|\^/| 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, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > 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, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, 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, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > 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_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[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_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[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, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, 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_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[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_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[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, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > 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 (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 (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, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; 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_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_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, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > 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, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, 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, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > 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 - 3 - 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[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_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[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 - 3 - 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 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_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 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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 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_y1_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_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 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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 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, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, glob_last; n := glob_max_terms; m := n - 4; 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[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_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[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 - 4; 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[1, 1] := glob_large_float; array_complex_pole[1, 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[1, 1] := glob_large_float; array_complex_pole[1, 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[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_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[2, 1] := glob_large_float; array_complex_pole[2, 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[2, 1] := glob_large_float; array_complex_pole[2, 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[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, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > 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_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 > ; > 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 > #BOTTOM GET NORMS > ; > fi;# end if 3 > ; > > # End Function number 8 > end; get_norms := proc() local iii; global DEBUGMASSIVE, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, 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_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; 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 end if end proc > # Begin Function number 9 > atomall := proc() > global > DEBUGMASSIVE, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre cos 1 $eq_no = 1 > array_tmp1[1] := cos(array_x[1]); > array_tmp1_g[1] := sin(array_x[1]); > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp2[1] := (array_m1[1] * (array_tmp1[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,4]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (3)) * factorial_3(0,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,2] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult FULL FULL $eq_no = 2 i = 1 > array_tmp5[1] := (array_m1[1] * (array_y2[1])); > #emit pre add FULL - CONST $eq_no = 2 i = 1 > array_tmp6[1] := array_tmp5[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[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; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := -array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := array_tmp1[1] * array_x[2] / 1; > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp2[2] := ats(2,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,5]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (3)) * factorial_3(1,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,3] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult FULL FULL $eq_no = 2 i = 2 > array_tmp5[2] := ats(2,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 2 > array_tmp6[2] := array_tmp5[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[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; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := -array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := array_tmp1[2] * array_x[2] / 2; > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp2[3] := ats(3,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (3)) * factorial_3(2,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,4] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult FULL FULL $eq_no = 2 i = 3 > array_tmp5[3] := ats(3,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 3 > array_tmp6[3] := array_tmp5[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[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; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := -array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := array_tmp1[3] * array_x[2] / 3; > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp2[4] := ats(4,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,7]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (3)) * factorial_3(3,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,5] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult FULL FULL $eq_no = 2 i = 4 > array_tmp5[4] := ats(4,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 4 > array_tmp6[4] := array_tmp5[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[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; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := -array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := array_tmp1[4] * array_x[2] / 4; > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp2[5] := ats(5,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,8]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (3)) * factorial_3(4,7); > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,7] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,6] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult FULL FULL $eq_no = 2 i = 5 > array_tmp5[5] := ats(5,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 5 > array_tmp6[5] := array_tmp5[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[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; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit cos LINEAR $eq_no = 1 > array_tmp1[kkk] := -array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit mult FULL FULL $eq_no = 1 > array_tmp2[kkk] := ats(kkk,array_m1,array_tmp1,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 3; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[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 > ; > #emit mult FULL FULL $eq_no = 2 > array_tmp5[kkk] := ats(kkk,array_m1,array_y2,1); > #emit FULL - NOT FULL add $eq_no = 2 > array_tmp6[kkk] := array_tmp5[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp6[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 > ; > 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, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, glob_last; array_tmp1[1] := cos(array_x[1]); array_tmp1_g[1] := sin(array_x[1]); array_tmp2[1] := array_m1[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; if not array_y2_set_initial[1, 4] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 3)*factorial_3(0, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 2] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 1] := temporary end if end if; kkk := 2; array_tmp5[1] := array_m1[1]*array_y2[1]; array_tmp6[1] := array_tmp5[1] + array_const_1D0[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp6[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_tmp1[2] := -array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := array_tmp1[1]*array_x[2]; array_tmp2[2] := ats(2, array_m1, array_tmp1, 1); array_tmp3[2] := array_tmp2[2]; if not array_y2_set_initial[1, 5] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 3)*factorial_3(1, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 3] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 2] := temporary end if end if; kkk := 3; array_tmp5[2] := ats(2, array_m1, array_y2, 1); array_tmp6[2] := array_tmp5[2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp6[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_tmp1[3] := -1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := 1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := ats(3, array_m1, array_tmp1, 1); array_tmp3[3] := array_tmp2[3]; if not array_y2_set_initial[1, 6] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 3)*factorial_3(2, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 4] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 3] := temporary end if end if; kkk := 4; array_tmp5[3] := ats(3, array_m1, array_y2, 1); array_tmp6[3] := array_tmp5[3]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp6[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_tmp1[4] := -1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := 1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := ats(4, array_m1, array_tmp1, 1); array_tmp3[4] := array_tmp2[4]; if not array_y2_set_initial[1, 7] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 3)*factorial_3(3, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 4] := temporary end if end if; kkk := 5; array_tmp5[4] := ats(4, array_m1, array_y2, 1); array_tmp6[4] := array_tmp5[4]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp6[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_tmp1[5] := -1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := 1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := ats(5, array_m1, array_tmp1, 1); array_tmp3[5] := array_tmp2[5]; if not array_y2_set_initial[1, 8] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 3)*factorial_3(4, 7); array_y2[8] := temporary; array_y2_higher[1, 8] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 7] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 6] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := ats(5, array_m1, array_y2, 1); array_tmp6[5] := array_tmp5[5]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp6[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; while kkk <= glob_max_terms do array_tmp1[kkk] := -array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := ats(kkk, array_m1, array_tmp1, 1); array_tmp3[kkk] := array_tmp2[kkk]; order_d := 3; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp3[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; array_tmp5[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp6[kkk] := array_tmp5[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp6[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; 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_y2 := proc(x) > return(1.0 + cos(x)); > end; exact_soln_y2 := proc(x) return 1.0 + 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_y1 := proc(x) > return( 1.0 - sin(x)); > end; exact_soln_y1 := proc(x) return 1.0 - sin(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, > INFO, > DEBUGL, > ALWAYS, > glob_iolevel, > glob_max_terms, > #Top Generate Globals Decl > glob_log10relerr, > glob_dump_analytic, > glob_last_good_h, > glob_dump, > glob_html_log, > MAX_UNCHANGED, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_iter, > glob_max_opt_iter, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_log10normmin, > glob_small_float, > glob_optimal_start, > glob_max_hours, > glob_abserr, > glob_next_display, > glob_display_interval, > glob_look_poles, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_percent_done, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > years_in_century, > djd_debug2, > glob_subiter_method, > glob_warned, > glob_max_trunc_err, > glob_optimal_done, > glob_neg_h, > glob_hmin, > glob_clock_sec, > days_in_year, > glob_optimal_expect_sec, > glob_max_sec, > glob_no_eqs, > glob_hmin_init, > glob_not_yet_start_msg, > min_in_hour, > glob_good_digits, > glob_current_iter, > glob_orig_start_sec, > glob_large_float, > glob_almost_1, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_iter, > glob_relerr, > glob_hmax, > glob_reached_optimal_h, > glob_not_yet_finished, > djd_debug, > glob_start, > glob_log10_abserr, > glob_h, > glob_disp_incr, > glob_initial_pass, > hours_in_day, > sec_in_minute, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > array_const_3, > #END CONST > array_type_pole, > array_last_rel_error, > array_1st_rel_error, > array_pole, > array_x, > array_tmp1_g, > array_y1_init, > array_y2_init, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_m1, > array_norms, > array_fact_1, > array_poles, > array_y1_set_initial, > array_y1_higher_work, > array_y2_higher, > array_real_pole, > array_y1_higher_work2, > array_complex_pole, > array_y2_higher_work2, > array_y2_set_initial, > array_y2_higher_work, > array_fact_2, > array_y1_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > INFO := 2; > DEBUGL := 3; > ALWAYS := 1; > glob_iolevel := 5; > glob_max_terms := 30; > glob_log10relerr := 0.0; > glob_dump_analytic := false; > glob_last_good_h := 0.1; > glob_dump := false; > glob_html_log := true; > MAX_UNCHANGED := 10; > glob_warned2 := false; > glob_unchanged_h_cnt := 0; > glob_max_iter := 1000; > glob_max_opt_iter := 10; > glob_smallish_float := 0.1e-100; > glob_max_rel_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_log10normmin := 0.1; > glob_small_float := 0.1e-50; > glob_optimal_start := 0.0; > glob_max_hours := 0.0; > glob_abserr := 0.1e-10; > glob_next_display := 0.0; > glob_display_interval := 0.0; > glob_look_poles := false; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10; > glob_display_flag := true; > glob_percent_done := 0.0; > glob_curr_iter_when_opt := 0; > glob_optimal_clock_start_sec := 0.0; > years_in_century := 100; > djd_debug2 := true; > glob_subiter_method := 3; > glob_warned := false; > glob_max_trunc_err := 0.1e-10; > glob_optimal_done := false; > glob_neg_h := false; > glob_hmin := 0.00000000001; > glob_clock_sec := 0.0; > days_in_year := 365; > glob_optimal_expect_sec := 0.1; > glob_max_sec := 10000.0; > glob_no_eqs := 0; > glob_hmin_init := 0.001; > glob_not_yet_start_msg := true; > min_in_hour := 60; > glob_good_digits := 0; > glob_current_iter := 0; > glob_orig_start_sec := 0.0; > glob_large_float := 9.0e100; > glob_almost_1 := 0.9990; > glob_max_minutes := 0.0; > glob_log10abserr := 0.0; > glob_normmax := 0.0; > glob_iter := 0; > glob_relerr := 0.1e-10; > glob_hmax := 1.0; > glob_reached_optimal_h := false; > glob_not_yet_finished := true; > djd_debug := true; > glob_start := 0; > glob_log10_abserr := 0.1e-10; > glob_h := 0.1; > glob_disp_incr := 0.1; > glob_initial_pass := true; > hours_in_day := 24; > sec_in_minute := 60; > #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/mtest4postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = m1 * cos(x) ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > 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 := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > 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,"glob_max_iter := 20;"); > 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_y2 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + 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_y1 := proc(x)"); > omniout_str(ALWAYS,"return( 1.0 - sin(x));"); > omniout_str(ALWAYS,"end;"); > 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_type_pole:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y2_higher_work2 := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_tmp1_g[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 > ; > 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_y2[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_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[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_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_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 <=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 > ; > ord := 1; > while (ord <=4) 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 <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_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_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 <=4) 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 <=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 <=4) 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 <= 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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1D0[1] := 1.0; > 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_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3[1] := 3; > 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 := 0.1; > x_end := 5.0; > glob_h := 0.00001; > 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); > glob_max_iter := 20; > #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_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_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 := 3; > #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 > ; > 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 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > 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) > ; > 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) > ; > 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 <= 4) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while (subiter <= 4 + 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_y2 > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =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_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 > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =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_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 > 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 ( y2 , x , 3 ) = m1 * cos(x) ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > 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,"2012-09-21T00:31:55-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest4") > ; > logitem_str(html_log_file,"diff ( y2 , x , 3 ) = m1 * cos(x) ;") > ; > 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,"mtest4 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest4 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 ( y1 , x , 1 ) = m1 * y2 + 1.0;") > ; > 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, INFO, DEBUGL, ALWAYS, glob_iolevel, glob_max_terms, glob_log10relerr, glob_dump_analytic, glob_last_good_h, glob_dump, glob_html_log, MAX_UNCHANGED, glob_warned2, glob_unchanged_h_cnt, glob_max_iter, glob_max_opt_iter, glob_smallish_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_log10normmin, glob_small_float, glob_optimal_start, glob_max_hours, glob_abserr, glob_next_display, glob_display_interval, glob_look_poles, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_percent_done, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, years_in_century, djd_debug2, glob_subiter_method, glob_warned, glob_max_trunc_err, glob_optimal_done, glob_neg_h, glob_hmin, glob_clock_sec, days_in_year, glob_optimal_expect_sec, glob_max_sec, glob_no_eqs, glob_hmin_init, glob_not_yet_start_msg, min_in_hour, glob_good_digits, glob_current_iter, glob_orig_start_sec, glob_large_float, glob_almost_1, glob_max_minutes, glob_log10abserr, glob_normmax, glob_iter, glob_relerr, glob_hmax, glob_reached_optimal_h, glob_not_yet_finished, djd_debug, glob_start, glob_log10_abserr, glob_h, glob_disp_incr, glob_initial_pass, hours_in_day, sec_in_minute, array_const_0D0, array_const_1D0, array_const_1, array_const_3, array_type_pole, array_last_rel_error, array_1st_rel_error, array_pole, array_x, array_tmp1_g, array_y1_init, array_y2_init, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_m1, array_norms, array_fact_1, array_poles, array_y1_set_initial, array_y1_higher_work, array_y2_higher, array_real_pole, array_y1_higher_work2, array_complex_pole, array_y2_higher_work2, array_y2_set_initial, array_y2_higher_work, array_fact_2, array_y1_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; INFO := 2; DEBUGL := 3; ALWAYS := 1; glob_iolevel := 5; glob_max_terms := 30; glob_log10relerr := 0.; glob_dump_analytic := false; glob_last_good_h := 0.1; glob_dump := false; glob_html_log := true; MAX_UNCHANGED := 10; glob_warned2 := false; glob_unchanged_h_cnt := 0; glob_max_iter := 1000; glob_max_opt_iter := 10; glob_smallish_float := 0.1*10^(-100); glob_max_rel_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_log10normmin := 0.1; glob_small_float := 0.1*10^(-50); glob_optimal_start := 0.; glob_max_hours := 0.; glob_abserr := 0.1*10^(-10); glob_next_display := 0.; glob_display_interval := 0.; glob_look_poles := false; glob_clock_start_sec := 0.; centuries_in_millinium := 10; glob_display_flag := true; glob_percent_done := 0.; glob_curr_iter_when_opt := 0; glob_optimal_clock_start_sec := 0.; years_in_century := 100; djd_debug2 := true; glob_subiter_method := 3; glob_warned := false; glob_max_trunc_err := 0.1*10^(-10); glob_optimal_done := false; glob_neg_h := false; glob_hmin := 0.1*10^(-10); glob_clock_sec := 0.; days_in_year := 365; glob_optimal_expect_sec := 0.1; glob_max_sec := 10000.0; glob_no_eqs := 0; glob_hmin_init := 0.001; glob_not_yet_start_msg := true; min_in_hour := 60; glob_good_digits := 0; glob_current_iter := 0; glob_orig_start_sec := 0.; glob_large_float := 0.90*10^101; glob_almost_1 := 0.9990; glob_max_minutes := 0.; glob_log10abserr := 0.; glob_normmax := 0.; glob_iter := 0; glob_relerr := 0.1*10^(-10); glob_hmax := 1.0; glob_reached_optimal_h := false; glob_not_yet_finished := true; djd_debug := true; glob_start := 0; glob_log10_abserr := 0.1*10^(-10); glob_h := 0.1; glob_disp_incr := 0.1; glob_initial_pass := true; hours_in_day := 24; sec_in_minute := 60; 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/mtest4postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = m1 * cos(x) ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); 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 := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "glob_h := 0.00001;"); 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, "glob_max_iter := 20;"); 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_y2 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + 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_y1 := proc(x)"); omniout_str(ALWAYS, "return( 1.0 - sin(x));"); omniout_str(ALWAYS, "end;"); 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_type_pole := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 5, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y2_higher_work2 := Array(0 .. 5, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 5, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[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_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[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_y2[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_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[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_fact_1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[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; ord := 1; while ord <= 4 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 <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_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_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 4 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 <= 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 <= 4 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 <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 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_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 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_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; 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 := 0.1; x_end := 5.0; glob_h := 0.00001; 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); glob_max_iter := 20; 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_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_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 := 3; 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; 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; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); 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); 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); 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 <= 4 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 4 + 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 := 3; 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 := 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 := 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 := 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; 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; 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 ( y2 , x , 3 ) = m1 * cos(x) ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); 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, "2012-09-21T00:31:55-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest4") ; logitem_str(html_log_file, "diff ( y2 , x , 3 ) = m1 * cos(x) ;"); 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, "mtest4 diffeq.mxt"); logitem_str(html_log_file, "mtest4 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 ( y1 , x , 1 ) = m1 * y2 + 1.0;"); 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/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0; glob_h := 0.00001; 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); glob_max_iter := 20; #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_y2 := proc(x) return(1.0 + cos(x)); end; exact_soln_y2p := proc(x) return( -sin(x)); end; exact_soln_y2pp := proc(x) return( -cos(x)); end; exact_soln_y1 := proc(x) return( 1.0 - sin(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.9950041652780257660955619878039 y2[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 y1[1] (analytic) = 0.90016658335317184769318580158938 y1[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 x[1] = 0.1 y2[1] (analytic) = 1.9950041652780257660955619878039 y2[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 y1[1] (analytic) = 0.90016658335317184769318580158938 y1[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.18 NO POLE NO POLE memory used=7.6MB, alloc=4.4MB, time=0.39 memory used=11.4MB, alloc=4.4MB, time=0.61 memory used=15.2MB, alloc=4.4MB, time=0.83 memory used=19.0MB, alloc=4.4MB, time=1.05 memory used=22.8MB, alloc=4.4MB, time=1.27 memory used=26.7MB, alloc=4.4MB, time=1.49 memory used=30.5MB, alloc=4.4MB, time=1.72 memory used=34.3MB, alloc=4.4MB, time=1.95 memory used=38.1MB, alloc=4.4MB, time=2.17 memory used=41.9MB, alloc=4.5MB, time=2.39 memory used=45.7MB, alloc=4.5MB, time=2.63 memory used=49.5MB, alloc=4.5MB, time=2.86 memory used=53.4MB, alloc=4.5MB, time=3.09 memory used=57.2MB, alloc=4.5MB, time=3.32 memory used=61.0MB, alloc=4.5MB, time=3.54 memory used=64.8MB, alloc=4.5MB, time=3.77 memory used=68.6MB, alloc=4.5MB, time=3.99 memory used=72.4MB, alloc=4.5MB, time=4.21 memory used=76.2MB, alloc=4.5MB, time=4.43 x[1] = 0.2 y2[1] (analytic) = 1.9800665778412416311241965167482 y2[1] (numeric) = 1.9798804674906269890802450981272 absolute error = 0.000186110350614642043951418621 relative error = 0.0093991966076993222787093535137006 % Correct digits = 4 h = 0.005 y1[1] (analytic) = 0.80133066920493878454058737288161 y1[1] (numeric) = 0.80133530408764884456847492778961 absolute error = 4.63488271006002788755490800e-06 relative error = 0.00057839826780355832202829167710196 % Correct digits = 5 h = 0.005 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=4.67 NO POLE NO POLE memory used=83.9MB, alloc=4.5MB, time=4.89 memory used=87.7MB, alloc=4.5MB, time=5.11 memory used=91.5MB, alloc=4.5MB, time=5.33 memory used=95.3MB, alloc=4.5MB, time=5.55 memory used=99.1MB, alloc=4.5MB, time=5.78 memory used=102.9MB, alloc=4.5MB, time=6.00 memory used=106.8MB, alloc=4.5MB, time=6.22 memory used=110.6MB, alloc=4.5MB, time=6.45 memory used=114.4MB, alloc=4.5MB, time=6.68 memory used=118.2MB, alloc=4.5MB, time=6.90 memory used=122.0MB, alloc=4.5MB, time=7.12 memory used=125.8MB, alloc=4.5MB, time=7.34 memory used=129.7MB, alloc=4.5MB, time=7.57 memory used=133.5MB, alloc=4.5MB, time=7.80 memory used=137.3MB, alloc=4.5MB, time=8.03 memory used=141.1MB, alloc=4.5MB, time=8.27 memory used=144.9MB, alloc=4.5MB, time=8.51 memory used=148.7MB, alloc=4.5MB, time=8.75 memory used=152.5MB, alloc=4.5MB, time=8.99 x[1] = 0.3 y2[1] (analytic) = 1.955336489125606019642310227568 y2[1] (numeric) = 1.9538200239350365784765222066217 absolute error = 0.0015164651905694411657880209463 relative error = 0.0775552033628533774995921784184 % Correct digits = 3 h = 0.005 y1[1] (analytic) = 0.70447979333866042489467925431497 y1[1] (numeric) = 0.70455507011115049461017511531191 absolute error = 7.527677249006971549586099694e-05 relative error = 0.010685440973873661652616103005471 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=9.24 NO POLE NO POLE memory used=160.2MB, alloc=4.5MB, time=9.48 memory used=164.0MB, alloc=4.5MB, time=9.73 memory used=167.8MB, alloc=4.5MB, time=9.97 memory used=171.6MB, alloc=4.5MB, time=10.21 memory used=175.4MB, alloc=4.5MB, time=10.46 memory used=179.2MB, alloc=4.5MB, time=10.70 memory used=183.1MB, alloc=4.5MB, time=10.94 memory used=186.9MB, alloc=4.5MB, time=11.19 memory used=190.7MB, alloc=4.5MB, time=11.43 memory used=194.5MB, alloc=4.5MB, time=11.66 memory used=198.3MB, alloc=4.5MB, time=11.91 memory used=202.1MB, alloc=4.5MB, time=12.15 memory used=205.9MB, alloc=4.5MB, time=12.39 memory used=209.8MB, alloc=4.5MB, time=12.64 memory used=213.6MB, alloc=4.5MB, time=12.88 memory used=217.4MB, alloc=4.5MB, time=13.13 memory used=221.2MB, alloc=4.5MB, time=13.37 memory used=225.0MB, alloc=4.5MB, time=13.61 memory used=228.8MB, alloc=4.5MB, time=13.85 memory used=232.7MB, alloc=4.5MB, time=14.10 x[1] = 0.4 y2[1] (analytic) = 1.9210609940028850827985267320518 y2[1] (numeric) = 1.9158551326743615994978862710975 absolute error = 0.0052058613285234833006404609543 relative error = 0.27098886213269629520118959910337 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 0.61058165769134950833368824320429 y1[1] (numeric) = 0.61096814704406119427419586577631 absolute error = 0.00038648935271168594050762257202 relative error = 0.063298552755912827438129044540337 % Correct digits = 3 h = 0.005 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.5MB, time=14.34 NO POLE NO POLE memory used=240.3MB, alloc=4.5MB, time=14.58 memory used=244.1MB, alloc=4.5MB, time=14.82 memory used=247.9MB, alloc=4.5MB, time=15.05 memory used=251.7MB, alloc=4.5MB, time=15.30 memory used=255.5MB, alloc=4.5MB, time=15.55 memory used=259.4MB, alloc=4.5MB, time=15.79 memory used=263.2MB, alloc=4.5MB, time=16.03 memory used=267.0MB, alloc=4.5MB, time=16.27 memory used=270.8MB, alloc=4.5MB, time=16.52 memory used=274.6MB, alloc=4.5MB, time=16.77 memory used=278.4MB, alloc=4.5MB, time=17.01 memory used=282.2MB, alloc=4.5MB, time=17.25 memory used=286.1MB, alloc=4.5MB, time=17.48 memory used=289.9MB, alloc=4.5MB, time=17.71 memory used=293.7MB, alloc=4.5MB, time=17.94 memory used=297.5MB, alloc=4.5MB, time=18.16 memory used=301.3MB, alloc=4.5MB, time=18.38 memory used=305.1MB, alloc=4.5MB, time=18.61 memory used=308.9MB, alloc=4.5MB, time=18.83 x[1] = 0.5 y2[1] (analytic) = 1.8775825618903727161162815826038 y2[1] (numeric) = 1.8650475945759776636968756545008 absolute error = 0.012534967314395052419405928103 relative error = 0.66761204374281664050956178836587 % Correct digits = 2 h = 0.005 y1[1] (analytic) = 0.52057446139579699972671206478443 y1[1] (numeric) = 0.52181217505227874892731951071411 absolute error = 0.00123771365648174920060744592968 relative error = 0.23775919647750553678720334670449 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.5MB, time=19.07 NO POLE NO POLE memory used=316.6MB, alloc=4.5MB, time=19.32 memory used=320.4MB, alloc=4.5MB, time=19.55 memory used=324.2MB, alloc=4.5MB, time=19.79 memory used=328.0MB, alloc=4.5MB, time=20.03 memory used=331.8MB, alloc=4.5MB, time=20.27 memory used=335.7MB, alloc=4.5MB, time=20.52 memory used=339.5MB, alloc=4.5MB, time=20.76 memory used=343.3MB, alloc=4.5MB, time=21.00 memory used=347.1MB, alloc=4.5MB, time=21.24 memory used=350.9MB, alloc=4.5MB, time=21.48 memory used=354.7MB, alloc=4.5MB, time=21.72 memory used=358.5MB, alloc=4.5MB, time=21.96 memory used=362.4MB, alloc=4.5MB, time=22.20 memory used=366.2MB, alloc=4.5MB, time=22.44 memory used=370.0MB, alloc=4.5MB, time=22.68 memory used=373.8MB, alloc=4.5MB, time=22.92 memory used=377.6MB, alloc=4.5MB, time=23.16 memory used=381.4MB, alloc=4.5MB, time=23.39 memory used=385.2MB, alloc=4.5MB, time=23.63 x[1] = 0.6 y2[1] (analytic) = 1.8253356149096782972409524989554 y2[1] (numeric) = 1.8004980874871347110231967992044 absolute error = 0.024837527422543586217755699751 relative error = 1.3607101740450400852211925298517 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.43535752660496464279905455434134 y1[1] (numeric) = 0.43841674700599751139319562293517 absolute error = 0.00305922040103286859414106859383 relative error = 0.70269151538265434238229529646496 % Correct digits = 2 h = 0.005 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.5MB, time=23.87 NO POLE NO POLE memory used=392.9MB, alloc=4.5MB, time=24.11 memory used=396.7MB, alloc=4.5MB, time=24.35 memory used=400.5MB, alloc=4.5MB, time=24.59 memory used=404.3MB, alloc=4.5MB, time=24.83 memory used=408.1MB, alloc=4.5MB, time=25.07 memory used=411.9MB, alloc=4.5MB, time=25.31 memory used=415.8MB, alloc=4.5MB, time=25.55 memory used=419.6MB, alloc=4.5MB, time=25.79 memory used=423.4MB, alloc=4.5MB, time=26.04 memory used=427.2MB, alloc=4.5MB, time=26.28 memory used=431.0MB, alloc=4.5MB, time=26.51 memory used=434.8MB, alloc=4.5MB, time=26.75 memory used=438.6MB, alloc=4.5MB, time=26.99 memory used=442.5MB, alloc=4.5MB, time=27.24 memory used=446.3MB, alloc=4.5MB, time=27.48 memory used=450.1MB, alloc=4.5MB, time=27.72 memory used=453.9MB, alloc=4.5MB, time=27.96 memory used=457.7MB, alloc=4.5MB, time=28.20 memory used=461.5MB, alloc=4.5MB, time=28.45 memory used=465.4MB, alloc=4.5MB, time=28.69 x[1] = 0.7 y2[1] (analytic) = 1.7648421872844884262558599901919 y2[1] (numeric) = 1.7213551519646309085552568527095 absolute error = 0.0434870353198575177006031374824 relative error = 2.4640750109656977210587789827388 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.35578231276230894632738564860128 y1[1] (numeric) = 0.36219906787746571225612028374838 absolute error = 0.0064167551151567659287346351471 relative error = 1.803562146003495063345309638926 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.5MB, time=28.93 NO POLE NO POLE memory used=473.0MB, alloc=4.5MB, time=29.17 memory used=476.8MB, alloc=4.5MB, time=29.39 memory used=480.6MB, alloc=4.5MB, time=29.62 memory used=484.4MB, alloc=4.5MB, time=29.86 memory used=488.2MB, alloc=4.5MB, time=30.09 memory used=492.1MB, alloc=4.5MB, time=30.33 memory used=495.9MB, alloc=4.5MB, time=30.57 memory used=499.7MB, alloc=4.5MB, time=30.80 memory used=503.5MB, alloc=4.5MB, time=31.03 memory used=507.3MB, alloc=4.5MB, time=31.27 memory used=511.1MB, alloc=4.5MB, time=31.49 memory used=514.9MB, alloc=4.5MB, time=31.72 memory used=518.8MB, alloc=4.5MB, time=31.94 memory used=522.6MB, alloc=4.5MB, time=32.17 memory used=526.4MB, alloc=4.5MB, time=32.40 memory used=530.2MB, alloc=4.5MB, time=32.63 memory used=534.0MB, alloc=4.5MB, time=32.85 memory used=537.8MB, alloc=4.5MB, time=33.07 memory used=541.6MB, alloc=4.5MB, time=33.30 x[1] = 0.8 y2[1] (analytic) = 1.6967067093471654209207499816423 y2[1] (numeric) = 1.6268236987761140516301203788076 absolute error = 0.0698830105710513692906296028347 relative error = 4.1187442818529288533558548791942 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.28264390910047723837282538941861 y1[1] (numeric) = 0.29465873874757977833959617513117 absolute error = 0.01201482964710253996677078571256 relative error = 4.2508715950540372625845674550443 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.5MB, time=33.53 NO POLE NO POLE memory used=549.3MB, alloc=4.5MB, time=33.76 memory used=553.1MB, alloc=4.5MB, time=33.98 memory used=556.9MB, alloc=4.5MB, time=34.22 memory used=560.7MB, alloc=4.5MB, time=34.45 memory used=564.5MB, alloc=4.5MB, time=34.70 memory used=568.4MB, alloc=4.5MB, time=34.94 memory used=572.2MB, alloc=4.5MB, time=35.18 memory used=576.0MB, alloc=4.5MB, time=35.41 memory used=579.8MB, alloc=4.5MB, time=35.63 memory used=583.6MB, alloc=4.5MB, time=35.86 memory used=587.4MB, alloc=4.5MB, time=36.09 memory used=591.2MB, alloc=4.5MB, time=36.31 memory used=595.1MB, alloc=4.5MB, time=36.53 memory used=598.9MB, alloc=4.5MB, time=36.75 memory used=602.7MB, alloc=4.5MB, time=36.97 memory used=606.5MB, alloc=4.5MB, time=37.20 memory used=610.3MB, alloc=4.5MB, time=37.42 memory used=614.1MB, alloc=4.5MB, time=37.65 memory used=617.9MB, alloc=4.5MB, time=37.87 x[1] = 0.9 y2[1] (analytic) = 1.6216099682706644564847161514071 y2[1] (numeric) = 1.5161729531688696698103957617081 absolute error = 0.105437015101794786674320389699 relative error = 6.5019959894694107213803811027616 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.21667309037251661153861768428645 y1[1] (numeric) = 0.23737171753779757074443569432319 absolute error = 0.02069862716528095920581801003674 relative error = 9.5529293137854408332041433396483 % Correct digits = 1 h = 0.005 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.5MB, time=38.09 NO POLE NO POLE memory used=625.6MB, alloc=4.5MB, time=38.31 memory used=629.4MB, alloc=4.5MB, time=38.54 memory used=633.2MB, alloc=4.5MB, time=38.76 memory used=637.0MB, alloc=4.5MB, time=38.99 memory used=640.8MB, alloc=4.5MB, time=39.21 memory used=644.6MB, alloc=4.5MB, time=39.43 memory used=648.5MB, alloc=4.5MB, time=39.66 memory used=652.3MB, alloc=4.5MB, time=39.88 memory used=656.1MB, alloc=4.5MB, time=40.10 memory used=659.9MB, alloc=4.5MB, time=40.33 memory used=663.7MB, alloc=4.5MB, time=40.55 memory used=667.5MB, alloc=4.5MB, time=40.78 memory used=671.4MB, alloc=4.5MB, time=41.00 memory used=675.2MB, alloc=4.5MB, time=41.23 memory used=679.0MB, alloc=4.5MB, time=41.45 memory used=682.8MB, alloc=4.5MB, time=41.67 memory used=686.6MB, alloc=4.5MB, time=41.91 memory used=690.4MB, alloc=4.5MB, time=42.13 memory used=694.2MB, alloc=4.5MB, time=42.35 x[1] = 1 y2[1] (analytic) = 1.540302305868139717400936607443 y2[1] (numeric) = 1.3887437565295881330561369077034 absolute error = 0.1515585493385515843447996997396 relative error = 9.839532717775858474426399343634 % Correct digits = 1 h = 0.005 y1[1] (analytic) = 0.1585290151921034933474976783697 y1[1] (numeric) = 0.19198351680974094875902596015009 absolute error = 0.03345450161763745541152828178039 relative error = 21.103077929991368144292111513748 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.5MB, time=42.57 NO POLE NO POLE memory used=701.9MB, alloc=4.5MB, time=42.80 memory used=705.7MB, alloc=4.6MB, time=43.02 memory used=709.5MB, alloc=4.6MB, time=43.24 memory used=713.3MB, alloc=4.6MB, time=43.46 memory used=717.1MB, alloc=4.6MB, time=43.69 memory used=720.9MB, alloc=4.6MB, time=43.91 memory used=724.8MB, alloc=4.6MB, time=44.13 memory used=728.6MB, alloc=4.6MB, time=44.38 memory used=732.4MB, alloc=4.6MB, time=44.62 memory used=736.2MB, alloc=4.6MB, time=44.87 memory used=740.0MB, alloc=4.6MB, time=45.12 memory used=743.8MB, alloc=4.6MB, time=45.34 memory used=747.6MB, alloc=4.6MB, time=45.57 memory used=751.5MB, alloc=4.6MB, time=45.80 memory used=755.3MB, alloc=4.6MB, time=46.02 memory used=759.1MB, alloc=4.6MB, time=46.24 memory used=762.9MB, alloc=4.6MB, time=46.46 memory used=766.7MB, alloc=4.6MB, time=46.69 memory used=770.5MB, alloc=4.6MB, time=46.91 memory used=774.4MB, alloc=4.6MB, time=47.13 x[1] = 1.1 y2[1] (analytic) = 1.4535961214255773877713700517847 y2[1] (numeric) = 1.2439551524793399729991366769653 absolute error = 0.2096409689462374147722333748194 relative error = 14.422229521404980903677486634811 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.1087926399385646600481974221283 y1[1] (numeric) = 0.16020170659782552231805716811174 absolute error = 0.05140906665926086226985974598344 relative error = 47.25417701812514758569283442109 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.6MB, time=47.35 NO POLE NO POLE memory used=782.0MB, alloc=4.6MB, time=47.57 memory used=785.8MB, alloc=4.6MB, time=47.80 memory used=789.6MB, alloc=4.6MB, time=48.01 memory used=793.4MB, alloc=4.6MB, time=48.23 memory used=797.2MB, alloc=4.6MB, time=48.46 memory used=801.1MB, alloc=4.6MB, time=48.68 memory used=804.9MB, alloc=4.6MB, time=48.90 memory used=808.7MB, alloc=4.6MB, time=49.13 memory used=812.5MB, alloc=4.6MB, time=49.35 memory used=816.3MB, alloc=4.6MB, time=49.58 memory used=820.1MB, alloc=4.6MB, time=49.80 memory used=823.9MB, alloc=4.6MB, time=50.03 memory used=827.8MB, alloc=4.6MB, time=50.27 memory used=831.6MB, alloc=4.6MB, time=50.51 memory used=835.4MB, alloc=4.6MB, time=50.75 memory used=839.2MB, alloc=4.6MB, time=50.97 memory used=843.0MB, alloc=4.6MB, time=51.20 memory used=846.8MB, alloc=4.6MB, time=51.42 memory used=850.6MB, alloc=4.6MB, time=51.65 x[1] = 1.2 y2[1] (analytic) = 1.3623577544766735776383733556231 y2[1] (numeric) = 1.0813101915976754994594975096798 absolute error = 0.2810475628789980781788758459433 relative error = 20.629497792006747223672941826104 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.06796091403277365032986556450517 y1[1] (numeric) = 0.14378779718413572247956167244617 absolute error = 0.075826883151362072149696107941 relative error = 111.57425445278019088617240877239 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.6MB, time=51.88 NO POLE NO POLE memory used=858.3MB, alloc=4.6MB, time=52.10 memory used=862.1MB, alloc=4.6MB, time=52.33 memory used=865.9MB, alloc=4.6MB, time=52.55 memory used=869.7MB, alloc=4.6MB, time=52.77 memory used=873.5MB, alloc=4.6MB, time=53.00 memory used=877.3MB, alloc=4.6MB, time=53.22 memory used=881.2MB, alloc=4.6MB, time=53.45 memory used=885.0MB, alloc=4.6MB, time=53.67 memory used=888.8MB, alloc=4.6MB, time=53.89 memory used=892.6MB, alloc=4.6MB, time=54.14 memory used=896.4MB, alloc=4.6MB, time=54.38 memory used=900.2MB, alloc=4.6MB, time=54.60 memory used=904.1MB, alloc=4.6MB, time=54.83 memory used=907.9MB, alloc=4.6MB, time=55.05 memory used=911.7MB, alloc=4.6MB, time=55.27 memory used=915.5MB, alloc=4.6MB, time=55.50 memory used=919.3MB, alloc=4.6MB, time=55.72 memory used=923.1MB, alloc=4.6MB, time=55.95 memory used=926.9MB, alloc=4.6MB, time=56.18 x[1] = 1.3 y2[1] (analytic) = 1.2674988286245874069979841092929 y2[1] (numeric) = 0.90040089677696429551484866179626 absolute error = 0.36709793184762311148313544749664 relative error = 28.962388252932387065643606240358 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.03644181458280703529865136996045 y1[1] (numeric) = 0.14454858292017544032936262073514 absolute error = 0.10810676833736840503071125077469 relative error = 296.65583224928743683862341327997 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=930.8MB, alloc=4.6MB, time=56.41 NO POLE NO POLE memory used=934.6MB, alloc=4.6MB, time=56.63 memory used=938.4MB, alloc=4.6MB, time=56.85 memory used=942.2MB, alloc=4.6MB, time=57.08 memory used=946.0MB, alloc=4.6MB, time=57.30 memory used=949.8MB, alloc=4.6MB, time=57.52 memory used=953.6MB, alloc=4.6MB, time=57.76 memory used=957.5MB, alloc=4.6MB, time=58.00 memory used=961.3MB, alloc=4.6MB, time=58.24 memory used=965.1MB, alloc=4.6MB, time=58.48 memory used=968.9MB, alloc=4.6MB, time=58.73 memory used=972.7MB, alloc=4.6MB, time=58.97 memory used=976.5MB, alloc=4.6MB, time=59.21 memory used=980.3MB, alloc=4.6MB, time=59.45 memory used=984.2MB, alloc=4.6MB, time=59.70 memory used=988.0MB, alloc=4.6MB, time=59.94 memory used=991.8MB, alloc=4.6MB, time=60.17 memory used=995.6MB, alloc=4.6MB, time=60.41 memory used=999.4MB, alloc=4.6MB, time=60.67 memory used=1003.2MB, alloc=4.6MB, time=60.90 memory used=1007.1MB, alloc=4.6MB, time=61.15 x[1] = 1.4 y2[1] (analytic) = 1.1699671429002409386167480352036 y2[1] (numeric) = 0.70091233959479535881240015269277 absolute error = 0.46905480330544557980434788251083 relative error = 40.091280011736215436657543739618 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.0145502700115398193405254211939 y1[1] (numeric) = 0.16432703358516594982553125204398 absolute error = 0.14977676357362613048500583085008 relative error = 1029.3744614693622681499035005557 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.6MB, time=61.43 NO POLE NO POLE memory used=1014.7MB, alloc=4.6MB, time=61.70 memory used=1018.5MB, alloc=4.6MB, time=61.94 memory used=1022.3MB, alloc=4.6MB, time=62.17 memory used=1026.1MB, alloc=4.6MB, time=62.39 memory used=1029.9MB, alloc=4.6MB, time=62.62 memory used=1033.8MB, alloc=4.6MB, time=62.84 memory used=1037.6MB, alloc=4.6MB, time=63.06 memory used=1041.4MB, alloc=4.6MB, time=63.29 memory used=1045.2MB, alloc=4.6MB, time=63.51 memory used=1049.0MB, alloc=4.6MB, time=63.73 memory used=1052.8MB, alloc=4.6MB, time=63.95 memory used=1056.6MB, alloc=4.6MB, time=64.18 memory used=1060.5MB, alloc=4.6MB, time=64.40 memory used=1064.3MB, alloc=4.6MB, time=64.62 memory used=1068.1MB, alloc=4.6MB, time=64.85 memory used=1071.9MB, alloc=4.6MB, time=65.07 memory used=1075.7MB, alloc=4.6MB, time=65.30 memory used=1079.5MB, alloc=4.6MB, time=65.51 memory used=1083.3MB, alloc=4.6MB, time=65.73 x[1] = 1.5 y2[1] (analytic) = 1.0707372016677029100881898514343 y2[1] (numeric) = 0.4826257869746723364770088948782 absolute error = 0.5881114146930305736111809565561 relative error = 54.925841165977115775538913667149 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.00250501339594556905827662885851 y1[1] (numeric) = 0.20499282429142808510193095997395 absolute error = 0.20248781089548251604365433111544 relative error = 8083.3025173922995550407797545741 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.6MB, time=65.95 NO POLE NO POLE memory used=1091.0MB, alloc=4.6MB, time=66.18 memory used=1094.8MB, alloc=4.6MB, time=66.40 memory used=1098.6MB, alloc=4.6MB, time=66.63 memory used=1102.4MB, alloc=4.6MB, time=66.85 memory used=1106.2MB, alloc=4.6MB, time=67.07 memory used=1110.1MB, alloc=4.6MB, time=67.30 memory used=1113.9MB, alloc=4.6MB, time=67.52 memory used=1117.7MB, alloc=4.6MB, time=67.74 memory used=1121.5MB, alloc=4.6MB, time=67.97 memory used=1125.3MB, alloc=4.6MB, time=68.20 memory used=1129.1MB, alloc=4.6MB, time=68.42 memory used=1132.9MB, alloc=4.6MB, time=68.64 memory used=1136.8MB, alloc=4.6MB, time=68.86 memory used=1140.6MB, alloc=4.6MB, time=69.08 memory used=1144.4MB, alloc=4.6MB, time=69.30 memory used=1148.2MB, alloc=4.6MB, time=69.53 memory used=1152.0MB, alloc=4.6MB, time=69.75 memory used=1155.8MB, alloc=4.6MB, time=69.97 memory used=1159.6MB, alloc=4.6MB, time=70.19 x[1] = 1.6 y2[1] (analytic) = 0.9708004776987112737942295370535 y2[1] (numeric) = 0.24542088669461033456298399958126 absolute error = 0.72537959100410093923124553747224 relative error = 74.719739809318788935228367332126 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.00042639695849483565788617445377 y1[1] (numeric) = 0.26843259855890369643072738329161 absolute error = 0.26800620160040886077284120883784 relative error = 62853.685107525184212340113933064 % Correct digits = -2 h = 0.005 TOP MAIN SOLVE Loop memory used=1163.5MB, alloc=4.6MB, time=70.41 NO POLE NO POLE memory used=1167.3MB, alloc=4.6MB, time=70.63 memory used=1171.1MB, alloc=4.6MB, time=70.85 memory used=1174.9MB, alloc=4.6MB, time=71.08 memory used=1178.7MB, alloc=4.6MB, time=71.31 memory used=1182.5MB, alloc=4.6MB, time=71.53 memory used=1186.3MB, alloc=4.6MB, time=71.75 memory used=1190.2MB, alloc=4.6MB, time=71.97 memory used=1194.0MB, alloc=4.6MB, time=72.19 memory used=1197.8MB, alloc=4.6MB, time=72.41 memory used=1201.6MB, alloc=4.6MB, time=72.64 memory used=1205.4MB, alloc=4.6MB, time=72.86 memory used=1209.2MB, alloc=4.6MB, time=73.08 memory used=1213.0MB, alloc=4.6MB, time=73.30 memory used=1216.9MB, alloc=4.6MB, time=73.52 memory used=1220.7MB, alloc=4.6MB, time=73.75 memory used=1224.5MB, alloc=4.6MB, time=73.98 memory used=1228.3MB, alloc=4.6MB, time=74.20 memory used=1232.1MB, alloc=4.6MB, time=74.42 memory used=1235.9MB, alloc=4.6MB, time=74.64 memory used=1239.8MB, alloc=4.6MB, time=74.87 x[1] = 1.7 y2[1] (analytic) = 0.87115550570447531591235714266513 y2[1] (numeric) = -0.01072313009324516417806018852151 absolute error = 0.88187863579772048009041733118664 relative error = 101.23090883579662568607527679884 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.00833518954753138465386660135212 y1[1] (numeric) = 0.35654006184695716681563641573281 absolute error = 0.34820487229942578216176981438069 relative error = 4177.5279411918458171961109308307 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1243.6MB, alloc=4.6MB, time=75.10 NO POLE NO POLE memory used=1247.4MB, alloc=4.6MB, time=75.32 memory used=1251.2MB, alloc=4.6MB, time=75.54 memory used=1255.0MB, alloc=4.6MB, time=75.76 memory used=1258.8MB, alloc=4.6MB, time=75.99 memory used=1262.6MB, alloc=4.6MB, time=76.21 memory used=1266.5MB, alloc=4.6MB, time=76.44 memory used=1270.3MB, alloc=4.6MB, time=76.66 memory used=1274.1MB, alloc=4.6MB, time=76.88 memory used=1277.9MB, alloc=4.6MB, time=77.10 memory used=1281.7MB, alloc=4.6MB, time=77.32 memory used=1285.5MB, alloc=4.6MB, time=77.55 memory used=1289.3MB, alloc=4.6MB, time=77.77 memory used=1293.2MB, alloc=4.6MB, time=77.99 memory used=1297.0MB, alloc=4.6MB, time=78.22 memory used=1300.8MB, alloc=4.6MB, time=78.44 memory used=1304.6MB, alloc=4.6MB, time=78.66 memory used=1308.4MB, alloc=4.6MB, time=78.88 memory used=1312.2MB, alloc=4.6MB, time=79.11 memory used=1316.0MB, alloc=4.6MB, time=79.33 x[1] = 1.8 y2[1] (analytic) = 0.77279790530691294468332569346942 y2[1] (numeric) = -0.2857272413471558063025202624588 absolute error = 1.0585251466540687509858459559282 relative error = 136.97308693321064534400847714884 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.02615236912180481346762682115664 y1[1] (numeric) = 0.4712060045256125854497905072973 absolute error = 0.44505363540380777198216368614066 relative error = 1701.7717719223365177641610405002 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1319.9MB, alloc=4.6MB, time=79.56 NO POLE NO POLE memory used=1323.7MB, alloc=4.6MB, time=79.78 memory used=1327.5MB, alloc=4.6MB, time=80.01 memory used=1331.3MB, alloc=4.6MB, time=80.23 memory used=1335.1MB, alloc=4.6MB, time=80.45 memory used=1338.9MB, alloc=4.6MB, time=80.67 memory used=1342.8MB, alloc=4.6MB, time=80.90 memory used=1346.6MB, alloc=4.6MB, time=81.13 memory used=1350.4MB, alloc=4.6MB, time=81.35 memory used=1354.2MB, alloc=4.6MB, time=81.57 memory used=1358.0MB, alloc=4.6MB, time=81.80 memory used=1361.8MB, alloc=4.6MB, time=82.02 memory used=1365.6MB, alloc=4.6MB, time=82.25 memory used=1369.5MB, alloc=4.6MB, time=82.47 memory used=1373.3MB, alloc=4.6MB, time=82.70 memory used=1377.1MB, alloc=4.6MB, time=82.92 memory used=1380.9MB, alloc=4.6MB, time=83.13 memory used=1384.7MB, alloc=4.6MB, time=83.35 memory used=1388.5MB, alloc=4.6MB, time=83.58 memory used=1392.3MB, alloc=4.6MB, time=83.80 x[1] = 1.9 y2[1] (analytic) = 0.67671043313649657772116630491969 y2[1] (numeric) = -0.57941342369791020320137011943549 absolute error = 1.2561238568344067809225364243552 relative error = 185.6220615681033869011738754865 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.05369991231258551151029038836504 y1[1] (numeric) = 0.61430835397340000896716921343442 absolute error = 0.56060844166081449745687882506938 relative error = 1043.9652832159767355417011009557 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=1396.2MB, alloc=4.6MB, time=84.02 NO POLE NO POLE memory used=1400.0MB, alloc=4.6MB, time=84.24 memory used=1403.8MB, alloc=4.6MB, time=84.46 memory used=1407.6MB, alloc=4.6MB, time=84.69 memory used=1411.4MB, alloc=4.6MB, time=84.91 memory used=1415.2MB, alloc=4.6MB, time=85.14 memory used=1419.0MB, alloc=4.6MB, time=85.36 memory used=1422.9MB, alloc=4.6MB, time=85.59 memory used=1426.7MB, alloc=4.6MB, time=85.81 memory used=1430.5MB, alloc=4.6MB, time=86.05 memory used=1434.3MB, alloc=4.6MB, time=86.27 memory used=1438.1MB, alloc=4.6MB, time=86.50 memory used=1441.9MB, alloc=4.6MB, time=86.72 memory used=1445.8MB, alloc=4.6MB, time=86.94 memory used=1449.6MB, alloc=4.6MB, time=87.16 memory used=1453.4MB, alloc=4.6MB, time=87.39 memory used=1457.2MB, alloc=4.6MB, time=87.61 memory used=1461.0MB, alloc=4.6MB, time=87.83 memory used=1464.8MB, alloc=4.6MB, time=88.06 memory used=1468.6MB, alloc=4.6MB, time=88.28 x[1] = 2 y2[1] (analytic) = 0.58385316345285761300243177049924 y2[1] (numeric) = -0.89150643119948238928816828987126 absolute error = 1.4753595946523400022906000603705 relative error = 252.69360294756128327636232446394 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.09070257317431830460398013408826 y1[1] (numeric) = 0.78770235519796079138820123723121 absolute error = 0.69699978202364248678422110314295 relative error = 768.44543393945553731343879446666 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=1472.5MB, alloc=4.6MB, time=88.50 NO POLE NO POLE memory used=1476.3MB, alloc=4.6MB, time=88.73 memory used=1480.1MB, alloc=4.6MB, time=88.95 memory used=1483.9MB, alloc=4.6MB, time=89.18 memory used=1487.7MB, alloc=4.6MB, time=89.39 memory used=1491.5MB, alloc=4.6MB, time=89.61 memory used=1495.3MB, alloc=4.6MB, time=89.84 memory used=1499.2MB, alloc=4.6MB, time=90.06 memory used=1503.0MB, alloc=4.6MB, time=90.28 memory used=1506.8MB, alloc=4.6MB, time=90.50 memory used=1510.6MB, alloc=4.6MB, time=90.72 memory used=1514.4MB, alloc=4.6MB, time=90.95 memory used=1518.2MB, alloc=4.6MB, time=91.17 memory used=1522.0MB, alloc=4.6MB, time=91.39 memory used=1525.9MB, alloc=4.6MB, time=91.62 memory used=1529.7MB, alloc=4.6MB, time=91.84 memory used=1533.5MB, alloc=4.6MB, time=92.06 memory used=1537.3MB, alloc=4.6MB, time=92.28 memory used=1541.1MB, alloc=4.6MB, time=92.50 memory used=1544.9MB, alloc=4.6MB, time=92.72 memory used=1548.7MB, alloc=4.6MB, time=92.94 x[1] = 2.1 y2[1] (analytic) = 0.49515389540014254837906147628083 y2[1] (numeric) = -1.2216365454955403003286118834636 absolute error = 1.7167904408956828487076733597444 relative error = 346.71855696668091021642642516168 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.13679063335112622931924068673098 y1[1] (numeric) = 0.993210978091405039021522818811 absolute error = 0.85642034474027880970228213208002 relative error = 626.08113125841280450494830552192 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=1552.6MB, alloc=4.6MB, time=93.16 NO POLE NO POLE memory used=1556.4MB, alloc=4.6MB, time=93.38 memory used=1560.2MB, alloc=4.6MB, time=93.60 memory used=1564.0MB, alloc=4.6MB, time=93.83 memory used=1567.8MB, alloc=4.6MB, time=94.05 memory used=1571.6MB, alloc=4.6MB, time=94.27 memory used=1575.5MB, alloc=4.6MB, time=94.50 memory used=1579.3MB, alloc=4.6MB, time=94.72 memory used=1583.1MB, alloc=4.6MB, time=94.94 memory used=1586.9MB, alloc=4.6MB, time=95.16 memory used=1590.7MB, alloc=4.6MB, time=95.38 memory used=1594.5MB, alloc=4.6MB, time=95.59 memory used=1598.3MB, alloc=4.6MB, time=95.82 memory used=1602.2MB, alloc=4.6MB, time=96.04 memory used=1606.0MB, alloc=4.6MB, time=96.27 memory used=1609.8MB, alloc=4.6MB, time=96.49 memory used=1613.6MB, alloc=4.6MB, time=96.72 memory used=1617.4MB, alloc=4.6MB, time=96.94 memory used=1621.2MB, alloc=4.6MB, time=97.16 memory used=1625.0MB, alloc=4.6MB, time=97.39 x[1] = 2.2 y2[1] (analytic) = 0.41149888274465429147585738734507 y2[1] (numeric) = -1.5693432699230496033782669180866 absolute error = 1.9808421526677038948541243054317 relative error = 481.37242547432813452409732209577 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.19150359618040981569596308958388 y1[1] (numeric) = 1.2326156471679547188401178142979 absolute error = 1.041112050987544903144154724714 relative error = 543.65143618856345083353474993887 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=1628.9MB, alloc=4.6MB, time=97.62 NO POLE NO POLE memory used=1632.7MB, alloc=4.6MB, time=97.85 memory used=1636.5MB, alloc=4.6MB, time=98.09 memory used=1640.3MB, alloc=4.6MB, time=98.34 memory used=1644.1MB, alloc=4.6MB, time=98.58 memory used=1647.9MB, alloc=4.6MB, time=98.83 memory used=1651.7MB, alloc=4.6MB, time=99.07 memory used=1655.6MB, alloc=4.6MB, time=99.32 memory used=1659.4MB, alloc=4.6MB, time=99.56 memory used=1663.2MB, alloc=4.6MB, time=99.79 memory used=1667.0MB, alloc=4.6MB, time=100.02 memory used=1670.8MB, alloc=4.6MB, time=100.26 memory used=1674.6MB, alloc=4.6MB, time=100.50 memory used=1678.5MB, alloc=4.6MB, time=100.75 memory used=1682.3MB, alloc=4.6MB, time=100.99 memory used=1686.1MB, alloc=4.6MB, time=101.24 memory used=1689.9MB, alloc=4.6MB, time=101.48 memory used=1693.7MB, alloc=4.6MB, time=101.72 memory used=1697.5MB, alloc=4.6MB, time=101.97 memory used=1701.3MB, alloc=4.6MB, time=102.21 x[1] = 2.3 y2[1] (analytic) = 0.33372397872017580668211942883398 y2[1] (numeric) = -1.9340799306427107771609700919238 absolute error = 2.2678039093628865838430895207578 relative error = 679.54478969712191698599785902952 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.2542947878232798226145937883565 y1[1] (numeric) = 1.5076473864092695490715834735166 absolute error = 1.2533525985859897264569896851601 relative error = 492.87388440576191804025260281302 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=1705.2MB, alloc=4.6MB, time=102.46 NO POLE NO POLE memory used=1709.0MB, alloc=4.6MB, time=102.70 memory used=1712.8MB, alloc=4.6MB, time=102.94 memory used=1716.6MB, alloc=4.6MB, time=103.19 memory used=1720.4MB, alloc=4.6MB, time=103.44 memory used=1724.2MB, alloc=4.6MB, time=103.67 memory used=1728.0MB, alloc=4.6MB, time=103.90 memory used=1731.9MB, alloc=4.6MB, time=104.14 memory used=1735.7MB, alloc=4.6MB, time=104.38 memory used=1739.5MB, alloc=4.6MB, time=104.63 memory used=1743.3MB, alloc=4.6MB, time=104.88 memory used=1747.1MB, alloc=4.6MB, time=105.12 memory used=1750.9MB, alloc=4.6MB, time=105.36 memory used=1754.7MB, alloc=4.6MB, time=105.61 memory used=1758.6MB, alloc=4.6MB, time=105.87 memory used=1762.4MB, alloc=4.6MB, time=106.43 memory used=1766.2MB, alloc=4.6MB, time=107.01 memory used=1770.0MB, alloc=4.6MB, time=107.60 memory used=1773.8MB, alloc=4.6MB, time=108.20 memory used=1777.6MB, alloc=4.6MB, time=108.79 memory used=1781.5MB, alloc=4.6MB, time=109.39 x[1] = 2.4 y2[1] (analytic) = 0.26260628445875450039117777266522 y2[1] (numeric) = -2.3152191388232550470906268829529 absolute error = 2.5778254232820095474818046556181 relative error = 981.63127687330280625658804441693 % Correct digits = 0 h = 0.005 y1[1] (analytic) = 0.32453681944884907343422847465872 y1[1] (numeric) = 1.8199784676952340507389635476358 absolute error = 1.4954416482463849773047350729771 relative error = 460.79259998481764308517187474945 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=1785.3MB, alloc=4.6MB, time=109.98 NO POLE NO POLE memory used=1789.1MB, alloc=4.6MB, time=110.56 memory used=1792.9MB, alloc=4.6MB, time=111.15 memory used=1796.7MB, alloc=4.6MB, time=111.74 memory used=1800.5MB, alloc=4.6MB, time=112.33 memory used=1804.3MB, alloc=4.6MB, time=112.91 memory used=1808.2MB, alloc=4.6MB, time=113.54 memory used=1812.0MB, alloc=4.6MB, time=114.16 memory used=1815.8MB, alloc=4.6MB, time=114.79 memory used=1819.6MB, alloc=4.6MB, time=115.41 memory used=1823.4MB, alloc=4.6MB, time=116.03 memory used=1827.2MB, alloc=4.6MB, time=116.66 memory used=1831.0MB, alloc=4.6MB, time=117.29 memory used=1834.9MB, alloc=4.6MB, time=117.92 memory used=1838.7MB, alloc=4.6MB, time=118.54 memory used=1842.5MB, alloc=4.6MB, time=119.17 memory used=1846.3MB, alloc=4.6MB, time=119.79 memory used=1850.1MB, alloc=4.6MB, time=120.41 memory used=1853.9MB, alloc=4.6MB, time=121.03 memory used=1857.7MB, alloc=4.6MB, time=121.66 x[1] = 2.5 y2[1] (analytic) = 0.19885638445306628516649720953265 y2[1] (numeric) = -2.7120590593032592480272735913411 absolute error = 2.9109154437563255331937708008738 relative error = 1463.8280041963422071249803465305 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.40152785589604350594814529781384 y1[1] (numeric) = 2.171214646266324674190022670604 absolute error = 1.7696867903702811682418773727902 relative error = 440.73823631017450173018961103661 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=1861.6MB, alloc=4.6MB, time=122.29 NO POLE NO POLE memory used=1865.4MB, alloc=4.6MB, time=122.91 memory used=1869.2MB, alloc=4.6MB, time=123.54 memory used=1873.0MB, alloc=4.6MB, time=124.10 memory used=1876.8MB, alloc=4.6MB, time=124.68 memory used=1880.6MB, alloc=4.6MB, time=125.27 memory used=1884.5MB, alloc=4.6MB, time=125.85 memory used=1888.3MB, alloc=4.6MB, time=126.42 memory used=1892.1MB, alloc=4.6MB, time=127.01 memory used=1895.9MB, alloc=4.6MB, time=127.58 memory used=1899.7MB, alloc=4.6MB, time=128.17 memory used=1903.5MB, alloc=4.6MB, time=128.75 memory used=1907.3MB, alloc=4.6MB, time=129.34 memory used=1911.2MB, alloc=4.6MB, time=129.92 memory used=1915.0MB, alloc=4.6MB, time=130.52 memory used=1918.8MB, alloc=4.6MB, time=131.11 memory used=1922.6MB, alloc=4.6MB, time=131.69 memory used=1926.4MB, alloc=4.6MB, time=132.26 memory used=1930.2MB, alloc=4.6MB, time=132.85 memory used=1934.0MB, alloc=4.6MB, time=133.43 x[1] = 2.6 y2[1] (analytic) = 0.1431112466310527662022978483548 y2[1] (numeric) = -3.123830423096082904756656404743 absolute error = 3.2669416697271356709589542530978 relative error = 2282.7986944656126903568178077205 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.48449862817853576474227306479063 y1[1] (numeric) = 2.56288806079825041338478574449 absolute error = 2.0783894326197146486425126796994 relative error = 428.9773616972629766384142262918 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=1937.9MB, alloc=4.6MB, time=134.02 NO POLE NO POLE memory used=1941.7MB, alloc=4.6MB, time=134.59 memory used=1945.5MB, alloc=4.6MB, time=135.17 memory used=1949.3MB, alloc=4.6MB, time=135.76 memory used=1953.1MB, alloc=4.6MB, time=136.33 memory used=1956.9MB, alloc=4.6MB, time=136.92 memory used=1960.7MB, alloc=4.6MB, time=137.51 memory used=1964.6MB, alloc=4.6MB, time=138.09 memory used=1968.4MB, alloc=4.6MB, time=138.69 memory used=1972.2MB, alloc=4.6MB, time=139.28 memory used=1976.0MB, alloc=4.6MB, time=139.87 memory used=1979.8MB, alloc=4.6MB, time=140.45 memory used=1983.6MB, alloc=4.6MB, time=141.02 memory used=1987.4MB, alloc=4.6MB, time=141.59 memory used=1991.3MB, alloc=4.6MB, time=142.17 memory used=1995.1MB, alloc=4.6MB, time=142.75 memory used=1998.9MB, alloc=4.6MB, time=143.31 memory used=2002.7MB, alloc=4.6MB, time=143.89 memory used=2006.5MB, alloc=4.6MB, time=144.49 memory used=2010.3MB, alloc=4.6MB, time=145.07 memory used=2014.2MB, alloc=4.6MB, time=145.65 x[1] = 2.7 y2[1] (analytic) = 0.09592785798293885201747271805667 y2[1] (numeric) = -3.5497042136712962248285268521651 absolute error = 3.6456320716542350768459995702218 relative error = 3800.3893220493103504854634936183 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.57262011976617006544394691414212 y1[1] (numeric) = 2.9964508690289741756304094210275 absolute error = 2.4238307492628041101864625068854 relative error = 423.28773747114885688945887445556 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2018.0MB, alloc=4.6MB, time=146.23 NO POLE NO POLE memory used=2021.8MB, alloc=4.6MB, time=146.81 memory used=2025.6MB, alloc=4.6MB, time=147.39 memory used=2029.4MB, alloc=4.6MB, time=147.98 memory used=2033.2MB, alloc=4.6MB, time=148.56 memory used=2037.0MB, alloc=4.6MB, time=149.14 memory used=2040.9MB, alloc=4.6MB, time=149.72 memory used=2044.7MB, alloc=4.6MB, time=150.31 memory used=2048.5MB, alloc=4.6MB, time=150.89 memory used=2052.3MB, alloc=4.6MB, time=151.47 memory used=2056.1MB, alloc=4.6MB, time=152.03 memory used=2059.9MB, alloc=4.6MB, time=152.62 memory used=2063.7MB, alloc=4.6MB, time=153.21 memory used=2067.6MB, alloc=4.6MB, time=153.79 memory used=2071.4MB, alloc=4.6MB, time=154.36 memory used=2075.2MB, alloc=4.6MB, time=154.94 memory used=2079.0MB, alloc=4.6MB, time=155.52 memory used=2082.8MB, alloc=4.6MB, time=156.12 memory used=2086.6MB, alloc=4.6MB, time=156.71 memory used=2090.4MB, alloc=4.6MB, time=157.29 x[1] = 2.8 y2[1] (analytic) = 0.05777765933134184741321188263385 y2[1] (numeric) = -3.9887999502138157220890159224619 absolute error = 4.0465776095451575695022278050958 relative error = 7003.7063743599363921981213733871 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 0.66501184984409508045614624728758 y1[1] (numeric) = 3.4732696825288259272347006528876 absolute error = 2.8082578326847308467785544056 relative error = 422.28688606723276837035595918454 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2094.3MB, alloc=4.6MB, time=157.87 NO POLE NO POLE memory used=2098.1MB, alloc=4.6MB, time=158.46 memory used=2101.9MB, alloc=4.6MB, time=159.04 memory used=2105.7MB, alloc=4.6MB, time=159.62 memory used=2109.5MB, alloc=4.6MB, time=160.20 memory used=2113.3MB, alloc=4.6MB, time=160.77 memory used=2117.2MB, alloc=4.6MB, time=161.35 memory used=2121.0MB, alloc=4.6MB, time=161.94 memory used=2124.8MB, alloc=4.6MB, time=162.52 memory used=2128.6MB, alloc=4.6MB, time=163.11 memory used=2132.4MB, alloc=4.6MB, time=163.70 memory used=2136.2MB, alloc=4.6MB, time=164.28 memory used=2140.0MB, alloc=4.6MB, time=164.87 memory used=2143.9MB, alloc=4.6MB, time=165.44 memory used=2147.7MB, alloc=4.6MB, time=166.02 memory used=2151.5MB, alloc=4.6MB, time=166.60 memory used=2155.3MB, alloc=4.6MB, time=167.18 memory used=2159.1MB, alloc=4.6MB, time=167.76 memory used=2162.9MB, alloc=4.6MB, time=168.33 memory used=2166.7MB, alloc=4.6MB, time=168.91 x[1] = 2.9 y2[1] (analytic) = 0.02904183485040947821889333065447 y2[1] (numeric) = -4.4401944850971602691904410305403 absolute error = 4.4692363199475697474093343611948 relative error = 15388.959902044740497848512199058 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 0.76075067078601767181574308126042 y1[1] (numeric) = 3.9946208562196450241096448417795 absolute error = 3.2338701854336273522939017605191 relative error = 425.08936365344901148344756056638 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2170.6MB, alloc=4.6MB, time=169.48 NO POLE NO POLE memory used=2174.4MB, alloc=4.6MB, time=170.04 memory used=2178.2MB, alloc=4.6MB, time=170.61 memory used=2182.0MB, alloc=4.6MB, time=171.18 memory used=2185.8MB, alloc=4.6MB, time=171.75 memory used=2189.6MB, alloc=4.6MB, time=172.32 memory used=2193.4MB, alloc=4.6MB, time=172.89 memory used=2197.3MB, alloc=4.6MB, time=173.47 memory used=2201.1MB, alloc=4.6MB, time=174.05 memory used=2204.9MB, alloc=4.6MB, time=174.62 memory used=2208.7MB, alloc=4.6MB, time=175.18 memory used=2212.5MB, alloc=4.6MB, time=175.75 memory used=2216.3MB, alloc=4.6MB, time=176.31 memory used=2220.2MB, alloc=4.6MB, time=176.88 memory used=2224.0MB, alloc=4.6MB, time=177.45 memory used=2227.8MB, alloc=4.6MB, time=178.02 memory used=2231.6MB, alloc=4.6MB, time=178.60 memory used=2235.4MB, alloc=4.6MB, time=179.18 memory used=2239.2MB, alloc=4.6MB, time=179.76 memory used=2243.0MB, alloc=4.6MB, time=180.32 memory used=2246.9MB, alloc=4.6MB, time=180.89 x[1] = 3 y2[1] (analytic) = 0.01000750339955454272842720526874 y2[1] (numeric) = -4.9029312276693828626248486067398 absolute error = 4.9129387310689374053532758120085 relative error = 49092.551208002824605684593370815 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 0.85887999194013277789925519719189 y1[1] (numeric) = 4.561686679708519379204423965257 absolute error = 3.7028066877683866013051687680651 relative error = 431.12038032275950339224701528602 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2250.7MB, alloc=4.6MB, time=181.46 NO POLE NO POLE memory used=2254.5MB, alloc=4.6MB, time=182.02 memory used=2258.3MB, alloc=4.6MB, time=182.59 memory used=2262.1MB, alloc=4.6MB, time=183.16 memory used=2265.9MB, alloc=4.6MB, time=183.74 memory used=2269.7MB, alloc=4.6MB, time=184.31 memory used=2273.6MB, alloc=4.6MB, time=184.87 memory used=2277.4MB, alloc=4.6MB, time=185.43 memory used=2281.2MB, alloc=4.6MB, time=186.00 memory used=2285.0MB, alloc=4.6MB, time=186.57 memory used=2288.8MB, alloc=4.6MB, time=187.14 memory used=2292.6MB, alloc=4.6MB, time=187.71 memory used=2296.4MB, alloc=4.6MB, time=188.29 memory used=2300.3MB, alloc=4.6MB, time=188.87 memory used=2304.1MB, alloc=4.6MB, time=189.44 memory used=2307.9MB, alloc=4.6MB, time=190.00 memory used=2311.7MB, alloc=4.6MB, time=190.57 memory used=2315.5MB, alloc=4.6MB, time=191.14 memory used=2319.3MB, alloc=4.6MB, time=191.72 memory used=2323.1MB, alloc=4.6MB, time=192.30 x[1] = 3.1 y2[1] (analytic) = 0.00086484972672053550762394545853 y2[1] (numeric) = -5.3760297021906580483428595737827 absolute error = 5.3768945519173785838504835192412 relative error = 621714.31472913552038821747732294 % Correct digits = -3 h = 0.005 y1[1] (analytic) = 0.95841933756670942080530172840333 y1[1] (numeric) = 5.1755525084910557673261492774213 absolute error = 4.217133170924346346520847549018 relative error = 440.00919071927832047753539146906 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2327.0MB, alloc=4.6MB, time=192.88 NO POLE NO POLE memory used=2330.8MB, alloc=4.6MB, time=193.47 memory used=2334.6MB, alloc=4.6MB, time=194.05 memory used=2338.4MB, alloc=4.6MB, time=194.62 memory used=2342.2MB, alloc=4.6MB, time=195.21 memory used=2346.0MB, alloc=4.6MB, time=195.78 memory used=2349.9MB, alloc=4.6MB, time=196.37 memory used=2353.7MB, alloc=4.6MB, time=196.98 memory used=2357.5MB, alloc=4.6MB, time=197.57 memory used=2361.3MB, alloc=4.6MB, time=198.15 memory used=2365.1MB, alloc=4.6MB, time=198.74 memory used=2368.9MB, alloc=4.6MB, time=199.32 memory used=2372.7MB, alloc=4.6MB, time=199.90 memory used=2376.6MB, alloc=4.6MB, time=200.50 memory used=2380.4MB, alloc=4.6MB, time=201.08 memory used=2384.2MB, alloc=4.6MB, time=201.67 memory used=2388.0MB, alloc=4.6MB, time=202.24 memory used=2391.8MB, alloc=4.6MB, time=202.83 memory used=2395.6MB, alloc=4.6MB, time=203.42 memory used=2399.4MB, alloc=4.6MB, time=204.00 x[1] = 3.2 y2[1] (analytic) = 0.00170522420524691533833927771642 y2[1] (numeric) = -5.8584953444227720685107247366632 absolute error = 5.8602005686280189838490640143796 relative error = 343661.58717407285531324428919537 % Correct digits = -3 h = 0.005 y1[1] (analytic) = 1.0583741434275799091372174146191 y1[1] (numeric) = 5.8372048636882498923429233213213 absolute error = 4.7788307202606699832057059067022 relative error = 451.5256490284491977955126234332 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2403.3MB, alloc=4.6MB, time=204.58 NO POLE NO POLE memory used=2407.1MB, alloc=4.6MB, time=205.15 memory used=2410.9MB, alloc=4.6MB, time=205.73 memory used=2414.7MB, alloc=4.6MB, time=206.31 memory used=2418.5MB, alloc=4.6MB, time=206.90 memory used=2422.3MB, alloc=4.6MB, time=207.50 memory used=2426.1MB, alloc=4.6MB, time=208.09 memory used=2430.0MB, alloc=4.6MB, time=208.69 memory used=2433.8MB, alloc=4.6MB, time=209.27 memory used=2437.6MB, alloc=4.6MB, time=209.86 memory used=2441.4MB, alloc=4.6MB, time=210.48 memory used=2445.2MB, alloc=4.6MB, time=211.12 memory used=2449.0MB, alloc=4.6MB, time=211.75 memory used=2452.9MB, alloc=4.6MB, time=212.31 memory used=2456.7MB, alloc=4.6MB, time=212.87 memory used=2460.5MB, alloc=4.6MB, time=213.44 memory used=2464.3MB, alloc=4.6MB, time=214.00 memory used=2468.1MB, alloc=4.6MB, time=214.58 memory used=2471.9MB, alloc=4.6MB, time=215.14 memory used=2475.7MB, alloc=4.6MB, time=215.69 memory used=2479.6MB, alloc=4.6MB, time=216.25 x[1] = 3.3 y2[1] (analytic) = 0.01252023009113511606340894889715 y2[1] (numeric) = -6.349329438986231865799538261407 absolute error = 6.3618496690773669818629472103042 relative error = 50812.561931923612349076739291823 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 1.1577456941432483820116542776025 y1[1] (numeric) = 6.5475305193037572675806354690047 absolute error = 5.3897848251605088855689811914022 relative error = 465.54134059198914607024157395432 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2483.4MB, alloc=4.6MB, time=216.84 NO POLE NO POLE memory used=2487.2MB, alloc=4.6MB, time=217.42 memory used=2491.0MB, alloc=4.6MB, time=217.98 memory used=2494.8MB, alloc=4.6MB, time=218.57 memory used=2498.6MB, alloc=4.6MB, time=219.15 memory used=2502.4MB, alloc=4.6MB, time=219.68 memory used=2506.3MB, alloc=4.6MB, time=220.21 memory used=2510.1MB, alloc=4.6MB, time=220.74 memory used=2513.9MB, alloc=4.6MB, time=221.28 memory used=2517.7MB, alloc=4.6MB, time=221.81 memory used=2521.5MB, alloc=4.6MB, time=222.36 memory used=2525.3MB, alloc=4.6MB, time=222.89 memory used=2529.1MB, alloc=4.6MB, time=223.42 memory used=2533.0MB, alloc=4.6MB, time=223.95 memory used=2536.8MB, alloc=4.6MB, time=224.48 memory used=2540.6MB, alloc=4.6MB, time=225.01 memory used=2544.4MB, alloc=4.6MB, time=225.54 memory used=2548.2MB, alloc=4.6MB, time=226.09 memory used=2552.0MB, alloc=4.6MB, time=226.62 memory used=2555.9MB, alloc=4.6MB, time=227.16 x[1] = 3.4 y2[1] (analytic) = 0.03320180742053898571779846023431 y2[1] (numeric) = -6.8475390981942055655643692292603 absolute error = 6.8807409056147445512821676894946 relative error = 20723.994987568797777641898884878 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 1.2555411020268313192499024293637 y1[1] (numeric) = 7.3073165861213885461439637158612 absolute error = 6.0517754840945572268940612864975 relative error = 482.00536599917927882707903874884 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2559.7MB, alloc=4.6MB, time=227.70 NO POLE NO POLE memory used=2563.5MB, alloc=4.6MB, time=228.23 memory used=2567.3MB, alloc=4.6MB, time=228.76 memory used=2571.1MB, alloc=4.6MB, time=229.29 memory used=2574.9MB, alloc=4.6MB, time=229.82 memory used=2578.7MB, alloc=4.6MB, time=230.37 memory used=2582.6MB, alloc=4.6MB, time=230.90 memory used=2586.4MB, alloc=4.6MB, time=231.43 memory used=2590.2MB, alloc=4.6MB, time=231.97 memory used=2594.0MB, alloc=4.6MB, time=232.52 memory used=2597.8MB, alloc=4.6MB, time=233.06 memory used=2601.6MB, alloc=4.6MB, time=233.58 memory used=2605.4MB, alloc=4.6MB, time=234.11 memory used=2609.3MB, alloc=4.6MB, time=234.65 memory used=2613.1MB, alloc=4.6MB, time=235.18 memory used=2616.9MB, alloc=4.6MB, time=235.70 memory used=2620.7MB, alloc=4.6MB, time=236.23 memory used=2624.5MB, alloc=4.6MB, time=236.76 memory used=2628.3MB, alloc=4.6MB, time=237.32 memory used=2632.1MB, alloc=4.6MB, time=237.87 x[1] = 3.5 y2[1] (analytic) = 0.06354331270920366230134237332824 y2[1] (numeric) = -7.3521471826580842665616385888394 absolute error = 7.4156904953672879288629809621676 relative error = 11670.292559823047456696703352757 % Correct digits = -2 h = 0.005 y1[1] (analytic) = 1.3507832276896198481203688000436 y1[1] (numeric) = 8.1172515914045532606458051106823 absolute error = 6.7664683637149334125254363106387 relative error = 500.92925533938583934337446932971 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2636.0MB, alloc=4.6MB, time=238.40 NO POLE NO POLE memory used=2639.8MB, alloc=4.6MB, time=238.93 memory used=2643.6MB, alloc=4.6MB, time=239.47 memory used=2647.4MB, alloc=4.6MB, time=240.01 memory used=2651.2MB, alloc=4.6MB, time=240.54 memory used=2655.0MB, alloc=4.6MB, time=241.09 memory used=2658.8MB, alloc=4.6MB, time=241.62 memory used=2662.7MB, alloc=4.6MB, time=242.17 memory used=2666.5MB, alloc=4.6MB, time=242.70 memory used=2670.3MB, alloc=4.6MB, time=243.23 memory used=2674.1MB, alloc=4.6MB, time=243.78 memory used=2677.9MB, alloc=4.6MB, time=244.31 memory used=2681.7MB, alloc=4.6MB, time=244.84 memory used=2685.6MB, alloc=4.6MB, time=245.37 memory used=2689.4MB, alloc=4.6MB, time=245.90 memory used=2693.2MB, alloc=4.6MB, time=246.43 memory used=2697.0MB, alloc=4.6MB, time=246.98 memory used=2700.8MB, alloc=4.6MB, time=247.51 memory used=2704.6MB, alloc=4.6MB, time=248.04 memory used=2708.4MB, alloc=4.6MB, time=248.58 memory used=2712.3MB, alloc=4.6MB, time=249.11 x[1] = 3.6 y2[1] (analytic) = 0.10324158366585299412970827473406 y2[1] (numeric) = -7.86220206454125368299520730998 absolute error = 7.9654436482071066771249155847141 relative error = 7715.344307374922369267615930377 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.4425204432948523842667273474927 y1[1] (numeric) = 8.9779275436096520316827224606739 absolute error = 7.5354071003147996474159951131812 relative error = 522.37783771737896528550808907247 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2716.1MB, alloc=4.6MB, time=249.65 NO POLE NO POLE memory used=2719.9MB, alloc=4.6MB, time=250.20 memory used=2723.7MB, alloc=4.6MB, time=250.74 memory used=2727.5MB, alloc=4.6MB, time=251.28 memory used=2731.3MB, alloc=4.6MB, time=251.82 memory used=2735.1MB, alloc=4.6MB, time=252.36 memory used=2739.0MB, alloc=4.6MB, time=252.91 memory used=2742.8MB, alloc=4.6MB, time=253.44 memory used=2746.6MB, alloc=4.6MB, time=253.99 memory used=2750.4MB, alloc=4.6MB, time=254.51 memory used=2754.2MB, alloc=4.6MB, time=255.04 memory used=2758.0MB, alloc=4.6MB, time=255.59 memory used=2761.8MB, alloc=4.6MB, time=256.15 memory used=2765.7MB, alloc=4.6MB, time=256.67 memory used=2769.5MB, alloc=4.6MB, time=257.23 memory used=2773.3MB, alloc=4.6MB, time=257.77 memory used=2777.1MB, alloc=4.6MB, time=258.31 memory used=2780.9MB, alloc=4.6MB, time=258.84 memory used=2784.7MB, alloc=4.6MB, time=259.36 memory used=2788.6MB, alloc=4.6MB, time=259.89 x[1] = 3.7 y2[1] (analytic) = 0.1518999682895918411643298936456 y2[1] (numeric) = -8.3767871359098712542607119939953 absolute error = 8.5286871041994630954250418876409 relative error = 5614.6733934399690196106397849492 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.5298361409084932132107776257012 y1[1] (numeric) = 9.8898429614834835336157947178968 absolute error = 8.3600068205749903204050170921956 relative error = 546.46419946716647415710830613028 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2792.4MB, alloc=4.6MB, time=260.42 NO POLE NO POLE memory used=2796.2MB, alloc=4.6MB, time=260.97 memory used=2800.0MB, alloc=4.6MB, time=261.51 memory used=2803.8MB, alloc=4.6MB, time=262.07 memory used=2807.6MB, alloc=4.6MB, time=262.59 memory used=2811.4MB, alloc=4.6MB, time=263.12 memory used=2815.3MB, alloc=4.6MB, time=263.65 memory used=2819.1MB, alloc=4.6MB, time=264.18 memory used=2822.9MB, alloc=4.6MB, time=264.71 memory used=2826.7MB, alloc=4.6MB, time=265.24 memory used=2830.5MB, alloc=4.6MB, time=265.77 memory used=2834.3MB, alloc=4.6MB, time=266.30 memory used=2838.1MB, alloc=4.6MB, time=266.86 memory used=2842.0MB, alloc=4.6MB, time=267.39 memory used=2845.8MB, alloc=4.6MB, time=267.92 memory used=2849.6MB, alloc=4.6MB, time=268.45 memory used=2853.4MB, alloc=4.6MB, time=268.98 memory used=2857.2MB, alloc=4.6MB, time=269.50 memory used=2861.0MB, alloc=4.6MB, time=270.03 memory used=2864.8MB, alloc=4.6MB, time=270.58 x[1] = 3.8 memory used=2868.7MB, alloc=4.6MB, time=271.11 y2[1] (analytic) = 0.20903228808558330000343182564927 y2[1] (numeric) = -8.8950299671763508003970469770927 absolute error = 9.104062255261934100400478802742 relative error = 4355.3377990746062568360700842705 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.6118578909427190757335860861189 y1[1] (numeric) = 10.853406837278926213733341797243 absolute error = 9.2415489463362071379997557111241 relative error = 573.34762563535608594313891642213 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2872.5MB, alloc=4.6MB, time=271.64 memory used=2876.3MB, alloc=4.6MB, time=272.17 memory used=2880.1MB, alloc=4.6MB, time=272.73 memory used=2883.9MB, alloc=4.6MB, time=273.27 memory used=2887.7MB, alloc=4.6MB, time=273.82 memory used=2891.6MB, alloc=4.6MB, time=274.36 memory used=2895.4MB, alloc=4.6MB, time=274.88 memory used=2899.2MB, alloc=4.6MB, time=275.42 memory used=2903.0MB, alloc=4.6MB, time=275.96 memory used=2906.8MB, alloc=4.6MB, time=276.51 memory used=2910.6MB, alloc=4.6MB, time=277.05 memory used=2914.4MB, alloc=4.6MB, time=277.58 memory used=2918.3MB, alloc=4.6MB, time=278.10 memory used=2922.1MB, alloc=4.6MB, time=278.65 memory used=2925.9MB, alloc=4.6MB, time=279.19 memory used=2929.7MB, alloc=4.6MB, time=279.73 memory used=2933.5MB, alloc=4.6MB, time=280.27 memory used=2937.3MB, alloc=4.6MB, time=280.81 memory used=2941.1MB, alloc=4.6MB, time=281.35 memory used=2945.0MB, alloc=4.6MB, time=281.90 x[1] = 3.9 y2[1] (analytic) = 0.27406769579985987062766951538565 y2[1] (numeric) = -9.4161110241274148034841901452408 absolute error = 9.6901787199272746741118596606264 relative error = 3535.6880319830197264564449008196 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.6877661591839738180908881253787 y1[1] (numeric) = 11.868943494489753737984769427084 absolute error = 10.181177335305779919893881301705 relative error = 603.23388284004499426719076224062 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=2948.8MB, alloc=4.6MB, time=282.45 NO POLE NO POLE memory used=2952.6MB, alloc=4.6MB, time=282.98 memory used=2956.4MB, alloc=4.6MB, time=283.53 memory used=2960.2MB, alloc=4.6MB, time=284.06 memory used=2964.0MB, alloc=4.6MB, time=284.61 memory used=2967.8MB, alloc=4.6MB, time=285.16 memory used=2971.7MB, alloc=4.6MB, time=285.69 memory used=2975.5MB, alloc=4.6MB, time=286.22 memory used=2979.3MB, alloc=4.6MB, time=286.78 memory used=2983.1MB, alloc=4.6MB, time=287.30 memory used=2986.9MB, alloc=4.6MB, time=287.83 memory used=2990.7MB, alloc=4.6MB, time=288.36 memory used=2994.6MB, alloc=4.6MB, time=288.90 memory used=2998.4MB, alloc=4.6MB, time=289.44 memory used=3002.2MB, alloc=4.6MB, time=289.98 memory used=3006.0MB, alloc=4.6MB, time=290.51 memory used=3009.8MB, alloc=4.6MB, time=291.06 memory used=3013.6MB, alloc=4.6MB, time=291.59 memory used=3017.4MB, alloc=4.6MB, time=292.12 memory used=3021.3MB, alloc=4.6MB, time=292.67 x[1] = 4 y2[1] (analytic) = 0.34635637913638808536083181690225 y2[1] (numeric) = -9.9392718564390514829657028703087 absolute error = 10.285628235575439568326534687211 relative error = 2969.6661748288945851547757754111 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.7568024953079282513726390945118 y1[1] (numeric) = 12.93669829156770364099174565379 absolute error = 11.179895796259775389619106559278 relative error = 636.37749981110934626273045523314 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=3025.1MB, alloc=4.6MB, time=293.20 NO POLE NO POLE memory used=3028.9MB, alloc=4.6MB, time=293.73 memory used=3032.7MB, alloc=4.6MB, time=294.26 memory used=3036.5MB, alloc=4.6MB, time=294.79 memory used=3040.3MB, alloc=4.6MB, time=295.32 memory used=3044.1MB, alloc=4.6MB, time=295.85 memory used=3048.0MB, alloc=4.6MB, time=296.39 memory used=3051.8MB, alloc=4.6MB, time=296.94 memory used=3055.6MB, alloc=4.6MB, time=297.50 memory used=3059.4MB, alloc=4.6MB, time=298.03 memory used=3063.2MB, alloc=4.6MB, time=298.58 memory used=3067.0MB, alloc=4.6MB, time=299.11 memory used=3070.8MB, alloc=4.6MB, time=299.64 memory used=3074.7MB, alloc=4.6MB, time=300.17 memory used=3078.5MB, alloc=4.6MB, time=300.71 memory used=3082.3MB, alloc=4.6MB, time=301.26 memory used=3086.1MB, alloc=4.6MB, time=301.79 memory used=3089.9MB, alloc=4.6MB, time=302.32 memory used=3093.7MB, alloc=4.6MB, time=302.86 memory used=3097.5MB, alloc=4.6MB, time=303.39 memory used=3101.4MB, alloc=4.6MB, time=303.92 x[1] = 4.1 y2[1] (analytic) = 0.42517605346673108846497132034021 y2[1] (numeric) = -10.463822675861441976971404756208 absolute error = 10.888998729328173065436376076548 relative error = 2561.056447215978655585975631183 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.8182771110644105042650370243584 y1[1] (numeric) = 14.056844114632143628579067035687 absolute error = 12.238567003567733124314030011329 relative error = 673.08590803320050685128721369625 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3105.2MB, alloc=4.6MB, time=304.46 memory used=3109.0MB, alloc=4.6MB, time=304.99 memory used=3112.8MB, alloc=4.6MB, time=305.52 memory used=3116.6MB, alloc=4.6MB, time=305.83 memory used=3120.4MB, alloc=4.6MB, time=306.05 memory used=3124.3MB, alloc=4.6MB, time=306.28 memory used=3128.1MB, alloc=4.6MB, time=306.50 memory used=3131.9MB, alloc=4.6MB, time=306.72 memory used=3135.7MB, alloc=4.6MB, time=306.94 memory used=3139.5MB, alloc=4.6MB, time=307.17 memory used=3143.3MB, alloc=4.6MB, time=307.39 memory used=3147.1MB, alloc=4.6MB, time=307.61 memory used=3151.0MB, alloc=4.6MB, time=307.83 memory used=3154.8MB, alloc=4.6MB, time=308.06 memory used=3158.6MB, alloc=4.6MB, time=308.28 memory used=3162.4MB, alloc=4.6MB, time=308.50 memory used=3166.2MB, alloc=4.6MB, time=308.72 memory used=3170.0MB, alloc=4.6MB, time=308.94 memory used=3173.8MB, alloc=4.6MB, time=309.17 memory used=3177.7MB, alloc=4.6MB, time=309.39 x[1] = 4.2 y2[1] (analytic) = 0.50973917865930042234445511862287 y2[1] (numeric) = -10.989149248355138852131756852309 absolute error = 11.498888427014439274476211970932 relative error = 2255.8376731524630755332472948647 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.8715757724135880600185770979088 y1[1] (numeric) = 15.229488594299326751601363966252 absolute error = 13.357912821885738691582786868343 relative error = 713.72546165519903945756013954748 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=3181.5MB, alloc=4.6MB, time=309.61 NO POLE NO POLE memory used=3185.3MB, alloc=4.6MB, time=309.83 memory used=3189.1MB, alloc=4.6MB, time=310.06 memory used=3192.9MB, alloc=4.6MB, time=310.28 memory used=3196.7MB, alloc=4.6MB, time=310.50 memory used=3200.5MB, alloc=4.6MB, time=310.73 memory used=3204.4MB, alloc=4.6MB, time=310.95 memory used=3208.2MB, alloc=4.6MB, time=311.18 memory used=3212.0MB, alloc=4.6MB, time=311.40 memory used=3215.8MB, alloc=4.6MB, time=311.62 memory used=3219.6MB, alloc=4.6MB, time=311.85 memory used=3223.4MB, alloc=4.6MB, time=312.07 memory used=3227.3MB, alloc=4.6MB, time=312.29 memory used=3231.1MB, alloc=4.6MB, time=312.52 memory used=3234.9MB, alloc=4.6MB, time=312.74 memory used=3238.7MB, alloc=4.6MB, time=312.96 memory used=3242.5MB, alloc=4.6MB, time=313.19 memory used=3246.3MB, alloc=4.6MB, time=313.41 memory used=3250.1MB, alloc=4.6MB, time=313.64 memory used=3254.0MB, alloc=4.6MB, time=313.86 x[1] = 4.3 y2[1] (analytic) = 0.59920082792002470309323760366397 y2[1] (numeric) = -11.514719031314549483535678386082 absolute error = 12.113919859234574186628915989746 relative error = 2021.6794261257960595101099445187 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.9161659367494549840317093602846 y1[1] (numeric) = 16.454681974523063099951940950907 absolute error = 14.538516037773608115920231590622 relative error = 758.72948991236383916458763821003 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=3257.8MB, alloc=4.6MB, time=314.08 NO POLE NO POLE memory used=3261.6MB, alloc=4.6MB, time=314.31 memory used=3265.4MB, alloc=4.6MB, time=314.53 memory used=3269.2MB, alloc=4.6MB, time=314.76 memory used=3273.0MB, alloc=4.6MB, time=314.98 memory used=3276.8MB, alloc=4.6MB, time=315.21 memory used=3280.7MB, alloc=4.6MB, time=315.43 memory used=3284.5MB, alloc=4.6MB, time=315.66 memory used=3288.3MB, alloc=4.6MB, time=315.88 memory used=3292.1MB, alloc=4.6MB, time=316.11 memory used=3295.9MB, alloc=4.6MB, time=316.34 memory used=3299.7MB, alloc=4.6MB, time=316.56 memory used=3303.5MB, alloc=4.6MB, time=316.78 memory used=3307.4MB, alloc=4.6MB, time=317.01 memory used=3311.2MB, alloc=4.6MB, time=317.24 memory used=3315.0MB, alloc=4.6MB, time=317.46 memory used=3318.8MB, alloc=4.6MB, time=317.69 memory used=3322.6MB, alloc=4.6MB, time=317.91 memory used=3326.4MB, alloc=4.6MB, time=318.13 memory used=3330.3MB, alloc=4.6MB, time=318.35 x[1] = 4.4 y2[1] (analytic) = 0.69266713002158031688086025778229 y2[1] (numeric) = -12.04008649455761595526129522901 absolute error = 12.732753624579196272142155486792 relative error = 1838.2211415434860211752944650337 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.9516020738895159540353923333804 y1[1] (numeric) = 17.732425554823953118089786591595 absolute error = 15.780823480934437164054394258215 relative error = 808.60866526358388843657340918623 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=3334.1MB, alloc=4.6MB, time=318.58 NO POLE NO POLE memory used=3337.9MB, alloc=4.6MB, time=318.80 memory used=3341.7MB, alloc=4.6MB, time=319.02 memory used=3345.5MB, alloc=4.6MB, time=319.25 memory used=3349.3MB, alloc=4.6MB, time=319.47 memory used=3353.1MB, alloc=4.6MB, time=319.69 memory used=3357.0MB, alloc=4.6MB, time=319.92 memory used=3360.8MB, alloc=4.6MB, time=320.14 memory used=3364.6MB, alloc=4.6MB, time=320.36 memory used=3368.4MB, alloc=4.6MB, time=320.58 memory used=3372.2MB, alloc=4.6MB, time=320.81 memory used=3376.0MB, alloc=4.6MB, time=321.04 memory used=3379.8MB, alloc=4.6MB, time=321.26 memory used=3383.7MB, alloc=4.6MB, time=321.48 memory used=3387.5MB, alloc=4.6MB, time=321.71 memory used=3391.3MB, alloc=4.6MB, time=321.93 memory used=3395.1MB, alloc=4.6MB, time=322.15 memory used=3398.9MB, alloc=4.6MB, time=322.37 memory used=3402.7MB, alloc=4.6MB, time=322.59 memory used=3406.5MB, alloc=4.6MB, time=322.81 memory used=3410.4MB, alloc=4.6MB, time=323.03 x[1] = 4.5 y2[1] (analytic) = 0.78920420056922029401951817520617 y2[1] (numeric) = -12.5648975719161214852523483141 absolute error = 13.354101772485341779271866489306 relative error = 1692.0971483493855476620133853364 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.9775301176650970553891350144986 y1[1] (numeric) = 19.062680621555218672757501813049 absolute error = 17.08515050389012161736836679855 relative error = 863.96411115411203390858164515232 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=3414.2MB, alloc=4.6MB, time=323.25 NO POLE NO POLE memory used=3418.0MB, alloc=4.6MB, time=323.48 memory used=3421.8MB, alloc=4.6MB, time=323.70 memory used=3425.6MB, alloc=4.6MB, time=323.92 memory used=3429.4MB, alloc=4.6MB, time=324.14 memory used=3433.3MB, alloc=4.6MB, time=324.37 memory used=3437.1MB, alloc=4.6MB, time=324.59 memory used=3440.9MB, alloc=4.6MB, time=324.81 memory used=3444.7MB, alloc=4.6MB, time=325.03 memory used=3448.5MB, alloc=4.6MB, time=325.25 memory used=3452.3MB, alloc=4.6MB, time=325.47 memory used=3456.1MB, alloc=4.6MB, time=325.69 memory used=3460.0MB, alloc=4.6MB, time=325.92 memory used=3463.8MB, alloc=4.6MB, time=326.15 memory used=3467.6MB, alloc=4.6MB, time=326.37 memory used=3471.4MB, alloc=4.6MB, time=326.60 memory used=3475.2MB, alloc=4.6MB, time=326.82 memory used=3479.0MB, alloc=4.6MB, time=327.04 memory used=3482.8MB, alloc=4.6MB, time=327.27 memory used=3486.7MB, alloc=4.6MB, time=327.49 x[1] = 4.6 y2[1] (analytic) = 0.88784747306494548257009217877081 y2[1] (numeric) = -13.088893198947804532857627716007 absolute error = 13.976740672012750015427719894778 relative error = 1574.2276794192509068814935643907 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.9936910036334644561381046599088 y1[1] (numeric) = 20.445377778966875972829810910282 absolute error = 18.451686775333411516691706250373 relative error = 925.50383894523065452084105219534 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=3490.5MB, alloc=4.6MB, time=327.71 NO POLE NO POLE memory used=3494.3MB, alloc=4.6MB, time=327.93 memory used=3498.1MB, alloc=4.6MB, time=328.15 memory used=3501.9MB, alloc=4.6MB, time=328.38 memory used=3505.7MB, alloc=4.6MB, time=328.60 memory used=3509.5MB, alloc=4.6MB, time=328.82 memory used=3513.4MB, alloc=4.6MB, time=329.04 memory used=3517.2MB, alloc=4.6MB, time=329.26 memory used=3521.0MB, alloc=4.6MB, time=329.48 memory used=3524.8MB, alloc=4.6MB, time=329.71 memory used=3528.6MB, alloc=4.6MB, time=329.94 memory used=3532.4MB, alloc=4.6MB, time=330.16 memory used=3536.3MB, alloc=4.6MB, time=330.38 memory used=3540.1MB, alloc=4.6MB, time=330.60 memory used=3543.9MB, alloc=4.6MB, time=330.82 memory used=3547.7MB, alloc=4.6MB, time=331.04 memory used=3551.5MB, alloc=4.6MB, time=331.27 memory used=3555.3MB, alloc=4.6MB, time=331.49 memory used=3559.1MB, alloc=4.6MB, time=331.71 memory used=3563.0MB, alloc=4.6MB, time=331.94 x[1] = 4.7 y2[1] (analytic) = 0.98761133653710926284949170367289 y2[1] (numeric) = -13.611911901422630557018795357069 absolute error = 14.599523237959739819868287060742 relative error = 1478.2660645786507919807539355309 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.999923257564100884179536541575 y1[1] (numeric) = 21.880426586835341565207122970732 absolute error = 19.880503329271240681027586429157 relative error = 994.06330988348123203362010513639 % Correct digits = 0 h = 0.005 TOP MAIN SOLVE Loop memory used=3566.8MB, alloc=4.6MB, time=332.16 NO POLE NO POLE memory used=3570.6MB, alloc=4.6MB, time=332.38 memory used=3574.4MB, alloc=4.6MB, time=332.60 memory used=3578.2MB, alloc=4.6MB, time=332.82 memory used=3582.0MB, alloc=4.6MB, time=333.05 memory used=3585.8MB, alloc=4.6MB, time=333.27 memory used=3589.7MB, alloc=4.6MB, time=333.49 memory used=3593.5MB, alloc=4.6MB, time=333.71 memory used=3597.3MB, alloc=4.6MB, time=333.93 memory used=3601.1MB, alloc=4.6MB, time=334.15 memory used=3604.9MB, alloc=4.6MB, time=334.38 memory used=3608.7MB, alloc=4.6MB, time=334.60 memory used=3612.5MB, alloc=4.6MB, time=334.82 memory used=3616.4MB, alloc=4.6MB, time=335.04 memory used=3620.2MB, alloc=4.6MB, time=335.27 memory used=3624.0MB, alloc=4.6MB, time=335.49 memory used=3627.8MB, alloc=4.6MB, time=335.71 memory used=3631.6MB, alloc=4.6MB, time=335.94 memory used=3635.4MB, alloc=4.6MB, time=336.17 memory used=3639.3MB, alloc=4.6MB, time=336.39 memory used=3643.1MB, alloc=4.6MB, time=336.61 x[1] = 4.8 y2[1] (analytic) = 1.0874989834394465693202152576495 y2[1] (numeric) = -14.133891408719922237500221283553 absolute error = 15.221390392159368806820436541202 relative error = 1399.669390404254721851428985776 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.9961646088358406717815964665036 y1[1] (numeric) = 23.36772540836246216043186295471 absolute error = 21.371560799526621488650266488206 relative error = 1070.6311846692079314937886262015 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=3646.9MB, alloc=4.6MB, time=336.84 NO POLE NO POLE memory used=3650.7MB, alloc=4.6MB, time=337.06 memory used=3654.5MB, alloc=4.6MB, time=337.29 memory used=3658.3MB, alloc=4.6MB, time=337.51 memory used=3662.1MB, alloc=4.6MB, time=337.73 memory used=3666.0MB, alloc=4.6MB, time=337.95 memory used=3669.8MB, alloc=4.6MB, time=338.17 memory used=3673.6MB, alloc=4.6MB, time=338.40 memory used=3677.4MB, alloc=4.6MB, time=338.62 memory used=3681.2MB, alloc=4.6MB, time=338.84 memory used=3685.0MB, alloc=4.6MB, time=339.06 memory used=3688.8MB, alloc=4.6MB, time=339.28 memory used=3692.7MB, alloc=4.6MB, time=339.51 memory used=3696.5MB, alloc=4.6MB, time=339.73 memory used=3700.3MB, alloc=4.6MB, time=339.96 memory used=3704.1MB, alloc=4.6MB, time=340.18 memory used=3707.9MB, alloc=4.6MB, time=340.40 memory used=3711.7MB, alloc=4.6MB, time=340.62 memory used=3715.5MB, alloc=4.6MB, time=340.86 memory used=3719.4MB, alloc=4.6MB, time=341.08 x[1] = 4.9 y2[1] (analytic) = 1.1865123694225754044943291441219 y2[1] (numeric) = -14.654869276015817352175224286195 absolute error = 15.841381645438392756669553430317 relative error = 1335.1214916661772880995970283925 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.9824526126243325122763772499183 y1[1] (numeric) = 24.907171369947016464629200905442 absolute error = 22.924718757322683952352823655524 relative error = 1156.3816764818092499287571806219 % Correct digits = -1 h = 0.005 TOP MAIN SOLVE Loop memory used=3723.2MB, alloc=4.6MB, time=341.30 NO POLE NO POLE memory used=3727.0MB, alloc=4.6MB, time=341.53 memory used=3730.8MB, alloc=4.6MB, time=341.75 memory used=3734.6MB, alloc=4.6MB, time=341.98 memory used=3738.4MB, alloc=4.6MB, time=342.19 memory used=3742.2MB, alloc=4.6MB, time=342.42 memory used=3746.1MB, alloc=4.6MB, time=342.64 memory used=3749.9MB, alloc=4.6MB, time=342.87 memory used=3753.7MB, alloc=4.6MB, time=343.09 memory used=3757.5MB, alloc=4.6MB, time=343.31 memory used=3761.3MB, alloc=4.6MB, time=343.53 memory used=3765.1MB, alloc=4.6MB, time=343.75 memory used=3769.0MB, alloc=4.6MB, time=343.98 memory used=3772.8MB, alloc=4.6MB, time=344.20 memory used=3776.6MB, alloc=4.6MB, time=344.42 memory used=3780.4MB, alloc=4.6MB, time=344.65 memory used=3784.2MB, alloc=4.6MB, time=344.87 memory used=3788.0MB, alloc=4.6MB, time=345.09 memory used=3791.8MB, alloc=4.6MB, time=345.32 memory used=3795.7MB, alloc=4.6MB, time=345.54 x[1] = 5 y2[1] (analytic) = 1.2836621854632262644666391715136 y2[1] (numeric) = -15.17498250904436289908826151596 absolute error = 16.458644694507589163554900687474 relative error = 1282.163242081348082470554368937 % Correct digits = -1 h = 0.005 y1[1] (analytic) = 1.958924274663138468893154406156 y1[1] (numeric) = 26.498670333313944434209235930007 absolute error = 24.539746058650805965316081523851 relative error = 1252.7153997757632689202322252368 % Correct digits = -1 h = 0.005 Finished! diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 980 Total Elapsed Time = 5 Minutes 45 Seconds Elapsed Time(since restart) = 5 Minutes 45 Seconds Time to Timeout = 4 Minutes 14 Seconds Percent Done = 100.1 % > quit memory used=3798.3MB, alloc=4.6MB, time=345.69