|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > ALWAYS, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_start_msg, > glob_max_sec, > glob_look_poles, > days_in_year, > glob_iter, > glob_small_float, > glob_max_iter, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > djd_debug2, > glob_log10normmin, > glob_log10relerr, > glob_relerr, > glob_clock_start_sec, > glob_max_opt_iter, > glob_start, > glob_max_trunc_err, > glob_hmin_init, > glob_hmin, > glob_disp_incr, > glob_dump, > glob_optimal_expect_sec, > glob_subiter_method, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > glob_no_eqs, > glob_hmax, > glob_reached_optimal_h, > glob_initial_pass, > glob_clock_sec, > years_in_century, > djd_debug, > glob_h, > glob_current_iter, > glob_warned2, > glob_large_float, > glob_almost_1, > hours_in_day, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_normmax, > glob_warned, > glob_unchanged_h_cnt, > glob_log10_relerr, > centuries_in_millinium, > glob_percent_done, > glob_max_rel_trunc_err, > glob_last_good_h, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_m1, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, ALWAYS, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_start_msg, glob_max_sec, glob_look_poles, days_in_year, glob_iter, glob_small_float, glob_max_iter, glob_max_hours, glob_optimal_done, glob_not_yet_finished, djd_debug2, glob_log10normmin, glob_log10relerr, glob_relerr, glob_clock_start_sec, glob_max_opt_iter, glob_start, glob_max_trunc_err, glob_hmin_init, glob_hmin, glob_disp_incr, glob_dump, glob_optimal_expect_sec, glob_subiter_method, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, sec_in_min, glob_log10abserr, glob_optimal_start, glob_no_eqs, glob_hmax, glob_reached_optimal_h, glob_initial_pass, glob_clock_sec, years_in_century, djd_debug, glob_h, glob_current_iter, glob_warned2, glob_large_float, glob_almost_1, hours_in_day, min_in_hour, glob_html_log, glob_max_minutes, glob_normmax, glob_warned, glob_unchanged_h_cnt, glob_log10_relerr, centuries_in_millinium, glob_percent_done, glob_max_rel_trunc_err, glob_last_good_h, glob_display_flag, array_const_1, array_const_0D0, array_y, array_x, array_last_rel_error, array_fact_1, array_m1, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_y_higher_work, array_fact_2, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 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_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > ALWAYS, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_start_msg, > glob_max_sec, > glob_look_poles, > days_in_year, > glob_iter, > glob_small_float, > glob_max_iter, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > djd_debug2, > glob_log10normmin, > glob_log10relerr, > glob_relerr, > glob_clock_start_sec, > glob_max_opt_iter, > glob_start, > glob_max_trunc_err, > glob_hmin_init, > glob_hmin, > glob_disp_incr, > glob_dump, > glob_optimal_expect_sec, > glob_subiter_method, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > glob_no_eqs, > glob_hmax, > glob_reached_optimal_h, > glob_initial_pass, > glob_clock_sec, > years_in_century, > djd_debug, > glob_h, > glob_current_iter, > glob_warned2, > glob_large_float, > glob_almost_1, > hours_in_day, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_normmax, > glob_warned, > glob_unchanged_h_cnt, > glob_log10_relerr, > centuries_in_millinium, > glob_percent_done, > glob_max_rel_trunc_err, > glob_last_good_h, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_m1, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_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 (abs(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"); > newline(); > 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 > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, ALWAYS, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_start_msg, glob_max_sec, glob_look_poles, days_in_year, glob_iter, glob_small_float, glob_max_iter, glob_max_hours, glob_optimal_done, glob_not_yet_finished, djd_debug2, glob_log10normmin, glob_log10relerr, glob_relerr, glob_clock_start_sec, glob_max_opt_iter, glob_start, glob_max_trunc_err, glob_hmin_init, glob_hmin, glob_disp_incr, glob_dump, glob_optimal_expect_sec, glob_subiter_method, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, sec_in_min, glob_log10abserr, glob_optimal_start, glob_no_eqs, glob_hmax, glob_reached_optimal_h, glob_initial_pass, glob_clock_sec, years_in_century, djd_debug, glob_h, glob_current_iter, glob_warned2, glob_large_float, glob_almost_1, hours_in_day, min_in_hour, glob_html_log, glob_max_minutes, glob_normmax, glob_warned, glob_unchanged_h_cnt, glob_log10_relerr, centuries_in_millinium, glob_percent_done, glob_max_rel_trunc_err, glob_last_good_h, glob_display_flag, array_const_1, array_const_0D0, array_y, array_x, array_last_rel_error, array_fact_1, array_m1, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_y_higher_work, array_fact_2, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(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"); newline(); 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 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > ALWAYS, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_start_msg, > glob_max_sec, > glob_look_poles, > days_in_year, > glob_iter, > glob_small_float, > glob_max_iter, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > djd_debug2, > glob_log10normmin, > glob_log10relerr, > glob_relerr, > glob_clock_start_sec, > glob_max_opt_iter, > glob_start, > glob_max_trunc_err, > glob_hmin_init, > glob_hmin, > glob_disp_incr, > glob_dump, > glob_optimal_expect_sec, > glob_subiter_method, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > glob_no_eqs, > glob_hmax, > glob_reached_optimal_h, > glob_initial_pass, > glob_clock_sec, > years_in_century, > djd_debug, > glob_h, > glob_current_iter, > glob_warned2, > glob_large_float, > glob_almost_1, > hours_in_day, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_normmax, > glob_warned, > glob_unchanged_h_cnt, > glob_log10_relerr, > centuries_in_millinium, > glob_percent_done, > glob_max_rel_trunc_err, > glob_last_good_h, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_m1, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > 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, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, ALWAYS, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_start_msg, glob_max_sec, glob_look_poles, days_in_year, glob_iter, glob_small_float, glob_max_iter, glob_max_hours, glob_optimal_done, glob_not_yet_finished, djd_debug2, glob_log10normmin, glob_log10relerr, glob_relerr, glob_clock_start_sec, glob_max_opt_iter, glob_start, glob_max_trunc_err, glob_hmin_init, glob_hmin, glob_disp_incr, glob_dump, glob_optimal_expect_sec, glob_subiter_method, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, sec_in_min, glob_log10abserr, glob_optimal_start, glob_no_eqs, glob_hmax, glob_reached_optimal_h, glob_initial_pass, glob_clock_sec, years_in_century, djd_debug, glob_h, glob_current_iter, glob_warned2, glob_large_float, glob_almost_1, hours_in_day, min_in_hour, glob_html_log, glob_max_minutes, glob_normmax, glob_warned, glob_unchanged_h_cnt, glob_log10_relerr, centuries_in_millinium, glob_percent_done, glob_max_rel_trunc_err, glob_last_good_h, glob_display_flag, array_const_1, array_const_0D0, array_y, array_x, array_last_rel_error, array_fact_1, array_m1, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_y_higher_work, array_fact_2, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > ALWAYS, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_start_msg, > glob_max_sec, > glob_look_poles, > days_in_year, > glob_iter, > glob_small_float, > glob_max_iter, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > djd_debug2, > glob_log10normmin, > glob_log10relerr, > glob_relerr, > glob_clock_start_sec, > glob_max_opt_iter, > glob_start, > glob_max_trunc_err, > glob_hmin_init, > glob_hmin, > glob_disp_incr, > glob_dump, > glob_optimal_expect_sec, > glob_subiter_method, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > glob_no_eqs, > glob_hmax, > glob_reached_optimal_h, > glob_initial_pass, > glob_clock_sec, > years_in_century, > djd_debug, > glob_h, > glob_current_iter, > glob_warned2, > glob_large_float, > glob_almost_1, > hours_in_day, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_normmax, > glob_warned, > glob_unchanged_h_cnt, > glob_log10_relerr, > centuries_in_millinium, > glob_percent_done, > glob_max_rel_trunc_err, > glob_last_good_h, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_m1, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_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_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(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 > #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 (abs(array_y_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 (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_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_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_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 ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(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 (abs(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 (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > 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 2 > 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 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > 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 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > 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 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > 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 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > 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 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, ALWAYS, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_start_msg, glob_max_sec, glob_look_poles, days_in_year, glob_iter, glob_small_float, glob_max_iter, glob_max_hours, glob_optimal_done, glob_not_yet_finished, djd_debug2, glob_log10normmin, glob_log10relerr, glob_relerr, glob_clock_start_sec, glob_max_opt_iter, glob_start, glob_max_trunc_err, glob_hmin_init, glob_hmin, glob_disp_incr, glob_dump, glob_optimal_expect_sec, glob_subiter_method, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, sec_in_min, glob_log10abserr, glob_optimal_start, glob_no_eqs, glob_hmax, glob_reached_optimal_h, glob_initial_pass, glob_clock_sec, years_in_century, djd_debug, glob_h, glob_current_iter, glob_warned2, glob_large_float, glob_almost_1, hours_in_day, min_in_hour, glob_html_log, glob_max_minutes, glob_normmax, glob_warned, glob_unchanged_h_cnt, glob_log10_relerr, centuries_in_millinium, glob_percent_done, glob_max_rel_trunc_err, glob_last_good_h, glob_display_flag, array_const_1, array_const_0D0, array_y, array_x, array_last_rel_error, array_fact_1, array_m1, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_y_higher_work, array_fact_2, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(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 - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_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 <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_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 abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(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 < abs(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 < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; 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; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > ALWAYS, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_start_msg, > glob_max_sec, > glob_look_poles, > days_in_year, > glob_iter, > glob_small_float, > glob_max_iter, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > djd_debug2, > glob_log10normmin, > glob_log10relerr, > glob_relerr, > glob_clock_start_sec, > glob_max_opt_iter, > glob_start, > glob_max_trunc_err, > glob_hmin_init, > glob_hmin, > glob_disp_incr, > glob_dump, > glob_optimal_expect_sec, > glob_subiter_method, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > glob_no_eqs, > glob_hmax, > glob_reached_optimal_h, > glob_initial_pass, > glob_clock_sec, > years_in_century, > djd_debug, > glob_h, > glob_current_iter, > glob_warned2, > glob_large_float, > glob_almost_1, > hours_in_day, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_normmax, > glob_warned, > glob_unchanged_h_cnt, > glob_log10_relerr, > centuries_in_millinium, > glob_percent_done, > glob_max_rel_trunc_err, > glob_last_good_h, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_m1, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, ALWAYS, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_start_msg, glob_max_sec, glob_look_poles, days_in_year, glob_iter, glob_small_float, glob_max_iter, glob_max_hours, glob_optimal_done, glob_not_yet_finished, djd_debug2, glob_log10normmin, glob_log10relerr, glob_relerr, glob_clock_start_sec, glob_max_opt_iter, glob_start, glob_max_trunc_err, glob_hmin_init, glob_hmin, glob_disp_incr, glob_dump, glob_optimal_expect_sec, glob_subiter_method, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, sec_in_min, glob_log10abserr, glob_optimal_start, glob_no_eqs, glob_hmax, glob_reached_optimal_h, glob_initial_pass, glob_clock_sec, years_in_century, djd_debug, glob_h, glob_current_iter, glob_warned2, glob_large_float, glob_almost_1, hours_in_day, min_in_hour, glob_html_log, glob_max_minutes, glob_normmax, glob_warned, glob_unchanged_h_cnt, glob_log10_relerr, centuries_in_millinium, glob_percent_done, glob_max_rel_trunc_err, glob_last_good_h, glob_display_flag, array_const_1, array_const_0D0, array_y, array_x, array_last_rel_error, array_fact_1, array_m1, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_y_higher_work, array_fact_2, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > ALWAYS, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_start_msg, > glob_max_sec, > glob_look_poles, > days_in_year, > glob_iter, > glob_small_float, > glob_max_iter, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > djd_debug2, > glob_log10normmin, > glob_log10relerr, > glob_relerr, > glob_clock_start_sec, > glob_max_opt_iter, > glob_start, > glob_max_trunc_err, > glob_hmin_init, > glob_hmin, > glob_disp_incr, > glob_dump, > glob_optimal_expect_sec, > glob_subiter_method, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > glob_no_eqs, > glob_hmax, > glob_reached_optimal_h, > glob_initial_pass, > glob_clock_sec, > years_in_century, > djd_debug, > glob_h, > glob_current_iter, > glob_warned2, > glob_large_float, > glob_almost_1, > hours_in_day, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_normmax, > glob_warned, > glob_unchanged_h_cnt, > glob_log10_relerr, > centuries_in_millinium, > glob_percent_done, > glob_max_rel_trunc_err, > glob_last_good_h, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_m1, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult $eq_no = 1 i = 1 > array_tmp1[1] := (array_y[1] * (array_y[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_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 $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_y,array_y,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_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_y_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 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, ALWAYS, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_start_msg, glob_max_sec, glob_look_poles, days_in_year, glob_iter, glob_small_float, glob_max_iter, glob_max_hours, glob_optimal_done, glob_not_yet_finished, djd_debug2, glob_log10normmin, glob_log10relerr, glob_relerr, glob_clock_start_sec, glob_max_opt_iter, glob_start, glob_max_trunc_err, glob_hmin_init, glob_hmin, glob_disp_incr, glob_dump, glob_optimal_expect_sec, glob_subiter_method, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, sec_in_min, glob_log10abserr, glob_optimal_start, glob_no_eqs, glob_hmax, glob_reached_optimal_h, glob_initial_pass, glob_clock_sec, years_in_century, djd_debug, glob_h, glob_current_iter, glob_warned2, glob_large_float, glob_almost_1, hours_in_day, min_in_hour, glob_html_log, glob_max_minutes, glob_normmax, glob_warned, glob_unchanged_h_cnt, glob_log10_relerr, centuries_in_millinium, glob_percent_done, glob_max_rel_trunc_err, glob_last_good_h, glob_display_flag, array_const_1, array_const_0D0, array_y, array_x, array_last_rel_error, array_fact_1, array_m1, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_y_higher_work, array_fact_2, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; array_tmp1[1] := array_y[1]*array_y[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_y, array_y, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_y, array_y, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_y, array_y, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_y, array_y, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_y, array_y, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_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_y_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_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * 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_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*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_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, 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_min * 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_min; > 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_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*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_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > 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 := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > 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 := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > 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 := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > 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 := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 2.0/(1.0 - 2.0*x); > end; exact_soln_y := proc(x) 2.0/(1.0 - 2.0*x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := 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; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > INFO, > ALWAYS, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_start_msg, > glob_max_sec, > glob_look_poles, > days_in_year, > glob_iter, > glob_small_float, > glob_max_iter, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > djd_debug2, > glob_log10normmin, > glob_log10relerr, > glob_relerr, > glob_clock_start_sec, > glob_max_opt_iter, > glob_start, > glob_max_trunc_err, > glob_hmin_init, > glob_hmin, > glob_disp_incr, > glob_dump, > glob_optimal_expect_sec, > glob_subiter_method, > glob_smallish_float, > glob_log10_abserr, > glob_dump_analytic, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > glob_no_eqs, > glob_hmax, > glob_reached_optimal_h, > glob_initial_pass, > glob_clock_sec, > years_in_century, > djd_debug, > glob_h, > glob_current_iter, > glob_warned2, > glob_large_float, > glob_almost_1, > hours_in_day, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_normmax, > glob_warned, > glob_unchanged_h_cnt, > glob_log10_relerr, > centuries_in_millinium, > glob_percent_done, > glob_max_rel_trunc_err, > glob_last_good_h, > glob_display_flag, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_fact_1, > array_m1, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_y_higher_work, > array_fact_2, > array_complex_pole, > array_poles, > array_real_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_iolevel := 5; > INFO := 2; > ALWAYS := 1; > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_orig_start_sec := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_not_yet_start_msg := true; > glob_max_sec := 10000.0; > glob_look_poles := false; > days_in_year := 365.0; > glob_iter := 0; > glob_small_float := 0.1e-50; > glob_max_iter := 1000; > glob_max_hours := 0.0; > glob_optimal_done := false; > glob_not_yet_finished := true; > djd_debug2 := true; > glob_log10normmin := 0.1; > glob_log10relerr := 0.0; > glob_relerr := 0.1e-10; > glob_clock_start_sec := 0.0; > glob_max_opt_iter := 10; > glob_start := 0; > glob_max_trunc_err := 0.1e-10; > glob_hmin_init := 0.001; > glob_hmin := 0.00000000001; > glob_disp_incr := 0.1; > glob_dump := false; > glob_optimal_expect_sec := 0.1; > glob_subiter_method := 3; > glob_smallish_float := 0.1e-100; > glob_log10_abserr := 0.1e-10; > glob_dump_analytic := false; > sec_in_min := 60.0; > glob_log10abserr := 0.0; > glob_optimal_start := 0.0; > glob_no_eqs := 0; > glob_hmax := 1.0; > glob_reached_optimal_h := false; > glob_initial_pass := true; > glob_clock_sec := 0.0; > years_in_century := 100.0; > djd_debug := true; > glob_h := 0.1; > glob_current_iter := 0; > glob_warned2 := false; > glob_large_float := 9.0e100; > glob_almost_1 := 0.9990; > hours_in_day := 24.0; > min_in_hour := 60.0; > glob_html_log := true; > glob_max_minutes := 0.0; > glob_normmax := 0.0; > glob_warned := false; > glob_unchanged_h_cnt := 0; > glob_log10_relerr := 0.1e-10; > centuries_in_millinium := 10.0; > glob_percent_done := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_last_good_h := 0.1; > glob_display_flag := true; > #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 := 1; > 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/nonlinear2postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;"); > 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 := 0.0;"); > omniout_str(ALWAYS,"x_end := 0.2 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.01;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"2.0/(1.0 - 2.0*x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_y[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_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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 > ; > 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_y_init[term] := 0.0; > term := term + 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_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 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 <=1 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 <=1 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_y_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_y_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_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_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_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_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_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 0.2 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.01; > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #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 := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * 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_y_higher[r_order,term_no] := array_y_init[it]* (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(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_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 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (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_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_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 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = y * y;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-18T00:46:46-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"nonlinear2") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;") > ; > 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_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 3 > 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 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 092 ") > ; > logitem_str(html_log_file,"nonlinear2 diffeq.mxt") > ; > logitem_str(html_log_file,"nonlinear2 maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := 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; global glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, INFO, ALWAYS, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_start_msg, glob_max_sec, glob_look_poles, days_in_year, glob_iter, glob_small_float, glob_max_iter, glob_max_hours, glob_optimal_done, glob_not_yet_finished, djd_debug2, glob_log10normmin, glob_log10relerr, glob_relerr, glob_clock_start_sec, glob_max_opt_iter, glob_start, glob_max_trunc_err, glob_hmin_init, glob_hmin, glob_disp_incr, glob_dump, glob_optimal_expect_sec, glob_subiter_method, glob_smallish_float, glob_log10_abserr, glob_dump_analytic, sec_in_min, glob_log10abserr, glob_optimal_start, glob_no_eqs, glob_hmax, glob_reached_optimal_h, glob_initial_pass, glob_clock_sec, years_in_century, djd_debug, glob_h, glob_current_iter, glob_warned2, glob_large_float, glob_almost_1, hours_in_day, min_in_hour, glob_html_log, glob_max_minutes, glob_normmax, glob_warned, glob_unchanged_h_cnt, glob_log10_relerr, centuries_in_millinium, glob_percent_done, glob_max_rel_trunc_err, glob_last_good_h, glob_display_flag, array_const_1, array_const_0D0, array_y, array_x, array_last_rel_error, array_fact_1, array_m1, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_y_higher_work, array_fact_2, array_complex_pole, array_poles, array_real_pole, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; glob_iolevel := 5; INFO := 2; ALWAYS := 1; MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_orig_start_sec := 0.; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_not_yet_start_msg := true; glob_max_sec := 10000.0; glob_look_poles := false; days_in_year := 365.0; glob_iter := 0; glob_small_float := 0.1*10^(-50); glob_max_iter := 1000; glob_max_hours := 0.; glob_optimal_done := false; glob_not_yet_finished := true; djd_debug2 := true; glob_log10normmin := 0.1; glob_log10relerr := 0.; glob_relerr := 0.1*10^(-10); glob_clock_start_sec := 0.; glob_max_opt_iter := 10; glob_start := 0; glob_max_trunc_err := 0.1*10^(-10); glob_hmin_init := 0.001; glob_hmin := 0.1*10^(-10); glob_disp_incr := 0.1; glob_dump := false; glob_optimal_expect_sec := 0.1; glob_subiter_method := 3; glob_smallish_float := 0.1*10^(-100); glob_log10_abserr := 0.1*10^(-10); glob_dump_analytic := false; sec_in_min := 60.0; glob_log10abserr := 0.; glob_optimal_start := 0.; glob_no_eqs := 0; glob_hmax := 1.0; glob_reached_optimal_h := false; glob_initial_pass := true; glob_clock_sec := 0.; years_in_century := 100.0; djd_debug := true; glob_h := 0.1; glob_current_iter := 0; glob_warned2 := false; glob_large_float := 0.90*10^101; glob_almost_1 := 0.9990; hours_in_day := 24.0; min_in_hour := 60.0; glob_html_log := true; glob_max_minutes := 0.; glob_normmax := 0.; glob_warned := false; glob_unchanged_h_cnt := 0; glob_log10_relerr := 0.1*10^(-10); centuries_in_millinium := 10.0; glob_percent_done := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_last_good_h := 0.1; glob_display_flag := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; 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/nonlinear2postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"); 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 := 0.0;"); omniout_str(ALWAYS, "x_end := 0.2 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.01;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "2.0/(1.0 - 2.0*x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y[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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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; 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_y_init[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 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 <= 1 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 <= 1 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_y_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_y_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_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_const_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_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 0.2; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; 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 := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 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; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*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_y_higher[r_order, term_no] := array_y_init[it]* 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(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() 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_y_higher_work[2, iii] := array_y_higher[2, iii]/( 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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*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_y_higher_work[1, iii] := array_y_higher[1, iii]/( 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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*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_y_higher_work[1, iii] := array_y_higher[1, iii]/( 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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_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 ( y , x , 1 ) = y * y;"); 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, "2012-06-18T00:46:46-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "nonlinear2"); logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"); 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_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, " 092 "); logitem_str(html_log_file, "nonlinear2 diffeq.mxt"); logitem_str(html_log_file, "nonlinear2 maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.ode################# diff ( y , x , 1 ) = y * y; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 0.2 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 2.0/(1.0 - 2.0*x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 2.0040080160320641282565130260521 y[1] (numeric) = 2.0040080160320687508995789943268 absolute error = 4.6226430659682747e-15 relative error = 2.3066988899181690753000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 2.0080321285140562248995983935743 y[1] (numeric) = 2.0080321285140655543073655875882 absolute error = 9.3294077671940139e-15 relative error = 4.6460450680626189222000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 2.012072434607645875251509054326 y[1] (numeric) = 2.012072434607659997023419326984 absolute error = 1.41217719102726580e-14 relative error = 7.0185206394055110259999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 2.0161290322580645161290322580645 y[1] (numeric) = 2.0161290322580835173702800717775 absolute error = 1.90012412478137130e-14 relative error = 9.4246156589156016480000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 2.020202020202020202020202020202 y[1] (numeric) = 2.0202020202020441713702589013358 absolute error = 2.39693500568811338e-14 relative error = 1.1864828278156161231000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 2.0242914979757085020242914979757 y[1] (numeric) = 2.0242914979757375296860220307395 absolute error = 2.90276617305327638e-14 relative error = 1.4339664894883185317200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 2.0283975659229208924949290060852 y[1] (numeric) = 2.0283975659229550702643117880012 absolute error = 3.41777693827819160e-14 relative error = 1.6849640305711484588000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 2.032520325203252032520325203252 y[1] (numeric) = 2.0325203252032914538167925160674 absolute error = 3.94212964673128154e-14 relative error = 1.9395277861917905176800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 2.0366598778004073319755600814664 y[1] (numeric) = 2.0366598778004520918729703719729 absolute error = 4.47598974102905065e-14 relative error = 2.1977109628452638691500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.34 NO POLE x[1] = 0.01 y[1] (analytic) = 2.0408163265306122448979591836735 y[1] (numeric) = 2.0408163265306624401562167986411 absolute error = 5.01952582576149676e-14 relative error = 2.4595676546231334124000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 2.0449897750511247443762781186094 y[1] (numeric) = 2.0449897750511804734736150971862 absolute error = 5.57290973369785768e-14 relative error = 2.7251528597782524055200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 2.049180327868852459016393442623 y[1] (numeric) = 2.0491803278689138221823285383749 absolute error = 6.13631659350957519e-14 relative error = 2.9945224976326726927199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 2.0533880903490759753593429158111 y[1] (numeric) = 2.0533880903491430746083333993544 absolute error = 6.70992489904835433e-14 relative error = 3.2677334258365485587100000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 2.0576131687242798353909465020576 y[1] (numeric) = 2.057613168724352774556748684261 absolute error = 7.29391658021822034e-14 relative error = 3.5448434579860550852400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.015 y[1] (analytic) = 2.0618556701030927835051546391753 y[1] (numeric) = 2.0618556701031716682759094544822 absolute error = 7.88847707548153069e-14 relative error = 3.8259113816085423846499999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 2.0661157024793388429752066115702 y[1] (numeric) = 2.0661157024794237809292670114148 absolute error = 8.49379540603998446e-14 relative error = 4.1109969765233524786400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 2.0703933747412008281573498964803 y[1] (numeric) = 2.0703933747412919287998672243688 absolute error = 9.11006425173278885e-14 relative error = 4.4001610335869370145500000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 2.0746887966804979253112033195021 y[1] (numeric) = 2.0746887966805953001114902724277 absolute error = 9.73748002869529256e-14 relative error = 4.6934653738311310139199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 2.0790020790020790020790020790021 y[1] (numeric) = 2.0790020790021827645086903047958 absolute error = 1.037624296882257937e-13 relative error = 4.9909728680036606769699999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 2.0833333333333333333333333333333 y[1] (numeric) = 2.0833333333334435989053441706738 absolute error = 1.102655720108373405e-13 relative error = 5.2927474565201923440000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 2.0876826722338204592901878914405 y[1] (numeric) = 2.0876826722339373455985352289142 absolute error = 1.168863083473374737e-13 relative error = 5.5988541698374649902300000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 2.0920502092050209205020920502092 y[1] (numeric) = 2.0920502092051445472625367633971 absolute error = 1.236267604447131879e-13 relative error = 5.9093591492572903816200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 2.0964360587002096436058700209644 y[1] (numeric) = 2.0964360587003401326974459424174 absolute error = 1.304890915759214530e-13 relative error = 6.2243296681714533080999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 2.1008403361344537815126050420168 y[1] (numeric) = 2.1008403361345912570200369285648 absolute error = 1.374755074318865480e-13 relative error = 6.5438341537577996848000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.72 NO POLE x[1] = 0.025 y[1] (analytic) = 2.1052631578947368421052631578947 y[1] (numeric) = 2.1052631578948814303622976434196 absolute error = 1.445882570344855249e-13 relative error = 6.8679422091380624327500000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 2.109704641350210970464135021097 y[1] (numeric) = 2.1097046413503628000978060811118 absolute error = 1.518296336710600148e-13 relative error = 7.1967246360082447015200000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 2.114164904862579281183932346723 y[1] (numeric) = 2.1141649048627384831597833542692 absolute error = 1.592019758510075462e-13 relative error = 7.5302534577526569352600000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 2.1186440677966101694915254237288 y[1] (numeric) = 2.1186440677967768771598104446815 absolute error = 1.667076682850209527e-13 relative error = 7.8686019430529889674400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 2.1231422505307855626326963906582 y[1] (numeric) = 2.1231422505309599117755839509769 absolute error = 1.743491428875603187e-13 relative error = 8.2118446300040910107699999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 2.1276595744680851063829787234043 y[1] (numeric) = 2.1276595744682672352627818816628 absolute error = 1.821288798031582585e-13 relative error = 8.5600573507484381494999999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 2.1321961620469083155650319829424 y[1] (numeric) = 2.132196162047098364973489159109 absolute error = 1.900494084571761666e-13 relative error = 8.9133172566415622135400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 2.1367521367521367521367521367521 y[1] (numeric) = 2.1367521367523348654453837831764 absolute error = 1.981133086316464243e-13 relative error = 9.2717028439610526572400000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 2.1413276231263383297644539614561 y[1] (numeric) = 2.1413276231265446529760208148833 absolute error = 2.063232115668534272e-13 relative error = 9.6352939801720550502400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 2.1459227467811158798283261802575 y[1] (numeric) = 2.1459227467813305616294155049699 absolute error = 2.146818010893247124e-13 relative error = 1.0004171930762531597840000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 2.1505376344086021505376344086022 y[1] (numeric) = 2.1505376344088253423524013310468 absolute error = 2.231918147669224446e-13 relative error = 1.0378419386661893673900000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 2.1551724137931034482758620689655 y[1] (numeric) = 2.155172413793335304320953814044 absolute error = 2.318560450917450785e-13 relative error = 1.0758120492256971642400000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 2.1598272138228941684665226781857 y[1] (numeric) = 2.1598272138231348458072142473516 absolute error = 2.406773406915691659e-13 relative error = 1.1143360874019652381170000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 2.1645021645021645021645021645022 y[1] (numeric) = 2.1645021645024141607720727465541 absolute error = 2.496586075705820519e-13 relative error = 1.1534227669760890797780000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 2.1691973969631236442516268980477 y[1] (numeric) = 2.1691973969633824470620070756586 absolute error = 2.588028103801776109e-13 relative error = 1.1930809558526187862490000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 2.1739130434782608695652173913043 y[1] (numeric) = 2.1739130434785289825389380005441 absolute error = 2.681129737206092398e-13 relative error = 1.2333196791148025030800000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=1.11 NO POLE x[1] = 0.041 y[1] (analytic) = 2.1786492374727668845315904139434 y[1] (numeric) = 2.1786492374730444767150647310213 absolute error = 2.775921834743170779e-13 relative error = 1.2741481221471153875610000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 2.1834061135371179039301310043668 y[1] (numeric) = 2.1834061135374051475183027742346 absolute error = 2.872435881717698678e-13 relative error = 1.3155756338267059945240000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 2.1881838074398249452954048140044 y[1] (numeric) = 2.1881838074401220156957955000548 absolute error = 2.970704003906860504e-13 relative error = 1.3576117297854352503280000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 2.1929824561403508771929824561404 y[1] (numeric) = 2.1929824561406579530911719797554 absolute error = 3.070758981895236150e-13 relative error = 1.4002660957442276844000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 2.1978021978021978021978021978022 y[1] (numeric) = 2.1978021978025150656243783517247 absolute error = 3.172634265761539225e-13 relative error = 1.4435485909215003473750000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 2.2026431718061674008810572687225 y[1] (numeric) = 2.2026431718064950372800699299472 absolute error = 3.276363990126612247e-13 relative error = 1.4874692515174819601380000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 2.2075055187637969094922737306843 y[1] (numeric) = 2.2075055187641351077912309676174 absolute error = 3.381982989572369331e-13 relative error = 1.5320382942762833069430000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 2.2123893805309734513274336283186 y[1] (numeric) = 2.2123893805313224040088777941901 absolute error = 3.489526814441658715e-13 relative error = 1.5772661201276297391800000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 2.2172949002217294900221729490022 y[1] (numeric) = 2.2172949002220893931968758798242 absolute error = 3.599031747029308220e-13 relative error = 1.6231633179102180072200000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 2.2222222222222222222222222222222 y[1] (numeric) = 2.2222222222225932757040397138728 absolute error = 3.710534818174916506e-13 relative error = 1.6697406681787124277000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 2.22717149220489977728285077951 y[1] (numeric) = 2.2271714922052821846652776057428 absolute error = 3.824073824268262328e-13 relative error = 1.7170091470964497852720000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 2.2321428571428571428571428571429 y[1] (numeric) = 2.2321428571432511115916107094418 absolute error = 3.939687344678522989e-13 relative error = 1.7649799304159782990720000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 2.2371364653243847874720357941834 y[1] (numeric) = 2.2371364653247905289479976764203 absolute error = 4.057414759618822369e-13 relative error = 1.8136643975496135989430000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 2.2421524663677130044843049327354 y[1] (numeric) = 2.242152466368130734111150729581 absolute error = 4.177296268457968456e-13 relative error = 1.8630741357322539313760000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 2.2471910112359550561797752808989 y[1] (numeric) = 2.2471910112363849934706244399729 absolute error = 4.299372908491590740e-13 relative error = 1.9132209442787578793000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 2.2522522522522522522522522522523 y[1] (numeric) = 2.2522522522526946209096707771845 absolute error = 4.423686574185249322e-13 relative error = 1.9641168389382506989680000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.0MB, time=1.51 NO POLE x[1] = 0.057 y[1] (analytic) = 2.2573363431151241534988713318284 y[1] (numeric) = 2.2573363431155791815025615778994 absolute error = 4.550280036902460710e-13 relative error = 2.0157740563477900945300000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 2.2624434389140271493212669683258 y[1] (numeric) = 2.2624434389144950690177800653574 absolute error = 4.679196965130970316e-13 relative error = 2.0682050585878888796720000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 2.2675736961451247165532879818594 y[1] (numeric) = 2.2675736961456057647478100817648 absolute error = 4.810481945220999054e-13 relative error = 2.1214225378424605828140000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 2.2727272727272727272727272727273 y[1] (numeric) = 2.2727272727277671453229922328854 absolute error = 4.944180502649601581e-13 relative error = 2.1754394211658246956400000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.061 y[1] (analytic) = 2.277904328018223234624145785877 y[1] (numeric) = 2.2779043280187312685365283555931 absolute error = 5.080339123825697161e-13 relative error = 2.2302688753594810536790000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 2.283105022831050228310502283105 y[1] (numeric) = 2.2831050228315721288383473602193 absolute error = 5.219005278450771143e-13 relative error = 2.2859243119614377606340000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 2.2883295194508009153318077803204 y[1] (numeric) = 2.2883295194513369380760528499514 absolute error = 5.360227442450696310e-13 relative error = 2.3424193923509542874700000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 2.2935779816513761467889908256881 y[1] (numeric) = 2.2935779816519265523011402846059 absolute error = 5.504055121494589178e-13 relative error = 2.3997680329716408816080000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 2.2988505747126436781609195402299 y[1] (numeric) = 2.2988505747132087320484312499651 absolute error = 5.650538875117097352e-13 relative error = 2.4579844106759373481200000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 2.3041474654377880184331797235023 y[1] (numeric) = 2.3041474654383679914673258245779 absolute error = 5.799730341461010756e-13 relative error = 2.5170829681940786681040000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 2.3094688221709006928406466512702 y[1] (numeric) = 2.3094688221714958610669124115154 absolute error = 5.951682262657602452e-13 relative error = 2.5770784197307418617160000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 2.3148148148148148148148148148148 y[1] (numeric) = 2.3148148148154254596659010782667 absolute error = 6.106448510862634519e-13 relative error = 2.6379857566926581122080000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 2.3201856148491879350348027842227 y[1] (numeric) = 2.320185614849814343446299435379 absolute error = 6.264084114966511563e-13 relative error = 2.6998202535505664836530000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 2.3255813953488372093023255813953 y[1] (numeric) = 2.3255813953494796738311253443527 absolute error = 6.424645287997629574e-13 relative error = 2.7625974738389807168200000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 2.3310023310023310023310023310023 y[1] (numeric) = 2.331002331002989821276526186161 absolute error = 6.588189455238551587e-13 relative error = 2.8263332762973386308230000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 2.3364485981308411214953271028037 y[1] (numeric) = 2.3364485981315165990236346272737 absolute error = 6.754775283075244700e-13 relative error = 2.8910438211562047316000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.0MB, time=1.90 NO POLE x[1] = 0.073 y[1] (analytic) = 2.3419203747072599531615925058548 y[1] (numeric) = 2.3419203747079523994324525294572 absolute error = 6.924462708600236024e-13 relative error = 2.9567455765723007822480000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 2.3474178403755868544600938967136 y[1] (numeric) = 2.3474178403762965857570930156056 absolute error = 7.097312969991188920e-13 relative error = 3.0234553252162464799200000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 2.3529411764705882352941176470588 y[1] (numeric) = 2.3529411764713155741578863536626 absolute error = 7.273388637687066038e-13 relative error = 3.0911901710170030661500000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 2.3584905660377358490566037735849 y[1] (numeric) = 2.3584905660384811244212422468923 absolute error = 7.452753646384733074e-13 relative error = 3.1599675460671268233760000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 2.3640661938534278959810874704492 y[1] (numeric) = 2.364066193854191443313875427204 absolute error = 7.635473327879567548e-13 relative error = 3.2298052176930570728040000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 2.3696682464454976303317535545024 y[1] (numeric) = 2.369668246446279791776230991612 absolute error = 7.821614444774371096e-13 relative error = 3.3007212956947846025120000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 2.3752969121140142517814726840855 y[1] (numeric) = 2.375296912114815376303980848353 absolute error = 8.011245225081642675e-13 relative error = 3.3727342397593715661750000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 2.3809523809523809523809523809524 y[1] (numeric) = 2.3809523809532013959207268864054 absolute error = 8.204435397745054530e-13 relative error = 3.4458628670529229026000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 2.3866348448687350835322195704057 y[1] (numeric) = 2.3866348448695752091551302487792 absolute error = 8.401256229106783735e-13 relative error = 3.5201263599957423849650000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 2.3923444976076555023923444976077 y[1] (numeric) = 2.3923444976085156804483793166601 absolute error = 8.601780560348190524e-13 relative error = 3.5955442742255436390319999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 2.3980815347721822541966426858513 y[1] (numeric) = 2.398081534773062862481235906003 absolute error = 8.806082845932201517e-13 relative error = 3.6721365467537280325890000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 2.4038461538461538461538461538462 y[1] (numeric) = 2.4038461538470552700731538190736 absolute error = 9.014239193076652274e-13 relative error = 3.7499235043198873459839999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 2.4096385542168674698795180722892 y[1] (numeric) = 2.4096385542177901026197469493497 absolute error = 9.226327402288770605e-13 relative error = 3.8289258719498398010749999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.086 y[1] (analytic) = 2.4154589371980676328502415458937 y[1] (numeric) = 2.4154589371990118755511407399544 absolute error = 9.442427008991940607e-13 relative error = 3.9091647817226634112980000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 2.4213075060532687651331719128329 y[1] (numeric) = 2.4213075060542350270657996007279 absolute error = 9.662619326276878950e-13 relative error = 3.9906617817523510063500000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 2.4271844660194174757281553398058 y[1] (numeric) = 2.4271844660204061744770363778483 absolute error = 9.886987488810380425e-13 relative error = 4.0734388453898767351000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=2.30 NO POLE x[1] = 0.089 y[1] (analytic) = 2.43309002433090024330900243309 y[1] (numeric) = 2.4330900243319118049587960181543 absolute error = 1.0115616497935850643e-12 relative error = 4.1575183806516346142730000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 2.4390243902439024390243902439024 y[1] (numeric) = 2.4390243902449372983511903380275 absolute error = 1.0348593268000941251e-12 relative error = 4.2429232398803859129100000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 2.4449877750611246943765281173594 y[1] (numeric) = 2.4449877750621832950439229912089 absolute error = 1.0586006673948738495e-12 relative error = 4.3296767296450340444550000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 2.4509803921568627450980392156863 y[1] (numeric) = 2.4509803921579455398580602287681 absolute error = 1.0827947600210130818e-12 relative error = 4.4178026208857333737440000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 2.4570024570024570024570024570025 y[1] (numeric) = 2.4570024570035644533560960766919 absolute error = 1.1074508990936196894e-12 relative error = 4.5073251593110321358579999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 2.4630541871921182266009852216749 y[1] (numeric) = 2.4630541871932508051911462930363 absolute error = 1.1325785901610713614e-12 relative error = 4.5982690760539497272840000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 2.4691358024691358024691358024691 y[1] (numeric) = 2.4691358024702939900243442210301 absolute error = 1.1581875552084185610e-12 relative error = 4.6906595985940951720500000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 2.4752475247524752475247524752475 y[1] (numeric) = 2.4752475247536595352628596898087 absolute error = 1.1842877381072145612e-12 relative error = 4.7845224619531468272480000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 2.4813895781637717121588089330025 y[1] (numeric) = 2.4813895781649826014690251200008 absolute error = 1.2108893102161869983e-12 relative error = 4.8798839201712336031490000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 2.4875621890547263681592039800995 y[1] (numeric) = 2.4875621890559643708353412898928 absolute error = 1.2380026761373097933e-12 relative error = 4.9767707580719853690660000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 2.4937655860349127182044887780549 y[1] (numeric) = 2.493765586036178356684120761864 absolute error = 1.2656384796319838091e-12 relative error = 5.0752103033242550744909999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 2.5 y[1] (numeric) = 2.500000000001293807609702189418 absolute error = 1.2938076097021894180e-12 relative error = 5.1752304388087576720000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 2.5062656641604010025062656641604 y[1] (numeric) = 2.5062656641617235237131072986134 absolute error = 1.3225212068416344530e-12 relative error = 5.2768596152981214674700000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 2.5125628140703517587939698492462 y[1] (numeric) = 2.5125628140717035494634319362691 absolute error = 1.3517906694620870229e-12 relative error = 5.3801268644591063511420000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 2.5188916876574307304785894206549 y[1] (numeric) = 2.518891687658812358139089675243 absolute error = 1.3816276605002545881e-12 relative error = 5.4850618121860107147570000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 2.5252525252525252525252525252525 y[1] (numeric) = 2.5252525252539372966394632740222 absolute error = 1.4120441142107487697e-12 relative error = 5.5916946922745651280120000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=2.71 NO POLE x[1] = 0.105 y[1] (analytic) = 2.5316455696202531645569620253165 y[1] (numeric) = 2.5316455696216962168001128851268 absolute error = 1.4430522431508598103e-12 relative error = 5.7000563604458962506849999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 2.5380710659898477157360406091371 y[1] (numeric) = 2.5380710659913223802814036648291 absolute error = 1.4746645453630556920e-12 relative error = 5.8101783087304394264799999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 2.544529262086513994910941475827 y[1] (numeric) = 2.5445292620880208887227027947019 absolute error = 1.5068938117613188749e-12 relative error = 5.9220926802219831783569999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 2.5510204081632653061224489795918 y[1] (numeric) = 2.5510204081648050592561766183331 absolute error = 1.5397531337276387413e-12 relative error = 6.0358322842123438658960000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 2.5575447570332480818414322250639 y[1] (numeric) = 2.5575447570348213377523574154331 absolute error = 1.5732559109251903692e-12 relative error = 6.1514306117174943435720000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 2.5641025641025641025641025641026 y[1] (numeric) = 2.5641025641041715184234375146253 absolute error = 1.6074158593349505227e-12 relative error = 6.2689218514063070385299999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 2.5706940874035989717223650385604 y[1] (numeric) = 2.5706940874052412187418877685828 absolute error = 1.6422470195227300224e-12 relative error = 6.3883409059434197871360000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 2.5773195876288659793814432989691 y[1] (numeric) = 2.5773195876305437431465871372371 absolute error = 1.6777637651438382680e-12 relative error = 6.5097234087580924798399999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 2.5839793281653746770025839793282 y[1] (numeric) = 2.5839793281670886578142768202849 absolute error = 1.7139808116928409567e-12 relative error = 6.6331057412512945024289999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 2.5906735751295336787564766839378 y[1] (numeric) = 2.5906735751312845919819828102371 absolute error = 1.7509132255061262993e-12 relative error = 6.7585250504536475152980000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 2.5974025974025974025974025974026 y[1] (numeric) = 2.5974025974043859790304278560621 absolute error = 1.7885764330252586595e-12 relative error = 6.8860192671472458390750000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 2.6041666666666666666666666666667 y[1] (numeric) = 2.6041666666684936528969960385459 absolute error = 1.8269862303293718792e-12 relative error = 7.0156271244647880161279999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 2.6109660574412532637075718015666 y[1] (numeric) = 2.6109660574431194225005169395646 absolute error = 1.8661587929451379980e-12 relative error = 7.1473881769798785323399999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 2.6178010471204188481675392670157 y[1] (numeric) = 2.6178010471223249588534824080499 absolute error = 1.9061106859431410342e-12 relative error = 7.2813428203027987506440000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 2.6246719160104986876640419947507 y[1] (numeric) = 2.6246719160124455465383717851236 absolute error = 1.9468588743297903729e-12 relative error = 7.4175323111965013207489999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 2.6315789473684210526315789473684 y[1] (numeric) = 2.6315789473704094733653231719248 absolute error = 1.9884207337442245564e-12 relative error = 7.5559987882280533143200000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=3.13 NO POLE x[1] = 0.121 y[1] (analytic) = 2.6385224274406332453825857519789 y[1] (numeric) = 2.6385224274426640594440557363099 absolute error = 2.0308140614699843310e-12 relative error = 7.6967852929712406144900000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 2.6455026455026455026455026455026 y[1] (numeric) = 2.6455026455047195597332742196686 absolute error = 2.0740570877715741660e-12 relative error = 7.8399357917765503474800000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 2.6525198938992042440318302387268 y[1] (numeric) = 2.6525198939013224125193966233252 absolute error = 2.1181684875663845984e-12 relative error = 7.9854951981252699359680000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 2.6595744680851063829787234042553 y[1] (numeric) = 2.6595744680872695503711662184644 absolute error = 2.1631673924428142091e-12 relative error = 8.1335093955849814262160000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 2.6666666666666666666666666666667 y[1] (numeric) = 2.6666666666688757400697024769847 absolute error = 2.2090734030358103180e-12 relative error = 8.2840252613842886924999999999999e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 2.673796791443850267379679144385 y[1] (numeric) = 2.6737967914461061739814505865687 absolute error = 2.2559066017714421837e-12 relative error = 8.4370906906251937670380000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 2.6809651474530831099195710455764 y[1] (numeric) = 2.6809651474553867974855635757427 absolute error = 2.3036875659925301663e-12 relative error = 8.5927546211521375202990000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 2.6881720430107526881720430107527 y[1] (numeric) = 2.6881720430131051255535207903519 absolute error = 2.3524373814777795992e-12 relative error = 8.7510670590973401090240000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 2.695417789757412398921832884097 y[1] (numeric) = 2.6954177897598145765782001937263 absolute error = 2.4021776563673096293e-12 relative error = 8.9120791051227187247030000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 2.7027027027027027027027027027027 y[1] (numeric) = 2.7027027027051556332382106284149 absolute error = 2.4529305355079257122e-12 relative error = 9.0758429813793251351400000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 2.7100271002710027100271002710027 y[1] (numeric) = 2.7100271002735074287423322314744 absolute error = 2.5047187152319604717e-12 relative error = 9.2424120592059341405730000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 2.7173913043478260869565217391304 y[1] (numeric) = 2.7173913043503836524151057411113 absolute error = 2.5575654585840019809e-12 relative error = 9.4118408875891272897120000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 2.7247956403269754768392370572207 y[1] (numeric) = 2.7247956403295869714502473991771 absolute error = 2.6114946110103419564e-12 relative error = 9.5841852224079549799880000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 2.7322404371584699453551912568306 y[1] (numeric) = 2.7322404371611364759717177664945 absolute error = 2.6665306165265096639e-12 relative error = 9.7595020564870253698740000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 2.739726027397260273972602739726 y[1] (numeric) = 2.7397260273999829725069815510679 absolute error = 2.7226985343788113419e-12 relative error = 9.9378496504826613979350000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 2.7472527472527472527472527472527 y[1] (numeric) = 2.7472527472555272768034691177767 absolute error = 2.7800240562163705240e-12 relative error = 1.0119287564627588707360000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=3.55 NO POLE x[1] = 0.137 y[1] (analytic) = 2.7548209366391184573002754820937 y[1] (numeric) = 2.7548209366419569908240662447732 absolute error = 2.8385335237907626795e-12 relative error = 1.0303876691360468526585000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 2.7624309392265193370165745856354 y[1] (numeric) = 2.7624309392294175909637755446756 absolute error = 2.8982539472009590402e-12 relative error = 1.0491679288867471725524000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 2.7700831024930747922437673130194 y[1] (numeric) = 2.7700831024960340052674692533382 absolute error = 2.9592130237019403188e-12 relative error = 1.0682759015564004550868000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 2.7777777777777777777777777777778 y[1] (numeric) = 2.7777777777807992169348737900673 absolute error = 3.0214391570960122895e-12 relative error = 1.0877180965545644242200000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 2.7855153203342618384401114206128 y[1] (numeric) = 2.7855153203373467999178379735686 absolute error = 3.0849614777265529558e-12 relative error = 1.1075011705038325111322000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 2.7932960893854748603351955307263 y[1] (numeric) = 2.7932960893886246701982901771324 absolute error = 3.1498098630946464061e-12 relative error = 1.1276319309878834133838000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.143 y[1] (analytic) = 2.8011204481792717086834733893557 y[1] (numeric) = 2.8011204481824877236425932019881 absolute error = 3.2160149591198126324e-12 relative error = 1.1481173404057731097668000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 2.8089887640449438202247191011236 y[1] (numeric) = 2.8089887640482274284267859278976 absolute error = 3.2836082020668267740e-12 relative error = 1.1689645199357903315440000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 2.8169014084507042253521126760563 y[1] (numeric) = 2.8169014084540568471932741128095 absolute error = 3.3526218411614367532e-12 relative error = 1.1901807536123100473860000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 2.8248587570621468926553672316384 y[1] (numeric) = 2.8248587570655699816172858680485 absolute error = 3.4230889619186364101e-12 relative error = 1.2117734925191972891754000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 2.83286118980169971671388101983 y[1] (numeric) = 2.8328611898051947602240890532794 absolute error = 3.4950435102080334494e-12 relative error = 1.2337503591034358076382000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.148 y[1] (analytic) = 2.8409090909090909090909090909091 y[1] (numeric) = 2.8409090909126594294079908601373 absolute error = 3.5685203170817692282e-12 relative error = 1.2561191516127827683264000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 2.8490028490028490028490028490028 y[1] (numeric) = 2.8490028490064925579733942512019 absolute error = 3.6435551243914021991e-12 relative error = 1.2788878486613821718841000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 2.8571428571428571428571428571429 y[1] (numeric) = 2.8571428571465773274683640174052 absolute error = 3.7201846112211602623e-12 relative error = 1.3020646139274060918050000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 2.8653295128939828080229226361032 y[1] (numeric) = 2.8653295128977812544440886371851 absolute error = 3.7984464211660010819e-12 relative error = 1.3256578009869343775831000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 2.8735632183908045977011494252874 y[1] (numeric) = 2.8735632183946829768916334206057 absolute error = 3.8783791904839953183e-12 relative error = 1.3496759582884303707684000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=38.1MB, alloc=4.1MB, time=3.98 x[1] = 0.153 y[1] (analytic) = 2.8818443804034582132564841498559 y[1] (numeric) = 2.8818443804074182358336378174453 absolute error = 3.9600225771536675894e-12 relative error = 1.3741278342723226535218000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.154 y[1] (analytic) = 2.8901734104046242774566473988439 y[1] (numeric) = 2.8901734104086676947475154945504 absolute error = 4.0434172908680957065e-12 relative error = 1.3990223826403611144490000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 2.8985507246376811594202898550725 y[1] (numeric) = 2.8985507246418097645442886374428 absolute error = 4.1286051239987823703e-12 relative error = 1.4243687677795799177535000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.156 y[1] (analytic) = 2.9069767441860465116279069767442 y[1] (numeric) = 2.9069767441902621406114705539089 absolute error = 4.2156289835635771647e-12 relative error = 1.4501763703458705446568000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 2.9154518950437317784256559766764 y[1] (numeric) = 2.9154518950480363113498902192456 absolute error = 4.3045329242342425692e-12 relative error = 1.4764547930123452012356000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 2.9239766081871345029239766081871 y[1] (numeric) = 2.9239766081915298651063972363327 absolute error = 4.3953621824206281456e-12 relative error = 1.5032138663878548257952000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.159 y[1] (analytic) = 2.9325513196480938416422287390029 y[1] (numeric) = 2.9325513196525820048536985834696 absolute error = 4.4881632114698444667e-12 relative error = 1.5304636551112169631447000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 2.9411764705882352941176470588235 y[1] (numeric) = 2.9411764705928182778356673741173 absolute error = 4.5829837180203152938e-12 relative error = 1.5582144641269071998920000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 2.9498525073746312684365781710914 y[1] (numeric) = 2.949852507379311141136130306733 absolute error = 4.6798726995521356416e-12 relative error = 1.5864768451481739825024000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.162 y[1] (analytic) = 2.9585798816568047337278106508876 y[1] (numeric) = 2.9585798816615836142109874283749 absolute error = 4.7788804831767774873e-12 relative error = 1.6152616033137507907074000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 2.967359050445103857566765578635 y[1] (numeric) = 2.9673590504499839163324764455536 absolute error = 4.8800587657108669186e-12 relative error = 1.6445798040445621515682000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 2.9761904761904761904761904761905 y[1] (numeric) = 2.9761904761954596511312709857275 absolute error = 4.9834606550805095370e-12 relative error = 1.6744427801070512044320000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.165 y[1] (analytic) = 2.9850746268656716417910447761194 y[1] (numeric) = 2.9850746268707607825041492442889 absolute error = 5.0891407131044681695e-12 relative error = 1.7048621388899968367825000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 2.9940119760479041916167664670659 y[1] (numeric) = 2.9940119760531013466164728688166 absolute error = 5.1971549997064017507e-12 relative error = 1.7358497699019381847338000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 3.003003003003003003003003003003 y[1] (numeric) = 3.0030030030083105641216113631832 absolute error = 5.3075611186083601802e-12 relative error = 1.7674178524965839400066000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 3.0120481927710843373493975903614 y[1] (numeric) = 3.0120481927765047556139573910901 absolute error = 5.4204182645598007287e-12 relative error = 1.7995788638338538419284000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.169 y[1] (analytic) = 3.0211480362537764350453172205438 y[1] (numeric) = 3.0211480362593122223174757716172 absolute error = 5.5357872721585510734e-12 relative error = 1.8323455870844804052954000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=4.44 NO POLE x[1] = 0.17 y[1] (analytic) = 3.030303030303030303030303030303 y[1] (numeric) = 3.0303030303086840336966254266597 absolute error = 5.6537306663223963567e-12 relative error = 1.8657311198863907977110000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 3.0395136778115501519756838905775 y[1] (numeric) = 3.0395136778173244646901562076622 absolute error = 5.7743127144723170847e-12 relative error = 1.8997488830613923208663000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 3.048780487804878048780487804878 y[1] (numeric) = 3.0487804878107756482609786605822 absolute error = 5.8975994804908557042e-12 relative error = 1.9344126296010006709776000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 3.0581039755351681957186544342508 y[1] (numeric) = 3.0581039755411918545991760812886 absolute error = 6.0236588805216470378e-12 relative error = 1.9697364539305785813606000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 3.0674846625766871165644171779141 y[1] (numeric) = 3.0674846625828396773050959942977 absolute error = 6.1525607406788163836e-12 relative error = 2.0057348014612941410536000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.175 y[1] (analytic) = 3.0769230769230769230769230769231 y[1] (numeric) = 3.0769230769293612999336608111109 absolute error = 6.2843768567377341878e-12 relative error = 2.0424224784397636110350000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.176 y[1] (analytic) = 3.0864197530864197530864197530864 y[1] (numeric) = 3.0864197530928389341423012763449 absolute error = 6.4191810558815232585e-12 relative error = 2.0798146621056135357540000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.177 y[1] (analytic) = 3.0959752321981424148606811145511 y[1] (numeric) = 3.0959752322046994641212618637723 absolute error = 6.5570492605807492212e-12 relative error = 2.1179269111675819984476000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 3.1055900621118012422360248447205 y[1] (numeric) = 3.1055900621184993017907117380959 absolute error = 6.6980595546868933754e-12 relative error = 2.1567751766091796668788000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.179 y[1] (analytic) = 3.115264797507788161993769470405 y[1] (numeric) = 3.1152647975146304542455929860082 absolute error = 6.8422922518235156032e-12 relative error = 2.1963758128353485086272000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.18 y[1] (analytic) = 3.125 y[1] (numeric) = 3.1250000000069898299661624701798 absolute error = 6.9898299661624701798e-12 relative error = 2.2367455891719904575360000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 3.1347962382445141065830721003135 y[1] (numeric) = 3.1347962382516548642687482465291 absolute error = 7.1407576856761462156e-12 relative error = 2.2779017017306906427764000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 3.1446540880503144654088050314465 y[1] (numeric) = 3.1446540880576096282567655058257 absolute error = 7.2951628479604743792e-12 relative error = 2.3198617856514308525856000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 3.1545741324921135646687697160883 y[1] (numeric) = 3.1545741324995667000874970963136 absolute error = 7.4531354187273802253e-12 relative error = 2.3626439277365795314201000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 3.1645569620253164556962025316456 y[1] (numeric) = 3.1645569620329312236692720116541 absolute error = 7.6147679730694800085e-12 relative error = 2.4062666794899556826860000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 3.1746031746031746031746031746032 y[1] (numeric) = 3.1746031746109547589542072904337 absolute error = 7.7801557796041158305e-12 relative error = 2.4507490705752964866075000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=4.86 NO POLE x[1] = 0.186 y[1] (analytic) = 3.1847133757961783439490445859873 y[1] (numeric) = 3.1847133758041277408366529083202 absolute error = 7.9493968876083223329e-12 relative error = 2.4961106227090132125306000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 3.1948881789137380191693290734824 y[1] (numeric) = 3.1948881789218606113865900898311 absolute error = 8.1225922172610163487e-12 relative error = 2.5423713640026981171431000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.188 y[1] (analytic) = 3.2051282051282051282051282051282 y[1] (numeric) = 3.2051282051365049738582418190244 absolute error = 8.2998456531136138962e-12 relative error = 2.5895518437714475356144000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.189 y[1] (analytic) = 3.2154340836012861736334405144695 y[1] (numeric) = 3.2154340836097674377743559305672 absolute error = 8.4812641409154160977e-12 relative error = 2.6376731478246944063847000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 3.2258064516129032258064516129032 y[1] (numeric) = 3.2258064516215701835943770909279 absolute error = 8.6669577879254780247e-12 relative error = 2.6867569142568981876570000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 3.2362459546925566343042071197411 y[1] (numeric) = 3.2362459547014136742710554134348 absolute error = 8.8570399668482936937e-12 relative error = 2.7368253497561227513533000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 3.2467532467532467532467532467532 y[1] (numeric) = 3.2467532467622983806702897554038 absolute error = 9.0516274235365086506e-12 relative error = 2.7879012464492446643848000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.193 y[1] (analytic) = 3.2573289902280130293159609120521 y[1] (numeric) = 3.2573289902372638697045709336563 absolute error = 9.2508403886100216042e-12 relative error = 2.8400079993032766324894000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 3.267973856209150326797385620915 y[1] (numeric) = 3.2679738562186051294905328928524 absolute error = 9.4548026931472719374e-12 relative error = 2.8931696241030652128444000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.195 y[1] (analytic) = 3.2786885245901639344262295081967 y[1] (numeric) = 3.2786885245998275763148407530347 absolute error = 9.6636418886112448380e-12 relative error = 2.9474107760264296755900000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 3.2894736842105263157894736842105 y[1] (numeric) = 3.2894736842204038051606534594763 absolute error = 9.8774893711797752658e-12 relative error = 3.0027567688386516808032000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 3.30033003300330033003300330033 y[1] (numeric) = 3.3003300330133968105436604121102 absolute error = 1.00964805106571117802e-11 relative error = 3.0592335947291048694006000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 3.3112582781456953642384105960265 y[1] (numeric) = 3.3112582781560161190225620240761 absolute error = 1.03207547841514280496e-11 relative error = 3.1168679448137312709792000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 3.3222591362126245847176079734219 y[1] (numeric) = 3.3222591362231750406323190345993 absolute error = 1.05504559147110611774e-11 relative error = 3.1756872303280294143974000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2 y[1] (analytic) = 3.3333333333333333333333333333333 y[1] (numeric) = 3.3333333333441190653484540636328 absolute error = 1.07857320151207302995e-11 relative error = 3.2357196045362190898500000000000e-10 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 3.344481605351170568561872909699 y[1] (numeric) = 3.344481605362197304298940775428 absolute error = 1.10267357370678657290e-11 relative error = 3.2969939853832918529710000000000e-10 % h = 0.001 Finished! diff ( y , x , 1 ) = y * y; Iterations = 201 Total Elapsed Time = 5 Seconds Elapsed Time(since restart) = 5 Seconds Time to Timeout = 14 Minutes 54 Seconds Percent Done = 101 % > quit memory used=49.5MB, alloc=4.1MB, time=5.25