|\^/| 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 > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > glob_last; > > > > local ret; > > if ((((array_x[1] >= glob_next_display) and not glob_neg_h) or ((array_x[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 DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, glob_last; if glob_next_display <= array_x[1] and not glob_neg_h or array_x[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 > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > 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_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[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_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[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 DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[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_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[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 > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_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_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_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_x[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 DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_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_x[1] end if; hnew := sz2; return hnew end proc > # Begin Function number 6 > prog_report := proc(x_start,x_end) > global > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > > > > > > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[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(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[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(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[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(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[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 > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > > > > > > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_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_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_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_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_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_y1_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_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_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_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_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 - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y2_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_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_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_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_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 DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_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_y1_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_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_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 - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y2_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_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_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 > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > 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_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[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_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[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 DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, 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_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 9 > atomall := proc() > global > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_y2_higher[6,1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp4[1] := array_y1[1] - array_const_2D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_y2_higher[6,2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp4[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_y2_higher[6,3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp4[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_y2_higher[6,4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp4[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_y2_higher[6,5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp4[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_y2_higher[6,kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_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_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit FULL - NOT FULL sub $eq_no = 2 > array_tmp4[kkk] := array_y1[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_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_y2_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 DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, glob_last; array_tmp1[1] := array_y2_higher[6, 1]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp4[1] := array_y1[1] - array_const_2D0[1]; if not array_y2_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_y2_higher[6, 2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp4[2] := array_y1[2]; if not array_y2_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_y2_higher[6, 3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp4[3] := array_y1[3]; if not array_y2_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_y2_higher[6, 4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp4[4] := array_y1[4]; if not array_y2_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_y2_higher[6, 5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp4[5] := array_y1[5]; if not array_y2_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y2_higher[6, kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_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_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp4[kkk] := array_y1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_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_y2_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_y1 := proc(x) > return(2.0 + sin(x)); > end; exact_soln_y1 := proc(x) return 2.0 + sin(x) end proc > exact_soln_y2 := proc(x) > return(2.0 - cos(x)); > end; exact_soln_y2 := proc(x) return 2.0 - cos(x) end proc > exact_soln_y2p := proc(x) > return(sin(x)); > end; exact_soln_y2p := proc(x) return sin(x) end proc > exact_soln_y2pp := proc(x) > return(cos(x)); > end; exact_soln_y2pp := proc(x) return cos(x) end proc > exact_soln_y2ppp := proc(x) > return(-sin(x)); > end; exact_soln_y2ppp := proc(x) return -sin(x) end proc > exact_soln_y2pppp := proc(x) > return(-cos(x)); > end; exact_soln_y2pppp := proc(x) return -cos(x) 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, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter; > global > DEBUGMASSIVE, > glob_iolevel, > ALWAYS, > INFO, > glob_max_terms, > DEBUGL, > #Top Generate Globals Decl > glob_max_minutes, > glob_max_sec, > glob_max_trunc_err, > glob_log10_abserr, > glob_optimal_done, > glob_clock_start_sec, > glob_clock_sec, > sec_in_minute, > glob_html_log, > glob_log10relerr, > glob_iter, > glob_neg_h, > glob_large_float, > glob_hmin, > min_in_hour, > glob_max_iter, > glob_look_poles, > glob_not_yet_finished, > djd_debug2, > glob_warned2, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > glob_current_iter, > glob_curr_iter_when_opt, > glob_next_display, > glob_last_good_h, > glob_log10abserr, > glob_max_hours, > glob_almost_1, > glob_dump, > glob_good_digits, > glob_percent_done, > glob_warned, > glob_unchanged_h_cnt, > glob_display_interval, > glob_hmax, > glob_not_yet_start_msg, > years_in_century, > djd_debug, > glob_max_opt_iter, > glob_normmax, > glob_optimal_start, > glob_relerr, > hours_in_day, > MAX_UNCHANGED, > glob_hmin_init, > glob_h, > glob_log10normmin, > glob_start, > glob_orig_start_sec, > glob_abserr, > glob_log10_relerr, > glob_dump_analytic, > glob_disp_incr, > glob_initial_pass, > glob_display_flag, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_reached_optimal_h, > centuries_in_millinium, > days_in_year, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_0D0, > array_const_1, > array_const_2D0, > #END CONST > array_x, > array_y2_init, > array_1st_rel_error, > array_fact_1, > array_y1, > array_y2, > array_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_norms, > array_last_rel_error, > array_y1_init, > array_y2_higher, > array_y2_set_initial, > array_y1_set_initial, > array_y2_higher_work, > array_fact_2, > array_complex_pole, > array_y1_higher, > array_y2_higher_work2, > array_y1_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > glob_max_terms := 30; > DEBUGL := 3; > glob_max_minutes := 0.0; > glob_max_sec := 10000.0; > glob_max_trunc_err := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_optimal_done := false; > glob_clock_start_sec := 0.0; > glob_clock_sec := 0.0; > sec_in_minute := 60; > glob_html_log := true; > glob_log10relerr := 0.0; > glob_iter := 0; > glob_neg_h := false; > glob_large_float := 9.0e100; > glob_hmin := 0.00000000001; > min_in_hour := 60; > glob_max_iter := 1000; > glob_look_poles := false; > glob_not_yet_finished := true; > djd_debug2 := true; > glob_warned2 := false; > glob_smallish_float := 0.1e-100; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_current_iter := 0; > glob_curr_iter_when_opt := 0; > glob_next_display := 0.0; > glob_last_good_h := 0.1; > glob_log10abserr := 0.0; > glob_max_hours := 0.0; > glob_almost_1 := 0.9990; > glob_dump := false; > glob_good_digits := 0; > glob_percent_done := 0.0; > glob_warned := false; > glob_unchanged_h_cnt := 0; > glob_display_interval := 0.0; > glob_hmax := 1.0; > glob_not_yet_start_msg := true; > years_in_century := 100; > djd_debug := true; > glob_max_opt_iter := 10; > glob_normmax := 0.0; > glob_optimal_start := 0.0; > glob_relerr := 0.1e-10; > hours_in_day := 24; > MAX_UNCHANGED := 10; > glob_hmin_init := 0.001; > glob_h := 0.1; > glob_log10normmin := 0.1; > glob_start := 0; > glob_orig_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_disp_incr := 0.1; > glob_initial_pass := true; > glob_display_flag := true; > glob_optimal_clock_start_sec := 0.0; > glob_no_eqs := 0; > glob_reached_optimal_h := false; > centuries_in_millinium := 10; > days_in_year := 365; > glob_optimal_expect_sec := 0.1; > glob_subiter_method := 3; > #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/mtest9postode.ode#################"); > omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.5;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"glob_subiter_method := 3;"); > 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_y1 := proc(x)"); > omniout_str(ALWAYS,"return(2.0 + sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return(sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return(cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"return(-sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"return(-cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > 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_x:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_m1:= 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_type_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_y2_higher := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2[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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_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_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=6) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_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_y2_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_y1_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 <=6) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_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 <=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 <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_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 <=6) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_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 <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[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_const_5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_5[1] := 5; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_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_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 > x_start := 0.5; > x_end := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > glob_subiter_method := 3; > #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_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := true; > array_y2_set_initial[2,3] := true; > array_y2_set_initial[2,4] := true; > array_y2_set_initial[2,5] := true; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_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_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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 := 5; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_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_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y1_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_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y2_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_x[1] , x_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 <= 2) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while (subiter <= 2 + 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_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_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_y2 > order_diff := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[6,iii] := array_y2_higher[6,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 := 6; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_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 := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_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 := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_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 := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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 := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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 := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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 := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 6; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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 := 6; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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 := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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 := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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 := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_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_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_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(y1,x,1) = diff(y2,x,5);"); > omniout_str(INFO,"diff(y2,x,1) = y1 - 2.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-09-21T01:53:27-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest9") > ; > logitem_str(html_log_file,"diff(y1,x,1) = diff(y2,x,5);") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[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,"mtest9 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest9 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(y2,x,1) = y1 - 2.0;") > ; > 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, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms, DEBUGL, glob_max_minutes, glob_max_sec, glob_max_trunc_err, glob_log10_abserr, glob_optimal_done, glob_clock_start_sec, glob_clock_sec, sec_in_minute, glob_html_log, glob_log10relerr, glob_iter, glob_neg_h, glob_large_float, glob_hmin, min_in_hour, glob_max_iter, glob_look_poles, glob_not_yet_finished, djd_debug2, glob_warned2, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, glob_current_iter, glob_curr_iter_when_opt, glob_next_display, glob_last_good_h, glob_log10abserr, glob_max_hours, glob_almost_1, glob_dump, glob_good_digits, glob_percent_done, glob_warned, glob_unchanged_h_cnt, glob_display_interval, glob_hmax, glob_not_yet_start_msg, years_in_century, djd_debug, glob_max_opt_iter, glob_normmax, glob_optimal_start, glob_relerr, hours_in_day, MAX_UNCHANGED, glob_hmin_init, glob_h, glob_log10normmin, glob_start, glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic, glob_disp_incr, glob_initial_pass, glob_display_flag, glob_optimal_clock_start_sec, glob_no_eqs, glob_reached_optimal_h, centuries_in_millinium, days_in_year, glob_optimal_expect_sec, glob_subiter_method, array_const_5, array_const_0D0, array_const_1, array_const_2D0, array_x, array_y2_init, array_1st_rel_error, array_fact_1, array_y1, array_y2, array_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_norms, array_last_rel_error, array_y1_init, array_y2_higher, array_y2_set_initial, array_y1_set_initial, array_y2_higher_work, array_fact_2, array_complex_pole, array_y1_higher, array_y2_higher_work2, array_y1_higher_work2, array_real_pole, array_poles, array_y1_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; glob_iolevel := 5; ALWAYS := 1; INFO := 2; glob_max_terms := 30; DEBUGL := 3; glob_max_minutes := 0.; glob_max_sec := 10000.0; glob_max_trunc_err := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_optimal_done := false; glob_clock_start_sec := 0.; glob_clock_sec := 0.; sec_in_minute := 60; glob_html_log := true; glob_log10relerr := 0.; glob_iter := 0; glob_neg_h := false; glob_large_float := 0.90*10^101; glob_hmin := 0.1*10^(-10); min_in_hour := 60; glob_max_iter := 1000; glob_look_poles := false; glob_not_yet_finished := true; djd_debug2 := true; glob_warned2 := false; glob_smallish_float := 0.1*10^(-100); glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_current_iter := 0; glob_curr_iter_when_opt := 0; glob_next_display := 0.; glob_last_good_h := 0.1; glob_log10abserr := 0.; glob_max_hours := 0.; glob_almost_1 := 0.9990; glob_dump := false; glob_good_digits := 0; glob_percent_done := 0.; glob_warned := false; glob_unchanged_h_cnt := 0; glob_display_interval := 0.; glob_hmax := 1.0; glob_not_yet_start_msg := true; years_in_century := 100; djd_debug := true; glob_max_opt_iter := 10; glob_normmax := 0.; glob_optimal_start := 0.; glob_relerr := 0.1*10^(-10); hours_in_day := 24; MAX_UNCHANGED := 10; glob_hmin_init := 0.001; glob_h := 0.1; glob_log10normmin := 0.1; glob_start := 0; glob_orig_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_disp_incr := 0.1; glob_initial_pass := true; glob_display_flag := true; glob_optimal_clock_start_sec := 0.; glob_no_eqs := 0; glob_reached_optimal_h := false; centuries_in_millinium := 10; days_in_year := 365; glob_optimal_expect_sec := 0.1; glob_subiter_method := 3; 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/mtest9postode.ode#################"); omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"); omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.5;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "glob_subiter_method := 3;"); 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_y1 := proc(x)"); omniout_str(ALWAYS, "return(2.0 + sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(2.0 - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return(sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return(cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "return(-sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "return(-cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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_x := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_m1 := 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_type_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 7, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 7, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[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_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_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_y2_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_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_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 <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[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_const_5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5[term] := 0.; term := term + 1 end do; array_const_5[1] := 5; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_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_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; x_start := 0.5; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[4] := exact_soln_y2ppp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; 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_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := true; array_y2_set_initial[2, 3] := true; array_y2_set_initial[2, 4] := true; array_y2_set_initial[2, 5] := true; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_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_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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 := 5; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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_y1_higher[1, 1]) then tmp := omniabs(array_y1_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_y2_higher[1, 1]) then tmp := omniabs(array_y2_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_x[1], x_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 <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + 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_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 5; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_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 := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_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 := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_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 := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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 := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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 := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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 := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 6; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_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 := 6; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_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 := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_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 := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_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(y1,x,1) = diff(y2,x,5);"); omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-09-21T01:53:27-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest9") ; logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[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, "mtest9 diffeq.mxt"); logitem_str(html_log_file, "mtest9 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(y2,x,1) = y1 - 2.0;"); 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/mtest9postode.ode################# diff(y1,x,1) = diff(y2,x,5); diff(y2,x,1) = y1 - 2.0; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; #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_y1 := proc(x) return(2.0 + sin(x)); end; exact_soln_y2 := proc(x) return(2.0 - cos(x)); end; exact_soln_y2p := proc(x) return(sin(x)); end; exact_soln_y2pp := proc(x) return(cos(x)); end; exact_soln_y2ppp := proc(x) return(-sin(x)); end; exact_soln_y2pppp := proc(x) return(-cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.5 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 x[1] = 0.5 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 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=0.42 memory used=11.4MB, alloc=3.9MB, time=0.66 memory used=15.2MB, alloc=3.9MB, time=0.90 x[1] = 0.6 y1[1] (analytic) = 2.5646424733950353572009454456587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0852169347908323569276575104431 relative error = 3.3227608009635531341618759185234 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.1746643850903217027590475010446 y2[1] (numeric) = 1.1746643439290575371052659196682 absolute error = 4.11612641656537815813764e-08 relative error = 3.5040871833778147935580774748863e-06 % Correct digits = 7 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=19.0MB, alloc=3.9MB, time=1.13 memory used=22.8MB, alloc=3.9MB, time=1.38 memory used=26.7MB, alloc=4.0MB, time=1.62 memory used=30.5MB, alloc=4.0MB, time=1.85 x[1] = 0.7 y1[1] (analytic) = 2.6442176872376910536726143513987 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1647921486334880533993264161831 relative error = 6.2321702720943467546253474014694 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.2351578127155115737441400098081 y2[1] (numeric) = 1.2351564575126770427459295000719 absolute error = 1.3552028345309982105097362e-06 relative error = 0.0001097190027524957310652525509067 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.0MB, time=2.09 NO POLE NO POLE memory used=38.1MB, alloc=4.0MB, time=2.33 memory used=41.9MB, alloc=4.0MB, time=2.56 memory used=45.7MB, alloc=4.0MB, time=2.80 memory used=49.5MB, alloc=4.0MB, time=3.03 x[1] = 0.8 y1[1] (analytic) = 2.7173560908995227616271746105814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2379305522953197613538866753658 relative error = 8.7559577889756041521810129460799 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.3032932906528345790792500183577 y2[1] (numeric) = 1.3032827159375980418980184284352 absolute error = 1.05747152365371812315899225e-05 relative error = 0.00081138415369576443588491457002772 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=53.4MB, alloc=4.0MB, time=3.27 memory used=57.2MB, alloc=4.0MB, time=3.51 memory used=61.0MB, alloc=4.0MB, time=3.74 memory used=64.8MB, alloc=4.0MB, time=3.98 x[1] = 0.9 y1[1] (analytic) = 2.7833269096274833884613823157136 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.303901371023280388188094380498 relative error = 10.91863733189552376379180407652 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.3783900317293355435152838485929 y2[1] (numeric) = 1.3783442980247437383822303464269 absolute error = 4.57337045918051330535021660e-05 relative error = 0.0033179073802809921242238058759687 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=68.6MB, alloc=4.0MB, time=4.22 memory used=72.4MB, alloc=4.0MB, time=4.45 memory used=76.2MB, alloc=4.0MB, time=4.70 memory used=80.1MB, alloc=4.0MB, time=4.94 x[1] = 1 y1[1] (analytic) = 2.8414709848078965066525023216303 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3620454462036935063792143864147 relative error = 12.74147961177123664409285238639 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.459697694131860282599063392557 y2[1] (numeric) = 1.4595546243388482987476512675577 absolute error = 0.0001430697930119838514121249993 relative error = 0.0098013303430662122785603401983507 % Correct digits = 4 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=83.9MB, alloc=4.0MB, time=5.17 memory used=87.7MB, alloc=4.0MB, time=5.41 memory used=91.5MB, alloc=4.0MB, time=5.65 memory used=95.3MB, alloc=4.0MB, time=5.89 x[1] = 1.1 y1[1] (analytic) = 2.8912073600614353399518025778717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4117818214572323396785146426561 relative error = 14.242555796775585723015743750369 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.5464038785744226122286299482153 y2[1] (numeric) = 1.5460393571884568522717555771806 absolute error = 0.0003645213859657599568743710347 relative error = 0.023572198118243203259986294063767 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.0MB, time=6.13 NO POLE NO POLE memory used=102.9MB, alloc=4.0MB, time=6.37 memory used=106.8MB, alloc=4.0MB, time=6.62 memory used=110.6MB, alloc=4.0MB, time=6.85 memory used=114.4MB, alloc=4.0MB, time=7.09 x[1] = 1.2 y1[1] (analytic) = 2.9320390859672263496701344354948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4526135473630233493968465002792 relative error = 15.436818340152323544492632327205 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.6376422455233264223616266443769 y2[1] (numeric) = 1.6368364006259254909604060324896 absolute error = 0.0008058448974009314012206118873 relative error = 0.049207627588003195669594000350954 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=118.2MB, alloc=4.0MB, time=7.34 memory used=122.0MB, alloc=4.0MB, time=7.58 memory used=125.8MB, alloc=4.0MB, time=7.82 memory used=129.7MB, alloc=4.0MB, time=8.05 x[1] = 1.3 y1[1] (analytic) = 2.9635581854171929647013486300396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.484132646812989964428060694824 relative error = 16.33619509126784726203727891981 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.7325011713754125930020158907071 y2[1] (numeric) = 1.7308959004474212695478537625208 absolute error = 0.0016052709279913234541621281863 relative error = 0.092656267973366937250076754416761 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=133.5MB, alloc=4.0MB, time=8.29 memory used=137.3MB, alloc=4.0MB, time=8.54 memory used=141.1MB, alloc=4.0MB, time=8.78 memory used=144.9MB, alloc=4.0MB, time=9.02 x[1] = 1.4 y1[1] (analytic) = 2.9854497299884601806594745788061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5060241913842571803861866435905 relative error = 16.949680522211075478308121687513 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.8300328570997590613832519647964 y2[1] (numeric) = 1.8270802441929222054967382681522 absolute error = 0.0029526129068368558865136966442 relative error = 0.16134207073834535808713192365853 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=148.7MB, alloc=4.0MB, time=9.26 memory used=152.5MB, alloc=4.0MB, time=9.51 memory used=156.4MB, alloc=4.0MB, time=9.75 memory used=160.2MB, alloc=4.0MB, time=9.99 x[1] = 1.5 y1[1] (analytic) = 2.9974949866040544309417233711415 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5180694479998514306684354359259 relative error = 17.283413327299230606516587229319 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.9292627983322970899118101485657 y2[1] (numeric) = 1.9241640611462172789980874221032 absolute error = 0.0050987371860798109137227264625 relative error = 0.2642842224754080461640089855004 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.0MB, time=10.23 NO POLE NO POLE memory used=167.8MB, alloc=4.0MB, time=10.47 memory used=171.6MB, alloc=4.0MB, time=10.71 memory used=175.4MB, alloc=4.0MB, time=10.95 memory used=179.2MB, alloc=4.0MB, time=11.19 x[1] = 1.6 y1[1] (analytic) = 2.9995736030415051643421138255462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5201480644373021640688258903306 relative error = 17.340733493249935902117102634504 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.0291995223012887262057704629465 y2[1] (numeric) = 2.0208342223349064329713174689354 absolute error = 0.0083652999663822932344529940111 relative error = 0.41224630079231024015416821396983 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=183.1MB, alloc=4.0MB, time=11.43 memory used=186.9MB, alloc=4.0MB, time=11.66 memory used=190.7MB, alloc=4.0MB, time=11.90 memory used=194.5MB, alloc=4.0MB, time=12.15 x[1] = 1.7 y1[1] (analytic) = 2.9916648104524686153461333986479 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5122392718482656150728454634323 relative error = 17.122214696598746546026089038197 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.1288444942955246840876428573349 y2[1] (numeric) = 2.1156898405304005730642330250514 absolute error = 0.0131546537651241110234098322835 relative error = 0.61792459714053643364945669812477 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=198.3MB, alloc=4.0MB, time=12.40 memory used=202.1MB, alloc=4.0MB, time=12.66 memory used=205.9MB, alloc=4.0MB, time=12.92 memory used=209.8MB, alloc=4.0MB, time=13.19 x[1] = 1.8 y1[1] (analytic) = 2.9738476308781951865323731788434 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4944220922739921862590852436278 relative error = 16.62566996171173547740151474368 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.2272020946930870553166743065306 y2[1] (numeric) = 2.2072422702479215676530270786965 absolute error = 0.0199598244451654876636472278341 relative error = 0.89618380355896673871102315114734 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=213.6MB, alloc=4.0MB, time=13.45 memory used=217.4MB, alloc=4.1MB, time=13.71 memory used=221.2MB, alloc=4.1MB, time=13.97 memory used=225.0MB, alloc=4.1MB, time=14.23 x[1] = 1.9 y1[1] (analytic) = 2.946300087687414488489709611635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4668745490832114882164216764194 relative error = 15.846130237523320315427786136 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.3232895668635034222788336950803 y2[1] (numeric) = 2.2939151077465022478422809899567 absolute error = 0.0293744591170011744365527051236 relative error = 1.2643477393417385337593224094058 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=228.8MB, alloc=4.1MB, time=14.49 memory used=232.6MB, alloc=4.1MB, time=14.75 memory used=236.5MB, alloc=4.1MB, time=15.00 memory used=240.3MB, alloc=4.1MB, time=15.26 memory used=244.1MB, alloc=4.1MB, time=15.52 x[1] = 2 y1[1] (analytic) = 2.9092974268256816953960198659117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4298718882214786951227319306961 relative error = 14.775797216804661008033397562996 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.4161468365471423869975682295008 y2[1] (numeric) = 2.3740441910289864074649644907608 absolute error = 0.04210264551815597953260373874 relative error = 1.7425532621321915395157578805133 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=247.9MB, alloc=4.1MB, time=15.78 memory used=251.7MB, alloc=4.1MB, time=16.03 memory used=255.5MB, alloc=4.1MB, time=16.29 memory used=259.4MB, alloc=4.1MB, time=16.54 x[1] = 2.1 y1[1] (analytic) = 2.863209366648873770680759313269 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3837838280446707704074713780534 relative error = 13.403973614889883026160836957163 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.5048461045998574516209385237192 y2[1] (numeric) = 2.4458775998420288030824356848787 absolute error = 0.0589685047578286485385028388405 relative error = 2.3541767555914861844046950458799 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=263.2MB, alloc=4.1MB, time=16.80 memory used=267.0MB, alloc=4.1MB, time=17.05 memory used=270.8MB, alloc=4.1MB, time=17.32 memory used=274.6MB, alloc=4.1MB, time=17.58 x[1] = 2.2 y1[1] (analytic) = 2.8084964038195901843040369104161 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3290708652153871840307489752005 relative error = 11.716976556133263962719611867981 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.5885011172553457085241426126549 y2[1] (numeric) = 2.5075756556760951539844410479219 absolute error = 0.080925461579250554539701564733 relative error = 3.1263444717017507896068397151985 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=278.4MB, alloc=4.1MB, time=17.84 memory used=282.2MB, alloc=4.1MB, time=18.09 memory used=286.1MB, alloc=4.1MB, time=18.36 memory used=289.9MB, alloc=4.1MB, time=18.62 x[1] = 2.3 y1[1] (analytic) = 2.7457052121767201773854062116435 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2662796735725171771121182764279 relative error = 9.6980430525321368048876479661976 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.666276021279824193317880571166 y2[1] (numeric) = 2.557210921765462142189115427344 absolute error = 0.109065099514362051128765143822 relative error = 4.0905404633242106959985549402993 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=293.7MB, alloc=4.1MB, time=18.87 memory used=297.5MB, alloc=4.1MB, time=19.13 memory used=301.3MB, alloc=4.1MB, time=19.38 memory used=305.1MB, alloc=4.1MB, time=19.64 x[1] = 2.4 y1[1] (analytic) = 2.6754631805511509265657715253413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1960376419469479262924835901257 relative error = 7.327241255720206481027789719703 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.7373937155412454996088222273348 y2[1] (numeric) = 2.5927682030882174124429820424403 absolute error = 0.1446255124530280871658401848945 relative error = 5.2833288697907420828780613368852 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.1MB, time=19.90 NO POLE NO POLE memory used=312.8MB, alloc=4.1MB, time=20.16 memory used=316.6MB, alloc=4.1MB, time=20.41 memory used=320.4MB, alloc=4.1MB, time=20.67 memory used=324.2MB, alloc=4.1MB, time=20.93 x[1] = 2.5 y1[1] (analytic) = 2.5984721441039564940518547021862 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1190466054997534937785667669706 relative error = 4.5814078003443404568246391535478 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.8011436155469337148335027904674 y2[1] (numeric) = 2.6121445463662595722209524843478 absolute error = 0.1889990691806741426125503061196 relative error = 6.7472109652532532157454999724029 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=328.0MB, alloc=4.1MB, time=21.19 memory used=331.8MB, alloc=4.1MB, time=21.43 memory used=335.6MB, alloc=4.1MB, time=21.68 memory used=339.5MB, alloc=4.1MB, time=21.92 x[1] = 2.6 y1[1] (analytic) = 2.5155013718214642352577269352094 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0360758332172612349844389999938 relative error = 1.4341408683525730691286516982016 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.8568887533689472337977021516452 y2[1] (numeric) = 2.6131492400652981917263267160453 absolute error = 0.2437395133036490420713754355999 relative error = 8.5316417384549025133081857215001 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=343.3MB, alloc=4.1MB, time=22.16 memory used=347.1MB, alloc=4.1MB, time=22.42 memory used=350.9MB, alloc=4.1MB, time=22.66 memory used=354.7MB, alloc=4.1MB, time=22.91 x[1] = 2.7 y1[1] (analytic) = 2.4273798802338299345560530858579 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0520456583703730657172348493577 relative error = 2.144108501276672780689309938242 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.9040721420170611479825272819433 y2[1] (numeric) = 2.5935038143948538038907930723533 absolute error = 0.31056832762220734409173420959 relative error = 10.694235970546450173798699557807 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=358.5MB, alloc=4.1MB, time=23.17 memory used=362.4MB, alloc=4.1MB, time=23.43 memory used=366.2MB, alloc=4.1MB, time=23.68 memory used=370.0MB, alloc=4.1MB, time=23.93 x[1] = 2.8 y1[1] (analytic) = 2.3349881501559049195438537527124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1444373884482980807294341825032 relative error = 6.1857867860551726918819921485196 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.9422223406686581525867881173662 y2[1] (numeric) = 2.5508420413082579043744282599335 absolute error = 0.3913802993604002482123598574327 relative error = 13.302199971449268637864632669484 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.1MB, time=24.19 NO POLE NO POLE memory used=377.6MB, alloc=4.1MB, time=24.45 memory used=381.4MB, alloc=4.1MB, time=24.72 memory used=385.2MB, alloc=4.1MB, time=24.98 memory used=389.1MB, alloc=4.1MB, time=25.24 x[1] = 2.9 y1[1] (analytic) = 2.2392493292139823281842569187396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.240176209390220672089031016476 relative error = 10.725746626639693401565065384338 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9709581651495905217811066693455 y2[1] (numeric) = 2.4827099345026529515656973572901 absolute error = 0.4882482306469375702154093120554 relative error = 16.434032507568271841945012571973 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=392.9MB, alloc=4.1MB, time=25.50 memory used=396.7MB, alloc=4.1MB, time=25.76 memory used=400.5MB, alloc=4.1MB, time=26.02 memory used=404.3MB, alloc=4.1MB, time=26.29 x[1] = 3 y1[1] (analytic) = 2.1411200080598672221007448028081 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3383055305443357781725431324075 relative error = 15.800400223754133331034738834859 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9899924966004454572715727947313 y2[1] (numeric) = 2.3865657494189923665814538147688 absolute error = 0.6034267471814530906901189799625 relative error = 20.181547206808572113544157946629 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=408.1MB, alloc=4.1MB, time=26.54 memory used=411.9MB, alloc=4.1MB, time=26.80 memory used=415.8MB, alloc=4.1MB, time=27.06 memory used=419.6MB, alloc=4.1MB, time=27.32 x[1] = 3.1 y1[1] (analytic) = 2.0415806624332905791946982715967 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4378448761709124210785896636189 relative error = 21.446366740614598083020123064929 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9991351502732794644923760545415 y2[1] (numeric) = 2.2597799832420405332669394545571 absolute error = 0.7393551670312389312254365999844 relative error = 24.652279073314495846868276664492 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=423.4MB, alloc=4.1MB, time=27.57 memory used=427.2MB, alloc=4.1MB, time=27.83 memory used=431.0MB, alloc=4.1MB, time=28.09 memory used=434.8MB, alloc=4.1MB, time=28.35 x[1] = 3.2 y1[1] (analytic) = 1.9416258565724200908627825853809 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5377996820317829094105053498347 relative error = 27.698419868654220745544080486422 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9982947757947530846616607222836 y2[1] (numeric) = 2.0996353749003727981957844706839 absolute error = 0.8986594008943802864658762515997 relative error = 29.972349888652095962786977346021 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.1MB, time=28.61 NO POLE NO POLE memory used=442.5MB, alloc=4.1MB, time=28.86 memory used=446.3MB, alloc=4.1MB, time=29.13 memory used=450.1MB, alloc=4.1MB, time=29.39 memory used=453.9MB, alloc=4.1MB, time=29.66 x[1] = 3.3 y1[1] (analytic) = 1.8422543058567516179883457223975 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.6371712327474513822849422128181 relative error = 34.586497136785412937875605652292 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9874797699088648839365910511028 y2[1] (numeric) = 1.9033269050663754706700074290202 absolute error = 1.0841528648424894132665836220826 relative error = 36.2898813830482352951396912052 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=457.7MB, alloc=4.1MB, time=29.91 memory used=461.5MB, alloc=4.1MB, time=30.17 memory used=465.3MB, alloc=4.1MB, time=30.43 memory used=469.2MB, alloc=4.1MB, time=30.69 x[1] = 3.4 y1[1] (analytic) = 1.7444588979731686807500975706363 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.7349666406310343195231903645793 relative error = 42.131496562341978198364752074382 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9667981925794610142822015397657 y2[1] (numeric) = 1.667961796156245822720015267279 absolute error = 1.2988363964232151915621862724867 relative error = 43.779061200450286626264442736104 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=473.0MB, alloc=4.1MB, time=30.96 memory used=476.8MB, alloc=4.1MB, time=31.21 memory used=480.6MB, alloc=4.1MB, time=31.48 memory used=484.4MB, alloc=4.1MB, time=31.74 x[1] = 3.5 y1[1] (analytic) = 1.6492167723103801518796311999564 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.8302087662938228483936567352592 relative error = 50.33957817023575535243909860192 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9364566872907963376986576266718 y2[1] (numeric) = 1.3905595123299920891046032950143 absolute error = 1.5458971749608042485940543316575 relative error = 52.644984741357247915850847000029 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=488.2MB, alloc=4.1MB, time=32.00 memory used=492.1MB, alloc=4.1MB, time=32.27 memory used=495.9MB, alloc=4.1MB, time=32.53 memory used=499.7MB, alloc=4.1MB, time=32.79 x[1] = 3.6 y1[1] (analytic) = 1.5574795567051476157332726525073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.9219459818990553845400152827083 relative error = 59.194740497874315807696969558115 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.8967584163341470058702917252659 y2[1] (numeric) = 1.0680517594914334673109551936223 absolute error = 1.8287066568427135385593365316436 relative error = 63.129415505658394083483809680872 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=503.5MB, alloc=4.1MB, time=33.05 memory used=507.3MB, alloc=4.1MB, time=33.30 memory used=511.1MB, alloc=4.1MB, time=33.57 memory used=514.9MB, alloc=4.1MB, time=33.83 memory used=518.8MB, alloc=4.1MB, time=34.10 x[1] = 3.7 y1[1] (analytic) = 1.4701638590915067867892223742988 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.0092616795126962134840655609168 relative error = 68.649604822715014515079302603509 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.8481000317104081588356701063544 y2[1] (numeric) = 0.69728248528820011755464301634067 absolute error = 2.1508175464222080412810270900137 relative error = 75.517626574743176944791703600668 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=522.6MB, alloc=4.1MB, time=34.35 memory used=526.4MB, alloc=4.1MB, time=34.59 memory used=530.2MB, alloc=4.1MB, time=34.84 memory used=534.0MB, alloc=4.1MB, time=35.10 x[1] = 3.8 y1[1] (analytic) = 1.3881421090572809242664139138811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.0912834295469220760068740213345 relative error = 78.614676582935563310623297832398 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.7909677119144166999965681743507 y2[1] (numeric) = 0.27500787911173316277962718824927 absolute error = 2.5159598328026835372169409861014 relative error = 90.14650445658161345897448594184 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=537.8MB, alloc=4.1MB, time=35.36 memory used=541.6MB, alloc=4.1MB, time=35.62 memory used=545.5MB, alloc=4.1MB, time=35.86 memory used=549.3MB, alloc=4.1MB, time=36.12 x[1] = 3.9 y1[1] (analytic) = 1.3122338408160261819091118746213 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.1671916977881768183641760605943 relative error = 88.946928625339108216977428906113 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.7259323042001401293723304846144 y2[1] (numeric) = -0.20210362790271531134174349373067 absolute error = 2.9280359321028554407140739783451 relative error = 107.41411030608912367852145435792 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=553.1MB, alloc=4.1MB, time=36.37 memory used=556.9MB, alloc=4.1MB, time=36.62 memory used=560.7MB, alloc=4.1MB, time=36.88 memory used=564.5MB, alloc=4.1MB, time=37.12 x[1] = 4 y1[1] (analytic) = 1.2431975046920717486273609054882 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.2362280339121312516459270297274 relative error = 99.439391508297246067351084937089 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.6536436208636119146391681830978 y2[1] (numeric) = -0.73747136287608225640873186083593 absolute error = 3.3911149837396941710479000439337 relative error = 127.7908969040867951801286177965 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=568.3MB, alloc=4.1MB, time=37.36 memory used=572.2MB, alloc=4.1MB, time=37.61 memory used=576.0MB, alloc=4.1MB, time=37.85 memory used=579.8MB, alloc=4.1MB, time=38.09 x[1] = 4.1 y1[1] (analytic) = 1.1817228889355894957349629756416 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.297702649668613504538324959574 relative error = 109.81446342614977936566418545847 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.5748239465332689115350286796598 y2[1] (numeric) = -1.3346024111854936612922123724617 absolute error = 3.9094263577187625728272410521215 relative error = 151.83276367234335355362518489169 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.1MB, time=38.33 NO POLE NO POLE memory used=587.4MB, alloc=4.1MB, time=38.58 memory used=591.2MB, alloc=4.1MB, time=38.83 memory used=595.1MB, alloc=4.1MB, time=39.08 memory used=598.9MB, alloc=4.1MB, time=39.32 x[1] = 4.2 y1[1] (analytic) = 1.1284242275864119399814229020912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.3510013110177910602918650331244 relative error = 119.72459275422059449340252138108 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.4902608213406995776555448813771 y2[1] (numeric) = -1.9970916164642645521346711161619 absolute error = 4.487352437804964129790215997539 relative error = 180.19608224768504433779206798881 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=602.7MB, alloc=4.1MB, time=39.57 memory used=606.5MB, alloc=4.1MB, time=39.83 memory used=610.3MB, alloc=4.1MB, time=40.09 memory used=614.1MB, alloc=4.1MB, time=40.35 x[1] = 4.3 y1[1] (analytic) = 1.0838340632505450159682906397154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.3955914753536579843049972955002 relative error = 128.76431205420099608987282961985 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.400799172079975296906762396336 y2[1] (numeric) = -2.7286215806018989923502058076476 absolute error = 5.1294207526818742892569682039836 relative error = 213.65472015878399730032347627556 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=617.9MB, alloc=4.1MB, time=40.61 memory used=621.8MB, alloc=4.1MB, time=40.85 memory used=625.6MB, alloc=4.1MB, time=41.10 memory used=629.4MB, alloc=4.1MB, time=41.35 x[1] = 4.4 y1[1] (analytic) = 1.0483979261104840459646076666196 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.431027612493718954308680268596 relative error = 136.4966084779255828724138855741 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.3073328699784196831191397422177 y2[1] (numeric) = -3.5329626637440900826245257907891 absolute error = 5.8402955337225097657436655330068 relative error = 253.11889800179259033473544010578 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=633.2MB, alloc=4.1MB, time=41.58 memory used=637.0MB, alloc=4.1MB, time=41.82 memory used=640.8MB, alloc=4.1MB, time=42.06 memory used=644.6MB, alloc=4.1MB, time=42.30 x[1] = 4.5 y1[1] (analytic) = 1.0224698823349029446108649855014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.4569556562693000556624229497142 relative error = 142.49374787863769058485415265588 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.2107957994307797059804818247938 y2[1] (numeric) = -4.4139729842927199609149520376147 absolute error = 6.6247687837234996668954338624085 relative error = 299.65539039965604065168257584476 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.1MB, time=42.54 NO POLE NO POLE memory used=652.3MB, alloc=4.1MB, time=42.79 memory used=656.1MB, alloc=4.1MB, time=43.03 memory used=659.9MB, alloc=4.1MB, time=43.27 memory used=663.7MB, alloc=4.1MB, time=43.51 x[1] = 4.6 y1[1] (analytic) = 1.0063089963665355438618953400912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.4731165422376674564113925951244 relative error = 146.38809228145895122441037922606 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.1121525269350545174299078212292 y2[1] (numeric) = -5.3755984189058598024504171483107 absolute error = 7.4877509458409143198803249695399 relative error = 354.50805992247127568106948029008 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=667.5MB, alloc=4.1MB, time=43.75 memory used=671.3MB, alloc=4.1MB, time=44.00 memory used=675.2MB, alloc=4.1MB, time=44.24 memory used=679.0MB, alloc=4.1MB, time=44.48 x[1] = 4.7 y1[1] (analytic) = 1.000076742435899115820463458425 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.4793487961683038844528244767906 relative error = 147.9235276049951910122724614831 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.0123886634628907371505082963271 y2[1] (numeric) = -6.4218726024977698197314653512222 absolute error = 8.4342612659606605568819736475493 relative error = 419.11691409785124513454722194263 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=682.8MB, alloc=4.1MB, time=44.72 memory used=686.6MB, alloc=4.1MB, time=44.97 memory used=690.4MB, alloc=4.1MB, time=45.21 memory used=694.2MB, alloc=4.1MB, time=45.45 x[1] = 4.8 y1[1] (analytic) = 1.0038353911641593282184035334964 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.4755901474400436720548844017192 relative error = 146.9952305356344314318455166902 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.9125010165605534306797847423505 y2[1] (numeric) = -7.5569169282388992625302525028518 absolute error = 9.4694179447994526932100372452023 relative error = 495.13270125363265950365956904905 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=698.0MB, alloc=4.1MB, time=45.69 memory used=701.9MB, alloc=4.1MB, time=45.94 memory used=705.7MB, alloc=4.1MB, time=46.18 memory used=709.5MB, alloc=4.1MB, time=46.42 x[1] = 4.9 y1[1] (analytic) = 1.0175473873756674877236227500817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.4618781512285355125496651851339 relative error = 143.6668374726833152905590963734 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.8134876305774245955056708558781 y2[1] (numeric) = -8.7849405475558864178905460878609 absolute error = 10.598428178133311013396216943739 relative error = 584.42241344423795471499006380776 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.1MB, time=46.66 NO POLE NO POLE memory used=717.1MB, alloc=4.1MB, time=46.90 memory used=720.9MB, alloc=4.1MB, time=47.14 memory used=724.8MB, alloc=4.1MB, time=47.38 memory used=728.6MB, alloc=4.1MB, time=47.62 x[1] = 5 y1[1] (analytic) = 1.041075725336861531106845593844 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.4383498132673414691664423413716 relative error = 138.15996072734610252137880693121 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.7163378145367737355333608284864 y2[1] (numeric) = -10.110240370131558610127725219069 absolute error = 11.826578184668332345661086047555 relative error = 689.05888365923080663530483771443 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=732.4MB, alloc=4.1MB, time=47.87 memory used=736.2MB, alloc=4.1MB, time=48.12 memory used=740.0MB, alloc=4.1MB, time=48.36 memory used=743.8MB, alloc=4.1MB, time=48.62 x[1] = 5.1 y1[1] (analytic) = 1.0741853176722677030538537524551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.4052402209319352972194341827605 relative error = 130.81916107148579912397325999302 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.622022257287019436679424447071 y2[1] (numeric) = -11.537201063904932200828780637455 absolute error = 13.159223321191951637508205084526 relative error = 811.28500315414636086528887513939 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=747.6MB, alloc=4.1MB, time=48.87 memory used=751.5MB, alloc=4.1MB, time=49.12 memory used=755.3MB, alloc=4.1MB, time=49.36 memory used=759.1MB, alloc=4.1MB, time=49.61 x[1] = 5.2 y1[1] (analytic) = 1.1165453442798467353269155595782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.3628801943243562649463723756374 relative error = 122.06223431108312311942398607324 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.5314833286996230413609060733914 y2[1] (numeric) = -13.070295055071212588852314712153 absolute error = 14.601778383770835630213220785544 relative error = 953.44024385620657560221177463833 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=762.9MB, alloc=4.1MB, time=49.85 memory used=766.7MB, alloc=4.1MB, time=50.10 memory used=770.5MB, alloc=4.1MB, time=50.34 memory used=774.3MB, alloc=4.1MB, time=50.59 x[1] = 5.3 y1[1] (analytic) = 1.1677325577760988364354403321454 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.3116929808281041638378476030702 relative error = 112.32820152982394741744170283331 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.4456256638208390705550533664392 y2[1] (numeric) = -14.714082528081794210328541440457 absolute error = 16.159708191902633280883594806896 relative error = 1117.8348998863205486908065435161 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=778.2MB, alloc=4.1MB, time=50.83 memory used=782.0MB, alloc=4.1MB, time=51.07 memory used=785.8MB, alloc=4.1MB, time=51.31 memory used=789.6MB, alloc=4.1MB, time=51.55 memory used=793.4MB, alloc=4.1MB, time=51.79 x[1] = 5.4 y1[1] (analytic) = 1.2272355124440126376415302172658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.2521900261601903626317577179498 relative error = 102.03339240619604933122843367796 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.3653071240573656375932481610193 y2[1] (numeric) = -16.473211425644260538659286447822 absolute error = 17.838518549701626176252534608841 relative error = 1306.5572013342919689611623935118 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=797.2MB, alloc=4.1MB, time=52.03 memory used=801.0MB, alloc=4.1MB, time=52.27 memory used=804.9MB, alloc=4.1MB, time=52.50 memory used=808.7MB, alloc=4.1MB, time=52.75 x[1] = 5.5 y1[1] (analytic) = 1.2944596744296080937680808244779 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.1849658641745949065052071107377 relative error = 91.541350231457720695768770094522 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.2913302257087399999725788186742 y2[1] (numeric) = -18.352417448722384084517986987855 absolute error = 19.643747674431124084490565806529 relative error = 1521.2024998214344040211142202049 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=812.5MB, alloc=4.1MB, time=52.99 memory used=816.3MB, alloc=4.1MB, time=53.23 memory used=820.1MB, alloc=4.1MB, time=53.48 memory used=823.9MB, alloc=4.1MB, time=53.72 x[1] = 5.6 y1[1] (analytic) = 1.3687333621276786885363308462833 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.1106921764765243117369570889323 relative error = 81.14744677151489757567330502288 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.2244341214897502023441903378427 y2[1] (numeric) = -20.356524056536126395849691942331 absolute error = 21.580958178025876598193882280174 relative error = 1762.5250553920088423478739482303 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=827.7MB, alloc=4.1MB, time=53.98 memory used=831.6MB, alloc=4.1MB, time=54.22 memory used=835.4MB, alloc=4.1MB, time=54.47 memory used=839.2MB, alloc=4.1MB, time=54.71 x[1] = 5.7 y1[1] (analytic) = 1.4493144574023622387726493921275 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.0301110812018407615006385430881 relative error = 71.075747291456073115977009474779 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.1652872151608403172507659690026 y2[1] (numeric) = -22.490442466561638057871061821171 absolute error = 23.655729681722478375121827790174 relative error = 2030.0342588464222387348518740895 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=843.0MB, alloc=4.1MB, time=54.97 memory used=846.8MB, alloc=4.1MB, time=55.21 memory used=850.6MB, alloc=4.1MB, time=55.46 memory used=854.5MB, alloc=4.1MB, time=55.70 x[1] = 5.8 y1[1] (analytic) = 1.5353978205862427885817734732974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.9440277180179602116915144619182 relative error = 61.484242413312354086143916861666 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.1144804830586809958353418982385 y2[1] (numeric) = -24.759171654531258693070368762466 absolute error = 25.873652137589939688905710660704 relative error = 2321.5886263508132123802314065683 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.1MB, time=55.94 NO POLE NO POLE memory used=862.1MB, alloc=4.1MB, time=56.18 memory used=865.9MB, alloc=4.1MB, time=56.42 memory used=869.7MB, alloc=4.1MB, time=56.66 memory used=873.5MB, alloc=4.1MB, time=56.90 x[1] = 5.9 y1[1] (analytic) = 1.6261233351697636401851535310166 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.853302203434439360088134404199 relative error = 52.474629997567590285553163231716 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.0725215692559642590938953199675 y2[1] (numeric) = -27.167798354433516961207496532456 absolute error = 28.240319923689481220301391852424 relative error = 2633.0771084893440411719757318438 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=877.3MB, alloc=4.1MB, time=57.14 memory used=881.2MB, alloc=4.1MB, time=57.38 memory used=885.0MB, alloc=4.1MB, time=57.62 memory used=888.8MB, alloc=4.1MB, time=57.87 x[1] = 6 y1[1] (analytic) = 1.7205845018010741271884445533881 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.7588410368031288730848433818275 relative error = 44.103677326442784508381081128136 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.0398297133496339794543477020771 y2[1] (numeric) = -29.721497058513130559313940525548 absolute error = 30.761326771862764538768288227625 relative error = 2958.3042662601359621154846647731 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=892.6MB, alloc=4.1MB, time=58.11 memory used=896.4MB, alloc=4.1MB, time=58.35 memory used=900.2MB, alloc=4.1MB, time=58.59 memory used=904.0MB, alloc=4.1MB, time=58.84 x[1] = 6.1 y1[1] (analytic) = 1.8178374957279044599758716367753 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.6615880428762985402974162984403 relative error = 36.394234601887958277381220979486 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.016731561557415403414978725352 y2[1] (numeric) = -32.425530017271006221692807764298 absolute error = 33.44226157882842162510778648965 relative error = 3289.1928256463314574863236864691 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=907.9MB, alloc=4.1MB, time=59.08 memory used=911.7MB, alloc=4.1MB, time=59.32 memory used=915.5MB, alloc=4.1MB, time=59.56 memory used=919.3MB, alloc=4.1MB, time=59.82 x[1] = 6.2 y1[1] (analytic) = 1.9169105971825034219994207109016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.562514941421699578273867224314 relative error = 29.344870973559764016777770017552 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.0034579029767825248605973761307 y2[1] (numeric) = -35.285247239464239719918816899425 absolute error = 36.288705142441022244779414275556 relative error = 3616.3654733088141316372519742725 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=923.1MB, alloc=4.1MB, time=60.08 NO POLE NO POLE memory used=926.9MB, alloc=4.1MB, time=60.32 memory used=930.7MB, alloc=4.1MB, time=60.59 memory used=934.6MB, alloc=4.1MB, time=60.84 memory used=938.4MB, alloc=4.1MB, time=61.09 x[1] = 6.3 y1[1] (analytic) = 2.0168139004843498903109663674941 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4626116381198531099623215677215 relative error = 22.937745421565875025611363648125 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.0001413636165848577133263378603 y2[1] (numeric) = -38.306086492106115862838298209808 absolute error = 39.306227855722700720551624547668 relative error = 3930.0672170570453011273324983366 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=942.2MB, alloc=4.1MB, time=61.33 memory used=946.0MB, alloc=4.1MB, time=61.58 memory used=949.8MB, alloc=4.1MB, time=61.84 memory used=953.6MB, alloc=4.1MB, time=62.09 x[1] = 6.4 y1[1] (analytic) = 2.116549204850493289480420488799 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3628763337537097107928674464166 relative error = 17.144715224295586860814857671433 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.0068150812418073414052609013278 y2[1] (numeric) = -41.493573300466108496569193602481 absolute error = 42.500388381707915837974454503809 relative error = 4221.2705365207549746754363488356 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=957.5MB, alloc=4.1MB, time=62.34 memory used=961.3MB, alloc=4.1MB, time=62.59 memory used=965.1MB, alloc=4.1MB, time=62.84 memory used=968.9MB, alloc=4.1MB, time=63.09 x[1] = 6.5 y1[1] (analytic) = 2.2151199880878155242969457490747 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2643055505163874759763421861409 relative error = 11.931884138906042382804670643412 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.0234123742719765001136867460559 y2[1] (numeric) = -44.853320948069880504501056612637 absolute error = 45.876733322341857004614743358693 relative error = 4482.7221631922447476039533268987 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=972.7MB, alloc=4.1MB, time=63.34 memory used=976.5MB, alloc=4.1MB, time=63.59 memory used=980.3MB, alloc=4.1MB, time=63.85 memory used=984.2MB, alloc=4.1MB, time=64.09 x[1] = 6.6 y1[1] (analytic) = 2.3115413635133781743549851055926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.167884175090824825918302829623 relative error = 7.2628670090356004527826116554547 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.0497674080414705337802622783318 y2[1] (numeric) = -48.391030476699283807295052403626 absolute error = 49.440797884740754341075314681958 relative error = 4709.6906901483476492605566336828 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.1MB, time=64.34 NO POLE NO POLE memory used=991.8MB, alloc=4.1MB, time=64.59 memory used=995.6MB, alloc=4.1MB, time=64.83 memory used=999.4MB, alloc=4.1MB, time=65.08 memory used=1003.2MB, alloc=4.1MB, time=65.33 x[1] = 6.7 y1[1] (analytic) = 2.4048499206165981616321928483868 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0745756179876048386410950868288 relative error = 3.1010508118728596728317600364229 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.0856168517646805588620981565234 y2[1] (numeric) = -52.112490686392359362883957766962 absolute error = 53.198107538157039921746055923485 relative error = 4900.2654529250359499617389013057 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1007.0MB, alloc=4.1MB, time=65.58 memory used=1010.9MB, alloc=4.1MB, time=65.83 memory used=1014.7MB, alloc=4.1MB, time=66.08 memory used=1018.5MB, alloc=4.1MB, time=66.34 x[1] = 6.8 y1[1] (analytic) = 2.4941133511386083222220793776203 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0146878125344053219487914424047 relative error = 0.58889915840032158609590037938184 % Correct digits = 2 h = 0.005 y2[1] (analytic) = 1.1306025096501748275583753601537 y2[1] (numeric) = -56.023578135443337166472161122312 absolute error = 57.154180645093511994030536482466 relative error = 5055.1966900177731369222338242542 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1022.3MB, alloc=4.1MB, time=66.59 memory used=1026.1MB, alloc=4.1MB, time=66.83 memory used=1029.9MB, alloc=4.1MB, time=67.08 memory used=1033.7MB, alloc=4.1MB, time=67.33 x[1] = 6.9 y1[1] (analytic) = 2.5784397643881998701737832329889 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0990142257839968699004952977733 relative error = 3.8400829506091061381748518223565 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.1842748998746429273432441636419 y2[1] (numeric) = -60.1302571404026362505356625175 absolute error = 61.314532040277279177878906681142 relative error = 5177.3901521316971180095398262128 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1037.6MB, alloc=4.1MB, time=67.58 memory used=1041.4MB, alloc=4.1MB, time=67.83 memory used=1045.2MB, alloc=4.1MB, time=68.08 memory used=1049.0MB, alloc=4.1MB, time=68.33 x[1] = 7 y1[1] (analytic) = 2.6569865987187890903969990915936 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.177561060114586090123711156378 relative error = 6.6827984830712670269245649688774 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.2460977456566953618588024782808 y2[1] (numeric) = -64.438579776076864684822073628513 absolute error = 65.684677521733560046680876106794 relative error = 5271.2299456988133366989197531291 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1052.8MB, alloc=4.1MB, time=68.92 memory used=1056.6MB, alloc=4.1MB, time=69.53 memory used=1060.4MB, alloc=4.1MB, time=70.14 memory used=1064.3MB, alloc=4.1MB, time=70.76 memory used=1068.1MB, alloc=4.1MB, time=71.37 x[1] = 7.1 y1[1] (analytic) = 2.7289690401258761520759857678532 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2495435015216731518026978326376 relative error = 9.1442408415949905131476801780446 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 1.3154533335571936593782000579107 y2[1] (numeric) = -68.954685875528819576350617759494 absolute error = 70.270139209086013235728817817405 relative error = 5341.8952551562170532258216494271 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1071.9MB, alloc=4.1MB, time=71.98 memory used=1075.7MB, alloc=4.1MB, time=72.59 memory used=1079.5MB, alloc=4.1MB, time=73.20 memory used=1083.3MB, alloc=4.1MB, time=73.82 x[1] = 7.2 y1[1] (analytic) = 2.7936678638491530524644457476436 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.314242325244950052191157812428 relative error = 11.248378137978892084200728955391 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.3916486854677453289951495209063 y2[1] (numeric) = -73.684803030077487069412129842741 absolute error = 75.076451715545232398407279363647 relative error = 5394.784797307617798644379293044 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1087.2MB, alloc=4.1MB, time=74.44 memory used=1091.0MB, alloc=4.1MB, time=75.06 memory used=1094.8MB, alloc=4.1MB, time=75.67 memory used=1098.6MB, alloc=4.1MB, time=76.26 x[1] = 7.3 y1[1] (analytic) = 2.8504366206285645175173662279669 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3710110820243615172440782927513 relative error = 13.01593865793612857873211413881 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.4739224826188948110845934232623 y2[1] (numeric) = -78.635246589298042345569056438717 absolute error = 80.109169071916937156653649861979 relative error = 5435.100557634304531099834132499 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1102.4MB, alloc=4.1MB, time=76.84 memory used=1106.2MB, alloc=4.1MB, time=77.44 memory used=1110.0MB, alloc=4.1MB, time=78.07 memory used=1113.9MB, alloc=4.1MB, time=78.67 x[1] = 7.4 y1[1] (analytic) = 2.8987080958116267592694988965346 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.419282557207423758996210961319 relative error = 14.464462903775977052444638867037 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.5614526724256093508659015312997 y2[1] (numeric) = -83.812419661021849623655455736042 absolute error = 85.373872333447458974521357267342 relative error = 5467.5927001248791724843544228431 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1117.7MB, alloc=4.1MB, time=79.27 memory used=1121.5MB, alloc=4.1MB, time=79.88 memory used=1125.3MB, alloc=4.1MB, time=80.48 memory used=1129.1MB, alloc=4.1MB, time=81.07 x[1] = 7.5 y1[1] (analytic) = 2.937999976774738857948463798149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4585744381705358576751758629334 relative error = 15.608388080177833538506535419887 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.6533646821649741890283806638281 y2[1] (numeric) = -89.222813111336462159776997551487 absolute error = 90.876177793501436348805378215315 relative error = 5496.4387937998624203884347329719 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1132.9MB, alloc=4.1MB, time=81.66 NO POLE NO POLE memory used=1136.7MB, alloc=4.1MB, time=82.28 memory used=1140.6MB, alloc=4.1MB, time=82.89 memory used=1144.4MB, alloc=4.1MB, time=83.50 memory used=1148.2MB, alloc=4.1MB, time=84.13 x[1] = 7.6 y1[1] (analytic) = 2.9679196720314864259034630180288 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4884941334272834256301750828132 relative error = 16.459142679320501160319327386212 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.7487401574177446199418472506482 y2[1] (numeric) = -94.873005564585622247310963329988 absolute error = 96.621745722003366867252810580636 relative error = 5525.2202742732610806935387265038 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1152.0MB, alloc=4.1MB, time=84.74 memory used=1155.8MB, alloc=4.1MB, time=85.35 memory used=1159.6MB, alloc=4.1MB, time=85.95 memory used=1163.4MB, alloc=4.1MB, time=86.54 x[1] = 7.7 y1[1] (analytic) = 2.9881682338770003685523936187237 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5087426952727973682791056835081 relative error = 17.025236046122105515593299961153 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.846626137962135474022615760428 y2[1] (numeric) = -100.76966340336926121690624614464 absolute error = 102.61628954133139669092886190507 relative error = 5556.9607421767964563871801448928 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1167.3MB, alloc=4.1MB, time=87.16 memory used=1171.1MB, alloc=4.1MB, time=87.79 memory used=1174.9MB, alloc=4.1MB, time=88.41 memory used=1178.7MB, alloc=4.1MB, time=89.03 x[1] = 7.8 y1[1] (analytic) = 2.9985433453746049634387733205961 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5191178067704019631654853853805 relative error = 17.312332922289275920123306622775 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 1.9460445794373504269674320870475 y2[1] (numeric) = -106.91954076854349943648335069669 absolute error = 108.86558534798084986345078278374 relative error = 5594.1979180896555085176431450476 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1182.5MB, alloc=4.1MB, time=89.67 memory used=1186.3MB, alloc=4.1MB, time=90.28 memory used=1190.1MB, alloc=4.1MB, time=90.89 memory used=1194.0MB, alloc=4.1MB, time=91.49 x[1] = 7.9 y1[1] (analytic) = 2.9989413418397720363049105120439 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5195158032355690360316225768283 relative error = 17.323306594481760871754251730352 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.0460021256395365944977529599585 y2[1] (numeric) = -113.32947955922064631123439331555 absolute error = 115.37548168486018290573214627551 relative error = 5639.0694925987073406096611922053 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1197.8MB, alloc=4.1MB, time=92.10 NO POLE NO POLE memory used=1201.6MB, alloc=4.1MB, time=92.72 memory used=1205.4MB, alloc=4.1MB, time=93.34 memory used=1209.2MB, alloc=4.1MB, time=93.96 memory used=1213.0MB, alloc=4.1MB, time=94.57 x[1] = 8 y1[1] (analytic) = 2.9893582466233817778081235982453 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5099327080191787775348356630297 relative error = 17.058266890399346607124909095316 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.1455000338086135258688413818312 y2[1] (numeric) = -120.00640943276920028362310195881 absolute error = 122.15190946657781380949194334064 relative error = 5693.4004913408550553318362969436 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1216.9MB, alloc=4.1MB, time=95.17 memory used=1220.7MB, alloc=4.1MB, time=95.79 memory used=1224.5MB, alloc=4.1MB, time=96.38 memory used=1228.3MB, alloc=4.1MB, time=96.97 x[1] = 8.1 y1[1] (analytic) = 2.9698898108450862432243199360998 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4904642722408832429510320008842 relative error = 16.514561262504246162343512872761 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.2435441537357914644650517681022 y2[1] (numeric) = -126.95734780481384883338481621216 absolute error = 129.20089195854964029784986798026 relative error = 5758.7853460968632545741994990779 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1232.1MB, alloc=4.1MB, time=97.59 memory used=1235.9MB, alloc=4.1MB, time=98.20 memory used=1239.7MB, alloc=4.1MB, time=98.81 memory used=1243.6MB, alloc=4.1MB, time=99.42 x[1] = 8.2 y1[1] (analytic) = 2.9407305566797729011536487499456 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.46130501807556990088036081473 relative error = 15.686748894002910235578526875906 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.3391548609838352074004881245196 y2[1] (numeric) = -134.18939984923546847752648728948 absolute error = 136.528554710219303684926975414 relative error = 5836.6616502165304024913690751934 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1247.4MB, alloc=4.1MB, time=100.02 memory used=1251.2MB, alloc=4.1MB, time=100.62 memory used=1255.0MB, alloc=4.1MB, time=101.23 memory used=1258.8MB, alloc=4.1MB, time=101.84 x[1] = 8.3 y1[1] (analytic) = 2.902171833756293640000504405253 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4227462951520906397272164700374 relative error = 14.56654944531414149055924854616 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.4313768449706201737093264654465 y2[1] (numeric) = -141.70975849817112477032667803282 absolute error = 144.14113534314174494403600449827 relative error = 5928.3749304967774833142246039007 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1262.6MB, alloc=4.1MB, time=102.46 NO POLE NO POLE memory used=1266.4MB, alloc=4.1MB, time=103.06 memory used=1270.3MB, alloc=4.1MB, time=103.66 memory used=1274.1MB, alloc=4.1MB, time=104.29 memory used=1277.9MB, alloc=4.1MB, time=104.88 x[1] = 8.4 y1[1] (analytic) = 2.8545989080882806628332392814224 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3751733694840776625599513462068 relative error = 13.142770020021150308365087474515 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.5192886541166852991448048405855 y2[1] (numeric) = -149.52570444201407230333556291239 absolute error = 152.04499309613075760248036775298 relative error = 6035.2350989109216014920337340068 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1281.7MB, alloc=4.1MB, time=105.47 memory used=1285.5MB, alloc=4.1MB, time=106.06 memory used=1289.3MB, alloc=4.1MB, time=106.67 memory used=1293.1MB, alloc=4.1MB, time=107.28 x[1] = 8.5 y1[1] (analytic) = 2.7984871126234902866669131603391 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3190615740192872863936252251235 relative error = 11.401216485152132051227929195622 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.602011902684823615348426522957 y2[1] (numeric) = -157.64460612941375470537492802656 absolute error = 160.24661803209857832072335454952 relative error = 6158.5659107382232334304712165291 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1297.0MB, alloc=4.1MB, time=107.89 memory used=1300.8MB, alloc=4.1MB, time=108.51 memory used=1304.6MB, alloc=4.1MB, time=109.13 memory used=1308.4MB, alloc=4.1MB, time=109.73 x[1] = 8.6 y1[1] (analytic) = 2.7343970978741131437171641875634 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2549715592699101434438762523478 relative error = 9.3245988107630952345215152561466 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.6787200473200127008644697851605 y2[1] (numeric) = -166.07391976727580464253817110183 absolute error = 168.75263981459581734340264088699 relative error = 6299.7490157072700016477293073654 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1312.2MB, alloc=4.1MB, time=110.34 memory used=1316.0MB, alloc=4.1MB, time=110.92 memory used=1319.9MB, alloc=4.1MB, time=111.52 memory used=1323.7MB, alloc=4.1MB, time=112.12 x[1] = 8.7 y1[1] (analytic) = 2.6629692300821827922023461866156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1835436914779797919290582514 relative error = 6.8924450723869380990766327727458 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.7486466455973991573187917808893 y2[1] (numeric) = -174.82118932076204381819030149289 absolute error = 177.56983596635944297550909327378 relative error = 6460.2642267888122419644584541072 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1327.5MB, alloc=4.1MB, time=112.74 memory used=1331.3MB, alloc=4.1MB, time=113.36 memory used=1335.1MB, alloc=4.1MB, time=113.97 memory used=1338.9MB, alloc=4.1MB, time=114.56 memory used=1342.7MB, alloc=4.1MB, time=115.15 x[1] = 8.8 y1[1] (analytic) = 2.5849171928917622535309313118124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1054916542875592532576433765968 relative error = 4.0810457904667000779090459473526 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.8110930140616555628890855042193 y2[1] (numeric) = -183.89404651329048297296794018258 absolute error = 186.7051395273521385358570256868 relative error = 6641.7275626745641374046146716138 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1346.6MB, alloc=4.1MB, time=115.76 memory used=1350.4MB, alloc=4.1MB, time=116.34 memory used=1354.2MB, alloc=4.1MB, time=116.95 memory used=1358.0MB, alloc=4.1MB, time=117.55 x[1] = 8.9 y1[1] (analytic) = 2.5010208564578849820161746471113 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0215953178536819817428867118957 relative error = 0.86346012660872938747886604992741 % Correct digits = 2 h = 0.005 y2[1] (analytic) = 2.8654352092411120596398276782254 y2[1] (numeric) = -193.30021082653532188477931978183 absolute error = 196.16564603577643394441914746006 relative error = 6845.9285138654159219960920490799 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1361.8MB, alloc=4.1MB, time=118.17 memory used=1365.6MB, alloc=4.1MB, time=118.79 memory used=1369.4MB, alloc=4.1MB, time=119.39 memory used=1373.3MB, alloc=4.1MB, time=119.99 x[1] = 9 y1[1] (analytic) = 2.4121184852417565697562725663524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0673070533624464305170153688632 relative error = 2.7903709446387549837868356378152 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.9111302618846769883682947111812 y2[1] (numeric) = -203.04748950042694936880428452986 absolute error = 205.95861976231162635717257924104 relative error = 7074.8678772269441326069657365073 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1377.1MB, alloc=4.1MB, time=120.58 memory used=1380.9MB, alloc=4.1MB, time=121.17 memory used=1384.7MB, alloc=4.1MB, time=121.78 memory used=1388.5MB, alloc=4.1MB, time=122.40 x[1] = 9.1 y1[1] (analytic) = 2.3190983623493517707939976839854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1603271762548512294792902512302 relative error = 6.9133409284301564490861082158704 % Correct digits = 1 h = 0.005 y2[1] (analytic) = 2.9477216021311120247190665895754 y2[1] (numeric) = -213.14377753315194327749429029394 absolute error = 216.09149913528305530221335688352 relative error = 7330.7974192357768791016326613746 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1392.3MB, alloc=4.1MB, time=122.99 memory used=1396.1MB, alloc=4.1MB, time=123.60 memory used=1400.0MB, alloc=4.1MB, time=124.22 memory used=1403.8MB, alloc=4.1MB, time=124.80 x[1] = 9.2 y1[1] (analytic) = 2.2228899141002469575280690577583 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2565356245039560427452188774573 relative error = 11.540635587785878391864526003963 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9748436214041637419414453384758 y2[1] (numeric) = -223.59705768115307050057240456955 absolute error = 226.57190130255723424251384990803 relative error = 7616.2625716646052379769251224896 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1407.6MB, alloc=4.1MB, time=125.38 NO POLE NO POLE memory used=1411.4MB, alloc=4.1MB, time=125.99 memory used=1415.2MB, alloc=4.1MB, time=126.61 memory used=1419.0MB, alloc=4.1MB, time=127.23 memory used=1422.8MB, alloc=4.1MB, time=127.86 x[1] = 9.3 y1[1] (analytic) = 2.1244544235070624079894062785863 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3549711150971405922838816566293 relative error = 16.708812915419107730536265346396 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9922253254526034077569092346352 y2[1] (numeric) = -234.4154004591292869650333064803 absolute error = 237.40762578458189037279021571494 relative error = 7934.1493357847861976272155969575 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1426.7MB, alloc=4.1MB, time=128.50 memory used=1430.5MB, alloc=4.1MB, time=129.11 memory used=1434.3MB, alloc=4.1MB, time=129.74 memory used=1438.1MB, alloc=4.1MB, time=130.37 x[1] = 9.4 y1[1] (analytic) = 2.0247754254533581210797730773676 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.454650113150844879193514857848 relative error = 22.454347649396538413117618677958 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9996930420352064721779474206729 y2[1] (numeric) = -245.606964140035737635143286778 absolute error = 248.60665718207094410732123419867 relative error = 8287.7365683189501640419662873954 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1441.9MB, alloc=4.1MB, time=130.99 memory used=1445.7MB, alloc=4.1MB, time=131.63 memory used=1449.6MB, alloc=4.1MB, time=132.26 memory used=1453.4MB, alloc=4.1MB, time=132.89 x[1] = 9.5 y1[1] (analytic) = 1.924848879538190692716517495466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5545766590660123075567704397496 relative error = 28.811438911457101713469278346326 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.997172156196378472891601640178 y2[1] (numeric) = -257.17999475508375651244024784259 absolute error = 260.17716691128013498533184948277 relative error = 8680.754836634516005482507165776 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1457.2MB, alloc=4.1MB, time=133.51 memory used=1461.0MB, alloc=4.1MB, time=134.10 memory used=1464.8MB, alloc=4.1MB, time=134.68 memory used=1468.6MB, alloc=4.1MB, time=135.29 x[1] = 9.6 y1[1] (analytic) = 1.8256732187770200148758982734796 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.653752319827182985397389661736 relative error = 35.808835508093714414422326202487 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9846878557941269100203420798837 y2[1] (numeric) = -269.14282609374086663573370368215 absolute error = 272.12751394953499354575404576203 relative error = 9117.4530502832379222109423104005 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1472.4MB, alloc=4.1MB, time=135.95 NO POLE NO POLE memory used=1476.3MB, alloc=4.1MB, time=136.56 memory used=1480.1MB, alloc=4.1MB, time=137.19 memory used=1483.9MB, alloc=4.1MB, time=137.82 memory used=1487.7MB, alloc=4.1MB, time=138.43 x[1] = 9.7 y1[1] (analytic) = 1.7282393735890568756622591031752 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.7511861650151461246110288320404 relative error = 43.465400481829561612393325687631 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9623648798313100340703563708914 y2[1] (numeric) = -281.50387970373078008110477993296 absolute error = 284.46624458356209011517513630385 relative error = 9602.6740838137683348276563627533 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1491.5MB, alloc=4.1MB, time=139.05 memory used=1495.3MB, alloc=4.1MB, time=139.67 memory used=1499.1MB, alloc=4.1MB, time=140.28 memory used=1503.0MB, alloc=4.1MB, time=140.91 x[1] = 9.8 y1[1] (analytic) = 1.6335208707480722518307470512711 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.8459046678561307484425408839445 relative error = 51.784135911820214261229049980478 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.9304262721047535185493777520892 y2[1] (numeric) = -294.27166489103339796190621385942 absolute error = 297.20209116313815148045559161151 relative error = 10141.940576777429051014670212856 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1506.8MB, alloc=4.1MB, time=141.55 memory used=1510.6MB, alloc=4.1MB, time=142.17 memory used=1514.4MB, alloc=4.1MB, time=142.78 memory used=1518.2MB, alloc=4.1MB, time=143.39 x[1] = 9.9 y1[1] (analytic) = 1.5424641062246789555861818924946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.936961432379524044687106042721 relative error = 60.744456133428108120268528386205 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.8891911526253610546344386986891 y2[1] (numeric) = -307.45477871988481042876235435409 absolute error = 310.34396987251017148339679305278 relative error = 10741.551994249520277087274250614 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1522.0MB, alloc=4.1MB, time=143.97 memory used=1525.8MB, alloc=4.1MB, time=144.57 memory used=1529.7MB, alloc=4.1MB, time=145.20 memory used=1533.5MB, alloc=4.1MB, time=145.81 x[1] = 10 y1[1] (analytic) = 1.4559788891106301865952523381486 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.023446649493572813678035597067 relative error = 70.29268467750481823479925933216 % Correct digits = 0 h = 0.005 y2[1] (analytic) = 2.8390715290764524522588639478241 y2[1] (numeric) = -321.06190601277729666956916193774 absolute error = 323.90097754185374912182802588556 relative error = 11408.6938009349296299574943922 % Correct digits = -2 h = 0.005 Finished! diff(y1,x,1) = diff(y2,x,5); diff(y2,x,1) = y1 - 2.0; Iterations = 1900 Total Elapsed Time = 2 Minutes 26 Seconds Elapsed Time(since restart) = 2 Minutes 26 Seconds Time to Timeout = 7 Minutes 33 Seconds Percent Done = 100.1 % > quit memory used=1536.8MB, alloc=4.1MB, time=146.33