00082584197564309094518702663178858 x2[1] (numeric) = 0.00082584204391140992771329261581701 absolute error = 6.826831898252626598402843e-11 relative error = 8.2665111481364314652917618571992e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=10.28 NO POLE NO POLE t[1] = 0.50026 x1[1] (analytic) = 0.0012914713680321220799653342081357 x1[1] (numeric) = 0.0012914712204038808425779818104761 absolute error = 1.476282412373873523976596e-10 relative error = 1.1431011549434170167906019499384e-05 % h = 1e-05 x2[1] (analytic) = 0.00082585103518907183810621381463082 x2[1] (numeric) = 0.00082585110902956210351101340560253 absolute error = 7.384049026540479959097171e-11 relative error = 8.9411391545328296941423707989173e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=10.57 memory used=144.9MB, alloc=4.6MB, time=10.88 NO POLE NO POLE t[1] = 0.50027 x1[1] (analytic) = 0.0012914604533730151452347007655986 x1[1] (numeric) = 0.0012914602941693101469346009512187 absolute error = 1.592037049983000998143799e-10 relative error = 1.2327416188586687633929217459241e-05 % h = 1e-05 x2[1] (analytic) = 0.00082586009497081957670682774383651 x2[1] (numeric) = 0.00082586017460217131389370807987832 absolute error = 7.963135173718688033604181e-11 relative error = 9.6422326520087551437886623833567e-06 % h = 1e-05 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.6MB, time=11.17 NO POLE NO POLE t[1] = 0.50028 x1[1] (analytic) = 0.0012914495388230542558422783879629 x1[1] (numeric) = 0.001291449367606955446475463355014 absolute error = 1.712160988093668150329489e-10 relative error = 1.3257668508318364518999355225805e-05 % h = 1e-05 x2[1] (analytic) = 0.00082586915498833833063452300511837 x2[1] (numeric) = 0.0008258692406292548425562602023171 absolute error = 8.564091651192173719719873e-11 relative error = 1.0369792356893511550960654957623e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.6MB, time=11.46 NO POLE NO POLE t[1] = 0.50029 x1[1] (analytic) = 0.0012914386243822383203330709771937 x1[1] (numeric) = 0.001291438440716806907889028004229 absolute error = 1.836654314124440429729647e-10 relative error = 1.4221770043489344177853795781894e-05 % h = 1e-05 x2[1] (analytic) = 0.00082587821524163226962380528805599 x2[1] (numeric) = 0.00082587830711082997378505913168284 absolute error = 9.186919770416125384362685e-11 relative error = 1.1123818985500485390587312571186e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.6MB, time=11.75 memory used=160.2MB, alloc=4.6MB, time=12.05 NO POLE NO POLE t[1] = 0.5003 x1[1] (analytic) = 0.0012914277100505662472629969306448 x1[1] (numeric) = 0.0012914275134988546975687617663999 absolute error = 1.965517115496942351642449e-10 relative error = 1.5219722329018183506269352860280e-05 % h = 1e-05 x2[1] (analytic) = 0.00082588727573070556349803310856235 x2[1] (numeric) = 0.00082588737404691399245801922673252 absolute error = 9.831620842895998611817017e-11 relative error = 1.1904313254127145484113357903710e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.6MB, time=12.35 NO POLE NO POLE t[1] = 0.50031 x1[1] (analytic) = 0.001291416795828036945198889031914 x1[1] (numeric) = 0.0012914165859530889816131305447053 absolute error = 2.098749479635857584872087e-10 relative error = 1.6251526899881855075088385706219e-05 % h = 1e-05 x2[1] (analytic) = 0.00082589633645556238216941953138531 x2[1] (numeric) = 0.00082589644143752418404459905172326 absolute error = 1.0498196180187517952033795e-10 relative error = 1.2711275879055042607864042488876e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.6MB, time=12.63 memory used=171.6MB, alloc=4.6MB, time=12.93 NO POLE NO POLE t[1] = 0.50032 x1[1] (analytic) = 0.0012914058817146493227184943416995 x1[1] (numeric) = 0.0012914056580794999258255904281733 absolute error = 2.236351493968929039135262e-10 relative error = 1.7317185291115749264321398516925e-05 % h = 1e-05 x2[1] (analytic) = 0.0008259053974162068956390338926443 x2[1] (numeric) = 0.00082590550928267783460582058252477 absolute error = 1.1186647093896678668988047e-10 relative error = 1.3544707576549809101457837953404e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.6MB, time=13.23 NO POLE NO POLE t[1] = 0.50033 x1[1] (analytic) = 0.0012913949677104022884104740886584 x1[1] (numeric) = 0.0012913947298780776957145788416236 absolute error = 2.378323245926958952470348e-10 relative error = 1.8416699037813676397326138886838e-05 % h = 1e-05 x2[1] (analytic) = 0.00082591445861264327399680352240172 x2[1] (numeric) = 0.00082591457758239223079428841333719 absolute error = 1.1896974895679748489093547e-10 relative error = 1.4404609062861158476267113698896e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.6MB, time=13.52 NO POLE NO POLE t[1] = 0.50034 x1[1] (analytic) = 0.0012913840538152947508744035602647 x1[1] (numeric) = 0.0012913838013488124564935056953443 absolute error = 2.524664822943808978649204e-10 relative error = 1.9550069675127868875063019227262e-05 % h = 1e-05 x2[1] (analytic) = 0.00082592352004487568742151546726956 x2[1] (numeric) = 0.00082592364633668465985420896401433 absolute error = 1.2629180897243269349674477e-10 relative error = 1.5290981054222885023926738106875e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.6MB, time=13.82 memory used=186.9MB, alloc=4.6MB, time=14.11 NO POLE NO POLE t[1] = 0.50035 x1[1] (analytic) = 0.0012913731400293256187207719936699 x1[1] (numeric) = 0.0012913728724916943730807445345025 absolute error = 2.675376312456400274591674e-10 relative error = 2.0717298738268983310427172969660e-05 % h = 1e-05 x2[1] (analytic) = 0.00082593258171290830618081821305085 x2[1] (numeric) = 0.00082593271554557240962140968799229 absolute error = 1.3383266410344059147494144e-10 relative error = 1.6203824266852863424890645688173e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.6MB, time=14.41 NO POLE NO POLE t[1] = 0.50036 x1[1] (analytic) = 0.001291362226352493800570982466564 x1[1] (numeric) = 0.0012913619433067136100996236882901 absolute error = 2.830457801904713587782739e-10 relative error = 2.1918387762506102662656868857110e-05 % h = 1e-05 x2[1] (analytic) = 0.00082594164361674530063122340741629 x2[1] (numeric) = 0.00082594178520907276852335828082356 absolute error = 1.4159232746789213487340727e-10 relative error = 1.7143139416953048357036337527957e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.6MB, time=14.70 memory used=198.3MB, alloc=4.6MB, time=14.97 NO POLE NO POLE t[1] = 0.50037 x1[1] (analytic) = 0.001291351312784798205057351788037 x1[1] (numeric) = 0.0012913510137938603318784174188035 absolute error = 2.989909378731789343692335e-10 relative error = 2.3153338283166738371818393800902e-05 % h = 1e-05 x2[1] (analytic) = 0.00082595070575639084121810758261578 x2[1] (numeric) = 0.00082595085532720302557918188931652 absolute error = 1.4957081218436107430670074e-10 relative error = 1.8108927220709474104317336862971e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.6MB, time=15.24 NO POLE NO POLE t[1] = 0.50038 x1[1] (analytic) = 0.0012913403993262377408231103894432 x1[1] (numeric) = 0.0012913400839531247024503370696582 absolute error = 3.153731130383727733197850e-10 relative error = 2.4422151835636832493367507042683e-05 % h = 1e-05 x2[1] (analytic) = 0.00082595976813184909847571387822485 x2[1] (numeric) = 0.00082595992589998047039968632128044 absolute error = 1.5776813137192397244305559e-10 relative error = 1.9101188394292254165463609518260e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.6MB, time=15.52 NO POLE NO POLE t[1] = 0.50039 x1[1] (analytic) = 0.0012913294859768113165224022152644 x1[1] (numeric) = 0.0012913291537844968855535222143378 absolute error = 3.321923144309688800009266e-10 relative error = 2.5724829955360759832787204403526e-05 % h = 1e-05 x2[1] (analytic) = 0.00082596883074312424302715376392631 x2[1] (numeric) = 0.00082596899692742239318737525587594 absolute error = 1.6618429815016022149194963e-10 relative error = 2.0119923653855580862729903237325e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.6MB, time=15.80 memory used=213.6MB, alloc=4.6MB, time=16.08 NO POLE NO POLE t[1] = 0.5004 x1[1] (analytic) = 0.0012913185727365178408202846139762 x1[1] (numeric) = 0.0012913182232879670446310318042771 absolute error = 3.494485507961892528096991e-10 relative error = 2.7061374177841330080302143161148e-05 % h = 1e-05 x2[1] (analytic) = 0.00082597789359022044558440876232671 x2[1] (numeric) = 0.00082597806840954608473646945457097 absolute error = 1.7481932563915206069224426e-10 relative error = 2.1165133715537724950692060430409e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.6MB, time=16.35 NO POLE NO POLE t[1] = 0.50041 x1[1] (analytic) = 0.001291307659605356222392728228914 x1[1] (numeric) = 0.0012913072924635253428308353166801 absolute error = 3.671418308795618929122339e-10 relative error = 2.8431786038639789945669404384598e-05 % h = 1e-05 x2[1] (analytic) = 0.00082598695667314187694833217180798 x2[1] (numeric) = 0.00082598714034636883643292597270232 absolute error = 1.8367322695948459380089434e-10 relative error = 2.2236819295461035225091258374683e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.6MB, time=16.64 memory used=225.0MB, alloc=4.6MB, time=16.92 NO POLE NO POLE t[1] = 0.50042 x1[1] (analytic) = 0.0012912967465833253699266168891408 x1[1] (numeric) = 0.0012912963613111619430058039020724 absolute error = 3.852721634269208129870684e-10 relative error = 2.9836067073375825293045796136101e-05 % h = 1e-05 x2[1] (analytic) = 0.00082599601999189270800865078941384 x2[1] (numeric) = 0.00082599621273790794025445737164266 absolute error = 1.9274601523224580658222882e-10 relative error = 2.3334981109731938131726224124668e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.6MB, time=17.19 NO POLE NO POLE t[1] = 0.50043 x1[1] (analytic) = 0.0012912858336704241921197475003156 x1[1] (numeric) = 0.0012912854298308670077137015315876 absolute error = 4.038395571844060459687280e-10 relative error = 3.1274218817727563275931637660009e-05 % h = 1e-05 x2[1] (analytic) = 0.00082600508354647710974396663377145 x2[1] (numeric) = 0.00082600528558418068877055093157313 absolute error = 2.0203770357902658429780168e-10 relative error = 2.4459619874440937375393367271237e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.6MB, time=17.47 NO POLE NO POLE t[1] = 0.50044 x1[1] (analytic) = 0.0012912749208666515976808299355639 x1[1] (numeric) = 0.0012912744980226306992171761439886 absolute error = 4.228440208984636537915753e-10 relative error = 3.2746242807431574472191073094572e-05 % h = 1e-05 x2[1] (analytic) = 0.00082601414733689925322175866804788 x2[1] (numeric) = 0.00082601435888520437514248786486153 absolute error = 2.1154830512192072919681365e-10 relative error = 2.5610736305662613528874885070492e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.6MB, time=17.75 memory used=240.3MB, alloc=4.6MB, time=18.02 NO POLE NO POLE t[1] = 0.50045 x1[1] (analytic) = 0.0012912640081720064953294869263476 x1[1] (numeric) = 0.0012912635658864431794837507924231 absolute error = 4.422855633158457361339245e-10 relative error = 3.4252140578282875019148761892439e-05 % h = 1e-05 x2[1] (analytic) = 0.00082602321136316330959838452294175 x2[1] (numeric) = 0.00082602343264099629312336253004612 absolute error = 2.2127783298352497800710437e-10 relative error = 2.6788331119455623641974796398549e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.6MB, time=18.30 NO POLE NO POLE t[1] = 0.50046 x1[1] (analytic) = 0.0012912530955864877937962539533377 x1[1] (numeric) = 0.0012912526334222946101858147909134 absolute error = 4.621641931836104391624243e-10 relative error = 3.5791913666134928748763203579190e-05 % h = 1e-05 x2[1] (analytic) = 0.00082603227562527345011908221970975 x2[1] (numeric) = 0.00082603250685157373705810164642499 absolute error = 2.3122630028693901942671524e-10 relative error = 2.7992405031862700850602932417643e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.6MB, time=18.58 memory used=251.7MB, alloc=4.6MB, time=18.86 NO POLE NO POLE t[1] = 0.50047 x1[1] (analytic) = 0.0012912421831100944018225791372872 x1[1] (numeric) = 0.0012912417006301751527006148605812 absolute error = 4.824799192491219642767060e-10 relative error = 3.7365563606899649322876443360954e-05 % h = 1e-05 x2[1] (analytic) = 0.00082604134012323384611797189322822 x2[1] (numeric) = 0.00082604158151695400188348350925112 absolute error = 2.4139372015576551161602290e-10 relative error = 2.9222958758910653985906874307795e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.6MB, time=19.14 NO POLE NO POLE t[1] = 0.50048 x1[1] (analytic) = 0.0012912312707428252281608231299048 x1[1] (numeric) = 0.0012912307675100749681102462756057 absolute error = 5.032327502600505768542991e-10 relative error = 3.8973091936547402368540338769428e-05 % h = 1e-05 x2[1] (analytic) = 0.00082605040485704866901805751508965 x2[1] (numeric) = 0.00082605065663715438312815720553305 absolute error = 2.5178010571411009969044340e-10 relative error = 3.0479993016610367183451842945883e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.6MB, time=19.42 NO POLE NO POLE t[1] = 0.50049 x1[1] (analytic) = 0.0012912203584846791815742590047308 x1[1] (numeric) = 0.0012912198340619842172016440089174 absolute error = 5.244226949643726149958134e-10 relative error = 4.0614500191107007613419311972452e-05 % h = 1e-05 x2[1] (analytic) = 0.00082605946982672209033122861673442 x2[1] (numeric) = 0.00082605973221219217691266183044125 absolute error = 2.6238547008658143321370683e-10 relative error = 3.1763508520956799492448510306785e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.6MB, time=19.69 memory used=267.0MB, alloc=4.6MB, time=19.97 NO POLE NO POLE t[1] = 0.5005 x1[1] (analytic) = 0.0012912094463356551708370721480129 x1[1] (numeric) = 0.001291208900285893060466573877625 absolute error = 5.460497621103704982703879e-10 relative error = 4.2289789906665741021269613054041e-05 % h = 1e-05 x2[1] (analytic) = 0.00082606853503225828165826201261726 x2[1] (numeric) = 0.00082606880824208467994944570432018 absolute error = 2.7320982639829118369170292e-10 relative error = 3.3073505987928984485028791944623e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.6MB, time=20.24 NO POLE NO POLE t[1] = 0.50051 x1[1] (analytic) = 0.0012911985342957521047343601495841 x1[1] (numeric) = 0.0012911979661817916581016236881777 absolute error = 5.681139604466327364614064e-10 relative error = 4.3998962619369336927495088590228e-05 % h = 1e-05 x2[1] (analytic) = 0.00082607760047366141468882352340884 x2[1] (numeric) = 0.00082607788472684918954288559030604 absolute error = 2.8425318777485406206689720e-10 relative error = 3.4409986133490029865569568536966e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.6MB, time=20.52 memory used=278.4MB, alloc=4.6MB, time=20.80 NO POLE NO POLE t[1] = 0.50052 x1[1] (analytic) = 0.0012911876223649688920621326937406 x1[1] (numeric) = 0.0012911870317496701700081943812614 absolute error = 5.906152987220539383124792e-10 relative error = 4.5742019865421990174779411122717e-05 % h = 1e-05 x2[1] (analytic) = 0.00082608666615093566120146969923256 x2[1] (numeric) = 0.00082608696166650300358930591255028 absolute error = 2.9551556734238783621331772e-10 relative error = 3.5772949673587117080064334110723e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.6MB, time=21.07 NO POLE NO POLE t[1] = 0.50053 x1[1] (analytic) = 0.0012911767105433044416273114501219 x1[1] (numeric) = 0.001291176096989518755792491176429 absolute error = 6.135537856858348202736929e-10 relative error = 4.7518963181086358248794926495767e-05 % h = 1e-05 x2[1] (analytic) = 0.00082609573206408519306364954293594 x2[1] (numeric) = 0.00082609603906106342057699797504885 absolute error = 3.0699697822751334843211291e-10 relative error = 3.7162397324151500925542838778231e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.6MB, time=21.35 NO POLE NO POLE t[1] = 0.50054 x1[1] (analytic) = 0.0012911657988307576622477299645915 x1[1] (numeric) = 0.0012911651619013275747655147164657 absolute error = 6.369294300874822152481258e-10 relative error = 4.9329794102683563413987927510145e-05 % h = 1e-05 x2[1] (analytic) = 0.0008261047982131141822317062333974 x2[1] (numeric) = 0.00082610511691054773958623918107718 absolute error = 3.1869743355735453294767978e-10 relative error = 3.8578329801098509159538626756735e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.6MB, time=21.62 memory used=293.7MB, alloc=4.6MB, time=21.90 NO POLE NO POLE t[1] = 0.50055 x1[1] (analytic) = 0.0012911548872273274627521335501181 x1[1] (numeric) = 0.0012911542264850867859430522114881 absolute error = 6.607422406768090813386300e-10 relative error = 5.1174514166593194849440441155002e-05 % h = 1e-05 x2[1] (analytic) = 0.00082611386459802680075087884886784 x2[1] (numeric) = 0.00082611419521497326028931225323101 absolute error = 3.3061694645953843340436317e-10 relative error = 4.0020747820327542109604553236466e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.6MB, time=22.17 NO POLE NO POLE t[1] = 0.50056 x1[1] (analytic) = 0.0012911439757330127519801791776594 x1[1] (numeric) = 0.0012911432907407865480456685827779 absolute error = 6.849922262039345105948815e-10 relative error = 5.3053124909253310784808632174391e-05 % h = 1e-05 x2[1] (analytic) = 0.0008261229312188272207553040903474 x2[1] (numeric) = 0.00082612327397435728295052445407297 absolute error = 3.4275553006219522036372557e-10 relative error = 4.1489652097722072282876219608531e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.6MB, time=22.45 memory used=305.1MB, alloc=4.6MB, time=22.73 NO POLE NO POLE t[1] = 0.50057 x1[1] (analytic) = 0.0012911330643478124387824353670451 x1[1] (numeric) = 0.0012911323546684170194986976063497 absolute error = 7.096793954192837377606954e-10 relative error = 5.4965627867160440636337600436523e-05 % h = 1e-05 x2[1] (analytic) = 0.00082613199807551961446801800499697 x2[1] (numeric) = 0.00082613235318871710842622680738502 absolute error = 3.5511319749395820880238805e-10 relative error = 4.2985043349149643975683390035864e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.6MB, time=23.00 NO POLE NO POLE t[1] = 0.50058 x1[1] (analytic) = 0.0012911221530717254320203820778627 x1[1] (numeric) = 0.0012911214182679683584322330562533 absolute error = 7.348037570735881490216094e-10 relative error = 5.6912024576869587142952822015641e-05 % h = 1e-05 x2[1] (analytic) = 0.00082614106516810815420095770958501 x2[1] (numeric) = 0.00082614143285807003816483332002671 absolute error = 3.6768996188396387561044170e-10 relative error = 4.4506922290461872883209314353659e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.6MB, time=23.28 NO POLE NO POLE t[1] = 0.50059 x1[1] (analytic) = 0.0012911112419047506405664106003432 x1[1] (numeric) = 0.0012911104815394307226811198476104 absolute error = 7.603653199178852907527328e-10 relative error = 5.8892316574994228502428019197517e-05 % h = 1e-05 x2[1] (analytic) = 0.00082615013249659701235496311396918 x2[1] (numeric) = 0.00082615051298243337420684020439929 absolute error = 3.8048583636185187709043011e-10 relative error = 4.6055289637494445709198019071113e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.6MB, time=23.55 memory used=320.4MB, alloc=4.6MB, time=23.83 NO POLE NO POLE t[1] = 0.5006 x1[1] (analytic) = 0.0012911003308468869733038234462486 x1[1] (numeric) = 0.0012910995444827942697849451793852 absolute error = 7.863640927035188782668634e-10 relative error = 6.0906505398206320507629647361939e-05 % h = 1e-05 x2[1] (analytic) = 0.00082615920006099036141977864461309 x2[1] (numeric) = 0.00082615959356182441918484510151576 absolute error = 3.9350083405776506645690267e-10 relative error = 4.7630146106067119775709537459028e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.6MB, time=24.10 NO POLE NO POLE t[1] = 0.50061 x1[1] (analytic) = 0.0012910894198981333391268342397601 x1[1] (numeric) = 0.0012910886070980491569880296768899 absolute error = 8.128000841821388045628702e-10 relative error = 6.2954592583236298682837838165476e-05 % h = 1e-05 x2[1] (analytic) = 0.00082616826786129237397405496813805 x2[1] (numeric) = 0.00082616867459626047632356630467673 absolute error = 4.0673496810234951133653868e-10 relative error = 4.9231492411983722632923075128680e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.6MB, time=24.38 memory used=331.8MB, alloc=4.6MB, time=24.66 NO POLE NO POLE t[1] = 0.50062 x1[1] (analytic) = 0.0012910785090584886469405676083676 x1[1] (numeric) = 0.0012910776693851855412394185340237 absolute error = 8.396733031057011490743439e-10 relative error = 6.5036579666873080420143956000663e-05 % h = 1e-05 x2[1] (analytic) = 0.00082617733589750722268535071490973 x2[1] (numeric) = 0.00082617775608575884943986198375227 absolute error = 4.2018825162675451126884254e-10 relative error = 5.0859329271032151668988141398423e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.6MB, time=24.93 NO POLE NO POLE t[1] = 0.50063 x1[1] (analytic) = 0.0012910675983279518056610590737599 x1[1] (numeric) = 0.0012910667313441935791928726552469 absolute error = 8.669837582264681864185130e-10 relative error = 6.7152468185964067115924599406209e-05 % h = 1e-05 x2[1] (analytic) = 0.00082618640416963908031013420266005 x2[1] (numeric) = 0.00082618683803033684294274941006966 absolute error = 4.3386069776263261520740961e-10 relative error = 5.2513657398984373719923594435692e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.6MB, time=25.21 NO POLE NO POLE t[1] = 0.50064 x1[1] (analytic) = 0.001291056687706521724215254942717 x1[1] (numeric) = 0.0012910557929750634272068597972885 absolute error = 8.947314582970083951454285e-10 relative error = 6.9302259677415146307392281862034e-05 % h = 1e-05 x2[1] (analytic) = 0.0008261954726776921196937851601439 x2[1] (numeric) = 0.00082619592043001176183342418190711 absolute error = 4.4775231964213963902176321e-10 relative error = 5.4194477511596424679564654678698e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.6MB, time=25.48 memory used=347.1MB, alloc=4.6MB, time=25.76 NO POLE NO POLE t[1] = 0.50065 x1[1] (analytic) = 0.0012910457771941973115410121980021 x1[1] (numeric) = 0.0012910448542777852413445457105888 absolute error = 9.229164120701964664874133e-10 relative error = 7.1485955678190693809222491968452e-05 % h = 1e-05 x2[1] (analytic) = 0.0008262045414216705137705964508309 x2[1] (numeric) = 0.00082620500328480091170527945059345 absolute error = 4.6186313039793468299976255e-10 relative error = 5.5901790324608409109557858732977e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.6MB, time=26.03 NO POLE NO POLE t[1] = 0.50066 x1[1] (analytic) = 0.0012910348667909774765870983892555 x1[1] (numeric) = 0.0012910339152523491773737852804756 absolute error = 9.515386282992133131087799e-10 relative error = 7.3703557725313575850257413917509e-05 % h = 1e-05 x2[1] (analytic) = 0.00082621361040157843556377579663232 x2[1] (numeric) = 0.0008262140865947215987439251472138 absolute error = 4.7619314316318014935058148e-10 relative error = 5.7635596553744499849403938043519e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.6MB, time=26.31 NO POLE NO POLE memory used=358.5MB, alloc=4.6MB, time=26.58 t[1] = 0.50067 x1[1] (analytic) = 0.0012910239564968611283131915238901 x1[1] (numeric) = 0.001291022975898745390767113668075 absolute error = 9.805981157375460778558151e-10 relative error = 7.5955067355865151210286209639791e-05 % h = 1e-05 x2[1] (analytic) = 0.00082622267961742005818544750166287 x2[1] (numeric) = 0.00082622317035979112972720720992126 absolute error = 4.9074237107154175970825839e-10 relative error = 5.9395896914712937626548659898752e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.6MB, time=26.86 NO POLE NO POLE t[1] = 0.50068 x1[1] (analytic) = 0.0012910130463118471756898799579863 x1[1] (numeric) = 0.0012910120362169640367017374509565 absolute error = 1.0100948831389881425070298e-09 relative error = 7.8240486106985273356901717528215e-05 % h = 1e-05 x2[1] (analytic) = 0.00082623174906919955483665417603757 x2[1] (numeric) = 0.00082623225458002681202522681185463 absolute error = 5.0551082725718857263581706e-10 relative error = 6.1182692123206030666521604172421e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.6MB, time=27.13 NO POLE NO POLE t[1] = 0.50069 x1[1] (analytic) = 0.0012910021362359345276986622871902 x1[1] (numeric) = 0.0012910010962069952700595257635119 absolute error = 1.0400289392576391365236783e-09 relative error = 8.0559815515872292582433910623071e-05 % h = 1e-05 x2[1] (analytic) = 0.00082624081875692109880735845970363 x2[1] (numeric) = 0.0008262413392554459536003595896622 absolute error = 5.2049852485479300112995857e-10 relative error = 6.2995982894900154303122886730788e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.6MB, time=27.41 memory used=373.8MB, alloc=4.6MB, time=27.70 NO POLE NO POLE t[1] = 0.5007 x1[1] (analytic) = 0.0012909912262691220933319472376107 x1[1] (numeric) = 0.001290990155868829245427001437069 absolute error = 1.0704002928479049458005417e-09 relative error = 8.2913057119783058140959698059477e-05 % h = 1e-05 x2[1] (analytic) = 0.00082624988868058886347644474630742 x2[1] (numeric) = 0.00082625042438606586300727487263156 absolute error = 5.3570547699953083012632414e-10 relative error = 6.4835769945455750588657811384472e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.6MB, time=27.97 NO POLE NO POLE t[1] = 0.50071 x1[1] (analytic) = 0.0012909803164114087815930535567197 x1[1] (numeric) = 0.001290979215202456117095332139739 absolute error = 1.1012089526644977214169807e-09 relative error = 8.5300212456032920385389482377189e-05 % h = 1e-05 x2[1] (analytic) = 0.00082625895884020702231172090709628 x2[1] (numeric) = 0.00082625950997190384939295491242554 absolute error = 5.5113169682708123400532926e-10 relative error = 6.6702053990517327904219491568997e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.6MB, time=28.25 NO POLE NO POLE memory used=385.2MB, alloc=4.6MB, time=28.52 t[1] = 0.50072 x1[1] (analytic) = 0.0012909694066627935014962099042517 x1[1] (numeric) = 0.0012909682742078660390603215159984 absolute error = 1.1324549274624358883882533e-09 relative error = 8.7721283061995732904630126201496e-05 % h = 1e-05 x2[1] (analytic) = 0.00082626802923577974886992001485561 x2[1] (numeric) = 0.00082626859601297722249671411342422 absolute error = 5.6677719747362679409856861e-10 relative error = 6.8594835745713460570019378851779e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.6MB, time=28.80 NO POLE NO POLE t[1] = 0.50073 x1[1] (analytic) = 0.0012909584970232751620665547431055 x1[1] (numeric) = 0.001290957332885049165022400326005 absolute error = 1.1641382259970441544171005e-09 relative error = 9.0176270475103854660824570489862e-05 % h = 1e-05 x2[1] (analytic) = 0.00082627709986731121679670206788081 x2[1] (numeric) = 0.0008262776825093032926502182636731 absolute error = 5.8264199207585351619579229e-10 relative error = 7.0514115926656788455765758813824e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.6MB, time=29.08 NO POLE NO POLE t[1] = 0.50074 x1[1] (analytic) = 0.0012909475874928526723401362302469 x1[1] (numeric) = 0.0012909463912339956483866175846482 absolute error = 1.1962588570239535186455987e-09 relative error = 9.2665176232848152126668005720594e-05 % h = 1e-05 x2[1] (analytic) = 0.00082628617073480559982665571398422 x2[1] (numeric) = 0.00082628676946089937077750376643738 absolute error = 5.9872609377095084805245316e-10 relative error = 7.2459895248944016591090187711941e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.6MB, time=29.36 memory used=400.5MB, alloc=4.6MB, time=29.64 NO POLE NO POLE t[1] = 0.50075 x1[1] (analytic) = 0.0012909366780715249413639121076118 x1[1] (numeric) = 0.0012909354492546956422626317003331 absolute error = 1.2288168292991012804072787e-09 relative error = 9.5188001872778001422800590348753e-05 % h = 1e-05 x2[1] (analytic) = 0.00082629524183826707178329997453724 x2[1] (numeric) = 0.00082629585686778276839499687236242 absolute error = 6.1502951569661169689782518e-10 relative error = 7.4432174428155914776021854221296e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.6MB, time=29.91 NO POLE NO POLE t[1] = 0.50076 x1[1] (analytic) = 0.0012909257687592908781957495930115 x1[1] (numeric) = 0.0012909245069471392994647016134993 absolute error = 1.2618121515787310479795122e-09 relative error = 9.7744748932501290455276788317647e-05 % h = 1e-05 x2[1] (analytic) = 0.00082630431317769980657908596854734 x2[1] (numeric) = 0.00082630494472997079761153291224037 absolute error = 6.3155227099103244694369303e-10 relative error = 7.6430954179857317191509897757424e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.6MB, time=30.19 NO POLE NO POLE t[1] = 0.50077 x1[1] (analytic) = 0.0012909148595561493919044252710381 x1[1] (numeric) = 0.0012909135643113167725116779348736 absolute error = 1.2952448326193927473361645e-09 relative error = 0.00010033541894968442105311122699753 % h = 1e-05 x2[1] (analytic) = 0.00082631338475310797821539863677017 x2[1] (numeric) = 0.00082631403304748077112837553038302 absolute error = 6.4829437279291297689361285e-10 relative error = 7.8456235219597122009993661625132e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.6MB, time=30.48 memory used=415.8MB, alloc=4.6MB, time=30.76 NO POLE NO POLE t[1] = 0.50078 x1[1] (analytic) = 0.0012909039504620993915696249839714 x1[1] (numeric) = 0.0012909026213472182136269940834568 absolute error = 1.3291148811779426309005146e-09 relative error = 0.00010296001346205231110590117057881 % h = 1e-05 x2[1] (analytic) = 0.00082632245656449576078255846585668 x2[1] (numeric) = 0.00082632312182033000223923591860082 absolute error = 6.6525583424145667745274414e-10 relative error = 8.0508018262908291006020883447069e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.6MB, time=31.03 NO POLE NO POLE t[1] = 0.50079 x1[1] (analytic) = 0.0012908930414771397862819437226871 x1[1] (numeric) = 0.0012908916780548337747386574242446 absolute error = 1.3634223060115432862984425e-09 relative error = 0.00010561853400738839670152559550141 % h = 1e-05 x2[1] (analytic) = 0.00082633152861186732845982321253521 x2[1] (numeric) = 0.0008263322110485358048302920507882 absolute error = 6.8243666847637046883825299e-10 relative error = 8.2586304025307849166913841056403e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.6MB, time=31.31 memory used=427.2MB, alloc=4.6MB, time=31.59 NO POLE NO POLE t[1] = 0.5008 x1[1] (analytic) = 0.0012908821326012694851428855175656 x1[1] (numeric) = 0.001290880734434153607479240405683 absolute error = 1.3981671158776636451118826e-09 relative error = 0.00010831098212353463426392078478139 % h = 1e-05 x2[1] (analytic) = 0.00082634060089522685551538962782877 x2[1] (numeric) = 0.00082634130073211549338020791811508 absolute error = 6.9983688863786481829028631e-10 relative error = 8.4691093222296884303483411528421e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.6MB, time=31.87 NO POLE NO POLE t[1] = 0.50081 x1[1] (analytic) = 0.0012908712238344873972648633294021 x1[1] (numeric) = 0.0012908697904851678631858716968573 absolute error = 1.4333493195340789916325448e-09 relative error = 0.00011103735934839150269093256725074 % h = 1e-05 x2[1] (analytic) = 0.0008263496734145785163063951813071 x2[1] (numeric) = 0.00082635039087108638296015276482471 absolute error = 7.1745650786665375758351761e-10 relative error = 8.6822386569360546660791107521847e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.6MB, time=32.15 NO POLE NO POLE t[1] = 0.50082 x1[1] (analytic) = 0.0012908603151767924317711989403184 x1[1] (numeric) = 0.0012908588462078666929002273244159 absolute error = 1.4689689257388709716159025e-09 relative error = 0.00011379766721991800549224514181277 % h = 1e-05 x2[1] (analytic) = 0.00082635874616992648527891978537406 x2[1] (numeric) = 0.00082635948146546578923382032463778 absolute error = 7.3529553930395490053926372e-10 relative error = 8.8980184781968048528959014719781e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.6MB, time=32.44 memory used=442.5MB, alloc=4.6MB, time=32.71 NO POLE NO POLE t[1] = 0.50083 x1[1] (analytic) = 0.0012908494066281834977961228446744 x1[1] (numeric) = 0.0012908479016022402473685218092274 absolute error = 1.5050259432504276010354470e-09 relative error = 0.00011659190727613167292738645005142 % h = 1e-05 x2[1] (analytic) = 0.00082636781916127493696798751958978 x2[1] (numeric) = 0.00082636857251527102845744805776281 absolute error = 7.5335399609148946053817303e-10 relative error = 9.1164488575572663854027698170387e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.6MB, time=32.99 NO POLE NO POLE t[1] = 0.50084 x1[1] (analytic) = 0.0012908384981886595044847741399822 x1[1] (numeric) = 0.0012908369566682786770414993027724 absolute error = 1.5415203808274432748372098e-09 relative error = 0.00011942008105510856414381021546847 % h = 1e-05 x2[1] (analytic) = 0.00082637689238862804599756835502798 x2[1] (numeric) = 0.00082637766402051941747983638851293 absolute error = 7.7163189137148226803348495e-10 relative error = 9.3375298665611727848862038832185e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.6MB, time=33.27 memory used=453.9MB, alloc=4.6MB, time=33.54 NO POLE NO POLE t[1] = 0.50085 x1[1] (analytic) = 0.0012908275898582193609932004178204 x1[1] (numeric) = 0.0012908260114059721320744247232694 absolute error = 1.5784522472289187756945510e-09 relative error = 0.00012228219009498326931505451198053 % h = 1e-05 x2[1] (analytic) = 0.00082638596585198998708057987866837 x2[1] (numeric) = 0.00082638675598122827374236794352897 absolute error = 7.9012923828666178806486060e-10 relative error = 9.5612615767506636604104999144732e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.6MB, time=33.82 NO POLE NO POLE t[1] = 0.50086 x1[1] (analytic) = 0.0012908166816368619764883576547494 x1[1] (numeric) = 0.0012908150658153107623270748915343 absolute error = 1.6158215512141612827632151e-09 relative error = 0.00012517823593394891177897696445637 % h = 1e-05 x2[1] (analytic) = 0.0008263950395513649350188890178239 x2[1] (numeric) = 0.00082639584839741491527902679060892 absolute error = 8.0884604998026013777278502e-10 relative error = 9.7876440596662846699179350327419e-05 % h = 1e-05 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.6MB, time=34.09 NO POLE NO POLE t[1] = 0.50087 x1[1] (analytic) = 0.0012908057735245862601481101032286 x1[1] (numeric) = 0.0012908041198962847173637296665745 absolute error = 1.6536283015427843804366541e-09 relative error = 0.00012810822011025715017606657562254 % h = 1e-05 x2[1] (analytic) = 0.00082640411348675706470331376460328 x2[1] (numeric) = 0.00082640494126909666071641767814378 absolute error = 8.2778233959601310391354050e-10 relative error = 0.00010016677386846987481333731061163 % h = 1e-05 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.6MB, time=34.37 memory used=469.2MB, alloc=4.6MB, time=34.65 NO POLE NO POLE t[1] = 0.50088 x1[1] (analytic) = 0.0012907948655213911211612301825339 x1[1] (numeric) = 0.0012907931736488841464531630809169 absolute error = 1.6918725069747080671016170e-09 relative error = 0.00013107214416221818058783211168751 % h = 1e-05 x2[1] (analytic) = 0.00082641318765817055111362490040834 x2[1] (numeric) = 0.00082641403459629082927378527515983 absolute error = 8.4693812027816016037475149e-10 relative error = 0.00010248361629830129733675814768003 % h = 1e-05 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.6MB, time=34.93 NO POLE NO POLE t[1] = 0.50089 x1[1] (analytic) = 0.0012907839576272754687273983696766 x1[1] (numeric) = 0.0012907822270730991985686344756699 absolute error = 1.7305541762701587638940067e-09 relative error = 0.00013407000962820073867526712622711 % h = 1e-05 x2[1] (analytic) = 0.00082642226206560956931854772046646 x2[1] (numeric) = 0.00082642312837901474076303341196731 absolute error = 8.6631340517144448569150085e-10 relative error = 0.00010482696860151474998169371387909 % h = 1e-05 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.6MB, time=35.21 memory used=480.6MB, alloc=4.6MB, time=35.50 NO POLE NO POLE t[1] = 0.5009 x1[1] (analytic) = 0.0012907730498422382120572030903234 x1[1] (numeric) = 0.0012907712801689200223878796353194 absolute error = 1.7696733181896693234550040e-09 relative error = 0.00013710181804663210181739160116466 % h = 1e-05 x2[1] (analytic) = 0.00082643133670907829447576375839823 x2[1] (numeric) = 0.00082643222261728571558874432141554 absolute error = 8.8590820742111298056301731e-10 relative error = 0.00010719683149345192739366189608399 % h = 1e-05 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.6MB, time=35.78 NO POLE NO POLE t[1] = 0.50091 x1[1] (analytic) = 0.0012907621421662782603721406097174 x1[1] (numeric) = 0.0012907603329363367662931019222591 absolute error = 1.8092299414940790386874583e-09 relative error = 0.00014016757095599809124987017593012 % h = 1e-05 x2[1] (analytic) = 0.00082644041158858090183191251081983 x2[1] (numeric) = 0.0008264413173111210747481978807545 absolute error = 9.0572254017291628536993467e-10 relative error = 0.0001095932056894385827626880419567 % h = 1e-05 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.6MB, time=36.05 NO POLE NO POLE t[1] = 0.50092 x1[1] (analytic) = 0.0012907512345993945229046149236005 x1[1] (numeric) = 0.0012907493853753395783709634110546 absolute error = 1.8492240549445336515125459e-09 relative error = 0.00014326726989484307420370703659717 % h = 1e-05 x2[1] (analytic) = 0.00082644948670412156672259316198068 x2[1] (numeric) = 0.00082645041246053813983139085410291 absolute error = 9.2575641657310879769212223e-10 relative error = 0.0001120160919047845274345942984929 % h = 1e-05 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.6MB, time=36.33 memory used=495.9MB, alloc=4.6MB, time=36.63 NO POLE NO POLE t[1] = 0.50093 x1[1] (analytic) = 0.0012907403271415859088979376491362 x1[1] (numeric) = 0.0012907384374859186064125760224418 absolute error = 1.8896556673024853616266944e-09 relative error = 0.00014640091640176996604401735086204 % h = 1e-05 x2[1] (analytic) = 0.00082645856205570446457236630843608 x2[1] (numeric) = 0.00082645950806555423302105613552277 absolute error = 9.4600984976844868982708669e-10 relative error = 0.00011446549085478363052233688950748 % h = 1e-05 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.6MB, time=36.91 NO POLE NO POLE t[1] = 0.50094 x1[1] (analytic) = 0.0012907294197928513276063279158343 x1[1] (numeric) = 0.001290727489268063997913492657059 absolute error = 1.9305247873296928352587753e-09 relative error = 0.00014956851201544023240887541363205 % h = 1e-05 x2[1] (analytic) = 0.00082646763764333377089475568375482 x2[1] (numeric) = 0.00082646860412618667709268199270049 absolute error = 9.6648285290619792630894567e-10 relative error = 0.00011694140325471381851739134781595 % h = 1e-05 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.6MB, time=37.19 memory used=507.3MB, alloc=4.6MB, time=37.47 NO POLE NO POLE t[1] = 0.50095 x1[1] (analytic) = 0.0012907185125531896882949122564762 x1[1] (numeric) = 0.0012907165407217659000736983289131 absolute error = 1.9718314237882212139275631e-09 relative error = 0.00015277005827457389134823937359346 % h = 1e-05 x2[1] (analytic) = 0.00082647671346701366129224988326191 x2[1] (numeric) = 0.00082647770064245279541453131123446 absolute error = 9.8717543913412228142797255e-10 relative error = 0.00011944382981983707490118566341949 % h = 1e-05 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.6MB, time=37.75 NO POLE NO POLE t[1] = 0.50096 x1[1] (analytic) = 0.0012907076054225999002397244980414 x1[1] (numeric) = 0.0012907055918470144597976012985802 absolute error = 2.0135755854404421231994612e-09 relative error = 0.0001560055567179495154629525660728 % h = 1e-05 x2[1] (analytic) = 0.00082648578952674831145630408881634 x2[1] (numeric) = 0.00082648679761436991194766083952926 absolute error = 1.00808762160049135675071292e-09 relative error = 0.00012197277126539943975658138039106 % h = 1e-05 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.6MB, time=38.02 NO POLE NO POLE t[1] = 0.50097 x1[1] (analytic) = 0.0012906966984010808727277056526351 x1[1] (numeric) = 0.0012906946426437998236940242061396 absolute error = 2.0557572810490336814464955e-09 relative error = 0.00015927500888440423404382152399411 % h = 1e-05 x2[1] (analytic) = 0.00082649486582254189716734179362378 x2[1] (numeric) = 0.00082649589504195535124594043429639 absolute error = 1.02921941345407859864067261e-09 relative error = 0.00012452822830663100937940263643915 % h = 1e-05 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.6MB, time=38.30 memory used=522.6MB, alloc=4.6MB, time=38.58 NO POLE NO POLE t[1] = 0.50098 x1[1] (analytic) = 0.0012906857914886315150567038084169 x1[1] (numeric) = 0.0012906836931121121380761952038423 absolute error = 2.0983765193769805086045746e-09 relative error = 0.00016257841631283373521077058378303 % h = 1e-05 x2[1] (analytic) = 0.00082650394235439859429475652708451 x2[1] (numeric) = 0.00082650499292522643845607230666162 absolute error = 1.05057082784416131577957711e-09 relative error = 0.00012711020165874593589001311976734 % h = 1e-05 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.6MB, time=38.85 NO POLE NO POLE t[1] = 0.50099 x1[1] (analytic) = 0.0012906748846852507365354740205306 x1[1] (numeric) = 0.0012906727432519415489617390885132 absolute error = 2.1414333091875737349320174e-09 relative error = 0.00016591578054219226805207315027245 % h = 1e-05 x2[1] (analytic) = 0.00082651301912232257879691357967621 x2[1] (numeric) = 0.00082651409126420049931761026887894 absolute error = 1.07214187792052069668920273e-09 relative error = 0.00012971869203694242684494098318453 % h = 1e-05 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.6MB, time=39.13 memory used=534.0MB, alloc=4.6MB, time=39.42 NO POLE NO POLE t[1] = 0.501 x1[1] (analytic) = 0.0012906639779909374464836782020351 x1[1] (numeric) = 0.0012906617930632782020726684336873 absolute error = 2.1849276592444110097683478e-09 relative error = 0.00016928710311149264476365959944152 % h = 1e-05 x2[1] (analytic) = 0.00082652209612631802672115172787186 x2[1] (numeric) = 0.00082652319005889486016297898165115 absolute error = 1.09393257683344182725377929e-09 relative error = 0.0001323537001564027448485516876632 % h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; Iterations = 100 Total Elapsed Time = 39 Seconds Elapsed Time(since restart) = 39 Seconds Expected Time Remaining = 2 Days 0 Hours 45 Minutes 0 Seconds Optimized Time Remaining = 2 Days 0 Hours 43 Minutes 49 Seconds Time to Timeout = 14 Minutes 20 Seconds Percent Done = 0.02244 % > quit memory used=534.5MB, alloc=4.6MB, time=39.45