|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > INFO, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_disp_incr, > sec_in_minute, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_optimal_done, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_max_iter, > glob_clock_start_sec, > years_in_century, > hours_in_day, > glob_display_flag, > djd_debug, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_start, > glob_warned2, > glob_optimal_start, > glob_look_poles, > glob_large_float, > glob_hmax, > min_in_hour, > djd_debug2, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_abserr, > glob_max_trunc_err, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_almost_1, > centuries_in_millinium, > glob_normmax, > glob_hmin, > glob_curr_iter_when_opt, > glob_last_good_h, > glob_clock_sec, > glob_max_opt_iter, > glob_log10normmin, > glob_current_iter, > glob_unchanged_h_cnt, > glob_relerr, > glob_reached_optimal_h, > glob_max_sec, > glob_log10_abserr, > days_in_year, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_x1_init, > array_x2_init, > array_type_pole, > array_norms, > array_x2, > array_x1, > array_m1, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_t, > array_last_rel_error, > array_fact_1, > array_real_pole, > array_x2_set_initial, > array_x1_higher_work, > array_complex_pole, > array_x1_set_initial, > array_x2_higher_work2, > array_poles, > array_x1_higher_work2, > array_x2_higher_work, > array_x2_higher, > array_x1_higher, > array_fact_2, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no, good_digits; > > > > > > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > good_digits := -trunc(log10(relerr/100.0)); > else > good_digits := -1; > fi;# end if 3 > ; > else > relerr := -1.0 ; > good_digits := -1; > 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,"%"); > print("good digits = ",good_digits); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > good_digits := -trunc(log10(relerr/100.0)); > else > good_digits := -1; > fi;# end if 3 > ; > else > relerr := -1.0 ; > good_digits := -1; > 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,"%"); > print("good digits = ",good_digits); > 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, good_digits; global INFO, DEBUGMASSIVE, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_iter, glob_disp_incr, sec_in_minute, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_hmin_init, glob_optimal_done, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_max_iter, glob_clock_start_sec, years_in_century, hours_in_day, glob_display_flag, djd_debug, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_start, glob_warned2, glob_optimal_start, glob_look_poles, glob_large_float, glob_hmax, min_in_hour, djd_debug2, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_abserr, glob_max_trunc_err, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_almost_1, centuries_in_millinium, glob_normmax, glob_hmin, glob_curr_iter_when_opt, glob_last_good_h, glob_clock_sec, glob_max_opt_iter, glob_log10normmin, glob_current_iter, glob_unchanged_h_cnt, glob_relerr, glob_reached_optimal_h, glob_max_sec, glob_log10_abserr, days_in_year, glob_orig_start_sec, glob_warned, glob_small_float, glob_max_hours, glob_log10_relerr, glob_dump_analytic, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_x1_init, array_x2_init, array_type_pole, array_norms, array_x2, array_x1, array_m1, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_t, array_last_rel_error, array_fact_1, array_real_pole, array_x2_set_initial, array_x1_higher_work, array_complex_pole, array_x1_set_initial, array_x2_higher_work2, array_poles, array_x1_higher_work2, array_x2_higher_work, array_x2_higher, array_x1_higher, array_fact_2, glob_last; if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then good_digits := -trunc(log10(relerr/100.0)) else good_digits := -1 end if else relerr := -1.0; good_digits := -1 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, "%"); print("good digits = ", good_digits); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "x1[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then good_digits := -trunc(log10(relerr/100.0)) else good_digits := -1 end if else relerr := -1.0; good_digits := -1 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, "%"); print("good digits = ", good_digits); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > INFO, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_disp_incr, > sec_in_minute, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_optimal_done, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_max_iter, > glob_clock_start_sec, > years_in_century, > hours_in_day, > glob_display_flag, > djd_debug, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_start, > glob_warned2, > glob_optimal_start, > glob_look_poles, > glob_large_float, > glob_hmax, > min_in_hour, > djd_debug2, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_abserr, > glob_max_trunc_err, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_almost_1, > centuries_in_millinium, > glob_normmax, > glob_hmin, > glob_curr_iter_when_opt, > glob_last_good_h, > glob_clock_sec, > glob_max_opt_iter, > glob_log10normmin, > glob_current_iter, > glob_unchanged_h_cnt, > glob_relerr, > glob_reached_optimal_h, > glob_max_sec, > glob_log10_abserr, > days_in_year, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_x1_init, > array_x2_init, > array_type_pole, > array_norms, > array_x2, > array_x1, > array_m1, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_t, > array_last_rel_error, > array_fact_1, > array_real_pole, > array_x2_set_initial, > array_x1_higher_work, > array_complex_pole, > array_x1_set_initial, > array_x2_higher_work2, > array_poles, > array_x1_higher_work2, > array_x2_higher_work, > array_x2_higher, > array_x1_higher, > array_fact_2, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_x2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(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 (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_x1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (omniabs(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"); > 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 > return(hnew); > #BOTTOM ADJUST FOR POLE > > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global INFO, DEBUGMASSIVE, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_iter, glob_disp_incr, sec_in_minute, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_hmin_init, glob_optimal_done, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_max_iter, glob_clock_start_sec, years_in_century, hours_in_day, glob_display_flag, djd_debug, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_start, glob_warned2, glob_optimal_start, glob_look_poles, glob_large_float, glob_hmax, min_in_hour, djd_debug2, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_abserr, glob_max_trunc_err, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_almost_1, centuries_in_millinium, glob_normmax, glob_hmin, glob_curr_iter_when_opt, glob_last_good_h, glob_clock_sec, glob_max_opt_iter, glob_log10normmin, glob_current_iter, glob_unchanged_h_cnt, glob_relerr, glob_reached_optimal_h, glob_max_sec, glob_log10_abserr, days_in_year, glob_orig_start_sec, glob_warned, glob_small_float, glob_max_hours, glob_log10_relerr, glob_dump_analytic, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_x1_init, array_x2_init, array_type_pole, array_norms, array_x2, array_x1, array_m1, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_t, array_last_rel_error, array_fact_1, array_real_pole, array_x2_set_initial, array_x1_higher_work, array_complex_pole, array_x1_set_initial, array_x2_higher_work2, array_poles, array_x1_higher_work2, array_x2_higher_work, array_x2_higher, array_x1_higher, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_x2_higher[1, 1]) then tmp := omniabs(array_x2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_x1_higher[1, 1]) then tmp := omniabs(array_x1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(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"); 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; return hnew end proc > # Begin Function number 5 > prog_report := proc(t_start,t_end) > global > INFO, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_disp_incr, > sec_in_minute, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_optimal_done, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_max_iter, > glob_clock_start_sec, > years_in_century, > hours_in_day, > glob_display_flag, > djd_debug, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_start, > glob_warned2, > glob_optimal_start, > glob_look_poles, > glob_large_float, > glob_hmax, > min_in_hour, > djd_debug2, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_abserr, > glob_max_trunc_err, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_almost_1, > centuries_in_millinium, > glob_normmax, > glob_hmin, > glob_curr_iter_when_opt, > glob_last_good_h, > glob_clock_sec, > glob_max_opt_iter, > glob_log10normmin, > glob_current_iter, > glob_unchanged_h_cnt, > glob_relerr, > glob_reached_optimal_h, > glob_max_sec, > glob_log10_abserr, > days_in_year, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_x1_init, > array_x2_init, > array_type_pole, > array_norms, > array_x2, > array_x1, > array_m1, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_t, > array_last_rel_error, > array_fact_1, > array_real_pole, > array_x2_set_initial, > array_x1_higher_work, > array_complex_pole, > array_x1_set_initial, > array_x2_higher_work2, > array_poles, > array_x1_higher_work2, > array_x2_higher_work, > array_x2_higher, > array_x1_higher, > array_fact_2, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > > > > > > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > > # End Function number 5 > end; prog_report := proc(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, DEBUGMASSIVE, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_iter, glob_disp_incr, sec_in_minute, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_hmin_init, glob_optimal_done, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_max_iter, glob_clock_start_sec, years_in_century, hours_in_day, glob_display_flag, djd_debug, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_start, glob_warned2, glob_optimal_start, glob_look_poles, glob_large_float, glob_hmax, min_in_hour, djd_debug2, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_abserr, glob_max_trunc_err, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_almost_1, centuries_in_millinium, glob_normmax, glob_hmin, glob_curr_iter_when_opt, glob_last_good_h, glob_clock_sec, glob_max_opt_iter, glob_log10normmin, glob_current_iter, glob_unchanged_h_cnt, glob_relerr, glob_reached_optimal_h, glob_max_sec, glob_log10_abserr, days_in_year, glob_orig_start_sec, glob_warned, glob_small_float, glob_max_hours, glob_log10_relerr, glob_dump_analytic, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_x1_init, array_x2_init, array_type_pole, array_norms, array_x2, array_x1, array_m1, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_t, array_last_rel_error, array_fact_1, array_real_pole, array_x2_set_initial, array_x1_higher_work, array_complex_pole, array_x1_set_initial, array_x2_higher_work2, array_poles, array_x1_higher_work2, array_x2_higher_work, array_x2_higher, array_x1_higher, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(t_end), convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_disp_incr, > sec_in_minute, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_optimal_done, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_max_iter, > glob_clock_start_sec, > years_in_century, > hours_in_day, > glob_display_flag, > djd_debug, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_start, > glob_warned2, > glob_optimal_start, > glob_look_poles, > glob_large_float, > glob_hmax, > min_in_hour, > djd_debug2, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_abserr, > glob_max_trunc_err, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_almost_1, > centuries_in_millinium, > glob_normmax, > glob_hmin, > glob_curr_iter_when_opt, > glob_last_good_h, > glob_clock_sec, > glob_max_opt_iter, > glob_log10normmin, > glob_current_iter, > glob_unchanged_h_cnt, > glob_relerr, > glob_reached_optimal_h, > glob_max_sec, > glob_log10_abserr, > days_in_year, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_x1_init, > array_x2_init, > array_type_pole, > array_norms, > array_x2, > array_x1, > array_m1, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_t, > array_last_rel_error, > array_fact_1, > array_real_pole, > array_x2_set_initial, > array_x1_higher_work, > array_complex_pole, > array_x1_set_initial, > array_x2_higher_work2, > array_poles, > array_x1_higher_work2, > array_x2_higher_work, > array_x2_higher, > array_x1_higher, > array_fact_2, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > > > > > > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((omniabs(array_x2_higher[1,m]) < glob_small_float) or (omniabs(array_x2_higher[1,m-1]) < glob_small_float) or (omniabs(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 (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_x1_higher[1,m]) < glob_small_float) or (omniabs(array_x1_higher[1,m-1]) < glob_small_float) or (omniabs(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 (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_x2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif ((omniabs(array_x2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_x2_higher[1,m-5]) >= (glob_large_float))) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(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 (omniabs(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 (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_x1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif ((omniabs(array_x1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_x1_higher[1,m-5]) >= (glob_large_float))) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(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 (omniabs(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 (omniabs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found ) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if ( not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found ) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if (array_pole[1] > array_poles[2,1]) then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global INFO, DEBUGMASSIVE, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_iter, glob_disp_incr, sec_in_minute, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_hmin_init, glob_optimal_done, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_max_iter, glob_clock_start_sec, years_in_century, hours_in_day, glob_display_flag, djd_debug, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_start, glob_warned2, glob_optimal_start, glob_look_poles, glob_large_float, glob_hmax, min_in_hour, djd_debug2, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_abserr, glob_max_trunc_err, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_almost_1, centuries_in_millinium, glob_normmax, glob_hmin, glob_curr_iter_when_opt, glob_last_good_h, glob_clock_sec, glob_max_opt_iter, glob_log10normmin, glob_current_iter, glob_unchanged_h_cnt, glob_relerr, glob_reached_optimal_h, glob_max_sec, glob_log10_abserr, days_in_year, glob_orig_start_sec, glob_warned, glob_small_float, glob_max_hours, glob_log10_relerr, glob_dump_analytic, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_x1_init, array_x2_init, array_type_pole, array_norms, array_x2, array_x1, array_m1, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_t, array_last_rel_error, array_fact_1, array_real_pole, array_x2_set_initial, array_x1_higher_work, array_complex_pole, array_x1_set_initial, array_x2_higher_work2, array_poles, array_x1_higher_work2, array_x2_higher_work, array_x2_higher, array_x1_higher, array_fact_2, glob_last; n := glob_max_terms; m := n - 3; while 10 <= m and (omniabs(array_x2_higher[1, m]) < glob_small_float or omniabs(array_x2_higher[1, m - 1]) < glob_small_float or omniabs(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 < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_x1_higher[1, m]) < glob_small_float or omniabs(array_x1_higher[1, m - 1]) < glob_small_float or omniabs(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 < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_x2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= omniabs(array_x2_higher[1, m]) or glob_large_float <= omniabs(array_x2_higher[1, m - 1]) or glob_large_float <= omniabs(array_x2_higher[1, m - 2]) or glob_large_float <= omniabs(array_x2_higher[1, m - 3]) or glob_large_float <= omniabs(array_x2_higher[1, m - 4]) or glob_large_float <= omniabs(array_x2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(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 < omniabs(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 < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_x1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= omniabs(array_x1_higher[1, m]) or glob_large_float <= omniabs(array_x1_higher[1, m - 1]) or glob_large_float <= omniabs(array_x1_higher[1, m - 2]) or glob_large_float <= omniabs(array_x1_higher[1, m - 3]) or glob_large_float <= omniabs(array_x1_higher[1, m - 4]) or glob_large_float <= omniabs(array_x1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(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 < omniabs(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 < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > INFO, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_disp_incr, > sec_in_minute, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_optimal_done, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_max_iter, > glob_clock_start_sec, > years_in_century, > hours_in_day, > glob_display_flag, > djd_debug, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_start, > glob_warned2, > glob_optimal_start, > glob_look_poles, > glob_large_float, > glob_hmax, > min_in_hour, > djd_debug2, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_abserr, > glob_max_trunc_err, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_almost_1, > centuries_in_millinium, > glob_normmax, > glob_hmin, > glob_curr_iter_when_opt, > glob_last_good_h, > glob_clock_sec, > glob_max_opt_iter, > glob_log10normmin, > glob_current_iter, > glob_unchanged_h_cnt, > glob_relerr, > glob_reached_optimal_h, > glob_max_sec, > glob_log10_abserr, > days_in_year, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_x1_init, > array_x2_init, > array_type_pole, > array_norms, > array_x2, > array_x1, > array_m1, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_t, > array_last_rel_error, > array_fact_1, > array_real_pole, > array_x2_set_initial, > array_x1_higher_work, > array_complex_pole, > array_x1_set_initial, > array_x2_higher_work2, > array_poles, > array_x1_higher_work2, > array_x2_higher_work, > array_x2_higher, > array_x1_higher, > array_fact_2, > glob_last; > > local iii; > > > > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2 > ; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_x2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_x2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_x1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_x1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3 > ; > > # End Function number 7 > end; get_norms := proc() local iii; global INFO, DEBUGMASSIVE, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_iter, glob_disp_incr, sec_in_minute, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_hmin_init, glob_optimal_done, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_max_iter, glob_clock_start_sec, years_in_century, hours_in_day, glob_display_flag, djd_debug, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_start, glob_warned2, glob_optimal_start, glob_look_poles, glob_large_float, glob_hmax, min_in_hour, djd_debug2, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_abserr, glob_max_trunc_err, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_almost_1, centuries_in_millinium, glob_normmax, glob_hmin, glob_curr_iter_when_opt, glob_last_good_h, glob_clock_sec, glob_max_opt_iter, glob_log10normmin, glob_current_iter, glob_unchanged_h_cnt, glob_relerr, glob_reached_optimal_h, glob_max_sec, glob_log10_abserr, days_in_year, glob_orig_start_sec, glob_warned, glob_small_float, glob_max_hours, glob_log10_relerr, glob_dump_analytic, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_x1_init, array_x2_init, array_type_pole, array_norms, array_x2, array_x1, array_m1, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_t, array_last_rel_error, array_fact_1, array_real_pole, array_x2_set_initial, array_x1_higher_work, array_complex_pole, array_x1_set_initial, array_x2_higher_work2, array_poles, array_x1_higher_work2, array_x2_higher_work, array_x2_higher, array_x1_higher, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_x2[iii]) then array_norms[iii] := omniabs(array_x2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_x1[iii]) then array_norms[iii] := omniabs(array_x1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > INFO, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_disp_incr, > sec_in_minute, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_optimal_done, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_max_iter, > glob_clock_start_sec, > years_in_century, > hours_in_day, > glob_display_flag, > djd_debug, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_start, > glob_warned2, > glob_optimal_start, > glob_look_poles, > glob_large_float, > glob_hmax, > min_in_hour, > djd_debug2, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_abserr, > glob_max_trunc_err, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_almost_1, > centuries_in_millinium, > glob_normmax, > glob_hmin, > glob_curr_iter_when_opt, > glob_last_good_h, > glob_clock_sec, > glob_max_opt_iter, > glob_log10normmin, > glob_current_iter, > glob_unchanged_h_cnt, > glob_relerr, > glob_reached_optimal_h, > glob_max_sec, > glob_log10_abserr, > days_in_year, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_x1_init, > array_x2_init, > array_type_pole, > array_norms, > array_x2, > array_x1, > array_m1, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_t, > array_last_rel_error, > array_fact_1, > array_real_pole, > array_x2_set_initial, > array_x1_higher_work, > array_complex_pole, > array_x1_set_initial, > array_x2_higher_work2, > array_poles, > array_x1_higher_work2, > array_x2_higher_work, > array_x2_higher, > array_x1_higher, > array_fact_2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_2D0[1] * array_x2[1]; > #emit pre diff $eq_no = 1 i = 1 > array_tmp6[1] := array_x1_higher[3,1]; > #emit pre diff $eq_no = 1 i = 1 > array_tmp8[1] := array_x1_higher[2,1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_x2_set_initial[1,3]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[1] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp12[1] := array_const_4D0[1] * array_x2[1]; > #emit pre diff $eq_no = 2 i = 1 > array_tmp13[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp16[1] := array_const_2D0[1] * array_x1[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_x1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[1] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_const_2D0[1] * array_x2[2]; > #emit pre diff $eq_no = 1 i = 2 > array_tmp6[2] := array_x1_higher[3,2]; > #emit pre diff $eq_no = 1 i = 2 > array_tmp8[2] := array_x1_higher[2,2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_x2_set_initial[1,4]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[2] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp12[2] := array_const_4D0[1] * array_x2[2]; > #emit pre diff $eq_no = 2 i = 2 > array_tmp13[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp16[2] := array_const_2D0[1] * array_x1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_x1_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[2] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_const_2D0[1] * array_x2[3]; > #emit pre diff $eq_no = 1 i = 3 > array_tmp6[3] := array_x1_higher[3,3]; > #emit pre diff $eq_no = 1 i = 3 > array_tmp8[3] := array_x1_higher[2,3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_x2_set_initial[1,5]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[3] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp12[3] := array_const_4D0[1] * array_x2[3]; > #emit pre diff $eq_no = 2 i = 3 > array_tmp13[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp16[3] := array_const_2D0[1] * array_x1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_x1_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[3] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_const_2D0[1] * array_x2[4]; > #emit pre diff $eq_no = 1 i = 4 > array_tmp6[4] := array_x1_higher[3,4]; > #emit pre diff $eq_no = 1 i = 4 > array_tmp8[4] := array_x1_higher[2,4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_x2_set_initial[1,6]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[4] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp12[4] := array_const_4D0[1] * array_x2[4]; > #emit pre diff $eq_no = 2 i = 4 > array_tmp13[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp16[4] := array_const_2D0[1] * array_x1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_x1_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[4] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_const_2D0[1] * array_x2[5]; > #emit pre diff $eq_no = 1 i = 5 > array_tmp6[5] := array_x1_higher[3,5]; > #emit pre diff $eq_no = 1 i = 5 > array_tmp8[5] := array_x1_higher[2,5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_x2_set_initial[1,7]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp10[5] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp12[5] := array_const_4D0[1] * array_x2[5]; > #emit pre diff $eq_no = 2 i = 5 > array_tmp13[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp16[5] := array_const_2D0[1] * array_x1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_x1_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[5] * expt(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 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp4[kkk] := array_const_2D0[1] * array_x2[kkk]; > #emit diff $eq_no = 1 > array_tmp6[kkk] := array_x1_higher[3,kkk]; > #emit diff $eq_no = 1 > array_tmp8[kkk] := array_x1_higher[2,kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_x2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp10[kkk] * expt(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 2 > fi;# end if 1 > ; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp12[kkk] := array_const_4D0[1] * array_x2[kkk]; > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp16[kkk] := array_const_2D0[1] * array_x1[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_x1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp17[kkk] * expt(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 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > > #BOTTOM ATOMALL ??? > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global INFO, DEBUGMASSIVE, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_iter, glob_disp_incr, sec_in_minute, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_hmin_init, glob_optimal_done, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_max_iter, glob_clock_start_sec, years_in_century, hours_in_day, glob_display_flag, djd_debug, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_start, glob_warned2, glob_optimal_start, glob_look_poles, glob_large_float, glob_hmax, min_in_hour, djd_debug2, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_abserr, glob_max_trunc_err, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_almost_1, centuries_in_millinium, glob_normmax, glob_hmin, glob_curr_iter_when_opt, glob_last_good_h, glob_clock_sec, glob_max_opt_iter, glob_log10normmin, glob_current_iter, glob_unchanged_h_cnt, glob_relerr, glob_reached_optimal_h, glob_max_sec, glob_log10_abserr, days_in_year, glob_orig_start_sec, glob_warned, glob_small_float, glob_max_hours, glob_log10_relerr, glob_dump_analytic, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_x1_init, array_x2_init, array_type_pole, array_norms, array_x2, array_x1, array_m1, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_t, array_last_rel_error, array_fact_1, array_real_pole, array_x2_set_initial, array_x1_higher_work, array_complex_pole, array_x1_set_initial, array_x2_higher_work2, array_poles, array_x1_higher_work2, array_x2_higher_work, array_x2_higher, array_x1_higher, array_fact_2, glob_last; array_tmp1[1] := array_x2_higher[2, 1]; array_tmp4[1] := array_const_2D0[1]*array_x2[1]; array_tmp6[1] := array_x1_higher[3, 1]; array_tmp8[1] := array_x1_higher[2, 1]; if not array_x2_set_initial[1, 3] then if 1 <= glob_max_terms then temporary := array_tmp10[1]*expt(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 end if; kkk := 2; array_tmp12[1] := array_const_4D0[1]*array_x2[1]; array_tmp13[1] := array_x2_higher[2, 1]; array_tmp16[1] := array_const_2D0[1]*array_x1[1]; if not array_x1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp17[1]*expt(glob_h, 1)*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 end if; kkk := 2; array_tmp1[2] := array_x2_higher[2, 2]; array_tmp4[2] := array_const_2D0[1]*array_x2[2]; array_tmp6[2] := array_x1_higher[3, 2]; array_tmp8[2] := array_x1_higher[2, 2]; if not array_x2_set_initial[1, 4] then if 2 <= glob_max_terms then temporary := array_tmp10[2]*expt(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 end if; kkk := 3; array_tmp12[2] := array_const_4D0[1]*array_x2[2]; array_tmp13[2] := array_x2_higher[2, 2]; array_tmp16[2] := array_const_2D0[1]*array_x1[2]; if not array_x1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp17[2]*expt(glob_h, 1)*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 end if; kkk := 3; array_tmp1[3] := array_x2_higher[2, 3]; array_tmp4[3] := array_const_2D0[1]*array_x2[3]; array_tmp6[3] := array_x1_higher[3, 3]; array_tmp8[3] := array_x1_higher[2, 3]; if not array_x2_set_initial[1, 5] then if 3 <= glob_max_terms then temporary := array_tmp10[3]*expt(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 end if; kkk := 4; array_tmp12[3] := array_const_4D0[1]*array_x2[3]; array_tmp13[3] := array_x2_higher[2, 3]; array_tmp16[3] := array_const_2D0[1]*array_x1[3]; if not array_x1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp17[3]*expt(glob_h, 1)*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 end if; kkk := 4; array_tmp1[4] := array_x2_higher[2, 4]; array_tmp4[4] := array_const_2D0[1]*array_x2[4]; array_tmp6[4] := array_x1_higher[3, 4]; array_tmp8[4] := array_x1_higher[2, 4]; if not array_x2_set_initial[1, 6] then if 4 <= glob_max_terms then temporary := array_tmp10[4]*expt(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 end if; kkk := 5; array_tmp12[4] := array_const_4D0[1]*array_x2[4]; array_tmp13[4] := array_x2_higher[2, 4]; array_tmp16[4] := array_const_2D0[1]*array_x1[4]; if not array_x1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp17[4]*expt(glob_h, 1)*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 end if; kkk := 5; array_tmp1[5] := array_x2_higher[2, 5]; array_tmp4[5] := array_const_2D0[1]*array_x2[5]; array_tmp6[5] := array_x1_higher[3, 5]; array_tmp8[5] := array_x1_higher[2, 5]; if not array_x2_set_initial[1, 7] then if 5 <= glob_max_terms then temporary := array_tmp10[5]*expt(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 end if; kkk := 6; array_tmp12[5] := array_const_4D0[1]*array_x2[5]; array_tmp13[5] := array_x2_higher[2, 5]; array_tmp16[5] := array_const_2D0[1]*array_x1[5]; if not array_x1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp17[5]*expt(glob_h, 1)*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 end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_x2_higher[2, kkk]; array_tmp4[kkk] := array_const_2D0[1]*array_x2[kkk]; array_tmp6[kkk] := array_x1_higher[3, kkk]; array_tmp8[kkk] := array_x1_higher[2, kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then if not array_x2_set_initial[1, kkk + order_d] then temporary := array_tmp10[kkk]*expt(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 end if; array_tmp12[kkk] := array_const_4D0[1]*array_x2[kkk]; array_tmp13[kkk] := array_x2_higher[2, kkk]; array_tmp16[kkk] := array_const_2D0[1]*array_x1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_x1_set_initial[2, kkk + order_d] then temporary := array_tmp17[kkk]*expt(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 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_minute, 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_minute * 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_minute; > 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_minute, years_in_century; secs := secs_in; if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*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_minute; 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_minute, 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_minute * 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_minute; > 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_minute, years_in_century; secs := convfloat(secs_in); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*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_minute; 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_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > > > > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (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_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < 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 (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 < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 17 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 18 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > > > > if (nnn <= glob_max_terms) then # if number 13 > if (array_fact_1[nnn] = 0) then # if number 14 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 18 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # Begin Function number 19 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > > > > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13 > if (array_fact_2[mmm,nnn] = 0) then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 19 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # Begin Function number 20 > convfp := proc(mmm) > (mmm); > > # End Function number 20 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 21 > convfloat := proc(mmm) > (mmm); > > # End Function number 21 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > > > > > > > > > > > > > > > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_x1 := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return(1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t)); > end; exact_soln_x1 := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 1.0 + 2.0*c1 + 6.0*c3*exp(-t) end proc > exact_soln_x1p := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return( - 6.0 * c3 * exp(-t)); > end; exact_soln_x1p := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return -6.0*c3*exp(-t) end proc > exact_soln_x2 := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return(1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); > end; exact_soln_x2 := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 1.0 + c1 + c2*exp(2.0*t) + c3*exp(-t) end proc > exact_soln_x2p := proc(t) > local c1,c2,c3; > c1 := 1.0; > c2 := 0.0002; > c3 := 0.0003; > return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); > end; exact_soln_x2p := proc(t) local c1, c2, c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 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 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > t_start,t_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter; > global > INFO, > DEBUGMASSIVE, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_disp_incr, > sec_in_minute, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_optimal_done, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_max_iter, > glob_clock_start_sec, > years_in_century, > hours_in_day, > glob_display_flag, > djd_debug, > glob_max_minutes, > glob_log10abserr, > MAX_UNCHANGED, > glob_start, > glob_warned2, > glob_optimal_start, > glob_look_poles, > glob_large_float, > glob_hmax, > min_in_hour, > djd_debug2, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_abserr, > glob_max_trunc_err, > glob_h, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > glob_almost_1, > centuries_in_millinium, > glob_normmax, > glob_hmin, > glob_curr_iter_when_opt, > glob_last_good_h, > glob_clock_sec, > glob_max_opt_iter, > glob_log10normmin, > glob_current_iter, > glob_unchanged_h_cnt, > glob_relerr, > glob_reached_optimal_h, > glob_max_sec, > glob_log10_abserr, > days_in_year, > glob_orig_start_sec, > glob_warned, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_3D0, > array_const_0D0, > array_const_4D0, > array_const_1, > array_const_2, > #END CONST > array_x1_init, > array_x2_init, > array_type_pole, > array_norms, > array_x2, > array_x1, > array_m1, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_1st_rel_error, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_t, > array_last_rel_error, > array_fact_1, > array_real_pole, > array_x2_set_initial, > array_x1_higher_work, > array_complex_pole, > array_x1_set_initial, > array_x2_higher_work2, > array_poles, > array_x1_higher_work2, > array_x2_higher_work, > array_x2_higher, > array_x1_higher, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > DEBUGMASSIVE := 4; > glob_max_terms := 30; > DEBUGL := 3; > ALWAYS := 1; > glob_iolevel := 5; > glob_iter := 0; > glob_disp_incr := 0.1; > sec_in_minute := 60; > glob_dump := false; > glob_optimal_expect_sec := 0.1; > glob_no_eqs := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_hmin_init := 0.001; > glob_optimal_done := false; > glob_percent_done := 0.0; > glob_log10relerr := 0.0; > glob_smallish_float := 0.1e-100; > glob_max_iter := 1000; > glob_clock_start_sec := 0.0; > years_in_century := 100; > hours_in_day := 24; > glob_display_flag := true; > djd_debug := true; > glob_max_minutes := 0.0; > glob_log10abserr := 0.0; > MAX_UNCHANGED := 10; > glob_start := 0; > glob_warned2 := false; > glob_optimal_start := 0.0; > glob_look_poles := false; > glob_large_float := 9.0e100; > glob_hmax := 1.0; > min_in_hour := 60; > djd_debug2 := true; > glob_html_log := true; > glob_subiter_method := 3; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_h := 0.1; > glob_not_yet_start_msg := true; > glob_initial_pass := true; > glob_not_yet_finished := true; > glob_almost_1 := 0.9990; > centuries_in_millinium := 10; > glob_normmax := 0.0; > glob_hmin := 0.00000000001; > glob_curr_iter_when_opt := 0; > glob_last_good_h := 0.1; > glob_clock_sec := 0.0; > glob_max_opt_iter := 10; > glob_log10normmin := 0.1; > glob_current_iter := 0; > glob_unchanged_h_cnt := 0; > glob_relerr := 0.1e-10; > glob_reached_optimal_h := false; > glob_max_sec := 10000.0; > glob_log10_abserr := 0.1e-10; > days_in_year := 365; > glob_orig_start_sec := 0.0; > glob_warned := false; > glob_small_float := 0.1e-50; > glob_max_hours := 0.0; > glob_log10_relerr := 0.1e-10; > glob_dump_analytic := false; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > 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/mtest6_revpostode.ode#################"); > omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#"); > omniout_str(ALWAYS,"# was complicatedrev.ode"); > omniout_str(ALWAYS,"#"); > omniout_str(ALWAYS,"t_start := 0.5;"); > omniout_str(ALWAYS,"t_end := 5.0;"); > omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);"); > omniout_str(ALWAYS,"array_x1_init[1 + 1] := exact_soln_x1p(t_start);"); > omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);"); > omniout_str(ALWAYS,"array_x2_init[1 + 1] := 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 := 1;"); > 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 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return(1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_x1p := proc(t)"); > omniout_str(ALWAYS,"local c1,c2,c3;"); > omniout_str(ALWAYS,"c1 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return( - 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 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return(1.0 + 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 := 1.0;"); > omniout_str(ALWAYS,"c2 := 0.0002;"); > omniout_str(ALWAYS,"c3 := 0.0003;"); > omniout_str(ALWAYS,"return( 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 > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_x1_init:= Array(0..(max_terms + 1),[]); > array_x2_init:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_x2:= Array(0..(max_terms + 1),[]); > array_x1:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_tmp7:= Array(0..(max_terms + 1),[]); > array_tmp8:= Array(0..(max_terms + 1),[]); > array_tmp9:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_tmp10:= Array(0..(max_terms + 1),[]); > array_tmp11:= Array(0..(max_terms + 1),[]); > array_tmp12:= Array(0..(max_terms + 1),[]); > array_tmp13:= Array(0..(max_terms + 1),[]); > array_tmp14:= Array(0..(max_terms + 1),[]); > array_tmp15:= Array(0..(max_terms + 1),[]); > array_tmp16:= Array(0..(max_terms + 1),[]); > array_tmp17:= Array(0..(max_terms + 1),[]); > array_t:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_x2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_x1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_x1_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > 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_x2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_t[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_fact_1[term] := 0.0; > term := term + 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_set_initial[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_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 <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_x1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_x1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_x2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_x2_higher[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_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 <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[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_x1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_t := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_t[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_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 > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > # > # was complicatedrev.ode > # > t_start := 0.5; > t_end := 5.0; > array_x1_init[0 + 1] := exact_soln_x1(t_start); > array_x1_init[1 + 1] := exact_soln_x1p(t_start); > array_x2_init[0 + 1] := exact_soln_x2(t_start); > array_x2_init[1 + 1] := 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 := 1; > #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 := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_x2_set_initial[1,1] := true; > array_x2_set_initial[1,2] := true; > array_x2_set_initial[1,3] := false; > array_x2_set_initial[1,4] := false; > array_x2_set_initial[1,5] := false; > array_x2_set_initial[1,6] := false; > array_x2_set_initial[1,7] := false; > array_x2_set_initial[1,8] := false; > array_x2_set_initial[1,9] := false; > array_x2_set_initial[1,10] := false; > array_x2_set_initial[1,11] := false; > array_x2_set_initial[1,12] := false; > array_x2_set_initial[1,13] := false; > array_x2_set_initial[1,14] := false; > array_x2_set_initial[1,15] := false; > array_x2_set_initial[1,16] := false; > array_x2_set_initial[1,17] := false; > array_x2_set_initial[1,18] := false; > array_x2_set_initial[1,19] := false; > array_x2_set_initial[1,20] := false; > array_x2_set_initial[1,21] := false; > array_x2_set_initial[1,22] := false; > array_x2_set_initial[1,23] := false; > array_x2_set_initial[1,24] := false; > array_x2_set_initial[1,25] := false; > array_x2_set_initial[1,26] := false; > array_x2_set_initial[1,27] := false; > array_x2_set_initial[1,28] := false; > array_x2_set_initial[1,29] := false; > array_x2_set_initial[1,30] := false; > array_x1_set_initial[2,1] := true; > array_x1_set_initial[2,2] := true; > array_x1_set_initial[2,3] := false; > array_x1_set_initial[2,4] := false; > array_x1_set_initial[2,5] := false; > array_x1_set_initial[2,6] := false; > array_x1_set_initial[2,7] := false; > array_x1_set_initial[2,8] := false; > array_x1_set_initial[2,9] := false; > array_x1_set_initial[2,10] := false; > array_x1_set_initial[2,11] := false; > array_x1_set_initial[2,12] := false; > array_x1_set_initial[2,13] := false; > array_x1_set_initial[2,14] := false; > array_x1_set_initial[2,15] := false; > array_x1_set_initial[2,16] := false; > array_x1_set_initial[2,17] := false; > array_x1_set_initial[2,18] := false; > array_x1_set_initial[2,19] := false; > array_x1_set_initial[2,20] := false; > array_x1_set_initial[2,21] := false; > array_x1_set_initial[2,22] := false; > array_x1_set_initial[2,23] := false; > array_x1_set_initial[2,24] := false; > array_x1_set_initial[2,25] := false; > array_x1_set_initial[2,26] := false; > array_x1_set_initial[2,27] := false; > array_x1_set_initial[2,28] := false; > array_x1_set_initial[2,29] := false; > array_x1_set_initial[2,30] := false; > if (glob_html_log) then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_t[1] := t_start; > array_t[2] := glob_h; > order_diff := 2; > #Start Series array_x2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x2[term_no] := array_x2_init[term_no] * expt(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]* expt(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_x1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_x1[term_no] := array_x1_init[term_no] * expt(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]* expt(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(); > if (omniabs(array_x2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(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) > ; > if (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_x1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 3) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while (subiter <= 3 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > #Jump Series array_x2 > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x2 > #BEFORE ADJUST SUBSERIES EQ =1 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_x1 > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[3,iii] := array_x1_higher[3,iii] / expt(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 > temp_sum := 0.0; > ord := 3; > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 2; > #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] / expt(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 > temp_sum := 0.0; > ord := 2; > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 3; > #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] / expt(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 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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] / expt(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 > 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 * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if (glob_html_log) then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-08-12T23:28:36-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest6_rev") > ; > logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 5 > 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 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 5 > ; > log_revs(html_log_file," 119 ") > ; > logitem_str(html_log_file,"mtest6_rev diffeq.mxt") > ; > logitem_str(html_log_file,"mtest6_rev maple results") > ; > logitem_str(html_log_file,"1st test with c++") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5 > 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 5 > ; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 5 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if (glob_html_log) then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > > # End Function number 8 > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global INFO, DEBUGMASSIVE, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_iter, glob_disp_incr, sec_in_minute, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_max_rel_trunc_err, glob_hmin_init, glob_optimal_done, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_max_iter, glob_clock_start_sec, years_in_century, hours_in_day, glob_display_flag, djd_debug, glob_max_minutes, glob_log10abserr, MAX_UNCHANGED, glob_start, glob_warned2, glob_optimal_start, glob_look_poles, glob_large_float, glob_hmax, min_in_hour, djd_debug2, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_abserr, glob_max_trunc_err, glob_h, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, glob_almost_1, centuries_in_millinium, glob_normmax, glob_hmin, glob_curr_iter_when_opt, glob_last_good_h, glob_clock_sec, glob_max_opt_iter, glob_log10normmin, glob_current_iter, glob_unchanged_h_cnt, glob_relerr, glob_reached_optimal_h, glob_max_sec, glob_log10_abserr, days_in_year, glob_orig_start_sec, glob_warned, glob_small_float, glob_max_hours, glob_log10_relerr, glob_dump_analytic, array_const_2D0, array_const_3D0, array_const_0D0, array_const_4D0, array_const_1, array_const_2, array_x1_init, array_x2_init, array_type_pole, array_norms, array_x2, array_x1, array_m1, array_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_1st_rel_error, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_t, array_last_rel_error, array_fact_1, array_real_pole, array_x2_set_initial, array_x1_higher_work, array_complex_pole, array_x1_set_initial, array_x2_higher_work2, array_poles, array_x1_higher_work2, array_x2_higher_work, array_x2_higher, array_x1_higher, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; DEBUGMASSIVE := 4; glob_max_terms := 30; DEBUGL := 3; ALWAYS := 1; glob_iolevel := 5; glob_iter := 0; glob_disp_incr := 0.1; sec_in_minute := 60; glob_dump := false; glob_optimal_expect_sec := 0.1; glob_no_eqs := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_hmin_init := 0.001; glob_optimal_done := false; glob_percent_done := 0.; glob_log10relerr := 0.; glob_smallish_float := 0.1*10^(-100); glob_max_iter := 1000; glob_clock_start_sec := 0.; years_in_century := 100; hours_in_day := 24; glob_display_flag := true; djd_debug := true; glob_max_minutes := 0.; glob_log10abserr := 0.; MAX_UNCHANGED := 10; glob_start := 0; glob_warned2 := false; glob_optimal_start := 0.; glob_look_poles := false; glob_large_float := 0.90*10^101; glob_hmax := 1.0; min_in_hour := 60; djd_debug2 := true; glob_html_log := true; glob_subiter_method := 3; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_h := 0.1; glob_not_yet_start_msg := true; glob_initial_pass := true; glob_not_yet_finished := true; glob_almost_1 := 0.9990; centuries_in_millinium := 10; glob_normmax := 0.; glob_hmin := 0.1*10^(-10); glob_curr_iter_when_opt := 0; glob_last_good_h := 0.1; glob_clock_sec := 0.; glob_max_opt_iter := 10; glob_log10normmin := 0.1; glob_current_iter := 0; glob_unchanged_h_cnt := 0; glob_relerr := 0.1*10^(-10); glob_reached_optimal_h := false; glob_max_sec := 10000.0; glob_log10_abserr := 0.1*10^(-10); days_in_year := 365; glob_orig_start_sec := 0.; glob_warned := false; glob_small_float := 0.1*10^(-50); glob_max_hours := 0.; glob_log10_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; 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/mtest6_revpostode.ode#################"); omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \ diff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#"); omniout_str(ALWAYS, "# was complicatedrev.ode"); omniout_str(ALWAYS, "#"); omniout_str(ALWAYS, "t_start := 0.5;"); omniout_str(ALWAYS, "t_end := 5.0;"); omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);"); omniout_str(ALWAYS, "array_x1_init[1 + 1] := exact_soln_x1p(t_start);") ; omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);"); omniout_str(ALWAYS, "array_x2_init[1 + 1] := 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 := 1;"); 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 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return(1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_x1p := proc(t)"); omniout_str(ALWAYS, "local c1,c2,c3;"); omniout_str(ALWAYS, "c1 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return( - 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 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return(1.0 + 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 := 1.0;"); omniout_str(ALWAYS, "c2 := 0.0002;"); omniout_str(ALWAYS, "c3 := 0.0003;"); omniout_str(ALWAYS, "return( 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_x1_init := Array(0 .. max_terms + 1, []); array_x2_init := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_x2 := Array(0 .. max_terms + 1, []); array_x1 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_tmp7 := Array(0 .. max_terms + 1, []); array_tmp8 := Array(0 .. max_terms + 1, []); array_tmp9 := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_tmp10 := Array(0 .. max_terms + 1, []); array_tmp11 := Array(0 .. max_terms + 1, []); array_tmp12 := Array(0 .. max_terms + 1, []); array_tmp13 := Array(0 .. max_terms + 1, []); array_tmp14 := Array(0 .. max_terms + 1, []); array_tmp15 := Array(0 .. max_terms + 1, []); array_tmp16 := Array(0 .. max_terms + 1, []); array_tmp17 := Array(0 .. max_terms + 1, []); array_t := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_x2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_x1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_x1_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); 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_x2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_t[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_fact_1[term] := 0.; term := term + 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_set_initial[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_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 <= 3 do term := 1; while term <= max_terms do array_x1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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 <= 3 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 <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1 end do; array_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1 end do; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_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; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; t_start := 0.5; t_end := 5.0; array_x1_init[1] := exact_soln_x1(t_start); array_x1_init[2] := exact_soln_x1p(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 := 1; 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 := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); chk_data(); array_x2_set_initial[1, 1] := true; array_x2_set_initial[1, 2] := true; array_x2_set_initial[1, 3] := false; array_x2_set_initial[1, 4] := false; array_x2_set_initial[1, 5] := false; array_x2_set_initial[1, 6] := false; array_x2_set_initial[1, 7] := false; array_x2_set_initial[1, 8] := false; array_x2_set_initial[1, 9] := false; array_x2_set_initial[1, 10] := false; array_x2_set_initial[1, 11] := false; array_x2_set_initial[1, 12] := false; array_x2_set_initial[1, 13] := false; array_x2_set_initial[1, 14] := false; array_x2_set_initial[1, 15] := false; array_x2_set_initial[1, 16] := false; array_x2_set_initial[1, 17] := false; array_x2_set_initial[1, 18] := false; array_x2_set_initial[1, 19] := false; array_x2_set_initial[1, 20] := false; array_x2_set_initial[1, 21] := false; array_x2_set_initial[1, 22] := false; array_x2_set_initial[1, 23] := false; array_x2_set_initial[1, 24] := false; array_x2_set_initial[1, 25] := false; array_x2_set_initial[1, 26] := false; array_x2_set_initial[1, 27] := false; array_x2_set_initial[1, 28] := false; array_x2_set_initial[1, 29] := false; array_x2_set_initial[1, 30] := false; array_x1_set_initial[2, 1] := true; array_x1_set_initial[2, 2] := true; array_x1_set_initial[2, 3] := false; array_x1_set_initial[2, 4] := false; array_x1_set_initial[2, 5] := false; array_x1_set_initial[2, 6] := false; array_x1_set_initial[2, 7] := false; array_x1_set_initial[2, 8] := false; array_x1_set_initial[2, 9] := false; array_x1_set_initial[2, 10] := false; array_x1_set_initial[2, 11] := false; array_x1_set_initial[2, 12] := false; array_x1_set_initial[2, 13] := false; array_x1_set_initial[2, 14] := false; array_x1_set_initial[2, 15] := false; array_x1_set_initial[2, 16] := false; array_x1_set_initial[2, 17] := false; array_x1_set_initial[2, 18] := false; array_x1_set_initial[2, 19] := false; array_x1_set_initial[2, 20] := false; array_x1_set_initial[2, 21] := false; array_x1_set_initial[2, 22] := false; array_x1_set_initial[2, 23] := false; array_x1_set_initial[2, 24] := false; array_x1_set_initial[2, 25] := false; array_x1_set_initial[2, 26] := false; array_x1_set_initial[2, 27] := false; array_x1_set_initial[2, 28] := false; array_x1_set_initial[2, 29] := false; array_x1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_t[1] := t_start; array_t[2] := glob_h; order_diff := 2; term_no := 1; while term_no <= order_diff do array_x2[term_no] := array_x2_init[term_no]* expt(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]* expt(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_x1[term_no] := array_x1_init[term_no]* expt(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]* expt(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(); if glob_small_float < omniabs(array_x2_higher[1, 1]) then tmp := omniabs(array_x2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); if glob_small_float < omniabs(array_x1_higher[1, 1]) then tmp := omniabs(array_x1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_t[1] <= t_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_t[1] := array_t[1] + glob_h; array_t[2] := glob_h; order_diff := 2; 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_x2[term_no] := array_x2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x2_higher[ord, term_no] := array_x2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[3, iii] := array_x1_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 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]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; 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*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_x1[term_no] := array_x1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_x1_higher[ord, term_no] := array_x1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\ ff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(INFO, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-08-12T23:28:36-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest6_rev"); logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \ 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 119 "); logitem_str(html_log_file, "mtest6_rev diffeq.mxt"); logitem_str(html_log_file, "mtest6_rev maple results"); logitem_str(html_log_file, "1st test with c++"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest6_revpostode.ode################# diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # # was complicatedrev.ode # t_start := 0.5; t_end := 5.0; array_x1_init[0 + 1] := exact_soln_x1(t_start); array_x1_init[1 + 1] := exact_soln_x1p(t_start); array_x2_init[0 + 1] := exact_soln_x2(t_start); array_x2_init[1 + 1] := 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 := 1; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return(1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t)); end; exact_soln_x1p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return( - 6.0 * c3 * exp(-t)); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return(1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion t[1] = 0.5 x2[1] (analytic) = 2.0007256155636055990741531973548 x2[1] (numeric) = 2.0007256155636055990741531973548 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 x1[1] (analytic) = 3.001091755187482740162486839163 x1[1] (numeric) = 3.001091755187482740162486839163 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 t[1] = 0.5 x2[1] (analytic) = 2.0007256155636055990741531973548 x2[1] (numeric) = 2.0007256155636055990741531973548 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 x1[1] (analytic) = 3.001091755187482740162486839163 x1[1] (numeric) = 3.001091755187482740162486839163 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50001 x2[1] (analytic) = 2.0007256246172587637000202407718 x2[1] (numeric) = 2.0007256246171409337724338679846 absolute error = 1.178299275863727872e-13 relative error = 5.8893596471487086153379523492624e-12 % "good digits = ", 13 h = 1e-05 x1[1] (analytic) = 3.001091744269985452912500608286 x1[1] (numeric) = 3.0010917442699308653350852142946 absolute error = 5.45875774153939914e-14 relative error = 1.8189239805686913799636088039690e-12 % "good digits = ", 13 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=2.8MB, time=0.45 t[1] = 0.50002 x2[1] (analytic) = 2.000725633671147590959298917551 x2[1] (numeric) = 2.0007256336706762684707145386144 absolute error = 4.713224885843789366e-13 relative error = 2.3557577343553373855852824301012e-11 % "good digits = ", 12 h = 1e-05 x1[1] (analytic) = 3.0010917333525973400895138324872 x1[1] (numeric) = 3.0010917333523789905076835894262 absolute error = 2.183495818302430610e-13 relative error = 7.2756716965235542876493719805115e-12 % "good digits = ", 13 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50003 x2[1] (analytic) = 2.0007256427252720850194141643805 x2[1] (numeric) = 2.0007256427242116031689952092442 absolute error = 1.0604818504189551363e-12 relative error = 5.3004861224971778221054068569123e-11 % "good digits = ", 12 h = 1e-05 x1[1] (analytic) = 3.0010917224353184006017877004751 x1[1] (numeric) = 3.0010917224348271156802819645578 absolute error = 4.912849215057359173e-13 relative error = 1.6370206809509616009051715368441e-11 % "good digits = ", 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50004 x2[1] (analytic) = 2.0007256517796322500478797260023 x2[1] (numeric) = 2.000725651777746937867275879874 absolute error = 1.8853121806038461283e-12 relative error = 9.4231419431588403858248547583045e-11 % "good digits = ", 12 h = 1e-05 x1[1] (analytic) = 3.0010917115181486333575943182919 x1[1] (numeric) = 3.0010917115172752408528803396894 absolute error = 8.733925047139786025e-13 relative error = 2.9102492981534359808945868993518e-11 % "good digits = ", 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50005 x2[1] (analytic) = 2.0007256608342280902122981569334 x2[1] (numeric) = 2.0007256608312822725655565505038 absolute error = 2.9458176467416064296e-12 relative error = 1.4723746010801451799562645362771e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.001091700601088037265216709204 x1[1] (numeric) = 3.001091700599723366025478714821 absolute error = 1.3646712397379943830e-12 relative error = 4.5472493874967721315260397998311e-11 % "good digits = ", 12 h = 1e-05 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=1.04 NO POLE NO POLE t[1] = 0.50006 x2[1] (analytic) = 2.0007256698890596096803608231877 x2[1] (numeric) = 2.0007256698848176072638372211336 absolute error = 4.2420024165236020541e-12 relative error = 2.1202319140328825841530606494207e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.0010916896841366112329488135932 x1[1] (numeric) = 3.0010916896821714911980770899526 absolute error = 1.9651200348717236406e-12 relative error = 6.5480173152542084926773839509160e-11 % "good digits = ", 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50007 x2[1] (analytic) = 2.0007256789441268126198479039976 x2[1] (numeric) = 2.0007256789383529419621178917634 absolute error = 5.7738706577300122342e-12 relative error = 2.8858882147087471891135728437278e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.0010916787672943541690954888471 x1[1] (numeric) = 3.0010916787646196163706754650842 absolute error = 2.6747377984200237629e-12 relative error = 8.9125494477352280194153634076557e-11 % "good digits = ", 12 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50008 x2[1] (analytic) = 2.0007256879994297031986283935353 x2[1] (numeric) = 2.0007256879918882766603985623932 absolute error = 7.5414265382298311421e-12 relative error = 3.7693455846866603473280395998846e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.0010916678505612649819725092502 x1[1] (numeric) = 3.0010916678470677415432738402158 absolute error = 3.4935234386986690344e-12 relative error = 1.1640842151285557822431916317911e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50009 x2[1] (analytic) = 2.0007256970549682855846601026355 x2[1] (numeric) = 2.000725697045423611358679233023 absolute error = 9.5446742259808696125e-12 relative error = 4.7706061055898146809657415612190e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.0010916569339373425799065658746 x1[1] (numeric) = 3.0010916569295158667158722153474 absolute error = 4.4214758640343505272e-12 relative error = 1.4732891792287168807147556435337e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=1.62 NO POLE NO POLE t[1] = 0.5001 x2[1] (analytic) = 2.0007257061107425639459896605159 x2[1] (numeric) = 2.0007257060989589460569599036528 absolute error = 1.17836178890297568631e-11 relative error = 5.8896718590856749359046366141339e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.0010916460174225858712352664712 x1[1] (numeric) = 3.001091646011963991888470590479 absolute error = 5.4585939827646759922e-12 relative error = 1.8188694737158275314480741113558e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50011 x2[1] (analytic) = 2.0007257151667525424507525165002 x2[1] (numeric) = 2.0007257151524942807552405742826 absolute error = 1.42582616955119422176e-11 relative error = 7.1265449268859788370102749566673e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.00109163510101699376430713536 x1[1] (numeric) = 3.0010916350944121170610689656106 absolute error = 6.6048767032381697494e-12 relative error = 2.2008247352353334758618256640134e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50012 x2[1] (analytic) = 2.0007257242229982252671729417388 x2[1] (numeric) = 2.0007257242060296154535212449124 absolute error = 1.69686098136516968264e-11 relative error = 8.4812273907467379422648646580771e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.001091624184720565167481613321 x1[1] (numeric) = 3.0010916241768602422336673407422 absolute error = 7.8603229338142725788e-12 relative error = 2.6191546004363047266784802123581e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50013 x2[1] (analytic) = 2.000725733279479616563564030932 x2[1] (numeric) = 2.0007257332595649501518019155422 absolute error = 1.99146664117621153898e-11 relative error = 9.9537213324682384981456171711279e-10 % "good digits = ", 11 h = 1e-05 x1[1] (analytic) = 3.0010916132685332989891290574857 x1[1] (numeric) = 3.0010916132593083674062657158738 absolute error = 9.2249315828633416119e-12 relative error = 3.0738587059714355321011771985812e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=2.20 NO POLE NO POLE t[1] = 0.50014 x2[1] (analytic) = 2.0007257423361967205083277040506 x2[1] (numeric) = 2.000725742313100284850082586172 absolute error = 2.30964356582451178786e-11 relative error = 1.1544028833895042293703297732632e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.001091602352455194137630741227 x1[1] (numeric) = 3.0010916023417564925788640910054 absolute error = 1.06987015587666502216e-11 relative error = 3.5649366884970443394574571169803e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50015 x2[1] (analytic) = 2.0007257513931495412699547080584 x2[1] (numeric) = 2.0007257513666356195483632568018 absolute error = 2.65139217215914512566e-11 relative error = 1.3252151976915987515590164508564e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915914364862495213788540507 x1[1] (numeric) = 3.001091591424204617751462466137 absolute error = 1.22816317699163879137e-11 relative error = 4.0923881846730737593761249792573e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50016 x2[1] (analytic) = 2.0007257604503380830170246186347 x2[1] (numeric) = 2.0007257604201709542466439274316 absolute error = 3.01671287703806912031e-11 relative error = 1.5078092843464189603087641054113e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.001091580520626464048776501486 x1[1] (numeric) = 3.0010915805066527429240608412686 absolute error = 1.39737211247156602174e-11 relative error = 4.6562128311630905296308943021885e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50017 x2[1] (analytic) = 2.0007257695077623499182058418952 x2[1] (numeric) = 2.0007257694737062889449245980614 absolute error = 3.40560609732812438338e-11 relative error = 1.7021853515517042102334012280498e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915696048758366282377049766 x1[1] (numeric) = 3.0010915695891008680966592164002 absolute error = 1.57749685315784885764e-11 relative error = 5.2564102646342854791839509564284e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=3.9MB, time=2.79 NO POLE NO POLE t[1] = 0.50018 x2[1] (analytic) = 2.000725778565422346142255616115 x2[1] (numeric) = 2.0007257785272416236432052686912 absolute error = 3.81807224990503474238e-11 relative error = 1.9083436075096217521601472841500e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915586892343661681874017715 x1[1] (numeric) = 3.0010915586715489932692575915318 absolute error = 1.76853728989298102397e-11 relative error = 5.8929801217574734921295459978502e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50019 x2[1] (analytic) = 2.0007257876233180758580200134503 x2[1] (numeric) = 2.000725787580776958341485939321 absolute error = 4.25411175165340741293e-11 relative error = 2.1262842604267668185923144591481e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915477737020515770614448153 x1[1] (numeric) = 3.0010915477539971184418559666634 absolute error = 1.97049331352054781519e-11 relative error = 6.5659220392070934714709750601569e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5002 x2[1] (analytic) = 2.0007257966814495432344339416603 x2[1] (numeric) = 2.0007257966343122930397666099508 absolute error = 4.71372501946673317095e-11 relative error = 2.3560075185141627091819791049736e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915368582788917633066026401 x1[1] (numeric) = 3.001091536836445243614454341795 absolute error = 2.18336481488522608451e-11 relative error = 7.2752356536612083034306897053637e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=22.8MB, alloc=3.9MB, time=3.39 t[1] = 0.50021 x2[1] (analytic) = 2.00072580573981675244052114583 x2[1] (numeric) = 2.0007258056878476277380472805806 absolute error = 5.19691247024738652494e-11 relative error = 2.5975135899872608762476101887373e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915259429648856353805592552 x1[1] (numeric) = 3.0010915259188933687870527169266 absolute error = 2.40715168483278423286e-11 relative error = 8.0209206018015048210273347781017e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50022 x2[1] (analytic) = 2.0007258147984197076453942100915 x2[1] (numeric) = 2.0007258147413829624363279512104 absolute error = 5.70367452090662588811e-11 relative error = 2.8508026830659410102166982742691e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915150277600321017519140388 x1[1] (numeric) = 3.0010915150013414939596510920582 absolute error = 2.64185381421008219806e-11 relative error = 8.8029765203132937683192025568023e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50023 x2[1] (analytic) = 2.0007258238572584130182545593471 x2[1] (numeric) = 2.0007258237949182971346086218402 absolute error = 6.23401158836459375069e-11 relative error = 3.1158750059745111251583251790624e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010915041126643300709001816284 x1[1] (numeric) = 3.0010915040837896191322494671898 absolute error = 2.88747109386507144386e-11 relative error = 9.6214030458855097642145037914955e-10 % "good digits = ", 11 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50024 x2[1] (analytic) = 2.000725832916332872728392460991 x2[1] (numeric) = 2.00072583284845363183288929247 absolute error = 6.78792408955031685210e-11 relative error = 3.3927307669417076442457323482748e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914931976777784513157918119 x1[1] (numeric) = 3.0010914931662377443048478423214 absolute error = 3.14400341464679494905e-11 relative error = 1.0476199815210711266514879818179e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=3.9MB, time=3.98 NO POLE NO POLE t[1] = 0.50025 x2[1] (analytic) = 2.0007258419756430909451870266318 x2[1] (numeric) = 2.0007258419019889665311699630998 absolute error = 7.36541244140170635320e-11 relative error = 3.6813701742006954852588480401045e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914822828003761515000894181 x1[1] (numeric) = 3.001091482248685869477446217453 absolute error = 3.41145066740538719651e-11 relative error = 1.1367366464985080535758980023723e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50026 x2[1] (analytic) = 2.0007258510351890718381062138146 x2[1] (numeric) = 2.0007258509555243012294506337296 absolute error = 7.96647706086555800850e-11 relative error = 3.9817934359890681460667950878371e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914713680321220799653342081 x1[1] (numeric) = 3.0010914713311339946500445925846 absolute error = 3.68981274299207416235e-11 relative error = 1.2294902631908423599365922810633e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50027 x2[1] (analytic) = 2.0007258600949708195767068277438 x2[1] (numeric) = 2.0007258600090596359277313043594 absolute error = 8.59111836489755233844e-11 relative error = 4.2940007605488477901453592842140e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914604533730151452347007656 x1[1] (numeric) = 3.0010914604135821198226429677162 absolute error = 3.97908953225917330494e-11 relative error = 1.3258807952684170215412215861342e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50028 x2[1] (analytic) = 2.0007258691549883383306345230051 x2[1] (numeric) = 2.0007258690625949706260119749892 absolute error = 9.23933677046225480159e-11 relative error = 4.6179923561264853320544455961620e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.001091449538823054255842278388 x1[1] (numeric) = 3.0010914494960302449952413428478 absolute error = 4.27928092606009355402e-11 relative error = 1.4259082064019373836675238692860e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=3.9MB, time=4.58 NO POLE NO POLE t[1] = 0.50029 x2[1] (analytic) = 2.000725878215241632269623805288 x2[1] (numeric) = 2.000725878116130305324292645619 absolute error = 9.91113269453311596690e-11 relative error = 4.9537684309728605229404986275983e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914386243822383203330709772 x1[1] (numeric) = 3.0010914385784783701678397179794 absolute error = 4.59038681524933529978e-11 relative error = 1.5295724602624711574576754191580e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5003 x2[1] (analytic) = 2.0007258872757307055634980331085 x2[1] (numeric) = 2.0007258871696656400225733162488 absolute error = 1.060650655409247168597e-10 relative error = 5.3013291933432820360488927706251e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914277100505662472629969306 x1[1] (numeric) = 3.001091427660926495340438093111 absolute error = 4.91240709068249038196e-11 relative error = 1.6368735205214484163193055179695e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50031 x2[1] (analytic) = 2.0007258963364555623821694195314 x2[1] (numeric) = 2.0007258962232009747208539868786 absolute error = 1.132545876613154326528e-10 relative error = 5.6606748514974875522163029282239e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914167958280369451988890319 x1[1] (numeric) = 3.0010914167433746205130364682426 absolute error = 5.24534164321624207893e-11 relative error = 1.7478113508506615923198461171508e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50032 x2[1] (analytic) = 2.0007259053974162068956390338926 x2[1] (numeric) = 2.0007259052767363094191346575084 absolute error = 1.206798974765043763842e-10 relative error = 6.0318056136996438453630485515919e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010914058817146493227184943417 x1[1] (numeric) = 3.0010914058258227456856348433742 absolute error = 5.58919036370836509675e-11 relative error = 1.8623859149222654725742165318079e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=3.9MB, time=5.17 NO POLE NO POLE t[1] = 0.50033 x2[1] (analytic) = 2.0007259144586126432739968035224 x2[1] (numeric) = 2.0007259143302716441174153281382 absolute error = 1.283409991565814753842e-10 relative error = 6.4147216882183468680353928497684e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010913949677104022884104740887 x1[1] (numeric) = 3.0010913949082708708582332185058 absolute error = 5.94395314301772555829e-11 relative error = 1.9805971764087771956525001227736e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50034 x2[1] (analytic) = 2.0007259235200448756874215154673 x2[1] (numeric) = 2.000725923383806978815695998768 absolute error = 1.362378968717255166993e-10 relative error = 6.8094232833266218368728425226630e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010913840538152947508744035603 x1[1] (numeric) = 3.0010913839907189960308315936374 absolute error = 6.30962987200428099229e-11 relative error = 2.1024450989830762479676275132627e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50035 x2[1] (analytic) = 2.000725932581712908306180818213 x2[1] (numeric) = 2.0007259324373423135139766693978 absolute error = 1.443705947922041488152e-10 relative error = 7.2159106073019233181353990361129e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010913731400293256187207719937 x1[1] (numeric) = 3.001091373073167121203429968769 absolute error = 6.68622044152908032247e-11 relative error = 2.2279296463184044601797196721495e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50036 x2[1] (analytic) = 2.0007259416436167453006312234074 x2[1] (numeric) = 2.0007259414908776482122573400276 absolute error = 1.527390970883738833798e-10 relative error = 7.6341838684261353132307832063476e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010913622263524938005709824666 x1[1] (numeric) = 3.0010913621556152463760283439006 absolute error = 7.07372474245426385660e-11 relative error = 2.3570507820883660035871017739617e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=3.9MB, time=5.76 NO POLE NO POLE t[1] = 0.50037 x2[1] (analytic) = 2.0007259507057563908412181075826 x2[1] (numeric) = 2.0007259505444129829105380106574 absolute error = 1.613434079306800969252e-10 relative error = 8.0642432749855713441916512349764e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.001091351312784798205057351788 x1[1] (numeric) = 3.0010913512380633715486267190322 absolute error = 7.47214266564306327558e-11 relative error = 2.4898084699669273865206484410730e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50038 x2[1] (analytic) = 2.0007259597681318490984757138783 x2[1] (numeric) = 2.0007259595979483176088186812872 absolute error = 1.701835314896570325911e-10 relative error = 8.5060890352709745392227586532225e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010913403993262377408231103894 x1[1] (numeric) = 3.0010913403205114967212250941638 absolute error = 7.88147410195980162256e-11 relative error = 2.6262026736284174507514567317154e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50039 x2[1] (analytic) = 2.0007259688307431242430271537639 x2[1] (numeric) = 2.000725968651483652307099351917 absolute error = 1.792594719359278018469e-10 relative error = 8.9597213575775177181831211572406e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010913294859768113165224022153 x1[1] (numeric) = 3.0010913294029596218938234692954 absolute error = 8.30171894226989329199e-11 relative error = 2.7662333567475273678751935411223e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=41.9MB, alloc=3.9MB, time=6.34 t[1] = 0.5004 x2[1] (analytic) = 2.0007259778935902204455844087623 x2[1] (numeric) = 2.0007259777050189870053800225468 absolute error = 1.885712334402043862155e-10 relative error = 9.4251404502048034781531179069078e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.001091318572736517840820284614 x1[1] (numeric) = 3.001091318485407747066421844427 absolute error = 8.73287707743984401870e-11 relative error = 2.9099004829993106357064386272003e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50041 x2[1] (analytic) = 2.0007259869566731418769483321718 x2[1] (numeric) = 2.0007259867585543217036606931766 absolute error = 1.981188201732876389952e-10 relative error = 9.9023465214568642789066025994571e-09 % "good digits = ", 10 h = 1e-05 x1[1] (analytic) = 3.0010913076596053562223927282289 x1[1] (numeric) = 3.0010913075678558722390202195586 absolute error = 9.17494839833725086703e-11 relative error = 3.0572040160591830746896875034220e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50042 x2[1] (analytic) = 2.0007259960199918927080086507894 x2[1] (numeric) = 2.0007259958120896564019413638064 absolute error = 2.079022363060672869830e-10 relative error = 1.0391339779642162528452962446941e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912967465833253699266168891 x1[1] (numeric) = 3.0010912966503039974116185946902 absolute error = 9.62793279583080221989e-11 relative error = 3.2081439196029228242870287447108e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50043 x2[1] (analytic) = 2.0007260050835464771097439666338 x2[1] (numeric) = 2.0007260048656249911002220344362 absolute error = 2.179214860095219321976e-10 relative error = 1.0892120433073590668564155898260e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912858336704241921197475003 x1[1] (numeric) = 3.0010912857327521225842169698218 absolute error = 1.009183016079027776785e-10 relative error = 3.3627201573066703393758169180810e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=3.9MB, time=6.92 NO POLE NO POLE t[1] = 0.50044 x2[1] (analytic) = 2.0007260141473368992532217586681 x2[1] (numeric) = 2.000726013919160325798502705066 absolute error = 2.281765734547190536021e-10 relative error = 1.1404688690068471260286729105166e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912749208666515976808299356 x1[1] (numeric) = 3.0010912748152002477568153449534 absolute error = 1.056664038408654849822e-10 relative error = 3.5209326928469283866430126533189e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50045 x2[1] (analytic) = 2.000726023211363163309598384523 x2[1] (numeric) = 2.0007260229726956604967833756958 absolute error = 2.386675028128150088272e-10 relative error = 1.1929044758948557069478796616440e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912640081720064953294869263 x1[1] (numeric) = 3.001091263897648372929413720085 absolute error = 1.105236335659157668413e-10 relative error = 3.6827814899005620409795219748917e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50046 x2[1] (analytic) = 2.0007260322756252734501190822198 x2[1] (numeric) = 2.0007260320262309951950640463256 absolute error = 2.493942782550550358942e-10 relative error = 1.2465188848040031152336998999337e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912530955864877937962539533 x1[1] (numeric) = 3.0010912529800964981020120952166 absolute error = 1.154899896917841587367e-10 relative error = 3.8482665121447986818945276227230e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50047 x2[1] (analytic) = 2.0007260413401232338461179718932 x2[1] (numeric) = 2.0007260410797663298933447169554 absolute error = 2.603569039527732549378e-10 relative error = 1.3013121165673506940913437387557e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912421831100944018225791373 x1[1] (numeric) = 3.0010912420625446232746104703482 absolute error = 1.205654711272121087891e-10 relative error = 4.0173877232572279898898341792695e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=3.9MB, time=7.52 NO POLE NO POLE t[1] = 0.50048 x2[1] (analytic) = 2.0007260504048570486690180575151 x2[1] (numeric) = 2.0007260501333016645916253875852 absolute error = 2.715553840773926699299e-10 relative error = 1.3572841920184028328682563181351e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912312707428252281608231299 x1[1] (numeric) = 3.0010912311449927484472088454798 absolute error = 1.257500767809519776501e-10 relative error = 4.1901450869158019428642015490878e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50049 x2[1] (analytic) = 2.0007260594698267220903312286167 x2[1] (numeric) = 2.000726059186836999289906058215 absolute error = 2.829897228004251704017e-10 relative error = 1.4144351319911069756023071888374e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010912203584846791815742590047 x1[1] (numeric) = 3.0010912202274408736198072206114 absolute error = 1.310438055617670383933e-10 relative error = 4.3665385667988348125176776999063e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5005 x2[1] (analytic) = 2.0007260685350322582816582620126 x2[1] (numeric) = 2.0007260682403723339881867288448 absolute error = 2.946599242934715331678e-10 relative error = 1.4727649573198536295799733969901e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001091209446335655170837072148 x1[1] (numeric) = 3.001091209309888998792405595743 absolute error = 1.364466563784314764050e-10 relative error = 4.5465681265850031607426021799412e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50051 x2[1] (analytic) = 2.0007260776004736614146888235234 x2[1] (numeric) = 2.0007260772939076686864673994746 absolute error = 3.065659927282214240488e-10 relative error = 1.5322736888394763738870226196929e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911985342957521047343601496 x1[1] (numeric) = 3.0010911983923371239650039708746 absolute error = 1.419586281397303892750e-10 relative error = 4.7302337299533458360179410177871e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=3.9MB, time=8.11 NO POLE NO POLE t[1] = 0.50052 x2[1] (analytic) = 2.0007260866661509356612014696992 x2[1] (numeric) = 2.0007260863474430033847480701044 absolute error = 3.187079322764533995948e-10 relative error = 1.5929613473852518679636919968066e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911876223649688920621326937 x1[1] (numeric) = 3.0010911874747852491376023460062 absolute error = 1.475797197544597866875e-10 relative error = 4.9175353405832639698069530049832e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50053 x2[1] (analytic) = 2.0007260957320640851930636495429 x2[1] (numeric) = 2.0007260954009783380830287407342 absolute error = 3.310857471100349088087e-10 relative error = 1.6548279537928998601588646547099e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911767105433044416273114501 x1[1] (numeric) = 3.0010911765572333743102007211378 absolute error = 1.533099301314265903123e-10 relative error = 5.1084729221545209729648516040639e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50054 x2[1] (analytic) = 2.0007261047982131141822317062334 x2[1] (numeric) = 2.000726104454513672781309411364 absolute error = 3.436994414009222948694e-10 relative error = 1.7178735288985831962837437404885e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911657988307576622477299646 x1[1] (numeric) = 3.0010911656396814994827990962694 absolute error = 1.591492581794486336952e-10 relative error = 5.3030464383472425321198091473212e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50055 x2[1] (analytic) = 2.0007261138645980268007508788489 x2[1] (numeric) = 2.0007261135080490074795900819938 absolute error = 3.565490193211607968551e-10 relative error = 1.7820980935389078281660236035393e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911548872273274627521335501 x1[1] (numeric) = 3.001091154722129624655397471401 absolute error = 1.650977028073546621491e-10 relative error = 5.5012558528419166060772851463097e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=3.9MB, time=8.70 NO POLE NO POLE t[1] = 0.50056 x2[1] (analytic) = 2.0007261229312188272207553040904 x2[1] (numeric) = 2.0007261225615843421778707526236 absolute error = 3.696344850428845514668e-10 relative error = 1.8475016685509228222050579430033e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911439757330127519801791777 x1[1] (numeric) = 3.0010911438045777498279958465326 absolute error = 1.711552629239843326451e-10 relative error = 5.7031011293193934222243538629596e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50057 x2[1] (analytic) = 2.000726131998075519614468018005 x2[1] (numeric) = 2.0007261316151196768761514232534 absolute error = 3.829558427383165947516e-10 relative error = 1.9140842747721203679260256467545e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001091133064347812438782435367 x1[1] (numeric) = 3.0010911328870258750005942216642 absolute error = 1.773219374381882137028e-10 relative error = 5.9085822314608854729073741710826e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50058 x2[1] (analytic) = 2.0007261410651681081542009577096 x2[1] (numeric) = 2.0007261406686550115744320938832 absolute error = 3.965130965797688638264e-10 relative error = 1.9818459330404357865360932330559e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911221530717254320203820779 x1[1] (numeric) = 3.0010911219694740001731925967958 absolute error = 1.835977252588277852821e-10 relative error = 6.1176991229479675118596405001734e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=61.0MB, alloc=3.9MB, time=9.28 t[1] = 0.50059 x2[1] (analytic) = 2.000726150132496597012354963114 x2[1] (numeric) = 2.000726149722190346272712764513 absolute error = 4.103062507396421986010e-10 relative error = 2.0507866641942475394775757094257e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911112419047506405664106003 x1[1] (numeric) = 3.0010911110519221253457909719274 absolute error = 1.899826252947754386729e-10 relative error = 6.3304517674625765505590584913832e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5006 x2[1] (analytic) = 2.0007261592000609903614197786446 x2[1] (numeric) = 2.0007261587757256809709934351428 absolute error = 4.243353093904263435018e-10 relative error = 2.1209064890723772369840936710165e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010911003308468869733038234462 x1[1] (numeric) = 3.001091100134370250518389347059 absolute error = 1.964766364549144763872e-10 relative error = 6.5468401286870118546657908287078e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50061 x2[1] (analytic) = 2.0007261682678612923739740549681 x2[1] (numeric) = 2.0007261678292610156692741057726 absolute error = 4.386002767046999491955e-10 relative error = 2.1922054285140896466367277271617e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010910894198981333391268342398 x1[1] (numeric) = 3.0010910892168183756909877221906 absolute error = 2.030797576481391120492e-10 relative error = 6.7668641703039349403932599035382e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50062 x2[1] (analytic) = 2.0007261773358975072226853507149 x2[1] (numeric) = 2.0007261768827963503675547764024 absolute error = 4.531011568551305743125e-10 relative error = 2.2646835033590927019186708004170e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010910785090584886469405676084 x1[1] (numeric) = 3.0010910782992665008635860973222 absolute error = 2.097919877833544702862e-10 relative error = 6.9905238559963695709058067118972e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=3.9MB, time=9.87 NO POLE NO POLE t[1] = 0.50063 x2[1] (analytic) = 2.0007261864041696390803101342026 x2[1] (numeric) = 2.0007261859363316850658354470322 absolute error = 4.678379540144746871704e-10 relative error = 2.3383407344475375107703775721153e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010910675983279518056610590738 x1[1] (numeric) = 3.0010910673817146260361844724538 absolute error = 2.166133257694765866200e-10 relative error = 7.2178191494477017527330096206244e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50064 x2[1] (analytic) = 2.0007261954726776921196937851601 x2[1] (numeric) = 2.000726194989867019764116117662 absolute error = 4.828106723555776674981e-10 relative error = 2.4131771426200183641477101668952e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010910566877065217242152549427 x1[1] (numeric) = 3.0010910564641627512087828475854 absolute error = 2.235437705154324073573e-10 relative error = 7.4487500143416797321506811806198e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50065 x2[1] (analytic) = 2.0007262045414216705137705964508 x2[1] (numeric) = 2.0007262040434023544623967882918 absolute error = 4.980193160513738081590e-10 relative error = 2.4891927487175727445755827982827e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001091045777194197311541012198 x1[1] (numeric) = 3.001091045546610876381381222717 absolute error = 2.305833209301597894810e-10 relative error = 7.6833164143624139915918532948257e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50066 x2[1] (analytic) = 2.0007262136104015784355637757966 x2[1] (numeric) = 2.0007262130969376891606774589216 absolute error = 5.134638892748863168750e-10 relative error = 2.5663875735816813347056022900700e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010910348667909774765870983893 x1[1] (numeric) = 3.0010910346290590015539795978486 absolute error = 2.377319759226075005407e-10 relative error = 7.9215183131943772460311046760080e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=3.9MB, time=10.47 NO POLE NO POLE t[1] = 0.50067 x2[1] (analytic) = 2.0007262226796174200581854475016 x2[1] (numeric) = 2.0007262221504730238589581295514 absolute error = 5.291443961992273179502e-10 relative error = 2.6447616380542680258722064696481e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010910239564968611283131915239 x1[1] (numeric) = 3.0010910237115071267265779729802 absolute error = 2.449897344017352185437e-10 relative error = 8.1633556745224044393855481734959e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50068 x2[1] (analytic) = 2.000726231749069199554836654176 x2[1] (numeric) = 2.0007262312040083585572388001812 absolute error = 5.450608409975978539948e-10 relative error = 2.7243149629776999266497995257713e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001091013046311847175689879958 x1[1] (numeric) = 3.0010910127939552518991763481118 absolute error = 2.523565952765135318462e-10 relative error = 8.4088284620316927409224816047089e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50069 x2[1] (analytic) = 2.0007262408187569210988073584597 x2[1] (numeric) = 2.000726240257543693255519470811 absolute error = 5.612132278432878876487e-10 relative error = 2.8050475691947873714083852380874e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010910021362359345276986622872 x1[1] (numeric) = 3.0010910018764033770717747232434 absolute error = 2.598325574559239390438e-10 relative error = 8.6579366394078015416437129977123e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5007 x2[1] (analytic) = 2.0007262498886805888634764447463 x2[1] (numeric) = 2.0007262493110790279538001414408 absolute error = 5.776015609096763033055e-10 relative error = 2.8869594775487839288711968078974e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010909912262691220933319472376 x1[1] (numeric) = 3.001090990958851502244373098375 absolute error = 2.674176198489588488626e-10 relative error = 8.9106801703366524506898778245189e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=3.9MB, time=11.05 NO POLE NO POLE t[1] = 0.50071 x2[1] (analytic) = 2.0007262589588402070223117209071 x2[1] (numeric) = 2.0007262583646143626520808120706 absolute error = 5.942258443702309088365e-10 relative error = 2.9700507088833864106723240159691e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010909803164114087815930535567 x1[1] (numeric) = 3.0010909800412996274169714735066 absolute error = 2.751117813646215800501e-10 relative error = 9.1670590185045292917380912530737e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50072 x2[1] (analytic) = 2.0007262680292357797488699200148 x2[1] (numeric) = 2.0007262674181496973503614827004 absolute error = 6.110860823985084373144e-10 relative error = 3.0543212840427348799128382518016e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010909694066627935014962099043 x1[1] (numeric) = 3.0010909691237477525895698486382 absolute error = 2.829150409119263612661e-10 relative error = 9.4270731475980780993995996609375e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50073 x2[1] (analytic) = 2.0007262770998673112167967020679 x2[1] (numeric) = 2.0007262764716850320486421533302 absolute error = 6.281822791681545487377e-10 relative error = 3.1397712238714126597204135992459e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010909584970232751620665547431 x1[1] (numeric) = 3.0010909582061958777621682237698 absolute error = 2.908273973998983309733e-10 relative error = 9.6907225213043071156074350458910e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50074 x2[1] (analytic) = 2.0007262861707348055998266557139 x2[1] (numeric) = 2.00072628552522036674692282396 absolute error = 6.455144388529038317539e-10 relative error = 3.2264005492144463418029474268728e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010909475874928526723401362302 x1[1] (numeric) = 3.0010909472886440029347665989014 absolute error = 2.988488497375735373288e-10 relative error = 9.9580071033105867860340577925372e-09 % "good digits = ", 10 h = 1e-05 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=3.9MB, time=11.64 NO POLE NO POLE t[1] = 0.50075 x2[1] (analytic) = 2.0007262952418382670717832999745 x2[1] (numeric) = 2.0007262945787557014452034945898 absolute error = 6.630825656265798053847e-10 relative error = 3.3142092809173057950121746749147e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010909366780715249413639121076 x1[1] (numeric) = 3.001090936371092128107364974033 absolute error = 3.069793968339989380746e-10 relative error = 1.0228926857304649756475677484864e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50076 x2[1] (analytic) = 2.0007263043131776998065790859686 x2[1] (numeric) = 2.0007263036322910361434841652196 absolute error = 6.808866636630949207490e-10 relative error = 3.4031974398259041738962834617879e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001090925768759290878195749593 x1[1] (numeric) = 3.0010909254535402532799633491646 absolute error = 3.152190375982324004284e-10 relative error = 1.0503481746974590869246569345178e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50077 x2[1] (analytic) = 2.0007263133847531079782153986368 x2[1] (numeric) = 2.0007263126858263708417648358494 absolute error = 6.989267371364505627874e-10 relative error = 3.4933650467865979272600252944745e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001090914859556149391904425271 x1[1] (numeric) = 3.0010909145359883784525617242962 absolute error = 3.235677709393427009748e-10 relative error = 1.0781671736008867159586718421317e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50078 x2[1] (analytic) = 2.0007263224565644957607825584659 memory used=80.1MB, alloc=3.9MB, time=12.22 x2[1] (numeric) = 2.0007263217393617055400455064792 absolute error = 7.172027902207370519867e-10 relative error = 3.5847121226461868067248226051387e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001090903950462099391569624984 x1[1] (numeric) = 3.0010909036184365036251600994278 absolute error = 3.320255957664095255562e-10 relative error = 1.1063496788096297852059466670902e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50079 x2[1] (analytic) = 2.0007263315286118673284598232125 x2[1] (numeric) = 2.000726330792897040238326177109 absolute error = 7.357148270901336461035e-10 relative error = 3.6772386882519138752843752475257e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908930414771397862819437227 x1[1] (numeric) = 3.0010908927008846287977584745594 absolute error = 3.405925109885234691633e-10 relative error = 1.1348956866926064356935830820700e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.5008 x2[1] (analytic) = 2.0007263406008952268555153896278 x2[1] (numeric) = 2.0007263398464323749366068477388 absolute error = 7.544628519189085418890e-10 relative error = 3.7709447644514655158662621412720e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908821326012694851428855176 x1[1] (numeric) = 3.001090881783332753970356849691 absolute error = 3.492685155147860358266e-10 relative error = 1.1638051936187710266612140704347e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50081 x2[1] (analytic) = 2.0007263496734145785163063951813 x2[1] (numeric) = 2.0007263488999677096348875183686 absolute error = 7.734468688814188768127e-10 relative error = 3.8658303720929714398880422388260e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908712238344873972648633294 x1[1] (numeric) = 3.0010908708657808791429552248226 absolute error = 3.580536082543096385068e-10 relative error = 1.1930781959571141351991023523689e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=3.9MB, time=12.82 NO POLE NO POLE t[1] = 0.50082 x2[1] (analytic) = 2.0007263587461699264852789197854 x2[1] (numeric) = 2.0007263579535030443331681889984 absolute error = 7.926668821521107307870e-10 relative error = 3.9618955320250046958178511845688e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908603151767924317711989403 x1[1] (numeric) = 3.0010908599482290043155535999542 absolute error = 3.669477881162175989861e-10 relative error = 1.2227146900766625558892376466976e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50083 x2[1] (analytic) = 2.0007263678191612749369679875196 x2[1] (numeric) = 2.0007263670070383790314488596282 absolute error = 8.121228959055191278914e-10 relative error = 4.0591402650965816777329960257258e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908494066281834977961228447 x1[1] (numeric) = 3.0010908490306771294881519750858 absolute error = 3.759510540096441477589e-10 relative error = 1.2527146723464793004444345858883e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50084 x2[1] (analytic) = 2.000726376892388628045997568355 x2[1] (numeric) = 2.000726376060573713729729530258 absolute error = 8.318149143162680380970e-10 relative error = 4.1575645921571621338800467043251e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.00109083849818865950448477414 x1[1] (numeric) = 3.0010908381131252546607503502174 absolute error = 3.850634048437344239226e-10 relative error = 1.2830781391356635973477637694006e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50085 x2[1] (analytic) = 2.0007263859658519899870805798786 x2[1] (numeric) = 2.0007263851141090484280102008878 absolute error = 8.517429415590703789908e-10 relative error = 4.2571685340566491752339252377019e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908275898582193609932004178 x1[1] (numeric) = 3.001090827195573379833348725349 absolute error = 3.942848395276444750688e-10 relative error = 1.3138050868133508914933155919135e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=3.9MB, time=13.43 NO POLE NO POLE t[1] = 0.50086 x2[1] (analytic) = 2.0007263950395513649350188890178 x2[1] (numeric) = 2.0007263941676443831262908715176 absolute error = 8.719069818087280175002e-10 relative error = 4.3579521116453892840579918613415e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908166816368619764883576547 x1[1] (numeric) = 3.0010908162780215050059471004806 absolute error = 4.036153569705412571741e-10 relative error = 1.3448955117487128438256311490640e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50087 x2[1] (analytic) = 2.0007264041134867570647033137646 x2[1] (numeric) = 2.0007264032211797178245715421474 absolute error = 8.923070392401317716172e-10 relative error = 4.4599153457741723224626290415985e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010908057735245862601481101032 x1[1] (numeric) = 3.0010908053604696301785454756122 absolute error = 4.130549560816026344910e-10 relative error = 1.3763494103109573309794662815464e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50088 x2[1] (analytic) = 2.0007264131876581705511136249004 x2[1] (numeric) = 2.0007264122747150525228522127772 absolute error = 9.129431180282614121232e-10 relative error = 4.5630582572942315409668217243937e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907948655213911211612301825 x1[1] (numeric) = 3.0010907944429177553511438507438 absolute error = 4.226036357700173794387e-10 relative error = 1.4081667788693284449192223332273e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50089 x2[1] (analytic) = 2.0007264222620656095693185477205 x2[1] (numeric) = 2.000726421328250387221132883407 absolute error = 9.338152223481856643135e-10 relative error = 4.6673808670572435870582354535451e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907839576272754687273983697 x1[1] (numeric) = 3.0010907835253658805237422258754 absolute error = 4.322613949449851724943e-10 relative error = 1.4403476137931064925797096841655e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=3.9MB, time=14.02 NO POLE NO POLE t[1] = 0.5009 x2[1] (analytic) = 2.0007264313367090782944757637584 x2[1] (numeric) = 2.0007264303817857219194135540368 absolute error = 9.549233563750622097216e-10 relative error = 4.7728831959153285137522921771310e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907730498422382120572030903 x1[1] (numeric) = 3.001090772607814005696340601007 absolute error = 4.420282325157166020833e-10 relative error = 1.4728919114516079955045787245865e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50091 x2[1] (analytic) = 2.0007264404115885809018319125108 x2[1] (numeric) = 2.0007264394353210566176942246666 absolute error = 9.762675242841376878442e-10 relative error = 4.8795652647210497881547421079113e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907621421662782603721406097 x1[1] (numeric) = 3.0010907616902621308689389761386 absolute error = 4.519041473914331644711e-10 relative error = 1.5057996682141856894880828768425e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50092 x2[1] (analytic) = 2.000726449486704121566722593162 x2[1] (numeric) = 2.0007264484888563913159748952964 absolute error = 9.978477302507476978656e-10 relative error = 4.9874270943274143000212339976926e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907512345993945229046149236 x1[1] (numeric) = 3.0010907507727102560415373512702 absolute error = 4.618891384813672636534e-10 relative error = 1.5390708804502285242131762096041e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50093 x2[1] (analytic) = 2.0007264585620557044645723663084 x2[1] (numeric) = 2.0007264575423917260142555659262 absolute error = 1.0196639784503168003822e-09 relative error = 5.0964687055878723703173825547857e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907403271415859088979376491 x1[1] (numeric) = 3.0010907398551583812141357264018 absolute error = 4.719832046947622112473e-10 relative error = 1.5727055445291616628919434635050e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=3.9MB, time=14.61 NO POLE NO POLE t[1] = 0.50094 x2[1] (analytic) = 2.0007264676376433337708947556838 x2[1] (numeric) = 2.000726466595927060712536236556 absolute error = 1.0417162730583585191278e-09 relative error = 5.2066901193563177597828317335708e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907294197928513276063279158 x1[1] (numeric) = 3.0010907289376065063867341015334 absolute error = 4.821863449408722263824e-10 relative error = 1.6067036568204464819060300030029e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50095 x2[1] (analytic) = 2.0007264767134670136612922498832 x2[1] (numeric) = 2.0007264756494623954108169071858 absolute error = 1.0640046182504753426974e-09 relative error = 5.3180913564870876774878180716682e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010907185125531896882949122565 x1[1] (numeric) = 3.001090718020054631559332476665 absolute error = 4.924985581289624355915e-10 relative error = 1.6410652136935805704457388457136e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50096 x2[1] (analytic) = 2.0007264857895267483114563040888 x2[1] (numeric) = 2.0007264847029977301090975778156 absolute error = 1.0865290182023587262732e-09 relative error = 5.4306724378349627894007273572821e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001090707605422599900239724498 x1[1] (numeric) = 3.0010907071025027567319308517966 absolute error = 5.029198431683088727014e-10 relative error = 1.6757902115180977301494608301233e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50097 x2[1] (analytic) = 2.0007264948658225418971673417936 x2[1] (numeric) = 2.0007264937565330648073782484454 absolute error = 1.1092894770897890933482e-09 relative error = 5.5444333842551672269436529779286e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010906966984010808727277056526 x1[1] (numeric) = 3.0010906961849508819045292269282 memory used=99.1MB, alloc=3.9MB, time=15.21 absolute error = 5.134501989681984787244e-10 relative error = 1.7108786466635679747454371948217e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50098 x2[1] (analytic) = 2.000726503942354398594294756527 x2[1] (numeric) = 2.0007265028100683995056589190752 absolute error = 1.1322859990886358374518e-09 relative error = 5.6593742166033685955579479621705e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010906857914886315150567038084 x1[1] (numeric) = 3.0010906852673990070771276020598 absolute error = 5.240896244379291017486e-10 relative error = 1.7463305154995975296895235377074e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.50099 x2[1] (analytic) = 2.0007265130191223225787969135797 x2[1] (numeric) = 2.000726511863603734203939589705 absolute error = 1.1555185883748573238747e-09 relative error = 5.7754949557356779832662756161220e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.0010906748846852507365354740205 x1[1] (numeric) = 3.0010906743498471322497259771914 absolute error = 5.348381184868094968291e-10 relative error = 1.7821458143958288318059526110796e-08 % "good digits = ", 9 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE t[1] = 0.501 x2[1] (analytic) = 2.0007265220961263180267211517279 x2[1] (numeric) = 2.0007265209171390689022202603348 absolute error = 1.1789872491245008913931e-09 relative error = 5.8927956225086499692311587547278e-08 % "good digits = ", 9 h = 1e-05 x1[1] (analytic) = 3.001090663977990937446483678202 x1[1] (numeric) = 3.001090663432295257422324352323 absolute error = 5.456956800241593258790e-10 relative error = 1.8183245397219405289274306185784e-08 % "good digits = ", 9 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; Iterations = 100 Total Elapsed Time = 15 Seconds Elapsed Time(since restart) = 15 Seconds Expected Time Remaining = 19 Hours 15 Minutes 15 Seconds Optimized Time Remaining = 19 Hours 11 Minutes 59 Seconds Time to Timeout = 44 Seconds Percent Done = 0.02244 % > quit memory used=102.3MB, alloc=3.9MB, time=15.67