|\^/| 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 > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > > > > local ret; > > if ((((array_x[1] >= glob_next_display) and not glob_neg_h) or ((array_x[1] <= glob_next_display) and glob_neg_h)) or (glob_next_display = 0.0)) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1 > ; > return(ret); > > # End Function number 3 > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; if glob_next_display <= array_x[1] and not glob_neg_h or array_x[1] <= glob_next_display and glob_neg_h or glob_next_display = 0. then ret := true else ret := false end if; return ret end proc > # Begin Function number 4 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > > > > > > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 4 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 4 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3 > ; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 4 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 4 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3 > ; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 3 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2 > ; > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > > # End Function number 4 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # Begin Function number 5 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > > # End Function number 5 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # Begin Function number 6 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > > > > > > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > > # End Function number 6 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 7 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > > > > > > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found ) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if ( not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found ) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if (array_pole[1] > array_poles[2,1]) then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > if (reached_interval()) then # if number 3 > display_pole(); > fi;# end if 3 > > # End Function number 7 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= omniabs(array_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= omniabs(array_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; if reached_interval() then display_pole() end if end proc > # Begin Function number 8 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > > local iii; > > > > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2 > ; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3 > ; > > # End Function number 8 > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 9 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_m1[1] * (array_y2[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp5[1] := array_y1[1] - array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre add FULL CONST $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_y1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp5[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre add FULL CONST $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_y1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp5[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre add FULL CONST $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_y1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp5[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre add FULL CONST $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_y1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp5[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_m1,array_y2,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit FULL - NOT FULL sub $eq_no = 2 > array_tmp5[kkk] := array_y1[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > > #BOTTOM ATOMALL ??? > # End Function number 9 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; array_tmp1[1] := array_m1[1]*array_y2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[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_tmp5[1] := array_y1[1] - array_const_1D0[1]; if not array_y2_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_y2, 1); array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[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_tmp5[2] := array_y1[2]; if not array_y2_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_y2, 1); array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[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_tmp5[3] := array_y1[3]; if not array_y2_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_y2, 1); array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[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_tmp5[4] := array_y1[4]; if not array_y2_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_y2, 1); array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := array_y1[5]; if not array_y2_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp5[kkk] := array_y1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > fprintf(fd,""); > if (secs >= 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := secs_in; fprintf(fd, ""); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs >= 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := convfloat(secs_in); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > > > > > > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats; > > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > > > > > > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > > local good_digits; > > > fprintf(file,""); > if (rel_error <> -1.0) then # if number 11 > if (rel_error <> 0.0) then # if number 12 > good_digits := -trunc(log10(rel_error/100.0)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 12 > ; > else > fprintf(file,"Unknown"); > fi;# end if 11 > ; > fprintf(file,""); > > # End Function number 9 > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if rel_error <> 0. then good_digits := -trunc(log10(rel_error/100.0)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # Begin Function number 10 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 10 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 11 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 11 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 12 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 11 > fprintf(file,"NA"); > elif (pole = 1) then # if number 12 > fprintf(file,"Real"); > elif (pole = 2) then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 12 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 13 > logstart := proc(file) > fprintf(file,""); > # End Function number 13 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 14 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 14 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 15 > not_reached_end := proc(x,x_end) > global neg_h; > local ret; > > > > if ((glob_neg_h and (x > x_end)) or (( not glob_neg_h) and (x < x_end))) then # if number 13 > ret := true; > else > ret := false; > fi;# end if 13 > ; > > > ret; > > # End Function number 15 > end; not_reached_end := proc(x, x_end) local ret; global neg_h; if glob_neg_h and x_end < x or not glob_neg_h and x < x_end then ret := true else ret := false end if; ret end proc > # Begin Function number 16 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > > > > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > > # End Function number 16 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # Begin Function number 17 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > > > > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > > # End Function number 17 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # Begin Function number 18 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > > > > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr; > > # End Function number 18 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 19 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 19 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 20 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > > > > if (nnn <= glob_max_terms) then # if number 13 > if (array_fact_1[nnn] = 0) then # if number 14 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 20 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # Begin Function number 21 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > > > > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13 > if (array_fact_2[mmm,nnn] = 0) then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 21 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # Begin Function number 22 > convfp := proc(mmm) > (mmm); > > # End Function number 22 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 23 > convfloat := proc(mmm) > (mmm); > > # End Function number 23 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > > > > > > > > > > > > > > > > > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(1.0 + cos(x)); > end; exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc > exact_soln_y2 := proc(x) > return(1.0 + sin(x)); > end; exact_soln_y2 := 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 > glob_max_terms, > glob_iolevel, > ALWAYS, > DEBUGMASSIVE, > INFO, > DEBUGL, > #Top Generate Globals Decl > glob_log10abserr, > glob_normmax, > glob_warned, > glob_max_iter, > glob_look_poles, > glob_optimal_done, > sec_in_minute, > glob_max_minutes, > MAX_UNCHANGED, > glob_h, > glob_almost_1, > days_in_year, > hours_in_day, > glob_relerr, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_not_yet_finished, > glob_current_iter, > glob_dump_analytic, > glob_display_interval, > glob_hmin, > glob_max_opt_iter, > glob_good_digits, > glob_iter, > glob_orig_start_sec, > glob_warned2, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_optimal_expect_sec, > glob_no_eqs, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_start, > glob_smallish_float, > glob_max_trunc_err, > glob_clock_start_sec, > djd_debug, > glob_log10relerr, > glob_max_sec, > glob_unchanged_h_cnt, > glob_log10_relerr, > glob_clock_sec, > glob_html_log, > glob_neg_h, > glob_hmin_init, > glob_initial_pass, > glob_log10normmin, > glob_subiter_method, > glob_small_float, > glob_max_rel_trunc_err, > glob_large_float, > glob_reached_optimal_h, > years_in_century, > djd_debug2, > glob_abserr, > glob_next_display, > centuries_in_millinium, > min_in_hour, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > array_const_1D0, > #END CONST > array_y2_init, > array_y1_init, > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_1st_rel_error, > array_last_rel_error, > array_pole, > array_m1, > array_y1, > array_x, > array_y2, > array_norms, > array_type_pole, > array_poles, > array_fact_2, > array_y2_set_initial, > array_y2_higher, > array_y1_higher_work2, > array_y1_higher_work, > array_complex_pole, > array_y1_set_initial, > array_real_pole, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > DEBUGMASSIVE := 4; > INFO := 2; > DEBUGL := 3; > glob_log10abserr := 0.0; > glob_normmax := 0.0; > glob_warned := false; > glob_max_iter := 1000; > glob_look_poles := false; > glob_optimal_done := false; > sec_in_minute := 60; > glob_max_minutes := 0.0; > MAX_UNCHANGED := 10; > glob_h := 0.1; > glob_almost_1 := 0.9990; > days_in_year := 365; > hours_in_day := 24; > glob_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_last_good_h := 0.1; > glob_hmax := 1.0; > glob_not_yet_finished := true; > glob_current_iter := 0; > glob_dump_analytic := false; > glob_display_interval := 0.0; > glob_hmin := 0.00000000001; > glob_max_opt_iter := 10; > glob_good_digits := 0; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_warned2 := false; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_hours := 0.0; > glob_disp_incr := 0.1; > glob_display_flag := true; > glob_dump := false; > glob_optimal_expect_sec := 0.1; > glob_no_eqs := 0; > glob_not_yet_start_msg := true; > glob_curr_iter_when_opt := 0; > glob_start := 0; > glob_smallish_float := 0.1e-100; > glob_max_trunc_err := 0.1e-10; > glob_clock_start_sec := 0.0; > djd_debug := true; > glob_log10relerr := 0.0; > glob_max_sec := 10000.0; > glob_unchanged_h_cnt := 0; > glob_log10_relerr := 0.1e-10; > glob_clock_sec := 0.0; > glob_html_log := true; > glob_neg_h := false; > glob_hmin_init := 0.001; > glob_initial_pass := true; > glob_log10normmin := 0.1; > glob_subiter_method := 3; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_large_float := 9.0e100; > glob_reached_optimal_h := false; > years_in_century := 100; > djd_debug2 := true; > glob_abserr := 0.1e-10; > glob_next_display := 0.0; > centuries_in_millinium := 10; > min_in_hour := 60; > glob_percent_done := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_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/mtest2postode.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 - 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 := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"# testing comment"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.005 ;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10000;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y2_init:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_fact_1:= 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_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > 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_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_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_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_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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[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_y2[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_type_pole[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 <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_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 <=2) 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 <= 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 <= 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 <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_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 <= 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[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_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_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_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_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_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_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_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_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 := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > # testing comment > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.005 ; > glob_display_interval := 0.1; > glob_look_poles := true; > glob_max_iter := 10000; > glob_max_minutes := 10; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1 > ; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := false; > array_y2_set_initial[2,3] := false; > array_y2_set_initial[2,4] := false; > array_y2_set_initial[2,5] := false; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := false; > if (glob_html_log) then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and not_reached_end(array_x[1] , x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3 > ; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 2) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while (subiter <= 2 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > if (reached_interval()) then # if number 4 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 4 > ; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y2 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 - 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,"2012-09-21T00:02:57-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest2") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;") > ; > 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,"mtest2 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest2 maple results") > ; > logitem_str(html_log_file,"c c++ Maple and Maxima") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 - 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 glob_max_terms, glob_iolevel, ALWAYS, DEBUGMASSIVE, INFO, DEBUGL, glob_log10abserr, glob_normmax, glob_warned, glob_max_iter, glob_look_poles, glob_optimal_done, sec_in_minute, glob_max_minutes, MAX_UNCHANGED, glob_h, glob_almost_1, days_in_year, hours_in_day, glob_relerr, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_not_yet_finished, glob_current_iter, glob_dump_analytic, glob_display_interval, glob_hmin, glob_max_opt_iter, glob_good_digits, glob_iter, glob_orig_start_sec, glob_warned2, glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours, glob_disp_incr, glob_display_flag, glob_dump, glob_optimal_expect_sec, glob_no_eqs, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_start, glob_smallish_float, glob_max_trunc_err, glob_clock_start_sec, djd_debug, glob_log10relerr, glob_max_sec, glob_unchanged_h_cnt, glob_log10_relerr, glob_clock_sec, glob_html_log, glob_neg_h, glob_hmin_init, glob_initial_pass, glob_log10normmin, glob_subiter_method, glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_reached_optimal_h, years_in_century, djd_debug2, glob_abserr, glob_next_display, centuries_in_millinium, min_in_hour, glob_percent_done, array_const_0D0, array_const_1, array_const_1D0, array_y2_init, array_y1_init, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_1st_rel_error, array_last_rel_error, array_pole, array_m1, array_y1, array_x, array_y2, array_norms, array_type_pole, array_poles, array_fact_2, array_y2_set_initial, array_y2_higher, array_y1_higher_work2, array_y1_higher_work, array_complex_pole, array_y1_set_initial, array_real_pole, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; DEBUGMASSIVE := 4; INFO := 2; DEBUGL := 3; glob_log10abserr := 0.; glob_normmax := 0.; glob_warned := false; glob_max_iter := 1000; glob_look_poles := false; glob_optimal_done := false; sec_in_minute := 60; glob_max_minutes := 0.; MAX_UNCHANGED := 10; glob_h := 0.1; glob_almost_1 := 0.9990; days_in_year := 365; hours_in_day := 24; glob_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_hmax := 1.0; glob_not_yet_finished := true; glob_current_iter := 0; glob_dump_analytic := false; glob_display_interval := 0.; glob_hmin := 0.1*10^(-10); glob_max_opt_iter := 10; glob_good_digits := 0; glob_iter := 0; glob_orig_start_sec := 0.; glob_warned2 := false; glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_max_hours := 0.; glob_disp_incr := 0.1; glob_display_flag := true; glob_dump := false; glob_optimal_expect_sec := 0.1; glob_no_eqs := 0; glob_not_yet_start_msg := true; glob_curr_iter_when_opt := 0; glob_start := 0; glob_smallish_float := 0.1*10^(-100); glob_max_trunc_err := 0.1*10^(-10); glob_clock_start_sec := 0.; djd_debug := true; glob_log10relerr := 0.; glob_max_sec := 10000.0; glob_unchanged_h_cnt := 0; glob_log10_relerr := 0.1*10^(-10); glob_clock_sec := 0.; glob_html_log := true; glob_neg_h := false; glob_hmin_init := 0.001; glob_initial_pass := true; glob_log10normmin := 0.1; glob_subiter_method := 3; glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_reached_optimal_h := false; years_in_century := 100; djd_debug2 := true; glob_abserr := 0.1*10^(-10); glob_next_display := 0.; centuries_in_millinium := 10; min_in_hour := 60; glob_percent_done := 0.; 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/mtest2postode.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 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 := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "# testing comment"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.005 ;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10000;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y2_init := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_fact_1 := 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_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); 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_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_1st_rel_error[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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[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_y2[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_type_pole[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 <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_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_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 <= 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 <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_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 <= 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[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_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 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_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_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[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_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_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_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 := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.005; glob_display_interval := 0.1; glob_look_poles := true; glob_max_iter := 10000; glob_max_minutes := 10; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := false; array_y2_set_initial[2, 3] := false; array_y2_set_initial[2, 4] := false; array_y2_set_initial[2, 5] := false; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and not_reached_end(array_x[1], x_end) and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 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 := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 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, "2012-09-21T00:02:57-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest2") ; logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;") ; 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, "mtest2 diffeq.mxt"); logitem_str(html_log_file, "mtest2 maple results"); logitem_str(html_log_file, "c c++ Maple and Maxima"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 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/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 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 := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); # testing comment glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.005 ; glob_display_interval := 0.1; glob_look_poles := true; glob_max_iter := 10000; glob_max_minutes := 10; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(1.0 + cos(x)); end; exact_soln_y2 := proc(x) return(1.0 + sin(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 x[1] = 0.1 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=3.1MB, time=0.43 memory used=7.6MB, alloc=4.3MB, time=1.04 memory used=11.4MB, alloc=4.3MB, time=1.62 memory used=15.2MB, alloc=4.4MB, time=2.21 memory used=19.0MB, alloc=4.4MB, time=2.81 memory used=22.8MB, alloc=4.4MB, time=3.45 memory used=26.7MB, alloc=4.4MB, time=4.06 memory used=30.5MB, alloc=4.4MB, time=4.65 memory used=34.3MB, alloc=4.4MB, time=5.24 memory used=38.1MB, alloc=4.4MB, time=5.84 x[1] = 0.2 y1[1] (analytic) = 1.9800665778412416311241965167482 y1[1] (numeric) = 1.9800665778412268551841859998226 absolute error = 1.47759400105169256e-14 relative error = 7.4623450422693995529372187961907e-13 % Correct digits = 14 h = 0.005 y2[1] (analytic) = 1.1986693307950612154594126271184 y2[1] (numeric) = 1.1986693307950577409432354359246 absolute error = 3.4745161771911938e-15 relative error = 2.8986444283900999098554668281786e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=6.47 NO POLE NO POLE memory used=45.7MB, alloc=4.4MB, time=7.07 memory used=49.5MB, alloc=4.4MB, time=7.67 memory used=53.4MB, alloc=4.4MB, time=8.30 memory used=57.2MB, alloc=4.4MB, time=8.93 memory used=61.0MB, alloc=4.4MB, time=9.53 memory used=64.8MB, alloc=4.4MB, time=10.19 memory used=68.6MB, alloc=4.4MB, time=10.81 memory used=72.4MB, alloc=4.4MB, time=11.46 memory used=76.2MB, alloc=4.4MB, time=12.19 memory used=80.1MB, alloc=4.4MB, time=12.80 x[1] = 0.3 y1[1] (analytic) = 1.955336489125606019642310227568 y1[1] (numeric) = 1.9553364891255773091442398299759 absolute error = 2.87104980703975921e-14 relative error = 1.4683149539768702250457943562275e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.295520206661339575105320745685 y2[1] (numeric) = 1.2955202066613297105240326465762 absolute error = 9.8645812880991088e-15 relative error = 7.6143785618913140419113888735939e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=83.9MB, alloc=4.4MB, time=13.41 memory used=87.7MB, alloc=4.4MB, time=14.00 memory used=91.5MB, alloc=4.4MB, time=14.58 memory used=95.3MB, alloc=4.4MB, time=15.18 memory used=99.1MB, alloc=4.4MB, time=15.79 memory used=102.9MB, alloc=4.4MB, time=16.39 memory used=106.8MB, alloc=4.4MB, time=16.97 memory used=110.6MB, alloc=4.4MB, time=17.56 memory used=114.4MB, alloc=4.4MB, time=18.13 memory used=118.2MB, alloc=4.4MB, time=18.69 x[1] = 0.4 y1[1] (analytic) = 1.9210609940028850827985267320518 y1[1] (numeric) = 1.9210609940028437094230565258272 absolute error = 4.13733754702062246e-14 relative error = 2.1536731836919535801808498131944e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.3894183423086504916663117567957 y2[1] (numeric) = 1.3894183423086314693164321835832 absolute error = 1.90223498795732125e-14 relative error = 1.3690872864083377603172378220777e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=19.28 NO POLE NO POLE memory used=125.8MB, alloc=4.4MB, time=19.85 memory used=129.7MB, alloc=4.4MB, time=20.44 memory used=133.5MB, alloc=4.4MB, time=21.03 memory used=137.3MB, alloc=4.4MB, time=21.61 memory used=141.1MB, alloc=4.4MB, time=22.19 memory used=144.9MB, alloc=4.4MB, time=22.78 memory used=148.7MB, alloc=4.4MB, time=23.38 memory used=152.5MB, alloc=4.4MB, time=24.00 memory used=156.4MB, alloc=4.4MB, time=24.61 memory used=160.2MB, alloc=4.4MB, time=25.21 x[1] = 0.5 y1[1] (analytic) = 1.8775825618903727161162815826038 y1[1] (numeric) = 1.8775825618903203592966237993703 absolute error = 5.23568196577832335e-14 relative error = 2.7885228975001641186420965099657e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.4794255386042030002732879352156 y2[1] (numeric) = 1.4794255386041722565895613300533 absolute error = 3.07436837266051623e-14 relative error = 2.0780825343606665034626212675162e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=164.0MB, alloc=4.4MB, time=25.81 memory used=167.8MB, alloc=4.4MB, time=26.43 memory used=171.6MB, alloc=4.4MB, time=27.04 memory used=175.4MB, alloc=4.4MB, time=27.64 memory used=179.2MB, alloc=4.4MB, time=28.25 memory used=183.1MB, alloc=4.4MB, time=28.85 memory used=186.9MB, alloc=4.4MB, time=29.46 memory used=190.7MB, alloc=4.4MB, time=30.07 memory used=194.5MB, alloc=4.4MB, time=30.68 memory used=198.3MB, alloc=4.4MB, time=31.30 x[1] = 0.6 y1[1] (analytic) = 1.8253356149096782972409524989554 y1[1] (numeric) = 1.8253356149096170147326356640928 absolute error = 6.12825083168348626e-14 relative error = 3.3573282532958882000221878937471e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.5646424733950353572009454456587 y2[1] (numeric) = 1.5646424733949905858840014951248 absolute error = 4.47713169439505339e-14 relative error = 2.8614407256121335847492862249450e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=202.1MB, alloc=4.4MB, time=31.89 memory used=205.9MB, alloc=4.4MB, time=32.51 memory used=209.8MB, alloc=4.4MB, time=33.11 memory used=213.6MB, alloc=4.4MB, time=33.72 memory used=217.4MB, alloc=4.4MB, time=34.31 memory used=221.2MB, alloc=4.4MB, time=34.92 memory used=225.0MB, alloc=4.4MB, time=35.52 memory used=228.8MB, alloc=4.4MB, time=36.13 memory used=232.7MB, alloc=4.4MB, time=36.74 memory used=236.5MB, alloc=4.4MB, time=37.36 x[1] = 0.7 y1[1] (analytic) = 1.7648421872844884262558599901919 y1[1] (numeric) = 1.7648421872844206182428652186915 absolute error = 6.78080129947715004e-14 relative error = 3.8421573035437081577920099401987e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.6442176872376910536726143513987 y2[1] (numeric) = 1.6442176872376302548457781470133 absolute error = 6.07988268362043854e-14 relative error = 3.6977358477603579082182945999739e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.4MB, time=37.96 NO POLE NO POLE memory used=244.1MB, alloc=4.4MB, time=38.59 memory used=247.9MB, alloc=4.4MB, time=39.20 memory used=251.7MB, alloc=4.4MB, time=39.82 memory used=255.5MB, alloc=4.4MB, time=40.42 memory used=259.4MB, alloc=4.4MB, time=41.02 memory used=263.2MB, alloc=4.4MB, time=41.62 memory used=267.0MB, alloc=4.4MB, time=42.23 memory used=270.8MB, alloc=4.4MB, time=42.83 memory used=274.6MB, alloc=4.4MB, time=43.42 memory used=278.4MB, alloc=4.4MB, time=44.03 x[1] = 0.8 y1[1] (analytic) = 1.6967067093471654209207499816423 y1[1] (numeric) = 1.6967067093470937881698658273435 absolute error = 7.16327508841542988e-14 relative error = 4.2218699607615818167897249941518e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.7173560908995227616271746105814 y2[1] (numeric) = 1.7173560908994442862703553796332 absolute error = 7.84753568192309482e-14 relative error = 4.5695448506620925754269164389001e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=282.2MB, alloc=4.4MB, time=44.64 memory used=286.1MB, alloc=4.4MB, time=45.26 memory used=289.9MB, alloc=4.4MB, time=45.86 memory used=293.7MB, alloc=4.4MB, time=46.47 memory used=297.5MB, alloc=4.4MB, time=47.07 memory used=301.3MB, alloc=4.4MB, time=47.68 memory used=305.1MB, alloc=4.4MB, time=48.30 memory used=308.9MB, alloc=4.4MB, time=48.92 memory used=312.8MB, alloc=4.4MB, time=49.53 memory used=316.6MB, alloc=4.4MB, time=50.11 x[1] = 0.9 y1[1] (analytic) = 1.6216099682706644564847161514071 y1[1] (numeric) = 1.6216099682705919531447090503113 absolute error = 7.25033400071010958e-14 relative error = 4.4710714305993643604270695719680e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.7833269096274833884613823157136 y2[1] (numeric) = 1.783326909627385977433757870366 absolute error = 9.74110276244453476e-14 relative error = 5.4623202901588805193483146217636e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=320.4MB, alloc=4.4MB, time=50.69 memory used=324.2MB, alloc=4.4MB, time=51.26 memory used=328.0MB, alloc=4.4MB, time=51.82 memory used=331.8MB, alloc=4.4MB, time=52.38 memory used=335.7MB, alloc=4.4MB, time=52.95 memory used=339.5MB, alloc=4.4MB, time=53.51 memory used=343.3MB, alloc=4.4MB, time=54.07 memory used=347.1MB, alloc=4.4MB, time=54.66 memory used=350.9MB, alloc=4.4MB, time=55.22 memory used=354.7MB, alloc=4.4MB, time=55.81 x[1] = 1 y1[1] (analytic) = 1.540302305868139717400936607443 y1[1] (numeric) = 1.5403023058680694991201401994235 absolute error = 7.02182807964080195e-14 relative error = 4.5587337322612031902196251374917e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.8414709848078965066525023216303 y2[1] (numeric) = 1.8414709848077793236888230770753 absolute error = 1.171829636792445550e-13 relative error = 6.3635519997872331772078300197915e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.4MB, time=56.39 NO POLE NO POLE memory used=362.4MB, alloc=4.4MB, time=56.95 memory used=366.2MB, alloc=4.4MB, time=57.50 memory used=370.0MB, alloc=4.4MB, time=58.06 memory used=373.8MB, alloc=4.4MB, time=58.64 memory used=377.6MB, alloc=4.4MB, time=59.21 memory used=381.4MB, alloc=4.4MB, time=59.78 memory used=385.2MB, alloc=4.4MB, time=60.35 memory used=389.1MB, alloc=4.4MB, time=60.92 memory used=392.9MB, alloc=4.4MB, time=61.48 memory used=396.7MB, alloc=4.4MB, time=62.05 x[1] = 1.1 y1[1] (analytic) = 1.4535961214255773877713700517847 y1[1] (numeric) = 1.4535961214255127558755542879812 absolute error = 6.46318958157638035e-14 relative error = 4.4463448177322953501048323498404e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.8912073600614353399518025778717 y2[1] (numeric) = 1.8912073600612979980986431970244 absolute error = 1.373418531593808473e-13 relative error = 7.2621255637943020575044827947272e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=400.5MB, alloc=4.4MB, time=62.62 memory used=404.3MB, alloc=4.4MB, time=63.18 memory used=408.1MB, alloc=4.4MB, time=63.74 memory used=411.9MB, alloc=4.4MB, time=64.30 memory used=415.8MB, alloc=4.4MB, time=64.87 memory used=419.6MB, alloc=4.4MB, time=65.47 memory used=423.4MB, alloc=4.4MB, time=66.03 memory used=427.2MB, alloc=4.4MB, time=66.60 memory used=431.0MB, alloc=4.4MB, time=67.17 memory used=434.8MB, alloc=4.4MB, time=67.74 x[1] = 1.2 y1[1] (analytic) = 1.3623577544766735776383733556231 y1[1] (numeric) = 1.3623577544766179201693666643354 absolute error = 5.56574690066912877e-14 relative error = 4.0853783687729771213608574626706e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.9320390859672263496701344354948 y2[1] (numeric) = 1.9320390859670689307172957765928 absolute error = 1.574189528386589020e-13 relative error = 8.1478140883392686238253378507823e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.4MB, time=68.33 NO POLE NO POLE memory used=442.5MB, alloc=4.4MB, time=68.89 memory used=446.3MB, alloc=4.4MB, time=69.47 memory used=450.1MB, alloc=4.4MB, time=70.04 memory used=453.9MB, alloc=4.4MB, time=70.62 memory used=457.7MB, alloc=4.4MB, time=71.18 memory used=461.5MB, alloc=4.4MB, time=71.73 memory used=465.4MB, alloc=4.4MB, time=72.32 memory used=469.2MB, alloc=4.4MB, time=72.89 memory used=473.0MB, alloc=4.4MB, time=73.48 x[1] = 1.3 y1[1] (analytic) = 1.2674988286245874069979841092929 y1[1] (numeric) = 1.2674988286245441374617110464206 absolute error = 4.32695362730628723e-14 relative error = 3.4137732750424976582796417123258e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.9635581854171929647013486300396 y2[1] (numeric) = 1.9635581854170160312587366056011 absolute error = 1.769334426120244385e-13 relative error = 9.0108581414118763317834124459018e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.4MB, time=74.08 NO POLE NO POLE memory used=480.6MB, alloc=4.4MB, time=74.68 memory used=484.4MB, alloc=4.4MB, time=75.29 memory used=488.2MB, alloc=4.4MB, time=75.85 memory used=492.1MB, alloc=4.4MB, time=76.42 memory used=495.9MB, alloc=4.4MB, time=76.98 memory used=499.7MB, alloc=4.4MB, time=77.54 memory used=503.5MB, alloc=4.4MB, time=78.12 memory used=507.3MB, alloc=4.5MB, time=78.68 memory used=511.1MB, alloc=4.5MB, time=79.25 memory used=514.9MB, alloc=4.5MB, time=79.82 x[1] = 1.4 y1[1] (analytic) = 1.1699671429002409386167480352036 y1[1] (numeric) = 1.1699671429002134333264612078888 absolute error = 2.75052902868273148e-14 relative error = 2.3509455332774756391281919247605e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.9854497299884601806594745788061 y2[1] (numeric) = 1.9854497299882647806299542043322 absolute error = 1.954000295203744739e-13 relative error = 9.8416004479504085360000435635517e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=518.8MB, alloc=4.5MB, time=80.37 memory used=522.6MB, alloc=4.5MB, time=80.92 memory used=526.4MB, alloc=4.5MB, time=81.47 memory used=530.2MB, alloc=4.5MB, time=82.02 memory used=534.0MB, alloc=4.5MB, time=82.58 memory used=537.8MB, alloc=4.5MB, time=83.13 memory used=541.6MB, alloc=4.5MB, time=83.68 memory used=545.5MB, alloc=4.5MB, time=84.24 memory used=549.3MB, alloc=4.5MB, time=84.80 memory used=553.1MB, alloc=4.5MB, time=85.37 x[1] = 1.5 y1[1] (analytic) = 1.0707372016677029100881898514343 y1[1] (numeric) = 1.070737201667694445014205443701 absolute error = 8.4650739844077333e-15 relative error = 7.9058371850937331959100308830216e-13 % Correct digits = 14 h = 0.005 y2[1] (analytic) = 1.9974949866040544309417233711415 y2[1] (numeric) = 1.9974949866038420942443981527412 absolute error = 2.123366973252184003e-13 relative error = 1.0630149199333535300584211335981e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.5MB, time=85.94 NO POLE NO POLE memory used=560.7MB, alloc=4.5MB, time=86.50 memory used=564.5MB, alloc=4.5MB, time=87.07 memory used=568.4MB, alloc=4.5MB, time=87.63 memory used=572.2MB, alloc=4.5MB, time=88.21 memory used=576.0MB, alloc=4.5MB, time=88.77 memory used=579.8MB, alloc=4.5MB, time=89.33 memory used=583.6MB, alloc=4.5MB, time=89.91 memory used=587.4MB, alloc=4.5MB, time=90.47 memory used=591.2MB, alloc=4.5MB, time=91.02 memory used=595.1MB, alloc=4.5MB, time=91.57 x[1] = 1.6 y1[1] (analytic) = 0.9708004776987112737942295370535 y1[1] (numeric) = 0.97080047769872496184505054506185 absolute error = 1.368805082100800835e-14 relative error = 1.4099756989670648033229314323353e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.9995736030415051643421138255462 y2[1] (numeric) = 1.9995736030412778918468945379703 absolute error = 2.272724952192875759e-13 relative error = 1.1366047985109857394160480749911e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=598.9MB, alloc=4.5MB, time=92.15 memory used=602.7MB, alloc=4.5MB, time=92.72 memory used=606.5MB, alloc=4.5MB, time=93.28 memory used=610.3MB, alloc=4.5MB, time=93.83 memory used=614.1MB, alloc=4.5MB, time=94.40 memory used=617.9MB, alloc=4.5MB, time=94.98 memory used=621.8MB, alloc=4.5MB, time=95.54 memory used=625.6MB, alloc=4.5MB, time=96.11 memory used=629.4MB, alloc=4.5MB, time=96.67 memory used=633.2MB, alloc=4.5MB, time=97.22 x[1] = 1.7 y1[1] (analytic) = 0.87115550570447531591235714266513 y1[1] (numeric) = 0.87115550570451404557346544275717 absolute error = 3.872966110830009204e-14 relative error = 4.4457804438692798266002000786847e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.9916648104524686153461333986479 y2[1] (numeric) = 1.9916648104522288600879834007932 absolute error = 2.397552581499978547e-13 relative error = 1.2037932130534052558405411434430e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.5MB, time=97.82 NO POLE NO POLE memory used=640.8MB, alloc=4.5MB, time=98.37 memory used=644.6MB, alloc=4.5MB, time=98.95 memory used=648.5MB, alloc=4.5MB, time=99.49 memory used=652.3MB, alloc=4.5MB, time=100.04 memory used=656.1MB, alloc=4.5MB, time=100.60 memory used=659.9MB, alloc=4.5MB, time=101.15 memory used=663.7MB, alloc=4.5MB, time=101.71 memory used=667.5MB, alloc=4.5MB, time=102.26 memory used=671.4MB, alloc=4.5MB, time=102.82 memory used=675.2MB, alloc=4.5MB, time=103.39 x[1] = 1.8 y1[1] (analytic) = 0.77279790530691294468332569346942 y1[1] (numeric) = 0.77279790530697932092907233453104 absolute error = 6.637624574664106162e-14 relative error = 8.5890819955419078350396120446288e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.9738476308781951865323731788434 y2[1] (numeric) = 1.973847630877945827380878606098 absolute error = 2.493591514945727454e-13 relative error = 1.2633150988641865001017339280344e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=679.0MB, alloc=4.5MB, time=103.95 memory used=682.8MB, alloc=4.5MB, time=104.51 memory used=686.6MB, alloc=4.5MB, time=105.09 memory used=690.4MB, alloc=4.5MB, time=105.66 memory used=694.2MB, alloc=4.5MB, time=106.22 memory used=698.1MB, alloc=4.5MB, time=106.79 memory used=701.9MB, alloc=4.5MB, time=107.34 memory used=705.7MB, alloc=4.5MB, time=107.92 memory used=709.5MB, alloc=4.5MB, time=108.48 memory used=713.3MB, alloc=4.5MB, time=109.04 x[1] = 1.9 y1[1] (analytic) = 0.67671043313649657772116630491969 y1[1] (numeric) = 0.67671043313659286609217025074981 absolute error = 9.628837100394583012e-14 relative error = 1.4228888205204290780030793455715e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.946300087687414488489709611635 y2[1] (numeric) = 1.9463000876871587965552493833071 absolute error = 2.556919344602283279e-13 relative error = 1.3137333552917854524867147896095e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=717.1MB, alloc=4.5MB, time=109.62 memory used=720.9MB, alloc=4.5MB, time=110.18 memory used=724.8MB, alloc=4.5MB, time=110.74 memory used=728.6MB, alloc=4.5MB, time=111.29 memory used=732.4MB, alloc=4.5MB, time=111.84 memory used=736.2MB, alloc=4.5MB, time=112.40 memory used=740.0MB, alloc=4.5MB, time=112.95 memory used=743.8MB, alloc=4.5MB, time=113.51 memory used=747.6MB, alloc=4.5MB, time=114.07 memory used=751.5MB, alloc=4.5MB, time=114.65 x[1] = 2 y1[1] (analytic) = 0.58385316345285761300243177049924 y1[1] (numeric) = 0.58385316345298568770594378642314 absolute error = 1.2807470351201592390e-13 relative error = 2.1936115367534037913763214974487e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.9092974268256816953960198659117 y2[1] (numeric) = 1.9092974268254232935564448903142 absolute error = 2.584018395749755975e-13 relative error = 1.3533870414552630670566959479251e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.5MB, time=115.21 NO POLE NO POLE memory used=759.1MB, alloc=4.5MB, time=115.78 memory used=762.9MB, alloc=4.5MB, time=116.34 memory used=766.7MB, alloc=4.5MB, time=116.90 memory used=770.5MB, alloc=4.5MB, time=117.46 memory used=774.3MB, alloc=4.5MB, time=118.03 memory used=778.2MB, alloc=4.5MB, time=118.61 memory used=782.0MB, alloc=4.5MB, time=119.17 memory used=785.8MB, alloc=4.5MB, time=119.73 memory used=789.6MB, alloc=4.5MB, time=120.29 memory used=793.4MB, alloc=4.5MB, time=120.85 x[1] = 2.1 y1[1] (analytic) = 0.49515389540014254837906147628083 y1[1] (numeric) = 0.49515389540030384522324442176089 absolute error = 1.6129684418294548006e-13 relative error = 3.2575093457075334318837952555909e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.863209366648873770680759313269 y2[1] (numeric) = 1.8632093666486165867108067142891 absolute error = 2.571839699525989799e-13 relative error = 1.3803278072563807034501821446099e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=797.2MB, alloc=4.5MB, time=121.43 memory used=801.1MB, alloc=4.5MB, time=121.99 memory used=804.9MB, alloc=4.5MB, time=122.54 memory used=808.7MB, alloc=4.5MB, time=123.09 memory used=812.5MB, alloc=4.5MB, time=123.65 memory used=816.3MB, alloc=4.5MB, time=124.20 memory used=820.1MB, alloc=4.5MB, time=124.79 memory used=823.9MB, alloc=4.5MB, time=125.34 memory used=827.8MB, alloc=4.5MB, time=125.90 memory used=831.6MB, alloc=4.5MB, time=126.46 x[1] = 2.2 y1[1] (analytic) = 0.41149888274465429147585738734507 y1[1] (numeric) = 0.41149888274484976639140455013269 absolute error = 1.9547491554716278762e-13 relative error = 4.7503146118736860009446826860069e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.8084964038195901843040369104161 y2[1] (numeric) = 1.8084964038193383981824256501836 absolute error = 2.517861216112602325e-13 relative error = 1.3922401011109647221869500395275e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.5MB, time=127.03 NO POLE NO POLE memory used=839.2MB, alloc=4.5MB, time=127.60 memory used=843.0MB, alloc=4.5MB, time=128.16 memory used=846.8MB, alloc=4.5MB, time=128.74 memory used=850.6MB, alloc=4.5MB, time=129.30 memory used=854.5MB, alloc=4.5MB, time=129.87 memory used=858.3MB, alloc=4.5MB, time=130.43 memory used=862.1MB, alloc=4.5MB, time=130.98 memory used=865.9MB, alloc=4.5MB, time=131.56 memory used=869.7MB, alloc=4.5MB, time=132.12 x[1] = 2.3 y1[1] (analytic) = 0.33372397872017580668211942883398 y1[1] (numeric) = 0.33372397872040590051674576369185 absolute error = 2.3009383462633485787e-13 relative error = 6.8947348497024308707486112665796e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.7457052121767201773854062116435 y2[1] (numeric) = 1.7457052121764781634404709391154 absolute error = 2.420139449352725281e-13 relative error = 1.3863391324443907220219132368945e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.5MB, time=132.70 NO POLE NO POLE memory used=877.3MB, alloc=4.5MB, time=133.28 memory used=881.2MB, alloc=4.5MB, time=133.83 memory used=885.0MB, alloc=4.5MB, time=134.42 memory used=888.8MB, alloc=4.5MB, time=135.00 memory used=892.6MB, alloc=4.5MB, time=135.59 memory used=896.4MB, alloc=4.5MB, time=136.18 memory used=900.2MB, alloc=4.5MB, time=136.77 memory used=904.1MB, alloc=4.5MB, time=137.38 memory used=907.9MB, alloc=4.5MB, time=138.00 memory used=911.7MB, alloc=4.5MB, time=138.63 x[1] = 2.4 y1[1] (analytic) = 0.26260628445875450039117777266522 y1[1] (numeric) = 0.26260628445901911058507378997338 absolute error = 2.6461019389601730816e-13 relative error = 1.0076308510338698540634304092200e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.6754631805511509265657715253413 y2[1] (numeric) = 1.6754631805509231911984563247144 absolute error = 2.277353673152006269e-13 relative error = 1.3592382689083390287738305454536e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=915.5MB, alloc=4.5MB, time=139.26 memory used=919.3MB, alloc=4.5MB, time=139.89 memory used=923.1MB, alloc=4.5MB, time=140.50 memory used=926.9MB, alloc=4.5MB, time=141.11 memory used=930.8MB, alloc=4.5MB, time=141.69 memory used=934.6MB, alloc=4.5MB, time=142.28 memory used=938.4MB, alloc=4.5MB, time=142.89 memory used=942.2MB, alloc=4.5MB, time=143.52 memory used=946.0MB, alloc=4.5MB, time=144.14 memory used=949.8MB, alloc=4.5MB, time=144.77 x[1] = 2.5 y1[1] (analytic) = 0.19885638445306628516649720953265 y1[1] (numeric) = 0.19885638445336474483075316561033 absolute error = 2.9845966425595607768e-13 relative error = 1.5008804724919353734660172507799e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.5984721441039564940518547021862 y2[1] (numeric) = 1.598472144103747609843864936697 absolute error = 2.088842079897654892e-13 relative error = 1.3067741515561920437736644390877e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.5MB, time=145.39 NO POLE NO POLE memory used=957.5MB, alloc=4.5MB, time=146.00 memory used=961.3MB, alloc=4.5MB, time=146.61 memory used=965.1MB, alloc=4.5MB, time=147.22 memory used=968.9MB, alloc=4.5MB, time=147.83 memory used=972.7MB, alloc=4.5MB, time=148.44 memory used=976.5MB, alloc=4.5MB, time=149.07 memory used=980.3MB, alloc=4.5MB, time=149.72 memory used=984.2MB, alloc=4.5MB, time=150.38 memory used=988.0MB, alloc=4.5MB, time=151.03 x[1] = 2.6 y1[1] (analytic) = 0.1431112466310527662022978483548 y1[1] (numeric) = 0.14311124663138383102862007743344 absolute error = 3.3106482632222907864e-13 relative error = 2.3133389870869415229266033353798e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.5155013718214642352577269352094 y2[1] (numeric) = 1.5155013718212787723316887273464 absolute error = 1.854629260382078630e-13 relative error = 1.2237727361163786734686516660081e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.5MB, time=151.69 NO POLE NO POLE memory used=995.6MB, alloc=4.5MB, time=152.34 memory used=999.4MB, alloc=4.5MB, time=153.00 memory used=1003.2MB, alloc=4.5MB, time=153.66 memory used=1007.0MB, alloc=4.5MB, time=154.31 memory used=1010.9MB, alloc=4.5MB, time=154.96 memory used=1014.7MB, alloc=4.5MB, time=155.62 memory used=1018.5MB, alloc=4.5MB, time=156.28 memory used=1022.3MB, alloc=4.5MB, time=156.94 memory used=1026.1MB, alloc=4.5MB, time=157.60 memory used=1029.9MB, alloc=4.5MB, time=158.25 x[1] = 2.7 y1[1] (analytic) = 0.09592785798293885201747271805667 y1[1] (numeric) = 0.09592785798330069534735750672717 absolute error = 3.61843329884788670500e-13 relative error = 3.7720359600768312184171274621642e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.4273798802338299345560530858579 y2[1] (numeric) = 1.4273798802336723901028369834047 absolute error = 1.575444532161024532e-13 relative error = 1.1037317773478346932670226918687e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1033.8MB, alloc=4.5MB, time=158.91 memory used=1037.6MB, alloc=4.5MB, time=159.51 memory used=1041.4MB, alloc=4.5MB, time=160.12 memory used=1045.2MB, alloc=4.5MB, time=160.73 memory used=1049.0MB, alloc=4.5MB, time=161.34 memory used=1052.8MB, alloc=4.5MB, time=161.95 memory used=1056.6MB, alloc=4.5MB, time=162.56 memory used=1060.5MB, alloc=4.5MB, time=163.17 memory used=1064.3MB, alloc=4.5MB, time=163.79 memory used=1068.1MB, alloc=4.5MB, time=164.39 x[1] = 2.8 y1[1] (analytic) = 0.05777765933134184741321188263385 y1[1] (numeric) = 0.057777659331732063689334856351803 absolute error = 3.90216276122973717953e-13 relative error = 6.7537570860247447562645365120756e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.3349881501559049195438537527124 y2[1] (numeric) = 1.3349881501557796464690908076208 absolute error = 1.252730747629450916e-13 relative error = 9.3838342121849720105279134309571e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.5MB, time=165.00 NO POLE NO POLE memory used=1075.7MB, alloc=4.5MB, time=165.62 memory used=1079.5MB, alloc=4.5MB, time=166.22 memory used=1083.3MB, alloc=4.5MB, time=166.84 memory used=1087.2MB, alloc=4.5MB, time=167.45 memory used=1091.0MB, alloc=4.5MB, time=168.06 memory used=1094.8MB, alloc=4.5MB, time=168.64 memory used=1098.6MB, alloc=4.5MB, time=169.25 memory used=1102.4MB, alloc=4.5MB, time=169.85 memory used=1106.2MB, alloc=4.5MB, time=170.45 memory used=1110.0MB, alloc=4.5MB, time=171.06 x[1] = 2.9 y1[1] (analytic) = 0.02904183485040947821889333065447 y1[1] (numeric) = 0.029041834850825094932105704075745 absolute error = 4.15616713212373421275e-13 relative error = 1.4310966071984029355404212528531e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.2392493292139823281842569187396 y2[1] (numeric) = 1.2392493292138934638509579117236 absolute error = 8.88643332990070160e-14 relative error = 7.1708195602067361986990055573548e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1113.9MB, alloc=4.5MB, time=171.67 memory used=1117.7MB, alloc=4.5MB, time=172.28 memory used=1121.5MB, alloc=4.5MB, time=172.89 memory used=1125.3MB, alloc=4.5MB, time=173.51 memory used=1129.1MB, alloc=4.5MB, time=174.11 memory used=1132.9MB, alloc=4.5MB, time=174.73 memory used=1136.8MB, alloc=4.5MB, time=175.33 memory used=1140.6MB, alloc=4.5MB, time=175.93 memory used=1144.4MB, alloc=4.5MB, time=176.54 memory used=1148.2MB, alloc=4.5MB, time=177.14 x[1] = 3 y1[1] (analytic) = 0.01000750339955454272842720526874 y1[1] (numeric) = 0.01000750339999204086177312842861 absolute error = 4.37498133345923159870e-13 relative error = 4.3717010714720038984378243778446e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.1411200080598672221007448028081 y2[1] (numeric) = 1.1411200080598186181574173792561 absolute error = 4.86039433274235520e-14 relative error = 4.2593191762591210239098128245489e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=1152.0MB, alloc=4.5MB, time=177.75 NO POLE NO POLE memory used=1155.8MB, alloc=4.5MB, time=178.36 memory used=1159.6MB, alloc=4.5MB, time=178.94 memory used=1163.5MB, alloc=4.5MB, time=179.55 memory used=1167.3MB, alloc=4.5MB, time=180.17 memory used=1171.1MB, alloc=4.5MB, time=180.78 memory used=1174.9MB, alloc=4.5MB, time=181.39 memory used=1178.7MB, alloc=4.5MB, time=181.99 memory used=1182.5MB, alloc=4.5MB, time=182.59 memory used=1186.3MB, alloc=4.5MB, time=183.20 x[1] = 3.1 y1[1] (analytic) = 0.00086484972672053550762394545853 y1[1] (numeric) = 0.00086484972717587836559508701913851 absolute error = 4.5534285797114156060851e-13 relative error = 5.2649939510043858381949150619671e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 1.0415806624332905791946982715967 y2[1] (numeric) = 1.0415806624332857334781832469608 absolute error = 4.8457165150246359e-15 relative error = 4.6522719649040971593570606745628e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop memory used=1190.2MB, alloc=4.5MB, time=183.80 NO POLE NO POLE memory used=1194.0MB, alloc=4.5MB, time=184.40 memory used=1197.8MB, alloc=4.5MB, time=184.99 memory used=1201.6MB, alloc=4.5MB, time=185.60 memory used=1205.4MB, alloc=4.5MB, time=186.21 memory used=1209.2MB, alloc=4.5MB, time=186.81 memory used=1213.0MB, alloc=4.5MB, time=187.40 memory used=1216.9MB, alloc=4.5MB, time=188.01 memory used=1220.7MB, alloc=4.5MB, time=188.61 memory used=1224.5MB, alloc=4.5MB, time=189.21 memory used=1228.3MB, alloc=4.5MB, time=189.81 x[1] = 3.2 y1[1] (analytic) = 0.00170522420524691533833927771642 y1[1] (numeric) = 0.0017052242057155855365775134984371 absolute error = 4.686701982382357820171e-13 relative error = 2.7484374007602868090052409035117e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 0.9416258565724200908627825853809 y2[1] (numeric) = 0.94162585657246208235209472887287 absolute error = 4.199148931214349197e-14 relative error = 4.4594664663304030992364962002050e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1232.1MB, alloc=4.5MB, time=190.42 memory used=1235.9MB, alloc=4.5MB, time=191.03 memory used=1239.8MB, alloc=4.5MB, time=191.64 memory used=1243.6MB, alloc=4.5MB, time=192.24 memory used=1247.4MB, alloc=4.5MB, time=192.85 memory used=1251.2MB, alloc=4.5MB, time=193.45 memory used=1255.0MB, alloc=4.5MB, time=194.06 memory used=1258.8MB, alloc=4.5MB, time=194.66 memory used=1262.6MB, alloc=4.5MB, time=195.26 memory used=1266.5MB, alloc=4.5MB, time=195.86 x[1] = 3.3 y1[1] (analytic) = 0.01252023009113511606340894889715 y1[1] (numeric) = 0.012520230091612160342676664116588 absolute error = 4.77044279267715219438e-13 relative error = 3.8101877984293910503683099604535e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.84225430585675161798834572239752 y2[1] (numeric) = 0.84225430585684304576015731365784 absolute error = 9.142777181159126032e-14 relative error = 1.0855126673242683741736270564109e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=1270.3MB, alloc=4.5MB, time=196.46 NO POLE NO POLE memory used=1274.1MB, alloc=4.5MB, time=197.07 memory used=1277.9MB, alloc=4.5MB, time=197.67 memory used=1281.7MB, alloc=4.5MB, time=198.27 memory used=1285.5MB, alloc=4.5MB, time=198.86 memory used=1289.3MB, alloc=4.5MB, time=199.45 memory used=1293.2MB, alloc=4.5MB, time=200.04 memory used=1297.0MB, alloc=4.5MB, time=200.64 memory used=1300.8MB, alloc=4.5MB, time=201.24 memory used=1304.6MB, alloc=4.5MB, time=201.83 memory used=1308.4MB, alloc=4.5MB, time=202.43 x[1] = 3.4 y1[1] (analytic) = 0.03320180742053898571779846023431 y1[1] (numeric) = 0.033201807421019067137669812821059 absolute error = 4.80081419871352586749e-13 relative error = 1.4459496550611554767630908430866e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.74445889797316868075009757063626 y2[1] (numeric) = 0.74445889797331160784835286570578 absolute error = 1.4292709825529506952e-13 relative error = 1.9198789704095437929418535191483e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1312.2MB, alloc=4.5MB, time=203.05 memory used=1316.0MB, alloc=4.5MB, time=203.64 memory used=1319.9MB, alloc=4.5MB, time=204.22 memory used=1323.7MB, alloc=4.5MB, time=204.81 memory used=1327.5MB, alloc=4.5MB, time=205.40 memory used=1331.3MB, alloc=4.5MB, time=205.99 memory used=1335.1MB, alloc=4.5MB, time=206.58 memory used=1338.9MB, alloc=4.5MB, time=207.18 memory used=1342.8MB, alloc=4.5MB, time=207.77 memory used=1346.6MB, alloc=4.5MB, time=208.36 x[1] = 3.5 y1[1] (analytic) = 0.06354331270920366230134237332824 y1[1] (numeric) = 0.063543312709681119265112297435446 absolute error = 4.77456963769924107206e-13 relative error = 7.5138821602665495472480421213141e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.64921677231038015187963119995636 y2[1] (numeric) = 0.64921677231057605496148951006228 absolute error = 1.9590308185831010592e-13 relative error = 3.0175295866301491172819755257866e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=1350.4MB, alloc=4.5MB, time=208.95 NO POLE NO POLE memory used=1354.2MB, alloc=4.5MB, time=209.55 memory used=1358.0MB, alloc=4.5MB, time=210.16 memory used=1361.8MB, alloc=4.5MB, time=210.75 memory used=1365.6MB, alloc=4.5MB, time=211.34 memory used=1369.5MB, alloc=4.5MB, time=211.93 memory used=1373.3MB, alloc=4.5MB, time=212.54 memory used=1377.1MB, alloc=4.5MB, time=213.13 memory used=1380.9MB, alloc=4.5MB, time=213.72 memory used=1384.7MB, alloc=4.5MB, time=214.31 memory used=1388.5MB, alloc=4.5MB, time=214.89 x[1] = 3.6 y1[1] (analytic) = 0.10324158366585299412970827473406 y1[1] (numeric) = 0.10324158366632190559380968432465 absolute error = 4.6891146410140959059e-13 relative error = 4.5418856186773255152339182762321e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.55747955670514761573327265250731 y2[1] (numeric) = 0.55747955670539734129166140796885 absolute error = 2.4972555838875546154e-13 relative error = 4.4795464763712574565163516475715e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1392.3MB, alloc=4.5MB, time=215.49 memory used=1396.2MB, alloc=4.5MB, time=216.10 memory used=1400.0MB, alloc=4.5MB, time=216.69 memory used=1403.8MB, alloc=4.5MB, time=217.30 memory used=1407.6MB, alloc=4.5MB, time=217.88 memory used=1411.4MB, alloc=4.5MB, time=218.47 memory used=1415.2MB, alloc=4.5MB, time=219.07 memory used=1419.0MB, alloc=4.5MB, time=219.66 memory used=1422.9MB, alloc=4.5MB, time=220.26 memory used=1426.7MB, alloc=4.5MB, time=220.85 x[1] = 3.7 y1[1] (analytic) = 0.1518999682895918411643298936456 y1[1] (numeric) = 0.1518999682900460972943739819315 absolute error = 4.5425613004408828590e-13 relative error = 2.9904952262930382403020630525947e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.47016385909150678678922237429879 y2[1] (numeric) = 0.47016385909181051467939994041942 absolute error = 3.0372789017756612063e-13 relative error = 6.4600433296692917408669089879626e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1430.5MB, alloc=4.5MB, time=221.44 memory used=1434.3MB, alloc=4.5MB, time=222.04 memory used=1438.1MB, alloc=4.5MB, time=222.63 memory used=1441.9MB, alloc=4.5MB, time=223.22 memory used=1445.7MB, alloc=4.5MB, time=223.82 memory used=1449.6MB, alloc=4.5MB, time=224.41 memory used=1453.4MB, alloc=4.5MB, time=225.01 memory used=1457.2MB, alloc=4.5MB, time=225.61 memory used=1461.0MB, alloc=4.5MB, time=226.20 memory used=1464.8MB, alloc=4.5MB, time=226.80 x[1] = 3.8 y1[1] (analytic) = 0.20903228808558330000343182564927 y1[1] (numeric) = 0.20903228808601667745604611851446 absolute error = 4.3337745261429286519e-13 relative error = 2.0732560341915062042083327042650e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.38814210905728092426641391388112 y2[1] (numeric) = 0.38814210905763813918089489813139 absolute error = 3.5721491448098425027e-13 relative error = 9.2031991929086847588656658022567e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=1468.6MB, alloc=4.5MB, time=227.40 NO POLE NO POLE memory used=1472.5MB, alloc=4.5MB, time=228.02 memory used=1476.3MB, alloc=4.5MB, time=228.62 memory used=1480.1MB, alloc=4.5MB, time=229.23 memory used=1483.9MB, alloc=4.5MB, time=229.82 memory used=1487.7MB, alloc=4.5MB, time=230.43 memory used=1491.5MB, alloc=4.5MB, time=231.03 memory used=1495.3MB, alloc=4.5MB, time=231.63 memory used=1499.2MB, alloc=4.5MB, time=232.23 memory used=1503.0MB, alloc=4.5MB, time=232.86 memory used=1506.8MB, alloc=4.5MB, time=233.45 x[1] = 3.9 y1[1] (analytic) = 0.27406769579985987062766951538565 y1[1] (numeric) = 0.27406769580026611156371709340264 absolute error = 4.0624093604757801699e-13 relative error = 1.4822649377263298969412909387938e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.31223384081602618190911187462131 y2[1] (numeric) = 0.31223384081643565335302558706921 absolute error = 4.0947144391371244790e-13 relative error = 1.3114255739978563626945875186375e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1510.6MB, alloc=4.5MB, time=234.05 memory used=1514.4MB, alloc=4.5MB, time=234.66 memory used=1518.2MB, alloc=4.5MB, time=235.28 memory used=1522.0MB, alloc=4.5MB, time=235.89 memory used=1525.9MB, alloc=4.5MB, time=236.49 memory used=1529.7MB, alloc=4.5MB, time=237.09 memory used=1533.5MB, alloc=4.5MB, time=237.70 memory used=1537.3MB, alloc=4.5MB, time=238.31 memory used=1541.1MB, alloc=4.5MB, time=238.92 memory used=1544.9MB, alloc=4.5MB, time=239.52 x[1] = 4 y1[1] (analytic) = 0.34635637913638808536083181690225 y1[1] (numeric) = 0.34635637913676097923236166052503 absolute error = 3.7289387152984362278e-13 relative error = 1.0766190374770190492015963042693e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.24319750469207174862736090548817 y2[1] (numeric) = 0.24319750469253151984584709881395 absolute error = 4.5977121848619332578e-13 relative error = 1.8905260523472052365573950667333e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1548.7MB, alloc=4.5MB, time=240.12 memory used=1552.6MB, alloc=4.5MB, time=240.72 memory used=1556.4MB, alloc=4.5MB, time=241.33 memory used=1560.2MB, alloc=4.5MB, time=241.95 memory used=1564.0MB, alloc=4.5MB, time=242.56 memory used=1567.8MB, alloc=4.5MB, time=243.17 memory used=1571.6MB, alloc=4.5MB, time=243.78 memory used=1575.5MB, alloc=4.5MB, time=244.38 memory used=1579.3MB, alloc=4.5MB, time=245.01 memory used=1583.1MB, alloc=4.5MB, time=245.65 x[1] = 4.1 y1[1] (analytic) = 0.42517605346673108846497132034021 y1[1] (numeric) = 0.42517605346706455556626515529844 absolute error = 3.3346710129383495823e-13 relative error = 7.8430358101041992169307780605731e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.18172288893558949573496297564155 y2[1] (numeric) = 0.18172288893609688193671702636873 absolute error = 5.0738620175405072718e-13 relative error = 2.7920874729979143643698544257117e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop memory used=1586.9MB, alloc=4.5MB, time=246.31 NO POLE NO POLE memory used=1590.7MB, alloc=4.5MB, time=246.96 memory used=1594.5MB, alloc=4.5MB, time=247.52 memory used=1598.3MB, alloc=4.5MB, time=248.11 memory used=1602.2MB, alloc=4.5MB, time=248.68 memory used=1606.0MB, alloc=4.5MB, time=249.26 memory used=1609.8MB, alloc=4.5MB, time=249.87 memory used=1613.6MB, alloc=4.5MB, time=250.45 memory used=1617.4MB, alloc=4.5MB, time=251.05 memory used=1621.2MB, alloc=4.5MB, time=251.62 memory used=1625.0MB, alloc=4.5MB, time=252.24 x[1] = 4.2 y1[1] (analytic) = 0.50973917865930042234445511862287 y1[1] (numeric) = 0.50973917865958859807756235771369 absolute error = 2.8817573310723909082e-13 relative error = 5.6533957987139545911605828349551e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.12842422758641193998142290209118 y2[1] (numeric) = 0.12842422758696353608923953639559 absolute error = 5.5159610781663430441e-13 relative error = 4.2951094056258626763973562536424e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1628.9MB, alloc=4.5MB, time=252.79 memory used=1632.7MB, alloc=4.5MB, time=253.34 memory used=1636.5MB, alloc=4.5MB, time=253.91 memory used=1640.3MB, alloc=4.5MB, time=254.47 memory used=1644.1MB, alloc=4.5MB, time=255.05 memory used=1647.9MB, alloc=4.5MB, time=255.62 memory used=1651.7MB, alloc=4.5MB, time=256.17 memory used=1655.6MB, alloc=4.5MB, time=256.73 memory used=1659.4MB, alloc=4.5MB, time=257.28 memory used=1663.2MB, alloc=4.5MB, time=257.84 x[1] = 4.3 y1[1] (analytic) = 0.59920082792002470309323760366397 y1[1] (numeric) = 0.59920082792026202187104969079202 absolute error = 2.3731877781208712805e-13 relative error = 3.9605882828279745039748367975776e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.08383406325054501596829063971536 y2[1] (numeric) = 0.083834063251136714009756462666521 absolute error = 5.91698041465822951161e-13 relative error = 7.0579668755585009355985643769715e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1667.0MB, alloc=4.5MB, time=258.39 memory used=1670.8MB, alloc=4.5MB, time=258.95 memory used=1674.6MB, alloc=4.5MB, time=259.49 memory used=1678.5MB, alloc=4.5MB, time=260.04 memory used=1682.3MB, alloc=4.5MB, time=260.59 memory used=1686.1MB, alloc=4.5MB, time=261.17 memory used=1689.9MB, alloc=4.5MB, time=261.74 memory used=1693.7MB, alloc=4.5MB, time=262.29 memory used=1697.5MB, alloc=4.5MB, time=262.84 memory used=1701.3MB, alloc=4.5MB, time=263.38 x[1] = 4.4 y1[1] (analytic) = 0.69266713002158031688086025778229 y1[1] (numeric) = 0.69266713002176159457654394070658 absolute error = 1.8127769568368292429e-13 relative error = 2.6170968395459323496333670209768e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.04839792611048404596460766661961 y2[1] (numeric) = 0.048397926111111062095359025650559 absolute error = 6.27016130751359030949e-13 relative error = 1.2955433861359891345738228045377e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop memory used=1705.2MB, alloc=4.5MB, time=263.94 NO POLE NO POLE memory used=1709.0MB, alloc=4.5MB, time=264.49 memory used=1712.8MB, alloc=4.5MB, time=265.05 memory used=1716.6MB, alloc=4.5MB, time=265.60 memory used=1720.4MB, alloc=4.5MB, time=266.15 memory used=1724.2MB, alloc=4.5MB, time=266.70 memory used=1728.0MB, alloc=4.5MB, time=267.26 memory used=1731.9MB, alloc=4.5MB, time=267.84 memory used=1735.7MB, alloc=4.5MB, time=268.39 memory used=1739.5MB, alloc=4.5MB, time=268.96 memory used=1743.3MB, alloc=4.5MB, time=269.51 x[1] = 4.5 y1[1] (analytic) = 0.78920420056922029401951817520617 y1[1] (numeric) = 0.78920420056934080787032454917954 absolute error = 1.2051385080637397337e-13 relative error = 1.5270300223877714479722755084912e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.02246988233490294461086498550137 y2[1] (numeric) = 0.022469882335559855640509340902349 absolute error = 6.56911029644355400979e-13 relative error = 2.9235178887606437154152031435494e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1747.1MB, alloc=4.5MB, time=270.06 memory used=1750.9MB, alloc=4.5MB, time=270.62 memory used=1754.7MB, alloc=4.5MB, time=271.18 memory used=1758.6MB, alloc=4.5MB, time=271.75 memory used=1762.4MB, alloc=4.5MB, time=272.31 memory used=1766.2MB, alloc=4.5MB, time=272.86 memory used=1770.0MB, alloc=4.5MB, time=273.43 memory used=1773.8MB, alloc=4.5MB, time=274.00 memory used=1777.6MB, alloc=4.5MB, time=274.56 memory used=1781.4MB, alloc=4.5MB, time=275.11 x[1] = 4.6 y1[1] (analytic) = 0.88784747306494548257009217877081 y1[1] (numeric) = 0.88784747306500104745634591642952 absolute error = 5.556488625373765871e-14 relative error = 6.2583819788236444451504678671598e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 0.00630899636653554386189534009117 y2[1] (numeric) = 0.0063089963672163330302740042708927 absolute error = 6.807891683786641797227e-13 relative error = 1.0790768116300336499900499934160e-08 % Correct digits = 9 h = 0.005 TOP MAIN SOLVE Loop memory used=1785.3MB, alloc=4.5MB, time=275.68 NO POLE NO POLE memory used=1789.1MB, alloc=4.5MB, time=276.23 memory used=1792.9MB, alloc=4.5MB, time=276.80 memory used=1796.7MB, alloc=4.5MB, time=277.35 memory used=1800.5MB, alloc=4.5MB, time=277.90 memory used=1804.3MB, alloc=4.5MB, time=278.45 memory used=1808.2MB, alloc=4.5MB, time=279.00 memory used=1812.0MB, alloc=4.5MB, time=279.58 memory used=1815.8MB, alloc=4.5MB, time=280.14 memory used=1819.6MB, alloc=4.5MB, time=280.71 memory used=1823.4MB, alloc=4.5MB, time=281.26 x[1] = 4.7 y1[1] (analytic) = 0.98761133653710926284949170367289 y1[1] (numeric) = 0.98761133653709630289594131721513 absolute error = 1.295995355038645776e-14 relative error = 1.3122524085059943582855708670141e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 7.674243589911582046345842503e-05 y2[1] (numeric) = 7.6742436597227450908984381888466e-05 absolute error = 6.98111630445525956858466e-13 relative error = 9.0968135460705277566467727978186e-07 % Correct digits = 8 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1827.2MB, alloc=4.5MB, time=281.81 memory used=1831.0MB, alloc=4.5MB, time=282.37 memory used=1834.9MB, alloc=4.5MB, time=282.93 memory used=1838.7MB, alloc=4.5MB, time=283.50 memory used=1842.5MB, alloc=4.5MB, time=284.06 memory used=1846.3MB, alloc=4.5MB, time=284.61 memory used=1850.1MB, alloc=4.5MB, time=285.16 memory used=1853.9MB, alloc=4.5MB, time=285.71 memory used=1857.7MB, alloc=4.5MB, time=286.26 memory used=1861.6MB, alloc=4.5MB, time=286.81 x[1] = 4.8 y1[1] (analytic) = 1.0874989834394465693202152576495 y1[1] (numeric) = 1.087498983439362183806725316674 absolute error = 8.43855134899409755e-14 relative error = 7.7595947007742353717947706861462e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 0.00383539116415932821840353349637 y2[1] (numeric) = 0.0038353911648677307565111630440808 absolute error = 7.084025381076295477108e-13 relative error = 1.8470150964716603942258912192038e-08 % Correct digits = 9 h = 0.005 TOP MAIN SOLVE Loop memory used=1865.4MB, alloc=4.5MB, time=287.36 NO POLE NO POLE memory used=1869.2MB, alloc=4.5MB, time=287.92 memory used=1873.0MB, alloc=4.5MB, time=288.47 memory used=1876.8MB, alloc=4.5MB, time=289.01 memory used=1880.6MB, alloc=4.5MB, time=289.56 memory used=1884.4MB, alloc=4.5MB, time=290.11 memory used=1888.3MB, alloc=4.5MB, time=290.69 memory used=1892.1MB, alloc=4.5MB, time=291.24 memory used=1895.9MB, alloc=4.5MB, time=291.80 memory used=1899.7MB, alloc=4.5MB, time=292.35 memory used=1903.5MB, alloc=4.5MB, time=292.90 x[1] = 4.9 y1[1] (analytic) = 1.1865123694225754044943291441219 y1[1] (numeric) = 1.1865123694224174271157907429258 absolute error = 1.579773785384011961e-13 relative error = 1.3314431657824351148068624514006e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.01754738737566748772362275008167 y2[1] (numeric) = 0.017547387376378744556286661960681 absolute error = 7.11256832663911879011e-13 relative error = 4.0533488971138432665231279838623e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1907.3MB, alloc=4.5MB, time=293.47 memory used=1911.2MB, alloc=4.5MB, time=294.02 memory used=1915.0MB, alloc=4.5MB, time=294.59 memory used=1918.8MB, alloc=4.5MB, time=295.14 memory used=1922.6MB, alloc=4.5MB, time=295.71 memory used=1926.4MB, alloc=4.5MB, time=296.26 memory used=1930.2MB, alloc=4.5MB, time=296.81 memory used=1934.0MB, alloc=4.5MB, time=297.20 memory used=1937.9MB, alloc=4.5MB, time=297.43 memory used=1941.7MB, alloc=4.5MB, time=297.67 x[1] = 5 y1[1] (analytic) = 1.2836621854632262644666391715136 y1[1] (numeric) = 1.2836621854629933150474766951284 absolute error = 2.329494191624763852e-13 relative error = 1.8147252587207244477405428153556e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.04107572533686153110684559384401 y2[1] (numeric) = 0.041075725337567878448343543949034 absolute error = 7.06347341497950105024e-13 relative error = 1.7196223212255024701053815502286e-09 % Correct digits = 10 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1945.5MB, alloc=4.5MB, time=297.90 memory used=1949.3MB, alloc=4.5MB, time=298.13 memory used=1953.1MB, alloc=4.5MB, time=298.36 memory used=1956.9MB, alloc=4.5MB, time=298.59 memory used=1960.7MB, alloc=4.5MB, time=298.83 memory used=1964.6MB, alloc=4.5MB, time=299.06 memory used=1968.4MB, alloc=4.5MB, time=299.29 memory used=1972.2MB, alloc=4.5MB, time=299.52 memory used=1976.0MB, alloc=4.5MB, time=299.75 memory used=1979.8MB, alloc=4.5MB, time=299.98 x[1] = 5.1 y1[1] (analytic) = 1.377977742712980563320575552929 y1[1] (numeric) = 1.3779777427126720911666909584752 absolute error = 3.084721538845944538e-13 relative error = 2.2385858952791969736637031894606e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.07418531767226770305385375245514 y2[1] (numeric) = 0.074185317672961134084978886384954 absolute error = 6.93431031125133929814e-13 relative error = 9.3472812799500285743027580968634e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop memory used=1983.6MB, alloc=4.5MB, time=300.21 NO POLE NO POLE memory used=1987.4MB, alloc=4.5MB, time=300.45 memory used=1991.3MB, alloc=4.5MB, time=300.68 memory used=1995.1MB, alloc=4.5MB, time=300.91 memory used=1998.9MB, alloc=4.5MB, time=301.15 memory used=2002.7MB, alloc=4.5MB, time=301.38 memory used=2006.5MB, alloc=4.5MB, time=301.61 memory used=2010.3MB, alloc=4.5MB, time=301.84 memory used=2014.1MB, alloc=4.5MB, time=302.08 memory used=2018.0MB, alloc=4.5MB, time=302.31 memory used=2021.8MB, alloc=4.5MB, time=302.54 x[1] = 5.2 y1[1] (analytic) = 1.4685166713003769586390939266086 y1[1] (numeric) = 1.4685166712999932767987196466876 absolute error = 3.836818403742799210e-13 relative error = 2.6127169535945971141749852267213e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.1165453442798467353269155595782 y2[1] (numeric) = 0.11654534428051908968086019073817 absolute error = 6.7235435394463115997e-13 relative error = 5.7690365762718509640226915864836e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2025.6MB, alloc=4.5MB, time=302.77 memory used=2029.4MB, alloc=4.5MB, time=303.01 memory used=2033.2MB, alloc=4.5MB, time=303.24 memory used=2037.0MB, alloc=4.5MB, time=303.47 memory used=2040.9MB, alloc=4.5MB, time=303.71 memory used=2044.7MB, alloc=4.5MB, time=303.94 memory used=2048.5MB, alloc=4.5MB, time=304.17 memory used=2052.3MB, alloc=4.5MB, time=304.41 memory used=2056.1MB, alloc=4.5MB, time=304.64 memory used=2059.9MB, alloc=4.5MB, time=304.87 x[1] = 5.3 y1[1] (analytic) = 1.5543743361791609294449466335608 y1[1] (numeric) = 1.5543743361787032392487385637881 absolute error = 4.576901962080697727e-13 relative error = 2.9445300630292656762759942198937e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.16773255777609883643544033214541 y2[1] (numeric) = 0.16773255777674189404155339540194 absolute error = 6.4305760611306325653e-13 relative error = 3.8338269840936998002128243640833e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop memory used=2063.7MB, alloc=4.5MB, time=305.11 NO POLE NO POLE memory used=2067.6MB, alloc=4.5MB, time=305.35 memory used=2071.4MB, alloc=4.5MB, time=305.58 memory used=2075.2MB, alloc=4.5MB, time=305.81 memory used=2079.0MB, alloc=4.5MB, time=306.04 memory used=2082.8MB, alloc=4.5MB, time=306.27 memory used=2086.6MB, alloc=4.5MB, time=306.50 memory used=2090.4MB, alloc=4.5MB, time=306.74 memory used=2094.3MB, alloc=4.5MB, time=306.96 memory used=2098.1MB, alloc=4.5MB, time=307.20 x[1] = 5.4 y1[1] (analytic) = 1.6346928759426343624067518389807 y1[1] (numeric) = 1.6346928759421047677654767274989 absolute error = 5.295946412751114818e-13 relative error = 3.2397195159349084932666552596512e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.22723551244401263764153021726577 y2[1] (numeric) = 0.22723551244461821586631442966396 absolute error = 6.0557822478421239819e-13 relative error = 2.6649805669499727991244694546599e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop memory used=2101.9MB, alloc=4.5MB, time=307.44 NO POLE NO POLE memory used=2105.7MB, alloc=4.5MB, time=307.67 memory used=2109.5MB, alloc=4.5MB, time=307.91 memory used=2113.3MB, alloc=4.5MB, time=308.16 memory used=2117.1MB, alloc=4.5MB, time=308.41 memory used=2121.0MB, alloc=4.5MB, time=308.65 memory used=2124.8MB, alloc=4.5MB, time=308.89 memory used=2128.6MB, alloc=4.5MB, time=309.12 memory used=2132.4MB, alloc=4.5MB, time=309.35 memory used=2136.2MB, alloc=4.5MB, time=309.58 memory used=2140.0MB, alloc=4.5MB, time=309.81 x[1] = 5.5 y1[1] (analytic) = 1.7086697742912600000274211813258 y1[1] (numeric) = 1.7086697742906615110815898939676 absolute error = 5.984889458312873582e-13 relative error = 3.5026601092626858854238168498395e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.29445967442960809376808082447793 y2[1] (numeric) = 0.29445967443016814673286616722957 absolute error = 5.6005296478534275164e-13 relative error = 1.9019682945388365070860017251521e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2143.9MB, alloc=4.5MB, time=310.05 memory used=2147.7MB, alloc=4.5MB, time=310.29 memory used=2151.5MB, alloc=4.5MB, time=310.52 memory used=2155.3MB, alloc=4.5MB, time=310.75 memory used=2159.1MB, alloc=4.5MB, time=310.99 memory used=2162.9MB, alloc=4.5MB, time=311.23 memory used=2166.7MB, alloc=4.5MB, time=311.46 memory used=2170.6MB, alloc=4.5MB, time=311.70 memory used=2174.4MB, alloc=4.5MB, time=311.93 memory used=2178.2MB, alloc=4.5MB, time=312.17 x[1] = 5.6 y1[1] (analytic) = 1.7755658785102497976558096621573 y1[1] (numeric) = 1.775565878509586323494283777152 absolute error = 6.634741615258850053e-13 relative error = 3.7366913250358171506257426544814e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.36873336212767868853633084628333 y2[1] (numeric) = 0.36873336212818540744382624112538 absolute error = 5.0671890749539484205e-13 relative error = 1.3742149735828267051570889514393e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop memory used=2182.0MB, alloc=4.5MB, time=312.40 NO POLE NO POLE memory used=2185.8MB, alloc=4.5MB, time=312.63 memory used=2189.6MB, alloc=4.5MB, time=312.87 memory used=2193.4MB, alloc=4.5MB, time=313.10 memory used=2197.3MB, alloc=4.5MB, time=313.33 memory used=2201.1MB, alloc=4.5MB, time=313.56 memory used=2204.9MB, alloc=4.5MB, time=313.79 memory used=2208.7MB, alloc=4.5MB, time=314.03 memory used=2212.5MB, alloc=4.5MB, time=314.27 memory used=2216.3MB, alloc=4.5MB, time=314.50 x[1] = 5.7 y1[1] (analytic) = 1.8347127848391596827492340309974 y1[1] (numeric) = 1.8347127848384360130417995781169 absolute error = 7.236697074344528805e-13 relative error = 3.9443214949739038994000459922952e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.44931445740236223877264939212753 y2[1] (numeric) = 0.44931445740280815204076098295426 absolute error = 4.4591326811159082673e-13 relative error = 9.9243026963691569268412502896690e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2220.1MB, alloc=4.5MB, time=314.74 NO POLE NO POLE memory used=2224.0MB, alloc=4.5MB, time=314.97 memory used=2227.8MB, alloc=4.5MB, time=315.20 memory used=2231.6MB, alloc=4.5MB, time=315.43 memory used=2235.4MB, alloc=4.5MB, time=315.67 memory used=2239.2MB, alloc=4.5MB, time=315.90 memory used=2243.0MB, alloc=4.5MB, time=316.13 memory used=2246.8MB, alloc=4.5MB, time=316.36 memory used=2250.7MB, alloc=4.5MB, time=316.59 memory used=2254.5MB, alloc=4.5MB, time=316.82 memory used=2258.3MB, alloc=4.5MB, time=317.05 x[1] = 5.8 y1[1] (analytic) = 1.8855195169413190041646581017615 y1[1] (numeric) = 1.8855195169405407796853510896093 absolute error = 7.782244793070121522e-13 relative error = 4.1273742982488151863592912964510e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.53539782058624278858177347329741 y2[1] (numeric) = 0.53539782058662086056326072675867 absolute error = 3.7807198148725346126e-13 relative error = 7.0615151379076819672904044479590e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2262.1MB, alloc=4.5MB, time=317.29 memory used=2265.9MB, alloc=4.5MB, time=317.52 memory used=2269.7MB, alloc=4.5MB, time=317.75 memory used=2273.6MB, alloc=4.5MB, time=317.98 memory used=2277.4MB, alloc=4.5MB, time=318.22 memory used=2281.2MB, alloc=4.5MB, time=318.45 memory used=2285.0MB, alloc=4.5MB, time=318.68 memory used=2288.8MB, alloc=4.5MB, time=318.91 memory used=2292.6MB, alloc=4.5MB, time=319.14 memory used=2296.4MB, alloc=4.5MB, time=319.38 x[1] = 5.9 y1[1] (analytic) = 1.9274784307440357409061046800325 y1[1] (numeric) = 1.9274784307432094130581614880085 absolute error = 8.263278479431920240e-13 relative error = 4.2870925804560988708793396397221e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.62612333516976364018515353101662 y2[1] (numeric) = 0.62612333517006736724628869255859 absolute error = 3.0372706113516154197e-13 relative error = 4.8509142540233012681294745692787e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2300.3MB, alloc=4.5MB, time=319.61 NO POLE NO POLE memory used=2304.1MB, alloc=4.5MB, time=319.84 memory used=2307.9MB, alloc=4.5MB, time=320.08 memory used=2311.7MB, alloc=4.5MB, time=320.31 memory used=2315.5MB, alloc=4.5MB, time=320.54 memory used=2319.3MB, alloc=4.5MB, time=320.78 memory used=2323.1MB, alloc=4.5MB, time=321.01 memory used=2327.0MB, alloc=4.5MB, time=321.25 memory used=2330.8MB, alloc=4.5MB, time=321.48 memory used=2334.6MB, alloc=4.5MB, time=321.71 memory used=2338.4MB, alloc=4.5MB, time=321.94 x[1] = 6 y1[1] (analytic) = 1.9601702866503660205456522979229 y1[1] (numeric) = 1.9601702866494988001337735863112 absolute error = 8.672204118787116117e-13 relative error = 4.4242095586534977973227413601885e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.72058450180107412718844455338811 y2[1] (numeric) = 0.72058450180129762992909604217176 absolute error = 2.2350274065148878365e-13 relative error = 3.1016867569709313312687446267454e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2342.2MB, alloc=4.5MB, time=322.18 memory used=2346.0MB, alloc=4.5MB, time=322.41 memory used=2349.8MB, alloc=4.5MB, time=322.64 memory used=2353.7MB, alloc=4.5MB, time=322.87 memory used=2357.5MB, alloc=4.5MB, time=323.11 memory used=2361.3MB, alloc=4.5MB, time=323.34 memory used=2365.1MB, alloc=4.5MB, time=323.57 memory used=2368.9MB, alloc=4.5MB, time=323.81 memory used=2372.7MB, alloc=4.5MB, time=324.04 memory used=2376.6MB, alloc=4.5MB, time=324.27 x[1] = 6.1 y1[1] (analytic) = 1.983268438442584596585021274648 y1[1] (numeric) = 1.983268438441684392214584727743 absolute error = 9.002043704365469050e-13 relative error = 4.5389940816254648557473763973924e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.81783749572790445997587163677534 y2[1] (numeric) = 0.81783749572804257039742644713165 absolute error = 1.3811042155481035631e-13 relative error = 1.6887269448545785838040164868466e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2380.4MB, alloc=4.5MB, time=324.50 NO POLE NO POLE memory used=2384.2MB, alloc=4.5MB, time=324.73 memory used=2388.0MB, alloc=4.5MB, time=324.97 memory used=2391.8MB, alloc=4.5MB, time=325.20 memory used=2395.6MB, alloc=4.5MB, time=325.44 memory used=2399.4MB, alloc=4.5MB, time=325.66 memory used=2403.3MB, alloc=4.5MB, time=325.89 memory used=2407.1MB, alloc=4.5MB, time=326.13 memory used=2410.9MB, alloc=4.5MB, time=326.36 memory used=2414.7MB, alloc=4.5MB, time=326.60 x[1] = 6.2 y1[1] (analytic) = 1.9965420970232174751394026238693 y1[1] (numeric) = 1.9965420970222928217537343634301 absolute error = 9.246533856682604392e-13 relative error = 4.6312741767222942251531162078931e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 0.91691059718250342199942071090163 y2[1] (numeric) = 0.91691059718255176446560053455173 absolute error = 4.834246617982365010e-14 relative error = 5.2723205870202724475555447122703e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop memory used=2418.5MB, alloc=4.5MB, time=326.83 NO POLE NO POLE memory used=2422.3MB, alloc=4.5MB, time=327.07 memory used=2426.1MB, alloc=4.5MB, time=327.31 memory used=2430.0MB, alloc=4.5MB, time=327.54 memory used=2433.8MB, alloc=4.5MB, time=327.77 memory used=2437.6MB, alloc=4.5MB, time=328.00 memory used=2441.4MB, alloc=4.5MB, time=328.24 memory used=2445.2MB, alloc=4.5MB, time=328.47 memory used=2449.0MB, alloc=4.5MB, time=328.70 memory used=2452.8MB, alloc=4.5MB, time=328.93 memory used=2456.7MB, alloc=4.5MB, time=329.16 x[1] = 6.3 y1[1] (analytic) = 1.9998586363834151422866736621397 y1[1] (numeric) = 1.9998586363824751204808988293657 absolute error = 9.400218057748327740e-13 relative error = 4.7004412645625154995893473946841e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.0168139004843498903109663674941 y2[1] (numeric) = 1.0168139004843049551996091852313 absolute error = 4.49351113571822628e-14 relative error = 4.4192070285209356800437456488451e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2460.5MB, alloc=4.5MB, time=329.39 memory used=2464.3MB, alloc=4.5MB, time=329.62 memory used=2468.1MB, alloc=4.5MB, time=329.86 memory used=2471.9MB, alloc=4.5MB, time=330.10 memory used=2475.7MB, alloc=4.5MB, time=330.33 memory used=2479.6MB, alloc=4.5MB, time=330.56 memory used=2483.4MB, alloc=4.5MB, time=330.80 memory used=2487.2MB, alloc=4.5MB, time=331.03 memory used=2491.0MB, alloc=4.5MB, time=331.26 memory used=2494.8MB, alloc=4.5MB, time=331.49 x[1] = 6.4 y1[1] (analytic) = 1.9931849187581926585947390986722 y1[1] (numeric) = 1.9931849187572468054665173636342 absolute error = 9.458531282217350380e-13 relative error = 4.7454359067247345655910873952328e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.116549204850493289480420488799 y2[1] (numeric) = 1.1165492048503524984912540222154 absolute error = 1.407909891664665836e-13 relative error = 1.2609474670246941279518961964540e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2498.6MB, alloc=4.5MB, time=331.73 NO POLE NO POLE memory used=2502.4MB, alloc=4.5MB, time=331.96 memory used=2506.3MB, alloc=4.5MB, time=332.19 memory used=2510.1MB, alloc=4.5MB, time=332.43 memory used=2513.9MB, alloc=4.5MB, time=332.68 memory used=2517.7MB, alloc=4.5MB, time=332.94 memory used=2521.5MB, alloc=4.5MB, time=333.20 memory used=2525.3MB, alloc=4.5MB, time=333.45 memory used=2529.1MB, alloc=4.5MB, time=333.68 memory used=2533.0MB, alloc=4.5MB, time=333.91 memory used=2536.8MB, alloc=4.5MB, time=334.14 x[1] = 6.5 y1[1] (analytic) = 1.9765876257280234998863132539441 y1[1] (numeric) = 1.9765876257270817122984120018375 absolute error = 9.417875879012521066e-13 relative error = 4.7647145800296593891138330708805e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.2151199880878155242969457490747 y2[1] (numeric) = 1.2151199880875772864606631211124 absolute error = 2.382378362826279623e-13 relative error = 1.9606116154630381127805392669551e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2540.6MB, alloc=4.5MB, time=334.37 memory used=2544.4MB, alloc=4.5MB, time=334.61 memory used=2548.2MB, alloc=4.5MB, time=334.84 memory used=2552.0MB, alloc=4.5MB, time=335.07 memory used=2555.8MB, alloc=4.5MB, time=335.30 memory used=2559.7MB, alloc=4.5MB, time=335.53 memory used=2563.5MB, alloc=4.5MB, time=335.76 memory used=2567.3MB, alloc=4.5MB, time=335.99 memory used=2571.1MB, alloc=4.5MB, time=336.23 memory used=2574.9MB, alloc=4.5MB, time=336.46 x[1] = 6.6 y1[1] (analytic) = 1.9502325919585294662197377216682 y1[1] (numeric) = 1.9502325919576018974554582577568 absolute error = 9.275687642794639114e-13 relative error = 4.7561955845889591633161624064587e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.3115413635133781743549851055926 y2[1] (numeric) = 1.3115413635130419318817750028553 absolute error = 3.362424732101027373e-13 relative error = 2.5637199295748551363052740288597e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2578.7MB, alloc=4.5MB, time=336.69 NO POLE NO POLE memory used=2582.6MB, alloc=4.5MB, time=336.93 memory used=2586.4MB, alloc=4.5MB, time=337.16 memory used=2590.2MB, alloc=4.5MB, time=337.39 memory used=2594.0MB, alloc=4.5MB, time=337.63 memory used=2597.8MB, alloc=4.5MB, time=337.86 memory used=2601.6MB, alloc=4.5MB, time=338.09 memory used=2605.4MB, alloc=4.5MB, time=338.32 memory used=2609.3MB, alloc=4.5MB, time=338.57 memory used=2613.1MB, alloc=4.5MB, time=338.80 x[1] = 6.7 y1[1] (analytic) = 1.9143831482353194411379018434766 y1[1] (numeric) = 1.9143831482344163920264902209375 absolute error = 9.030491114116225391e-13 relative error = 4.7171806346292498184446574458389e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.4048499206165981616321928483868 y2[1] (numeric) = 1.4048499206161644248423494373857 absolute error = 4.337367898434110011e-13 relative error = 3.0874243823357371958090554940112e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2616.9MB, alloc=4.5MB, time=339.05 NO POLE NO POLE memory used=2620.7MB, alloc=4.5MB, time=339.31 memory used=2624.5MB, alloc=4.5MB, time=339.54 memory used=2628.3MB, alloc=4.5MB, time=339.78 memory used=2632.1MB, alloc=4.5MB, time=340.01 memory used=2636.0MB, alloc=4.5MB, time=340.25 memory used=2639.8MB, alloc=4.5MB, time=340.48 memory used=2643.6MB, alloc=4.5MB, time=340.71 memory used=2647.4MB, alloc=4.5MB, time=340.95 memory used=2651.2MB, alloc=4.5MB, time=341.18 memory used=2655.0MB, alloc=4.5MB, time=341.41 x[1] = 6.8 y1[1] (analytic) = 1.8693974903498251724416246398463 y1[1] (numeric) = 1.8693974903489569781157075373864 absolute error = 8.681943259171024599e-13 relative error = 4.6442467714805534329166970759452e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.4941133511386083222220793776203 y2[1] (numeric) = 1.4941133511380786929163478452901 absolute error = 5.296293057315323302e-13 relative error = 3.5447732618674580249533316812957e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2658.8MB, alloc=4.5MB, time=341.64 memory used=2662.7MB, alloc=4.5MB, time=341.87 memory used=2666.5MB, alloc=4.5MB, time=342.11 memory used=2670.3MB, alloc=4.5MB, time=342.34 memory used=2674.1MB, alloc=4.5MB, time=342.57 memory used=2677.9MB, alloc=4.5MB, time=342.82 memory used=2681.7MB, alloc=4.5MB, time=343.07 memory used=2685.5MB, alloc=4.5MB, time=343.31 memory used=2689.4MB, alloc=4.5MB, time=343.54 memory used=2693.2MB, alloc=4.5MB, time=343.77 x[1] = 6.9 y1[1] (analytic) = 1.8157251001253570726567558363581 y1[1] (numeric) = 1.8157251001245339861763986142407 absolute error = 8.230864803572221174e-13 relative error = 4.5331007447129331056692595450996e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.5784397643881998701737832329889 y2[1] (numeric) = 1.5784397643875770529254763768184 absolute error = 6.228172483068561705e-13 relative error = 3.9457777379820312860420129281921e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2697.0MB, alloc=4.5MB, time=344.00 NO POLE NO POLE memory used=2700.8MB, alloc=4.5MB, time=344.24 memory used=2704.6MB, alloc=4.5MB, time=344.48 memory used=2708.4MB, alloc=4.5MB, time=344.71 memory used=2712.3MB, alloc=4.5MB, time=344.95 memory used=2716.1MB, alloc=4.5MB, time=345.18 memory used=2719.9MB, alloc=4.5MB, time=345.41 memory used=2723.7MB, alloc=4.5MB, time=345.65 memory used=2727.5MB, alloc=4.5MB, time=345.88 memory used=2731.3MB, alloc=4.5MB, time=346.11 memory used=2735.1MB, alloc=4.5MB, time=346.35 x[1] = 7 y1[1] (analytic) = 1.7539022543433046381411975217192 y1[1] (numeric) = 1.7539022543425367122783723105878 absolute error = 7.679258628252111314e-13 relative error = 4.3783846045214054281623545316121e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.6569865987187890903969990915936 y2[1] (numeric) = 1.6569865987180768913803174589222 absolute error = 7.121990166816326714e-13 relative error = 4.2981579768497666819617513452123e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2739.0MB, alloc=4.5MB, time=346.58 memory used=2742.8MB, alloc=4.5MB, time=346.82 memory used=2746.6MB, alloc=4.5MB, time=347.07 memory used=2750.4MB, alloc=4.5MB, time=347.32 memory used=2754.2MB, alloc=4.5MB, time=347.58 memory used=2758.0MB, alloc=4.5MB, time=347.85 memory used=2761.8MB, alloc=4.5MB, time=348.09 memory used=2765.7MB, alloc=4.5MB, time=348.35 memory used=2769.5MB, alloc=4.5MB, time=348.60 memory used=2773.3MB, alloc=4.5MB, time=348.86 x[1] = 7.1 y1[1] (analytic) = 1.6845466664428063406217999420893 y1[1] (numeric) = 1.6845466664421033091440063563372 absolute error = 7.030314777935857521e-13 relative error = 4.1734164555865395375226261400146e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.7289690401258761520759857678532 y2[1] (numeric) = 1.7289690401250794651839485130786 absolute error = 7.966868920372547746e-13 relative error = 4.6078725156307752534861500047707e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2777.1MB, alloc=4.5MB, time=349.11 memory used=2780.9MB, alloc=4.5MB, time=349.34 memory used=2784.7MB, alloc=4.5MB, time=349.60 memory used=2788.5MB, alloc=4.5MB, time=349.86 memory used=2792.4MB, alloc=4.5MB, time=350.11 memory used=2796.2MB, alloc=4.5MB, time=350.37 memory used=2800.0MB, alloc=4.5MB, time=350.65 memory used=2803.8MB, alloc=4.5MB, time=350.94 memory used=2807.6MB, alloc=4.5MB, time=351.18 memory used=2811.4MB, alloc=4.5MB, time=351.41 x[1] = 7.2 y1[1] (analytic) = 1.6083513145322546710048504790937 y1[1] (numeric) = 1.6083513145316258308266356023584 absolute error = 6.288401782148767353e-13 relative error = 3.9098434063067734323968130062200e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.7936678638491530524644457476436 y2[1] (numeric) = 1.7936678638482778326138587662411 absolute error = 8.752198505869814025e-13 relative error = 4.8794978614869532963386869343875e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2815.3MB, alloc=4.5MB, time=351.64 NO POLE NO POLE memory used=2819.1MB, alloc=4.5MB, time=351.87 memory used=2822.9MB, alloc=4.5MB, time=352.11 memory used=2826.7MB, alloc=4.5MB, time=352.34 memory used=2830.5MB, alloc=4.5MB, time=352.57 memory used=2834.3MB, alloc=4.5MB, time=352.80 memory used=2838.1MB, alloc=4.5MB, time=353.03 memory used=2842.0MB, alloc=4.5MB, time=353.27 memory used=2845.8MB, alloc=4.5MB, time=353.50 memory used=2849.6MB, alloc=4.5MB, time=353.74 memory used=2853.4MB, alloc=4.5MB, time=353.98 x[1] = 7.3 y1[1] (analytic) = 1.5260775173811051889154065767377 y1[1] (numeric) = 1.5260775173805592845010346615213 absolute error = 5.459044143719152164e-13 relative error = 3.5771735587110892212457731286241e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.8504366206285645175173662279669 y2[1] (numeric) = 1.8504366206276177411857091711811 absolute error = 9.467763316570567858e-13 relative error = 5.1165023492425890422941701088846e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2857.2MB, alloc=4.5MB, time=354.21 memory used=2861.0MB, alloc=4.5MB, time=354.44 memory used=2864.8MB, alloc=4.5MB, time=354.68 memory used=2868.7MB, alloc=4.5MB, time=354.91 memory used=2872.5MB, alloc=4.5MB, time=355.15 memory used=2876.3MB, alloc=4.5MB, time=355.38 memory used=2880.1MB, alloc=4.5MB, time=355.61 memory used=2883.9MB, alloc=4.5MB, time=355.84 memory used=2887.7MB, alloc=4.5MB, time=356.08 memory used=2891.5MB, alloc=4.5MB, time=356.31 x[1] = 7.4 y1[1] (analytic) = 1.4385473275743906491340984687003 y1[1] (numeric) = 1.4385473275739357605332478455027 absolute error = 4.548886008506231976e-13 relative error = 3.1621385833557140539279128387410e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.8987080958116267592694988965346 y2[1] (numeric) = 1.8987080958106163724578358886144 absolute error = 1.0103868116630079202e-12 relative error = 5.3214436378705454181780566813798e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2895.4MB, alloc=4.5MB, time=356.54 memory used=2899.2MB, alloc=4.5MB, time=356.77 memory used=2903.0MB, alloc=4.5MB, time=357.00 memory used=2906.8MB, alloc=4.5MB, time=357.23 memory used=2910.6MB, alloc=4.5MB, time=357.47 memory used=2914.4MB, alloc=4.5MB, time=357.70 memory used=2918.2MB, alloc=4.5MB, time=357.93 memory used=2922.1MB, alloc=4.5MB, time=358.16 memory used=2925.9MB, alloc=4.5MB, time=358.39 memory used=2929.7MB, alloc=4.5MB, time=358.62 x[1] = 7.5 y1[1] (analytic) = 1.3466353178350258109716193361719 y1[1] (numeric) = 1.3466353178346692468525370358664 absolute error = 3.565641190823003055e-13 relative error = 2.6478149975714688532486096513685e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.937999976774738857948463798149 y2[1] (numeric) = 1.937999976773673711913766772617 absolute error = 1.0651460346970255320e-12 relative error = 5.4961096360262316212874350785223e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=2933.5MB, alloc=4.5MB, time=358.86 NO POLE NO POLE memory used=2937.3MB, alloc=4.5MB, time=359.09 memory used=2941.1MB, alloc=4.5MB, time=359.32 memory used=2945.0MB, alloc=4.5MB, time=359.56 memory used=2948.8MB, alloc=4.5MB, time=359.80 memory used=2952.6MB, alloc=4.5MB, time=360.02 memory used=2956.4MB, alloc=4.5MB, time=360.25 memory used=2960.2MB, alloc=4.5MB, time=360.49 memory used=2964.0MB, alloc=4.5MB, time=360.72 memory used=2967.8MB, alloc=4.5MB, time=360.95 memory used=2971.7MB, alloc=4.5MB, time=361.18 x[1] = 7.6 y1[1] (analytic) = 1.2512598425822553800581527493518 y1[1] (numeric) = 1.2512598425820035770691622573167 absolute error = 2.518029889904920351e-13 relative error = 2.0123956705174848447149802511379e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.9679196720314864259034630180288 y2[1] (numeric) = 1.9679196720303762011513536695897 absolute error = 1.1102247521093484391e-12 relative error = 5.6416162096863525129891250869679e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2975.5MB, alloc=4.5MB, time=361.42 memory used=2979.3MB, alloc=4.5MB, time=361.65 memory used=2983.1MB, alloc=4.5MB, time=361.87 memory used=2986.9MB, alloc=4.5MB, time=362.11 memory used=2990.7MB, alloc=4.5MB, time=362.34 memory used=2994.5MB, alloc=4.5MB, time=362.57 memory used=2998.4MB, alloc=4.5MB, time=362.80 memory used=3002.2MB, alloc=4.5MB, time=363.03 memory used=3006.0MB, alloc=4.5MB, time=363.27 memory used=3009.8MB, alloc=4.5MB, time=363.50 x[1] = 7.7 y1[1] (analytic) = 1.153373862037864525977384239572 y1[1] (numeric) = 1.1533738620377229557181898507918 absolute error = 1.415702591943887802e-13 relative error = 1.2274446634697632775505428374369e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.9881682338770003685523936187237 y2[1] (numeric) = 1.988168233875855487725531172718 absolute error = 1.1448808268624460057e-12 relative error = 5.7584705728342050430127202300232e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3013.6MB, alloc=4.5MB, time=363.73 NO POLE NO POLE memory used=3017.4MB, alloc=4.5MB, time=363.96 memory used=3021.2MB, alloc=4.5MB, time=364.19 memory used=3025.1MB, alloc=4.5MB, time=364.43 memory used=3028.9MB, alloc=4.5MB, time=364.66 memory used=3032.7MB, alloc=4.5MB, time=364.89 memory used=3036.5MB, alloc=4.5MB, time=365.12 memory used=3040.3MB, alloc=4.5MB, time=365.36 memory used=3044.1MB, alloc=4.5MB, time=365.59 memory used=3048.0MB, alloc=4.5MB, time=365.82 x[1] = 7.8 y1[1] (analytic) = 1.0539554205626495730325679129525 y1[1] (numeric) = 1.0539554205626226578517867776119 absolute error = 2.69151807811353406e-14 relative error = 2.5537304762631029478365496890653e-12 % Correct digits = 13 h = 0.005 memory used=3051.8MB, alloc=4.5MB, time=366.05 y2[1] (analytic) = 1.9985433453746049634387733205961 y2[1] (numeric) = 1.99854334537343649387523063419 absolute error = 1.1684695635426864061e-12 relative error = 5.8466060605939454425144302056950e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3055.6MB, alloc=4.5MB, time=366.28 memory used=3059.4MB, alloc=4.5MB, time=366.53 memory used=3063.2MB, alloc=4.5MB, time=366.76 memory used=3067.0MB, alloc=4.5MB, time=366.99 memory used=3070.8MB, alloc=4.5MB, time=367.22 memory used=3074.7MB, alloc=4.5MB, time=367.46 memory used=3078.5MB, alloc=4.5MB, time=367.69 memory used=3082.3MB, alloc=4.5MB, time=367.92 memory used=3086.1MB, alloc=4.5MB, time=368.16 memory used=3089.9MB, alloc=4.5MB, time=368.39 x[1] = 7.9 y1[1] (analytic) = 0.95399787436046340550224704004151 y1[1] (numeric) = 0.9539978743605544442575666311571 absolute error = 9.103875531959111559e-14 relative error = 9.5428677323438741310463564279958e-12 % Correct digits = 13 h = 0.005 y2[1] (analytic) = 1.9989413418397720363049105120439 y2[1] (numeric) = 1.9989413418385915831732190382528 absolute error = 1.1804531316914737911e-12 relative error = 5.9053915539363269492624250752968e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3093.7MB, alloc=4.5MB, time=368.62 memory used=3097.5MB, alloc=4.5MB, time=368.85 memory used=3101.4MB, alloc=4.5MB, time=369.08 memory used=3105.2MB, alloc=4.5MB, time=369.32 memory used=3109.0MB, alloc=4.5MB, time=369.56 memory used=3112.8MB, alloc=4.5MB, time=369.79 memory used=3116.6MB, alloc=4.5MB, time=370.02 memory used=3120.4MB, alloc=4.5MB, time=370.25 memory used=3124.2MB, alloc=4.5MB, time=370.50 memory used=3128.1MB, alloc=4.5MB, time=370.73 x[1] = 8 y1[1] (analytic) = 0.85449996619138647413115861816881 y1[1] (numeric) = 0.85449996619159757895418119740613 absolute error = 2.1110482302257923732e-13 relative error = 2.4705070962553680554876443463391e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.9893582466233817778081235982453 y2[1] (numeric) = 1.9893582466222013688496151907816 absolute error = 1.1804089585084074637e-12 relative error = 5.9336168360422932214873387949265e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3131.9MB, alloc=4.5MB, time=370.96 NO POLE NO POLE memory used=3135.7MB, alloc=4.5MB, time=371.19 memory used=3139.5MB, alloc=4.5MB, time=371.42 memory used=3143.3MB, alloc=4.5MB, time=371.65 memory used=3147.1MB, alloc=4.5MB, time=371.88 memory used=3151.0MB, alloc=4.5MB, time=372.11 memory used=3154.8MB, alloc=4.5MB, time=372.35 memory used=3158.6MB, alloc=4.5MB, time=372.58 memory used=3162.4MB, alloc=4.5MB, time=372.81 memory used=3166.2MB, alloc=4.5MB, time=373.05 memory used=3170.0MB, alloc=4.5MB, time=373.28 x[1] = 8.1 y1[1] (analytic) = 0.75645584626420853553494823189785 y1[1] (numeric) = 0.75645584626454058053503548494036 absolute error = 3.3204500008725304251e-13 relative error = 4.3894828987980239320575952298983e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.9698898108450862432243199360998 y2[1] (numeric) = 1.9698898108439182062474142297979 absolute error = 1.1680369769057063019e-12 relative error = 5.9294533657424034036558383951963e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3173.8MB, alloc=4.5MB, time=373.52 memory used=3177.7MB, alloc=4.5MB, time=373.75 memory used=3181.5MB, alloc=4.5MB, time=373.98 memory used=3185.3MB, alloc=4.5MB, time=374.22 memory used=3189.1MB, alloc=4.5MB, time=374.45 memory used=3192.9MB, alloc=4.5MB, time=374.68 memory used=3196.7MB, alloc=4.5MB, time=374.91 memory used=3200.5MB, alloc=4.5MB, time=375.15 memory used=3204.4MB, alloc=4.5MB, time=375.38 memory used=3208.2MB, alloc=4.5MB, time=375.61 x[1] = 8.2 y1[1] (analytic) = 0.66084513901616479259951187548036 y1[1] (numeric) = 0.66084513901661737532083677105669 absolute error = 4.5258272132489557633e-13 relative error = 6.8485443049286777987516674583424e-11 % Correct digits = 12 h = 0.005 y2[1] (analytic) = 1.9407305566797729011536487499456 y2[1] (numeric) = 1.9407305566786297355273882753246 absolute error = 1.1431656262604746210e-12 relative error = 5.8903881444326679484392822299817e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3212.0MB, alloc=4.5MB, time=375.84 NO POLE NO POLE memory used=3215.8MB, alloc=4.5MB, time=376.07 memory used=3219.6MB, alloc=4.5MB, time=376.31 memory used=3223.4MB, alloc=4.5MB, time=376.54 memory used=3227.2MB, alloc=4.5MB, time=376.77 memory used=3231.1MB, alloc=4.5MB, time=377.01 memory used=3234.9MB, alloc=4.5MB, time=377.24 memory used=3238.7MB, alloc=4.5MB, time=377.47 memory used=3242.5MB, alloc=4.5MB, time=377.71 memory used=3246.3MB, alloc=4.5MB, time=377.94 memory used=3250.1MB, alloc=4.5MB, time=378.17 x[1] = 8.3 y1[1] (analytic) = 0.56862315502937982629067353455349 y1[1] (numeric) = 0.56862315502995124260543084107344 absolute error = 5.7141631475730651995e-13 relative error = 1.0049121455980496884178789183114e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.902171833756293640000504405253 y2[1] (numeric) = 1.9021718337551878834845979267977 absolute error = 1.1057565159064784553e-12 relative error = 5.8131263237291107999726963929190e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3253.9MB, alloc=4.5MB, time=378.40 memory used=3257.8MB, alloc=4.5MB, time=378.63 memory used=3261.6MB, alloc=4.5MB, time=378.87 memory used=3265.4MB, alloc=4.5MB, time=379.10 memory used=3269.2MB, alloc=4.5MB, time=379.33 memory used=3273.0MB, alloc=4.5MB, time=379.57 memory used=3276.8MB, alloc=4.5MB, time=379.80 memory used=3280.7MB, alloc=4.5MB, time=380.04 memory used=3284.5MB, alloc=4.5MB, time=380.28 memory used=3288.3MB, alloc=4.5MB, time=380.51 x[1] = 8.4 y1[1] (analytic) = 0.48071134588331470085519515941454 y1[1] (numeric) = 0.48071134588400193383486665886312 absolute error = 6.8723297967149944858e-13 relative error = 1.4296167243747866598640423838443e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.8545989080882806628332392814224 y2[1] (numeric) = 1.854598908087224755157938495443 absolute error = 1.0559076753007859794e-12 relative error = 5.6934557153881586075180838088076e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3292.1MB, alloc=4.5MB, time=380.74 memory used=3295.9MB, alloc=4.5MB, time=380.97 memory used=3299.7MB, alloc=4.5MB, time=381.20 memory used=3303.5MB, alloc=4.5MB, time=381.44 memory used=3307.4MB, alloc=4.5MB, time=381.67 memory used=3311.2MB, alloc=4.5MB, time=381.90 memory used=3315.0MB, alloc=4.5MB, time=382.13 memory used=3318.8MB, alloc=4.5MB, time=382.37 memory used=3322.6MB, alloc=4.5MB, time=382.60 memory used=3326.4MB, alloc=4.5MB, time=382.83 x[1] = 8.5 y1[1] (analytic) = 0.397988097315176384651573477043 y1[1] (numeric) = 0.39798809731597510780876612689928 absolute error = 7.9872315719264985628e-13 relative error = 2.0069021224022227503746119472407e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.7984871126234902866669131603391 y2[1] (numeric) = 1.7984871126224964313371643967097 absolute error = 9.938553297487636294e-13 relative error = 5.5260631158985973415910295272860e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3330.2MB, alloc=4.5MB, time=383.07 NO POLE NO POLE memory used=3334.1MB, alloc=4.5MB, time=383.30 memory used=3337.9MB, alloc=4.5MB, time=383.54 memory used=3341.7MB, alloc=4.5MB, time=383.77 memory used=3345.5MB, alloc=4.5MB, time=384.00 memory used=3349.3MB, alloc=4.5MB, time=384.24 memory used=3353.1MB, alloc=4.5MB, time=384.47 memory used=3356.9MB, alloc=4.5MB, time=384.71 memory used=3360.8MB, alloc=4.5MB, time=384.94 memory used=3364.6MB, alloc=4.5MB, time=385.18 memory used=3368.4MB, alloc=4.5MB, time=385.41 x[1] = 8.6 y1[1] (analytic) = 0.32127995267998729913553021483952 y1[1] (numeric) = 0.32127995268089189427279491475957 absolute error = 9.0459513726469992005e-13 relative error = 2.8155978289928565379681238678331e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.7343970978741131437171641875634 y2[1] (numeric) = 1.734397097873193169560748293724 absolute error = 9.199741564158938394e-13 relative error = 5.3042879139011788892534578529303e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3372.2MB, alloc=4.5MB, time=385.64 memory used=3376.0MB, alloc=4.5MB, time=385.87 memory used=3379.8MB, alloc=4.5MB, time=386.11 memory used=3383.7MB, alloc=4.5MB, time=386.35 memory used=3387.5MB, alloc=4.5MB, time=386.58 memory used=3391.3MB, alloc=4.5MB, time=386.82 memory used=3395.1MB, alloc=4.5MB, time=387.05 memory used=3398.9MB, alloc=4.5MB, time=387.29 memory used=3402.7MB, alloc=4.5MB, time=387.52 memory used=3406.5MB, alloc=4.5MB, time=387.75 x[1] = 8.7 y1[1] (analytic) = 0.25135335440260084268120821911072 y1[1] (numeric) = 0.25135335440360443242208838685113 absolute error = 1.00358974088016774041e-12 relative error = 3.9927445697529280314145043191336e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.6629692300821827922023461866156 y2[1] (numeric) = 1.6629692300813480162104189323011 absolute error = 8.347759919272543145e-13 relative error = 5.0197921694919169419843572458500e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3410.4MB, alloc=4.5MB, time=387.99 memory used=3414.2MB, alloc=4.5MB, time=388.22 memory used=3418.0MB, alloc=4.5MB, time=388.45 memory used=3421.8MB, alloc=4.5MB, time=388.68 memory used=3425.6MB, alloc=4.5MB, time=388.92 memory used=3429.4MB, alloc=4.5MB, time=389.15 memory used=3433.2MB, alloc=4.5MB, time=389.39 memory used=3437.1MB, alloc=4.5MB, time=389.63 memory used=3440.9MB, alloc=4.5MB, time=389.86 memory used=3444.7MB, alloc=4.5MB, time=390.09 x[1] = 8.8 y1[1] (analytic) = 0.18890698593834443711091449578068 y1[1] (numeric) = 0.18890698593943893202402956491869 absolute error = 1.09449491311506913801e-12 relative error = 5.7938297394268466698096904926224e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.5849171928917622535309313118124 y2[1] (numeric) = 1.5849171928910233465509554925544 absolute error = 7.389069799758192580e-13 relative error = 4.6621172594364112282905543625710e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3448.5MB, alloc=4.5MB, time=390.33 NO POLE NO POLE memory used=3452.3MB, alloc=4.5MB, time=390.56 memory used=3456.1MB, alloc=4.5MB, time=390.80 memory used=3459.9MB, alloc=4.5MB, time=391.03 memory used=3463.8MB, alloc=4.5MB, time=391.26 memory used=3467.6MB, alloc=4.5MB, time=391.49 memory used=3471.4MB, alloc=4.5MB, time=391.73 memory used=3475.2MB, alloc=4.5MB, time=391.97 memory used=3479.0MB, alloc=4.5MB, time=392.21 memory used=3482.8MB, alloc=4.5MB, time=392.44 memory used=3486.6MB, alloc=4.5MB, time=392.67 x[1] = 8.9 y1[1] (analytic) = 0.13456479075888794036017232177465 y1[1] (numeric) = 0.13456479076006410042123190644279 absolute error = 1.17616006105958466814e-12 relative error = 8.7404740454508517571071890978498e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 1.5010208564578849820161746471113 y2[1] (numeric) = 1.5010208564572518388513331749565 absolute error = 6.331431648414721548e-13 relative error = 4.2180837269347870783680477306296e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3490.5MB, alloc=4.5MB, time=392.90 memory used=3494.3MB, alloc=4.5MB, time=393.14 memory used=3498.1MB, alloc=4.5MB, time=393.38 memory used=3501.9MB, alloc=4.5MB, time=393.61 memory used=3505.7MB, alloc=4.5MB, time=393.84 memory used=3509.5MB, alloc=4.5MB, time=394.07 memory used=3513.4MB, alloc=4.5MB, time=394.30 memory used=3517.2MB, alloc=4.5MB, time=394.53 memory used=3521.0MB, alloc=4.5MB, time=394.77 memory used=3524.8MB, alloc=4.5MB, time=395.00 x[1] = 9 y1[1] (analytic) = 0.08886973811532301163170528881883 y1[1] (numeric) = 0.088869738116570521602833667884728 absolute error = 1.247509971128379065898e-12 relative error = 1.4037511503741925777611419239454e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.4121184852417565697562725663524 y2[1] (numeric) = 1.4121184852412381852019023927835 absolute error = 5.183845543701735689e-13 relative error = 3.6709706712848917998791605127582e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3528.6MB, alloc=4.5MB, time=395.23 memory used=3532.4MB, alloc=4.5MB, time=395.46 memory used=3536.2MB, alloc=4.5MB, time=395.69 memory used=3540.1MB, alloc=4.5MB, time=395.92 memory used=3543.9MB, alloc=4.5MB, time=396.16 memory used=3547.7MB, alloc=4.5MB, time=396.39 memory used=3551.5MB, alloc=4.5MB, time=396.62 memory used=3555.3MB, alloc=4.5MB, time=396.86 memory used=3559.1MB, alloc=4.5MB, time=397.09 memory used=3562.9MB, alloc=4.5MB, time=397.32 x[1] = 9.1 y1[1] (analytic) = 0.05227839786888797528093341042463 y1[1] (numeric) = 0.052278397870195533423437324281944 absolute error = 1.307558142503913857314e-12 relative error = 2.5011442504095376548655254702270e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.3190983623493517707939976839854 y2[1] (numeric) = 1.3190983623489561231004180849937 absolute error = 3.956476935795989917e-13 relative error = 2.9993797647882692806251349624088e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3566.8MB, alloc=4.5MB, time=397.55 NO POLE NO POLE memory used=3570.6MB, alloc=4.5MB, time=397.79 memory used=3574.4MB, alloc=4.5MB, time=398.03 memory used=3578.2MB, alloc=4.5MB, time=398.26 memory used=3582.0MB, alloc=4.5MB, time=398.49 memory used=3585.8MB, alloc=4.5MB, time=398.72 memory used=3589.6MB, alloc=4.5MB, time=398.95 memory used=3593.5MB, alloc=4.5MB, time=399.19 memory used=3597.3MB, alloc=4.5MB, time=399.43 memory used=3601.1MB, alloc=4.5MB, time=399.66 memory used=3604.9MB, alloc=4.5MB, time=399.89 x[1] = 9.2 y1[1] (analytic) = 0.0251563785958362580585546615242 y1[1] (numeric) = 0.025156378597191677436162989012362 absolute error = 1.355419377608327488162e-12 relative error = 5.3879749521366674813785948709255e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 1.2228899141002469575280690577583 y2[1] (numeric) = 1.2228899140999809007206245515018 absolute error = 2.660568074445062565e-13 relative error = 2.1756398869334049357922940465300e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3608.7MB, alloc=4.5MB, time=400.12 memory used=3612.5MB, alloc=4.5MB, time=400.35 memory used=3616.4MB, alloc=4.5MB, time=400.58 memory used=3620.2MB, alloc=4.5MB, time=400.81 memory used=3624.0MB, alloc=4.5MB, time=401.04 memory used=3627.8MB, alloc=4.5MB, time=401.28 memory used=3631.6MB, alloc=4.5MB, time=401.51 memory used=3635.4MB, alloc=4.5MB, time=401.74 memory used=3639.2MB, alloc=4.5MB, time=401.97 memory used=3643.1MB, alloc=4.5MB, time=402.20 x[1] = 9.3 y1[1] (analytic) = 0.00777467454739659224309076536484 y1[1] (numeric) = 0.0077746745487869137195807702044418 absolute error = 1.3903214764900048396018e-12 relative error = 1.7882696799900959908797482250745e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 1.1244544235070624079894062785863 y2[1] (numeric) = 1.1244544235069315744010329290693 absolute error = 1.308335883733495170e-13 relative error = 1.1635294916204114608318495182002e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3646.9MB, alloc=4.5MB, time=402.43 NO POLE NO POLE memory used=3650.7MB, alloc=4.5MB, time=402.66 memory used=3654.5MB, alloc=4.5MB, time=402.90 memory used=3658.3MB, alloc=4.5MB, time=403.13 memory used=3662.1MB, alloc=4.5MB, time=403.37 memory used=3665.9MB, alloc=4.5MB, time=403.60 memory used=3669.8MB, alloc=4.5MB, time=403.84 memory used=3673.6MB, alloc=4.5MB, time=404.08 memory used=3677.4MB, alloc=4.5MB, time=404.32 memory used=3681.2MB, alloc=4.5MB, time=404.55 memory used=3685.0MB, alloc=4.5MB, time=404.78 x[1] = 9.4 y1[1] (analytic) = 0.00030695796479352782205257932708 y1[1] (numeric) = 0.00030695796620514371185686100940899 absolute error = 1.41161588980428168232899e-12 relative error = 4.5987270301123831988590599731501e-07 % Correct digits = 8 h = 0.005 y2[1] (analytic) = 1.0247754254533581210797730773676 y2[1] (numeric) = 1.0247754254533668353595518889669 absolute error = 8.7142797788115993e-15 relative error = 8.5035994837175407632817573911865e-13 % Correct digits = 14 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3688.8MB, alloc=4.5MB, time=405.01 memory used=3692.6MB, alloc=4.5MB, time=405.24 memory used=3696.5MB, alloc=4.5MB, time=405.47 memory used=3700.3MB, alloc=4.5MB, time=405.71 memory used=3704.1MB, alloc=4.5MB, time=405.93 memory used=3707.9MB, alloc=4.5MB, time=406.17 memory used=3711.7MB, alloc=4.5MB, time=406.40 memory used=3715.5MB, alloc=4.5MB, time=406.63 memory used=3719.3MB, alloc=4.5MB, time=406.86 memory used=3723.2MB, alloc=4.5MB, time=407.10 x[1] = 9.5 y1[1] (analytic) = 0.00282784380362152710839835982201 y1[1] (numeric) = 0.0028278438050403143029959119591906 absolute error = 1.4187871945975521371806e-12 relative error = 5.0172049558768336552773707426823e-08 % Correct digits = 9 h = 0.005 y2[1] (analytic) = 0.92484887953819069271651749546599 y2[1] (numeric) = 0.92484887953834189847031584210668 absolute error = 1.5120575379834664069e-13 relative error = 1.6349239010144981535672231245323e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3727.0MB, alloc=4.5MB, time=407.33 NO POLE NO POLE memory used=3730.8MB, alloc=4.5MB, time=407.56 memory used=3734.6MB, alloc=4.5MB, time=407.79 memory used=3738.4MB, alloc=4.5MB, time=408.02 memory used=3742.2MB, alloc=4.5MB, time=408.25 memory used=3746.1MB, alloc=4.5MB, time=408.49 memory used=3749.9MB, alloc=4.5MB, time=408.72 memory used=3753.7MB, alloc=4.5MB, time=408.95 memory used=3757.5MB, alloc=4.5MB, time=409.19 memory used=3761.3MB, alloc=4.5MB, time=409.42 x[1] = 9.6 y1[1] (analytic) = 0.01531214420587308997965792011627 y1[1] (numeric) = 0.015312144207284551247941818151541 absolute error = 1.411461268283898035271e-12 relative error = 9.2179204251650221165484605290024e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.82567321877702001487589827347958 y2[1] (numeric) = 0.82567321877731521497331961178684 absolute error = 2.9520009742133830726e-13 relative error = 3.5752655010245593551619970262008e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3765.1MB, alloc=4.5MB, time=409.65 NO POLE NO POLE memory used=3768.9MB, alloc=4.5MB, time=409.89 memory used=3772.8MB, alloc=4.5MB, time=410.13 memory used=3776.6MB, alloc=4.5MB, time=410.36 memory used=3780.4MB, alloc=4.5MB, time=410.59 memory used=3784.2MB, alloc=4.5MB, time=410.82 memory used=3788.0MB, alloc=4.5MB, time=411.06 memory used=3791.8MB, alloc=4.5MB, time=411.29 memory used=3795.6MB, alloc=4.5MB, time=411.52 memory used=3799.5MB, alloc=4.5MB, time=411.75 memory used=3803.3MB, alloc=4.5MB, time=411.98 x[1] = 9.7 y1[1] (analytic) = 0.03763512016868996592964362910856 y1[1] (numeric) = 0.037635120170079377978570980174038 absolute error = 1.389412048927351065478e-12 relative error = 3.6917964993858417575717770210470e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.72823937358905687566225910317516 y2[1] (numeric) = 0.72823937358949608710889706919287 absolute error = 4.3921144663796601771e-13 relative error = 6.0311411682309231635898722296841e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3807.1MB, alloc=4.5MB, time=412.22 memory used=3810.9MB, alloc=4.5MB, time=412.45 memory used=3814.7MB, alloc=4.5MB, time=412.68 memory used=3818.5MB, alloc=4.5MB, time=412.91 memory used=3822.3MB, alloc=4.5MB, time=413.15 memory used=3826.2MB, alloc=4.5MB, time=413.38 memory used=3830.0MB, alloc=4.5MB, time=413.61 memory used=3833.8MB, alloc=4.5MB, time=413.85 memory used=3837.6MB, alloc=4.5MB, time=414.08 memory used=3841.4MB, alloc=4.5MB, time=414.31 x[1] = 9.8 y1[1] (analytic) = 0.06957372789524648145062224791078 y1[1] (numeric) = 0.069573727896599048234708975769367 absolute error = 1.352566784086727858587e-12 relative error = 1.9440769166821373034916193749910e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.63352087074807225183074705127114 y2[1] (numeric) = 0.63352087074865397595751031052615 absolute error = 5.8172412676325925501e-13 relative error = 9.1823987752187150852887326075173e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop memory used=3845.2MB, alloc=4.5MB, time=414.54 NO POLE NO POLE memory used=3849.1MB, alloc=4.5MB, time=414.77 memory used=3852.9MB, alloc=4.5MB, time=415.01 memory used=3856.7MB, alloc=4.5MB, time=415.24 memory used=3860.5MB, alloc=4.5MB, time=415.47 memory used=3864.3MB, alloc=4.5MB, time=415.71 memory used=3868.1MB, alloc=4.5MB, time=415.94 memory used=3871.9MB, alloc=4.5MB, time=416.18 memory used=3875.8MB, alloc=4.5MB, time=416.41 memory used=3879.6MB, alloc=4.5MB, time=416.64 memory used=3883.4MB, alloc=4.5MB, time=416.87 x[1] = 9.9 y1[1] (analytic) = 0.11080884737463894536556130131089 y1[1] (numeric) = 0.11080884737593995505146343906222 absolute error = 1.30100968590213775133e-12 relative error = 1.1741027153756881171573819248723e-09 % Correct digits = 10 h = 0.005 y2[1] (analytic) = 0.54246410622467895558618189249464 y2[1] (numeric) = 0.54246410622540016414970884018233 absolute error = 7.2120856352694768769e-13 relative error = 1.3295046718321229655254077069926e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3887.2MB, alloc=4.5MB, time=417.11 memory used=3891.0MB, alloc=4.5MB, time=417.34 memory used=3894.8MB, alloc=4.5MB, time=417.57 memory used=3898.6MB, alloc=4.5MB, time=417.80 memory used=3902.5MB, alloc=4.5MB, time=418.03 memory used=3906.3MB, alloc=4.5MB, time=418.26 memory used=3910.1MB, alloc=4.5MB, time=418.49 memory used=3913.9MB, alloc=4.5MB, time=418.72 memory used=3917.7MB, alloc=4.5MB, time=418.96 memory used=3921.5MB, alloc=4.5MB, time=419.20 x[1] = 10 y1[1] (analytic) = 0.16092847092354754774113605217594 y1[1] (numeric) = 0.16092847092478253166778151085831 absolute error = 1.23498392664545868237e-12 relative error = 7.6741170754810921661720803770323e-10 % Correct digits = 11 h = 0.005 y2[1] (analytic) = 0.45597888911063018659525233814862 y2[1] (numeric) = 0.4559788891114863242167930910881 absolute error = 8.5613762154075293948e-13 relative error = 1.8775817082466634211849202297960e-10 % Correct digits = 11 h = 0.005 Finished! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 1980 Total Elapsed Time = 6 Minutes 59 Seconds Elapsed Time(since restart) = 6 Minutes 59 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.1 % > quit memory used=3923.9MB, alloc=4.5MB, time=419.34