|\^/| 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 > DEBUGL, > glob_iolevel, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_start, > glob_warned, > glob_relerr, > glob_dump_analytic, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_subiter_method, > glob_max_trunc_err, > glob_large_float, > djd_debug2, > glob_last_good_h, > glob_reached_optimal_h, > glob_not_yet_start_msg, > sec_in_min, > MAX_UNCHANGED, > glob_warned2, > glob_h, > days_in_year, > glob_optimal_start, > glob_no_eqs, > glob_html_log, > glob_log10relerr, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_sec, > min_in_hour, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_log10_relerr, > glob_almost_1, > glob_max_opt_iter, > glob_log10abserr, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_hmin_init, > glob_clock_start_sec, > djd_debug, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > glob_initial_pass, > years_in_century, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > hours_in_day, > glob_max_minutes, > glob_current_iter, > glob_unchanged_h_cnt, > glob_hmax, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3, > array_const_0D0, > array_const_1D0, > #END CONST > array_pole, > array_y1_init, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y2_init, > array_x, > array_1st_rel_error, > array_type_pole, > array_norms, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_complex_pole, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_poles, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[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," "); > ; > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[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[2] := relerr; > else > array_last_rel_error[2] := 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump, glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2, glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg, sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year, glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec, min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter, glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr, glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, glob_initial_pass, years_in_century, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day, glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax, centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done, array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole, array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y2_init, array_x, array_1st_rel_error, array_type_pole, array_norms, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_complex_pole, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_poles, array_y1_set_initial, array_y1_higher, array_real_pole, 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_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[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, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[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[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGL, > glob_iolevel, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_start, > glob_warned, > glob_relerr, > glob_dump_analytic, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_subiter_method, > glob_max_trunc_err, > glob_large_float, > djd_debug2, > glob_last_good_h, > glob_reached_optimal_h, > glob_not_yet_start_msg, > sec_in_min, > MAX_UNCHANGED, > glob_warned2, > glob_h, > days_in_year, > glob_optimal_start, > glob_no_eqs, > glob_html_log, > glob_log10relerr, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_sec, > min_in_hour, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_log10_relerr, > glob_almost_1, > glob_max_opt_iter, > glob_log10abserr, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_hmin_init, > glob_clock_start_sec, > djd_debug, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > glob_initial_pass, > years_in_century, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > hours_in_day, > glob_max_minutes, > glob_current_iter, > glob_unchanged_h_cnt, > glob_hmax, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3, > array_const_0D0, > array_const_1D0, > #END CONST > array_pole, > array_y1_init, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y2_init, > array_x, > array_1st_rel_error, > array_type_pole, > array_norms, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_complex_pole, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_poles, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump, glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2, glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg, sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year, glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec, min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter, glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr, glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, glob_initial_pass, years_in_century, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day, glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax, centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done, array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole, array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y2_init, array_x, array_1st_rel_error, array_type_pole, array_norms, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_complex_pole, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_poles, array_y1_set_initial, array_y1_higher, array_real_pole, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < 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 > DEBUGL, > glob_iolevel, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_start, > glob_warned, > glob_relerr, > glob_dump_analytic, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_subiter_method, > glob_max_trunc_err, > glob_large_float, > djd_debug2, > glob_last_good_h, > glob_reached_optimal_h, > glob_not_yet_start_msg, > sec_in_min, > MAX_UNCHANGED, > glob_warned2, > glob_h, > days_in_year, > glob_optimal_start, > glob_no_eqs, > glob_html_log, > glob_log10relerr, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_sec, > min_in_hour, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_log10_relerr, > glob_almost_1, > glob_max_opt_iter, > glob_log10abserr, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_hmin_init, > glob_clock_start_sec, > djd_debug, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > glob_initial_pass, > years_in_century, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > hours_in_day, > glob_max_minutes, > glob_current_iter, > glob_unchanged_h_cnt, > glob_hmax, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3, > array_const_0D0, > array_const_1D0, > #END CONST > array_pole, > array_y1_init, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y2_init, > array_x, > array_1st_rel_error, > array_type_pole, > array_norms, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_complex_pole, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_poles, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump, glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2, glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg, sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year, glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec, min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter, glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr, glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, glob_initial_pass, years_in_century, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day, glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax, centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done, array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole, array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y2_init, array_x, array_1st_rel_error, array_type_pole, array_norms, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_complex_pole, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_poles, array_y1_set_initial, array_y1_higher, array_real_pole, 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 > DEBUGL, > glob_iolevel, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_start, > glob_warned, > glob_relerr, > glob_dump_analytic, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_subiter_method, > glob_max_trunc_err, > glob_large_float, > djd_debug2, > glob_last_good_h, > glob_reached_optimal_h, > glob_not_yet_start_msg, > sec_in_min, > MAX_UNCHANGED, > glob_warned2, > glob_h, > days_in_year, > glob_optimal_start, > glob_no_eqs, > glob_html_log, > glob_log10relerr, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_sec, > min_in_hour, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_log10_relerr, > glob_almost_1, > glob_max_opt_iter, > glob_log10abserr, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_hmin_init, > glob_clock_start_sec, > djd_debug, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > glob_initial_pass, > years_in_century, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > hours_in_day, > glob_max_minutes, > glob_current_iter, > glob_unchanged_h_cnt, > glob_hmax, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3, > array_const_0D0, > array_const_1D0, > #END CONST > array_pole, > array_y1_init, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y2_init, > array_x, > array_1st_rel_error, > array_type_pole, > array_norms, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_complex_pole, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_poles, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 3 - 1; > while ((m >= 10) and ((abs(array_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (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 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y1_higher[1,m]) < glob_small_float) or (abs(array_y1_higher[1,m-1]) < glob_small_float) or (abs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (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[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 3 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((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 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump, glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2, glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg, sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year, glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec, min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter, glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr, glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, glob_initial_pass, years_in_century, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day, glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax, centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done, array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole, array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y2_init, array_x, array_1st_rel_error, array_type_pole, array_norms, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_complex_pole, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_poles, array_y1_set_initial, array_y1_higher, array_real_pole, glob_last; n := glob_max_terms; m := n - 4; while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or abs(array_y2_higher[1, m - 1]) < glob_small_float or abs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < 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; m := n - 2; while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or abs(array_y1_higher[1, m - 1]) < glob_small_float or abs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 4; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y2_higher[1, m]) or glob_large_float <= abs(array_y2_higher[1, m - 1]) or glob_large_float <= abs(array_y2_higher[1, m - 2]) or glob_large_float <= abs(array_y2_higher[1, m - 3]) or glob_large_float <= abs(array_y2_higher[1, m - 4]) or glob_large_float <= abs(array_y2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if 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; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_y1_higher[1, m]) or glob_large_float <= abs(array_y1_higher[1, m - 1]) or glob_large_float <= abs(array_y1_higher[1, m - 2]) or glob_large_float <= abs(array_y1_higher[1, m - 3]) or glob_large_float <= abs(array_y1_higher[1, m - 4]) or glob_large_float <= abs(array_y1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < 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[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if 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; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if 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; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGL, > glob_iolevel, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_start, > glob_warned, > glob_relerr, > glob_dump_analytic, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_subiter_method, > glob_max_trunc_err, > glob_large_float, > djd_debug2, > glob_last_good_h, > glob_reached_optimal_h, > glob_not_yet_start_msg, > sec_in_min, > MAX_UNCHANGED, > glob_warned2, > glob_h, > days_in_year, > glob_optimal_start, > glob_no_eqs, > glob_html_log, > glob_log10relerr, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_sec, > min_in_hour, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_log10_relerr, > glob_almost_1, > glob_max_opt_iter, > glob_log10abserr, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_hmin_init, > glob_clock_start_sec, > djd_debug, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > glob_initial_pass, > years_in_century, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > hours_in_day, > glob_max_minutes, > glob_current_iter, > glob_unchanged_h_cnt, > glob_hmax, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3, > array_const_0D0, > array_const_1D0, > #END CONST > array_pole, > array_y1_init, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y2_init, > array_x, > array_1st_rel_error, > array_type_pole, > array_norms, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_complex_pole, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_poles, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > 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_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump, glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2, glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg, sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year, glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec, min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter, glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr, glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, glob_initial_pass, years_in_century, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day, glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax, centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done, array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole, array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y2_init, array_x, array_1st_rel_error, array_type_pole, array_norms, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_complex_pole, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_poles, array_y1_set_initial, array_y1_higher, array_real_pole, 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_y2[iii]) then array_norms[iii] := abs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y1[iii]) then array_norms[iii] := abs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGL, > glob_iolevel, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_start, > glob_warned, > glob_relerr, > glob_dump_analytic, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_subiter_method, > glob_max_trunc_err, > glob_large_float, > djd_debug2, > glob_last_good_h, > glob_reached_optimal_h, > glob_not_yet_start_msg, > sec_in_min, > MAX_UNCHANGED, > glob_warned2, > glob_h, > days_in_year, > glob_optimal_start, > glob_no_eqs, > glob_html_log, > glob_log10relerr, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_sec, > min_in_hour, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_log10_relerr, > glob_almost_1, > glob_max_opt_iter, > glob_log10abserr, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_hmin_init, > glob_clock_start_sec, > djd_debug, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > glob_initial_pass, > years_in_century, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > hours_in_day, > glob_max_minutes, > glob_current_iter, > glob_unchanged_h_cnt, > glob_hmax, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3, > array_const_0D0, > array_const_1D0, > #END CONST > array_pole, > array_y1_init, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y2_init, > array_x, > array_1st_rel_error, > array_type_pole, > array_norms, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_complex_pole, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_poles, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre cos $eq_no = 1 > array_tmp1_g[1] := sin(array_x[1]); > array_tmp1[1] := cos(array_x[1]); > # emit pre mult $eq_no = 1 i = 1 > array_tmp2[1] := (array_m1[1] * (array_tmp1[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y2_set_initial[1,4] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * (glob_h ^ (3)) * factorial_3(0,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,2] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult $eq_no = 2 i = 1 > array_tmp5[1] := (array_m1[1] * (array_y2[1])); > #emit pre add $eq_no = 2 i = 1 > array_tmp6[1] := array_tmp5[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_y1_set_initial[2,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre cos $eq_no = 1 > array_tmp1_g[2] := (att(1,array_tmp1,array_x,1)); > array_tmp1[2] := (-att(1,array_tmp1_g,array_x,1)); > # emit pre mult $eq_no = 1 i = 2 > array_tmp2[2] := ats(2,array_m1,array_tmp1,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y2_set_initial[1,5] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * (glob_h ^ (3)) * factorial_3(1,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,3] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult $eq_no = 2 i = 2 > array_tmp5[2] := ats(2,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 2 > array_tmp6[2] := array_tmp5[2] + array_const_1D0[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre cos $eq_no = 1 > array_tmp1_g[3] := (att(2,array_tmp1,array_x,1)); > array_tmp1[3] := (-att(2,array_tmp1_g,array_x,1)); > # emit pre mult $eq_no = 1 i = 3 > array_tmp2[3] := ats(3,array_m1,array_tmp1,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y2_set_initial[1,6] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * (glob_h ^ (3)) * factorial_3(2,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,4] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult $eq_no = 2 i = 3 > array_tmp5[3] := ats(3,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 3 > array_tmp6[3] := array_tmp5[3] + array_const_1D0[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre cos $eq_no = 1 > array_tmp1_g[4] := (att(3,array_tmp1,array_x,1)); > array_tmp1[4] := (-att(3,array_tmp1_g,array_x,1)); > # emit pre mult $eq_no = 1 i = 4 > array_tmp2[4] := ats(4,array_m1,array_tmp1,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y2_set_initial[1,7] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * (glob_h ^ (3)) * factorial_3(3,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,5] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult $eq_no = 2 i = 4 > array_tmp5[4] := ats(4,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 4 > array_tmp6[4] := array_tmp5[4] + array_const_1D0[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre cos $eq_no = 1 > array_tmp1_g[5] := (att(4,array_tmp1,array_x,1)); > array_tmp1[5] := (-att(4,array_tmp1_g,array_x,1)); > # emit pre mult $eq_no = 1 i = 5 > array_tmp2[5] := ats(5,array_m1,array_tmp1,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y2_set_initial[1,8] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * (glob_h ^ (3)) * factorial_3(4,7); > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,7] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,6] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult $eq_no = 2 i = 5 > array_tmp5[5] := ats(5,array_m1,array_y2,1); > #emit pre add $eq_no = 2 i = 5 > array_tmp6[5] := array_tmp5[5] + array_const_1D0[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit cos $eq_no = 1 > array_tmp1_g[kkk] := (att(kkk-1,array_tmp1,array_x,1)); > array_tmp1[kkk] := (-att(kkk-1,array_tmp1_g,array_x,1)); > #emit mult $eq_no = 1 > array_tmp2[kkk] := ats(kkk,array_m1,array_tmp1,1); > #emit add $eq_no = 1 > array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 3; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y2_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp3[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit mult $eq_no = 2 > array_tmp5[kkk] := ats(kkk,array_m1,array_y2,1); > #emit add $eq_no = 2 > array_tmp6[kkk] := array_tmp5[kkk] + array_const_1D0[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp6[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump, glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2, glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg, sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year, glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec, min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter, glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr, glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, glob_initial_pass, years_in_century, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day, glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax, centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done, array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole, array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y2_init, array_x, array_1st_rel_error, array_type_pole, array_norms, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_complex_pole, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_poles, array_y1_set_initial, array_y1_higher, array_real_pole, glob_last; array_tmp1_g[1] := sin(array_x[1]); array_tmp1[1] := cos(array_x[1]); array_tmp2[1] := array_m1[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; if not array_y2_set_initial[1, 4] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*glob_h^3*factorial_3(0, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 2] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 1] := temporary end if end if; kkk := 2; array_tmp5[1] := array_m1[1]*array_y2[1]; array_tmp6[1] := array_tmp5[1] + array_const_1D0[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp6[1]*glob_h*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1_g[2] := att(1, array_tmp1, array_x, 1); array_tmp1[2] := -att(1, array_tmp1_g, array_x, 1); array_tmp2[2] := ats(2, array_m1, array_tmp1, 1); array_tmp3[2] := array_const_0D0[2] + array_tmp2[2]; if not array_y2_set_initial[1, 5] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*glob_h^3*factorial_3(1, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 3] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 2] := temporary end if end if; kkk := 3; array_tmp5[2] := ats(2, array_m1, array_y2, 1); array_tmp6[2] := array_tmp5[2] + array_const_1D0[2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp6[2]*glob_h*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1_g[3] := att(2, array_tmp1, array_x, 1); array_tmp1[3] := -att(2, array_tmp1_g, array_x, 1); array_tmp2[3] := ats(3, array_m1, array_tmp1, 1); array_tmp3[3] := array_const_0D0[3] + array_tmp2[3]; if not array_y2_set_initial[1, 6] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*glob_h^3*factorial_3(2, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 4] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 3] := temporary end if end if; kkk := 4; array_tmp5[3] := ats(3, array_m1, array_y2, 1); array_tmp6[3] := array_tmp5[3] + array_const_1D0[3]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp6[3]*glob_h*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1_g[4] := att(3, array_tmp1, array_x, 1); array_tmp1[4] := -att(3, array_tmp1_g, array_x, 1); array_tmp2[4] := ats(4, array_m1, array_tmp1, 1); array_tmp3[4] := array_const_0D0[4] + array_tmp2[4]; if not array_y2_set_initial[1, 7] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*glob_h^3*factorial_3(3, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 4] := temporary end if end if; kkk := 5; array_tmp5[4] := ats(4, array_m1, array_y2, 1); array_tmp6[4] := array_tmp5[4] + array_const_1D0[4]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp6[4]*glob_h*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1_g[5] := att(4, array_tmp1, array_x, 1); array_tmp1[5] := -att(4, array_tmp1_g, array_x, 1); array_tmp2[5] := ats(5, array_m1, array_tmp1, 1); array_tmp3[5] := array_const_0D0[5] + array_tmp2[5]; if not array_y2_set_initial[1, 8] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*glob_h^3*factorial_3(4, 7); array_y2[8] := temporary; array_y2_higher[1, 8] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 7] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 6] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := ats(5, array_m1, array_y2, 1); array_tmp6[5] := array_tmp5[5] + array_const_1D0[5]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp6[5]*glob_h*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1); array_tmp1[kkk] := -att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp2[kkk] := ats(kkk, array_m1, array_tmp1, 1); array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk]; order_d := 3; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp5[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp6[kkk] := array_tmp5[kkk] + array_const_1D0[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp6[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_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) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! 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_y2 := proc(x) > 1.0 + cos(x); > end; exact_soln_y2 := proc(x) 1.0 + cos(x) end proc > exact_soln_y2p := proc(x) > -sin(x); > end; exact_soln_y2p := proc(x) -sin(x) end proc > exact_soln_y2pp := proc(x) > -cos(x); > end; exact_soln_y2pp := proc(x) -cos(x) end proc > exact_soln_y1 := proc(x) > 1.0 - sin(x); > end; exact_soln_y1 := proc(x) 1.0 - sin(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, > 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 > DEBUGL, > glob_iolevel, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_iter, > glob_start, > glob_warned, > glob_relerr, > glob_dump_analytic, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_dump, > glob_subiter_method, > glob_max_trunc_err, > glob_large_float, > djd_debug2, > glob_last_good_h, > glob_reached_optimal_h, > glob_not_yet_start_msg, > sec_in_min, > MAX_UNCHANGED, > glob_warned2, > glob_h, > days_in_year, > glob_optimal_start, > glob_no_eqs, > glob_html_log, > glob_log10relerr, > glob_max_hours, > glob_optimal_done, > glob_not_yet_finished, > glob_clock_sec, > min_in_hour, > glob_log10normmin, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_log10_relerr, > glob_almost_1, > glob_max_opt_iter, > glob_log10abserr, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_hmin_init, > glob_clock_start_sec, > djd_debug, > glob_curr_iter_when_opt, > glob_optimal_clock_start_sec, > glob_initial_pass, > years_in_century, > glob_smallish_float, > glob_small_float, > glob_max_rel_trunc_err, > hours_in_day, > glob_max_minutes, > glob_current_iter, > glob_unchanged_h_cnt, > glob_hmax, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_percent_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_3, > array_const_0D0, > array_const_1D0, > #END CONST > array_pole, > array_y1_init, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_last_rel_error, > array_y2_init, > array_x, > array_1st_rel_error, > array_type_pole, > array_norms, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_complex_pole, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_poles, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > glob_iolevel := 5; > INFO := 2; > DEBUGMASSIVE := 4; > ALWAYS := 1; > glob_max_terms := 30; > glob_iter := 0; > glob_start := 0; > glob_warned := false; > glob_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_look_poles := false; > glob_hmin := 0.00000000001; > glob_disp_incr := 0.1; > glob_display_flag := true; > glob_dump := false; > glob_subiter_method := 3; > glob_max_trunc_err := 0.1e-10; > glob_large_float := 9.0e100; > djd_debug2 := true; > glob_last_good_h := 0.1; > glob_reached_optimal_h := false; > glob_not_yet_start_msg := true; > sec_in_min := 60.0; > MAX_UNCHANGED := 10; > glob_warned2 := false; > glob_h := 0.1; > days_in_year := 365.0; > glob_optimal_start := 0.0; > glob_no_eqs := 0; > glob_html_log := true; > glob_log10relerr := 0.0; > glob_max_hours := 0.0; > glob_optimal_done := false; > glob_not_yet_finished := true; > glob_clock_sec := 0.0; > min_in_hour := 60.0; > glob_log10normmin := 0.1; > glob_normmax := 0.0; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_log10_relerr := 0.1e-10; > glob_almost_1 := 0.9990; > glob_max_opt_iter := 10; > glob_log10abserr := 0.0; > glob_max_iter := 1000; > glob_abserr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_hmin_init := 0.001; > glob_clock_start_sec := 0.0; > djd_debug := true; > glob_curr_iter_when_opt := 0; > glob_optimal_clock_start_sec := 0.0; > glob_initial_pass := true; > years_in_century := 100.0; > glob_smallish_float := 0.1e-100; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > hours_in_day := 24.0; > glob_max_minutes := 0.0; > glob_current_iter := 0; > glob_unchanged_h_cnt := 0; > glob_hmax := 1.0; > centuries_in_millinium := 10.0; > glob_optimal_expect_sec := 0.1; > glob_percent_done := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest4postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = m1 * cos(x) ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > 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_y2 := proc(x)"); > omniout_str(ALWAYS,"1.0 + cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"-sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"1.0 - sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_pole:= Array(1..(max_terms + 1),[]); > array_y1_init:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_y2:= Array(1..(max_terms + 1),[]); > array_y1:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1_g:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_tmp6:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_y2_higher := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work2 := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > 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_y1_init[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_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_y2_init[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_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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=4 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=4 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=4 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3[1] := 3; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1D0[1] := 1.0; > array_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 > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0; > glob_h := 0.00001; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 100; > 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_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 3; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* (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_y2(); > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_y1(); > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (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; > if glob_subiter_method = 1 then # if number 3 > atomall(); > elif glob_subiter_method = 2 then # if number 4 > subiter := 1; > while subiter <= 4 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 4 + glob_max_terms do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2 > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 3 ) = m1 * cos(x) ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-13T02:09:15-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest4") > ; > logitem_str(html_log_file,"diff ( y2 , x , 3 ) = m1 * cos(x) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 5 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"mtest4 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest4 maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 5 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if glob_html_log then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `subiter` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump, glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2, glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg, sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year, glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr, glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec, min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter, glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr, glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt, glob_optimal_clock_start_sec, glob_initial_pass, years_in_century, glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day, glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax, centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done, array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole, array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_last_rel_error, array_y2_init, array_x, array_1st_rel_error, array_type_pole, array_norms, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_complex_pole, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_poles, array_y1_set_initial, array_y1_higher, array_real_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; glob_iolevel := 5; INFO := 2; DEBUGMASSIVE := 4; ALWAYS := 1; glob_max_terms := 30; glob_iter := 0; glob_start := 0; glob_warned := false; glob_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_look_poles := false; glob_hmin := 0.1*10^(-10); glob_disp_incr := 0.1; glob_display_flag := true; glob_dump := false; glob_subiter_method := 3; glob_max_trunc_err := 0.1*10^(-10); glob_large_float := 0.90*10^101; djd_debug2 := true; glob_last_good_h := 0.1; glob_reached_optimal_h := false; glob_not_yet_start_msg := true; sec_in_min := 60.0; MAX_UNCHANGED := 10; glob_warned2 := false; glob_h := 0.1; days_in_year := 365.0; glob_optimal_start := 0.; glob_no_eqs := 0; glob_html_log := true; glob_log10relerr := 0.; glob_max_hours := 0.; glob_optimal_done := false; glob_not_yet_finished := true; glob_clock_sec := 0.; min_in_hour := 60.0; glob_log10normmin := 0.1; glob_normmax := 0.; glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_log10_relerr := 0.1*10^(-10); glob_almost_1 := 0.9990; glob_max_opt_iter := 10; glob_log10abserr := 0.; glob_max_iter := 1000; glob_abserr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_clock_start_sec := 0.; djd_debug := true; glob_curr_iter_when_opt := 0; glob_optimal_clock_start_sec := 0.; glob_initial_pass := true; years_in_century := 100.0; glob_smallish_float := 0.1*10^(-100); glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); hours_in_day := 24.0; glob_max_minutes := 0.; glob_current_iter := 0; glob_unchanged_h_cnt := 0; glob_hmax := 1.0; centuries_in_millinium := 10.0; glob_optimal_expect_sec := 0.1; glob_percent_done := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest4postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = m1 * cos(x) ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); 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_y2 := proc(x)"); omniout_str(ALWAYS, "1.0 + cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "-sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "1.0 - sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_pole := Array(1 .. max_terms + 1, []); array_y1_init := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_y2 := Array(1 .. max_terms + 1, []); array_y1 := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1_g := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_tmp6 := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y2_higher := Array(1 .. 5, 1 .. max_terms + 1, []); array_y2_higher_work := Array(1 .. 5, 1 .. max_terms + 1, []); array_y2_higher_work2 := Array(1 .. 5, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[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_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 4 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 4 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 4 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[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_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_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; x_start := 0.1; x_end := 5.0; glob_h := 0.00001; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); glob_max_iter := 20; glob_h := 0.0001; glob_look_poles := true; glob_max_iter := 100; 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_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 3; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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_y2(); if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_y1(); if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and 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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 4 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 4 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 3; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y2 , x , 3 ) = m1 * cos(x) ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-13T02:09:15-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest4") ; logitem_str(html_log_file, "diff ( y2 , x , 3 ) = m1 * cos(x) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_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, " 090 "); logitem_str(html_log_file, "mtest4 diffeq.mxt"); logitem_str(html_log_file, "mtest4 maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0; glob_h := 0.00001; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y2 := proc(x) 1.0 + cos(x); end; exact_soln_y2p := proc(x) -sin(x); end; exact_soln_y2pp := proc(x) -cos(x); end; exact_soln_y1 := proc(x) 1.0 - sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.9950041652780257660955619878039 y2[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 0.90016658335317184769318580158938 y1[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % h = 0.0001 x[1] = 0.1 y2[1] (analytic) = 1.9950041652780257660955619878039 y2[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 0.90016658335317184769318580158938 y1[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.52 NO POLE NO POLE x[1] = 0.1001 y2[1] (analytic) = 1.99499417696135689993881931509 y2[1] (numeric) = 1.9949941769611744232787116245154 absolute error = 1.824766601076905746e-13 relative error = 9.1467264523862895092208640632915e-12 % h = 0.0001 y1[1] (analytic) = 0.90006708343597696196220785831547 y1[1] (numeric) = 0.9000670834359769665241056640093 absolute error = 4.56189780569383e-18 relative error = 5.0683975557454370671940508023476e-16 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.2MB, time=1.15 memory used=11.4MB, alloc=4.3MB, time=1.83 NO POLE NO POLE x[1] = 0.1002 y2[1] (analytic) = 1.9949841786947462724601257815688 y2[1] (numeric) = 1.9949841786932864293424290473843 absolute error = 1.4598431176967341845e-12 relative error = 7.3175673937016502868475485055980e-11 % h = 0.0001 y1[1] (analytic) = 0.89996758451811124103868599099689 y1[1] (numeric) = 0.89996758451811131403024504725983 absolute error = 7.299155905626294e-17 relative error = 8.1104653447430954744631119827502e-15 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=2.46 NO POLE NO POLE x[1] = 0.1003 y2[1] (analytic) = 1.9949741704782938663255043431386 y2[1] (numeric) = 1.994974170473366795108886204824 absolute error = 4.9270712166181383146e-12 relative error = 2.4697418590822536474212144758846e-10 % h = 0.0001 y1[1] (analytic) = 0.89986808660056967410044825122023 y1[1] (numeric) = 0.8998680866005700436262581048533 absolute error = 3.6952580985363307e-16 relative error = 4.1064442150581222368751418271897e-14 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=3.13 memory used=22.8MB, alloc=4.3MB, time=3.80 NO POLE NO POLE x[1] = 0.1004 y2[1] (analytic) = 1.9949641523120997636993956593421 y2[1] (numeric) = 1.9949641523004205414034965767649 absolute error = 1.16792222958990825772e-11 relative error = 5.8543519603413609177295971327085e-10 % h = 0.0001 y1[1] (analytic) = 0.89976858968434724032208115905533 y1[1] (numeric) = 0.89976858968434840822521669394597 absolute error = 1.16790313553489064e-15 relative error = 1.2980038966959372876805633836775e-13 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=4.44 NO POLE NO POLE x[1] = 0.1005 y2[1] (analytic) = 1.994954124196264146243657271722 y2[1] (numeric) = 1.9949541241734526990648649663917 absolute error = 2.28114471787923053303e-11 relative error = 1.1434572305256734194027721442207e-09 % h = 0.0001 y1[1] (analytic) = 0.89966909377043890886497991131759 y1[1] (numeric) = 0.89966909377044176023760955369446 absolute error = 2.85137262964237687e-15 relative error = 3.1693570996114910933945414025662e-13 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=5.08 memory used=34.3MB, alloc=4.3MB, time=5.74 NO POLE NO POLE x[1] = 0.1006 y2[1] (analytic) = 1.9949440861308872951165617872037 y2[1] (numeric) = 1.9949440860914683089547371917492 absolute error = 3.94189861618245954545e-11 relative error = 1.9759444104659650727992486352611e-09 % h = 0.0001 y1[1] (analytic) = 0.8995695988598396388673986899624 y1[1] (numeric) = 0.89956959885984555157034048863801 absolute error = 5.91270294179867561e-15 relative error = 6.5728132089976547584843886895827e-13 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=6.39 NO POLE NO POLE x[1] = 0.1007 y2[1] (analytic) = 1.9949340381160695909717940665135 y2[1] (numeric) = 1.9949340380534724219679496771165 absolute error = 6.25971690038443893970e-11 relative error = 3.1378064541401318392960817288265e-09 % h = 0.0001 y1[1] (analytic) = 0.89947010495354437943450107071087 y1[1] (numeric) = 0.89947010495355533362572555711659 absolute error = 1.095419122448640572e-14 relative error = 1.2178493942333041978804010386043e-12 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=7.04 memory used=45.7MB, alloc=4.3MB, time=7.70 NO POLE NO POLE x[1] = 0.1008 y2[1] (analytic) = 1.9949239801519115139574474176422 y2[1] (numeric) = 1.9949239800584700990423789440502 absolute error = 9.34414149150684735920e-11 relative error = 4.6839586793654663998291634036852e-09 % h = 0.0001 y1[1] (analytic) = 0.89937061205254806962841053200644 y1[1] (numeric) = 0.89937061205256675730048926473487 absolute error = 1.868767207873272843e-14 relative error = 2.0778610984501295371662388738465e-12 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=8.33 NO POLE NO POLE x[1] = 0.1009 y2[1] (analytic) = 1.9949139122385136437150187943654 y2[1] (numeric) = 1.9949139121054664111688910019977 absolute error = 1.330472325461277923677e-10 relative error = 6.6693220058220010769330063871715e-09 % h = 0.0001 y1[1] (analytic) = 0.89927112015784563845826106440201 y1[1] (numeric) = 0.89927112015787557298475976288216 absolute error = 2.993452649869848015e-14 relative error = 3.3287543464582946463493444904738e-12 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=8.97 NO POLE NO POLE memory used=57.2MB, alloc=4.3MB, time=9.65 x[1] = 0.101 y2[1] (analytic) = 1.994903834375976659378402999829 y2[1] (numeric) = 1.9949038341934664394012906383798 absolute error = 1.825102199771123614492e-10 relative error = 9.1488229573834646568524884215014e-09 % h = 0.0001 y1[1] (analytic) = 0.89917162927043200487024788047681 y1[1] (numeric) = 0.89917162927047763056106305231824 absolute error = 4.562569081517184143e-14 relative error = 5.0741915480798164168468314235371e-12 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=10.29 NO POLE NO POLE x[1] = 0.1011 y2[1] (analytic) = 1.9948937465644013395728858952114 y2[1] (numeric) = 1.9948937463214752748662706080447 absolute error = 2.429260647066152871667e-10 relative error = 1.2177393664448628443366136222802e-08 % h = 0.0001 y1[1] (analytic) = 0.89907213939130207773767822538281 y1[1] (numeric) = 0.89907213939136887940331619183528 absolute error = 6.680166563796645247e-14 relative error = 7.4300673673631037168863894606624e-12 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=10.98 NO POLE NO POLE x[1] = 0.1012 y2[1] (analytic) = 1.9948836488038885624141366134714 y2[1] (numeric) = 1.9948836484884980187733607219927 absolute error = 3.153905436407758914787e-10 relative error = 1.5809971866273041700968326349160e-08 % h = 0.0001 y1[1] (analytic) = 0.8989726505214507558510222881199 y1[1] (numeric) = 0.89897265052154536837581951200581 absolute error = 9.461252479722388591e-14 relative error = 1.0524516484716605688813760799454e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=11.68 memory used=72.4MB, alloc=4.3MB, time=12.40 NO POLE NO POLE x[1] = 0.1013 y2[1] (analytic) = 1.9948735410945393055071987781922 y2[1] (numeric) = 1.9948735406935397824248768352726 absolute error = 4.009995230823219429196e-10 relative error = 2.0101500913301156645078880562496e-08 % h = 0.0001 y1[1] (analytic) = 0.89887316266187292790796421363949 y1[1] (numeric) = 0.89887316266200324583224783402686 absolute error = 1.3031792428362038737e-13 relative error = 1.4497921363866748838717791351294e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=13.10 NO POLE NO POLE x[1] = 0.1014 y2[1] (analytic) = 1.9948634234364546459454807275319 y2[1] (numeric) = 1.9948634229356056872258697339501 absolute error = 5.008489587196109935818e-10 relative error = 2.5106929769498843137019778003200e-08 % h = 0.0001 y1[1] (analytic) = 0.89877367581356347250345321587596 y1[1] (numeric) = 0.89877367581373875961464069367038 absolute error = 1.7528711118747779442e-13 relative error = 1.9502920023643233769177408139558e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=13.81 memory used=83.9MB, alloc=4.3MB, time=14.49 NO POLE NO POLE x[1] = 0.1015 y2[1] (analytic) = 1.9948532958297357603097447432905 y2[1] (numeric) = 1.9948532952137008646940739210493 absolute error = 6.160348956156708222412e-10 relative error = 3.0881213014686293241474724043789e-08 % h = 0.0001 y1[1] (analytic) = 0.89867418997751725811975479180544 y1[1] (numeric) = 0.89867418997774825705239157035 absolute error = 2.3099893263677854456e-13 relative error = 2.5704413814594764490762267468424e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=15.15 NO POLE NO POLE x[1] = 0.1016 y2[1] (analytic) = 1.9948431582744839246670952851026 y2[1] (numeric) = 1.9948431575268304564698563013668 absolute error = 7.476534681972389837358e-10 relative error = 3.7479310846871315804223605312719e-08 % h = 0.0001 y1[1] (analytic) = 0.89857470515472914311650203663147 y1[1] (numeric) = 0.89857470515502818496123612131424 absolute error = 2.9904184473408468277e-13 relative error = 3.3279575200438285343181335819351e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=15.87 memory used=95.3MB, alloc=4.4MB, time=16.61 NO POLE NO POLE x[1] = 0.1017 y2[1] (analytic) = 1.9948330107708005145699662297676 y2[1] (numeric) = 1.9948330098739996143261647650598 absolute error = 8.968009002438014647078e-10 relative error = 4.4956189084583021208015155203357e-08 % h = 0.0001 y1[1] (analytic) = 0.89847522134619397572074706019696 y1[1] (numeric) = 0.89847522134657508964223942097632 absolute error = 3.8111392149236077936e-13 relative error = 4.2417855544344802674925343665021e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=17.29 NO POLE NO POLE x[1] = 0.1018 y2[1] (analytic) = 1.9948228533187870050551071157262 y2[1] (numeric) = 1.9948228522542135001784766699085 absolute error = 1.0645735048766304458177e-09 relative error = 5.3366819169205896464382129553377e-08 % h = 0.0001 y1[1] (analytic) = 0.89837573855290659401701250472195 y1[1] (numeric) = 0.89837573855338561688078220539064 absolute error = 4.7902286376970066869e-13 relative error = 5.3320992900064870513032294759163e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.4MB, time=17.98 memory used=106.8MB, alloc=4.4MB, time=18.71 NO POLE NO POLE x[1] = 0.1019 y2[1] (analytic) = 1.9948126859185449706425683926936 y2[1] (numeric) = 1.9948126846664772860947472221527 absolute error = 1.2520676845478211705409e-09 relative error = 6.2766178167314270799339786596333e-08 % h = 0.0001 y1[1] (analytic) = 0.89827625677586182593734316396666 y1[1] (numeric) = 0.89827625677645651194554612188617 absolute error = 5.9468600820295791951e-13 relative error = 6.6203019807896821576767887482565e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=19.41 NO POLE NO POLE x[1] = 0.102 y2[1] (analytic) = 1.9948025085701760853346856764599 y2[1] (numeric) = 1.9948025071097961543053577558044 absolute error = 1.4603799310293279206555e-09 relative error = 7.3209248773007171890854485583811e-08 % h = 0.0001 y1[1] (analytic) = 0.89817677601605448925135770391935 y1[1] (numeric) = 0.89817677601678461958749798386676 absolute error = 7.3013033614027994741e-13 relative error = 8.1290271095500827063755351573316e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=20.11 memory used=118.2MB, alloc=4.4MB, time=20.86 NO POLE NO POLE x[1] = 0.1021 y2[1] (analytic) = 1.9947923212737821226150630088674 y2[1] (numeric) = 1.9947923195831752972130639103354 absolute error = 1.6906068254019990985320e-09 relative error = 8.4751019310243572916105746994516e-08 % h = 0.0001 y1[1] (analytic) = 0.89807729627447939155630048510842 y1[1] (numeric) = 0.89807729627536688403887303078865 absolute error = 8.8749248257254568023e-13 relative error = 9.8821391683561870782388740917658e-11 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=21.55 NO POLE NO POLE x[1] = 0.1022 y2[1] (analytic) = 1.9947821240294649554475551229758 y2[1] (numeric) = 1.9947821220856199174029437066414 absolute error = 1.9438450380446114163344e-09 relative error = 9.7446483735178030566541248191329e-08 % h = 0.0001 y1[1] (analytic) = 0.89797781755213133026709348663827 y1[1] (numeric) = 0.89797781755320034901215719332527 absolute error = 1.06901874506370668700e-12 relative error = 1.1904734439630472527998256181427e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=22.25 NO POLE NO POLE memory used=129.7MB, alloc=4.4MB, time=22.93 x[1] = 0.1023 y2[1] (analytic) = 1.9947719168373265562752487134242 y2[1] (numeric) = 1.9947719146161352276523455211831 absolute error = 2.2211913286229031922411e-09 relative error = 1.1135064163849671418870538602525e-07 % h = 0.0001 y1[1] (analytic) = 0.89787833985000509260638833204834 y1[1] (numeric) = 0.89787833985128215769906836372953 absolute error = 1.27706509268003168119e-12 relative error = 1.4223141777686401974782330864558e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.4MB, time=23.60 NO POLE NO POLE x[1] = 0.1024 y2[1] (analytic) = 1.9947616996974689970194427120013 y2[1] (numeric) = 1.9947616971737264509408359582044 absolute error = 2.5237425460786067537969e-09 relative error = 1.2651849824775382620900373453923e-07 % h = 0.0001 y1[1] (analytic) = 0.89777886316909545559461841709491 y1[1] (numeric) = 0.89777886317060955276953667140383 absolute error = 1.51409717491825430892e-12 relative error = 1.6864923390751249157970631216319e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=24.27 NO POLE NO POLE x[1] = 0.1025 y2[1] (analytic) = 1.9947514726099944490786275684329 y2[1] (numeric) = 1.9947514697573988204601476199284 absolute error = 2.8525956286184799485045e-09 relative error = 1.4300506442970841400045668259641e-07 % h = 0.0001 y1[1] (analytic) = 0.89767938751039718604005113955504 y1[1] (numeric) = 0.8976793875121798763706837636879 absolute error = 1.78269033063262413286e-12 relative error = 1.9858875623475051558089266390322e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=24.97 memory used=144.9MB, alloc=4.4MB, time=25.72 NO POLE NO POLE x[1] = 0.1026 y2[1] (analytic) = 1.9947412355750051833274635363984 y2[1] (numeric) = 1.9947412323661575796241267746318 absolute error = 3.2088476037033367617666e-09 relative error = 1.6086535669266157334966724075990e-07 % h = 0.0001 y1[1] (analytic) = 0.89757991287490504052884023115219 y1[1] (numeric) = 0.89757991287699057012580109187476 absolute error = 2.08552959696086072257e-12 relative error = 2.3235029739926000693965212389151e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=26.43 NO POLE NO POLE x[1] = 0.1027 y2[1] (analytic) = 1.9947309885926035701157579647845 y2[1] (numeric) = 1.9947309849990079820786809224982 absolute error = 3.5935955880370770422863e-09 relative error = 1.8015439718879404368209392822332e-07 % h = 0.0001 y1[1] (analytic) = 0.89748043926361376541507819170298 y1[1] (numeric) = 0.89748043926603917513332720246495 absolute error = 2.42540971824901076197e-12 relative error = 2.7024652707072579618143422490288e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=27.14 memory used=156.4MB, alloc=4.4MB, time=27.86 NO POLE NO POLE x[1] = 0.1028 y2[1] (analytic) = 1.9947207316628920792674415941882 y2[1] (numeric) = 1.9947207276549552917117262591505 absolute error = 4.0079367875557153350377e-09 relative error = 2.0092721371650419520396658627643e-07 % h = 0.0001 y1[1] (analytic) = 0.89738096667751809681084882558455 y1[1] (numeric) = 0.89738096668032333196582403366934 absolute error = 2.80523515497520808479e-12 relative error = 3.1260247978752757645965323298269e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=28.56 NO POLE NO POLE x[1] = 0.1029 y2[1] (analytic) = 1.9947104647859732800795438586784 y2[1] (numeric) = 1.9947104603330047826631350367639 absolute error = 4.4529684974164088219145e-09 relative error = 2.2323883972274640811901382610085e-07 % h = 0.0001 y1[1] (analytic) = 0.89728149511761276057627988062199 y1[1] (numeric) = 0.89728149512084078066895221717064 absolute error = 3.22802009267233654865e-12 relative error = 3.5975556280130552563247192871495e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=29.26 memory used=167.8MB, alloc=4.4MB, time=29.98 NO POLE NO POLE x[1] = 0.103 y2[1] (analytic) = 1.9947001879619498413211671928266 y2[1] (numeric) = 1.9947001830321617393346828226584 absolute error = 4.9297881019864843701682e-09 relative error = 2.4714431430536984407839773636823e-07 % h = 0.0001 y1[1] (analytic) = 0.89718202458489247230959578949541 y1[1] (numeric) = 0.89718202458858936076044538515399 absolute error = 3.69688845084959565858e-12 relative error = 4.1205556392640270771203238752033e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=30.69 NO POLE NO POLE x[1] = 0.1031 y2[1] (analytic) = 1.9946899011909245312324603440163 y2[1] (numeric) = 1.994689895751431456399995655273 absolute error = 5.4394930748324646887433e-09 relative error = 2.7269868221545761002207735415589e-07 % h = 0.0001 y1[1] (analytic) = 0.89708255508035193733717051376591 y1[1] (numeric) = 0.89708255508456701122908348261677 absolute error = 4.21507389191296885086e-12 relative error = 4.6986465939418736040119216279093e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=31.40 memory used=179.2MB, alloc=4.4MB, time=32.13 NO POLE NO POLE x[1] = 0.1032 y2[1] (analytic) = 1.9946796044730002175235906900428 y2[1] (numeric) = 1.9946795984898192388144970974212 absolute error = 5.9831809787090935926216e-09 relative error = 2.9995699385966631457009447431168e-07 % h = 0.0001 y1[1] (analytic) = 0.89698308660498585070358049062019 y1[1] (numeric) = 0.896983086609771770533665084968 absolute error = 4.78591983008459434781e-12 relative error = 5.3355742171225817752733014021050e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=32.83 NO POLE NO POLE x[1] = 0.1033 y2[1] (analytic) = 1.994669297808279867373715562012 y2[1] (numeric) = 1.9946692912463304018253551867284 absolute error = 6.5619494655483603752836e-09 relative error = 3.2897430530256601712210629546185e-07 % h = 0.0001 y1[1] (analytic) = 0.89688361915978889716165768243304 y1[1] (numeric) = 0.89688361916520177660197872092749 absolute error = 5.41287944032103849445e-12 relative error = 6.0352082752853569733903710267088e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.4MB, time=33.53 memory used=190.7MB, alloc=4.4MB, time=34.25 NO POLE NO POLE x[1] = 0.1034 y2[1] (analytic) = 1.9946589811968665474299525725501 y2[1] (numeric) = 1.9946589740199702709814292831519 absolute error = 7.1768962764485232893982e-09 relative error = 3.5980567826898056982368630812027e-07 % h = 0.0001 y1[1] (analytic) = 0.89678415274575575116254272924732 y1[1] (numeric) = 0.89678415275185526682977320073513 absolute error = 6.09951566723047148781e-12 relative error = 6.8015426550024290974140545197743e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=34.95 NO POLE NO POLE x[1] = 0.1035 y2[1] (analytic) = 1.9946486546388634238063489493329 y2[1] (numeric) = 1.994648646809744182143216813484 absolute error = 7.8291192416631321358489e-09 relative error = 3.9250618014632835255780092980491e-07 % h = 0.0001 y1[1] (analytic) = 0.89668468736388107684573820427085 y1[1] (numeric) = 0.8966846873707305780797269496806 absolute error = 6.84950123398874540975e-12 relative error = 7.6386954416777819768161791784521e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=35.66 NO POLE NO POLE x[1] = 0.1036 y2[1] (analytic) = 1.9946383181343737620828498739466 y2[1] (numeric) = 1.9946383096146574814927999127389 absolute error = 8.5197162805900499612077e-09 relative error = 4.2713088398696340112005630734011e-07 % h = 0.0001 y1[1] (analytic) = 0.89658522301515952802916197248966 y1[1] (numeric) = 0.89658522302282614668041634696372 absolute error = 7.66661865125437447406e-12 relative error = 8.5509089983348373001513652066981e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.4MB, time=36.36 memory used=205.9MB, alloc=4.4MB, time=37.09 NO POLE NO POLE x[1] = 0.1037 y2[1] (analytic) = 1.9946279716835009273042658260886 y2[1] (numeric) = 1.9946279624337155255437919623233 absolute error = 9.2497854017604738637653e-09 relative error = 4.6373486851051692873621589111174e-07 % h = 0.0001 y1[1] (analytic) = 0.8964857597005857481992006524971 y1[1] (numeric) = 0.89648575970914050842528306989589 absolute error = 8.55476022608241739879e-12 relative error = 9.5425500444531242533307129742170e-10 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.4MB, time=37.81 NO POLE NO POLE x[1] = 0.1038 y2[1] (analytic) = 1.9946176152863483839792389331209 y2[1] (numeric) = 1.9946176052659236811512840248924 absolute error = 1.00204247028279549082285e-08 relative error = 5.0237321810623924108064124209519e-07 % h = 0.0001 y1[1] (analytic) = 0.8963862974211543705007631816383 y1[1] (numeric) = 0.89638629743067229857160044345283 absolute error = 9.51792807083726181453e-12 relative error = 1.0618109734853966083374378555839e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.4MB, time=38.50 memory used=217.4MB, alloc=4.4MB, time=39.23 NO POLE NO POLE x[1] = 0.1039 y2[1] (analytic) = 1.9946072489430196960792083249843 y2[1] (numeric) = 1.9946072381102873255217911757902 absolute error = 1.08327323705574171491941e-08 relative error = 5.4310102283534204495426488312609e-07 % h = 0.0001 y1[1] (analytic) = 0.8962868361778600177273344845693 y1[1] (numeric) = 0.89628683618842025183943879518901 absolute error = 1.056023411210431061971e-11 relative error = 1.1782203738635214825233999142496e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.4MB, time=39.93 NO POLE NO POLE x[1] = 0.104 y2[1] (analytic) = 1.9945968726536185270373744944846 y2[1] (numeric) = 1.9945968609658118462231987309764 absolute error = 1.16878066808141757635082e-08 relative error = 5.8597337843334115078072053175156e-07 % h = 0.0001 y1[1] (analytic) = 0.89618737597169730231102924533054 y1[1] (numeric) = 0.89618737598338320241062981552416 absolute error = 1.168590009960057019362e-11 relative error = 1.3039572318155065450212517161209e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.4MB, time=40.65 memory used=228.8MB, alloc=4.4MB, time=41.36 NO POLE NO POLE x[1] = 0.1041 y2[1] (analytic) = 1.994586486418248639747662662962 y2[1] (numeric) = 1.9945864738315026411947083713392 absolute error = 1.25867459985529542916228e-08 relative error = 6.3104538631239956907944305475863e-07 % h = 0.0001 y1[1] (analytic) = 0.89608791680366082631264578303401 y1[1] (numeric) = 0.89608791681656008392772992341208 absolute error = 1.289925761508414037807e-11 relative error = 1.4395080408064980716119286837914e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.4MB, time=42.06 NO POLE NO POLE x[1] = 0.1042 y2[1] (analytic) = 1.994576090237013896563685151352 y2[1] (numeric) = 1.994576076706365118756784163295 absolute error = 1.35306487778069009880570e-08 relative error = 6.7837215356367100107435647737993e-07 % h = 0.0001 y1[1] (analytic) = 0.8959884586747451814117200312635 y1[1] (numeric) = 0.8959884586889499294929826374023 absolute error = 1.420474808126260613880e-11 relative error = 1.5853717694391758020891199253046e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=42.77 memory used=240.3MB, alloc=4.4MB, time=43.50 NO POLE NO POLE x[1] = 0.1043 y2[1] (analytic) = 1.9945656841100182592977027566508 y2[1] (numeric) = 1.9945656695894046976210984755754 absolute error = 1.45206135616766042810754e-08 relative error = 7.2800879295964372359707072737318e-07 % h = 0.0001 y1[1] (analytic) = 0.89588900158594494889657962128759 y1[1] (numeric) = 0.89588900160155187166727995210479 absolute error = 1.560692277070033081720e-11 relative error = 1.7420598693668769582193398419192e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.4MB, time=44.22 NO POLE NO POLE x[1] = 0.1044 y2[1] (analytic) = 1.9945552680373657892195851337935 y2[1] (numeric) = 1.9945552524796268069004777921022 absolute error = 1.55577389823191073416913e-08 relative error = 7.8001042295648486844329376444174e-07 % h = 0.0001 y1[1] (analytic) = 0.89578954553825469965439806918463 y1[1] (numeric) = 0.89578954555536514246912272006822 absolute error = 1.711044281472465088359e-11 relative error = 1.9100962832116407287695417862346e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.4MB, time=44.91 memory used=251.7MB, alloc=4.4MB, time=45.63 NO POLE NO POLE x[1] = 0.1045 y2[1] (analytic) = 1.9945448420191606470557701829557 y2[1] (numeric) = 1.9945448253760368861188484208509 absolute error = 1.66431237609369217621048e-08 relative error = 8.3443216769638509634132774606047e-07 % h = 0.0001 y1[1] (analytic) = 0.89569009053266899416124906697927 y1[1] (numeric) = 0.89569009055138907337358003908216 absolute error = 1.872007921233097210289e-11 relative error = 2.0900174524871763581678118234067e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.4MB, time=46.32 NO POLE NO POLE x[1] = 0.1046 y2[1] (analytic) = 1.9945344060555070929882224422906 y2[1] (numeric) = 1.9945343882776403852211820986031 absolute error = 1.77778667077670403436875e-08 relative error = 8.9132915700990366569163478039905e-07 % h = 0.0001 y1[1] (analytic) = 0.89559063657018238247216087789009 y1[1] (numeric) = 0.89559063659062309531124764491352 absolute error = 2.044071283908676702343e-11 relative error = 2.2823723255267579774981332104502e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=47.02 NO POLE NO POLE memory used=263.2MB, alloc=4.4MB, time=47.71 x[1] = 0.1047 y2[1] (analytic) = 1.9945239601465094866533904861099 y2[1] (numeric) = 1.9945239411834427645834414914885 absolute error = 1.89630667220699489946214e-08 relative error = 9.5075652641831389623628895443660e-07 % h = 0.0001 y1[1] (analytic) = 0.89549118365178940421117083578751 y1[1] (numeric) = 0.89549118367406673866720530948782 absolute error = 2.227733445603447370031e-11 relative error = 2.4877223654160493187498738235876e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=48.40 NO POLE NO POLE x[1] = 0.1048 y2[1] (analytic) = 1.9945135042922722871411633285203 y2[1] (numeric) = 1.9945134840924494950225255912171 absolute error = 2.01998227921186377373032e-08 relative error = 1.0127694171359490278173485286054e-06 % h = 0.0001 y1[1] (analytic) = 0.89539173177848458856137994896177 y1[1] (numeric) = 0.89539173180271963327997324452555 absolute error = 2.423504471859329556378e-11 relative error = 2.7066415579308614552852743374823e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.4MB, time=49.08 NO POLE NO POLE x[1] = 0.1049 y2[1] (analytic) = 1.9945030384929000529938258325255 y2[1] (numeric) = 1.9945030170036660578062150069017 absolute error = 2.14892339951876108256238e-08 relative error = 1.0774229760725484743831487285138e-06 % h = 0.0001 y1[1] (analytic) = 0.89529228095126245425500760830018 y1[1] (numeric) = 0.89529228097758150844046751064416 absolute error = 2.631905418545990234398e-11 relative error = 2.9397164194798467137344885385773e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.4MB, time=49.73 memory used=278.4MB, alloc=4.4MB, time=50.42 NO POLE NO POLE x[1] = 0.105 y2[1] (analytic) = 1.9944925627484974422050131246041 y2[1] (numeric) = 1.994492539916097944663117152372 absolute error = 2.28323994975418959722321e-08 relative error = 1.1447723558356044734015172133317e-06 % h = 0.0001 y1[1] (analytic) = 0.89519283117111750956344639997322 y1[1] (numeric) = 0.89519283119965219289095443193607 absolute error = 2.853468332750803196285e-11 relative error = 3.1875460050521319046192925243014e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=51.10 NO POLE NO POLE x[1] = 0.1051 y2[1] (analytic) = 1.9944820770591692122186640147742 y2[1] (numeric) = 1.9944820528287506577926113288801 absolute error = 2.42304185544260526858941e-08 relative error = 1.2148727147327091308390463239344e-06 % h = 0.0001 y1[1] (analytic) = 0.89509338243904425228731702272891 y1[1] (numeric) = 0.89509338246993161482400401603321 absolute error = 3.088736253668699330430e-11 relative error = 3.4507419161698940211901659228082e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.4MB, time=51.75 memory used=289.9MB, alloc=4.4MB, time=52.42 NO POLE NO POLE x[1] = 0.1052 y2[1] (analytic) = 1.9944715814250202199279734221549 y2[1] (numeric) = 1.9944715557406297098747937030986 absolute error = 2.56843905100531797190563e-08 relative error = 1.2877792167739018618654927179009e-06 % h = 0.0001 y1[1] (analytic) = 0.89499393475603716974652330989487 y1[1] (numeric) = 0.89499393478941980188144237966848 absolute error = 3.338263213491906977361e-11 relative error = 3.7299283088458815581019609711825e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.4MB, time=53.11 NO POLE NO POLE x[1] = 0.1053 y2[1] (analytic) = 1.9944610758461554216743438060354 y2[1] (numeric) = 1.9944610486507406240804221803111 absolute error = 2.71954147975939216257243e-08 relative error = 1.3635470316740172274425070557493e-06 % h = 0.0001 y1[1] (analytic) = 0.89489448812309073877030735618759 y1[1] (numeric) = 0.89489448815911688115330317974469 absolute error = 3.602614238299582355710e-11 relative error = 4.0257419015458846037166955065570e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.4MB, time=53.79 memory used=301.3MB, alloc=4.4MB, time=54.48 NO POLE NO POLE x[1] = 0.1054 y2[1] (analytic) = 1.9944505603226798732463356024613 y2[1] (numeric) = 1.9944505315580889340808611726966 absolute error = 2.87645909391654744297647e-08 relative error = 1.4422313348550331669557928272315e-06 % h = 0.0001 y1[1] (analytic) = 0.89479504254119942568730474942828 y1[1] (numeric) = 0.89479504258002307917677804992142 absolute error = 3.882365348947330049314e-11 relative error = 4.3388319831561568619824542926901e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.4MB, time=55.13 NO POLE NO POLE x[1] = 0.1055 y2[1] (analytic) = 1.9944400348546987298786166663504 y2[1] (numeric) = 1.9944400044616801840580262626074 absolute error = 3.03930185458205904037430e-08 relative error = 1.5238873074484196270500608722426e-06 % h = 0.0001 y1[1] (analytic) = 0.89469559801135768631559990726483 y1[1] (numeric) = 0.89469559805313872193516604273027 absolute error = 4.178103561956613546544e-11 relative error = 4.6698604209557927619815435485522e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.4MB, time=55.81 memory used=312.8MB, alloc=4.4MB, time=56.47 NO POLE NO POLE x[1] = 0.1056 y2[1] (analytic) = 1.9944294994423172462509107191469 y2[1] (numeric) = 1.9944294673605199287143287607417 absolute error = 3.20817973175365819584052e-08 relative error = 1.6085701362974875868259323034508e-06 % h = 0.0001 y1[1] (analytic) = 0.8945961545345599659527815189992 y1[1] (numeric) = 0.89459615457946423485682207722908 absolute error = 4.490426890404055822988e-11 relative error = 5.0195016685940628154370846509922e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.4MB, time=57.12 NO POLE NO POLE x[1] = 0.1057 y2[1] (analytic) = 1.9944189540856407764869448020247 y2[1] (numeric) = 1.9944189202536137332826201591112 absolute error = 3.38320270432043246429135e-08 relative error = 1.6963350139597384795581147722653e-06 % h = 0.0001 y1[1] (analytic) = 0.89449671211180069936599809261988 y1[1] (numeric) = 0.89449671216000014281410439220554 absolute error = 4.819944344810629958566e-11 relative error = 5.3884427740727103845754685397635e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.4MB, time=57.78 memory used=324.2MB, alloc=4.4MB, time=58.44 NO POLE NO POLE x[1] = 0.1058 y2[1] (analytic) = 1.994408398784774774153395734651 y2[1] (numeric) = 1.9944083631399671735361364787042 absolute error = 3.56448076006172592559468e-08 relative error = 1.7872371387092140110942289407859e-06 % h = 0.0001 y1[1] (analytic) = 0.89439727074407431078201360713865 y1[1] (numeric) = 0.89439727079574707012232100494082 absolute error = 5.167275934030739780217e-11 relative error = 5.7773833877332130249748577961275e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.4MB, time=59.12 NO POLE NO POLE x[1] = 0.1059 y2[1] (analytic) = 1.994397833539824792258835579521 y2[1] (numeric) = 1.9943977960185858357984425117452 absolute error = 3.75212389564603930677758e-08 relative error = 1.8813317145388463750936537921124e-06 % h = 0.0001 y1[1] (analytic) = 0.89429783043237521387726327033124 y1[1] (numeric) = 0.89429783048770574053867517554369 absolute error = 5.533052666141190521245e-11 relative error = 6.1870357702490115701357626305076e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.4MB, time=59.80 NO POLE NO POLE x[1] = 0.106 y2[1] (analytic) = 1.9943872583508964832526761118722 y2[1] (numeric) = 1.9943872188884753169533759584507 absolute error = 3.94624211662993001534215e-08 relative error = 1.9786739511628088652657461814442e-06 % h = 0.0001 y1[1] (analytic) = 0.89419839117769781176790938198128 y1[1] (numeric) = 0.89419839123687697726120987686564 absolute error = 5.917916549330049488436e-11 relative error = 6.6181248006227101267043242175504e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.4MB, time=60.46 memory used=339.5MB, alloc=4.4MB, time=61.12 NO POLE NO POLE x[1] = 0.1061 y2[1] (analytic) = 1.994376673218095599024112295192 y2[1] (numeric) = 1.9943766317486412244549914581827 absolute error = 4.14694543745691208370093e-08 relative error = 2.0793190640188668847669974348900e-06 % h = 0.0001 y1[1] (analytic) = 0.89409895298103649699989730272694 y1[1] (numeric) = 0.89409895304426170292775127000769 absolute error = 6.322520592785396728075e-11 relative error = 7.0713879841882501514662259609813e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.4MB, time=61.77 NO POLE NO POLE x[1] = 0.1062 y2[1] (analytic) = 1.9943660781415279909010647623259 y2[1] (numeric) = 1.9943660345980891763375045148999 absolute error = 4.35434388145635602474260e-08 relative error = 2.1833222742707293529164810597531e-06 % h = 0.0001 y1[1] (analytic) = 0.89399951584338565153901152860976 y1[1] (numeric) = 0.89399951591086093961485118542928 absolute error = 6.747528807583965681952e-11 relative error = 7.5475754606180617833543018355690e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.4MB, time=62.43 memory used=350.9MB, alloc=4.4MB, time=63.11 NO POLE NO POLE x[1] = 0.1063 y2[1] (analytic) = 1.9943554731212996096491213021998 y2[1] (numeric) = 1.994355427435824801225235316807 absolute error = 4.56854748084238859853928e-08 relative error = 2.2907388088104005093892734058765e-06 % h = 0.0001 y1[1] (analytic) = 0.89390007976573964676093187142512 y1[1] (numeric) = 0.89390007983767580883672860966998 absolute error = 7.193616207579673824486e-11 relative error = 8.0474500119351956059291122895103e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.4MB, time=63.77 NO POLE NO POLE x[1] = 0.1064 y2[1] (analytic) = 1.9943448581575165054704773521646 y2[1] (numeric) = 1.9943448102608537383425524501035 absolute error = 4.78966627671279249020611e-08 relative error = 2.4016239002605321160472502083941e-06 % h = 0.0001 y1[1] (analytic) = 0.89380064474909284344128974497372 y1[1] (numeric) = 0.89380064482570753154421017769447 absolute error = 7.661468810292043272075e-11 relative error = 8.5717870705304380179413597925105e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.4MB, time=64.43 memory used=362.4MB, alloc=4.4MB, time=65.09 NO POLE NO POLE x[1] = 0.1065 y2[1] (analytic) = 1.9943342332502848280028754959752 y2[1] (numeric) = 1.9943341830721816375238165067316 absolute error = 5.01781031904790589892436e-08 relative error = 2.5160327869767760565669847389794e-06 % h = 0.0001 y1[1] (analytic) = 0.89370121079443959174572455731352 y1[1] (numeric) = 0.89370121087595742812366967087148 absolute error = 8.151783637794511355796e-11 relative error = 9.1213747271844133917775997113632e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.4MB, time=65.74 NO POLE NO POLE x[1] = 0.1066 y2[1] (analytic) = 1.9943235983997108263185439674139 y2[1] (numeric) = 1.9943235458688141592233235860243 absolute error = 5.25308966670952203813896e-08 relative error = 2.6340207130501373340243297961610e-06 % h = 0.0001 y1[1] (analytic) = 0.89360177790277423121994020911169 y1[1] (numeric) = 0.89360177798942691839596652059725 absolute error = 8.665268717602631148556e-11 relative error = 9.6970137390946762017412660385115e-09 % h = 0.0001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.4MB, time=66.41 memory used=373.8MB, alloc=4.4MB, time=67.08 NO POLE NO POLE x[1] = 0.1067 y2[1] (analytic) = 1.9943129536059008489231341595696 y2[1] (numeric) = 1.9943128986497569745252486901542 absolute error = 5.49561438743978854694154e-08 relative error = 2.7556429283093274665954030751268e-06 % h = 0.0001 y1[1] (analytic) = 0.89350234607509109077976169819579 y1[1] (numeric) = 0.89350234616711752161538331757413 absolute error = 9.202643083562161937834e-11 relative error = 1.0299517537907796306342566637091e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.4MB, time=67.75 NO POLE NO POLE x[1] = 0.1068 y2[1] (analytic) = 1.994302298868961343754657139781 y2[1] (numeric) = 1.9943022414140157651535890132834 absolute error = 5.74549455786010681264976e-08 relative error = 2.8809546883231182815335770601424e-06 % h = 0.0001 y1[1] (analytic) = 0.89340291531238448870119183040385 y1[1] (numeric) = 0.89340291541003085646856232675495 absolute error = 9.764636776737049635110e-11 relative error = 1.0929712237756440570901086788794e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.4MB, time=68.43 memory used=385.2MB, alloc=4.4MB, time=69.10 NO POLE NO POLE x[1] = 0.1069 y2[1] (analytic) = 1.9942916341889988581824191702586 y2[1] (numeric) = 1.9942915741605962234821071243154 absolute error = 6.00284026347003120459432e-08 relative error = 3.0100112544026961075824175111837e-06 % h = 0.0001 y1[1] (analytic) = 0.89330348561564873261046803683264 y1[1] (numeric) = 0.8933034857191686410734410079638 absolute error = 1.0351990846297297113116e-10 relative error = 1.1588436643301454018989697965700e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.4MB, time=69.78 NO POLE NO POLE x[1] = 0.107 y2[1] (analytic) = 1.9942809595661200390059562343918 y2[1] (numeric) = 1.9942808968885040525442740431489 absolute error = 6.26776159864616821912429e-08 relative error = 3.1428678936040163659841756261263e-06 % h = 0.0001 y1[1] (analytic) = 0.89320405698587811947411929758354 y1[1] (numeric) = 0.89320405709553269297818654220386 absolute error = 1.0965457350406724462032e-10 relative error = 1.2276542257778943703417683844300e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.4MB, time=70.46 NO POLE NO POLE memory used=396.7MB, alloc=4.4MB, time=71.12 x[1] = 0.1071 y2[1] (analytic) = 1.9942702750004316324539675687545 y2[1] (numeric) = 1.9942702095967449660432122103351 absolute error = 6.54036866664107553584194e-08 relative error = 3.2795798787301585602437468211860e-06 % h = 0.0001 y1[1] (analytic) = 0.89310462942406693558902317210554 y1[1] (numeric) = 0.89310462954012492916012936366292 absolute error = 1.1605799357110619155738e-10 relative error = 1.2994893291052368489621909576562e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.4MB, time=71.78 NO POLE NO POLE x[1] = 0.1072 y2[1] (analytic) = 1.9942595804920404841832482008192 y2[1] (numeric) = 1.994259512284324688361638350038 absolute error = 6.82077157958216098507812e-08 relative error = 3.4202024883336816648079809990039e-06 % h = 0.0001 y1[1] (analytic) = 0.89300520293120945657246293623481 y1[1] (numeric) = 0.89300520305394736602469569742728 absolute error = 1.2273790945223276119247e-10 relative error = 1.3744366667669637946536489673021e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.4MB, time=72.48 NO POLE NO POLE x[1] = 0.1073 y2[1] (analytic) = 1.99424887604105353927762049239 y2[1] (numeric) = 1.994248804950248954571806226199 absolute error = 7.10908045847058142661910e-08 relative error = 3.5647910067189799128201960995143e-06 % h = 0.0001 y1[1] (analytic) = 0.89290577750829994735218482603007 y1[1] (numeric) = 0.8929057776380021194043391029147 absolute error = 1.2970217205215427688463e-10 relative error = 1.4525852034925223542220269510775e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.4MB, time=73.15 memory used=411.9MB, alloc=4.4MB, time=73.85 NO POLE NO POLE x[1] = 0.1074 y2[1] (analytic) = 1.9942381616475778422468646887649 y2[1] (numeric) = 1.9942380875935235104454492918062 absolute error = 7.40540543318014153969587e-08 relative error = 3.7134007239446389831098289999440e-06 % h = 0.0001 y1[1] (analytic) = 0.89280635315633266215645538850346 y1[1] (numeric) = 0.89280635329329140455747102303704 absolute error = 1.3695874240101563453358e-10 relative error = 1.5340251770927285343654648280971e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.4MB, time=74.53 NO POLE NO POLE x[1] = 0.1075 y2[1] (analytic) = 1.9942274373117205370256484736392 y2[1] (numeric) = 1.9942273602131541124637232311685 absolute error = 7.70985664245619252424707e-08 relative error = 3.8660869358257925865772802360662e-06 % h = 0.0001 y1[1] (analytic) = 0.89270692987630184450411893934616 y1[1] (numeric) = 0.89270693002081753616739033910338 absolute error = 1.4451569166327139975722e-10 relative error = 1.6188480992669817422382266108716e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.4MB, time=75.18 memory used=423.4MB, alloc=4.4MB, time=75.85 NO POLE NO POLE x[1] = 0.1076 y2[1] (analytic) = 1.9942167030335888669724555297596 y2[1] (numeric) = 1.9942166228081465278271483950961 absolute error = 8.02254423391453071346635e-08 relative error = 4.0229049439364794521338606603488e-06 % h = 0.0001 y1[1] (analytic) = 0.89260750766920172719465512774823 y1[1] (numeric) = 0.89260750782158292834121193147423 absolute error = 1.5238120114655680372600e-10 relative error = 1.7071467564109815169804727814343e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.4MB, time=76.50 NO POLE NO POLE x[1] = 0.1077 y2[1] (analytic) = 1.9942059588132901748685131053403 y2[1] (numeric) = 1.9942058753775065344655521288868 absolute error = 8.34357836404029609764535e-08 relative error = 4.1839100556120007123569809078341e-06 % h = 0.0001 y1[1] (analytic) = 0.89250808653602653229823660841207 y1[1] (numeric) = 0.89250808669659009460879424597757 absolute error = 1.6056356231055763756550e-10 relative error = 1.7990152104249467728173986988878e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.4MB, time=77.15 memory used=434.8MB, alloc=4.4MB, time=77.83 NO POLE NO POLE x[1] = 0.1078 y2[1] (analytic) = 1.9941952046509319029167185862516 y2[1] (numeric) = 1.9941951179202399210480109930193 absolute error = 8.67306919818687075932323e-08 relative error = 4.3491575839512776890206313758693e-06 % h = 0.0001 y1[1] (analytic) = 0.89240866647777047114578682085902 y1[1] (numeric) = 0.89240866664684164792166586609748 absolute error = 1.6907117677587904523846e-10 relative error = 1.8945487995223378745496492211458e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.4MB, time=78.52 NO POLE NO POLE x[1] = 0.1079 y2[1] (analytic) = 1.9941844405466215927405650739918 y2[1] (numeric) = 1.9941843504353524869927928764546 absolute error = 9.01112691057477721975372e-08 relative error = 4.5187028478192100786612577068235e-06 % h = 0.0001 y1[1] (analytic) = 0.89230924749542774431903787612839 y1[1] (numeric) = 0.89230924767334030065195109094608 absolute error = 1.7791255633291321481769e-10 relative error = 1.9938441390390818664787786779588e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.4MB, time=79.20 memory used=446.3MB, alloc=4.4MB, time=79.87 NO POLE NO POLE x[1] = 0.108 y2[1] (analytic) = 1.9941736665004668853830659694533 y2[1] (numeric) = 1.9941735729218500424772990024445 absolute error = 9.35786168429057669670088e-08 relative error = 4.6926011718490345383392843264975e-06 % h = 0.0001 y1[1] (analytic) = 0.89220982958999254164058855096841 y1[1] (numeric) = 0.89220982977708886459129451902946 absolute error = 1.8709632295070596806105e-10 relative error = 2.0969991222433011760287293246426e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.4MB, time=80.54 NO POLE NO POLE x[1] = 0.1081 y2[1] (analytic) = 1.9941628825125755213056785624931 y2[1] (numeric) = 1.9941627853787384084480058267497 absolute error = 9.71338371128576727357434e-08 relative error = 4.8709078864446836717563652398303e-06 % h = 0.0001 y1[1] (analytic) = 0.89211041276245904216396238961858 y1[1] (numeric) = 0.89211041295909025094978463781848 absolute error = 1.9663120878582224819990e-10 relative error = 2.2041129211455461135467094471689e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.4MB, time=81.21 memory used=457.7MB, alloc=4.4MB, time=81.88 NO POLE NO POLE x[1] = 0.1082 y2[1] (analytic) = 1.9941520885830553403872266273193 y2[1] (numeric) = 1.9941519878050234166304068281667 absolute error = 1.007780319237568197991526e-07 relative error = 5.0536783277831454158887142457739e-06 % h = 0.0001 y1[1] (analytic) = 0.89201099701382141416366591328264 y1[1] (numeric) = 0.89201099722034747035487641913507 absolute error = 2.0652605619121050585243e-10 relative error = 2.3152859873095314899871832224814e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.4MB, time=82.57 NO POLE NO POLE x[1] = 0.1083 y2[1] (analytic) = 1.9941412847120142819228220237039 y2[1] (numeric) = 1.9941411801997109095389541912644 absolute error = 1.045123033723838678324395e-07 relative error = 5.2409678378168228282967535904767e-06 % h = 0.0001 y1[1] (analytic) = 0.89191158234507381512524693739185 y1[1] (numeric) = 0.8919115825618636328503129203649 absolute error = 2.1678981772506598297305e-10 relative error = 2.4306200526633776744004874213524e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.4MB, time=83.23 NO POLE NO POLE memory used=469.2MB, alloc=4.4MB, time=83.91 x[1] = 0.1084 y2[1] (analytic) = 1.9941304708995603846227853040322 y2[1] (numeric) = 1.9941303625618067404870003812313 absolute error = 1.083377536441357849228009e-07 relative error = 5.4328317642758942752713573860206e-06 % h = 0.0001 y1[1] (analytic) = 0.89181216875721039173535299675779 y1[1] (numeric) = 0.89181216898464194789504589150716 absolute error = 2.2743155615969289474937e-10 relative error = 2.5502181303113564133720569665738e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.4MB, time=84.57 NO POLE NO POLE x[1] = 0.1085 y2[1] (analytic) = 1.9941196471458017866115653262008 y2[1] (numeric) = 1.994119534890316773596739610734 absolute error = 1.122554850130148257154668e-07 relative error = 5.6293254606706740209770987268510e-06 % h = 0.0001 y1[1] (analytic) = 0.89171275625122527987178987871414 y1[1] (numeric) = 0.89171275648968572436215538807225 absolute error = 2.3846044449036550935811e-10 relative error = 2.6741845153461417347768195062293e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.4MB, time=85.22 NO POLE NO POLE x[1] = 0.1086 y2[1] (analytic) = 1.994108813450846725426657872374 y2[1] (numeric) = 1.9941086971842468838091491986866 absolute error = 1.162665998416175086736874e-07 relative error = 5.8305042862939732177528916190998e-06 % h = 0.0001 y1[1] (analytic) = 0.89161334482811260459358026434694 y1[1] (numeric) = 0.89161334507799837053776838983819 absolute error = 2.4988576594418812549125e-10 relative error = 2.8026247856615662584338528494158e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.4MB, time=85.87 memory used=484.4MB, alloc=4.4MB, time=86.34 NO POLE NO POLE x[1] = 0.1087 y2[1] (analytic) = 1.9940979698148035380175232736096 y2[1] (numeric) = 1.9940978494426029568939308208328 absolute error = 1.203722005811235924527768e-07 relative error = 6.0364236062234612977304060498383e-06 % h = 0.0001 y1[1] (analytic) = 0.89151393448886648013102247791261 y1[1] (numeric) = 0.89151393475058339411997642547659 absolute error = 2.6171691398895394756398e-10 relative error = 2.9356458027658832364702364940755e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.4MB, time=86.61 NO POLE NO POLE x[1] = 0.1088 y2[1] (analytic) = 1.9940871162377806607445030403653 y2[1] (numeric) = 1.9940869916643908894594516520406 absolute error = 1.245733897712850513883247e-07 relative error = 6.2471387913240277659307772089501e-06 % h = 0.0001 y1[1] (analytic) = 0.89141452523448100987574934454329 y1[1] (numeric) = 0.89141452550844440221775220305892 absolute error = 2.7396339234200285851563e-10 relative error = 3.0733557125955346464199646919138e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.4MB, time=86.88 memory used=495.9MB, alloc=4.4MB, time=87.17 NO POLE NO POLE x[1] = 0.1089 y2[1] (analytic) = 1.9940762527198866293777354988961 y2[1] (numeric) = 1.9940761238486165889626854002105 absolute error = 1.288712700404150500986856e-07 relative error = 6.4627052182501443950000770045207e-06 % h = 0.0001 y1[1] (analytic) = 0.89131511706595028637078715633878 y1[1] (numeric) = 0.89131511735258510134986524645401 absolute error = 2.8663481497907809011523e-10 relative error = 3.2158639463294256603104204723759e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.4MB, time=87.44 NO POLE NO POLE x[1] = 0.109 y2[1] (analytic) = 1.9940653792612300790960704335539 y2[1] (numeric) = 1.9940652459942859737191532316971 absolute error = 1.332669441053769172018568e-07 relative error = 6.6831782694482278217441436888072e-06 % h = 0.0001 y1[1] (analytic) = 0.89121570998426839130061474694456 y1[1] (numeric) = 0.89121571028400929744379653762757 absolute error = 2.9974090614318179068301e-10 relative error = 3.3632812212037058132066223069484e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.4MB, time=87.72 memory used=507.3MB, alloc=4.4MB, time=88.01 NO POLE NO POLE x[1] = 0.1091 y2[1] (analytic) = 1.994054495861919744485982735 y2[1] (numeric) = 1.9940543581004049729128645881459 absolute error = 1.377615147715731181468541e-07 relative error = 6.9086133331590025456232824829970e-06 % h = 0.0001 y1[1] (analytic) = 0.89111630399042939548122267471527 y1[1] (numeric) = 0.8911163043037208958346521648546 absolute error = 3.1329150035342949013933e-10 relative error = 3.5157195413270571949071627343929e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.4MB, time=88.28 NO POLE NO POLE x[1] = 0.1092 y2[1] (analytic) = 1.9940436025220644595404850543411 y2[1] (numeric) = 1.994043460165979526606257894645 absolute error = 1.423560849329342271596961e-07 relative error = 7.1390658034198643293674878280466e-06 % h = 0.0001 y1[1] (analytic) = 0.89101689908542735885017251456312 y1[1] (numeric) = 0.89101689941272390126407597685554 absolute error = 3.2729654241390346229242e-10 relative error = 3.6732921984964899887063771872081e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.4MB, time=88.55 memory used=518.8MB, alloc=4.4MB, time=88.84 NO POLE NO POLE x[1] = 0.1093 y2[1] (analytic) = 1.9940326992417731576580394631999 y2[1] (numeric) = 1.994032552190015585750141159092 absolute error = 1.470517575719078983041079e-07 relative error = 7.3745910800672440018728703353784e-06 % h = 0.0001 y1[1] (analytic) = 0.89091749527025633045665625859053 y1[1] (numeric) = 0.89091749561202241787916124286705 absolute error = 3.4176608742250498427652e-10 relative error = 3.8361137730136456813616548355275e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.4MB, time=89.12 NO POLE NO POLE x[1] = 0.1094 y2[1] (analytic) = 1.9940217860211548716414681197318 y2[1] (numeric) = 1.9940216341715191121936324626781 absolute error = 1.518496357594478356570537e-07 relative error = 7.6152445687389716635399437942642e-06 % h = 0.0001 y1[1] (analytic) = 0.89081809254591034845155582560653 y1[1] (numeric) = 0.89081809290262064923136131865832 absolute error = 3.5671030077980549305179e-10 relative error = 4.0043001345016082686245164072221e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.4MB, time=89.39 memory used=530.2MB, alloc=4.4MB, time=89.67 NO POLE NO POLE x[1] = 0.1095 y2[1] (analytic) = 1.9940108628603187336968629405976 y2[1] (numeric) = 1.9940107061094960786941003413884 absolute error = 1.567508226550027625992092e-07 relative error = 7.8610816808766412942145352947692e-06 % h = 0.0001 y1[1] (analytic) = 0.89071869091338344007750267962617 y1[1] (numeric) = 0.89071869128552289827539931850373 absolute error = 3.7213945819789663887756e-10 relative error = 4.1779684427222237809186742548651e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.4MB, time=89.94 NO POLE NO POLE x[1] = 0.1096 y2[1] (analytic) = 1.9939999297593739754324942789029 y2[1] (numeric) = 1.99399976800295246892710405842 absolute error = 1.617564215065053902204829e-07 relative error = 8.1121578337279757638920287658771e-06 % h = 0.0001 y1[1] (analytic) = 0.89061929037366962165893755745254 y1[1] (numeric) = 0.89061929076173356736817679312284 absolute error = 3.8806394570923923567030e-10 relative error = 4.3572371483939284539686680176220e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.4MB, time=90.21 NO POLE NO POLE x[1] = 0.1097 y2[1] (analytic) = 1.9939889867184299278577186081169 y2[1] (numeric) = 1.9939888198508942774963337674181 absolute error = 1.668675356503613848406988e-07 relative error = 8.3685284503491922463458602652124e-06 % h = 0.0001 y1[1] (analytic) = 0.89051989092776289859217030544061 y1[1] (numeric) = 0.89051989133225715826768141359862 absolute error = 4.0449425967551110815801e-10 relative error = 4.5422259940100858694089367709856e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.4MB, time=90.48 memory used=545.5MB, alloc=4.4MB, time=90.76 NO POLE NO POLE x[1] = 0.1098 y2[1] (analytic) = 1.9939780337375960213818852119796 y2[1] (numeric) = 1.9939778616523275099435505664308 absolute error = 1.720852685114383346455488e-07 relative error = 8.6302489596073680358410102711020e-06 % h = 0.0001 y1[1] (analytic) = 0.89042049257665726533543982554245 y1[1] (numeric) = 0.89042049299809827213189366128477 absolute error = 4.2144100679645383574232e-10 relative error = 4.7330560146578333906214260871920e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.4MB, time=91.04 NO POLE NO POLE x[1] = 0.1099 y2[1] (analytic) = 1.993967070816981785813241880409 y2[1] (numeric) = 1.9939668934062581827585264424833 absolute error = 1.774107236030547154379257e-07 relative error = 8.8973747961828067670934061770431e-06 % h = 0.0001 y1[1] (analytic) = 0.89032109532134670539897413073309 y1[1] (numeric) = 0.89032109576026160951769252371317 absolute error = 4.3891490411871839298008e-10 relative error = 4.9298495388374382192783349283567e-08 % h = 0.0001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.4MB, time=91.31 memory used=556.9MB, alloc=4.4MB, time=91.59 NO POLE NO POLE x[1] = 0.11 y2[1] (analytic) = 1.9939560979566968503578396114198 y2[1] (numeric) = 1.9939559151116923233889841066717 absolute error = 1.828450045269688555047481e-07 relative error = 9.1699614005714050386362058277292e-06 % h = 0.0001 y1[1] (analytic) = 0.89022169916282519133505050991655 y1[1] (numeric) = 0.89022169961975197037976019651228 absolute error = 4.5692677904470968659573e-10 relative error = 5.1327301892821633982842758414925e-08 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 100 Total Elapsed Time = 1 Minutes 31 Seconds Elapsed Time(since restart) = 1 Minutes 31 Seconds Expected Time Remaining = 12 Hours 19 Minutes 2 Seconds Optimized Time Remaining = 12 Hours 18 Minutes 48 Seconds Time to Timeout = 13 Minutes 28 Seconds Percent Done = 0.2061 % > quit memory used=558.4MB, alloc=4.4MB, time=91.69