|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_max_minutes, > glob_current_iter, > glob_small_float, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_start_msg, > glob_not_yet_finished, > years_in_century, > sec_in_minute, > glob_good_digits, > glob_normmax, > glob_hmin_init, > glob_clock_start_sec, > days_in_year, > glob_curr_iter_when_opt, > glob_max_iter, > glob_relerr, > glob_large_float, > glob_reached_optimal_h, > glob_warned, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > glob_optimal_done, > glob_clock_sec, > glob_almost_1, > centuries_in_millinium, > MAX_UNCHANGED, > glob_no_eqs, > glob_subiter_method, > glob_max_sec, > glob_log10_relerr, > glob_last_good_h, > hours_in_day, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_hmin, > glob_initial_pass, > min_in_hour, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10relerr, > glob_iter, > glob_start, > glob_percent_done, > glob_max_rel_trunc_err, > glob_orig_start_sec, > glob_optimal_start, > glob_h, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_2D0, > array_const_0D0, > #END CONST > array_x, > array_m1, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_type_pole, > array_norms, > array_y1, > array_y2, > array_y1_init, > array_y2_init, > array_pole, > array_last_rel_error, > array_y1_higher, > array_fact_2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y2_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher, > array_y1_set_initial, > 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_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[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_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[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 glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, glob_max_minutes, glob_current_iter, glob_small_float, glob_log10_abserr, glob_look_poles, glob_not_yet_start_msg, glob_not_yet_finished, years_in_century, sec_in_minute, glob_good_digits, glob_normmax, glob_hmin_init, glob_clock_start_sec, days_in_year, glob_curr_iter_when_opt, glob_max_iter, glob_relerr, glob_large_float, glob_reached_optimal_h, glob_warned, glob_smallish_float, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, glob_optimal_done, glob_clock_sec, glob_almost_1, centuries_in_millinium, MAX_UNCHANGED, glob_no_eqs, glob_subiter_method, glob_max_sec, glob_log10_relerr, glob_last_good_h, hours_in_day, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_hmin, glob_initial_pass, min_in_hour, djd_debug, glob_dump, glob_log10normmin, glob_log10relerr, glob_iter, glob_start, glob_percent_done, glob_max_rel_trunc_err, glob_orig_start_sec, glob_optimal_start, glob_h, djd_debug2, glob_log10abserr, glob_warned2, glob_unchanged_h_cnt, glob_max_trunc_err, glob_max_hours, glob_dump_analytic, glob_hmax, array_const_5, array_const_1, array_const_2D0, array_const_0D0, array_x, array_m1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_type_pole, array_norms, array_y1, array_y2, array_y1_init, array_y2_init, array_pole, array_last_rel_error, array_y1_higher, array_fact_2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y2_higher_work2, array_real_pole, array_poles, array_y1_higher_work2, array_y2_set_initial, array_y2_higher, array_y1_set_initial, 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_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then glob_good_digits := -trunc(log10(relerr/100.0)) else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_max_minutes, > glob_current_iter, > glob_small_float, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_start_msg, > glob_not_yet_finished, > years_in_century, > sec_in_minute, > glob_good_digits, > glob_normmax, > glob_hmin_init, > glob_clock_start_sec, > days_in_year, > glob_curr_iter_when_opt, > glob_max_iter, > glob_relerr, > glob_large_float, > glob_reached_optimal_h, > glob_warned, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > glob_optimal_done, > glob_clock_sec, > glob_almost_1, > centuries_in_millinium, > MAX_UNCHANGED, > glob_no_eqs, > glob_subiter_method, > glob_max_sec, > glob_log10_relerr, > glob_last_good_h, > hours_in_day, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_hmin, > glob_initial_pass, > min_in_hour, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10relerr, > glob_iter, > glob_start, > glob_percent_done, > glob_max_rel_trunc_err, > glob_orig_start_sec, > glob_optimal_start, > glob_h, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_2D0, > array_const_0D0, > #END CONST > array_x, > array_m1, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_type_pole, > array_norms, > array_y1, > array_y2, > array_y1_init, > array_y2_init, > array_pole, > array_last_rel_error, > array_y1_higher, > array_fact_2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y2_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher, > array_y1_set_initial, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, glob_max_minutes, glob_current_iter, glob_small_float, glob_log10_abserr, glob_look_poles, glob_not_yet_start_msg, glob_not_yet_finished, years_in_century, sec_in_minute, glob_good_digits, glob_normmax, glob_hmin_init, glob_clock_start_sec, days_in_year, glob_curr_iter_when_opt, glob_max_iter, glob_relerr, glob_large_float, glob_reached_optimal_h, glob_warned, glob_smallish_float, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, glob_optimal_done, glob_clock_sec, glob_almost_1, centuries_in_millinium, MAX_UNCHANGED, glob_no_eqs, glob_subiter_method, glob_max_sec, glob_log10_relerr, glob_last_good_h, hours_in_day, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_hmin, glob_initial_pass, min_in_hour, djd_debug, glob_dump, glob_log10normmin, glob_log10relerr, glob_iter, glob_start, glob_percent_done, glob_max_rel_trunc_err, glob_orig_start_sec, glob_optimal_start, glob_h, djd_debug2, glob_log10abserr, glob_warned2, glob_unchanged_h_cnt, glob_max_trunc_err, glob_max_hours, glob_dump_analytic, glob_hmax, array_const_5, array_const_1, array_const_2D0, array_const_0D0, array_x, array_m1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_type_pole, array_norms, array_y1, array_y2, array_y1_init, array_y2_init, array_pole, array_last_rel_error, array_y1_higher, array_fact_2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y2_higher_work2, array_real_pole, array_poles, array_y1_higher_work2, array_y2_set_initial, array_y2_higher, array_y1_set_initial, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_max_minutes, > glob_current_iter, > glob_small_float, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_start_msg, > glob_not_yet_finished, > years_in_century, > sec_in_minute, > glob_good_digits, > glob_normmax, > glob_hmin_init, > glob_clock_start_sec, > days_in_year, > glob_curr_iter_when_opt, > glob_max_iter, > glob_relerr, > glob_large_float, > glob_reached_optimal_h, > glob_warned, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > glob_optimal_done, > glob_clock_sec, > glob_almost_1, > centuries_in_millinium, > MAX_UNCHANGED, > glob_no_eqs, > glob_subiter_method, > glob_max_sec, > glob_log10_relerr, > glob_last_good_h, > hours_in_day, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_hmin, > glob_initial_pass, > min_in_hour, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10relerr, > glob_iter, > glob_start, > glob_percent_done, > glob_max_rel_trunc_err, > glob_orig_start_sec, > glob_optimal_start, > glob_h, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_2D0, > array_const_0D0, > #END CONST > array_x, > array_m1, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_type_pole, > array_norms, > array_y1, > array_y2, > array_y1_init, > array_y2_init, > array_pole, > array_last_rel_error, > array_y1_higher, > array_fact_2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y2_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher, > array_y1_set_initial, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > > > > > > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, glob_max_minutes, glob_current_iter, glob_small_float, glob_log10_abserr, glob_look_poles, glob_not_yet_start_msg, glob_not_yet_finished, years_in_century, sec_in_minute, glob_good_digits, glob_normmax, glob_hmin_init, glob_clock_start_sec, days_in_year, glob_curr_iter_when_opt, glob_max_iter, glob_relerr, glob_large_float, glob_reached_optimal_h, glob_warned, glob_smallish_float, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, glob_optimal_done, glob_clock_sec, glob_almost_1, centuries_in_millinium, MAX_UNCHANGED, glob_no_eqs, glob_subiter_method, glob_max_sec, glob_log10_relerr, glob_last_good_h, hours_in_day, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_hmin, glob_initial_pass, min_in_hour, djd_debug, glob_dump, glob_log10normmin, glob_log10relerr, glob_iter, glob_start, glob_percent_done, glob_max_rel_trunc_err, glob_orig_start_sec, glob_optimal_start, glob_h, djd_debug2, glob_log10abserr, glob_warned2, glob_unchanged_h_cnt, glob_max_trunc_err, glob_max_hours, glob_dump_analytic, glob_hmax, array_const_5, array_const_1, array_const_2D0, array_const_0D0, array_x, array_m1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_type_pole, array_norms, array_y1, array_y2, array_y1_init, array_y2_init, array_pole, array_last_rel_error, array_y1_higher, array_fact_2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y2_higher_work2, array_real_pole, array_poles, array_y1_higher_work2, array_y2_set_initial, array_y2_higher, array_y1_set_initial, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_max_minutes, > glob_current_iter, > glob_small_float, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_start_msg, > glob_not_yet_finished, > years_in_century, > sec_in_minute, > glob_good_digits, > glob_normmax, > glob_hmin_init, > glob_clock_start_sec, > days_in_year, > glob_curr_iter_when_opt, > glob_max_iter, > glob_relerr, > glob_large_float, > glob_reached_optimal_h, > glob_warned, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > glob_optimal_done, > glob_clock_sec, > glob_almost_1, > centuries_in_millinium, > MAX_UNCHANGED, > glob_no_eqs, > glob_subiter_method, > glob_max_sec, > glob_log10_relerr, > glob_last_good_h, > hours_in_day, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_hmin, > glob_initial_pass, > min_in_hour, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10relerr, > glob_iter, > glob_start, > glob_percent_done, > glob_max_rel_trunc_err, > glob_orig_start_sec, > glob_optimal_start, > glob_h, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_2D0, > array_const_0D0, > #END CONST > array_x, > array_m1, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_type_pole, > array_norms, > array_y1, > array_y2, > array_y1_init, > array_y2_init, > array_pole, > array_last_rel_error, > array_y1_higher, > array_fact_2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y2_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher, > array_y1_set_initial, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > > > > > > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * 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 glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, glob_max_minutes, glob_current_iter, glob_small_float, glob_log10_abserr, glob_look_poles, glob_not_yet_start_msg, glob_not_yet_finished, years_in_century, sec_in_minute, glob_good_digits, glob_normmax, glob_hmin_init, glob_clock_start_sec, days_in_year, glob_curr_iter_when_opt, glob_max_iter, glob_relerr, glob_large_float, glob_reached_optimal_h, glob_warned, glob_smallish_float, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, glob_optimal_done, glob_clock_sec, glob_almost_1, centuries_in_millinium, MAX_UNCHANGED, glob_no_eqs, glob_subiter_method, glob_max_sec, glob_log10_relerr, glob_last_good_h, hours_in_day, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_hmin, glob_initial_pass, min_in_hour, djd_debug, glob_dump, glob_log10normmin, glob_log10relerr, glob_iter, glob_start, glob_percent_done, glob_max_rel_trunc_err, glob_orig_start_sec, glob_optimal_start, glob_h, djd_debug2, glob_log10abserr, glob_warned2, glob_unchanged_h_cnt, glob_max_trunc_err, glob_max_hours, glob_dump_analytic, glob_hmax, array_const_5, array_const_1, array_const_2D0, array_const_0D0, array_x, array_m1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_type_pole, array_norms, array_y1, array_y2, array_y1_init, array_y2_init, array_pole, array_last_rel_error, array_y1_higher, array_fact_2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y2_higher_work2, array_real_pole, array_poles, array_y1_higher_work2, array_y2_set_initial, array_y2_higher, array_y1_set_initial, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= omniabs(array_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= omniabs(array_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*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 > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_max_minutes, > glob_current_iter, > glob_small_float, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_start_msg, > glob_not_yet_finished, > years_in_century, > sec_in_minute, > glob_good_digits, > glob_normmax, > glob_hmin_init, > glob_clock_start_sec, > days_in_year, > glob_curr_iter_when_opt, > glob_max_iter, > glob_relerr, > glob_large_float, > glob_reached_optimal_h, > glob_warned, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > glob_optimal_done, > glob_clock_sec, > glob_almost_1, > centuries_in_millinium, > MAX_UNCHANGED, > glob_no_eqs, > glob_subiter_method, > glob_max_sec, > glob_log10_relerr, > glob_last_good_h, > hours_in_day, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_hmin, > glob_initial_pass, > min_in_hour, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10relerr, > glob_iter, > glob_start, > glob_percent_done, > glob_max_rel_trunc_err, > glob_orig_start_sec, > glob_optimal_start, > glob_h, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_2D0, > array_const_0D0, > #END CONST > array_x, > array_m1, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_type_pole, > array_norms, > array_y1, > array_y2, > array_y1_init, > array_y2_init, > array_pole, > array_last_rel_error, > array_y1_higher, > array_fact_2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y2_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher, > array_y1_set_initial, > glob_last; > > local iii; > > > > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2 > ; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3 > ; > > # End Function number 7 > end; get_norms := proc() local iii; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, glob_max_minutes, glob_current_iter, glob_small_float, glob_log10_abserr, glob_look_poles, glob_not_yet_start_msg, glob_not_yet_finished, years_in_century, sec_in_minute, glob_good_digits, glob_normmax, glob_hmin_init, glob_clock_start_sec, days_in_year, glob_curr_iter_when_opt, glob_max_iter, glob_relerr, glob_large_float, glob_reached_optimal_h, glob_warned, glob_smallish_float, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, glob_optimal_done, glob_clock_sec, glob_almost_1, centuries_in_millinium, MAX_UNCHANGED, glob_no_eqs, glob_subiter_method, glob_max_sec, glob_log10_relerr, glob_last_good_h, hours_in_day, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_hmin, glob_initial_pass, min_in_hour, djd_debug, glob_dump, glob_log10normmin, glob_log10relerr, glob_iter, glob_start, glob_percent_done, glob_max_rel_trunc_err, glob_orig_start_sec, glob_optimal_start, glob_h, djd_debug2, glob_log10abserr, glob_warned2, glob_unchanged_h_cnt, glob_max_trunc_err, glob_max_hours, glob_dump_analytic, glob_hmax, array_const_5, array_const_1, array_const_2D0, array_const_0D0, array_x, array_m1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_type_pole, array_norms, array_y1, array_y2, array_y1_init, array_y2_init, array_pole, array_last_rel_error, array_y1_higher, array_fact_2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y2_higher_work2, array_real_pole, array_poles, array_y1_higher_work2, array_y2_set_initial, array_y2_higher, array_y1_set_initial, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_max_minutes, > glob_current_iter, > glob_small_float, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_start_msg, > glob_not_yet_finished, > years_in_century, > sec_in_minute, > glob_good_digits, > glob_normmax, > glob_hmin_init, > glob_clock_start_sec, > days_in_year, > glob_curr_iter_when_opt, > glob_max_iter, > glob_relerr, > glob_large_float, > glob_reached_optimal_h, > glob_warned, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > glob_optimal_done, > glob_clock_sec, > glob_almost_1, > centuries_in_millinium, > MAX_UNCHANGED, > glob_no_eqs, > glob_subiter_method, > glob_max_sec, > glob_log10_relerr, > glob_last_good_h, > hours_in_day, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_hmin, > glob_initial_pass, > min_in_hour, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10relerr, > glob_iter, > glob_start, > glob_percent_done, > glob_max_rel_trunc_err, > glob_orig_start_sec, > glob_optimal_start, > glob_h, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_2D0, > array_const_0D0, > #END CONST > array_x, > array_m1, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_type_pole, > array_norms, > array_y1, > array_y2, > array_y1_init, > array_y2_init, > array_pole, > array_last_rel_error, > array_y1_higher, > array_fact_2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y2_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher, > array_y1_set_initial, > 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_y2_higher[6,1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp4[1] := array_y1[1] - array_const_2D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_y2_higher[6,2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp4[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_y2_higher[6,3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp4[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_y2_higher[6,4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp4[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_y2_higher[6,5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp4[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_y2_higher[6,kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit FULL - NOT FULL sub $eq_no = 2 > array_tmp4[kkk] := array_y1[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > > #BOTTOM ATOMALL ??? > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, glob_max_minutes, glob_current_iter, glob_small_float, glob_log10_abserr, glob_look_poles, glob_not_yet_start_msg, glob_not_yet_finished, years_in_century, sec_in_minute, glob_good_digits, glob_normmax, glob_hmin_init, glob_clock_start_sec, days_in_year, glob_curr_iter_when_opt, glob_max_iter, glob_relerr, glob_large_float, glob_reached_optimal_h, glob_warned, glob_smallish_float, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, glob_optimal_done, glob_clock_sec, glob_almost_1, centuries_in_millinium, MAX_UNCHANGED, glob_no_eqs, glob_subiter_method, glob_max_sec, glob_log10_relerr, glob_last_good_h, hours_in_day, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_hmin, glob_initial_pass, min_in_hour, djd_debug, glob_dump, glob_log10normmin, glob_log10relerr, glob_iter, glob_start, glob_percent_done, glob_max_rel_trunc_err, glob_orig_start_sec, glob_optimal_start, glob_h, djd_debug2, glob_log10abserr, glob_warned2, glob_unchanged_h_cnt, glob_max_trunc_err, glob_max_hours, glob_dump_analytic, glob_hmax, array_const_5, array_const_1, array_const_2D0, array_const_0D0, array_x, array_m1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_type_pole, array_norms, array_y1, array_y2, array_y1_init, array_y2_init, array_pole, array_last_rel_error, array_y1_higher, array_fact_2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y2_higher_work2, array_real_pole, array_poles, array_y1_higher_work2, array_y2_set_initial, array_y2_higher, array_y1_set_initial, glob_last; array_tmp1[1] := array_y2_higher[6, 1]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[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_tmp4[1] := array_y1[1] - array_const_2D0[1]; if not array_y2_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_y2_higher[6, 2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[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_tmp4[2] := array_y1[2]; if not array_y2_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_y2_higher[6, 3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[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_tmp4[3] := array_y1[3]; if not array_y2_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_y2_higher[6, 4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[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_tmp4[4] := array_y1[4]; if not array_y2_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_y2_higher[6, 5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp4[5] := array_y1[5]; if not array_y2_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y2_higher[6, kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp4[kkk] := array_y1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > fprintf(fd,""); > if (secs >= 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := secs_in; fprintf(fd, ""); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs >= 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_minute * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_minute; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := convfloat(secs_in); if 0. <= secs then sec_in_millinium := convfloat(sec_in_minute*min_in_hour* hours_in_day*days_in_year*years_in_century* centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_minute; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > > > > > > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats; > > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > > > > > > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > > local good_digits; > > > fprintf(file,""); > if (rel_error <> -1.0) then # if number 11 > if (rel_error <> 0.0) then # if number 12 > good_digits := -trunc(log10(rel_error/100.0)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 12 > ; > else > fprintf(file,"Unknown"); > fi;# end if 11 > ; > fprintf(file,""); > > # End Function number 9 > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if rel_error <> 0. then good_digits := -trunc(log10(rel_error/100.0)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # Begin Function number 10 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 10 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 11 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 11 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 12 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 11 > fprintf(file,"NA"); > elif (pole = 1) then # if number 12 > fprintf(file,"Real"); > elif (pole = 2) then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 12 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 13 > logstart := proc(file) > fprintf(file,""); > # End Function number 13 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 14 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 14 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 15 > 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 + sin(x)); > end; exact_soln_y1 := proc(x) return 2.0 + sin(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 > exact_soln_y2p := proc(x) > return(sin(x)); > end; exact_soln_y2p := proc(x) return sin(x) end proc > exact_soln_y2pp := proc(x) > return(cos(x)); > end; exact_soln_y2pp := proc(x) return cos(x) end proc > exact_soln_y2ppp := proc(x) > return(-sin(x)); > end; exact_soln_y2ppp := proc(x) return -sin(x) end proc > exact_soln_y2pppp := proc(x) > return(-cos(x)); > end; exact_soln_y2pppp := proc(x) return -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 > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > glob_max_minutes, > glob_current_iter, > glob_small_float, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_start_msg, > glob_not_yet_finished, > years_in_century, > sec_in_minute, > glob_good_digits, > glob_normmax, > glob_hmin_init, > glob_clock_start_sec, > days_in_year, > glob_curr_iter_when_opt, > glob_max_iter, > glob_relerr, > glob_large_float, > glob_reached_optimal_h, > glob_warned, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_disp_incr, > glob_optimal_done, > glob_clock_sec, > glob_almost_1, > centuries_in_millinium, > MAX_UNCHANGED, > glob_no_eqs, > glob_subiter_method, > glob_max_sec, > glob_log10_relerr, > glob_last_good_h, > hours_in_day, > glob_display_flag, > glob_max_opt_iter, > glob_html_log, > glob_optimal_expect_sec, > glob_hmin, > glob_initial_pass, > min_in_hour, > djd_debug, > glob_dump, > glob_log10normmin, > glob_log10relerr, > glob_iter, > glob_start, > glob_percent_done, > glob_max_rel_trunc_err, > glob_orig_start_sec, > glob_optimal_start, > glob_h, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_unchanged_h_cnt, > glob_max_trunc_err, > glob_max_hours, > glob_dump_analytic, > glob_hmax, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_2D0, > array_const_0D0, > #END CONST > array_x, > array_m1, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_type_pole, > array_norms, > array_y1, > array_y2, > array_y1_init, > array_y2_init, > array_pole, > array_last_rel_error, > array_y1_higher, > array_fact_2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y2_higher_work2, > array_real_pole, > array_poles, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher, > array_y1_set_initial, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_iolevel := 5; > INFO := 2; > DEBUGMASSIVE := 4; > DEBUGL := 3; > ALWAYS := 1; > glob_max_terms := 30; > glob_max_minutes := 0.0; > glob_current_iter := 0; > glob_small_float := 0.1e-50; > glob_log10_abserr := 0.1e-10; > glob_look_poles := false; > glob_not_yet_start_msg := true; > glob_not_yet_finished := true; > years_in_century := 100; > sec_in_minute := 60; > glob_good_digits := 0; > glob_normmax := 0.0; > glob_hmin_init := 0.001; > glob_clock_start_sec := 0.0; > days_in_year := 365; > glob_curr_iter_when_opt := 0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_reached_optimal_h := false; > glob_warned := false; > glob_smallish_float := 0.1e-100; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_disp_incr := 0.1; > glob_optimal_done := false; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > centuries_in_millinium := 10; > MAX_UNCHANGED := 10; > glob_no_eqs := 0; > glob_subiter_method := 3; > glob_max_sec := 10000.0; > glob_log10_relerr := 0.1e-10; > glob_last_good_h := 0.1; > hours_in_day := 24; > glob_display_flag := true; > glob_max_opt_iter := 10; > glob_html_log := true; > glob_optimal_expect_sec := 0.1; > glob_hmin := 0.00000000001; > glob_initial_pass := true; > min_in_hour := 60; > djd_debug := true; > glob_dump := false; > glob_log10normmin := 0.1; > glob_log10relerr := 0.0; > glob_iter := 0; > glob_start := 0; > glob_percent_done := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_orig_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_h := 0.1; > djd_debug2 := true; > glob_log10abserr := 0.0; > glob_warned2 := false; > glob_unchanged_h_cnt := 0; > glob_max_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_dump_analytic := false; > glob_hmax := 1.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest9postode.ode#################"); > omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.5;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"glob_subiter_method := 3;"); > 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 + sin(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,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return(sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return(cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"return(-sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"return(-cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_x:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= 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_fact_1:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y2_higher_work2 := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > 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_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_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_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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 <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_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 <=6) 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 <=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 <=6) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_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 <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=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 <=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 <=6) 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 <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_5[1] := 5; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.5; > x_end := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > glob_subiter_method := 3; > #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_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := true; > array_y2_set_initial[2,3] := true; > array_y2_set_initial[2,4] := true; > array_y2_set_initial[2,5] := true; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := false; > if (glob_html_log) then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 5; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (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_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y2 > order_diff := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[6,iii] := array_y2_higher[6,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 := 6; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 4; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 4; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 6; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 6; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_str(INFO,"diff(y2,x,1) = y1 - 2.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-09-02T22:05:37-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest9") > ; > logitem_str(html_log_file,"diff(y1,x,1) = diff(y2,x,5);") > ; > 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,"mtest9 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest9 maple results") > ; > logitem_str(html_log_file,"c c++ Maple and Maxima") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff(y2,x,1) = y1 - 2.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 5 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if (glob_html_log) then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > > # End Function number 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 glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, glob_max_minutes, glob_current_iter, glob_small_float, glob_log10_abserr, glob_look_poles, glob_not_yet_start_msg, glob_not_yet_finished, years_in_century, sec_in_minute, glob_good_digits, glob_normmax, glob_hmin_init, glob_clock_start_sec, days_in_year, glob_curr_iter_when_opt, glob_max_iter, glob_relerr, glob_large_float, glob_reached_optimal_h, glob_warned, glob_smallish_float, glob_optimal_clock_start_sec, glob_abserr, glob_disp_incr, glob_optimal_done, glob_clock_sec, glob_almost_1, centuries_in_millinium, MAX_UNCHANGED, glob_no_eqs, glob_subiter_method, glob_max_sec, glob_log10_relerr, glob_last_good_h, hours_in_day, glob_display_flag, glob_max_opt_iter, glob_html_log, glob_optimal_expect_sec, glob_hmin, glob_initial_pass, min_in_hour, djd_debug, glob_dump, glob_log10normmin, glob_log10relerr, glob_iter, glob_start, glob_percent_done, glob_max_rel_trunc_err, glob_orig_start_sec, glob_optimal_start, glob_h, djd_debug2, glob_log10abserr, glob_warned2, glob_unchanged_h_cnt, glob_max_trunc_err, glob_max_hours, glob_dump_analytic, glob_hmax, array_const_5, array_const_1, array_const_2D0, array_const_0D0, array_x, array_m1, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_type_pole, array_norms, array_y1, array_y2, array_y1_init, array_y2_init, array_pole, array_last_rel_error, array_y1_higher, array_fact_2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y2_higher_work2, array_real_pole, array_poles, array_y1_higher_work2, array_y2_set_initial, array_y2_higher, array_y1_set_initial, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_iolevel := 5; INFO := 2; DEBUGMASSIVE := 4; DEBUGL := 3; ALWAYS := 1; glob_max_terms := 30; glob_max_minutes := 0.; glob_current_iter := 0; glob_small_float := 0.1*10^(-50); glob_log10_abserr := 0.1*10^(-10); glob_look_poles := false; glob_not_yet_start_msg := true; glob_not_yet_finished := true; years_in_century := 100; sec_in_minute := 60; glob_good_digits := 0; glob_normmax := 0.; glob_hmin_init := 0.001; glob_clock_start_sec := 0.; days_in_year := 365; glob_curr_iter_when_opt := 0; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_reached_optimal_h := false; glob_warned := false; glob_smallish_float := 0.1*10^(-100); glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_disp_incr := 0.1; glob_optimal_done := false; glob_clock_sec := 0.; glob_almost_1 := 0.9990; centuries_in_millinium := 10; MAX_UNCHANGED := 10; glob_no_eqs := 0; glob_subiter_method := 3; glob_max_sec := 10000.0; glob_log10_relerr := 0.1*10^(-10); glob_last_good_h := 0.1; hours_in_day := 24; glob_display_flag := true; glob_max_opt_iter := 10; glob_html_log := true; glob_optimal_expect_sec := 0.1; glob_hmin := 0.1*10^(-10); glob_initial_pass := true; min_in_hour := 60; djd_debug := true; glob_dump := false; glob_log10normmin := 0.1; glob_log10relerr := 0.; glob_iter := 0; glob_start := 0; glob_percent_done := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_orig_start_sec := 0.; glob_optimal_start := 0.; glob_h := 0.1; djd_debug2 := true; glob_log10abserr := 0.; glob_warned2 := false; glob_unchanged_h_cnt := 0; glob_max_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_dump_analytic := false; glob_hmax := 1.0; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest9postode.ode#################"); omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"); omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.5;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "glob_subiter_method := 3;"); 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 + sin(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, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return(sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return(cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "return(-sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "return(-cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_x := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_1st_rel_error := 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_fact_1 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y2_higher_work2 := Array(0 .. 7, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 7, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_x[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_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_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[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_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; 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 <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 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 <= 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 <= 6 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_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 <= 3 do array_poles[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 <= 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 <= 6 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 <= 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; 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_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_const_5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5[term] := 0.; term := term + 1 end do; array_const_5[1] := 5; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.5; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[4] := exact_soln_y2ppp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; 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_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := true; array_y2_set_initial[2, 3] := true; array_y2_set_initial[2, 4] := true; array_y2_set_initial[2, 5] := true; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 5; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and 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_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 5; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 6; 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 := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; 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 := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; 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 := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 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 := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 5; 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 := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 4; 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 := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 6; 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 := 6; 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 := 5; 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 := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"); omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-09-02T22:05:37-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest9") ; logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"); 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, "mtest9 diffeq.mxt"); logitem_str(html_log_file, "mtest9 maple results"); logitem_str(html_log_file, "c c++ Maple and Maxima"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest9postode.ode################# diff(y1,x,1) = diff(y2,x,5); diff(y2,x,1) = y1 - 2.0; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; #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 + sin(x)); end; exact_soln_y2 := proc(x) return(2.0 - cos(x)); end; exact_soln_y2p := proc(x) return(sin(x)); end; exact_soln_y2pp := proc(x) return(cos(x)); end; exact_soln_y2ppp := proc(x) return(-sin(x)); end; exact_soln_y2pppp := proc(x) return(-cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.5 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 x[1] = 0.5 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50001 y1[1] (analytic) = 2.479434314405850480806678394328 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 8.7758016474805333904591124e-06 relative error = 0.00035394370387196517465434156954291 % Correct digits = 5 h = 1e-05 y2[1] (analytic) = 1.1224222324088923741036176930462 y2[1] (numeric) = 1.1224222324088923741036176926467 absolute error = 3.995e-28 relative error = 3.5592666330442419607621867384583e-26 % Correct digits = 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50002 y1[1] (analytic) = 2.4794430901595545298998833339551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 1.75515553515296265953987395e-05 relative error = 0.00070788296860647716066745198593803 % Correct digits = 5 h = 1e-05 y2[1] (analytic) = 1.1224270267959152410818964164796 y2[1] (numeric) = 1.1224270267959152410818964036948 absolute error = 1.27848e-26 relative error = 1.1390317316659366367494933191236e-24 % Correct digits = 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.48 NO POLE NO POLE x[1] = 0.50003 y1[1] (analytic) = 2.4794518658653142699775323565007 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 2.63272611112697042444212851e-05 relative error = 0.001061817794235809588896300381047 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224318212706954053798523049938 y2[1] (numeric) = 1.1224318212706954053798522079092 absolute error = 9.70846e-26 relative error = 8.6494874931549392314604213592582e-24 % Correct digits = 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50004 y1[1] (analytic) = 2.4794606415231288234690494952701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 3.51029189258231957615600545e-05 relative error = 0.0014157481807922358127118646817542 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224366158332323875500073461544 y2[1] (numeric) = 1.1224366158332323875500069370396 absolute error = 4.091148e-25 relative error = 3.6448810937648956007252078500415e-23 % Correct digits = 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50005 y1[1] (analytic) = 2.4794694171329973128086533022272 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 4.38785287943125353653670116e-05 relative error = 0.0017696741283080289079946886795967 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224414104835257081361078457399 y2[1] (numeric) = 1.1224414104835257081361065972168 absolute error = 1.2485231e-24 relative error = 1.1123280808591699917975157407833e-22 % Correct digits = 23 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50006 y1[1] (analytic) = 2.479478192694918860435356935751 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 5.26540907158601620690005354e-05 relative error = 0.0021235956368154616731304393721065 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224462052215748876731244756871 y2[1] (numeric) = 1.1224462052215748876731213689528 absolute error = 3.1067343e-24 relative error = 2.7678246721736829776748308562343e-22 % Correct digits = 23 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=7.6MB, alloc=3.9MB, time=1.07 x[1] = 0.50007 y1[1] (analytic) = 2.4794869682088925887929682483919 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 6.14296046895885196803131763e-05 relative error = 0.0024775127063468066290054645919845 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224510000473794466872523220381 y2[1] (numeric) = 1.1224510000473794466872456071405 absolute error = 6.7148976e-24 relative error = 5.9823525478765304199413033019012e-22 % Correct digits = 23 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50008 y1[1] (analytic) = 2.479495743674917620330089874627 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 7.02050707146200568019394114e-05 relative error = 0.0028314253369343360190023508918322 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.122455794960938905695910932887 y2[1] (numeric) = 1.1224557949609389056958978410541 absolute error = 1.30918329e-23 relative error = 1.1663562127589702987089467615430e-21 % Correct digits = 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50009 y1[1] (analytic) = 2.4795045190929930775001193186155 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 7.89804887900772268313833999e-05 relative error = 0.0031853335286103218089954817287952 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224605899622527852077443663289 y2[1] (numeric) = 1.1224605899622527852077207743489 absolute error = 2.35919800e-23 relative error = 2.1018092047929606539733033254184e-21 % Correct digits = 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5001 y1[1] (analytic) = 2.4795132944631180827612490419532 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 8.77558589150824879611067376e-05 relative error = 0.0035392372814070356873465959087753 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224653850513206057226212384082 y2[1] (numeric) = 1.1224653850513206057225812850611 absolute error = 3.99533471e-23 relative error = 3.5594279905721351037455693725130e-21 % Correct digits = 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50011 y1[1] (analytic) = 2.4795220697852917585764665514268 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 9.65311810887583031786162112e-05 relative error = 0.0038931365953567490649003463184343 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224701802281418877316347710696 y2[1] (numeric) = 1.1224701802281418877315704256082 absolute error = 6.43454614e-23 relative error = 5.7324873776978017431645753870461e-21 % Correct digits = 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=1.67 NO POLE NO POLE x[1] = 0.50012 y1[1] (analytic) = 2.4795308450595132274135544867676 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000105306455310227140266551552 relative error = 0.0042470314704917330749798589288452 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224749754927161517171028401079 y2[1] (numeric) = 1.1224749754927161517170034227887 absolute error = 9.94173192e-23 relative error = 8.8569742195241597673021312393736e-21 % Correct digits = 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50013 y1[1] (analytic) = 2.4795396202857816117450907084046 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000114081681578611471802773189 relative error = 0.004600921906844258573382292070781 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224797708450429181525680231208 y2[1] (numeric) = 1.1224797708450429181524196777821 absolute error = 1.483453387e-22 relative error = 1.3215858544009245111008885871068e-20 % Correct digits = 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50014 y1[1] (analytic) = 2.4795483954640960340484483852173 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001228568598930337751604500017 relative error = 0.0049548079044465961383743959937303 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224845662851217075027976474608 y2[1] (numeric) = 1.1224845662851217075025827661492 absolute error = 2.148813116e-22 relative error = 1.9143364466128268561038839057737e-20 % Correct digits = 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50015 y1[1] (analytic) = 2.479557170594455616805796082288 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001316319902526165325081470724 relative error = 0.0053086894633310160706880727005611 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.122489361812952040223783838189 y2[1] (numeric) = 1.1224893618129520402234804378318 absolute error = 3.034003572e-22 relative error = 2.7029241213473312563366101893919e-20 % Correct digits = 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50016 memory used=15.2MB, alloc=3.9MB, time=2.26 y1[1] (analytic) = 2.4795659456768594825040978486537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001404070726564822308099134381 relative error = 0.0056625665835297883935159360618576 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224941574285334367627435660298 y2[1] (numeric) = 1.1224941574285334367623246171528 absolute error = 4.189488770e-22 relative error = 3.7323034086854344251475049158701e-20 % Correct digits = 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50017 y1[1] (analytic) = 2.479574720711306753635113305057 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001491821071037533618253698414 relative error = 0.0060164392650751828525068721857212 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1224989531318654175581186953255 y2[1] (numeric) = 1.1224989531318654175575514028162 absolute error = 5.672925093e-22 relative error = 5.0538355311353006379301157396555e-20 % Correct digits = 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50018 y1[1] (analytic) = 2.4795834956977965526953977316975 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001579570935935524221097964819 relative error = 0.0063703075079994689157616001035174 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1225037489229475030395760319929 y2[1] (numeric) = 1.122503748922947503038821067907 absolute error = 7.549640859e-22 relative error = 6.7257154964907232330767278629198e-20 % Correct digits = 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50019 y1[1] (analytic) = 2.4795922706363280021863021559814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001667320321250019130142207658 relative error = 0.0067241713123349157738282326788046 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1225085448017792136280073714805 y2[1] (numeric) = 1.1225085448017792136270180598915 absolute error = 9.893115890e-22 relative error = 8.8133991815153611292734088557356e-20 % Correct digits = 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5002 y1[1] (analytic) = 2.4796010455269002246139734402722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001755069226972243406855050566 relative error = 0.0070780306781137923396978378563839 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.122513340768360069735529546726 y2[1] (numeric) = 1.1225133407683600697342510006169 absolute error = 1.2785461091e-21 relative error = 1.1390030413579187786875203485615e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=3.9MB, time=2.88 NO POLE NO POLE x[1] = 0.50021 y1[1] (analytic) = 2.4796098203695123424893543696396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000184281765309342216066434424 relative error = 0.0074318856053683672488000001345095 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1225181368226895917654844761153 y2[1] (numeric) = 1.1225181368226895917638526863116 absolute error = 1.6317898037e-21 relative error = 1.4536868048464804456094573978165e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50022 y1[1] (analytic) = 2.4796185951641634783281837396084 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001930565599604780548958043928 relative error = 0.0077857360941309088589983823328401 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.122522932964767300112439211442 y2[1] (numeric) = 1.1225229329647673001103800875851 absolute error = 2.0591238569e-21 relative error = 1.8343713045233881681904363510594e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50023 y1[1] (analytic) = 2.479627369910852754650996443907 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002018313066497543777085086914 relative error = 0.0081395821444336852505862876399874 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1225277291945927151621859858683 y2[1] (numeric) = 1.1225277291945927151596143494279 absolute error = 2.5716364404e-21 relative error = 2.2909335542607348984429822144377e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50024 y1[1] (analytic) = 2.4796361446095792939831235622154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002106060053762937098356269998 relative error = 0.0084934237563089642262822219366202 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.122532525512165357291742261886 y2[1] (numeric) = 1.1225325255121653572885607912117 absolute error = 3.1814706743e-21 relative error = 2.8341901922605101955047085173875e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50025 y1[1] (analytic) = 2.4796449192603422188546924479126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000219380656139218581404512697 relative error = 0.0088472609297890133112254563900813 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1225373219174847468693507792792 y2[1] (numeric) = 1.1225373219174847468654489066893 absolute error = 3.9018725899e-21 relative error = 3.4759401881043364404844490227396e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=3.9MB, time=3.47 NO POLE NO POLE x[1] = 0.50026 y1[1] (analytic) = 2.4796536938631406518006268158238 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002281552589376515273388806082 relative error = 0.0092010936649060997529715903366345 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.122542118410550404254479603087 y2[1] (numeric) = 1.1225421184105504042497323639945 absolute error = 4.7472390925e-21 relative error = 4.2290075487072096133884298968137e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50027 y1[1] (analytic) = 2.4796624684179737153606468299665 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002369298137707150873588947509 relative error = 0.0095549219616924905214881144150421 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.122546914991361849797822171568 y2[1] (numeric) = 1.1225469149913618497920890056423 absolute error = 5.7331659257e-21 relative error = 5.1072840245114543711778079340564e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50028 y1[1] (analytic) = 2.4796712429248405320792691912968 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002457043206375318059812560812 relative error = 0.009908745820180452309149974003882 % Correct digits = 4 h = 1e-05 y2[1] (analytic) = 1.1225517116599186038412973441651 y2[1] (numeric) = 1.1225517116599186038344208485288 absolute error = 6.8764956363e-21 relative error = 6.1257718151190713532449932677428e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50029 y1[1] (analytic) = 2.4796800173837402245058072254549 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002544787795372242325192902393 relative error = 0.010262565240402251530735132922271 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1225565084162201867180494494711 y2[1] (numeric) = 1.122556508416220186709854083931 absolute error = 8.1953655401e-21 relative error = 7.3006262746296705526871710623495e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=3.9MB, time=4.09 NO POLE NO POLE x[1] = 0.5003 y1[1] (analytic) = 2.4796887917946719151943709705102 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002632531904689149210830352946 relative error = 0.010616380222390154323420137410111 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1225613052602661187524483331957 y2[1] (numeric) = 1.1225613052602661187427390775073 absolute error = 9.7092556884e-21 relative error = 8.6491986165057654875810979512255e-19 % Correct digits = 20 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50031 y1[1] (analytic) = 2.479697566157634726703867264706 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002720275534317264305793294904 relative error = 0.010970190766176426546775680387851 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1225661021920559202600894061327 y2[1] (numeric) = 1.1225661021920559202486503692969 absolute error = 1.14390368358e-20 relative error = 1.0190078618499861911384661163058e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50032 y1[1] (analytic) = 2.4797063404726277815979998342031 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002808018684247813247118989875 relative error = 0.011323996871793333782762165967528 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1225708992115891115477936921289 y2[1] (numeric) = 1.1225708992115891115343866737203 absolute error = 1.34070184086e-20 relative error = 1.1943137327019700502571650932494e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50033 y1[1] (analytic) = 2.4797151147396502024452693808242 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002895761354472021719814456086 relative error = 0.011677798539273141335725274291684 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122575696318865212913607876053 y2[1] (numeric) = 1.1225756963188652128979708795791 absolute error = 1.56369964739e-20 relative error = 1.3929569761020681114369312460497e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50034 y1[1] (analytic) = 2.4797238889587011118189736697964 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002983503544981115456857345808 relative error = 0.012031595768648114232391526591284 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122580493513883744646804351766 y2[1] (numeric) = 1.1225804935138837446286500500558 absolute error = 1.81543017102e-20 relative error = 1.6171937616138056426769266082305e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=3.9MB, time=4.69 NO POLE NO POLE x[1] = 0.50035 y1[1] (analytic) = 2.4797326631297796322972076174941 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003071245255766320239196822785 relative error = 0.012385388559950517221863850555367 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1225852907966442270278812700922 y2[1] (numeric) = 1.1225852907966442270068954227142 absolute error = 2.09858473780e-20 relative error = 1.8694211967722616387640576462941e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50036 y1[1] (analytic) = 2.4797414372528848864628633791814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003158986486818861895754439658 relative error = 0.012739176913212614775617145976122 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1225900881671461803285625867913 y2[1] (numeric) = 1.1225900881671461803044024094991 absolute error = 2.41601772922e-20 relative error = 2.1521815974383260959406935851818e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50037 y1[1] (analytic) = 2.4797502113280159969036304367535 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003246727238129966303425015379 relative error = 0.013092960828466671087493850649221 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122594885625389124811798110531 y2[1] (numeric) = 1.1225948856253891247840905967365 absolute error = 2.77075137945e-20 relative error = 2.4681667580432948002410778846088e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50038 y1[1] (analytic) = 2.4797589853551720862119956864779 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003334467509690859387077512623 relative error = 0.013446740305744950073699506561664 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122599683171372580731763550861 y2[1] (numeric) = 1.1225996831713725807001037451333 absolute error = 3.16598057277e-20 relative error = 2.8202222218930479063720883563726e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=3.9MB, time=5.29 NO POLE NO POLE x[1] = 0.50039 y1[1] (analytic) = 2.4797677593343522769852435267356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.00034222073014927671195559152 relative error = 0.013800515345079715372798326375175 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122604480805096068333860566187 y2[1] (numeric) = 1.1226044808050960682978097897777 absolute error = 3.60507764093e-20 relative error = 3.2113515513001992402616865175045e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5004 y1[1] (analytic) = 2.479776533265555691825455945761 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003509946613526915521680105454 relative error = 0.014154285946503230345708760152732 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122609278526559107854716811747 y2[1] (numeric) = 1.1226092785265591078138008401388 absolute error = 4.09159716082e-20 relative error = 3.6447205978827115783013948433269e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50041 y1[1] (analytic) = 2.4797853071487814533395126093814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003597685445784530662246741658 relative error = 0.014508052110047758075699062364507 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122614076335761219522185987587 y2[1] (numeric) = 1.122614076335761219475893180067 absolute error = 4.62928075200e-20 relative error = 4.1236617726281157856472170360737e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50042 y1[1] (analytic) = 2.4797940809840286841390909487572 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003685423798256838658030135416 relative error = 0.014861813835745561368382859217553 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226188742327019235553478865384 y2[1] (numeric) = 1.1226188742327019235031272677936 absolute error = 5.22206187448e-20 relative error = 4.6516783160707357821329826116805e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50043 y1[1] (analytic) = 2.47980285477129650684066624812 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003773161670935065673783129044 relative error = 0.01521557112362890275171471619634 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226236722173807401645084421961 y2[1] (numeric) = 1.1226236722173807401057677359312 absolute error = 5.87407062649e-20 relative error = 5.2324485683503086307085170459310e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=3.9MB, time=5.89 NO POLE NO POLE x[1] = 0.50044 y1[1] (analytic) = 2.479811628510584044065511732511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003860899063810437922237972954 relative error = 0.015569323973730044475985705910888 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226284702897971895511997768975 y2[1] (numeric) = 1.1226284702897971894853033914733 absolute error = 6.58963854242e-20 relative error = 5.8698302393123342876781301582948e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50045 y1[1] (analytic) = 2.4798204022018904184396986555191 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003948635976874181664107203035 relative error = 0.015923072386081248513818976228299 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226332684499507919081802497024 y2[1] (numeric) = 1.1226332684499507918344472157947 absolute error = 7.37330339077e-20 relative error = 6.5678646785076247061295252655984e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50046 y1[1] (analytic) = 2.4798291758452147525940963870185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004036372410117523208084518029 relative error = 0.016276816360714776560165318679622 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226380666978410674194345043735 y2[1] (numeric) = 1.1226380666978410673371363646511 absolute error = 8.22981397224e-20 relative error = 7.3307811452068469773503915849845e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50047 y1[1] (analytic) = 2.479837949440556169164372500905 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004124108363531688910845656894 relative error = 0.016630555897662890032298737109762 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226428650334675362601735173582 y2[1] (numeric) = 1.1226428650334675361685321681794 absolute error = 9.16413491788e-20 relative error = 8.1630010783587926383144042729077e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=41.9MB, alloc=3.9MB, time=6.48 x[1] = 0.50048 y1[1] (analytic) = 2.4798467229879137907909928628329 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004211843837107905177049276173 relative error = 0.016984290996957850069812016647055 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226476634568297185968346457712 y2[1] (numeric) = 1.1226476634568297184950201308976 absolute error = 1.018145148736e-19 relative error = 9.0691423665458129090464648149306e-18 % Correct digits = 19 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50049 y1[1] (analytic) = 2.4798554964872867401192217179509 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004299578830837398459337827353 relative error = 0.017338021658631917534612292927974 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226524619679271345870816753773 y2[1] (numeric) = 1.1226524619679271344742099317047 absolute error = 1.128717436726e-19 relative error = 1.0054023617847338178601455608806e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5005 y1[1] (analytic) = 2.4798642699386741397991217786374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004387313344711395258338434218 relative error = 0.017691747882717353010916621593082 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226572605667593043798048685764 y2[1] (numeric) = 1.1226572605667593042549354238809 absolute error = 1.248694446955e-19 relative error = 1.1122668429762903931962601000164e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50051 y1[1] (analytic) = 2.4798730433420751124855543122355 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004475047378721122122663770199 relative error = 0.018045469669246416805247548066326 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122662059253325748115121012388 y2[1] (numeric) = 1.1226620592533257479772546350875 absolute error = 1.378663773005e-19 relative error = 1.2280309659007618933478670552983e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50052 y1[1] (analytic) = 2.4798818166974887808381792287879 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004562780932857805648912935723 relative error = 0.018399187018251368946428677625718 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226668580276259859243734664374 y2[1] (numeric) = 1.1226668580276259857724497673668 absolute error = 1.519236990706e-19 relative error = 1.3532393691349312355277262136338e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=3.9MB, time=7.08 NO POLE NO POLE x[1] = 0.50053 y1[1] (analytic) = 2.4798905900049142675214551687704 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004650514007112672481672335548 relative error = 0.018752899929764469185580245712977 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226716568896595379301322109427 y2[1] (numeric) = 1.1226716568896595377630271971423 absolute error = 1.671050138004e-19 relative error = 1.4884584711380463713596548067796e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50054 y1[1] (analytic) = 2.4798993632643506952046395908258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004738246601476949313516556102 relative error = 0.019106608403817976996114688554705 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226764558394259242461938947025 y2[1] (numeric) = 1.1226764558394259240627174752186 absolute error = 1.834764194839e-19 relative error = 1.6342768972269446989258093188181e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50055 y1[1] (analytic) = 2.4799081364757971865617888594967 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004825978715941862885009242811 relative error = 0.019460312440444151573732214034598 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226812548769246649775818830842 y2[1] (numeric) = 1.1226812548769246647764753267813 absolute error = 2.011065563029e-19 relative error = 1.7913059065455453556813232734104e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50056 y1[1] (analytic) = 2.4799169096392528642717583329585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004913710350498639984703977429 relative error = 0.019814012039675251836416372869099 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226860540021552802205463060138 y2[1] (numeric) = 1.1226860540021552800004796513971 absolute error = 2.200666546167e-19 relative error = 1.9601798190349439071301761693433e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=49.5MB, alloc=3.9MB, time=7.68 x[1] = 0.50057 y1[1] (analytic) = 2.4799256827547168510182024507512 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005001441505138507449145155356 relative error = 0.020167707201543536424429630030038 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226908532151172900625641059664 y2[1] (numeric) = 1.1226908532151172898221335230139 absolute error = 2.404305829525e-19 relative error = 2.1415564423987644099877173726111e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50058 y1[1] (analytic) = 2.479934455822188269489574821511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005089172179852692162868862954 relative error = 0.02052139792608126370030893645457 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1226956525158102145823390859571 y2[1] (numeric) = 1.1226956525158102143200641899607 absolute error = 2.622748959964e-19 relative error = 2.3361174990628775780801008997780e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50059 y1[1] (analytic) = 2.4799432288416662423791283107017 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005176902374632421058403754861 relative error = 0.02087508421332069174886130104239 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227004519042335738498019575333 y2[1] (numeric) = 1.1227004519042335735641230749474 absolute error = 2.856788825859e-19 relative error = 2.5445690531375009051046252174807e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5006 y1[1] (analytic) = 2.4799520018131498923849151283452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005264632089468921116271931296 relative error = 0.021228766063294078377159362912004 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227052513803868879261103887678 y2[1] (numeric) = 1.1227052513803868876153857750652 absolute error = 3.107246137026e-19 relative error = 2.7676419373701007982103010934476e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50061 y1[1] (analytic) = 2.4799607747366383422097869167518 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005352361324353419364989815362 relative error = 0.021582443476033681114536963944263 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227100509442696768636490522525 y2[1] (numeric) = 1.1227100509442696765261520617864 absolute error = 3.374969904661e-19 relative error = 3.0060921800980033165967616462193e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=3.9MB, time=8.28 NO POLE NO POLE x[1] = 0.50062 y1[1] (analytic) = 2.4799695476121307145613948382496 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000544009007927714288106903034 relative error = 0.021936116451571757212584721584918 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227148505958814607060296730933 y2[1] (numeric) = 1.1227148505958814603399458809642 absolute error = 3.660837921291e-19 relative error = 3.2607014322007128236114417328622e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50063 y1[1] (analytic) = 2.4799783204396261321521896629142 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005527818354231318789017276986 relative error = 0.022289784989940563645145601954591 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227196503352217594880910769056 y2[1] (numeric) = 1.1227196503352217590915153528331 absolute error = 3.965757240725e-19 relative error = 3.5322773940412495291852094483977e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50064 y1[1] (analytic) = 2.4799870932191237176994218562974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005615546149207174261339210818 relative error = 0.022643449091172357108310493213705 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227244501622900932358992378111 y2[1] (numeric) = 1.1227244501622900928068327720086 absolute error = 4.290664658025e-19 relative error = 3.8216542424143193609823053585511e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50065 y1[1] (analytic) = 2.479995865950622593925141667155 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005703273464195936518537319394 relative error = 0.022997108755299394020413779186427 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227292500770859819667473264348 y2[1] (numeric) = 1.1227292500770859815030946074873 absolute error = 4.636527189475e-19 relative error = 4.1296930574817201524256738569570e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=57.2MB, alloc=3.9MB, time=8.88 x[1] = 0.50066 y1[1] (analytic) = 2.480004638634121883556199215175 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005791000299188832829112799594 relative error = 0.023350763982353930522028913296007 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227340500796089456891557579036 y2[1] (numeric) = 1.1227340500796089451887215026469 absolute error = 5.004342552567e-19 relative error = 4.4572822497119068041638594806951e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50067 y1[1] (analytic) = 2.4800134112696207093242445787049 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005878726654177090509566434893 relative error = 0.023704414772368222475963992759089 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227388501698585044028722398452 y2[1] (numeric) = 1.1227388501698585038633582752462 absolute error = 5.395139645990e-19 relative error = 4.8053379868112450873236754042402e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50068 y1[1] (analytic) = 2.4800221838571181939657278824785 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005966452529151936924399472629 relative error = 0.024058061125374525467257333055124 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227436503478341780988718203883 y2[1] (numeric) = 1.1227436503478341775178739174251 absolute error = 5.809979029632e-19 relative error = 5.1748046206558603898155421564199e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50069 y1[1] (analytic) = 2.480030956396613460221899385342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006054177924104599486114501264 relative error = 0.024411703041405094803173042662797 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227484506135354867593569361635 y2[1] (numeric) = 1.1227484506135354861343615957046 absolute error = 6.249953404589e-19 relative error = 5.5666551142187366590230819035094e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5007 y1[1] (analytic) = 2.4800397288881056308388095679803 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006141902839026305655216327647 relative error = 0.024765340520492185513196598099757 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227532509669619503577574603049 y2[1] (numeric) = 1.1227532509669619496861386509869 absolute error = 6.716188093180e-19 relative error = 5.9818914684911743152819590829224e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=3.9MB, time=9.49 NO POLE NO POLE x[1] = 0.50071 y1[1] (analytic) = 2.4800485013315938285673092206422 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006229627273908282940212854266 relative error = 0.025118973562668052349030419213205 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122758051408113088858730750453 y2[1] (numeric) = 1.1227580514081130881377465985551 absolute error = 7.209841518979e-19 relative error = 6.4215451494084039071648007475089e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50072 y1[1] (analytic) = 2.4800572737270771761630495308651 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006317351228741758897615956495 relative error = 0.025472602167964949784589444745552 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227628519369884222181616967581 y2[1] (numeric) = 1.1227628519369884214449511280734 absolute error = 7.732105686847e-19 relative error = 6.8866775147642134635569525741851e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50073 y1[1] (analytic) = 2.4800660460745547963864821711998 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006405074703517961131942359842 relative error = 0.025826226336415132015996708199294 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227676525535874703831627698847 y2[1] (numeric) = 1.1227676525535874695547421035873 absolute error = 8.284206662974e-19 relative error = 7.3783802411234957335512311578925e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50074 y1[1] (analytic) = 2.4800748183740258120028593869342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006492797698228117295714517186 relative error = 0.026179846068050852961578913952735 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227724532579097532920740690167 y2[1] (numeric) = 1.1227724532579097524053335635233 absolute error = 8.867405054934e-19 relative error = 7.8977757507353866336545321042499e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50075 y1[1] (analytic) = 2.480083590625489345782234083817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006580520212863455089461486014 relative error = 0.026533461362904366261862013670887 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227772540499547908744633698639 y2[1] (numeric) = 1.1227772540499547899261637206889 absolute error = 9.482996491750e-19 relative error = 8.4460176384443222387808409501547e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=3.9MB, time=10.10 NO POLE NO POLE x[1] = 0.50076 y1[1] (analytic) = 2.4800923628289445204994599157805 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006668242247415202261719805649 relative error = 0.026887072221007925279566782975256 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227820549297221030511261726687 y2[1] (numeric) = 1.1227820549297221020378949622728 absolute error = 1.0132312103959e-18 relative error = 9.0242910985901072313302646579111e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50077 y1[1] (analytic) = 2.480101134984390458934191372663 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006755963801874586609034374474 relative error = 0.027240678642393783099604398392658 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227868558972112097340857502142 y2[1] (numeric) = 1.1227868558972112086524138498448 absolute error = 1.0816719003694e-18 relative error = 9.6338133519121353341623557689430e-17 % Correct digits = 18 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50078 y1[1] (analytic) = 2.4801099070918262838708838679312 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006843684876232835975959327156 relative error = 0.027594280627094192529072014599176 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227916569524216308265931958329 y2[1] (numeric) = 1.1227916569524216296728311193557 absolute error = 1.1537620764772e-18 relative error = 1.0275834072447963894216575485395e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50079 y1[1] (analytic) = 2.4801186791512511180987938264016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000693140547048117825505891186 relative error = 0.027947878175141406097248341918952 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1227964580953528862231274714163 y2[1] (numeric) = 1.1227964580953528849934816811375 absolute error = 1.2296457902788e-18 relative error = 1.0951635814426242085838399194376e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.0MB, time=10.69 NO POLE NO POLE x[1] = 0.5008 y1[1] (analytic) = 2.4801274511626640844119787719614 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007019125584610841386908367458 relative error = 0.02830147128656767605558922409793 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228012593260044958093954554259 y2[1] (numeric) = 1.1228012593260044944999246199032 absolute error = 1.3094708355227e-18 relative error = 1.1662534439164679757720513902576e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50081 y1[1] (analytic) = 2.4801362231260643056092974152893 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007106845218613053360094800737 relative error = 0.0286550599614052543777232163687 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122806060644375979462331990904 y2[1] (numeric) = 1.122806060644375978068943194747 absolute error = 1.3933887961570e-18 relative error = 1.2409879541951681054469308470174e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50082 y1[1] (analytic) = 2.4801449950414509044944097415756 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.00071945643724790422112180636 relative error = 0.029008644199686392759447163782211 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228108620504668570500999334863 y2[1] (numeric) = 1.1228108620504668555685448391442 absolute error = 1.4815550943421e-18 relative error = 1.3195054878935689394547849394911e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50083 y1[1] (analytic) = 2.4801537669088230038757770982416 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000728228304620003602489163026 relative error = 0.02936222400144334261872177980637 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228156635442766484320901994154 y2[1] (numeric) = 1.1228156635442766468579611609511 absolute error = 1.5741290384643e-18 relative error = 1.4019478794011555456214390852527e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50084 y1[1] (analytic) = 2.4801625387281797265666622826591 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007370001239767262933743474435 relative error = 0.029715799366708355095667225223748 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228204651258048734589218135542 y2[1] (numeric) = 1.1228204651258048717876479424051 absolute error = 1.6712738711491e-18 relative error = 1.4884604645693240188726415993014e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.0MB, time=11.29 NO POLE NO POLE x[1] = 0.50085 y1[1] (analytic) = 2.4801713104995201953851296298689 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007457718953171951118416946533 relative error = 0.030069370295513681052558687284047 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228252667950510519724419574014 y2[1] (numeric) = 1.1228252667950510501992851401248 absolute error = 1.7731568172766e-18 relative error = 1.5791921233994227210636125757021e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50086 y1[1] (analytic) = 2.480180082222843533154045100299 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007545436186405328807571650834 relative error = 0.030422936787891571073821959139541 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122830068552014703805726017107 y2[1] (numeric) = 1.1228300685520147019257768851098 absolute error = 1.8799491319972e-18 relative error = 1.6742953227299612743714910706170e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50087 y1[1] (analytic) = 2.4801888538981488627010763674821 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007633152939458624277884322665 relative error = 0.03077649884387427546602901954734 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228348703966953487830776314892 y2[1] (numeric) = 1.1228348703966953467912514827409 absolute error = 1.9918261487483e-18 relative error = 1.7739261589236106852206799196067e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50088 y1[1] (analytic) = 2.4801976255254353068586929057734 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007720869212323065854049705578 relative error = 0.031130056463494044257893612878792 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228396723290925067200287400517 y2[1] (numeric) = 1.1228396723290925046110614127799 absolute error = 2.1089673272718e-18 relative error = 1.8782444005538164151977761779855e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.0MB, time=11.90 NO POLE NO POLE x[1] = 0.50089 y1[1] (analytic) = 2.4802063971047019884641660780667 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007808585004989881908781428511 relative error = 0.03148360964678312720026682935539 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228444743492056974233396310026 y2[1] (numeric) = 1.1228444743492056951917833293697 absolute error = 2.2315563016329e-18 relative error = 1.9874135310914696382133339539698e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5009 y1[1] (analytic) = 2.4802151686359480303595692235113 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007896300317450300862812882957 relative error = 0.031837158393773773766132685611939 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122849276457034440690998989273 y2[1] (numeric) = 1.1228492764570344383312180610343 absolute error = 2.3597809282387e-18 relative error = 2.1016007915903007249743875471720e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50091 y1[1] (analytic) = 2.480223940119172555391777745227 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007984015149695551184898100114 relative error = 0.03219070270449823315060370547815 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.122854078652578256312223944538 y2[1] (numeric) = 1.1228540786525782538183906106788 absolute error = 2.4938333338592e-18 relative error = 2.2209772233733104509968929012797e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50092 y1[1] (analytic) = 2.4802327115543746864124691980204 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008071729501716861391812628048 relative error = 0.032544242578988754270916501107622 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228588809358366640674601192374 y2[1] (numeric) = 1.1228588809358366614335501555895 absolute error = 2.6339099636479e-18 relative error = 2.3457177107177451923058629568554e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50093 y1[1] (analytic) = 2.4802414829415535462781233760988 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008159443373505460048354408832 relative error = 0.032897778017277585766427354305087 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228636833068091837283816765975 y2[1] (numeric) = 1.1228636833068091809481700474336 absolute error = 2.7802116291639e-18 relative error = 2.4760010235403081845483112855713e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.0MB, time=12.49 NO POLE NO POLE x[1] = 0.50094 y1[1] (analytic) = 2.4802502542807082578500224007851 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008247156765052575767344655695 relative error = 0.033251309019396975998607798188918 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228684857654953350578913686542 y2[1] (numeric) = 1.1228684857654953321249478122596 absolute error = 2.9329435563946e-18 relative error = 2.6120098600818052498660718375319e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50095 y1[1] (analytic) = 2.4802590255718379439942508082317 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008334869676349437209628730161 relative error = 0.033604835585379173051040199108315 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228732883118946378101205842765 y2[1] (numeric) = 1.1228732883118946347178051504969 absolute error = 3.0923154337796e-18 relative error = 2.7539308895917592819579790905393e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50096 y1[1] (analytic) = 2.4802677968149417275816956371335 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008422582107387273084077019179 relative error = 0.033958357715256424729413338819153 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228780909460066117304293971914 y2[1] (numeric) = 1.1228780909460066084718879369562 absolute error = 3.2585414602352e-18 relative error = 2.9019547950124590791288756842512e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50097 y1[1] (analytic) = 2.4802765680100187314880465164412 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008510294058157312147585812256 relative error = 0.034311875409060978561517996966876 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228828936678307765554066140091 y2[1] (numeric) = 1.1228828936678307731235662208291 absolute error = 3.4318403931800e-18 relative error = 3.0562763156628877547099264931206e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=83.9MB, alloc=4.0MB, time=13.09 x[1] = 0.50098 y1[1] (analytic) = 2.4802853391570680785937957530734 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008598005528650783205078178578 relative error = 0.034665388666825081797242533815951 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228876964773666520128698222493 y2[1] (numeric) = 1.1228876964773666484004342256885 absolute error = 3.6124355965608e-18 relative error = 3.2170942899218182096905805510018e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.50099 y1[1] (analytic) = 2.4802941102560888917842384196288 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008685716518858915109504844132 relative error = 0.035018897488580981408568473278276 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228924993746137578218654383686 y2[1] (numeric) = 1.1228924993746137540213103494882 absolute error = 3.8005550888804e-18 relative error = 3.3846116979115005140643729263235e-16 % Correct digits = 17 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.501 y1[1] (analytic) = 2.4803028813070802939494724420977 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008773427028772936761845068821 relative error = 0.035372401874360924089566086208289 % Correct digits = 3 h = 1e-05 y2[1] (analytic) = 1.1228973023595716136926687557886 y2[1] (numeric) = 1.1228973023595716096962371645632 absolute error = 3.9964315912254e-18 relative error = 3.5590357041802490577700971005932e-16 % Correct digits = 17 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff(y1,x,1) = diff(y2,x,5); diff(y2,x,1) = y1 - 2.0; Iterations = 100 Total Elapsed Time = 13 Seconds Elapsed Time(since restart) = 13 Seconds Expected Time Remaining = 1 Days 10 Hours 37 Minutes 51 Seconds Optimized Time Remaining = 1 Days 10 Hours 30 Minutes 1 Seconds Time to Timeout = 46 Seconds Percent Done = 0.01063 % > quit memory used=85.8MB, alloc=4.0MB, time=13.37