|\^/| 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, > ALWAYS, > glob_iolevel, > INFO, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_last_good_h, > years_in_century, > days_in_year, > glob_log10normmin, > glob_subiter_method, > glob_max_minutes, > hours_in_day, > glob_hmin, > glob_h, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned, > glob_hmin_init, > glob_not_yet_finished, > djd_debug2, > glob_html_log, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_clock_sec, > glob_good_digits, > glob_log10relerr, > glob_log10abserr, > glob_hmax, > glob_iter, > glob_optimal_clock_start_sec, > sec_in_minute, > glob_display_flag, > glob_smallish_float, > glob_dump_analytic, > glob_look_poles, > glob_optimal_done, > glob_almost_1, > min_in_hour, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_max_rel_trunc_err, > glob_disp_incr, > centuries_in_millinium, > glob_dump, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_initial_pass, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp4_g, > array_last_rel_error, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_x, > array_fact_1, > array_y2_init, > array_m1, > array_1st_rel_error, > array_norms, > array_y2, > array_y1, > array_y2_higher, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_set_initial, > array_complex_pole, > array_y2_higher_work, > array_fact_2, > array_real_pole, > array_y1_higher, > array_poles, > 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 := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 3 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > 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_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > glob_good_digits := -trunc(log10(relerr/100.0)); > else > glob_good_digits := Digits; > fi;# end if 3 > ; > else > relerr := -1.0 ; > glob_good_digits := -1; > 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_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > 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, ALWAYS, glob_iolevel, INFO, glob_max_terms, DEBUGMASSIVE, glob_last_good_h, years_in_century, days_in_year, glob_log10normmin, glob_subiter_method, glob_max_minutes, hours_in_day, glob_hmin, glob_h, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_warned, glob_hmin_init, glob_not_yet_finished, djd_debug2, glob_html_log, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_reached_optimal_h, glob_not_yet_start_msg, glob_clock_sec, glob_good_digits, glob_log10relerr, glob_log10abserr, glob_hmax, glob_iter, glob_optimal_clock_start_sec, sec_in_minute, glob_display_flag, glob_smallish_float, glob_dump_analytic, glob_look_poles, glob_optimal_done, glob_almost_1, min_in_hour, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_max_rel_trunc_err, glob_disp_incr, centuries_in_millinium, glob_dump, glob_max_iter, glob_abserr, glob_log10_abserr, glob_large_float, glob_initial_pass, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_start, glob_warned2, glob_log10_relerr, glob_max_opt_iter, array_const_0D0, array_const_1, array_tmp4_g, array_last_rel_error, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_x, array_fact_1, array_y2_init, array_m1, array_1st_rel_error, array_norms, array_y2, array_y1, array_y2_higher, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_y2_higher_work2, array_y1_set_initial, array_complex_pole, array_y2_higher_work, array_fact_2, array_real_pole, array_y1_higher, array_poles, 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 := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGL, > ALWAYS, > glob_iolevel, > INFO, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_last_good_h, > years_in_century, > days_in_year, > glob_log10normmin, > glob_subiter_method, > glob_max_minutes, > hours_in_day, > glob_hmin, > glob_h, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned, > glob_hmin_init, > glob_not_yet_finished, > djd_debug2, > glob_html_log, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_clock_sec, > glob_good_digits, > glob_log10relerr, > glob_log10abserr, > glob_hmax, > glob_iter, > glob_optimal_clock_start_sec, > sec_in_minute, > glob_display_flag, > glob_smallish_float, > glob_dump_analytic, > glob_look_poles, > glob_optimal_done, > glob_almost_1, > min_in_hour, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_max_rel_trunc_err, > glob_disp_incr, > centuries_in_millinium, > glob_dump, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_initial_pass, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp4_g, > array_last_rel_error, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_x, > array_fact_1, > array_y2_init, > array_m1, > array_1st_rel_error, > array_norms, > array_y2, > array_y1, > array_y2_higher, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_set_initial, > array_complex_pole, > array_y2_higher_work, > array_fact_2, > array_real_pole, > array_y1_higher, > array_poles, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGL, ALWAYS, glob_iolevel, INFO, glob_max_terms, DEBUGMASSIVE, glob_last_good_h, years_in_century, days_in_year, glob_log10normmin, glob_subiter_method, glob_max_minutes, hours_in_day, glob_hmin, glob_h, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_warned, glob_hmin_init, glob_not_yet_finished, djd_debug2, glob_html_log, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_reached_optimal_h, glob_not_yet_start_msg, glob_clock_sec, glob_good_digits, glob_log10relerr, glob_log10abserr, glob_hmax, glob_iter, glob_optimal_clock_start_sec, sec_in_minute, glob_display_flag, glob_smallish_float, glob_dump_analytic, glob_look_poles, glob_optimal_done, glob_almost_1, min_in_hour, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_max_rel_trunc_err, glob_disp_incr, centuries_in_millinium, glob_dump, glob_max_iter, glob_abserr, glob_log10_abserr, glob_large_float, glob_initial_pass, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_start, glob_warned2, glob_log10_relerr, glob_max_opt_iter, array_const_0D0, array_const_1, array_tmp4_g, array_last_rel_error, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_x, array_fact_1, array_y2_init, array_m1, array_1st_rel_error, array_norms, array_y2, array_y1, array_y2_higher, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_y2_higher_work2, array_y1_set_initial, array_complex_pole, array_y2_higher_work, array_fact_2, array_real_pole, array_y1_higher, array_poles, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > DEBUGL, > ALWAYS, > glob_iolevel, > INFO, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_last_good_h, > years_in_century, > days_in_year, > glob_log10normmin, > glob_subiter_method, > glob_max_minutes, > hours_in_day, > glob_hmin, > glob_h, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned, > glob_hmin_init, > glob_not_yet_finished, > djd_debug2, > glob_html_log, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_clock_sec, > glob_good_digits, > glob_log10relerr, > glob_log10abserr, > glob_hmax, > glob_iter, > glob_optimal_clock_start_sec, > sec_in_minute, > glob_display_flag, > glob_smallish_float, > glob_dump_analytic, > glob_look_poles, > glob_optimal_done, > glob_almost_1, > min_in_hour, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_max_rel_trunc_err, > glob_disp_incr, > centuries_in_millinium, > glob_dump, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_initial_pass, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp4_g, > array_last_rel_error, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_x, > array_fact_1, > array_y2_init, > array_m1, > array_1st_rel_error, > array_norms, > array_y2, > array_y1, > array_y2_higher, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_set_initial, > array_complex_pole, > array_y2_higher_work, > array_fact_2, > array_real_pole, > array_y1_higher, > array_poles, > 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, ALWAYS, glob_iolevel, INFO, glob_max_terms, DEBUGMASSIVE, glob_last_good_h, years_in_century, days_in_year, glob_log10normmin, glob_subiter_method, glob_max_minutes, hours_in_day, glob_hmin, glob_h, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_warned, glob_hmin_init, glob_not_yet_finished, djd_debug2, glob_html_log, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_reached_optimal_h, glob_not_yet_start_msg, glob_clock_sec, glob_good_digits, glob_log10relerr, glob_log10abserr, glob_hmax, glob_iter, glob_optimal_clock_start_sec, sec_in_minute, glob_display_flag, glob_smallish_float, glob_dump_analytic, glob_look_poles, glob_optimal_done, glob_almost_1, min_in_hour, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_max_rel_trunc_err, glob_disp_incr, centuries_in_millinium, glob_dump, glob_max_iter, glob_abserr, glob_log10_abserr, glob_large_float, glob_initial_pass, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_start, glob_warned2, glob_log10_relerr, glob_max_opt_iter, array_const_0D0, array_const_1, array_tmp4_g, array_last_rel_error, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_x, array_fact_1, array_y2_init, array_m1, array_1st_rel_error, array_norms, array_y2, array_y1, array_y2_higher, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_y2_higher_work2, array_y1_set_initial, array_complex_pole, array_y2_higher_work, array_fact_2, array_real_pole, array_y1_higher, array_poles, 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, > ALWAYS, > glob_iolevel, > INFO, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_last_good_h, > years_in_century, > days_in_year, > glob_log10normmin, > glob_subiter_method, > glob_max_minutes, > hours_in_day, > glob_hmin, > glob_h, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned, > glob_hmin_init, > glob_not_yet_finished, > djd_debug2, > glob_html_log, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_clock_sec, > glob_good_digits, > glob_log10relerr, > glob_log10abserr, > glob_hmax, > glob_iter, > glob_optimal_clock_start_sec, > sec_in_minute, > glob_display_flag, > glob_smallish_float, > glob_dump_analytic, > glob_look_poles, > glob_optimal_done, > glob_almost_1, > min_in_hour, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_max_rel_trunc_err, > glob_disp_incr, > centuries_in_millinium, > glob_dump, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_initial_pass, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp4_g, > array_last_rel_error, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_x, > array_fact_1, > array_y2_init, > array_m1, > array_1st_rel_error, > array_norms, > array_y2, > array_y1, > array_y2_higher, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_set_initial, > array_complex_pole, > array_y2_higher_work, > array_fact_2, > array_real_pole, > array_y1_higher, > array_poles, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > > > > > > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * 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, ALWAYS, glob_iolevel, INFO, glob_max_terms, DEBUGMASSIVE, glob_last_good_h, years_in_century, days_in_year, glob_log10normmin, glob_subiter_method, glob_max_minutes, hours_in_day, glob_hmin, glob_h, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_warned, glob_hmin_init, glob_not_yet_finished, djd_debug2, glob_html_log, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_reached_optimal_h, glob_not_yet_start_msg, glob_clock_sec, glob_good_digits, glob_log10relerr, glob_log10abserr, glob_hmax, glob_iter, glob_optimal_clock_start_sec, sec_in_minute, glob_display_flag, glob_smallish_float, glob_dump_analytic, glob_look_poles, glob_optimal_done, glob_almost_1, min_in_hour, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_max_rel_trunc_err, glob_disp_incr, centuries_in_millinium, glob_dump, glob_max_iter, glob_abserr, glob_log10_abserr, glob_large_float, glob_initial_pass, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_start, glob_warned2, glob_log10_relerr, glob_max_opt_iter, array_const_0D0, array_const_1, array_tmp4_g, array_last_rel_error, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_x, array_fact_1, array_y2_init, array_m1, array_1st_rel_error, array_norms, array_y2, array_y1, array_y2_higher, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_y2_higher_work2, array_y1_set_initial, array_complex_pole, array_y2_higher_work, array_fact_2, array_real_pole, array_y1_higher, array_poles, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= omniabs(array_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= omniabs(array_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*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, > ALWAYS, > glob_iolevel, > INFO, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_last_good_h, > years_in_century, > days_in_year, > glob_log10normmin, > glob_subiter_method, > glob_max_minutes, > hours_in_day, > glob_hmin, > glob_h, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned, > glob_hmin_init, > glob_not_yet_finished, > djd_debug2, > glob_html_log, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_clock_sec, > glob_good_digits, > glob_log10relerr, > glob_log10abserr, > glob_hmax, > glob_iter, > glob_optimal_clock_start_sec, > sec_in_minute, > glob_display_flag, > glob_smallish_float, > glob_dump_analytic, > glob_look_poles, > glob_optimal_done, > glob_almost_1, > min_in_hour, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_max_rel_trunc_err, > glob_disp_incr, > centuries_in_millinium, > glob_dump, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_initial_pass, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp4_g, > array_last_rel_error, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_x, > array_fact_1, > array_y2_init, > array_m1, > array_1st_rel_error, > array_norms, > array_y2, > array_y1, > array_y2_higher, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_set_initial, > array_complex_pole, > array_y2_higher_work, > array_fact_2, > array_real_pole, > array_y1_higher, > array_poles, > glob_last; > > local iii; > > > > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2 > ; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3 > ; > > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGL, ALWAYS, glob_iolevel, INFO, glob_max_terms, DEBUGMASSIVE, glob_last_good_h, years_in_century, days_in_year, glob_log10normmin, glob_subiter_method, glob_max_minutes, hours_in_day, glob_hmin, glob_h, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_warned, glob_hmin_init, glob_not_yet_finished, djd_debug2, glob_html_log, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_reached_optimal_h, glob_not_yet_start_msg, glob_clock_sec, glob_good_digits, glob_log10relerr, glob_log10abserr, glob_hmax, glob_iter, glob_optimal_clock_start_sec, sec_in_minute, glob_display_flag, glob_smallish_float, glob_dump_analytic, glob_look_poles, glob_optimal_done, glob_almost_1, min_in_hour, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_max_rel_trunc_err, glob_disp_incr, centuries_in_millinium, glob_dump, glob_max_iter, glob_abserr, glob_log10_abserr, glob_large_float, glob_initial_pass, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_start, glob_warned2, glob_log10_relerr, glob_max_opt_iter, array_const_0D0, array_const_1, array_tmp4_g, array_last_rel_error, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_x, array_fact_1, array_y2_init, array_m1, array_1st_rel_error, array_norms, array_y2, array_y1, array_y2_higher, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_y2_higher_work2, array_y1_set_initial, array_complex_pole, array_y2_higher_work, array_fact_2, array_real_pole, array_y1_higher, array_poles, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGL, > ALWAYS, > glob_iolevel, > INFO, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_last_good_h, > years_in_century, > days_in_year, > glob_log10normmin, > glob_subiter_method, > glob_max_minutes, > hours_in_day, > glob_hmin, > glob_h, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned, > glob_hmin_init, > glob_not_yet_finished, > djd_debug2, > glob_html_log, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_clock_sec, > glob_good_digits, > glob_log10relerr, > glob_log10abserr, > glob_hmax, > glob_iter, > glob_optimal_clock_start_sec, > sec_in_minute, > glob_display_flag, > glob_smallish_float, > glob_dump_analytic, > glob_look_poles, > glob_optimal_done, > glob_almost_1, > min_in_hour, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_max_rel_trunc_err, > glob_disp_incr, > centuries_in_millinium, > glob_dump, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_initial_pass, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp4_g, > array_last_rel_error, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_x, > array_fact_1, > array_y2_init, > array_m1, > array_1st_rel_error, > array_norms, > array_y2, > array_y1, > array_y2_higher, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_set_initial, > array_complex_pole, > array_y2_higher_work, > array_fact_2, > array_real_pole, > array_y1_higher, > array_poles, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_y1_higher[2,1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre sin 1 $eq_no = 2 > array_tmp4[1] := sin(array_x[1]); > array_tmp4_g[1] := cos(array_x[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_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_y1_higher[2,2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 2 > array_tmp4[2] := array_tmp4_g[1] * array_x[2] / 1; > array_tmp4_g[2] := -array_tmp4[1] * array_x[2] / 1; > #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_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_y1_higher[2,3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre sin ID_LINEAR iii = 3 $eq_no = 2 > array_tmp4[3] := array_tmp4_g[2] * array_x[2] / 2; > array_tmp4_g[3] := -array_tmp4[2] * array_x[2] / 2; > #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_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_y1_higher[2,4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre sin ID_LINEAR iii = 4 $eq_no = 2 > array_tmp4[4] := array_tmp4_g[3] * array_x[2] / 3; > array_tmp4_g[4] := -array_tmp4[3] * array_x[2] / 3; > #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_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_y1_higher[2,5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre sin ID_LINEAR iii = 5 $eq_no = 2 > array_tmp4[5] := array_tmp4_g[4] * array_x[2] / 4; > array_tmp4_g[5] := -array_tmp4[4] * array_x[2] / 4; > #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_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_y1_higher[2,kkk]; > #emit assign $eq_no = 1 > order_d := 1; > 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_tmp2[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit sin LINEAR $eq_no = 2 > array_tmp4[kkk] := array_tmp4_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp4_g[kkk] := -array_tmp4[kkk - 1] * array_x[2] / (kkk - 1); > #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_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > > #BOTTOM ATOMALL ??? > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGL, ALWAYS, glob_iolevel, INFO, glob_max_terms, DEBUGMASSIVE, glob_last_good_h, years_in_century, days_in_year, glob_log10normmin, glob_subiter_method, glob_max_minutes, hours_in_day, glob_hmin, glob_h, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_warned, glob_hmin_init, glob_not_yet_finished, djd_debug2, glob_html_log, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_reached_optimal_h, glob_not_yet_start_msg, glob_clock_sec, glob_good_digits, glob_log10relerr, glob_log10abserr, glob_hmax, glob_iter, glob_optimal_clock_start_sec, sec_in_minute, glob_display_flag, glob_smallish_float, glob_dump_analytic, glob_look_poles, glob_optimal_done, glob_almost_1, min_in_hour, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_max_rel_trunc_err, glob_disp_incr, centuries_in_millinium, glob_dump, glob_max_iter, glob_abserr, glob_log10_abserr, glob_large_float, glob_initial_pass, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_start, glob_warned2, glob_log10_relerr, glob_max_opt_iter, array_const_0D0, array_const_1, array_tmp4_g, array_last_rel_error, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_x, array_fact_1, array_y2_init, array_m1, array_1st_rel_error, array_norms, array_y2, array_y1, array_y2_higher, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_y2_higher_work2, array_y1_set_initial, array_complex_pole, array_y2_higher_work, array_fact_2, array_real_pole, array_y1_higher, array_poles, glob_last; array_tmp1[1] := array_y1_higher[2, 1]; if not array_y2_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp4[1] := sin(array_x[1]); array_tmp4_g[1] := cos(array_x[1]); if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_y1_higher[2, 2]; if not array_y2_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp4[2] := array_tmp4_g[1]*array_x[2]; array_tmp4_g[2] := -array_tmp4[1]*array_x[2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_y1_higher[2, 3]; if not array_y2_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp4[3] := 1/2*array_tmp4_g[2]*array_x[2]; array_tmp4_g[3] := -1/2*array_tmp4[2]*array_x[2]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_y1_higher[2, 4]; if not array_y2_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp4[4] := 1/3*array_tmp4_g[3]*array_x[2]; array_tmp4_g[4] := -1/3*array_tmp4[3]*array_x[2]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_y1_higher[2, 5]; if not array_y2_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp4[5] := 1/4*array_tmp4_g[4]*array_x[2]; array_tmp4_g[5] := -1/4*array_tmp4[4]*array_x[2]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y1_higher[2, kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_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_tmp4[kkk] := array_tmp4_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4_g[kkk] := -array_tmp4[kkk - 1]*array_x[2]/(kkk - 1); 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_tmp4[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > fprintf(fd,""); > if (secs >= 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := secs_in; fprintf(fd, ""); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs >= 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := convfloat(secs_in); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > > > > > > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats; > > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > > > > > > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > > local good_digits; > > > fprintf(file,""); > if (rel_error <> -1.0) then # if number 11 > if (rel_error <> 0.0) then # if number 12 > good_digits := -trunc(log10(rel_error/100.0)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 12 > ; > else > fprintf(file,"Unknown"); > fi;# end if 11 > ; > fprintf(file,""); > > # End Function number 9 > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if rel_error <> 0. then good_digits := -trunc(log10(rel_error/100.0)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # Begin Function number 10 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 10 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 11 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 11 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 12 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 11 > fprintf(file,"NA"); > elif (pole = 1) then # if number 12 > fprintf(file,"Real"); > elif (pole = 2) then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 12 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 13 > logstart := proc(file) > fprintf(file,""); > # End Function number 13 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 14 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 14 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 15 > 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 15 > 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 16 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > > > > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > > # End Function number 16 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # Begin Function number 17 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > > > > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr; > > # End Function number 17 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 18 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 18 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 19 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > > > > if (nnn <= glob_max_terms) then # if number 13 > if (array_fact_1[nnn] = 0) then # if number 14 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 19 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # Begin Function number 20 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > > > > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 13 > if (array_fact_2[mmm,nnn] = 0) then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 13 > ; > ret; > > # End Function number 20 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # Begin Function number 21 > convfp := proc(mmm) > (mmm); > > # End Function number 21 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 22 > convfloat := proc(mmm) > (mmm); > > # End Function number 22 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > > > > > > > > > > > > > > > > > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(2.0 - cos(x)); > end; exact_soln_y1 := proc(x) return 2.0 - cos(x) end proc > exact_soln_y2 := proc(x) > return(2.0 - cos(x)); > end; exact_soln_y2 := proc(x) return 2.0 - cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter; > global > DEBUGL, > ALWAYS, > glob_iolevel, > INFO, > glob_max_terms, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_last_good_h, > years_in_century, > days_in_year, > glob_log10normmin, > glob_subiter_method, > glob_max_minutes, > hours_in_day, > glob_hmin, > glob_h, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned, > glob_hmin_init, > glob_not_yet_finished, > djd_debug2, > glob_html_log, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_hours, > glob_relerr, > glob_reached_optimal_h, > glob_not_yet_start_msg, > glob_clock_sec, > glob_good_digits, > glob_log10relerr, > glob_log10abserr, > glob_hmax, > glob_iter, > glob_optimal_clock_start_sec, > sec_in_minute, > glob_display_flag, > glob_smallish_float, > glob_dump_analytic, > glob_look_poles, > glob_optimal_done, > glob_almost_1, > min_in_hour, > djd_debug, > glob_normmax, > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_max_rel_trunc_err, > glob_disp_incr, > centuries_in_millinium, > glob_dump, > glob_max_iter, > glob_abserr, > glob_log10_abserr, > glob_large_float, > glob_initial_pass, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_start, > glob_warned2, > glob_log10_relerr, > glob_max_opt_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp4_g, > array_last_rel_error, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_x, > array_fact_1, > array_y2_init, > array_m1, > array_1st_rel_error, > array_norms, > array_y2, > array_y1, > array_y2_higher, > array_y1_higher_work, > array_y2_set_initial, > array_y1_higher_work2, > array_y2_higher_work2, > array_y1_set_initial, > array_complex_pole, > array_y2_higher_work, > array_fact_2, > array_real_pole, > array_y1_higher, > array_poles, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > ALWAYS := 1; > glob_iolevel := 5; > INFO := 2; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > glob_last_good_h := 0.1; > years_in_century := 100; > days_in_year := 365; > glob_log10normmin := 0.1; > glob_subiter_method := 3; > glob_max_minutes := 0.0; > hours_in_day := 24; > glob_hmin := 0.00000000001; > glob_h := 0.1; > glob_clock_start_sec := 0.0; > MAX_UNCHANGED := 10; > glob_orig_start_sec := 0.0; > glob_warned := false; > glob_hmin_init := 0.001; > glob_not_yet_finished := true; > djd_debug2 := true; > glob_html_log := true; > glob_unchanged_h_cnt := 0; > glob_optimal_start := 0.0; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_relerr := 0.1e-10; > glob_reached_optimal_h := false; > glob_not_yet_start_msg := true; > glob_clock_sec := 0.0; > glob_good_digits := 0; > glob_log10relerr := 0.0; > glob_log10abserr := 0.0; > glob_hmax := 1.0; > glob_iter := 0; > glob_optimal_clock_start_sec := 0.0; > sec_in_minute := 60; > glob_display_flag := true; > glob_smallish_float := 0.1e-100; > glob_dump_analytic := false; > glob_look_poles := false; > glob_optimal_done := false; > glob_almost_1 := 0.9990; > min_in_hour := 60; > djd_debug := true; > glob_normmax := 0.0; > glob_curr_iter_when_opt := 0; > glob_max_sec := 10000.0; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_disp_incr := 0.1; > centuries_in_millinium := 10; > glob_dump := false; > glob_max_iter := 1000; > glob_abserr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_large_float := 9.0e100; > glob_initial_pass := true; > glob_optimal_expect_sec := 0.1; > glob_percent_done := 0.0; > glob_current_iter := 0; > glob_start := 0; > glob_warned2 := false; > glob_log10_relerr := 0.1e-10; > glob_max_opt_iter := 10; > #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/mtest5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = sin ( x ) ;"); > 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,"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,"glob_h := 0.00001 ;"); > 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 := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 1;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#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_tmp4_g:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[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 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_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 <= max_terms) do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_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_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_h := 0.00001 ; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 1; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := false; > array_y2_set_initial[1,3] := false; > 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 := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (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 <= 2) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while (subiter <= 2 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = sin ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-09-02T21:55:50-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest5") > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 5 > ; > log_revs(html_log_file," 126 ") > ; > logitem_str(html_log_file,"mtest5 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest5 maple results") > ; > logitem_str(html_log_file,"c c++ Maple and Maxima") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = sin ( x ) ;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 5 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if (glob_html_log) then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > > # End Function number 8 > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global DEBUGL, ALWAYS, glob_iolevel, INFO, glob_max_terms, DEBUGMASSIVE, glob_last_good_h, years_in_century, days_in_year, glob_log10normmin, glob_subiter_method, glob_max_minutes, hours_in_day, glob_hmin, glob_h, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_warned, glob_hmin_init, glob_not_yet_finished, djd_debug2, glob_html_log, glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_hours, glob_relerr, glob_reached_optimal_h, glob_not_yet_start_msg, glob_clock_sec, glob_good_digits, glob_log10relerr, glob_log10abserr, glob_hmax, glob_iter, glob_optimal_clock_start_sec, sec_in_minute, glob_display_flag, glob_smallish_float, glob_dump_analytic, glob_look_poles, glob_optimal_done, glob_almost_1, min_in_hour, djd_debug, glob_normmax, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_max_rel_trunc_err, glob_disp_incr, centuries_in_millinium, glob_dump, glob_max_iter, glob_abserr, glob_log10_abserr, glob_large_float, glob_initial_pass, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_start, glob_warned2, glob_log10_relerr, glob_max_opt_iter, array_const_0D0, array_const_1, array_tmp4_g, array_last_rel_error, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_x, array_fact_1, array_y2_init, array_m1, array_1st_rel_error, array_norms, array_y2, array_y1, array_y2_higher, array_y1_higher_work, array_y2_set_initial, array_y1_higher_work2, array_y2_higher_work2, array_y1_set_initial, array_complex_pole, array_y2_higher_work, array_fact_2, array_real_pole, array_y1_higher, array_poles, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; ALWAYS := 1; glob_iolevel := 5; INFO := 2; glob_max_terms := 30; DEBUGMASSIVE := 4; glob_last_good_h := 0.1; years_in_century := 100; days_in_year := 365; glob_log10normmin := 0.1; glob_subiter_method := 3; glob_max_minutes := 0.; hours_in_day := 24; glob_hmin := 0.1*10^(-10); glob_h := 0.1; glob_clock_start_sec := 0.; MAX_UNCHANGED := 10; glob_orig_start_sec := 0.; glob_warned := false; glob_hmin_init := 0.001; glob_not_yet_finished := true; djd_debug2 := true; glob_html_log := true; glob_unchanged_h_cnt := 0; glob_optimal_start := 0.; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_relerr := 0.1*10^(-10); glob_reached_optimal_h := false; glob_not_yet_start_msg := true; glob_clock_sec := 0.; glob_good_digits := 0; glob_log10relerr := 0.; glob_log10abserr := 0.; glob_hmax := 1.0; glob_iter := 0; glob_optimal_clock_start_sec := 0.; sec_in_minute := 60; glob_display_flag := true; glob_smallish_float := 0.1*10^(-100); glob_dump_analytic := false; glob_look_poles := false; glob_optimal_done := false; glob_almost_1 := 0.9990; min_in_hour := 60; djd_debug := true; glob_normmax := 0.; glob_curr_iter_when_opt := 0; glob_max_sec := 10000.0; glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_disp_incr := 0.1; centuries_in_millinium := 10; glob_dump := false; glob_max_iter := 1000; glob_abserr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_initial_pass := true; glob_optimal_expect_sec := 0.1; glob_percent_done := 0.; glob_current_iter := 0; glob_start := 0; glob_warned2 := false; glob_log10_relerr := 0.1*10^(-10); glob_max_opt_iter := 10; 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/mtest5postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = sin ( x ) ;"); 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, "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, "glob_h := 0.00001 ;"); 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 := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 1;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(2.0 - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(2.0 - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#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_tmp4_g := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_fact_1[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_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[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; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_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 <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_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_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_h := 0.00001; glob_max_iter := 20; glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := false; array_y2_set_initial[1, 3] := false; 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 := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and 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 <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = sin ( x ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-09-02T21:55:50-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest5") ; logitem_str(html_log_file, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 126 "); logitem_str(html_log_file, "mtest5 diffeq.mxt"); logitem_str(html_log_file, "mtest5 maple results"); logitem_str(html_log_file, "c c++ Maple and Maxima"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = sin ( x ) ;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; ! #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; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_h := 0.00001 ; glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(2.0 - cos(x)); end; exact_soln_y2 := proc(x) return(2.0 - cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.0049958347219742339044380121961 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 y1[1] (analytic) = 1.0049958347219742339044380121961 y1[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 x[1] = 0.1 y2[1] (analytic) = 1.0049958347219742339044380121961 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 y1[1] (analytic) = 1.0049958347219742339044380121961 y1[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10001 y2[1] (analytic) = 1.0049968331058908938105450091859 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.983839166599061069969898e-07 relative error = 9.9341996290122834565802086137134e-05 % Correct digits = 6 h = 1e-05 y1[1] (analytic) = 1.0049968331058908938105450091859 y1[1] (numeric) = 1.0049968331058908938105450091859 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.42 NO POLE NO POLE x[1] = 0.10002 y2[1] (analytic) = 1.0049978315893078704052337474888 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.9968673336365007957352927e-06 relative error = 0.0001986936957345118099834771074684 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.0049978315893078704052337474888 y1[1] (numeric) = 1.0049978315893078704052337474889 absolute error = 1e-31 relative error = 9.9502702251466127230499902706776e-30 % Correct digits = 31 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10003 y2[1] (analytic) = 1.0049988301722250638401625302775 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.9954502508299357245180814e-06 relative error = 0.00029805509826480197407321031787913 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.0049988301722250638401625302775 y1[1] (numeric) = 1.0049988301722250638401625302777 absolute error = 2e-31 relative error = 1.9900520676797834238260773452238e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10004 y2[1] (analytic) = 1.0049998288546423742570396390407 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.9941326681403526016268446e-06 relative error = 0.00039742620381262193185599541517614 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.0049998288546423742570396390407 y1[1] (numeric) = 1.004999828854642374257039639041 absolute error = 3e-31 relative error = 2.9850751352057229397974855504976e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.2MB, time=0.89 NO POLE NO POLE x[1] = 0.10005 y2[1] (analytic) = 1.005000827636559701787623343569 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.9929145854678831853313729e-06 relative error = 0.00049680701230959384566888730731937 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005000827636559701787623343569 y1[1] (numeric) = 1.0050008276365597017876233435693 absolute error = 3e-31 relative error = 2.9850721686021292702280477641349e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10006 y2[1] (analytic) = 1.0050018265179769465537219119414 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.9917960027126492838997453e-06 relative error = 0.00059619752368733343528026511824364 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.0050018265179769465537219119414 y1[1] (numeric) = 1.0050018265179769465537219119418 absolute error = 4e-31 relative error = 3.9800922689451948911480813648241e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.2MB, time=1.35 NO POLE NO POLE x[1] = 0.10007 y2[1] (analytic) = 1.005002825498894008667193620514 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.9907769197747627556083179e-06 relative error = 0.00069559773787744997800510559211385 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005002825498894008667193620514 y1[1] (numeric) = 1.0050028254988940086671936205144 absolute error = 4e-31 relative error = 3.9800883127013675676254620436410e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10008 y2[1] (analytic) = 1.0050038245793107882299467639077 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.9898573365543255087517116e-06 relative error = 0.00079500765481154630882026657724745 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.0050038245793107882299467639077 y1[1] (numeric) = 1.0050038245793107882299467639082 absolute error = 5e-31 relative error = 4.9751054450891997233617248214292e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10009 y2[1] (analytic) = 1.005004823759227185333939664999 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.9890372529514295016528029e-06 relative error = 0.00089442727442121882047978099730167 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.005004823759227185333939664999 y1[1] (numeric) = 1.0050048237592271853339396649995 absolute error = 5e-31 relative error = 4.9751004988189678086034377689314e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.2MB, time=1.80 NO POLE NO POLE x[1] = 0.1001 y2[1] (analytic) = 1.00500582303864310006118068491 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.9883166688661567426727139e-06 relative error = 0.00099385659663805746363016092130897 % Correct digits = 5 h = 1e-05 y1[1] (analytic) = 1.00500582303864310006118068491 y1[1] (numeric) = 1.0050058230386431000611806849105 absolute error = 5e-31 relative error = 4.9750955520660171187561148494063e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10011 y2[1] (analytic) = 1.0050068224175584324837282330007 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.09876955841985792902208046e-05 relative error = 0.0010932956213936457469257120406553 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050068224175584324837282330007 y1[1] (numeric) = 1.0050068224175584324837282330013 absolute error = 6e-31 relative error = 5.9701087257964212691672835618657e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=2.25 NO POLE NO POLE x[1] = 0.10012 y2[1] (analytic) = 1.0050078218959730826636907768617 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.19871739988487592527646656e-05 relative error = 0.0011927443486195607371438583635881 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050078218959730826636907768617 y1[1] (numeric) = 1.0050078218959730826636907768624 absolute error = 7e-31 relative error = 6.9651199199567622411508184446695e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10013 y2[1] (analytic) = 1.005008821473886950653226852308 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.29867519127167487888401119e-05 relative error = 0.0012922027782473730593004771965457 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005008821473886950653226852308 y1[1] (numeric) = 1.0050088214738869506532268523087 absolute error = 7e-31 relative error = 6.9651129924752410138704008941011e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10014 y2[1] (analytic) = 1.0050098211512999364945450733735 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.39864293257025901070611774e-05 relative error = 0.0013916709102086468967652443721462 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050098211512999364945450733735 y1[1] (numeric) = 1.0050098211512999364945450733742 absolute error = 7e-31 relative error = 6.9651060643179325655474624755414e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=2.72 NO POLE NO POLE x[1] = 0.10015 y2[1] (analytic) = 1.0050108209282119402199041423072 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.49862062377063154661301111e-05 relative error = 0.0014911487444349399913769898229782 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050108209282119402199041423072 y1[1] (numeric) = 1.0050108209282119402199041423079 absolute error = 7e-31 relative error = 6.9650991354848416633242198602594e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10016 y2[1] (analytic) = 1.0050118208046228618516128595696 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.59860826486279471748473735e-05 relative error = 0.0015906362808578036435590633515801 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050118208046228618516128595696 y1[1] (numeric) = 1.0050118208046228618516128595704 absolute error = 8e-31 relative error = 7.9601053782582549426189112955395e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10017 y2[1] (analytic) = 1.0050128207805326014020301338309 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.69860585583674975921216348e-05 relative error = 0.0016901335194087827124347107554504 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050128207805326014020301338309 y1[1] (numeric) = 1.0050128207805326014020301338318 absolute error = 9e-31 relative error = 8.9551096403031405874143887255839e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=3.19 NO POLE NO POLE x[1] = 0.10018 y2[1] (analytic) = 1.0050138208559410588735649919693 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.79861339668249691269797732e-05 relative error = 0.0017896404600194156159424601375767 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050138208559410588735649919693 y1[1] (numeric) = 1.0050138208559410588735649919703 absolute error = 1.0e-30 relative error = 9.9501119213298884448637861286635e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10019 y2[1] (analytic) = 1.0050148210308481342586765890711 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.89863088739003542385768750e-05 relative error = 0.0018891571026212343309515185712748 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050148210308481342586765890711 y1[1] (numeric) = 1.0050148210308481342586765890721 absolute error = 1.0e-30 relative error = 9.9501020191353555342505576215004e-29 % Correct digits = 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=3.66 NO POLE NO POLE x[1] = 0.1002 y2[1] (analytic) = 1.0050158213052537275398742184312 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 1.99865832794936354362062351e-05 relative error = 0.0019886834471457643933771789796758 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050158213052537275398742184312 y1[1] (numeric) = 1.0050158213052537275398742184323 absolute error = 1.1e-30 relative error = 1.0945101327572998496564678775822e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10021 y2[1] (analytic) = 1.0050168216791577386897173215551 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.09869571835047852793093590e-05 relative error = 0.0020882194935245248982962373389525 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050168216791577386897173215551 y1[1] (numeric) = 1.0050168216791577386897173215562 absolute error = 1.1e-30 relative error = 1.0945090433035207011470855644591e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10022 y2[1] (analytic) = 1.0050178221525600676708154981614 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.19874305858337663774859653e-05 relative error = 0.0021877652416890285000624201054235 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050178221525600676708154981614 y1[1] (numeric) = 1.0050178221525600676708154981626 absolute error = 1.2e-30 relative error = 1.1940086768111480867511923347706e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=4.15 NO POLE NO POLE x[1] = 0.10023 y2[1] (analytic) = 1.0050188227254606144358285161858 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.29880034863805313905039897e-05 relative error = 0.0022873206915707814124218219656749 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050188227254606144358285161858 y1[1] (numeric) = 1.005018822725460614435828516187 absolute error = 1.2e-30 relative error = 1.1940074880844317103279962011874e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10024 y2[1] (analytic) = 1.0050198233978592789274663217855 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.39886758850450230283095894e-05 relative error = 0.0023868858431012834086283537998899 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050198233978592789274663217855 y1[1] (numeric) = 1.0050198233978592789274663217868 absolute error = 1.3e-30 relative error = 1.2935068241786971276928799456824e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=38.1MB, alloc=4.3MB, time=4.63 x[1] = 0.10025 y2[1] (analytic) = 1.0050208241697559610784890493453 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.49894477817271740510371492e-05 relative error = 0.0024864606962120278215592009873741 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050208241697559610784890493453 y1[1] (numeric) = 1.0050208241697559610784890493466 absolute error = 1.3e-30 relative error = 1.2935055361404329713193430807390e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10026 y2[1] (analytic) = 1.005021825041150560811707031484 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.59903191763269072690192879e-05 relative error = 0.0025860452508345015438302919146182 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005021825041150560811707031484 y1[1] (numeric) = 1.0050218250411505608117070314854 absolute error = 1.4e-30 relative error = 1.3930045747441127266425346498185e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10027 y2[1] (analytic) = 1.0050228260120429780399808090625 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.69912900687441355427968664e-05 relative error = 0.0026856395069001850279117768248349 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050228260120429780399808090625 y1[1] (numeric) = 1.0050228260120429780399808090639 absolute error = 1.4e-30 relative error = 1.3930031873556910569164049414034e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=5.12 NO POLE NO POLE x[1] = 0.10028 y2[1] (analytic) = 1.005023827082433112666221141192 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.79923604588787617831289959e-05 relative error = 0.0027852434643405522862435168494127 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005023827082433112666221141192 y1[1] (numeric) = 1.0050238270824331126662211411934 absolute error = 1.4e-30 relative error = 1.3930017998321252991449620480002e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10029 y2[1] (analytic) = 1.005024828252320864583389015244 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.89935303466306789510030479e-05 relative error = 0.002884857123087070891350583390073 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005024828252320864583389015244 y1[1] (numeric) = 1.0050248282523208645833890152455 absolute error = 1.5e-30 relative error = 1.4925004416143747228707976279177e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003 y2[1] (analytic) = 1.0050258295217061336744956568614 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 2.99947997318997700576446653e-05 relative error = 0.0029844804830712019759587677817198 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050258295217061336744956568614 y1[1] (numeric) = 1.0050258295217061336744956568628 absolute error = 1.4e-30 relative error = 1.3929990243795653382939996571786e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=5.60 NO POLE NO POLE x[1] = 0.10031 y2[1] (analytic) = 1.0050268308905888198126025399691 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.09961686145859081645277730e-05 relative error = 0.0030841135442244002331101010764273 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050268308905888198126025399691 y1[1] (numeric) = 1.0050268308905888198126025399706 absolute error = 1.5e-30 relative error = 1.4924974676256139766278741845281e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10032 y2[1] (analytic) = 1.0050278323589688228608213967881 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.19976369945889563833845920e-05 relative error = 0.0031837563064781139162783843461922 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050278323589688228608213967881 y1[1] (numeric) = 1.0050278323589688228608213967896 absolute error = 1.5e-30 relative error = 1.4924959804140433742597720449242e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=6.09 NO POLE NO POLE x[1] = 0.10033 y2[1] (analytic) = 1.0050288339268460426723142278479 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.29992048718087678762156518e-05 relative error = 0.0032834087697637848394847289867068 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050288339268460426723142278479 y1[1] (numeric) = 1.0050288339268460426723142278495 absolute error = 1.6e-30 relative error = 1.5919941259281926933790612198451e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10034 y2[1] (analytic) = 1.0050298355942203790902933120021 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.40008722461451858552998060e-05 relative error = 0.0033830709340128483774131075093248 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050298355942203790902933120021 y1[1] (numeric) = 1.0050298355942203790902933120038 absolute error = 1.7e-30 relative error = 1.6914920729640637376452291796323e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10035 y2[1] (analytic) = 1.0050308373610917319480212164436 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.50026391174980435832042475e-05 relative error = 0.0034827427991567334655259144626732 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050308373610917319480212164436 y1[1] (numeric) = 1.0050308373610917319480212164454 absolute error = 1.8e-30 relative error = 1.7909898214926995155034469642591e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=6.57 NO POLE NO POLE x[1] = 0.10036 y2[1] (analytic) = 1.0050318392274600010688108067214 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.60045054857671643727945253e-05 relative error = 0.0035824243651268626001795376825405 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050318392274600010688108067214 y1[1] (numeric) = 1.0050318392274600010688108067233 absolute error = 1.9e-30 relative error = 1.8904873714851433084414114471136e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10037 y2[1] (analytic) = 1.0050328411933250862660252567584 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.70064713508523615872445623e-05 relative error = 0.0036821156318546518387399398099841 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050328411933250862660252567584 y1[1] (numeric) = 1.0050328411933250862660252567603 absolute error = 1.9e-30 relative error = 1.8904854867668167374703095948555e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10038 y2[1] (analytic) = 1.0050338432586868873430780588698 y2[1] (numeric) = 1.0049958347219742339044380121961 memory used=57.2MB, alloc=4.3MB, time=7.04 absolute error = 3.80085367126534386400466737e-05 relative error = 0.003781816599271510799698250037496 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050338432586868873430780588698 y1[1] (numeric) = 1.0050338432586868873430780588717 absolute error = 1.9e-30 relative error = 1.8904836018650932946348436320201e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10039 y2[1] (analytic) = 1.0050348454235453040934330337829 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 3.90107015710701889950215868e-05 relative error = 0.003881527267308842662786366162465 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050348454235453040934330337829 y1[1] (numeric) = 1.0050348454235453040934330337849 absolute error = 2.0e-30 relative error = 1.9899807545052360808375758111022e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004 y2[1] (analytic) = 1.0050358476879002363006043406579 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.00129659260023961663284618e-05 relative error = 0.003981247635898044169092566907773 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050358476879002363006043406579 y1[1] (numeric) = 1.0050358476879002363006043406599 absolute error = 2.0e-30 relative error = 1.9899787700120641904581887659316e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=7.53 NO POLE NO POLE x[1] = 0.10041 y2[1] (analytic) = 1.0050368500517515837381564871092 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.10153297773498337184749131e-05 relative error = 0.0040809777049705056211771344594198 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050368500517515837381564871092 y1[1] (numeric) = 1.0050368500517515837381564871113 absolute error = 2.1e-30 relative error = 2.0894756245921394098585370966586e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10042 y2[1] (analytic) = 1.0050378525150992461697043392284 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.20177931250122652663270323e-05 relative error = 0.0041807174744576108831879873402072 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050378525150992461697043392284 y1[1] (numeric) = 1.0050378525150992461697043392306 absolute error = 2.2e-30 relative error = 2.1889722804912446505871315943541e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10043 y2[1] (analytic) = 1.0050388550779431233489131316078 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.30203559688894444751194117e-05 relative error = 0.0042804669442907373809763234997295 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050388550779431233489131316078 y1[1] (numeric) = 1.00503885507794312334891313161 absolute error = 2.2e-30 relative error = 2.1889700969117107753305002276640e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=8.01 NO POLE NO POLE x[1] = 0.10044 y2[1] (analytic) = 1.0050398577402831150194984773648 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.40230183088811150604651687e-05 relative error = 0.0043802261144012561022122736601054 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050398577402831150194984773648 y1[1] (numeric) = 1.0050398577402831150194984773671 absolute error = 2.3e-30 relative error = 2.2884664546252785319660920066854e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10045 y2[1] (analytic) = 1.005040860502119120915226378168 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.50257801448870107883659719e-05 relative error = 0.0044799949847205315965005649966872 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005040860502119120915226378168 y1[1] (numeric) = 1.0050408605021191209152263781703 absolute error = 2.3e-30 relative error = 2.2884641713481364151072243515515e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=8.51 NO POLE NO POLE x[1] = 0.10046 y2[1] (analytic) = 1.0050418633634510407599132342634 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.60286414768068554752220673e-05 relative error = 0.0045797735551799219754961949941943 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050418633634510407599132342634 y1[1] (numeric) = 1.0050418633634510407599132342658 absolute error = 2.4e-30 relative error = 2.3879602307989566488563637003242e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10047 y2[1] (analytic) = 1.0050428663242787742674258545023 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.70316023045403629878423062e-05 relative error = 0.0046795618257107789130201156371013 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050428663242787742674258545023 y1[1] (numeric) = 1.0050428663242787742674258545047 absolute error = 2.4e-30 relative error = 2.3879578477856047546113359580491e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10048 y2[1] (analytic) = 1.0050438693846022211416814663697 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.80346626279872372434541736e-05 relative error = 0.0047793597962444476451749278145263 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050438693846022211416814663697 y1[1] (numeric) = 1.0050438693846022211416814663722 absolute error = 2.5e-30 relative error = 2.4874536088964687938726450437004e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=9.00 NO POLE NO POLE x[1] = 0.10049 y2[1] (analytic) = 1.0050448725444212810766477260142 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 4.90378224470471722097138181e-05 relative error = 0.0048791674667122669704605860387514 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050448725444212810766477260142 y1[1] (numeric) = 1.0050448725444212810766477260167 absolute error = 2.5e-30 relative error = 2.4874511261083064073467217377973e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005 y2[1] (analytic) = 1.005045875803735853756342728278 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.00410817616198519047160819e-05 relative error = 0.0049789848370455692498901133377252 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005045875803735853756342728278 y1[1] (numeric) = 1.0050458758037358537563427282806 absolute error = 2.6e-30 relative error = 2.5869465888020069480183284734526e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10051 y2[1] (analytic) = 1.0050468791625458388548350167294 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.10444405716049503970045333e-05 relative error = 0.0050788119071756804071053265599672 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050468791625458388548350167294 y1[1] (numeric) = 1.0050468791625458388548350167321 absolute error = 2.7e-30 relative error = 2.6864418525927585667728569903141e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=9.48 NO POLE NO POLE x[1] = 0.10052 y2[1] (analytic) = 1.0050478826208511360362435936947 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.20478988769021318055814986e-05 relative error = 0.0051786486770339199284925717830868 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050478826208511360362435936947 y1[1] (numeric) = 1.0050478826208511360362435936974 absolute error = 2.7e-30 relative error = 2.6864391703997652811978583337360e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10053 y2[1] (analytic) = 1.0050488861786516449547379302918 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.30514566774110502999180957e-05 relative error = 0.0052784951465516008632984700543869 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050488861786516449547379302918 y1[1] (numeric) = 1.0050488861786516449547379302946 absolute error = 2.8e-30 relative error = 2.7859341356478935333409720574865e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=9.96 NO POLE NO POLE x[1] = 0.10054 y2[1] (analytic) = 1.0050498898359472652545379764653 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.40551139730313500999642692e-05 relative error = 0.0053783513156600298237456734432949 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050498898359472652545379764653 y1[1] (numeric) = 1.0050498898359472652545379764681 absolute error = 2.8e-30 relative error = 2.7859313535739401527290665913824e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10055 y2[1] (analytic) = 1.0050508935927378965699141710215 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.50588707636626654761588254e-05 relative error = 0.0054782171842905069851486312460687 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050508935927378965699141710215 y1[1] (numeric) = 1.0050508935927378965699141710244 absolute error = 2.9e-30 relative error = 2.8854260202022412909564220688342e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10056 y2[1] (analytic) = 1.0050518974490234385251874516654 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.60627270492046207494394693e-05 relative error = 0.0055780927523743260860293665513526 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050518974490234385251874516654 y1[1] (numeric) = 1.0050518974490234385251874516683 absolute error = 2.9e-30 relative error = 2.8854231382087301118554864223378e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.3MB, time=10.44 NO POLE NO POLE x[1] = 0.10057 y2[1] (analytic) = 1.005052901404803790734729265038 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.70666828295568302912528419e-05 relative error = 0.0056779780198427744282332629970839 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005052901404803790734729265038 y1[1] (numeric) = 1.0050529014048037907347292650409 absolute error = 2.9e-30 relative error = 2.8854202559353350322149895272731e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10058 y2[1] (analytic) = 1.005053905460078852802961576755 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.80707381046188985235645589e-05 relative error = 0.0057778729866271328770448618278295 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005053905460078852802961576755 y1[1] (numeric) = 1.0050539054600788528029615767579 absolute error = 2.9e-30 relative error = 2.8854173733820580349833555426466e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=10.91 NO POLE NO POLE x[1] = 0.10059 y2[1] (analytic) = 1.0050549096148485243243568814462 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 5.90748928742904199188692501e-05 relative error = 0.0058777776526586758613036691825486 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050549096148485243243568814462 y1[1] (numeric) = 1.0050549096148485243243568814492 absolute error = 3.0e-30 relative error = 2.9849115419471390723738665468172e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006 y2[1] (analytic) = 1.0050559138691127048834382127963 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.00791471384709790002006002e-05 relative error = 0.0059776920178686713735199736820613 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050559138691127048834382127963 y1[1] (numeric) = 1.0050559138691127048834382127994 absolute error = 3.1e-30 relative error = 3.0844055113969604425703261345313e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10061 y2[1] (analytic) = 1.0050569182228712940547791535863 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.10835008970601503411413902e-05 relative error = 0.0060776160821883809699906742362709 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050569182228712940547791535863 y1[1] (numeric) = 1.0050569182228712940547791535895 absolute error = 3.2e-30 relative error = 3.1838992817025714427716282548551e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=11.39 NO POLE NO POLE x[1] = 0.10062 y2[1] (analytic) = 1.005057922676124191403003845736 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.20879541499574985658335399e-05 relative error = 0.0061775498455490597709151181205229 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005057922676124191403003845736 y1[1] (numeric) = 1.0050579226761241914030038457393 absolute error = 3.3e-30 relative error = 3.2833928528350216439749817600516e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10063 y2[1] (analytic) = 1.0050589272288712964827870003477 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.30925068970625783489881516e-05 relative error = 0.0062774933078819564605109493306875 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050589272288712964827870003477 y1[1] (numeric) = 1.005058927228871296482787000351 absolute error = 3.3e-30 relative error = 3.2833895710957914530371056223606e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10064 y2[1] (analytic) = 1.0050599318811125088388539077504 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.40971591382749344158955543e-05 relative error = 0.0063774464691183132871299671469624 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050599318811125088388539077504 y1[1] (numeric) = 1.0050599318811125088388539077538 absolute error = 3.4e-30 relative error = 3.3828828432513638939157702750843e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=11.87 NO POLE NO POLE x[1] = 0.10065 y2[1] (analytic) = 1.0050609366328477280059804475458 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.51019108734941015424353497e-05 relative error = 0.0064774093291893660633739950353692 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050609366328477280059804475458 y1[1] (numeric) = 1.0050609366328477280059804475493 absolute error = 3.5e-30 relative error = 3.4823759161565765136827145519030e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10066 y2[1] (analytic) = 1.0050619414840768535089930986545 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.61067621026196045550864584e-05 relative error = 0.0065773818880263441662107597274 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050619414840768535089930986545 y1[1] (numeric) = 1.005061941484076853508993098658 absolute error = 3.5e-30 relative error = 3.4823724345107443573525850390296e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.3MB, time=12.35 NO POLE NO POLE x[1] = 0.10067 y2[1] (analytic) = 1.0050629464347997848627689493635 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.71117128255509583309371674e-05 relative error = 0.006677364145560470537089780586889 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050629464347997848627689493635 y1[1] (numeric) = 1.0050629464347997848627689493671 absolute error = 3.6e-30 relative error = 3.5818652083136350924808587809545e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10068 y2[1] (analytic) = 1.005063951485016421572235707375 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.81167630421876677976951789e-05 relative error = 0.0067773561017229616820582692637498 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005063951485016421572235707375 y1[1] (numeric) = 1.0050639514850164215722357073786 absolute error = 3.6e-30 relative error = 3.5818616264973752812962397788892e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10069 y2[1] (analytic) = 1.0050649566347266631323717098554 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 6.91219127524292279336976593e-05 relative error = 0.0068773577564450276718770395247757 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050649566347266631323717098554 y1[1] (numeric) = 1.0050649566347266631323717098591 absolute error = 3.7e-30 relative error = 3.6813541011207502449094986653217e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.3MB, time=12.83 NO POLE NO POLE x[1] = 0.1007 y2[1] (analytic) = 1.0050659618839304090282059334865 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.01271619561751237679212904e-05 relative error = 0.0069773691096578721421364274601216 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050659618839304090282059334865 y1[1] (numeric) = 1.0050659618839304090282059334902 absolute error = 3.7e-30 relative error = 3.6813504190954711063712791382018e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10071 y2[1] (analytic) = 1.0050669672326275587348180045164 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.11325106533248303799923203e-05 relative error = 0.007077390161292692293372221816382 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050669672326275587348180045164 y1[1] (numeric) = 1.0050669672326275587348180045201 absolute error = 3.7e-30 relative error = 3.6813467367131341565442522315353e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=106.8MB, alloc=4.3MB, time=13.31 x[1] = 0.10072 y2[1] (analytic) = 1.0050679726808180117173382088121 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.21379588437778129001966160e-05 relative error = 0.0071774209112806788911816046548815 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050679726808180117173382088121 y1[1] (numeric) = 1.0050679726808180117173382088159 absolute error = 3.8e-30 relative error = 3.7808388121892484673281113782678e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10073 y2[1] (analytic) = 1.0050689782285016674309475019133 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.31435065274335265094897172e-05 relative error = 0.0072774613595530162663391022850707 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050689782285016674309475019133 y1[1] (numeric) = 1.0050689782285016674309475019172 absolute error = 3.9e-30 relative error = 3.8803306882220157108040731183470e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10074 y2[1] (analytic) = 1.0050699838756784253208775190866 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.41491537041914164395068905e-05 relative error = 0.0073775115060408823149125463930762 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050699838756784253208775190866 y1[1] (numeric) = 1.0050699838756784253208775190906 absolute error = 4.0e-30 relative error = 3.9798223647824884036462758039581e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.3MB, time=13.80 NO POLE NO POLE x[1] = 0.10075 y2[1] (analytic) = 1.0050709896223481848224105853811 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.51549003739509179725731850e-05 relative error = 0.0074775713506754484983790454645292 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050709896223481848224105853811 y1[1] (numeric) = 1.0050709896223481848224105853851 absolute error = 4.0e-30 relative error = 3.9798183822846042309378745984598e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10076 y2[1] (analytic) = 1.0050719954685108453608797256847 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.61607465366114564417134886e-05 relative error = 0.0075776408933878798437409664316709 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050719954685108453608797256847 y1[1] (numeric) = 1.0050719954685108453608797256887 absolute error = 4.0e-30 relative error = 3.9798143994007253095907466438352e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10077 y2[1] (analytic) = 1.0050730014141663063516686747817 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.71666921920724472306625856e-05 relative error = 0.0076777201341093349436419266040638 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050730014141663063516686747817 y1[1] (numeric) = 1.0050730014141663063516686747858 absolute error = 4.1e-30 relative error = 4.0793056765341257390620785747452e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.3MB, time=14.30 NO POLE NO POLE x[1] = 0.10078 y2[1] (analytic) = 1.0050740074593144672002118874115 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.81727373402332957738752154e-05 relative error = 0.0077778090727709659564827958626505 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050740074593144672002118874115 y1[1] (numeric) = 1.0050740074593144672002118874156 absolute error = 4.1e-30 relative error = 4.0793015932868690356355681771059e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10079 y2[1] (analytic) = 1.0050750136039552273019945483274 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 7.91788819809933975565361313e-05 relative error = 0.0078779077093039186065377090173098 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050750136039552273019945483274 y1[1] (numeric) = 1.0050750136039552273019945483316 absolute error = 4.2e-30 relative error = 4.1787925708548048274099320300501e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.3MB, time=14.79 NO POLE NO POLE x[1] = 0.1008 y2[1] (analytic) = 1.0050760198480884860425525823578 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.01851261142521381145701617e-05 relative error = 0.0079780160436393321840700885563683 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050760198480884860425525823578 y1[1] (numeric) = 1.0050760198480884860425525823621 absolute error = 4.3e-30 relative error = 4.2782833488057157115896709594674e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10081 y2[1] (analytic) = 1.0050770261917141427974726644672 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.11914697399088930346522711e-05 relative error = 0.0080781340757083395454486775290407 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050770261917141427974726644672 y1[1] (numeric) = 1.0050770261917141427974726644715 absolute error = 4.3e-30 relative error = 4.2782790651308682846960854358244e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10082 y2[1] (analytic) = 1.0050780326348320969323922298186 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.21979128578630279542176225e-05 relative error = 0.008178261805442067113263582719613 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050780326348320969323922298186 y1[1] (numeric) = 1.005078032634832096932392229823 absolute error = 4.4e-30 relative error = 4.3777695433908870678435064126717e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.3MB, time=15.27 NO POLE NO POLE x[1] = 0.10083 y2[1] (analytic) = 1.0050790391774422478029994838373 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.32044554680138985614716412e-05 relative error = 0.008278399232771634876442328113009 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050790391774422478029994838373 y1[1] (numeric) = 1.0050790391774422478029994838418 absolute error = 4.5e-30 relative error = 4.4772598219566938488247061938148e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10084 y2[1] (analytic) = 1.0050800458195444947550334122751 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.42110975702608505954000790e-05 relative error = 0.0083785463576281563903659185518897 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050800458195444947550334122751 y1[1] (numeric) = 1.0050800458195444947550334122796 absolute error = 4.5e-30 relative error = 4.4772553377384883174591672569357e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10085 y2[1] (analytic) = 1.0050810525611387371242837912755 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.52178391645032198457790794e-05 relative error = 0.008478703179942738776984913644615 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050810525611387371242837912755 y1[1] (numeric) = 1.0050810525611387371242837912801 absolute error = 4.6e-30 relative error = 4.5767453164879790341191855534815e-28 % Correct digits = 29 memory used=125.8MB, alloc=4.3MB, time=15.76 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10086 y2[1] (analytic) = 1.0050820594022248742365911974407 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.62246802506403321531852446e-05 relative error = 0.0085788696996464827249355120032966 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050820594022248742365911974407 y1[1] (numeric) = 1.0050820594022248742365911974453 absolute error = 4.6e-30 relative error = 4.5767407317327520167836459692289e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10087 y2[1] (analytic) = 1.0050830663428028054078470178983 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.72316208285715034090057022e-05 relative error = 0.0086790459166704824896556456026553 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050830663428028054078470178983 y1[1] (numeric) = 1.005083066342802805407847017903 absolute error = 4.7e-30 relative error = 4.6762304105887454047670620548004e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.3MB, time=16.24 NO POLE NO POLE x[1] = 0.10088 y2[1] (analytic) = 1.0050840733828724299439934603705 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.82386608981960395554481744e-05 relative error = 0.008779231830945825893501084537885 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050840733828724299439934603705 y1[1] (numeric) = 1.0050840733828724299439934603752 absolute error = 4.7e-30 relative error = 4.6762257252579129204884830811584e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10089 y2[1] (analytic) = 1.0050850805224336471410235632427 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 8.92458004594132365855510466e-05 relative error = 0.0088794274424035943258615518727518 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050850805224336471410235632427 y1[1] (numeric) = 1.0050850805224336471410235632475 absolute error = 4.8e-30 relative error = 4.7757151041432290890597835315869e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009 y2[1] (analytic) = 1.0050860877614863562849812056346 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.02530395121223805431934385e-05 relative error = 0.0089796327509748627432768488859733 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050860877614863562849812056346 y1[1] (numeric) = 1.0050860877614863562849812056395 absolute error = 4.9e-30 relative error = 4.8752042831606706483750651610827e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.3MB, time=16.71 NO POLE NO POLE x[1] = 0.10091 y2[1] (analytic) = 1.0050870951000304566519611174712 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.12603780562227475231052751e-05 relative error = 0.0090798477565906996695529904568522 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050870951000304566519611174712 y1[1] (numeric) = 1.0050870951000304566519611174761 absolute error = 4.9e-30 relative error = 4.8751993970356684144324394031278e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10092 y2[1] (analytic) = 1.0050881025380658475081088895551 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.22678160916136036708773590e-05 relative error = 0.0091800724591821671958783507290823 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050881025380658475081088895551 y1[1] (numeric) = 1.0050881025380658475081088895601 absolute error = 5.0e-30 relative error = 4.9746882759570166881833556361213e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.3MB, time=17.20 NO POLE NO POLE x[1] = 0.10093 y2[1] (analytic) = 1.0050891100755924281096209836404 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.32753536181942051829714443e-05 relative error = 0.0092803068586803209809398190822087 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050891100755924281096209836404 y1[1] (numeric) = 1.0050891100755924281096209836454 absolute error = 5.0e-30 relative error = 4.9746832891503039079756548105492e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10094 y2[1] (analytic) = 1.0050901177126100977027447425064 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.42829906358637983067303103e-05 relative error = 0.0093805509550162102510389662313073 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050901177126100977027447425064 y1[1] (numeric) = 1.0050901177126100977027447425115 absolute error = 5.1e-30 relative error = 5.0741718678983825780235134897780e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10095 y2[1] (analytic) = 1.0050911254491187555237784000336 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.52907271445216193403878375e-05 relative error = 0.0094808047481208778002082207032339 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050911254491187555237784000336 y1[1] (numeric) = 1.0050911254491187555237784000387 absolute error = 5.1e-30 relative error = 5.0741667803713782969474625337224e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.3MB, time=17.67 NO POLE NO POLE x[1] = 0.10096 y2[1] (analytic) = 1.0050921332851183007990710912796 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.62985631440668946330790835e-05 relative error = 0.0095810682379253599903270554503152 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050921332851183007990710912796 y1[1] (numeric) = 1.0050921332851183007990710912848 absolute error = 5.2e-30 relative error = 5.1736550588690124198740983105197e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10097 y2[1] (analytic) = 1.0050931412206086327450228625568 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.73064986343988405848503607e-05 relative error = 0.0096813414243606867512381847901416 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050931412206086327450228625568 y1[1] (numeric) = 1.005093141220608632745022862562 absolute error = 5.2e-30 relative error = 5.1736498705831365092851526841420e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10098 y2[1] (analytic) = 1.0050941492555896505680846815105 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.83145336154166636466693144e-05 relative error = 0.0097816243073578815808637715318198 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050941492555896505680846815105 y1[1] (numeric) = 1.0050941492555896505680846815157 absolute error = 5.2e-30 relative error = 5.1736446817955458654415535448377e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.3MB, time=18.15 NO POLE NO POLE x[1] = 0.10099 y2[1] (analytic) = 1.0050951573900612534647584471984 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 9.93226680870195603204350023e-05 relative error = 0.0098819168868479615453216443878069 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.0050951573900612534647584471984 y1[1] (numeric) = 1.0050951573900612534647584472037 absolute error = 5.3e-30 relative error = 5.2731325596698256741171001692120e-28 % Correct digits = 29 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.101 y2[1] (analytic) = 1.005096165624023340621597000171 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0.0001003309020491067171589879749 relative error = 0.0099822191627619372790415256212222 % Correct digits = 4 h = 1e-05 y1[1] (analytic) = 1.005096165624023340621597000171 y1[1] (numeric) = 1.0050961656240233406215970001764 absolute error = 5.4e-30 relative error = 5.3726202374350513729644780671544e-28 % Correct digits = 29 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; Iterations = 100 Total Elapsed Time = 18 Seconds Elapsed Time(since restart) = 18 Seconds Expected Time Remaining = 1 Days 0 Hours 47 Minutes 9 Seconds Optimized Time Remaining = 1 Days 0 Hours 44 Minutes 5 Seconds Time to Timeout = 41 Seconds Percent Done = 0.02061 % > quit memory used=147.9MB, alloc=4.3MB, time=18.51