|\^/| 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 > reached_interval := proc() > global > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > glob_last; > > > > local ret; > > if ((((array_t[1] >= glob_next_display) and not glob_neg_h) or ((array_t[1] <= glob_next_display) and glob_neg_h)) or (glob_next_display = 0.0)) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1 > ; > return(ret); > > # End Function number 3 > end; reached_interval := proc() local ret; global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last ; if glob_next_display <= array_t[1] and not glob_neg_h or array_t[1] <= glob_next_display and glob_neg_h or glob_next_display = 0. then ret := true else ret := false end if; return ret end proc > # Begin Function number 4 > display_alot := proc(iter) > global > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > > > > > > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_t[1]; > omniout_float(ALWAYS,"t[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_x1(ind_var); > omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x1[term_no]; > abserr := 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 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 4 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 4 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3 > ; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_x2(ind_var); > omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_x2[term_no]; > abserr := 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 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 4 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 4 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3 > ; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 3 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2 > ; > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > > # End Function number 4 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last ; if reached_interval() then if 0 <= iter then ind_var := array_t[1]; omniout_float(ALWAYS, "t[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_x1(ind_var); omniout_float(ALWAYS, "x1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x1[term_no]; abserr := 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 glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_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, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_x2(ind_var); omniout_float(ALWAYS, "x2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_x2[term_no]; abserr := 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 glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_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, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # Begin Function number 5 > adjust_for_pole := proc(h_param) > global > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > 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 (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 (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 5 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last ; hnew := h_param; glob_normmax := glob_small_float; 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_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_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 6 > prog_report := proc(t_start,t_end) > global > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > 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 6 > end; prog_report := proc(t_start, t_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, 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 7 > check_for_pole := proc() > global > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > > > > > > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((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[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((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[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_x1_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif ((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 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]); > rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]); > rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]); > rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]); > rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((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) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_x2_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif ((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 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]); > rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]); > rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]); > rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]); > rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((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) * omniabs(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 (reached_interval()) 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 (reached_interval()) 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 (reached_interval()) 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 (reached_interval()) 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 > if (reached_interval()) then # if number 3 > display_pole(); > fi;# end if 3 > > # End Function number 7 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last ; 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[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 3; while 10 <= m and (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[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < 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[1, 1] := glob_large_float; array_complex_pole[1, 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[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1]; rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2]; rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3]; rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4]; rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if 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)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < 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[2, 1] := glob_large_float; array_complex_pole[2, 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[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1]; rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2]; rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3]; rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4]; rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if 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)*omniabs(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 reached_interval() 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 reached_interval() 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 reached_interval() 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 reached_interval() 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; if reached_interval() then display_pole() end if end proc > # Begin Function number 8 > get_norms := proc() > global > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > 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_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 > ; > 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 > #BOTTOM GET NORMS > ; > fi;# end if 3 > ; > > # End Function number 8 > end; get_norms := proc() local iii; global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, 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_x1[iii]) then array_norms[iii] := omniabs(array_x1[iii]) end if; 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 end if end proc > # Begin Function number 9 > atomall := proc() > global > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp1[1] := array_const_4D0[1] * array_x2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre diff $eq_no = 1 i = 1 > array_tmp3[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_2D0[1] * array_x1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_x1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 1 > array_tmp9[1] := array_x2_higher[2,1]; > #emit pre mult CONST FULL $eq_no = 2 i = 1 > array_tmp11[1] := array_const_2D0[1] * array_x2[1]; > #emit pre diff $eq_no = 2 i = 1 > array_tmp13[1] := array_x1_higher[3,1]; > #emit pre diff $eq_no = 2 i = 1 > array_tmp15[1] := array_x1_higher[2,1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_x2_set_initial[2,3]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp1[2] := array_const_4D0[1] * array_x2[2]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre diff $eq_no = 1 i = 2 > array_tmp3[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_const_2D0[1] * array_x1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_x1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 2 > array_tmp9[2] := array_x2_higher[2,2]; > #emit pre mult CONST FULL $eq_no = 2 i = 2 > array_tmp11[2] := array_const_2D0[1] * array_x2[2]; > #emit pre diff $eq_no = 2 i = 2 > array_tmp13[2] := array_x1_higher[3,2]; > #emit pre diff $eq_no = 2 i = 2 > array_tmp15[2] := array_x1_higher[2,2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_x2_set_initial[2,4]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp1[3] := array_const_4D0[1] * array_x2[3]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre diff $eq_no = 1 i = 3 > array_tmp3[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_const_2D0[1] * array_x1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_x1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 3 > array_tmp9[3] := array_x2_higher[2,3]; > #emit pre mult CONST FULL $eq_no = 2 i = 3 > array_tmp11[3] := array_const_2D0[1] * array_x2[3]; > #emit pre diff $eq_no = 2 i = 3 > array_tmp13[3] := array_x1_higher[3,3]; > #emit pre diff $eq_no = 2 i = 3 > array_tmp15[3] := array_x1_higher[2,3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_x2_set_initial[2,5]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp1[4] := array_const_4D0[1] * array_x2[4]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre diff $eq_no = 1 i = 4 > array_tmp3[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_const_2D0[1] * array_x1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_x1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 4 > array_tmp9[4] := array_x2_higher[2,4]; > #emit pre mult CONST FULL $eq_no = 2 i = 4 > array_tmp11[4] := array_const_2D0[1] * array_x2[4]; > #emit pre diff $eq_no = 2 i = 4 > array_tmp13[4] := array_x1_higher[3,4]; > #emit pre diff $eq_no = 2 i = 4 > array_tmp15[4] := array_x1_higher[2,4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_x2_set_initial[2,6]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp1[5] := array_const_4D0[1] * array_x2[5]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre diff $eq_no = 1 i = 5 > array_tmp3[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_const_2D0[1] * array_x1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_x1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp7[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; > #emit pre diff $eq_no = 2 i = 5 > array_tmp9[5] := array_x2_higher[2,5]; > #emit pre mult CONST FULL $eq_no = 2 i = 5 > array_tmp11[5] := array_const_2D0[1] * array_x2[5]; > #emit pre diff $eq_no = 2 i = 5 > array_tmp13[5] := array_x1_higher[3,5]; > #emit pre diff $eq_no = 2 i = 5 > array_tmp15[5] := array_x1_higher[2,5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_x2_set_initial[2,7]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp17[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; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp1[kkk] := array_const_4D0[1] * array_x2[kkk]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit diff $eq_no = 1 > array_tmp3[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp6[kkk] := array_const_2D0[1] * array_x1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_x1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp7[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 > ; > #emit diff $eq_no = 2 > array_tmp9[kkk] := array_x2_higher[2,kkk]; > #emit mult CONST FULL $eq_no = 2 i = 1 > array_tmp11[kkk] := array_const_2D0[1] * array_x2[kkk]; > #emit diff $eq_no = 2 > array_tmp13[kkk] := array_x1_higher[3,kkk]; > #emit diff $eq_no = 2 > array_tmp15[kkk] := array_x1_higher[2,kkk]; > #emit assign $eq_no = 2 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_x2_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_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 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > > #BOTTOM ATOMALL ??? > # End Function number 9 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last ; array_tmp1[1] := array_const_4D0[1]*array_x2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_x2_higher[2, 1]; array_tmp6[1] := array_const_2D0[1]*array_x1[1]; if not array_x1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp7[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_tmp9[1] := array_x2_higher[2, 1]; array_tmp11[1] := array_const_2D0[1]*array_x2[1]; array_tmp13[1] := array_x1_higher[3, 1]; array_tmp15[1] := array_x1_higher[2, 1]; if not array_x2_set_initial[2, 3] then if 1 <= glob_max_terms then temporary := array_tmp17[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_tmp1[2] := array_const_4D0[1]*array_x2[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_x2_higher[2, 2]; array_tmp6[2] := array_const_2D0[1]*array_x1[2]; if not array_x1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp7[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_tmp9[2] := array_x2_higher[2, 2]; array_tmp11[2] := array_const_2D0[1]*array_x2[2]; array_tmp13[2] := array_x1_higher[3, 2]; array_tmp15[2] := array_x1_higher[2, 2]; if not array_x2_set_initial[2, 4] then if 2 <= glob_max_terms then temporary := array_tmp17[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_tmp1[3] := array_const_4D0[1]*array_x2[3]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_x2_higher[2, 3]; array_tmp6[3] := array_const_2D0[1]*array_x1[3]; if not array_x1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp7[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_tmp9[3] := array_x2_higher[2, 3]; array_tmp11[3] := array_const_2D0[1]*array_x2[3]; array_tmp13[3] := array_x1_higher[3, 3]; array_tmp15[3] := array_x1_higher[2, 3]; if not array_x2_set_initial[2, 5] then if 3 <= glob_max_terms then temporary := array_tmp17[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_tmp1[4] := array_const_4D0[1]*array_x2[4]; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_x2_higher[2, 4]; array_tmp6[4] := array_const_2D0[1]*array_x1[4]; if not array_x1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp7[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_tmp9[4] := array_x2_higher[2, 4]; array_tmp11[4] := array_const_2D0[1]*array_x2[4]; array_tmp13[4] := array_x1_higher[3, 4]; array_tmp15[4] := array_x1_higher[2, 4]; if not array_x2_set_initial[2, 6] then if 4 <= glob_max_terms then temporary := array_tmp17[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_tmp1[5] := array_const_4D0[1]*array_x2[5]; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_x2_higher[2, 5]; array_tmp6[5] := array_const_2D0[1]*array_x1[5]; if not array_x1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp7[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; array_tmp9[5] := array_x2_higher[2, 5]; array_tmp11[5] := array_const_2D0[1]*array_x2[5]; array_tmp13[5] := array_x1_higher[3, 5]; array_tmp15[5] := array_x1_higher[2, 5]; if not array_x2_set_initial[2, 7] then if 5 <= glob_max_terms then temporary := array_tmp17[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; while kkk <= glob_max_terms do array_tmp1[kkk] := array_const_4D0[1]*array_x2[kkk]; array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_x2_higher[2, kkk]; array_tmp6[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[1, kkk + order_d] then temporary := array_tmp7[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; array_tmp9[kkk] := array_x2_higher[2, kkk]; array_tmp11[kkk] := array_const_2D0[1]*array_x2[kkk]; array_tmp13[kkk] := array_x1_higher[3, kkk]; array_tmp15[kkk] := array_x1_higher[2, kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then if not array_x2_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_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; 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); > fprintf(fd,""); > 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); > 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; fprintf(fd, ""); 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 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 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > > local good_digits; > > > fprintf(file,""); > if (rel_error <> -1.0) then # if number 11 > if (rel_error <> 0.0) then # if number 12 > good_digits := -trunc(log10(rel_error/100.0)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 12 > ; > else > fprintf(file,"Unknown"); > fi;# end if 11 > ; > fprintf(file,""); > > # End Function number 9 > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if rel_error <> 0. then good_digits := -trunc(log10(rel_error/100.0)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # Begin Function number 10 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 10 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 11 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 11 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 12 > 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 12 > 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 13 > logstart := proc(file) > fprintf(file,""); > # End Function number 13 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 14 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 14 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 15 > not_reached_end := proc(x,x_end) > global neg_h; > local ret; > > > > if ((glob_neg_h and (x > x_end)) or (( not glob_neg_h) and (x < x_end))) then # if number 13 > ret := true; > else > ret := false; > fi;# end if 13 > ; > > > ret; > > # End Function number 15 > end; not_reached_end := proc(x, x_end) local ret; global neg_h; if glob_neg_h and x_end < x or not glob_neg_h and x < x_end then ret := true else ret := false end if; ret end proc > # Begin Function number 16 > 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 16 > 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 17 > 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 17 > 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 18 > 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 18 > 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 19 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 19 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 20 > 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 20 > 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 21 > 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 21 > 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 22 > convfp := proc(mmm) > (mmm); > > # End Function number 22 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 23 > convfloat := proc(mmm) > (mmm); > > # End Function number 23 > 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(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 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(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 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 > DEBUGL, > DEBUGMASSIVE, > glob_max_terms, > ALWAYS, > INFO, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_h, > glob_optimal_done, > glob_clock_sec, > glob_max_minutes, > hours_in_day, > glob_subiter_method, > glob_normmax, > glob_iter, > glob_max_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > days_in_year, > sec_in_minute, > djd_debug, > glob_max_opt_iter, > glob_look_poles, > glob_hmin, > glob_html_log, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_large_float, > glob_hmin_init, > glob_reached_optimal_h, > centuries_in_millinium, > glob_dump, > glob_log10normmin, > glob_smallish_float, > glob_display_interval, > glob_not_yet_finished, > glob_clock_start_sec, > years_in_century, > glob_optimal_expect_sec, > glob_last_good_h, > glob_hmax, > glob_not_yet_start_msg, > glob_log10abserr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_initial_pass, > min_in_hour, > glob_percent_done, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_next_display, > glob_neg_h, > glob_display_flag, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_optimal_start, > glob_almost_1, > djd_debug2, > glob_good_digits, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_4D0, > array_const_2, > array_const_1, > array_const_2D0, > array_const_3D0, > array_const_0D0, > #END CONST > array_fact_1, > array_type_pole, > array_norms, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > array_x2_init, > array_t, > array_pole, > array_1st_rel_error, > array_x1_init, > array_last_rel_error, > array_x1, > array_x2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_m1, > array_fact_2, > array_x1_higher, > array_x1_higher_work2, > array_x1_higher_work, > array_complex_pole, > array_poles, > array_x2_higher_work2, > array_real_pole, > array_x2_higher, > array_x2_higher_work, > array_x1_set_initial, > array_x2_set_initial, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_max_terms := 30; > ALWAYS := 1; > INFO := 2; > glob_iolevel := 5; > glob_log10relerr := 0.0; > glob_dump_analytic := false; > glob_h := 0.1; > glob_optimal_done := false; > glob_clock_sec := 0.0; > glob_max_minutes := 0.0; > hours_in_day := 24; > glob_subiter_method := 3; > glob_normmax := 0.0; > glob_iter := 0; > glob_max_sec := 10000.0; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_disp_incr := 0.1; > days_in_year := 365; > sec_in_minute := 60; > djd_debug := true; > glob_max_opt_iter := 10; > glob_look_poles := false; > glob_hmin := 0.00000000001; > glob_html_log := true; > glob_start := 0; > glob_warned2 := false; > glob_log10_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_reached_optimal_h := false; > centuries_in_millinium := 10; > glob_dump := false; > glob_log10normmin := 0.1; > glob_smallish_float := 0.1e-100; > glob_display_interval := 0.0; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > years_in_century := 100; > glob_optimal_expect_sec := 0.1; > glob_last_good_h := 0.1; > glob_hmax := 1.0; > glob_not_yet_start_msg := true; > glob_log10abserr := 0.0; > glob_current_iter := 0; > glob_curr_iter_when_opt := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_log10_abserr := 0.1e-10; > glob_initial_pass := true; > min_in_hour := 60; > glob_percent_done := 0.0; > MAX_UNCHANGED := 10; > glob_max_trunc_err := 0.1e-10; > glob_next_display := 0.0; > glob_neg_h := false; > glob_display_flag := true; > glob_orig_start_sec := 0.0; > glob_unchanged_h_cnt := 0; > glob_small_float := 0.1e-50; > glob_optimal_start := 0.0; > glob_almost_1 := 0.9990; > djd_debug2 := true; > glob_good_digits := 0; > glob_warned := false; > glob_no_eqs := 0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > #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/mtest6postode.ode#################"); > omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#"); > omniout_str(ALWAYS,"# was complicated.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 := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.005 ;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10000;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > 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(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(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_fact_1:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_norms:= 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_x2_init:= Array(0..(max_terms + 1),[]); > array_t:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_x1_init:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_x1:= Array(0..(max_terms + 1),[]); > array_x2:= 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_m1:= Array(0..(max_terms + 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_x1_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_higher_work2 := 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_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_x2_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_x2_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_x2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x2_init[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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_m1[term] := 0.0; > term := term + 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 > ; > 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 <=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_x1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_x2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_x2_higher[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_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_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_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_x2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_4D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4D0[1] := 4.0; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3D0[1] := 3.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #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 complicated.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 := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.005 ; > glob_display_interval := 0.1; > glob_look_poles := true; > glob_max_iter := 10000; > glob_max_minutes := 10; > #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)); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1 > ; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_x1_set_initial[1,1] := true; > array_x1_set_initial[1,2] := true; > array_x1_set_initial[1,3] := false; > array_x1_set_initial[1,4] := false; > array_x1_set_initial[1,5] := false; > array_x1_set_initial[1,6] := false; > array_x1_set_initial[1,7] := false; > array_x1_set_initial[1,8] := false; > array_x1_set_initial[1,9] := false; > array_x1_set_initial[1,10] := false; > array_x1_set_initial[1,11] := false; > array_x1_set_initial[1,12] := false; > array_x1_set_initial[1,13] := false; > array_x1_set_initial[1,14] := false; > array_x1_set_initial[1,15] := false; > array_x1_set_initial[1,16] := false; > array_x1_set_initial[1,17] := false; > array_x1_set_initial[1,18] := false; > array_x1_set_initial[1,19] := false; > array_x1_set_initial[1,20] := false; > array_x1_set_initial[1,21] := false; > array_x1_set_initial[1,22] := false; > array_x1_set_initial[1,23] := false; > array_x1_set_initial[1,24] := false; > array_x1_set_initial[1,25] := false; > array_x1_set_initial[1,26] := false; > array_x1_set_initial[1,27] := false; > array_x1_set_initial[1,28] := false; > array_x1_set_initial[1,29] := false; > array_x1_set_initial[1,30] := false; > array_x2_set_initial[2,1] := true; > array_x2_set_initial[2,2] := true; > array_x2_set_initial[2,3] := false; > array_x2_set_initial[2,4] := false; > array_x2_set_initial[2,5] := false; > array_x2_set_initial[2,6] := false; > array_x2_set_initial[2,7] := false; > array_x2_set_initial[2,8] := false; > array_x2_set_initial[2,9] := false; > array_x2_set_initial[2,10] := false; > array_x2_set_initial[2,11] := false; > array_x2_set_initial[2,12] := false; > array_x2_set_initial[2,13] := false; > array_x2_set_initial[2,14] := false; > array_x2_set_initial[2,15] := false; > array_x2_set_initial[2,16] := false; > array_x2_set_initial[2,17] := false; > array_x2_set_initial[2,18] := false; > array_x2_set_initial[2,19] := false; > array_x2_set_initial[2,20] := false; > array_x2_set_initial[2,21] := false; > array_x2_set_initial[2,22] := false; > array_x2_set_initial[2,23] := false; > array_x2_set_initial[2,24] := false; > array_x2_set_initial[2,25] := false; > array_x2_set_initial[2,26] := false; > array_x2_set_initial[2,27] := false; > array_x2_set_initial[2,28] := false; > array_x2_set_initial[2,29] := false; > array_x2_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; > glob_next_display := t_start; > 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 > ; > 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 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > 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) > ; > 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) > ; > 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 not_reached_end(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 > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3 > ; > 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 > if (reached_interval()) then # if number 4 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 4 > ; > array_t[1] := array_t[1] + glob_h; > array_t[2] := glob_h; > #Jump Series array_x1 > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_x1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / 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_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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / 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_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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / 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_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 =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x1[term_no] := array_x1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_x2 > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_x2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / 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_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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / 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_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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / 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_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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / 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_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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / 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_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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_x2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / 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_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 =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_x2[term_no] := array_x2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); > omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(t_start,t_end); > if (glob_html_log) then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-09-21T01:00:34-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest6") > ; > logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") > ; > logitem_float(html_log_file,t_start) > ; > logitem_float(html_log_file,t_end) > ; > logitem_float(html_log_file,array_t[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > 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," 130 ") > ; > logitem_str(html_log_file,"mtest6 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest6 maple results") > ; > logitem_str(html_log_file,"c c++ Maple and Maxima") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > 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 9 > 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 DEBUGL, DEBUGMASSIVE, glob_max_terms, ALWAYS, INFO, glob_iolevel, glob_log10relerr, glob_dump_analytic, glob_h, glob_optimal_done, glob_clock_sec, glob_max_minutes, hours_in_day, glob_subiter_method, glob_normmax, glob_iter, glob_max_sec, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, days_in_year, sec_in_minute, djd_debug, glob_max_opt_iter, glob_look_poles, glob_hmin, glob_html_log, glob_start, glob_warned2, glob_log10_relerr, glob_large_float, glob_hmin_init, glob_reached_optimal_h, centuries_in_millinium, glob_dump, glob_log10normmin, glob_smallish_float, glob_display_interval, glob_not_yet_finished, glob_clock_start_sec, years_in_century, glob_optimal_expect_sec, glob_last_good_h, glob_hmax, glob_not_yet_start_msg, glob_log10abserr, glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_initial_pass, min_in_hour, glob_percent_done, MAX_UNCHANGED, glob_max_trunc_err, glob_next_display, glob_neg_h, glob_display_flag, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_optimal_start, glob_almost_1, djd_debug2, glob_good_digits, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, array_const_4D0, array_const_2, array_const_1, array_const_2D0, array_const_3D0, array_const_0D0, array_fact_1, array_type_pole, array_norms, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_x2_init, array_t, array_pole, array_1st_rel_error, array_x1_init, array_last_rel_error, array_x1, array_x2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_m1, array_fact_2, array_x1_higher, array_x1_higher_work2, array_x1_higher_work, array_complex_pole, array_poles, array_x2_higher_work2, array_real_pole, array_x2_higher, array_x2_higher_work, array_x1_set_initial, array_x2_set_initial, glob_last ; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; DEBUGMASSIVE := 4; glob_max_terms := 30; ALWAYS := 1; INFO := 2; glob_iolevel := 5; glob_log10relerr := 0.; glob_dump_analytic := false; glob_h := 0.1; glob_optimal_done := false; glob_clock_sec := 0.; glob_max_minutes := 0.; hours_in_day := 24; glob_subiter_method := 3; glob_normmax := 0.; glob_iter := 0; glob_max_sec := 10000.0; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_disp_incr := 0.1; days_in_year := 365; sec_in_minute := 60; djd_debug := true; glob_max_opt_iter := 10; glob_look_poles := false; glob_hmin := 0.1*10^(-10); glob_html_log := true; glob_start := 0; glob_warned2 := false; glob_log10_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_reached_optimal_h := false; centuries_in_millinium := 10; glob_dump := false; glob_log10normmin := 0.1; glob_smallish_float := 0.1*10^(-100); glob_display_interval := 0.; glob_not_yet_finished := true; glob_clock_start_sec := 0.; years_in_century := 100; glob_optimal_expect_sec := 0.1; glob_last_good_h := 0.1; glob_hmax := 1.0; glob_not_yet_start_msg := true; glob_log10abserr := 0.; glob_current_iter := 0; glob_curr_iter_when_opt := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_log10_abserr := 0.1*10^(-10); glob_initial_pass := true; min_in_hour := 60; glob_percent_done := 0.; MAX_UNCHANGED := 10; glob_max_trunc_err := 0.1*10^(-10); glob_next_display := 0.; glob_neg_h := false; glob_display_flag := true; glob_orig_start_sec := 0.; glob_unchanged_h_cnt := 0; glob_small_float := 0.1*10^(-50); glob_optimal_start := 0.; glob_almost_1 := 0.9990; djd_debug2 := true; glob_good_digits := 0; glob_warned := false; glob_no_eqs := 0; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); 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/mtest6postode.ode#################"); omniout_str(ALWAYS, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \ diff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#"); omniout_str(ALWAYS, "# was complicated.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 := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.005 ;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10000;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); 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(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(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_fact_1 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_norms := 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_x2_init := Array(0 .. max_terms + 1, []); array_t := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_x1_init := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_x1 := Array(0 .. max_terms + 1, []); array_x2 := 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_m1 := Array(0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_x1_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_higher_work2 := 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_poles := Array(0 .. 3, 0 .. 4, []); array_x2_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_x2_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_x1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_x2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2_init[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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_m1[term] := 0.; term := term + 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; 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 <= 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_x1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_x2_higher[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_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_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_t := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_t[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_x2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1 end do; array_x1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1 end do; array_const_4D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4D0[term] := 0.; term := term + 1 end do; array_const_4D0[1] := 4.0; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; 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 := 100; glob_h := 0.005; glob_display_interval := 0.1; glob_look_poles := true; glob_max_iter := 10000; glob_max_minutes := 10; 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); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_x1_set_initial[1, 1] := true; array_x1_set_initial[1, 2] := true; array_x1_set_initial[1, 3] := false; array_x1_set_initial[1, 4] := false; array_x1_set_initial[1, 5] := false; array_x1_set_initial[1, 6] := false; array_x1_set_initial[1, 7] := false; array_x1_set_initial[1, 8] := false; array_x1_set_initial[1, 9] := false; array_x1_set_initial[1, 10] := false; array_x1_set_initial[1, 11] := false; array_x1_set_initial[1, 12] := false; array_x1_set_initial[1, 13] := false; array_x1_set_initial[1, 14] := false; array_x1_set_initial[1, 15] := false; array_x1_set_initial[1, 16] := false; array_x1_set_initial[1, 17] := false; array_x1_set_initial[1, 18] := false; array_x1_set_initial[1, 19] := false; array_x1_set_initial[1, 20] := false; array_x1_set_initial[1, 21] := false; array_x1_set_initial[1, 22] := false; array_x1_set_initial[1, 23] := false; array_x1_set_initial[1, 24] := false; array_x1_set_initial[1, 25] := false; array_x1_set_initial[1, 26] := false; array_x1_set_initial[1, 27] := false; array_x1_set_initial[1, 28] := false; array_x1_set_initial[1, 29] := false; array_x1_set_initial[1, 30] := false; array_x2_set_initial[2, 1] := true; array_x2_set_initial[2, 2] := true; array_x2_set_initial[2, 3] := false; array_x2_set_initial[2, 4] := false; array_x2_set_initial[2, 5] := false; array_x2_set_initial[2, 6] := false; array_x2_set_initial[2, 7] := false; array_x2_set_initial[2, 8] := false; array_x2_set_initial[2, 9] := false; array_x2_set_initial[2, 10] := false; array_x2_set_initial[2, 11] := false; array_x2_set_initial[2, 12] := false; array_x2_set_initial[2, 13] := false; array_x2_set_initial[2, 14] := false; array_x2_set_initial[2, 15] := false; array_x2_set_initial[2, 16] := false; array_x2_set_initial[2, 17] := false; array_x2_set_initial[2, 18] := false; array_x2_set_initial[2, 19] := false; array_x2_set_initial[2, 20] := false; array_x2_set_initial[2, 21] := false; array_x2_set_initial[2, 22] := false; array_x2_set_initial[2, 23] := false; array_x2_set_initial[2, 24] := false; array_x2_set_initial[2, 25] := false; array_x2_set_initial[2, 26] := false; array_x2_set_initial[2, 27] := false; array_x2_set_initial[2, 28] := false; array_x2_set_initial[2, 29] := false; array_x2_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; glob_next_display := t_start; 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; 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; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); 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); 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); 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 not_reached_end(array_t[1], t_end) and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; 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; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval 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_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; 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; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;"); omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\ ff(x1,t,2) - diff (x1,t,1) + x1;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(t_start, t_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-09-21T01:00:34-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest6") ; logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;") ; logitem_float(html_log_file, t_start); logitem_float(html_log_file, t_end); logitem_float(html_log_file, array_t[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); 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, " 130 "); logitem_str(html_log_file, "mtest6 diffeq.mxt"); logitem_str(html_log_file, "mtest6 maple results"); logitem_str(html_log_file, "c c++ Maple and Maxima"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \ 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); 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/mtest6postode.ode################# diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # # was complicated.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 := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.005 ; glob_display_interval := 0.1; glob_look_poles := true; glob_max_iter := 10000; glob_max_minutes := 10; #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(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(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 x1[1] (analytic) = 2.001091755187482740162486839163 x1[1] (numeric) = 2.001091755187482740162486839163 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 x2[1] (analytic) = 1.0007256155636055990741531973548 x2[1] (numeric) = 1.0007256155636055990741531973548 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 t[1] = 0.5 x1[1] (analytic) = 2.001091755187482740162486839163 x1[1] (numeric) = 2.001091755187482740162486839163 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 x2[1] (analytic) = 1.0007256155636055990741531973548 x2[1] (numeric) = 1.0007256155636055990741531973548 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=2.8MB, time=0.18 memory used=7.6MB, alloc=3.9MB, time=0.43 memory used=11.4MB, alloc=3.9MB, time=0.68 memory used=15.2MB, alloc=3.9MB, time=0.92 memory used=19.0MB, alloc=3.9MB, time=1.17 t[1] = 0.6 x1[1] (analytic) = 2.000987860944969247578731226051 x1[1] (numeric) = 2.000982579668734466146238155247 absolute error = 5.2812762347814324930708040e-06 relative error = 0.00026393344696690676499951456627037 % Correct digits = 5 h = 0.005 x2[1] (analytic) = 1.0008286668753755174276946911611 x2[1] (numeric) = 1.0008161509169525818808594948668 absolute error = 1.25159584229355468351962943e-05 relative error = 0.0012505595450229095203804419740368 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=22.8MB, alloc=3.9MB, time=1.42 memory used=26.7MB, alloc=3.9MB, time=1.68 memory used=30.5MB, alloc=3.9MB, time=1.93 memory used=34.3MB, alloc=3.9MB, time=2.18 memory used=38.1MB, alloc=3.9MB, time=2.43 t[1] = 0.7 x1[1] (analytic) = 2.0008938535468245371264686401681 x1[1] (numeric) = 2.000873404149986192129989471331 absolute error = 2.04493968383449964791688371e-05 relative error = 0.0010220130769104011137157287405776 % Correct digits = 4 h = 0.005 x2[1] (analytic) = 1.000960015584506357771856261807 x2[1] (numeric) = 1.0009066862702995646875657923788 absolute error = 5.33293142067930842904694282e-05 relative error = 0.0053278166336795838279499877335098 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=3.9MB, time=2.68 NO POLE NO POLE memory used=45.7MB, alloc=3.9MB, time=2.93 memory used=49.5MB, alloc=3.9MB, time=3.18 memory used=53.4MB, alloc=4.0MB, time=3.44 memory used=57.2MB, alloc=4.0MB, time=3.68 memory used=61.0MB, alloc=4.0MB, time=3.93 t[1] = 0.8 x1[1] (analytic) = 2.000808792135410998864574184293 x1[1] (numeric) = 2.000764228631237918113740787415 absolute error = 4.45635041730807508333968780e-05 relative error = 0.0022272745076014628076063407733946 % Correct digits = 4 h = 0.005 x2[1] (analytic) = 1.0011254051741141894381598879868 x2[1] (numeric) = 1.0009972216236465474942720898908 absolute error = 0.000128183550467641943887798096 relative error = 0.01280394542033906912022378773212 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=64.8MB, alloc=4.0MB, time=4.18 memory used=68.6MB, alloc=4.0MB, time=4.43 memory used=72.4MB, alloc=4.0MB, time=4.68 memory used=76.2MB, alloc=4.0MB, time=4.94 memory used=80.1MB, alloc=4.0MB, time=5.19 t[1] = 0.9 x1[1] (analytic) = 2.0007318253875330784013902176314 x1[1] (numeric) = 2.000655053112489644097492103499 absolute error = 7.67722750434343038981141324e-05 relative error = 0.0038372096684453873344705727302837 % Correct digits = 4 h = 0.005 x2[1] (analytic) = 1.0013319003908047689503112410625 x2[1] (numeric) = 1.0010877569769935303009783874028 absolute error = 0.0002441434138112386493328536597 relative error = 0.024381867162721286488706584612248 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=83.9MB, alloc=4.0MB, time=5.44 memory used=87.7MB, alloc=4.0MB, time=5.69 memory used=91.5MB, alloc=4.0MB, time=5.94 memory used=95.3MB, alloc=4.0MB, time=6.19 memory used=99.1MB, alloc=4.0MB, time=6.45 t[1] = 1 x1[1] (analytic) = 2.0006621829941085961788719427863 x1[1] (numeric) = 2.000545877593741370081243419583 absolute error = 0.0001163054003672260976285232033 relative error = 0.0058133452691732407916387672706403 % Correct digits = 4 h = 0.005 x2[1] (analytic) = 1.0015881750521375627419247426231 x2[1] (numeric) = 1.0011782923303405131076846849148 absolute error = 0.0004098827217970496342400577083 relative error = 0.040923278849185018987870044617463 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=102.9MB, alloc=4.0MB, time=6.70 memory used=106.8MB, alloc=4.0MB, time=6.95 memory used=110.6MB, alloc=4.0MB, time=7.21 memory used=114.4MB, alloc=4.0MB, time=7.47 memory used=118.2MB, alloc=4.0MB, time=7.72 t[1] = 1.1 x1[1] (analytic) = 2.0005991679506565431959199244316 x1[1] (numeric) = 2.000436702074993096064994735667 absolute error = 0.0001624658756634471309251887646 relative error = 0.0081208609033798340766463529804479 % Correct digits = 4 h = 0.005 x2[1] (analytic) = 1.0019048640249962480512810095053 x2[1] (numeric) = 1.0012688276836874959143909824268 absolute error = 0.0006360363413087521368900270785 relative error = 0.063482708203808444798380797217593 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=122.0MB, alloc=4.0MB, time=7.97 memory used=125.8MB, alloc=4.0MB, time=8.22 memory used=129.7MB, alloc=4.0MB, time=8.47 memory used=133.5MB, alloc=4.0MB, time=8.72 memory used=137.3MB, alloc=4.0MB, time=8.98 t[1] = 1.2 x1[1] (analytic) = 2.0005421495814419637739609596927 x1[1] (numeric) = 2.000327526556244822048746051751 absolute error = 0.0002146230251971417252149079417 relative error = 0.010728243103602973267566694838174 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.002294993539701980959441081236 x2[1] (numeric) = 1.0013593630370344787210972799388 absolute error = 0.0009356305026675022383438012972 relative error = 0.093348815338609282343202966865883 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.0MB, time=9.23 NO POLE NO POLE memory used=144.9MB, alloc=4.0MB, time=9.48 memory used=148.7MB, alloc=4.0MB, time=9.73 memory used=152.5MB, alloc=4.0MB, time=9.96 memory used=156.4MB, alloc=4.0MB, time=10.19 memory used=160.2MB, alloc=4.0MB, time=10.43 t[1] = 1.3 x1[1] (analytic) = 2.0004905572274612226856201997016 x1[1] (numeric) = 2.000218351037496548032497367835 absolute error = 0.0002722061899646746531228318666 relative error = 0.013606971999004745526694615434472 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0027745071449105418604868650168 x2[1] (numeric) = 1.0014498983903814615278035774508 absolute error = 0.001324608754529080332683287566 relative error = 0.13209437865552575847506281741196 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=164.0MB, alloc=4.0MB, time=10.67 memory used=167.8MB, alloc=4.0MB, time=10.90 memory used=171.6MB, alloc=4.0MB, time=11.15 memory used=175.4MB, alloc=4.0MB, time=11.40 memory used=179.2MB, alloc=4.0MB, time=11.64 t[1] = 1.4 x1[1] (analytic) = 2.0004438745350948916584917502317 x1[1] (numeric) = 2.000109175518748274016248683919 absolute error = 0.0003346990163466176422430663127 relative error = 0.01673123753219030052612551904698 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0033629084434018919173815615742 x2[1] (numeric) = 1.0015404337437284443345098749628 absolute error = 0.0018224746996734475828716866114 relative error = 0.18163664256842024633704111397444 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=183.1MB, alloc=4.0MB, time=11.89 memory used=186.9MB, alloc=4.0MB, time=12.13 memory used=190.7MB, alloc=4.0MB, time=12.39 memory used=194.5MB, alloc=4.0MB, time=12.64 memory used=198.3MB, alloc=4.0MB, time=12.89 t[1] = 1.5 x1[1] (analytic) = 2.0004016342882671736920799048474 x1[1] (numeric) = 2.000000000000000000000000000003 absolute error = 0.0004016342882671736920799048444 relative error = 0.020077682470504136984688765962524 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0040840464326820624968656900721 x2[1] (numeric) = 1.0016309690970754271412161724748 absolute error = 0.0024530773356066353556495175973 relative error = 0.24430996033867367915243917425418 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=202.1MB, alloc=4.0MB, time=13.14 memory used=205.9MB, alloc=4.0MB, time=13.39 memory used=209.8MB, alloc=4.0MB, time=13.65 memory used=213.6MB, alloc=4.0MB, time=13.90 memory used=217.4MB, alloc=4.0MB, time=14.15 t[1] = 1.6 x1[1] (analytic) = 2.0003634137323903797352733226818 x1[1] (numeric) = 1.999890824481251725983751316087 absolute error = 0.0004725892511386537515220065948 relative error = 0.023625169701382919736142239192746 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0049670749948202663512576065259 x2[1] (numeric) = 1.0017215044504224099479224699868 absolute error = 0.0032455705443978564033351365391 relative error = 0.32295292305119394130996941978113 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=221.2MB, alloc=4.0MB, time=14.40 memory used=225.0MB, alloc=4.0MB, time=14.65 memory used=228.8MB, alloc=4.0MB, time=14.90 memory used=232.6MB, alloc=4.0MB, time=15.45 memory used=236.5MB, alloc=4.0MB, time=16.04 t[1] = 1.7 x1[1] (analytic) = 2.000328830343294922370403021508 x1[1] (numeric) = 1.999781648962503451967502632171 absolute error = 0.000547181380791470402900389337 relative error = 0.027354571532999579263746454508052 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.006047625066695223064699720858 x2[1] (numeric) = 1.0018120398037693927546287674988 absolute error = 0.0042355852629258303100709533592 relative error = 0.42101240114204684395524683252874 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.0MB, time=16.65 NO POLE NO POLE memory used=244.1MB, alloc=4.0MB, time=17.27 memory used=247.9MB, alloc=4.0MB, time=17.89 memory used=251.7MB, alloc=4.0MB, time=18.50 memory used=255.5MB, alloc=4.0MB, time=19.11 memory used=259.4MB, alloc=4.0MB, time=19.72 t[1] = 1.8 x1[1] (analytic) = 2.0002975379987988557689342484968 x1[1] (numeric) = 1.999672473443755177951253948255 absolute error = 0.0006250645550436778176803002418 relative error = 0.031248578932363469128233079563575 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0073692365552020735120079945959 x2[1] (numeric) = 1.0019025751571163755613350650108 absolute error = 0.0054666613980856979506729295851 relative error = 0.5426670975956624282453648109687 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=263.2MB, alloc=4.0MB, time=20.33 memory used=267.0MB, alloc=4.0MB, time=20.94 memory used=270.8MB, alloc=4.0MB, time=21.56 memory used=274.6MB, alloc=4.0MB, time=22.16 memory used=278.4MB, alloc=4.0MB, time=22.77 t[1] = 1.9 x1[1] (analytic) = 2.0002692235146007430947538217244 x1[1] (numeric) = 1.999563297925006903935005264339 absolute error = 0.0007059255895938391597485573854 relative error = 0.035291528824979010846167288836246 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0089851074844269551233038693665 x2[1] (numeric) = 1.0019931105104633583680413625228 absolute error = 0.0069919969739635967552625068437 relative error = 0.69297325818770955365598220149544 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=282.2MB, alloc=4.0MB, time=23.38 memory used=286.1MB, alloc=4.0MB, time=24.00 memory used=289.9MB, alloc=4.0MB, time=24.60 memory used=293.7MB, alloc=4.0MB, time=25.20 memory used=297.5MB, alloc=4.0MB, time=25.80 t[1] = 2 x1[1] (analytic) = 2.000243603509825902845409199091 x1[1] (numeric) = 1.999454122406258629918756580423 absolute error = 0.000789481103567272926652618668 relative error = 0.039469247754722027122054277820973 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0109602305915998316231902520891 x2[1] (numeric) = 1.0020836458638103411747476600348 absolute error = 0.0088765847277894904484425920543 relative error = 0.87803500663869209054597749059994 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=301.3MB, alloc=4.0MB, time=26.40 memory used=305.1MB, alloc=4.0MB, time=27.05 memory used=308.9MB, alloc=4.0MB, time=27.66 memory used=312.8MB, alloc=4.0MB, time=28.27 memory used=316.6MB, alloc=4.0MB, time=28.87 t[1] = 2.1 x1[1] (analytic) = 2.0002204215708553674383935652769 x1[1] (numeric) = 1.999344946887510355902507896507 absolute error = 0.0008754746833450115358856687699 relative error = 0.043768910361262348186930318301609 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0133740031366609229020699411436 x2[1] (numeric) = 1.0021741812171573239814539575468 absolute error = 0.0111998219195035989206159835968 relative error = 1.1052012272702066468448288880726 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=320.4MB, alloc=4.0MB, time=29.49 memory used=324.2MB, alloc=4.0MB, time=30.11 memory used=328.0MB, alloc=4.0MB, time=30.72 memory used=331.8MB, alloc=4.0MB, time=31.34 memory used=335.6MB, alloc=4.0MB, time=31.92 t[1] = 2.2 x1[1] (analytic) = 2.0001994456850522009900014599665 x1[1] (numeric) = 1.999235771368762081886259212591 absolute error = 0.0009636743162901191037422473755 relative error = 0.048178911276523647452037070237065 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.016323414680502323653880405673 x2[1] (numeric) = 1.0022647165705043067881602550588 absolute error = 0.0140586981099980168657201506142 relative error = 1.3832897980036793334604848709813 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.0MB, time=32.52 NO POLE NO POLE memory used=343.3MB, alloc=4.0MB, time=33.12 memory used=347.1MB, alloc=4.0MB, time=33.73 memory used=350.9MB, alloc=4.0MB, time=34.34 memory used=354.7MB, alloc=4.0MB, time=34.93 memory used=358.5MB, alloc=4.0MB, time=35.53 t[1] = 2.3 x1[1] (analytic) = 2.0001804659187010467207138932488 x1[1] (numeric) = 1.999126595850013807870010528675 absolute error = 0.0010538700686872388507033645738 relative error = 0.052688749172599621432191138355332 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0199269407815036028672097929056 x2[1] (numeric) = 1.0023552519238512895948665525708 absolute error = 0.0175716888576523132723432403348 relative error = 1.7228379950615160993171030558086 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=362.4MB, alloc=4.0MB, time=36.13 memory used=366.2MB, alloc=4.0MB, time=36.72 memory used=370.0MB, alloc=4.0MB, time=37.31 memory used=373.8MB, alloc=4.0MB, time=37.89 memory used=377.6MB, alloc=4.0MB, time=38.46 t[1] = 2.4 x1[1] (analytic) = 2.0001632923159209425060753099961 x1[1] (numeric) = 1.999017420331265533853761844759 absolute error = 0.0011458719846554086523134652371 relative error = 0.057288921812410751440394329043843 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0243292988897337999024221749256 x2[1] (numeric) = 1.0024457872771982724015728500828 absolute error = 0.0218835116125355275008493248428 relative error = 2.136374663524217582901032842887 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=381.4MB, alloc=4.0MB, time=39.04 memory used=385.2MB, alloc=4.0MB, time=39.62 memory used=389.1MB, alloc=4.0MB, time=40.19 memory used=392.9MB, alloc=4.0MB, time=40.79 memory used=396.7MB, alloc=4.0MB, time=41.38 t[1] = 2.5 x1[1] (analytic) = 2.000147752997523017831305151614 x1[1] (numeric) = 1.998908244812517259837513160843 absolute error = 0.001239508185005757993791990771 relative error = 0.061970831062263678688701106703575 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0297072573201024903227739746104 x2[1] (numeric) = 1.0025363226305452552082791475948 absolute error = 0.0271709346895572351144948270156 relative error = 2.6387047868606674663348114391756 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=400.5MB, alloc=4.0MB, time=41.95 memory used=404.3MB, alloc=4.0MB, time=42.53 memory used=408.1MB, alloc=4.0MB, time=43.13 memory used=411.9MB, alloc=4.0MB, time=43.75 memory used=415.8MB, alloc=4.0MB, time=44.35 t[1] = 2.6 x1[1] (analytic) = 2.0001336924407858009847707790263 x1[1] (numeric) = 1.998799069293768985821264476927 absolute error = 0.0013346231470168151635063020993 relative error = 0.066726696923352129503652399618679 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0362767304484945360381252899358 x2[1] (numeric) = 1.0026268579838922380149854451068 absolute error = 0.033649872464602298023139844829 relative error = 3.2471898167624423179099928646102 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=419.6MB, alloc=4.0MB, time=44.95 memory used=423.4MB, alloc=4.0MB, time=45.57 memory used=427.2MB, alloc=4.0MB, time=46.16 memory used=431.0MB, alloc=4.0MB, time=46.72 memory used=434.8MB, alloc=4.0MB, time=47.30 t[1] = 2.7 x1[1] (analytic) = 2.0001209699229315495772277930615 x1[1] (numeric) = 1.998689893775020711805015793011 absolute error = 0.0014310761479108377722120000505 relative error = 0.071549479728017643229046230056891 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0443014448946593423345569015332 x2[1] (numeric) = 1.0027173933372392208216917426188 absolute error = 0.0415840515574201215128651589144 relative error = 3.9819969378300327139155802587732 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.0MB, time=47.86 NO POLE NO POLE memory used=442.5MB, alloc=4.0MB, time=48.43 memory used=446.3MB, alloc=4.0MB, time=48.98 memory used=450.1MB, alloc=4.0MB, time=49.54 memory used=453.9MB, alloc=4.0MB, time=50.10 memory used=457.7MB, alloc=4.0MB, time=50.66 t[1] = 2.8 x1[1] (analytic) = 2.0001094581127253923369921184987 x1[1] (numeric) = 1.998580718256272437788767109095 absolute error = 0.0015287398564529545482250094037 relative error = 0.07643280972709621393060546797345 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0541035245040180910200828957228 x2[1] (numeric) = 1.0028079286905862036283980401308 absolute error = 0.051295595813431887391684855592 relative error = 4.8662768524152065823460385923252 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=461.5MB, alloc=4.0MB, time=51.22 memory used=465.3MB, alloc=4.0MB, time=51.80 memory used=469.2MB, alloc=4.0MB, time=52.37 memory used=473.0MB, alloc=4.0MB, time=52.95 memory used=476.8MB, alloc=4.0MB, time=53.51 t[1] = 2.9 x1[1] (analytic) = 2.0000990417961015330122539037555 x1[1] (numeric) = 1.998471542737524163772518425179 absolute error = 0.0016274990585773692397354785765 relative error = 0.081370923367668074962056176034187 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0660764189479466529927580297123 x2[1] (numeric) = 1.0028984640439331864351043376428 absolute error = 0.0631779549040134665576536920695 relative error = 5.9262125848689519281865263419286 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=480.6MB, alloc=4.0MB, time=54.06 memory used=484.4MB, alloc=4.0MB, time=54.62 memory used=488.2MB, alloc=4.0MB, time=55.18 memory used=492.1MB, alloc=4.0MB, time=55.75 memory used=495.9MB, alloc=4.0MB, time=56.32 t[1] = 3 x1[1] (analytic) = 2.0000896167230621550973628163482 x1[1] (numeric) = 1.998362367218775889756269741263 absolute error = 0.0017272495042862653410930750852 relative error = 0.086358605626691026535317531639289 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.0807006948190573837045712388334 x2[1] (numeric) = 1.0029889993972801692418106351548 absolute error = 0.0777116954217772144627606036786 relative error = 7.1908619837418119056855429617648 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=499.7MB, alloc=4.0MB, time=56.88 memory used=503.5MB, alloc=4.0MB, time=57.44 memory used=507.3MB, alloc=4.0MB, time=58.00 memory used=511.1MB, alloc=4.0MB, time=58.56 memory used=514.9MB, alloc=4.0MB, time=59.14 t[1] = 3.1 x1[1] (analytic) = 2.0000810885643084040509230031659 x1[1] (numeric) = 1.998253191700027615740021057347 absolute error = 0.0018278968642807883109019458189 relative error = 0.091391137825961006216578247803942 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.098563322979369318255832918741 x2[1] (numeric) = 1.0030795347506271520485169326668 absolute error = 0.0954837882287421662073159860742 relative error = 8.6916963484439323866934564733202 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=518.8MB, alloc=4.0MB, time=59.70 memory used=522.6MB, alloc=4.0MB, time=60.28 memory used=526.4MB, alloc=4.0MB, time=60.84 memory used=530.2MB, alloc=4.0MB, time=61.40 memory used=534.0MB, alloc=4.0MB, time=61.95 t[1] = 3.2 x1[1] (analytic) = 2.0000733719671610591872989426719 x1[1] (numeric) = 1.998144016181279341723772373431 absolute error = 0.0019293557858817174635265692409 relative error = 0.096464250408179290615720820478411 % Correct digits = 3 h = 0.005 x2[1] (analytic) = 1.120381236235609921186409479002 x2[1] (numeric) = 1.0031700701039741348552232301788 absolute error = 0.1172111661316357863311862488232 relative error = 10.461721630170797705469540673281 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.0MB, time=62.54 NO POLE NO POLE memory used=541.6MB, alloc=4.0MB, time=63.11 memory used=545.5MB, alloc=4.0MB, time=63.67 memory used=549.3MB, alloc=4.0MB, time=64.22 memory used=553.1MB, alloc=4.0MB, time=64.77 memory used=556.9MB, alloc=4.0MB, time=65.32 t[1] = 3.3 x1[1] (analytic) = 2.0000663897013222320098020866685 x1[1] (numeric) = 1.998034840662531067707523689515 absolute error = 0.0020315490387911643022783971535 relative error = 0.10157408020313483183354197336803 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.1470301027986149509830540232634 x2[1] (numeric) = 1.0032606054573211176619295276908 absolute error = 0.1437694973412938333211244955726 relative error = 12.534064885525987458295749631505 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=560.7MB, alloc=4.0MB, time=65.88 memory used=564.5MB, alloc=4.0MB, time=66.46 memory used=568.3MB, alloc=4.0MB, time=67.03 memory used=572.2MB, alloc=4.0MB, time=67.60 memory used=576.0MB, alloc=4.0MB, time=68.16 t[1] = 3.4 x1[1] (analytic) = 2.0000600718859285869430683202366 x1[1] (numeric) = 1.997925665143782793691275005599 absolute error = 0.0021344067421457932517933146376 relative error = 0.10671713175760687811796106862931 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.1795794703110716373394135141758 x2[1] (numeric) = 1.0033511408106681004686358252028 absolute error = 0.176228329500403536870777688973 relative error = 14.939928502988413036655673760769 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=579.8MB, alloc=4.0MB, time=68.72 memory used=583.6MB, alloc=4.0MB, time=69.31 memory used=587.4MB, alloc=4.0MB, time=69.87 memory used=591.2MB, alloc=4.0MB, time=70.46 memory used=595.0MB, alloc=4.0MB, time=71.06 t[1] = 3.5 x1[1] (analytic) = 2.0000543552901601733013316153263 x1[1] (numeric) = 1.997816489625034519675026321683 absolute error = 0.0022378656651256536263052936433 relative error = 0.11189024234298835869466151052165 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.2193356909007184154029659835453 x2[1] (numeric) = 1.0034416761640150832753421227148 absolute error = 0.2158940147367033321276238608305 relative error = 17.705871840528450688779234498993 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=598.9MB, alloc=4.0MB, time=71.65 memory used=602.7MB, alloc=4.0MB, time=72.25 memory used=606.5MB, alloc=4.0MB, time=72.81 memory used=610.3MB, alloc=4.0MB, time=73.38 memory used=614.1MB, alloc=4.0MB, time=73.96 t[1] = 3.6 x1[1] (analytic) = 2.0000491827004051266094428135124 x1[1] (numeric) = 1.997707314106286245658777637767 absolute error = 0.0023418685941188809506651757454 relative error = 0.11709055029121642537939789673816 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.2678943499956177537057107719784 x2[1] (numeric) = 1.0035322115173620660820484202268 absolute error = 0.2643621384782556876236623517516 relative error = 20.850486357886949120754590759501 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=617.9MB, alloc=4.0MB, time=74.53 memory used=621.8MB, alloc=4.0MB, time=75.10 memory used=625.6MB, alloc=4.0MB, time=75.66 memory used=629.4MB, alloc=4.0MB, time=76.21 memory used=633.2MB, alloc=4.0MB, time=76.76 t[1] = 3.7 x1[1] (analytic) = 2.0000445023476466109041649632894 x1[1] (numeric) = 1.997598138587537971642528953851 absolute error = 0.0024463637601086392616360094384 relative error = 0.12231546634272909234916049763024 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.3272043030571264098306275940663 x2[1] (numeric) = 1.0036227468707090488887547177388 absolute error = 0.3235815561864173609418728763275 relative error = 24.38068920068062411259078777179 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.0MB, time=77.31 NO POLE NO POLE memory used=640.8MB, alloc=4.0MB, time=77.87 memory used=644.6MB, alloc=4.0MB, time=78.42 memory used=648.5MB, alloc=4.0MB, time=78.97 memory used=652.3MB, alloc=4.0MB, time=79.53 memory used=656.1MB, alloc=4.0MB, time=80.08 t[1] = 3.8 x1[1] (analytic) = 2.0000402673893410980724014499806 x1[1] (numeric) = 1.997488963068789697626280269935 absolute error = 0.0025513043205514004461211800456 relative error = 0.1275626477201694576060874431041 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.3996458902523804415291985419666 x2[1] (numeric) = 1.0037132822240560316954610152508 absolute error = 0.3959326080283244098337375267158 relative error = 28.288055627908205420443702432971 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=659.9MB, alloc=4.0MB, time=80.64 memory used=663.7MB, alloc=4.0MB, time=81.25 memory used=667.5MB, alloc=4.0MB, time=81.84 memory used=671.3MB, alloc=4.0MB, time=82.42 memory used=675.2MB, alloc=4.0MB, time=82.98 t[1] = 3.9 x1[1] (analytic) = 2.0000364354406024478992496495787 x1[1] (numeric) = 1.997379787550041423610031586019 absolute error = 0.0026566478905610242892180635597 relative error = 0.13282997466872508096502290107137 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.4881264680983335567662847164884 x2[1] (numeric) = 1.0038038175774030145021673127628 absolute error = 0.4843226505209305422641174037256 relative error = 32.545799090573470025824939871073 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=679.0MB, alloc=4.0MB, time=83.53 memory used=682.8MB, alloc=4.0MB, time=84.10 memory used=686.6MB, alloc=4.0MB, time=84.66 memory used=690.4MB, alloc=4.0MB, time=85.21 memory used=694.2MB, alloc=4.0MB, time=85.79 t[1] = 4 x1[1] (analytic) = 2.0000329681499997215245286924383 x1[1] (numeric) = 1.997270612031293149593782902103 absolute error = 0.0027623561187065719307457903353 relative error = 0.13811552922858614706199093428871 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.596197092100012275202806535297 x2[1] (numeric) = 1.0038943529307499973088736102748 absolute error = 0.5923027391692622778939329250222 relative error = 37.107118043299292320514900252767 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=698.0MB, alloc=4.0MB, time=86.34 memory used=701.9MB, alloc=4.0MB, time=86.91 memory used=705.7MB, alloc=4.0MB, time=87.47 memory used=709.5MB, alloc=4.0MB, time=88.02 memory used=713.3MB, alloc=4.0MB, time=88.59 t[1] = 4.1 x1[1] (analytic) = 2.0000298308157231702455755706566 x1[1] (numeric) = 1.997161436512544875577534218187 absolute error = 0.0028683943031782946680413524696 relative error = 0.1434175760272737667208851732164 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.7281950332690914726879769619009 x2[1] (numeric) = 1.0039848882840969801155799077868 absolute error = 0.7242101449849944925723970541141 relative error = 41.90557958120402440358726434631 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=717.1MB, alloc=4.0MB, time=89.15 memory used=720.9MB, alloc=4.0MB, time=89.70 memory used=724.7MB, alloc=4.0MB, time=90.25 memory used=728.6MB, alloc=4.0MB, time=90.83 memory used=732.4MB, alloc=4.0MB, time=91.39 t[1] = 4.2 x1[1] (analytic) = 2.0000269920382768598711815718484 x1[1] (numeric) = 1.997052260993796601561285534271 absolute error = 0.0029747310444802583098960375774 relative error = 0.14873454489974840282379155229707 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 1.8894178482130173604315585987732 x2[1] (numeric) = 1.0040754236374439629222862052988 absolute error = 0.8853424245755733975092723934744 relative error = 46.857947563738576182677864661969 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.0MB, time=91.97 NO POLE NO POLE memory used=740.0MB, alloc=4.0MB, time=92.52 memory used=743.8MB, alloc=4.0MB, time=93.07 memory used=747.6MB, alloc=4.0MB, time=93.65 memory used=751.5MB, alloc=4.0MB, time=94.21 memory used=755.3MB, alloc=4.0MB, time=94.79 t[1] = 4.3 x1[1] (analytic) = 2.0000244234062219616771630150341 x1[1] (numeric) = 1.996943085475048327545036850355 absolute error = 0.0030813379311736341321261646791 relative error = 0.15406501516245675392310017884966 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 2.0863359888402997245931410071143 x2[1] (numeric) = 1.0041659589907909457289925028108 absolute error = 1.0821700298495087788641485043035 relative error = 51.869403376923886199088643976764 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=759.1MB, alloc=4.0MB, time=95.34 memory used=762.9MB, alloc=4.0MB, time=95.89 memory used=766.7MB, alloc=4.0MB, time=96.45 memory used=770.5MB, alloc=4.0MB, time=97.02 memory used=774.3MB, alloc=4.0MB, time=97.58 t[1] = 4.4 x1[1] (analytic) = 2.0000220992118255231941220908952 x1[1] (numeric) = 1.996833909956300053528788166439 absolute error = 0.0031881892555254696653339244562 relative error = 0.15940770138399373095454761444332 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 2.3268524844575479522378282673268 x2[1] (numeric) = 1.0042564943441379285356988003228 absolute error = 1.322595990113410023702129467004 relative error = 56.840560325496646477238051995811 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=778.2MB, alloc=4.0MB, time=98.12 memory used=782.0MB, alloc=4.0MB, time=98.70 memory used=785.8MB, alloc=4.0MB, time=99.30 memory used=789.6MB, alloc=4.0MB, time=99.89 memory used=793.4MB, alloc=4.0MB, time=100.48 t[1] = 4.5 x1[1] (analytic) = 2.0000199961937688361516930576417 x1[1] (numeric) = 1.996724734437551779512539482523 absolute error = 0.0032952617562170566391535751187 relative error = 0.16476144051000779661457789148857 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 2.6206201182140382742339481808269 x2[1] (numeric) = 1.0043470296974849113424050978348 absolute error = 1.6162730885165533628915430829921 relative error = 61.675214857850099026818244640629 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=797.2MB, alloc=4.0MB, time=101.04 memory used=801.0MB, alloc=4.0MB, time=101.62 memory used=804.9MB, alloc=4.0MB, time=102.18 memory used=808.7MB, alloc=4.0MB, time=102.73 memory used=812.5MB, alloc=4.0MB, time=103.29 t[1] = 4.6 x1[1] (analytic) = 2.0000180933043403404469558395698 x1[1] (numeric) = 1.996615558918803505496290798607 absolute error = 0.0034025343855368349506650409628 relative error = 0.17012518021351096837388683204131 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 2.9794288272995065674453606895232 x2[1] (numeric) = 1.0044375650508318941491113953468 absolute error = 1.9749912622486746732962492941764 relative error = 66.287579825787159785623929877997 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=816.3MB, alloc=4.0MB, time=103.85 memory used=820.1MB, alloc=4.0MB, time=104.40 memory used=823.9MB, alloc=4.0MB, time=104.95 memory used=827.7MB, alloc=4.0MB, time=105.50 memory used=831.6MB, alloc=4.0MB, time=106.07 t[1] = 4.7 x1[1] (analytic) = 2.0000163714987830524707656973337 x1[1] (numeric) = 1.996506383400055231480042114691 absolute error = 0.0035099880987278209907235826427 relative error = 0.17549796835400338166248471057802 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 3.4176788746265273882567947609929 x2[1] (numeric) = 1.0045281004041788769558176928588 absolute error = 2.4131507742223485113009770681341 relative error = 70.60788513918088995493815735887 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.0MB, time=106.65 NO POLE NO POLE memory used=839.2MB, alloc=4.0MB, time=107.21 memory used=843.0MB, alloc=4.0MB, time=107.78 memory used=846.8MB, alloc=4.0MB, time=108.33 memory used=850.6MB, alloc=4.0MB, time=108.89 memory used=854.5MB, alloc=4.0MB, time=109.45 t[1] = 4.8 x1[1] (analytic) = 2.0000148135446882360519144516482 x1[1] (numeric) = 1.996397207881306957463793430775 absolute error = 0.0036176056633812785881210208732 relative error = 0.18087894343990802540665211652891 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 3.952958782039569229119504631582 x2[1] (numeric) = 1.0046186357575258597625239903708 absolute error = 2.9483401462820433693569806412112 relative error = 74.585653654623166297717865271655 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=858.3MB, alloc=4.0MB, time=110.00 memory used=862.1MB, alloc=4.0MB, time=110.55 memory used=865.9MB, alloc=4.0MB, time=111.11 memory used=869.7MB, alloc=4.0MB, time=111.69 memory used=873.5MB, alloc=4.0MB, time=112.26 t[1] = 4.9 x1[1] (analytic) = 2.0000134038495276638129328248836 x1[1] (numeric) = 1.996288032362558683447544746859 absolute error = 0.0037253714869689803653880780246 relative error = 0.18626732599884421386466464257326 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 4.6067512195406235265012085377755 x2[1] (numeric) = 1.0047091711108728425692302878828 absolute error = 3.6020420484297506839319782498927 relative error = 78.190505125408952927741856407738 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=877.3MB, alloc=4.0MB, time=112.81 memory used=881.2MB, alloc=4.0MB, time=113.36 memory used=885.0MB, alloc=4.0MB, time=113.92 memory used=888.8MB, alloc=4.0MB, time=114.48 memory used=892.6MB, alloc=4.0MB, time=115.03 t[1] = 5 x1[1] (analytic) = 2.0000121283045983538407739448872 x1[1] (numeric) = 1.996178856843810409431296062943 absolute error = 0.0038332714607879444094778819442 relative error = 0.19166241076934828773912839087652 % Correct digits = 2 h = 0.005 x2[1] (analytic) = 5.4052951803454430290317091198713 x2[1] (numeric) = 1.0047997064642198253759365853948 absolute error = 4.4004954738812232036557725344765 relative error = 81.4108263667479336270907071395 % Correct digits = 0 h = 0.005 Finished! diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1; Iterations = 900 Total Elapsed Time = 1 Minutes 55 Seconds Elapsed Time(since restart) = 1 Minutes 55 Seconds Time to Timeout = 8 Minutes 4 Seconds Percent Done = 100.1 % > quit memory used=894.2MB, alloc=4.0MB, time=115.26