|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > glob_max_terms, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_log10abserr, > glob_start, > glob_dump_analytic, > glob_last_good_h, > glob_large_float, > glob_initial_pass, > glob_clock_start_sec, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_look_poles, > glob_disp_incr, > glob_iter, > glob_relerr, > glob_hmin, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_optimal_done, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_max_rel_trunc_err, > glob_max_hours, > glob_not_yet_start_msg, > min_in_hour, > djd_debug2, > glob_display_flag, > glob_orig_start_sec, > glob_max_sec, > glob_hmax, > days_in_year, > hours_in_day, > glob_warned2, > glob_abserr, > glob_reached_optimal_h, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_hmin_init, > centuries_in_millinium, > sec_in_minute, > glob_optimal_expect_sec, > glob_smallish_float, > glob_small_float, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_max_trunc_err, > glob_h, > glob_clock_sec, > glob_almost_1, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_log10_abserr, > djd_debug, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5, > array_const_1D0, > #END CONST > array_pole, > array_y2_init, > array_y1_init, > array_type_pole, > array_1st_rel_error, > array_norms, > array_m1, > array_y2, > array_y1, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_last_rel_error, > array_y1_higher_work, > array_y2_higher, > array_y1_set_initial, > array_y2_set_initial, > array_real_pole, > array_fact_2, > array_poles, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > array_complex_pole, > array_y1_higher_work2, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no, good_digits; > > > > > > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > good_digits := -trunc(log10(relerr/100.0)); > else > good_digits := -1; > fi;# end if 3 > ; > else > relerr := -1.0 ; > 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,"%"); > print("good digits = ",good_digits); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) then # if number 3 > good_digits := -trunc(log10(relerr/100.0)); > else > good_digits := -1; > fi;# end if 3 > ; > else > relerr := -1.0 ; > 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,"%"); > print("good digits = ",good_digits); > 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, good_digits; global glob_max_terms, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_log10abserr, glob_start, glob_dump_analytic, glob_last_good_h, glob_large_float, glob_initial_pass, glob_clock_start_sec, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_start, glob_look_poles, glob_disp_incr, glob_iter, glob_relerr, glob_hmin, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_optimal_done, years_in_century, glob_dump, glob_max_opt_iter, glob_normmax, glob_max_rel_trunc_err, glob_max_hours, glob_not_yet_start_msg, min_in_hour, djd_debug2, glob_display_flag, glob_orig_start_sec, glob_max_sec, glob_hmax, days_in_year, hours_in_day, glob_warned2, glob_abserr, glob_reached_optimal_h, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_hmin_init, centuries_in_millinium, sec_in_minute, glob_optimal_expect_sec, glob_smallish_float, glob_small_float, glob_percent_done, glob_current_iter, glob_warned, glob_max_trunc_err, glob_h, glob_clock_sec, glob_almost_1, glob_subiter_method, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr, djd_debug, glob_log10normmin, array_const_1, array_const_0D0, array_const_5, array_const_1D0, array_pole, array_y2_init, array_y1_init, array_type_pole, array_1st_rel_error, array_norms, array_m1, array_y2, array_y1, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_last_rel_error, array_y1_higher_work, array_y2_higher, array_y1_set_initial, array_y2_set_initial, array_real_pole, array_fact_2, array_poles, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, array_complex_pole, array_y1_higher_work2, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then good_digits := -trunc(log10(relerr/100.0)) else good_digits := -1 end if else relerr := -1.0; 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, "%"); print("good digits = ", good_digits); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if relerr <> 0. then good_digits := -trunc(log10(relerr/100.0)) else good_digits := -1 end if else relerr := -1.0; 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, "%"); print("good digits = ", good_digits); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_log10abserr, > glob_start, > glob_dump_analytic, > glob_last_good_h, > glob_large_float, > glob_initial_pass, > glob_clock_start_sec, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_look_poles, > glob_disp_incr, > glob_iter, > glob_relerr, > glob_hmin, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_optimal_done, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_max_rel_trunc_err, > glob_max_hours, > glob_not_yet_start_msg, > min_in_hour, > djd_debug2, > glob_display_flag, > glob_orig_start_sec, > glob_max_sec, > glob_hmax, > days_in_year, > hours_in_day, > glob_warned2, > glob_abserr, > glob_reached_optimal_h, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_hmin_init, > centuries_in_millinium, > sec_in_minute, > glob_optimal_expect_sec, > glob_smallish_float, > glob_small_float, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_max_trunc_err, > glob_h, > glob_clock_sec, > glob_almost_1, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_log10_abserr, > djd_debug, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5, > array_const_1D0, > #END CONST > array_pole, > array_y2_init, > array_y1_init, > array_type_pole, > array_1st_rel_error, > array_norms, > array_m1, > array_y2, > array_y1, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_last_rel_error, > array_y1_higher_work, > array_y2_higher, > array_y1_set_initial, > array_y2_set_initial, > array_real_pole, > array_fact_2, > array_poles, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > array_complex_pole, > array_y1_higher_work2, > glob_last; > > local hnew, sz2, tmp; > > > > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_log10abserr, glob_start, glob_dump_analytic, glob_last_good_h, glob_large_float, glob_initial_pass, glob_clock_start_sec, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_start, glob_look_poles, glob_disp_incr, glob_iter, glob_relerr, glob_hmin, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_optimal_done, years_in_century, glob_dump, glob_max_opt_iter, glob_normmax, glob_max_rel_trunc_err, glob_max_hours, glob_not_yet_start_msg, min_in_hour, djd_debug2, glob_display_flag, glob_orig_start_sec, glob_max_sec, glob_hmax, days_in_year, hours_in_day, glob_warned2, glob_abserr, glob_reached_optimal_h, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_hmin_init, centuries_in_millinium, sec_in_minute, glob_optimal_expect_sec, glob_smallish_float, glob_small_float, glob_percent_done, glob_current_iter, glob_warned, glob_max_trunc_err, glob_h, glob_clock_sec, glob_almost_1, glob_subiter_method, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr, djd_debug, glob_log10normmin, array_const_1, array_const_0D0, array_const_5, array_const_1D0, array_pole, array_y2_init, array_y1_init, array_type_pole, array_1st_rel_error, array_norms, array_m1, array_y2, array_y1, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_last_rel_error, array_y1_higher_work, array_y2_higher, array_y1_set_initial, array_y2_set_initial, array_real_pole, array_fact_2, array_poles, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, array_complex_pole, array_y1_higher_work2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_log10abserr, > glob_start, > glob_dump_analytic, > glob_last_good_h, > glob_large_float, > glob_initial_pass, > glob_clock_start_sec, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_look_poles, > glob_disp_incr, > glob_iter, > glob_relerr, > glob_hmin, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_optimal_done, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_max_rel_trunc_err, > glob_max_hours, > glob_not_yet_start_msg, > min_in_hour, > djd_debug2, > glob_display_flag, > glob_orig_start_sec, > glob_max_sec, > glob_hmax, > days_in_year, > hours_in_day, > glob_warned2, > glob_abserr, > glob_reached_optimal_h, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_hmin_init, > centuries_in_millinium, > sec_in_minute, > glob_optimal_expect_sec, > glob_smallish_float, > glob_small_float, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_max_trunc_err, > glob_h, > glob_clock_sec, > glob_almost_1, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_log10_abserr, > djd_debug, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5, > array_const_1D0, > #END CONST > array_pole, > array_y2_init, > array_y1_init, > array_type_pole, > array_1st_rel_error, > array_norms, > array_m1, > array_y2, > array_y1, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_last_rel_error, > array_y1_higher_work, > array_y2_higher, > array_y1_set_initial, > array_y2_set_initial, > array_real_pole, > array_fact_2, > array_poles, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > array_complex_pole, > array_y1_higher_work2, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > > > > > > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_log10abserr, glob_start, glob_dump_analytic, glob_last_good_h, glob_large_float, glob_initial_pass, glob_clock_start_sec, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_start, glob_look_poles, glob_disp_incr, glob_iter, glob_relerr, glob_hmin, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_optimal_done, years_in_century, glob_dump, glob_max_opt_iter, glob_normmax, glob_max_rel_trunc_err, glob_max_hours, glob_not_yet_start_msg, min_in_hour, djd_debug2, glob_display_flag, glob_orig_start_sec, glob_max_sec, glob_hmax, days_in_year, hours_in_day, glob_warned2, glob_abserr, glob_reached_optimal_h, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_hmin_init, centuries_in_millinium, sec_in_minute, glob_optimal_expect_sec, glob_smallish_float, glob_small_float, glob_percent_done, glob_current_iter, glob_warned, glob_max_trunc_err, glob_h, glob_clock_sec, glob_almost_1, glob_subiter_method, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr, djd_debug, glob_log10normmin, array_const_1, array_const_0D0, array_const_5, array_const_1D0, array_pole, array_y2_init, array_y1_init, array_type_pole, array_1st_rel_error, array_norms, array_m1, array_y2, array_y1, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_last_rel_error, array_y1_higher_work, array_y2_higher, array_y1_set_initial, array_y2_set_initial, array_real_pole, array_fact_2, array_poles, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, array_complex_pole, array_y1_higher_work2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_max_terms, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_log10abserr, > glob_start, > glob_dump_analytic, > glob_last_good_h, > glob_large_float, > glob_initial_pass, > glob_clock_start_sec, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_look_poles, > glob_disp_incr, > glob_iter, > glob_relerr, > glob_hmin, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_optimal_done, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_max_rel_trunc_err, > glob_max_hours, > glob_not_yet_start_msg, > min_in_hour, > djd_debug2, > glob_display_flag, > glob_orig_start_sec, > glob_max_sec, > glob_hmax, > days_in_year, > hours_in_day, > glob_warned2, > glob_abserr, > glob_reached_optimal_h, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_hmin_init, > centuries_in_millinium, > sec_in_minute, > glob_optimal_expect_sec, > glob_smallish_float, > glob_small_float, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_max_trunc_err, > glob_h, > glob_clock_sec, > glob_almost_1, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_log10_abserr, > djd_debug, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5, > array_const_1D0, > #END CONST > array_pole, > array_y2_init, > array_y1_init, > array_type_pole, > array_1st_rel_error, > array_norms, > array_m1, > array_y2, > array_y1, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_last_rel_error, > array_y1_higher_work, > array_y2_higher, > array_y1_set_initial, > array_y2_set_initial, > array_real_pole, > array_fact_2, > array_poles, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > array_complex_pole, > array_y1_higher_work2, > 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 - 5 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 5 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found ) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if ( not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if ( not found ) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if (array_pole[1] > array_poles[2,1]) then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_max_terms, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_log10abserr, glob_start, glob_dump_analytic, glob_last_good_h, glob_large_float, glob_initial_pass, glob_clock_start_sec, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_start, glob_look_poles, glob_disp_incr, glob_iter, glob_relerr, glob_hmin, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_optimal_done, years_in_century, glob_dump, glob_max_opt_iter, glob_normmax, glob_max_rel_trunc_err, glob_max_hours, glob_not_yet_start_msg, min_in_hour, djd_debug2, glob_display_flag, glob_orig_start_sec, glob_max_sec, glob_hmax, days_in_year, hours_in_day, glob_warned2, glob_abserr, glob_reached_optimal_h, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_hmin_init, centuries_in_millinium, sec_in_minute, glob_optimal_expect_sec, glob_smallish_float, glob_small_float, glob_percent_done, glob_current_iter, glob_warned, glob_max_trunc_err, glob_h, glob_clock_sec, glob_almost_1, glob_subiter_method, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr, djd_debug, glob_log10normmin, array_const_1, array_const_0D0, array_const_5, array_const_1D0, array_pole, array_y2_init, array_y1_init, array_type_pole, array_1st_rel_error, array_norms, array_m1, array_y2, array_y1, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_last_rel_error, array_y1_higher_work, array_y2_higher, array_y1_set_initial, array_y2_set_initial, array_real_pole, array_fact_2, array_poles, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, array_complex_pole, array_y1_higher_work2, glob_last; n := glob_max_terms; m := n - 6; while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 6; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= omniabs(array_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= omniabs(array_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > glob_max_terms, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_log10abserr, > glob_start, > glob_dump_analytic, > glob_last_good_h, > glob_large_float, > glob_initial_pass, > glob_clock_start_sec, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_look_poles, > glob_disp_incr, > glob_iter, > glob_relerr, > glob_hmin, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_optimal_done, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_max_rel_trunc_err, > glob_max_hours, > glob_not_yet_start_msg, > min_in_hour, > djd_debug2, > glob_display_flag, > glob_orig_start_sec, > glob_max_sec, > glob_hmax, > days_in_year, > hours_in_day, > glob_warned2, > glob_abserr, > glob_reached_optimal_h, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_hmin_init, > centuries_in_millinium, > sec_in_minute, > glob_optimal_expect_sec, > glob_smallish_float, > glob_small_float, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_max_trunc_err, > glob_h, > glob_clock_sec, > glob_almost_1, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_log10_abserr, > djd_debug, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5, > array_const_1D0, > #END CONST > array_pole, > array_y2_init, > array_y1_init, > array_type_pole, > array_1st_rel_error, > array_norms, > array_m1, > array_y2, > array_y1, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_last_rel_error, > array_y1_higher_work, > array_y2_higher, > array_y1_set_initial, > array_y2_set_initial, > array_real_pole, > array_fact_2, > array_poles, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > array_complex_pole, > array_y1_higher_work2, > glob_last; > > local iii; > > > > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2 > ; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3 > ; > > # End Function number 7 > end; get_norms := proc() local iii; global glob_max_terms, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_log10abserr, glob_start, glob_dump_analytic, glob_last_good_h, glob_large_float, glob_initial_pass, glob_clock_start_sec, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_start, glob_look_poles, glob_disp_incr, glob_iter, glob_relerr, glob_hmin, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_optimal_done, years_in_century, glob_dump, glob_max_opt_iter, glob_normmax, glob_max_rel_trunc_err, glob_max_hours, glob_not_yet_start_msg, min_in_hour, djd_debug2, glob_display_flag, glob_orig_start_sec, glob_max_sec, glob_hmax, days_in_year, hours_in_day, glob_warned2, glob_abserr, glob_reached_optimal_h, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_hmin_init, centuries_in_millinium, sec_in_minute, glob_optimal_expect_sec, glob_smallish_float, glob_small_float, glob_percent_done, glob_current_iter, glob_warned, glob_max_trunc_err, glob_h, glob_clock_sec, glob_almost_1, glob_subiter_method, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr, djd_debug, glob_log10normmin, array_const_1, array_const_0D0, array_const_5, array_const_1D0, array_pole, array_y2_init, array_y1_init, array_type_pole, array_1st_rel_error, array_norms, array_m1, array_y2, array_y1, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_last_rel_error, array_y1_higher_work, array_y2_higher, array_y1_set_initial, array_y2_set_initial, array_real_pole, array_fact_2, array_poles, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, array_complex_pole, array_y1_higher_work2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_max_terms, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_log10abserr, > glob_start, > glob_dump_analytic, > glob_last_good_h, > glob_large_float, > glob_initial_pass, > glob_clock_start_sec, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_look_poles, > glob_disp_incr, > glob_iter, > glob_relerr, > glob_hmin, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_optimal_done, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_max_rel_trunc_err, > glob_max_hours, > glob_not_yet_start_msg, > min_in_hour, > djd_debug2, > glob_display_flag, > glob_orig_start_sec, > glob_max_sec, > glob_hmax, > days_in_year, > hours_in_day, > glob_warned2, > glob_abserr, > glob_reached_optimal_h, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_hmin_init, > centuries_in_millinium, > sec_in_minute, > glob_optimal_expect_sec, > glob_smallish_float, > glob_small_float, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_max_trunc_err, > glob_h, > glob_clock_sec, > glob_almost_1, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_log10_abserr, > djd_debug, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5, > array_const_1D0, > #END CONST > array_pole, > array_y2_init, > array_y1_init, > array_type_pole, > array_1st_rel_error, > array_norms, > array_m1, > array_y2, > array_y1, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_last_rel_error, > array_y1_higher_work, > array_y2_higher, > array_y1_set_initial, > array_y2_set_initial, > array_real_pole, > array_fact_2, > array_poles, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > array_complex_pole, > array_y1_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > > > > > > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[1] * expt(glob_h , (5)) * factorial_3(0,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,4] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,3] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,2] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > # emit pre mult FULL FULL $eq_no = 2 i = 1 > array_tmp3[1] := (array_m1[1] * (array_y2[1])); > #emit pre add FULL - CONST $eq_no = 2 i = 1 > array_tmp4[1] := array_tmp3[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp1[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,7]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[2] * expt(glob_h , (5)) * factorial_3(1,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,5] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,4] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,3] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > # emit pre mult FULL FULL $eq_no = 2 i = 2 > array_tmp3[2] := ats(2,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp1[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,8]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[3] * expt(glob_h , (5)) * factorial_3(2,7); > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,7] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,6] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,5] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,4] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > # emit pre mult FULL FULL $eq_no = 2 i = 3 > array_tmp3[3] := ats(3,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp1[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,9]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[4] * expt(glob_h , (5)) * factorial_3(3,8); > array_y2[9] := temporary; > array_y2_higher[1,9] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,8] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,7] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,6] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,5] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > # emit pre mult FULL FULL $eq_no = 2 i = 4 > array_tmp3[4] := ats(4,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp1[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,10]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[5] * expt(glob_h , (5)) * factorial_3(4,9); > array_y2[10] := temporary; > array_y2_higher[1,10] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,9] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,8] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,7] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,6] := temporary > ; > temporary := temporary / glob_h * (6.0); > array_y2_higher[6,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > # emit pre mult FULL FULL $eq_no = 2 i = 5 > array_tmp3[5] := ats(5,array_m1,array_y2,1); > #emit pre add FULL CONST $eq_no = 2 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp1[kkk] := array_y1[kkk]; > #emit assign $eq_no = 1 > order_d := 5; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp1[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit mult FULL FULL $eq_no = 2 > array_tmp3[kkk] := ats(kkk,array_m1,array_y2,1); > #emit FULL - NOT FULL add $eq_no = 2 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while ((adj2 <= order_d + 1) and (term >= 1)) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > > #BOTTOM ATOMALL ??? > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_max_terms, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_log10abserr, glob_start, glob_dump_analytic, glob_last_good_h, glob_large_float, glob_initial_pass, glob_clock_start_sec, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_start, glob_look_poles, glob_disp_incr, glob_iter, glob_relerr, glob_hmin, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_optimal_done, years_in_century, glob_dump, glob_max_opt_iter, glob_normmax, glob_max_rel_trunc_err, glob_max_hours, glob_not_yet_start_msg, min_in_hour, djd_debug2, glob_display_flag, glob_orig_start_sec, glob_max_sec, glob_hmax, days_in_year, hours_in_day, glob_warned2, glob_abserr, glob_reached_optimal_h, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_hmin_init, centuries_in_millinium, sec_in_minute, glob_optimal_expect_sec, glob_smallish_float, glob_small_float, glob_percent_done, glob_current_iter, glob_warned, glob_max_trunc_err, glob_h, glob_clock_sec, glob_almost_1, glob_subiter_method, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr, djd_debug, glob_log10normmin, array_const_1, array_const_0D0, array_const_5, array_const_1D0, array_pole, array_y2_init, array_y1_init, array_type_pole, array_1st_rel_error, array_norms, array_m1, array_y2, array_y1, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_last_rel_error, array_y1_higher_work, array_y2_higher, array_y1_set_initial, array_y2_set_initial, array_real_pole, array_fact_2, array_poles, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, array_complex_pole, array_y1_higher_work2, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; if not array_y2_set_initial[1, 6] then if 1 <= glob_max_terms then temporary := array_tmp1[1]*expt(glob_h, 5)*factorial_3(0, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 4] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 3] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 2] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 1] := temporary end if end if; kkk := 2; array_tmp3[1] := array_m1[1]*array_y2[1]; array_tmp4[1] := array_tmp3[1] + array_const_1D0[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_y1[2]; if not array_y2_set_initial[1, 7] then if 2 <= glob_max_terms then temporary := array_tmp1[2]*expt(glob_h, 5)*factorial_3(1, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 4] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 3] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 2] := temporary end if end if; kkk := 3; array_tmp3[2] := ats(2, array_m1, array_y2, 1); array_tmp4[2] := array_tmp3[2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_y1[3]; if not array_y2_set_initial[1, 8] then if 3 <= glob_max_terms then temporary := array_tmp1[3]*expt(glob_h, 5)*factorial_3(2, 7); array_y2[8] := temporary; array_y2_higher[1, 8] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 7] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 6] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 5] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 4] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 3] := temporary end if end if; kkk := 4; array_tmp3[3] := ats(3, array_m1, array_y2, 1); array_tmp4[3] := array_tmp3[3]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_y1[4]; if not array_y2_set_initial[1, 9] then if 4 <= glob_max_terms then temporary := array_tmp1[4]*expt(glob_h, 5)*factorial_3(3, 8); array_y2[9] := temporary; array_y2_higher[1, 9] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 8] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 7] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 5] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 4] := temporary end if end if; kkk := 5; array_tmp3[4] := ats(4, array_m1, array_y2, 1); array_tmp4[4] := array_tmp3[4]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_y1[5]; if not array_y2_set_initial[1, 10] then if 5 <= glob_max_terms then temporary := array_tmp1[5]*expt(glob_h, 5)*factorial_3(4, 9); array_y2[10] := temporary; array_y2_higher[1, 10] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 9] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 8] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 7] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 6] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[6, 5] := temporary end if end if; kkk := 6; array_tmp3[5] := ats(5, array_m1, array_y2, 1); array_tmp4[5] := array_tmp3[5]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y1[kkk]; order_d := 5; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp1[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp3[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > 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); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_minute, years_in_century; secs := 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); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_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 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 11 > fprintf(file,"NA"); > elif (pole = 1) then # if number 12 > fprintf(file,"Real"); > elif (pole = 2) then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > > > > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_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 15 > 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 16 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > > > > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr; > > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_2 := proc(nnn) > local ret; > > > > ret := nnn!; > > # End Function number 17 > end; factorial_2 := proc(nnn) local ret; ret := nnn! end proc > # Begin Function number 18 > 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 18 > 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 19 > 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 19 > 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 20 > convfp := proc(mmm) > (mmm); > > # End Function number 20 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 21 > convfloat := proc(mmm) > (mmm); > > # End Function number 21 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > > > > > > > > > > > > > > > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(1.0 + cos(x)); > end; exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc > exact_soln_y2 := proc(x) > return(1.0 + sin(x)); > end; exact_soln_y2 := proc(x) return 1.0 + sin(x) end proc > exact_soln_y2p := proc(x) > return( cos(x)); > end; exact_soln_y2p := proc(x) return cos(x) end proc > exact_soln_y2pp := proc(x) > return( -sin(x)); > end; exact_soln_y2pp := proc(x) return -sin(x) end proc > exact_soln_y2ppp := proc(x) > return( -cos(x)); > end; exact_soln_y2ppp := proc(x) return -cos(x) end proc > exact_soln_y2pppp := proc(x) > return( sin(x)); > end; exact_soln_y2pppp := proc(x) return sin(x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter; > global > glob_max_terms, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_log10abserr, > glob_start, > glob_dump_analytic, > glob_last_good_h, > glob_large_float, > glob_initial_pass, > glob_clock_start_sec, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_look_poles, > glob_disp_incr, > glob_iter, > glob_relerr, > glob_hmin, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_optimal_done, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_normmax, > glob_max_rel_trunc_err, > glob_max_hours, > glob_not_yet_start_msg, > min_in_hour, > djd_debug2, > glob_display_flag, > glob_orig_start_sec, > glob_max_sec, > glob_hmax, > days_in_year, > hours_in_day, > glob_warned2, > glob_abserr, > glob_reached_optimal_h, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_log10_relerr, > glob_hmin_init, > centuries_in_millinium, > sec_in_minute, > glob_optimal_expect_sec, > glob_smallish_float, > glob_small_float, > glob_percent_done, > glob_current_iter, > glob_warned, > glob_max_trunc_err, > glob_h, > glob_clock_sec, > glob_almost_1, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_log10_abserr, > djd_debug, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_5, > array_const_1D0, > #END CONST > array_pole, > array_y2_init, > array_y1_init, > array_type_pole, > array_1st_rel_error, > array_norms, > array_m1, > array_y2, > array_y1, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_fact_1, > array_last_rel_error, > array_y1_higher_work, > array_y2_higher, > array_y1_set_initial, > array_y2_set_initial, > array_real_pole, > array_fact_2, > array_poles, > array_y1_higher, > array_y2_higher_work2, > array_y2_higher_work, > array_complex_pole, > array_y1_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_log10relerr := 0.0; > glob_log10abserr := 0.0; > glob_start := 0; > glob_dump_analytic := false; > glob_last_good_h := 0.1; > glob_large_float := 9.0e100; > glob_initial_pass := true; > glob_clock_start_sec := 0.0; > glob_max_minutes := 0.0; > glob_unchanged_h_cnt := 0; > glob_optimal_start := 0.0; > glob_look_poles := false; > glob_disp_incr := 0.1; > glob_iter := 0; > glob_relerr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_not_yet_finished := true; > glob_html_log := true; > MAX_UNCHANGED := 10; > glob_optimal_done := false; > years_in_century := 100; > glob_dump := false; > glob_max_opt_iter := 10; > glob_normmax := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_not_yet_start_msg := true; > min_in_hour := 60; > djd_debug2 := true; > glob_display_flag := true; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_hmax := 1.0; > days_in_year := 365; > hours_in_day := 24; > glob_warned2 := false; > glob_abserr := 0.1e-10; > glob_reached_optimal_h := false; > glob_optimal_clock_start_sec := 0.0; > glob_max_iter := 1000; > glob_log10_relerr := 0.1e-10; > glob_hmin_init := 0.001; > centuries_in_millinium := 10; > sec_in_minute := 60; > glob_optimal_expect_sec := 0.1; > glob_smallish_float := 0.1e-100; > glob_small_float := 0.1e-50; > glob_percent_done := 0.0; > glob_current_iter := 0; > glob_warned := false; > glob_max_trunc_err := 0.1e-10; > glob_h := 0.1; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > glob_subiter_method := 3; > glob_curr_iter_when_opt := 0; > glob_no_eqs := 0; > glob_log10_abserr := 0.1e-10; > djd_debug := true; > glob_log10normmin := 0.1; > #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/mtest7postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 5 ) = y1 ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"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 := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"glob_max_minutes := 1;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return( cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return( -sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"return( -cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"return( sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_pole:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_x:= 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_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y1_higher_work := Array(0..(2+ 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),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(6+ 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_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[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_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_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[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 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 <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_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[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 <=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 <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_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_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1D0[1] := 1.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 5.0; > 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 := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > glob_max_minutes := 1; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := true; > array_y2_set_initial[1,5] := true; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > if (glob_html_log) then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 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 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 6) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while (subiter <= 6 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2 > order_diff := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / 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 := 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / 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 := 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / 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 := 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / 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 := 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / 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 := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / 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 := 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / 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 := 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 5 ) = y1 ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-08-12T23:30:21-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest7") > ; > logitem_str(html_log_file,"diff ( y2 , x , 5 ) = y1 ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 5 > ; > log_revs(html_log_file," 119 ") > ; > logitem_str(html_log_file,"mtest7 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest7 maple results") > ; > logitem_str(html_log_file,"1st test with c++") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 5 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if (glob_html_log) then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > > # End Function number 8 > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global glob_max_terms, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_log10abserr, glob_start, glob_dump_analytic, glob_last_good_h, glob_large_float, glob_initial_pass, glob_clock_start_sec, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_start, glob_look_poles, glob_disp_incr, glob_iter, glob_relerr, glob_hmin, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_optimal_done, years_in_century, glob_dump, glob_max_opt_iter, glob_normmax, glob_max_rel_trunc_err, glob_max_hours, glob_not_yet_start_msg, min_in_hour, djd_debug2, glob_display_flag, glob_orig_start_sec, glob_max_sec, glob_hmax, days_in_year, hours_in_day, glob_warned2, glob_abserr, glob_reached_optimal_h, glob_optimal_clock_start_sec, glob_max_iter, glob_log10_relerr, glob_hmin_init, centuries_in_millinium, sec_in_minute, glob_optimal_expect_sec, glob_smallish_float, glob_small_float, glob_percent_done, glob_current_iter, glob_warned, glob_max_trunc_err, glob_h, glob_clock_sec, glob_almost_1, glob_subiter_method, glob_curr_iter_when_opt, glob_no_eqs, glob_log10_abserr, djd_debug, glob_log10normmin, array_const_1, array_const_0D0, array_const_5, array_const_1D0, array_pole, array_y2_init, array_y1_init, array_type_pole, array_1st_rel_error, array_norms, array_m1, array_y2, array_y1, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_fact_1, array_last_rel_error, array_y1_higher_work, array_y2_higher, array_y1_set_initial, array_y2_set_initial, array_real_pole, array_fact_2, array_poles, array_y1_higher, array_y2_higher_work2, array_y2_higher_work, array_complex_pole, array_y1_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_log10relerr := 0.; glob_log10abserr := 0.; glob_start := 0; glob_dump_analytic := false; glob_last_good_h := 0.1; glob_large_float := 0.90*10^101; glob_initial_pass := true; glob_clock_start_sec := 0.; glob_max_minutes := 0.; glob_unchanged_h_cnt := 0; glob_optimal_start := 0.; glob_look_poles := false; glob_disp_incr := 0.1; glob_iter := 0; glob_relerr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_not_yet_finished := true; glob_html_log := true; MAX_UNCHANGED := 10; glob_optimal_done := false; years_in_century := 100; glob_dump := false; glob_max_opt_iter := 10; glob_normmax := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_not_yet_start_msg := true; min_in_hour := 60; djd_debug2 := true; glob_display_flag := true; glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_hmax := 1.0; days_in_year := 365; hours_in_day := 24; glob_warned2 := false; glob_abserr := 0.1*10^(-10); glob_reached_optimal_h := false; glob_optimal_clock_start_sec := 0.; glob_max_iter := 1000; glob_log10_relerr := 0.1*10^(-10); glob_hmin_init := 0.001; centuries_in_millinium := 10; sec_in_minute := 60; glob_optimal_expect_sec := 0.1; glob_smallish_float := 0.1*10^(-100); glob_small_float := 0.1*10^(-50); glob_percent_done := 0.; glob_current_iter := 0; glob_warned := false; glob_max_trunc_err := 0.1*10^(-10); glob_h := 0.1; glob_clock_sec := 0.; glob_almost_1 := 0.9990; glob_subiter_method := 3; glob_curr_iter_when_opt := 0; glob_no_eqs := 0; glob_log10_abserr := 0.1*10^(-10); djd_debug := true; glob_log10normmin := 0.1; 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/mtest7postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "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 := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "glob_max_minutes := 1;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(1.0 +\tcos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(1.0 +\tsin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return(\tcos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return( -sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "return(\t-cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "return( sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_pole := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_x := 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_last_rel_error := Array(0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 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, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 7, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_pole[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_y1_init[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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[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_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_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[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_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[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 <= 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 <= 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; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_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_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 5.0; 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 := 20; glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := true; array_y2_set_initial[1, 5] := true; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 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; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 6 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 6 + 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 := 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; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1) ; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y2 , x , 5 ) = y1 ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-08-12T23:30:21-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest7") ; logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 119 "); logitem_str(html_log_file, "mtest7 diffeq.mxt"); logitem_str(html_log_file, "mtest7 maple results"); logitem_str(html_log_file, "1st test with c++"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;") ; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 5.0; 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 := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; glob_max_minutes := 1; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(1.0 + cos(x)); end; exact_soln_y2 := proc(x) return(1.0 + sin(x)); end; exact_soln_y2p := proc(x) return( cos(x)); end; exact_soln_y2pp := proc(x) return( -sin(x)); end; exact_soln_y2ppp := proc(x) return( -cos(x)); end; exact_soln_y2pppp := proc(x) return( sin(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 x[1] = 0 y2[1] (analytic) = 1 y2[1] (numeric) = 1 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 y1[1] (analytic) = 2 y1[1] (numeric) = 2 absolute error = 0 relative error = 0 % "good digits = ", -1 h = 1e-05 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.48 NO POLE NO POLE x[1] = 1e-05 y2[1] (analytic) = 1.0000099999999998333333333341667 y2[1] (numeric) = 1.000009999999999833333333335 absolute error = 8.333e-28 relative error = 8.3329166708332930558888862430754e-26 % "good digits = ", 27 h = 1e-05 y1[1] (analytic) = 1.9999999999500000000004166666667 y1[1] (numeric) = 1.9999999999500000000004166666666 absolute error = 1e-31 relative error = 5.0000000001250000000020833333333e-30 % "good digits = ", 31 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=7.6MB, alloc=4.3MB, time=1.00 x[1] = 2e-05 y2[1] (analytic) = 1.0000199999999986666666666933333 y2[1] (numeric) = 1.00001999999999866666666672 absolute error = 2.66667e-26 relative error = 2.6666166676666502224844404622814e-24 % "good digits = ", 25 h = 1e-05 y1[1] (analytic) = 1.9999999998000000000066666666666 y1[1] (numeric) = 1.9999999998000000000066666666663 absolute error = 3e-31 relative error = 1.5000000001500000000100000000006e-29 % "good digits = ", 30 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 3e-05 y2[1] (analytic) = 1.0000299999999955000000002025 y2[1] (numeric) = 1.000029999999995500000000405 absolute error = 2.025000e-25 relative error = 2.0249392518224544385934749867452e-23 % "good digits = ", 24 h = 1e-05 y1[1] (analytic) = 1.999999999550000000033749999999 y1[1] (numeric) = 1.9999999995500000000337499999977 absolute error = 1.3e-30 relative error = 6.5000000014625000002193750000279e-29 % "good digits = ", 30 h = 1e-05 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=1.51 NO POLE NO POLE x[1] = 4e-05 y2[1] (analytic) = 1.0000399999999893333333341866667 y2[1] (numeric) = 1.00003999999998933333333504 absolute error = 8.533333e-25 relative error = 8.5329916803328777034697774781099e-23 % "good digits = ", 24 h = 1e-05 y1[1] (analytic) = 1.999999999200000000106666666661 y1[1] (numeric) = 1.9999999992000000001066666666549 absolute error = 6.1e-30 relative error = 3.0500000012200000003253333334070e-28 % "good digits = ", 29 h = 1e-05 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=2.04 NO POLE NO POLE x[1] = 5e-05 y2[1] (analytic) = 1.0000499999999791666666692708333 y2[1] (numeric) = 1.000049999999979166666671875 absolute error = 2.6041667e-24 relative error = 2.6040364981751454934856975826404e-22 % "good digits = ", 23 h = 1e-05 y1[1] (analytic) = 1.999999998750000000260416666645 y1[1] (numeric) = 1.9999999987500000002604166666228 absolute error = 2.22e-29 relative error = 1.1100000006937500002890625001024e-27 % "good digits = ", 28 h = 1e-05 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=2.55 NO POLE NO POLE x[1] = 6e-05 y2[1] (analytic) = 1.00005999999996400000000648 y2[1] (numeric) = 1.00005999999996400000001296 absolute error = 6.4800000e-24 relative error = 6.4796112233268336559846386998089e-22 % "good digits = ", 23 h = 1e-05 y1[1] (analytic) = 1.9999999982000000005399999999352 y1[1] (numeric) = 1.9999999982000000005399999998698 absolute error = 6.54e-29 relative error = 3.2700000029430000017658000009006e-27 % "good digits = ", 28 h = 1e-05 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=3.08 NO POLE NO POLE x[1] = 7e-05 y2[1] (analytic) = 1.0000699999999428333333473391667 y2[1] (numeric) = 1.000069999999942833333361345 absolute error = 1.40058333e-23 relative error = 1.4004852960293580060156489679079e-21 % "good digits = ", 22 h = 1e-05 y1[1] (analytic) = 1.9999999975500000010004166665033 y1[1] (numeric) = 1.9999999975500000010004166663392 absolute error = 1.641e-28 relative error = 8.2050000100511250082084187556979e-27 % "good digits = ", 28 h = 1e-05 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=3.61 NO POLE NO POLE x[1] = 8e-05 y2[1] (analytic) = 1.0000799999999146666666939733333 y2[1] (numeric) = 1.00007999999991466666672128 absolute error = 2.73066667e-23 relative error = 2.7304482341415016781149896495315e-21 % "good digits = ", 22 h = 1e-05 y1[1] (analytic) = 1.9999999968000000017066666663026 y1[1] (numeric) = 1.9999999968000000017066666659377 absolute error = 3.649e-28 relative error = 1.8245000029192000031138133361565e-26 % "good digits = ", 27 h = 1e-05 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=4.14 NO POLE NO POLE x[1] = 9e-05 y2[1] (analytic) = 1.0000899999998785000000492075 y2[1] (numeric) = 1.000089999999878500000098415 absolute error = 4.92075000e-23 relative error = 4.9203071723550858595938355817144e-21 % "good digits = ", 22 h = 1e-05 y1[1] (analytic) = 1.9999999959500000027337499992619 y1[1] (numeric) = 1.9999999959500000027337499985229 absolute error = 7.390e-28 relative error = 3.6950000074823750101012062615911e-26 % "good digits = ", 27 h = 1e-05 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=4.66 NO POLE NO POLE x[1] = 0.0001 y2[1] (analytic) = 1.0000999999998333333334166666666 y2[1] (numeric) = 1.0000999999998333333335 absolute error = 8.33333334e-23 relative error = 8.3325000899923895110631980367746e-21 % "good digits = ", 22 h = 1e-05 y1[1] (analytic) = 1.9999999950000000041666666652778 y1[1] (numeric) = 1.9999999950000000041666666638879 absolute error = 1.3899e-27 relative error = 6.9495000173737500289562500410213e-26 % "good digits = ", 27 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=38.1MB, alloc=4.4MB, time=5.21 x[1] = 0.00011 y2[1] (analytic) = 1.0001099999997781666668008758333 y2[1] (numeric) = 1.000109999999778166666935085 absolute error = 1.342091667e-22 relative error = 1.3419440531544506983454599938542e-20 % "good digits = ", 21 h = 1e-05 y1[1] (analytic) = 1.9999999939500000061004166642062 y1[1] (numeric) = 1.9999999939500000061004166617446 absolute error = 2.4616e-27 relative error = 1.2308000037231700075083928462039e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00012 y2[1] (analytic) = 1.0001199999997120000002073599999 y2[1] (numeric) = 1.00011999999971200000041472 absolute error = 2.073600001e-22 relative error = 2.0733511988567343170267975936677e-20 % "good digits = ", 21 h = 1e-05 y1[1] (analytic) = 1.9999999928000000086399999958528 y1[1] (numeric) = 1.9999999928000000086399999917044 absolute error = 4.1484e-27 relative error = 2.0742000074671200179210880365590e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=5.73 NO POLE NO POLE x[1] = 0.00013 y2[1] (analytic) = 1.0001299999996338333336427441665 y2[1] (numeric) = 1.0001299999996338333339521549999 absolute error = 3.094108334e-22 relative error = 3.0937061522013466370056297683589e-20 % "good digits = ", 21 h = 1e-05 y1[1] (analytic) = 1.9999999915500000119004166599628 y1[1] (numeric) = 1.9999999915500000119004166532576 absolute error = 6.7052e-27 relative error = 3.3526000141647350398973370121875e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=6.26 NO POLE NO POLE x[1] = 0.00014 y2[1] (analytic) = 1.0001399999995426666671148533331 y2[1] (numeric) = 1.0001399999995426666675630399998 absolute error = 4.481866667e-22 relative error = 4.4812392935009592858015404580155e-20 % "good digits = ", 21 h = 1e-05 y1[1] (analytic) = 1.999999990200000016006666656209 y1[1] (numeric) = 1.9999999902000000160066666457499 absolute error = 1.04591e-26 relative error = 5.2295500256247950837076638990949e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.5MB, time=6.79 NO POLE NO POLE x[1] = 0.00015 y2[1] (analytic) = 1.0001499999994375000006328124997 y2[1] (numeric) = 1.0001499999994375000012656249997 absolute error = 6.328125000e-22 relative error = 6.3271759236150167839354392150464e-20 % "good digits = ", 21 h = 1e-05 y1[1] (analytic) = 1.9999999887500000210937499841797 y1[1] (numeric) = 1.9999999887500000210937499683579 absolute error = 1.58218e-26 relative error = 7.9109000444988126668705474068998e-25 % "good digits = ", 26 h = 1e-05 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.5MB, time=7.34 NO POLE NO POLE x[1] = 0.00016 y2[1] (analytic) = 1.0001599999993173333342071466661 y2[1] (numeric) = 1.0001599999993173333350809599995 absolute error = 8.738133334e-22 relative error = 8.7367354563329510059029445474992e-20 % "good digits = ", 21 h = 1e-05 y1[1] (analytic) = 1.999999987200000027306666643365 y1[1] (numeric) = 1.9999999872000000273066666200617 absolute error = 2.33033e-26 relative error = 1.1651650074570560318167723820555e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.5MB, time=7.88 NO POLE NO POLE x[1] = 0.00017 y2[1] (analytic) = 1.0001699999991811666678498808325 y2[1] (numeric) = 1.0001699999991811666690330949992 absolute error = 1.1832141667e-21 relative error = 1.1830130544817068003653162426860e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999855500000348004166331423 y1[1] (numeric) = 1.9999999855500000348004165996162 absolute error = 3.35261e-26 relative error = 1.6763050121113036833361126992544e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.5MB, time=8.43 NO POLE NO POLE x[1] = 0.00018 y2[1] (analytic) = 1.0001799999990280000015746399988 y2[1] (numeric) = 1.0001799999990280000031492799988 absolute error = 1.5746400000e-21 relative error = 1.5743566158106843514448288710932e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999838000000437399999527608 y1[1] (numeric) = 1.9999999838000000437399999055198 absolute error = 4.72410e-26 relative error = 2.3620500191326051033160674742207e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.5MB, time=8.97 NO POLE NO POLE x[1] = 0.00019 y2[1] (analytic) = 1.0001899999988568333353967491649 y2[1] (numeric) = 1.0001899999988568333374601649982 absolute error = 2.0634158333e-21 relative error = 2.0630238587691922335792460487480e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999819500000543004166013252 y1[1] (numeric) = 1.9999999819500000543004165359818 absolute error = 6.53434e-26 relative error = 3.2671700294862094274086932281309e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0002 y2[1] (analytic) = 1.0001999999986666666693333333308 y2[1] (numeric) = 1.0001999999986666666719999999974 absolute error = 2.6666666666e-21 relative error = 2.6661334399155717302333977269286e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999800000000666666665777778 y1[1] (numeric) = 1.9999999800000000666666664888869 absolute error = 8.88909e-26 relative error = 4.4445450444454502963030016790503e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=9.50 NO POLE NO POLE x[1] = 0.00021 y2[1] (analytic) = 1.0002099999984565000034034174964 y2[1] (numeric) = 1.0002099999984565000068068349964 absolute error = 3.4034175000e-21 relative error = 3.4027029323894502874042074142665e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999779500000810337498808804 y1[1] (numeric) = 1.9999999779500000810337497617587 absolute error = 1.191217e-25 relative error = 5.9560850656658376076439058840678e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=10.04 NO POLE NO POLE x[1] = 0.00022 y2[1] (analytic) = 1.0002199999982253333376280266617 y2[1] (numeric) = 1.000219999998225333341922719995 absolute error = 4.2946933333e-21 relative error = 4.2937487085917297921354706523285e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999758000000976066665091946 y1[1] (numeric) = 1.9999999758000000976066663517203 absolute error = 1.574743e-25 relative error = 7.8737150952719522685270807028673e-24 % "good digits = ", 25 h = 1e-05 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=10.58 NO POLE NO POLE x[1] = 0.00023 y2[1] (analytic) = 1.0002299999979721666720302858266 y2[1] (numeric) = 1.0002299999979721666773939049932 absolute error = 5.3636191666e-21 relative error = 5.3623858178727632891224163674096e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999735500001166004164610613 y1[1] (numeric) = 1.9999999735500001166004162554536 absolute error = 2.056077e-25 relative error = 1.0280385135958092823697183476986e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=11.13 NO POLE NO POLE x[1] = 0.00024 y2[1] (analytic) = 1.0002399999976960000066355199909 y2[1] (numeric) = 1.0002399999976960000132710399909 absolute error = 6.6355200000e-21 relative error = 6.6339278573295254836231980982552e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999712000001382399997345792 y1[1] (numeric) = 1.999999971200000138239999469156 absolute error = 2.654232e-25 relative error = 1.3271160191104705834605173370378e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=11.68 NO POLE NO POLE x[1] = 0.00025 y2[1] (analytic) = 1.0002499999973958333414713541546 y2[1] (numeric) = 1.0002499999973958333496093749879 absolute error = 8.1380208333e-21 relative error = 8.1359868366120344570398730411937e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.9999999687500001627604163275825 y1[1] (numeric) = 1.9999999687500001627604159884958 absolute error = 3.390867e-25 relative error = 1.6954335264911487134494653339275e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=12.23 NO POLE NO POLE x[1] = 0.00026 y2[1] (analytic) = 1.0002599999970706666765678133174 y2[1] (numeric) = 1.0002599999970706666864689599841 absolute error = 9.9011466667e-21 relative error = 9.8985730377391840320055553154294e-19 % "good digits = ", 20 h = 1e-05 y1[1] (analytic) = 1.999999966200000190406666237617 y1[1] (numeric) = 1.9999999662000001904066658085647 absolute error = 4.290523e-25 relative error = 2.1452615362549197584720952551344e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.5MB, time=12.79 NO POLE NO POLE x[1] = 0.00027 y2[1] (analytic) = 1.0002699999967195000119574224792 y2[1] (numeric) = 1.0002699999967195000239148449793 absolute error = 1.19574225001e-20 relative error = 1.1954194867524983990442554861738e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.999999963550000221433749461916 y1[1] (numeric) = 1.9999999635500002214337489238293 absolute error = 5.380867e-25 relative error = 2.6904335490331511332527851832619e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=95.3MB, alloc=4.5MB, time=13.33 x[1] = 0.00028 y2[1] (analytic) = 1.0002799999963413333476753066399 y2[1] (numeric) = 1.0002799999963413333620172799733 absolute error = 1.43419733334e-20 relative error = 1.4337958705015053596369463671912e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999608000002561066659973746 y1[1] (numeric) = 1.9999999608000002561066653280797 absolute error = 6.692949e-25 relative error = 3.3464745655909010570544387990179e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00029 y2[1] (analytic) = 1.0002899999959351666837592907991 y2[1] (numeric) = 1.0002899999959351667008519149658 absolute error = 1.70926241667e-20 relative error = 1.7087668742834036654572930637656e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999579500002947004158405232 y1[1] (numeric) = 1.9999999579500002947004150143768 absolute error = 8.261464e-25 relative error = 4.1307320868486415173284560417874e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=13.87 NO POLE NO POLE x[1] = 0.0003 y2[1] (analytic) = 1.0002999999955000000202499999566 y2[1] (numeric) = 1.0002999999955000000404999999566 absolute error = 2.02500000000e-20 relative error = 2.0243926822044484324991763133255e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999550000003374999989875 y1[1] (numeric) = 1.999999955000000337499997974997 absolute error = 1.0125030e-24 relative error = 5.0625151139065892085988342846351e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=14.41 NO POLE NO POLE x[1] = 0.00031 y2[1] (analytic) = 1.0003099999950348333571909591121 y2[1] (numeric) = 1.0003099999950348333810485849454 absolute error = 2.38576258333e-20 relative error = 2.3850232261417380989540879944031e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999519500003848004154340227 y1[1] (numeric) = 1.9999999519500003848004142013756 absolute error = 1.2326471e-24 relative error = 6.1632356480717352591156207023619e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=14.94 NO POLE NO POLE x[1] = 0.00032 y2[1] (analytic) = 1.0003199999945386666946286932652 y2[1] (numeric) = 1.0003199999945386667225907199318 absolute error = 2.79620266666e-20 relative error = 2.7953081680614864339381504417568e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999488000004369066651753586 y1[1] (numeric) = 1.9999999488000004369066636840473 absolute error = 1.4913113e-24 relative error = 7.4565566908878496578192924867651e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=15.47 NO POLE NO POLE x[1] = 0.00033 y2[1] (analytic) = 1.0003299999940105000326128274154 y2[1] (numeric) = 1.0003299999940105000652256549154 absolute error = 3.26128275000e-20 relative error = 3.2602068817485499875160280865087e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999455500004941337482062945 y1[1] (numeric) = 1.9999999455500004941337464125857 absolute error = 1.7937088e-24 relative error = 8.9685442441686148316603471294399e-23 % "good digits = ", 24 h = 1e-05 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.5MB, time=16.02 NO POLE NO POLE x[1] = 0.00034 y2[1] (analytic) = 1.0003399999934493333711961865625 y2[1] (numeric) = 1.0003399999934493334090590398957 absolute error = 3.78628533332e-20 relative error = 3.7849984338772759890945824110516e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.999999942200000556806664521105 y1[1] (numeric) = 1.9999999422000005568066623755399 absolute error = 2.1455651e-24 relative error = 1.0727825810034162923324855059816e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.5MB, time=16.61 NO POLE NO POLE x[1] = 0.00035 y2[1] (analytic) = 1.0003499999928541667104348957057 y2[1] (numeric) = 1.0003499999928541667542031248723 absolute error = 4.37682291666e-20 relative error = 4.3752915646436398301736231448719e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.99999993875000062526041411352 y1[1] (numeric) = 1.9999999387500006252604115603698 absolute error = 2.5531502e-24 relative error = 1.2765751390951132356918927842468e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.5MB, time=17.19 NO POLE NO POLE x[1] = 0.00036 y2[1] (analytic) = 1.0003599999922240000503884798445 y2[1] (numeric) = 1.0003599999922240001007769598445 absolute error = 5.03884800000e-20 relative error = 5.0370346675588467964743982894828e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999352000006998399969766912 y1[1] (numeric) = 1.9999999352000006998399939533788 absolute error = 3.0233124e-24 relative error = 1.5116562489776619379174944313652e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00037 y2[1] (analytic) = 1.0003699999915578333911199639783 y2[1] (numeric) = 1.0003699999915578334489065948116 absolute error = 5.77866308333e-20 relative error = 5.7765257688442940041795259517481e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999315500007809004131031578 y1[1] (numeric) = 1.9999999315500007809004095396452 memory used=125.8MB, alloc=4.5MB, time=17.76 absolute error = 3.5635126e-24 relative error = 1.7817563609806107588742640530026e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00038 y2[1] (analytic) = 1.0003799999908546667326959731063 y2[1] (numeric) = 1.0003799999908546667987252797729 absolute error = 6.60293066666e-20 relative error = 6.6004225061680192162217563373731e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999278000008688066624848106 y1[1] (numeric) = 1.9999999278000008688066583029507 absolute error = 4.1818599e-24 relative error = 2.0909300254825730116139172548653e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=18.34 NO POLE NO POLE x[1] = 0.00039 y2[1] (analytic) = 1.0003899999901135000751868322277 y2[1] (numeric) = 1.0003899999901135001503736647276 absolute error = 7.51868324999e-20 relative error = 7.5157521067426748394508400344721e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999239500009639337451128559 y1[1] (numeric) = 1.9999999239500009639337402257079 absolute error = 4.8871480e-24 relative error = 2.4435740929169037054434999764187e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.5MB, time=18.92 NO POLE NO POLE x[1] = 0.0004 y2[1] (analytic) = 1.0003999999893333334186666663416 y2[1] (numeric) = 1.0003999999893333335039999996748 absolute error = 8.53333333332e-20 relative error = 8.5299213648650398112395113330910e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999200000010666666609777778 y1[1] (numeric) = 1.9999999200000010666666552888849 absolute error = 5.6888929e-24 relative error = 2.8444465637778610340762821057289e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=19.50 NO POLE NO POLE x[1] = 0.00041 y2[1] (analytic) = 1.0004099999885131667632135004469 y2[1] (numeric) = 1.0004099999885131668597603346135 absolute error = 9.65468341666e-20 relative error = 9.6507266188571248660895315105007e-18 % "good digits = ", 19 h = 1e-05 y1[1] (analytic) = 1.9999999159500011774004100692997 y1[1] (numeric) = 1.9999999159500011774004034719286 absolute error = 6.5973711e-24 relative error = 3.2986856886272641226238335135311e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=20.09 NO POLE NO POLE x[1] = 0.00042 y2[1] (analytic) = 1.0004199999876520001089093595426 y2[1] (numeric) = 1.0004199999876520002178187195425 absolute error = 1.089093599999e-19 relative error = 1.0886363727358934065812160109304e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999999118000012965399923763448 y1[1] (numeric) = 1.9999999118000012965399847526854 absolute error = 7.6236594e-24 relative error = 3.8118298681016947121898027433230e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=20.68 NO POLE NO POLE x[1] = 0.00043 y2[1] (analytic) = 1.0004299999867488334558403686273 y2[1] (numeric) = 1.0004299999867488335783474044606 absolute error = 1.225070358333e-19 relative error = 1.2245438045132859209482166730382e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999999075500014245004078869958 y1[1] (numeric) = 1.9999999075500014245003991073206 absolute error = 8.7796752e-24 relative error = 4.3898378029202493133256540996540e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.5MB, time=21.26 NO POLE NO POLE x[1] = 0.00044 y2[1] (analytic) = 1.0004399999858026668040968526998 y2[1] (numeric) = 1.0004399999858026669415270393664 absolute error = 1.374301866666e-19 relative error = 1.3736974398119855666140596821177e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.999999903200001561706656588453 y1[1] (numeric) = 1.9999999032000015617066465102349 absolute error = 1.00782181e-23 relative error = 5.0391092938928858896104132825145e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=152.5MB, alloc=4.5MB, time=21.84 x[1] = 0.00045 y2[1] (analytic) = 1.0004499999848125001537734367586 y2[1] (numeric) = 1.0004499999848125003075468742585 absolute error = 1.537734374999e-19 relative error = 1.5370427058047317065900874841097e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998987500017085937384669922 y1[1] (numeric) = 1.9999998987500017085937269339799 absolute error = 1.15330123e-23 relative error = 5.7665064419293836963666498735021e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00046 y2[1] (analytic) = 1.0004599999837773335049691458019 y2[1] (numeric) = 1.0004599999837773336766049591352 absolute error = 1.716358133333e-19 relative error = 1.7155689716338795186974386533992e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.999999894200001865606653507921 y1[1] (numeric) = 1.9999998942000018656066403491707 absolute error = 1.31587503e-23 relative error = 6.5793754980489577095265102903889e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=22.42 NO POLE NO POLE x[1] = 0.00047 y2[1] (analytic) = 1.0004699999826961668577875048281 y2[1] (numeric) = 1.0004699999826961670489083439947 absolute error = 1.911208391666e-19 relative error = 1.9103105457425566932874929695812e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998895500020332004016955343 y1[1] (numeric) = 1.9999998895500020332003867243972 absolute error = 1.49711371e-23 relative error = 7.4855689633905383934115711335205e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.5MB, time=23.01 NO POLE NO POLE x[1] = 0.00048 y2[1] (analytic) = 1.0004799999815680002123366388352 y2[1] (numeric) = 1.0004799999815680004246732788351 absolute error = 2.123366399999e-19 relative error = 2.1223476731550047096003327157464e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998848000022118399830130689 y1[1] (numeric) = 1.9999998848000022118399660261328 absolute error = 1.69869361e-23 relative error = 8.4934685392237784661929848933373e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.5MB, time=23.59 NO POLE NO POLE x[1] = 0.00049 y2[1] (analytic) = 1.000489999980391833568729372821 y2[1] (numeric) = 1.0004899999803918338041254136542 absolute error = 2.353960408332e-19 relative error = 2.3528075326871175540801769206243e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998799500024020003974426568 y1[1] (numeric) = 1.9999998799500024020003782186418 absolute error = 1.92240150e-23 relative error = 9.6120080769607732755468053237946e-22 % "good digits = ", 23 h = 1e-05 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.5MB, time=24.18 NO POLE NO POLE x[1] = 0.0005 y2[1] (analytic) = 1.0004999999791666669270833317832 y2[1] (numeric) = 1.0004999999791666671874999984498 absolute error = 2.604166666666e-19 relative error = 2.6028652341031747709804964088448e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998750000026041666449652779 y1[1] (numeric) = 1.9999998750000026041666232638839 absolute error = 2.17013940e-23 relative error = 1.0850697678168590757024438269613e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.5MB, time=24.77 NO POLE NO POLE x[1] = 0.00051 y2[1] (analytic) = 1.0005099999778915002875210407194 y2[1] (numeric) = 1.0005099999778915005750420832193 absolute error = 2.875210424999e-19 relative error = 2.8737448152067787292688098744698e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998699500028188337255607115 y1[1] (numeric) = 1.9999998699500028188337011214177 absolute error = 2.44392938e-23 relative error = 1.2219647694582574117654364020697e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=25.34 NO POLE NO POLE x[1] = 0.00052 y2[1] (analytic) = 1.0005199999765653336501700246268 y2[1] (numeric) = 1.0005199999765653339670067179601 absolute error = 3.168366933333e-19 relative error = 3.1667202388829918764457250138803e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998648000030465066392074867 y1[1] (numeric) = 1.9999998648000030465066117483013 absolute error = 2.74591854e-23 relative error = 1.3729593628120508347297293432330e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=179.2MB, alloc=4.5MB, time=25.92 x[1] = 0.00053 y2[1] (analytic) = 1.0005299999751871670151629085026 y2[1] (numeric) = 1.0005299999751871673636591526691 absolute error = 3.484962441665e-19 relative error = 3.4831163900646916986531377161991e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998595500032877003858828319 y1[1] (numeric) = 1.9999998595500032877003550989916 absolute error = 3.07838403e-23 relative error = 1.5391921230897643137774304200033e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00054 y2[1] (analytic) = 1.0005399999737560003826375173434 y2[1] (numeric) = 1.0005399999737560007652750373433 absolute error = 3.826375199999e-19 relative error = 3.8243100726601287225733782821688e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998542000035429399655626234 y1[1] (numeric) = 1.9999998542000035429399311252411 absolute error = 3.44373823e-23 relative error = 1.7218692405242645839792143088955e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.5MB, time=26.50 NO POLE NO POLE x[1] = 0.00055 y2[1] (analytic) = 1.000549999972270833752736976146 y2[1] (numeric) = 1.0005499999722708341721406219792 absolute error = 4.194036458332e-19 relative error = 4.1917310063947161120784830627339e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998487500038127603782213327 y1[1] (numeric) = 1.9999998487500038127603397759929 absolute error = 3.84453398e-23 relative error = 1.9222671353714484478938038213281e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=27.08 NO POLE NO POLE x[1] = 0.00056 y2[1] (analytic) = 1.0005599999707306671256098099066 y2[1] (numeric) = 1.0005599999707306675845529565731 absolute error = 4.589431466665e-19 relative error = 4.5868628236180283189750153597278e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998432000040977066238319732 y1[1] (numeric) = 1.9999998432000040977065809972739 absolute error = 4.28346993e-23 relative error = 2.1417351329120300322020342110010e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=27.66 NO POLE NO POLE x[1] = 0.00057 y2[1] (analytic) = 1.0005699999691345005014100436212 y2[1] (numeric) = 1.0005699999691345010028200911211 absolute error = 5.014100474999e-19 relative error = 5.0112440660360340118208092407770e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998375500043983337023660458 y1[1] (numeric) = 1.9999998375500043983336547320855 absolute error = 4.76339603e-23 relative error = 2.3816982084534317438782438437300e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=28.27 NO POLE NO POLE x[1] = 0.00058 y2[1] (analytic) = 1.0005799999674813338802973022857 y2[1] (numeric) = 1.0005799999674813344272612756189 absolute error = 5.469639733332e-19 relative error = 5.4664691813845592418028433583774e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998318000047152066137934829 y1[1] (numeric) = 1.999999831800004715206560920293 absolute error = 5.28731899e-23 relative error = 2.6436597173317759949014692801137e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=28.85 NO POLE NO POLE x[1] = 0.00059 y2[1] (analytic) = 1.0005899999657701672624369108955 y2[1] (numeric) = 1.000589999965770167858207160062 absolute error = 5.957702491665e-19 relative error = 5.9541895200519802430157510373969e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998259500050489003580825925 y1[1] (numeric) = 1.9999998259500050489002994985121 absolute error = 5.85840804e-23 relative error = 2.9292042749139946297601263997109e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=29.44 NO POLE NO POLE x[1] = 0.0006 y2[1] (analytic) = 1.0005999999640000006479999944457 y2[1] (numeric) = 1.0005999999640000012959999944455 absolute error = 6.479999999998e-19 relative error = 6.4761143316321608152530838880889e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998200000053999999352000004 y1[1] (numeric) = 1.9999998200000053999998703999944 absolute error = 6.48000060e-23 relative error = 3.2400005916000444960025122961245e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.5MB, time=30.02 NO POLE NO POLE x[1] = 0.00061 y2[1] (analytic) = 1.0006099999621698340371635779311 y2[1] (numeric) = 1.0006099999621698347409938287642 absolute error = 7.038302508331e-19 relative error = 7.0340117614226300280020801769441e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998139500057691003451105916 y1[1] (numeric) = 1.99999981395000576910027355451 absolute error = 7.15560816e-23 relative error = 3.5778044128252451827120967376330e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=209.8MB, alloc=4.5MB, time=30.60 x[1] = 0.00062 y2[1] (analytic) = 1.000619999960278667430110686346 y2[1] (numeric) = 1.0006199999602786681935547130125 absolute error = 7.634440266665e-19 relative error = 7.6297098468630071777887757336804e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998078000061568065877774511 y1[1] (numeric) = 1.9999998078000061568065088882288 absolute error = 7.88892223e-23 relative error = 3.9444614940627374367858117351419e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00063 y2[1] (analytic) = 1.0006299999583255008270304446846 y2[1] (numeric) = 1.0006299999583255016540608971844 absolute error = 8.270304524998e-19 relative error = 8.2650975139086813302698300748617e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999998015500065637336631618031 y1[1] (numeric) = 1.9999998015500065637335763235993 absolute error = 8.68382038e-23 relative error = 4.3419106208260671018940560075277e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.5MB, time=31.18 NO POLE NO POLE x[1] = 0.00064 y2[1] (analytic) = 1.0006399999563093342281181779404 y2[1] (numeric) = 1.0006399999563093351229030312736 absolute error = 8.947848533332e-19 relative error = 8.9421255733557397462780647702764e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999997952000069905065712229497 y1[1] (numeric) = 1.9999997952000069905064757792256 absolute error = 9.54437241e-23 relative error = 4.7721866936719007520014163968731e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.5MB, time=31.76 NO POLE NO POLE x[1] = 0.00065 y2[1] (analytic) = 1.0006499999542291676335755111067 y2[1] (numeric) = 1.0006499999542291686004843652732 absolute error = 9.669088541665e-19 relative error = 9.6628077170911654946364589452342e-17 % "good digits = ", 18 h = 1e-05 y1[1] (analytic) = 1.9999997887500074377603119182083 y1[1] (numeric) = 1.9999997887500074377602071697426 absolute error = 1.047484657e-22 relative error = 5.2374238382028734328269261025123e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.5MB, time=32.35 NO POLE NO POLE x[1] = 0.00066 y2[1] (analytic) = 1.0006599999520840010436104691763 y2[1] (numeric) = 1.0006599999520840020872209491761 absolute error = 1.0436104799998e-18 relative error = 1.0429221514298289695995714919546e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997822000079061398852028481 y1[1] (numeric) = 1.9999997822000079061397704056887 absolute error = 1.147971594e-22 relative error = 5.7398585950705783131234913432067e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.5MB, time=32.94 NO POLE NO POLE x[1] = 0.00067 y2[1] (analytic) = 1.0006699999498728344584375771414 y2[1] (numeric) = 1.0006699999498728355835418329746 absolute error = 1.1251042558332e-18 relative error = 1.1243509407592518270101536582790e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997755500083963002910300258 y1[1] (numeric) = 1.9999997755500083963001653933772 absolute error = 1.256366486e-22 relative error = 6.2818331349786972009056036597840e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.5MB, time=33.51 NO POLE NO POLE x[1] = 0.00068 y2[1] (analytic) = 1.0006799999475946678782779599941 y2[1] (numeric) = 1.0006799999475946690898892666606 absolute error = 1.2116113066665e-18 relative error = 1.2107879709097331272180022468691e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997688000089089065293507197 y1[1] (numeric) = 1.9999997688000089089063920347649 absolute error = 1.373159548e-22 relative error = 6.8657985336862799107552647011604e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.5MB, time=34.10 NO POLE NO POLE x[1] = 0.00069 y2[1] (analytic) = 1.0006899999452485013033594427255 y2[1] (numeric) = 1.0006899999452485026067189002254 absolute error = 1.3033594574999e-18 relative error = 1.3024607596470552104890038008691e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997619500094446336001136637 y1[1] (numeric) = 1.9999997619500094446334502273192 absolute error = 1.498863445e-22 relative error = 7.4943181170111784867111704486271e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=236.5MB, alloc=4.5MB, time=34.70 x[1] = 0.0007 y2[1] (analytic) = 1.0006999999428333347339166503265 y2[1] (numeric) = 1.0006999999428333361344999836598 absolute error = 1.4005833333333e-18 relative error = 1.3996036108856906876473507043409e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997550000100041665032652792 y1[1] (numeric) = 1.9999997550000100041663398638834 absolute error = 1.634013958e-22 relative error = 8.1700707908336310097455312118873e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00071 y2[1] (analytic) = 1.0007099999403481681701911077875 y2[1] (numeric) = 1.0007099999403481696737155669541 absolute error = 1.5035244591666e-18 relative error = 1.5024577142790862036989488548526e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997479500105882002387496073 y1[1] (numeric) = 1.9999997479500105882000608325392 absolute error = 1.779170681e-22 relative error = 8.8958545261000195562104560044218e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.5MB, time=35.24 NO POLE NO POLE x[1] = 0.00072 y2[1] (analytic) = 1.000719999937792001612431340098 y2[1] (numeric) = 1.000719999937792003224862700098 absolute error = 1.6124313600000e-18 relative error = 1.6112712448039750969289126132276e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997408000111974398065082386 y1[1] (numeric) = 1.9999997408000111974396130164682 absolute error = 1.934917704e-22 relative error = 9.6745897738267805226324331903988e-21 % "good digits = ", 22 h = 1e-05 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.5MB, time=35.76 NO POLE NO POLE x[1] = 0.00073 y2[1] (analytic) = 1.0007299999351638350608929722472 y2[1] (numeric) = 1.0007299999351638367884526330806 absolute error = 1.7275596608334e-18 relative error = 1.7262994623378200280539472983010e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997335500118326002064802433 y1[1] (numeric) = 1.9999997335500118325999962938106 absolute error = 2.101864327e-22 relative error = 1.0509323035104499175487945081844e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.5MB, time=36.28 NO POLE NO POLE x[1] = 0.00074 y2[1] (analytic) = 1.0007399999324626685158388292237 y2[1] (numeric) = 1.0007399999324626703650110158904 absolute error = 1.8491721866667e-18 relative error = 1.8478048112311847293544261060419e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997262000124944064386020992 y1[1] (numeric) = 1.9999997262000124944062105375222 absolute error = 2.280645770e-22 relative error = 1.1403230411102172041589617824498e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.5MB, time=36.80 NO POLE NO POLE x[1] = 0.00075 y2[1] (analytic) = 1.0007499999296875019775390360151 y2[1] (numeric) = 1.0007499999296875039550780985152 absolute error = 1.9775390625001e-18 relative error = 1.9760570198741359033746393070330e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997187500131835935028076197 y1[1] (numeric) = 1.9999997187500131835932556152294 absolute error = 2.471923903e-22 relative error = 1.2359621253071657241090574949126e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.5MB, time=37.31 NO POLE NO POLE x[1] = 0.00076 y2[1] (analytic) = 1.0007599999268373354462711176087 y2[1] (numeric) = 1.0007599999268373375592089309422 absolute error = 2.1129378133335e-18 relative error = 2.1113332002557763726482515829414e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997112000139009063990278797 y1[1] (numeric) = 1.9999997112000139009061313890825 absolute error = 2.676387972e-22 relative error = 1.3381941792352301805112234293844e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.5MB, time=37.85 NO POLE NO POLE x[1] = 0.00077 y2[1] (analytic) = 1.000769999923911168922320098991 y2[1] (numeric) = 1.0007699999239111711779735631578 absolute error = 2.2556534641668e-18 relative error = 2.2539179475187085763678987272312e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999997035500146471001271911418 y1[1] (numeric) = 1.9999997035500146470998377156063 absolute error = 2.894755355e-22 relative error = 1.4473778920375774473254638511932e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.5MB, time=38.36 NO POLE NO POLE x[1] = 0.00078 y2[1] (analytic) = 1.0007799999209080024059786051477 y2[1] (numeric) = 1.0007799999209080048119572451478 absolute error = 2.4059786400001e-18 relative error = 2.4041034395074295484055438536198e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996958000154229396872227802 y1[1] (numeric) = 1.9999996958000154229393744455493 absolute error = 3.127772309e-22 relative error = 1.5638863923671082191744065632622e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=267.0MB, alloc=4.5MB, time=38.87 x[1] = 0.00079 y2[1] (analytic) = 1.0007899999178268358975469610637 y2[1] (numeric) = 1.0007899999178268384617606268971 absolute error = 2.5642136658334e-18 relative error = 2.5621895363102581173161311558692e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996879500162292000790452044 y1[1] (numeric) = 1.9999996879500162291997414237306 absolute error = 3.376214738e-22 relative error = 1.6881076323869796448602386035273e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.0008 y2[1] (analytic) = 1.0007999999146666693973332917232 y2[1] (numeric) = 1.0007999999146666721279999583899 absolute error = 2.7306666666667e-18 relative error = 2.7284838797956940617092852641583e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996800000170666663025777819 y1[1] (numeric) = 1.9999996800000170666659384888851 absolute error = 3.640888968e-22 relative error = 1.8204447752711485089220105155751e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.5MB, time=39.38 NO POLE NO POLE x[1] = 0.00081 y2[1] (analytic) = 1.0008099999114265029056536221095 y2[1] (numeric) = 1.0008099999114265058113072896096 absolute error = 2.9056536675001e-18 relative error = 2.9033019931428099346066133664629e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996719500179361333577367595 y1[1] (numeric) = 1.9999996719500179361329654735063 absolute error = 3.922632532e-22 relative error = 1.9613165877049357090841427740605e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.5MB, time=39.92 NO POLE NO POLE x[1] = 0.00082 y2[1] (analytic) = 1.0008199999081053364228319772053 y2[1] (numeric) = 1.0008199999081053395123306705387 absolute error = 3.0894986933334e-18 relative error = 3.0869673803651763842572586080654e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996638000188384062444351836 y1[1] (numeric) = 1.9999996638000188384058222036874 absolute error = 4.222314962e-22 relative error = 2.1111578358856123269469528918889e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.5MB, time=40.45 NO POLE NO POLE x[1] = 0.00083 y2[1] (analytic) = 1.000829999904702169949200481992 y2[1] (numeric) = 1.0008299999047021732317343511587 absolute error = 3.2825338691667e-18 relative error = 3.2798116258298201801674276972207e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996555500197742999625828204 y1[1] (numeric) = 1.9999996555500197742995084989602 absolute error = 4.540838602e-22 relative error = 2.2704196920230090106827113558871e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.5MB, time=40.97 NO POLE NO POLE x[1] = 0.00084 y2[1] (analytic) = 1.0008399999012160034850994614503 y2[1] (numeric) = 1.0008399999012160069701989814504 absolute error = 3.4850995200001e-18 relative error = 3.4821744937693168868718114248445e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996472000207446395120860734 y1[1] (numeric) = 1.9999996472000207446390241721322 absolute error = 4.879139412e-22 relative error = 2.4395701363401467464003646515156e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.5MB, time=41.50 NO POLE NO POLE x[1] = 0.00085 y2[1] (analytic) = 1.0008499998976458370308775405601 y2[1] (numeric) = 1.0008499998976458407284218113935 absolute error = 3.6975442708334e-18 relative error = 3.6944040277879179017175270701200e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996387500217502598928479017 y1[1] (numeric) = 1.9999996387500217502593690291216 absolute error = 5.238187801e-22 relative error = 2.6190943735738927437927222836412e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.5MB, time=42.02 NO POLE NO POLE x[1] = 0.00086 y2[1] (analytic) = 1.0008599998939906705868917443 y2[1] (numeric) = 1.0008599998939906745071168909668 absolute error = 3.9202251466668e-18 relative error = 3.9168566503627114150952425537969e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996302000227920061047677364 y1[1] (numeric) = 1.9999996302000227920055428687902 absolute error = 5.618989462e-22 relative error = 2.8094952504756397959293481889650e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=293.7MB, alloc=4.5MB, time=42.53 x[1] = 0.00087 y2[1] (analytic) = 1.0008699998902495041535075976479 y2[1] (numeric) = 1.000869999890249508307015270148 absolute error = 4.1535076725001e-18 relative error = 4.1498972623373198140153288735518e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996215500238707331477413956 y1[1] (numeric) = 1.9999996215500238707325454827745 absolute error = 6.022586211e-22 relative error = 3.0112936753120097700211723050528e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00088 y2[1] (analytic) = 1.0008799998864213377310992255802 y2[1] (numeric) = 1.0008799998864213421288651989137 absolute error = 4.3977659733335e-18 relative error = 4.3938993424112313258884885737191e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996128000249873060216609995 y1[1] (numeric) = 1.9999996128000249873053766553147 absolute error = 6.450056848e-22 relative error = 3.2250290483655834711830798925509e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.5MB, time=43.06 NO POLE NO POLE x[1] = 0.00089 y2[1] (analytic) = 1.0008899998825051713200494530727 y2[1] (numeric) = 1.0008899998825051759734323272395 absolute error = 4.6533828741668e-18 relative error = 4.6492450466215690537860403733818e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999996039500261425997264148834 y1[1] (numeric) = 1.9999996039500261425990361630816 absolute error = 6.902518018e-22 relative error = 3.4512596924356554821203312193378e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.5MB, time=43.58 NO POLE NO POLE x[1] = 0.0009 y2[1] (analytic) = 1.0008999998785000049207499050998 y2[1] (numeric) = 1.0008999998785000098414999050999 absolute error = 4.9207500000001e-18 relative error = 4.9163253078203951450776008774403e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995950000273374992618875107 y1[1] (numeric) = 1.9999995950000273374985237750018 absolute error = 7.381125089e-22 relative error = 3.6905632918390161520151374839424e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.5MB, time=44.10 NO POLE NO POLE x[1] = 0.00091 y2[1] (analytic) = 1.0009099998744048385336011066347 y2[1] (numeric) = 1.0009099998744048437338689824681 absolute error = 5.2002678758334e-18 relative error = 5.1955399351449527700389185617860e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995859500285728996279593838 y1[1] (numeric) = 1.9999995859500285728988392520804 absolute error = 7.887073034e-22 relative error = 3.9435373334107601102144084890139e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.5MB, time=44.61 NO POLE NO POLE x[1] = 0.00092 y2[1] (analytic) = 1.0009199998702186721590125826495 y2[1] (numeric) = 1.0009199998702186776513586093162 absolute error = 5.4923460266667e-18 relative error = 5.4872977134824449341751247123212e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995768000298497058245069553 y1[1] (numeric) = 1.9999995768000298497049823472222 absolute error = 8.421597331e-22 relative error = 4.2107995565051233109200687695448e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.5MB, time=45.14 NO POLE NO POLE x[1] = 0.00093 y2[1] (analytic) = 1.0009299998659405057974029581149 y2[1] (numeric) = 1.000929999865940511594806035615 absolute error = 5.7974030775001e-18 relative error = 5.7920165029288509713923418113847e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995675500311688328514025369 y1[1] (numeric) = 1.9999995675500311688319528050507 absolute error = 8.985974862e-22 relative error = 4.4929884024963473091704365760006e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.5MB, time=45.70 NO POLE NO POLE x[1] = 0.00094 y2[1] (analytic) = 1.0009399998615693394492000580005 y2[1] (numeric) = 1.0009399998615693455650669113339 absolute error = 6.1158668533334e-18 relative error = 6.1101233382412816050508516316124e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995582000325312057085142081 y1[1] (numeric) = 1.9999995582000325312047503617252 absolute error = 9.581524829e-22 relative error = 4.7907634727795732123517056943897e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.5MB, time=46.25 NO POLE NO POLE x[1] = 0.00095 y2[1] (analytic) = 1.0009499998571041731148410072743 y2[1] (numeric) = 1.0009499998571041795630154864411 absolute error = 6.4481744791668e-18 relative error = 6.4420545282854715107234480370303e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995487500339377593957057239 y1[1] (numeric) = 1.9999995487500339377583747447554 absolute error = 1.0209609685e-21 relative error = 5.1048059942717658347283687848278e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=324.2MB, alloc=4.5MB, time=46.81 x[1] = 0.00096 y2[1] (analytic) = 1.0009599998525440067947723309033 y2[1] (numeric) = 1.0009599998525440135895448109034 absolute error = 6.7947724800001e-18 relative error = 6.7882557554758122148285535721184e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995392000353894389128364211 y1[1] (numeric) = 1.9999995392000353894378256728149 absolute error = 1.0871636062e-21 relative error = 5.4358192834126667129811748954540e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.00097 y2[1] (analytic) = 1.0009699998478878404894500538526 y2[1] (numeric) = 1.0009699998478878476455669346861 absolute error = 7.1561168808335e-18 relative error = 7.1491821752110228472438530030316e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995295500368871992597611237 y1[1] (numeric) = 1.9999995295500368871981028555518 absolute error = 1.1569055719e-21 relative error = 5.7845292201657791259544108197673e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.5MB, time=47.34 NO POLE NO POLE x[1] = 0.00098 y2[1] (analytic) = 1.0009799998431346741993398010862 y2[1] (numeric) = 1.000979999843134681732013107753 absolute error = 7.5326733066668e-18 relative error = 7.5252985153022621864074345513933e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995198000384320054363300477 y1[1] (numeric) = 1.999999519800038432004205993398 absolute error = 1.2303366497e-21 relative error = 6.1516847255193843864137843032006e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.5MB, time=47.88 NO POLE NO POLE x[1] = 0.00099 y2[1] (analytic) = 1.0009899998382835079249168975664 y2[1] (numeric) = 1.0009899998382835158498339800665 absolute error = 7.9249170825001e-18 relative error = 7.9170791753967794600603989541153e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995099500400248324423887043 y1[1] (numeric) = 1.999999509950040024831134777376 absolute error = 1.3076113283e-21 relative error = 6.5380582434875902682039583821701e-20 % "good digits = ", 21 h = 1e-05 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.5MB, time=48.42 NO POLE NO POLE x[1] = 0.001 y2[1] (analytic) = 1.000999999833333341666666468254 y2[1] (numeric) = 1.0009999998333333499999998015874 absolute error = 8.3333333333334e-18 relative error = 8.3250083263945068115458042628277e-16 % "good digits = ", 17 h = 1e-05 y1[1] (analytic) = 1.9999995000000416666652777778026 y1[1] (numeric) = 1.9999995000000416666638888889039 absolute error = 1.3888888987e-21 relative error = 6.9444462296114127268948873513077e-20 % "good digits = ", 21 h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 100 Total Elapsed Time = 48 Seconds Elapsed Time(since restart) = 48 Seconds Expected Time Remaining = 2 Days 18 Hours 50 Minutes 14 Seconds Optimized Time Remaining = 2 Days 18 Hours 46 Minutes 46 Seconds Time to Timeout = 11 Seconds Percent Done = 0.0202 % > quit memory used=337.9MB, alloc=4.5MB, time=48.73