|\^/| 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, > INFO, > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_smallish_float, > glob_optimal_start, > glob_disp_incr, > glob_reached_optimal_h, > days_in_year, > glob_relerr, > centuries_in_millinium, > glob_log10_relerr, > glob_large_float, > glob_hmin, > glob_dump, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_unchanged_h_cnt, > glob_almost_1, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_log10_abserr, > glob_dump_analytic, > glob_not_yet_start_msg, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmax, > min_in_hour, > glob_look_poles, > glob_not_yet_finished, > years_in_century, > glob_html_log, > glob_warned2, > glob_max_hours, > glob_hmin_init, > hours_in_day, > sec_in_min, > glob_max_opt_iter, > glob_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > djd_debug2, > glob_subiter_method, > glob_normmax, > glob_display_flag, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_last_good_h, > glob_initial_pass, > glob_clock_sec, > djd_debug, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_fact_1, > array_last_rel_error, > array_type_pole, > array_y_init, > array_pole, > array_real_pole, > array_poles, > array_y_higher, > array_y_higher_work, > array_complex_pole, > array_y_higher_work2, > array_fact_2, > array_y_set_initial, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr, glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium, glob_log10_relerr, glob_large_float, glob_hmin, glob_dump, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr, glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished, years_in_century, glob_html_log, glob_warned2, glob_max_hours, glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err, glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax, glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned, glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole, array_y_init, array_pole, array_real_pole, array_poles, array_y_higher, array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2, array_y_set_initial, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > INFO, > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_smallish_float, > glob_optimal_start, > glob_disp_incr, > glob_reached_optimal_h, > days_in_year, > glob_relerr, > centuries_in_millinium, > glob_log10_relerr, > glob_large_float, > glob_hmin, > glob_dump, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_unchanged_h_cnt, > glob_almost_1, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_log10_abserr, > glob_dump_analytic, > glob_not_yet_start_msg, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmax, > min_in_hour, > glob_look_poles, > glob_not_yet_finished, > years_in_century, > glob_html_log, > glob_warned2, > glob_max_hours, > glob_hmin_init, > hours_in_day, > sec_in_min, > glob_max_opt_iter, > glob_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > djd_debug2, > glob_subiter_method, > glob_normmax, > glob_display_flag, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_last_good_h, > glob_initial_pass, > glob_clock_sec, > djd_debug, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_fact_1, > array_last_rel_error, > array_type_pole, > array_y_init, > array_pole, > array_real_pole, > array_poles, > array_y_higher, > array_y_higher_work, > array_complex_pole, > array_y_higher_work2, > array_fact_2, > array_y_set_initial, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr, glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium, glob_log10_relerr, glob_large_float, glob_hmin, glob_dump, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr, glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished, years_in_century, glob_html_log, glob_warned2, glob_max_hours, glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err, glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax, glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned, glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole, array_y_init, array_pole, array_real_pole, array_poles, array_y_higher, array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2, array_y_set_initial, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > INFO, > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_smallish_float, > glob_optimal_start, > glob_disp_incr, > glob_reached_optimal_h, > days_in_year, > glob_relerr, > centuries_in_millinium, > glob_log10_relerr, > glob_large_float, > glob_hmin, > glob_dump, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_unchanged_h_cnt, > glob_almost_1, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_log10_abserr, > glob_dump_analytic, > glob_not_yet_start_msg, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmax, > min_in_hour, > glob_look_poles, > glob_not_yet_finished, > years_in_century, > glob_html_log, > glob_warned2, > glob_max_hours, > glob_hmin_init, > hours_in_day, > sec_in_min, > glob_max_opt_iter, > glob_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > djd_debug2, > glob_subiter_method, > glob_normmax, > glob_display_flag, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_last_good_h, > glob_initial_pass, > glob_clock_sec, > djd_debug, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_fact_1, > array_last_rel_error, > array_type_pole, > array_y_init, > array_pole, > array_real_pole, > array_poles, > array_y_higher, > array_y_higher_work, > array_complex_pole, > array_y_higher_work2, > array_fact_2, > array_y_set_initial, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr, glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium, glob_log10_relerr, glob_large_float, glob_hmin, glob_dump, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr, glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished, years_in_century, glob_html_log, glob_warned2, glob_max_hours, glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err, glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax, glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned, glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole, array_y_init, array_pole, array_real_pole, array_poles, array_y_higher, array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2, array_y_set_initial, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_max_terms, > INFO, > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_smallish_float, > glob_optimal_start, > glob_disp_incr, > glob_reached_optimal_h, > days_in_year, > glob_relerr, > centuries_in_millinium, > glob_log10_relerr, > glob_large_float, > glob_hmin, > glob_dump, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_unchanged_h_cnt, > glob_almost_1, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_log10_abserr, > glob_dump_analytic, > glob_not_yet_start_msg, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmax, > min_in_hour, > glob_look_poles, > glob_not_yet_finished, > years_in_century, > glob_html_log, > glob_warned2, > glob_max_hours, > glob_hmin_init, > hours_in_day, > sec_in_min, > glob_max_opt_iter, > glob_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > djd_debug2, > glob_subiter_method, > glob_normmax, > glob_display_flag, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_last_good_h, > glob_initial_pass, > glob_clock_sec, > djd_debug, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_fact_1, > array_last_rel_error, > array_type_pole, > array_y_init, > array_pole, > array_real_pole, > array_poles, > array_y_higher, > array_y_higher_work, > array_complex_pole, > array_y_higher_work2, > array_fact_2, > array_y_set_initial, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr, glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium, glob_log10_relerr, glob_large_float, glob_hmin, glob_dump, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr, glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished, years_in_century, glob_html_log, glob_warned2, glob_max_hours, glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err, glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax, glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned, glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole, array_y_init, array_pole, array_real_pole, array_poles, array_y_higher, array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2, array_y_set_initial, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > glob_max_terms, > INFO, > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_smallish_float, > glob_optimal_start, > glob_disp_incr, > glob_reached_optimal_h, > days_in_year, > glob_relerr, > centuries_in_millinium, > glob_log10_relerr, > glob_large_float, > glob_hmin, > glob_dump, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_unchanged_h_cnt, > glob_almost_1, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_log10_abserr, > glob_dump_analytic, > glob_not_yet_start_msg, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmax, > min_in_hour, > glob_look_poles, > glob_not_yet_finished, > years_in_century, > glob_html_log, > glob_warned2, > glob_max_hours, > glob_hmin_init, > hours_in_day, > sec_in_min, > glob_max_opt_iter, > glob_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > djd_debug2, > glob_subiter_method, > glob_normmax, > glob_display_flag, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_last_good_h, > glob_initial_pass, > glob_clock_sec, > djd_debug, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_fact_1, > array_last_rel_error, > array_type_pole, > array_y_init, > array_pole, > array_real_pole, > array_poles, > array_y_higher, > array_y_higher_work, > array_complex_pole, > array_y_higher_work2, > array_fact_2, > array_y_set_initial, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr, glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium, glob_log10_relerr, glob_large_float, glob_hmin, glob_dump, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr, glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished, years_in_century, glob_html_log, glob_warned2, glob_max_hours, glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err, glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax, glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned, glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole, array_y_init, array_pole, array_real_pole, array_poles, array_y_higher, array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2, array_y_set_initial, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_max_terms, > INFO, > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_smallish_float, > glob_optimal_start, > glob_disp_incr, > glob_reached_optimal_h, > days_in_year, > glob_relerr, > centuries_in_millinium, > glob_log10_relerr, > glob_large_float, > glob_hmin, > glob_dump, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_unchanged_h_cnt, > glob_almost_1, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_log10_abserr, > glob_dump_analytic, > glob_not_yet_start_msg, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmax, > min_in_hour, > glob_look_poles, > glob_not_yet_finished, > years_in_century, > glob_html_log, > glob_warned2, > glob_max_hours, > glob_hmin_init, > hours_in_day, > sec_in_min, > glob_max_opt_iter, > glob_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > djd_debug2, > glob_subiter_method, > glob_normmax, > glob_display_flag, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_last_good_h, > glob_initial_pass, > glob_clock_sec, > djd_debug, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_fact_1, > array_last_rel_error, > array_type_pole, > array_y_init, > array_pole, > array_real_pole, > array_poles, > array_y_higher, > array_y_higher_work, > array_complex_pole, > array_y_higher_work2, > array_fact_2, > array_y_set_initial, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult $eq_no = 1 i = 1 > array_tmp1[1] := (array_y[1] * (array_y[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_y,array_y,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_y,array_y,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr, glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium, glob_log10_relerr, glob_large_float, glob_hmin, glob_dump, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr, glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished, years_in_century, glob_html_log, glob_warned2, glob_max_hours, glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err, glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax, glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned, glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole, array_y_init, array_pole, array_real_pole, array_poles, array_y_higher, array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2, array_y_set_initial, glob_last; array_tmp1[1] := array_y[1]*array_y[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_y, array_y, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_y, array_y, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_y, array_y, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_y, array_y, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_y, array_y, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 13 > if array_fact_1[nnn] = 0 then # if number 14 > ret := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > if array_fact_2[mmm,nnn] = 0 then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0/(1.0 - x); > end; exact_soln_y := proc(x) 1.0/(1.0 - x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > glob_max_terms, > INFO, > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_iter, > glob_smallish_float, > glob_optimal_start, > glob_disp_incr, > glob_reached_optimal_h, > days_in_year, > glob_relerr, > centuries_in_millinium, > glob_log10_relerr, > glob_large_float, > glob_hmin, > glob_dump, > glob_log10normmin, > glob_max_minutes, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_unchanged_h_cnt, > glob_almost_1, > glob_optimal_expect_sec, > glob_current_iter, > glob_max_sec, > glob_log10_abserr, > glob_dump_analytic, > glob_not_yet_start_msg, > glob_clock_start_sec, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_small_float, > glob_abserr, > glob_hmax, > min_in_hour, > glob_look_poles, > glob_not_yet_finished, > years_in_century, > glob_html_log, > glob_warned2, > glob_max_hours, > glob_hmin_init, > hours_in_day, > sec_in_min, > glob_max_opt_iter, > glob_start, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > djd_debug2, > glob_subiter_method, > glob_normmax, > glob_display_flag, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_last_good_h, > glob_initial_pass, > glob_clock_sec, > djd_debug, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_m1, > array_norms, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_fact_1, > array_last_rel_error, > array_type_pole, > array_y_init, > array_pole, > array_real_pole, > array_poles, > array_y_higher, > array_y_higher_work, > array_complex_pole, > array_y_higher_work2, > array_fact_2, > array_y_set_initial, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > INFO := 2; > ALWAYS := 1; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_iolevel := 5; > glob_iter := 0; > glob_smallish_float := 0.1e-100; > glob_optimal_start := 0.0; > glob_disp_incr := 0.1; > glob_reached_optimal_h := false; > days_in_year := 365.0; > glob_relerr := 0.1e-10; > centuries_in_millinium := 10.0; > glob_log10_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmin := 0.00000000001; > glob_dump := false; > glob_log10normmin := 0.1; > glob_max_minutes := 0.0; > glob_log10relerr := 0.0; > glob_curr_iter_when_opt := 0; > glob_unchanged_h_cnt := 0; > glob_almost_1 := 0.9990; > glob_optimal_expect_sec := 0.1; > glob_current_iter := 0; > glob_max_sec := 10000.0; > glob_log10_abserr := 0.1e-10; > glob_dump_analytic := false; > glob_not_yet_start_msg := true; > glob_clock_start_sec := 0.0; > MAX_UNCHANGED := 10; > glob_orig_start_sec := 0.0; > glob_small_float := 0.1e-50; > glob_abserr := 0.1e-10; > glob_hmax := 1.0; > min_in_hour := 60.0; > glob_look_poles := false; > glob_not_yet_finished := true; > years_in_century := 100.0; > glob_html_log := true; > glob_warned2 := false; > glob_max_hours := 0.0; > glob_hmin_init := 0.001; > hours_in_day := 24.0; > sec_in_min := 60.0; > glob_max_opt_iter := 10; > glob_start := 0; > glob_optimal_clock_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_max_rel_trunc_err := 0.1e-10; > glob_h := 0.1; > glob_optimal_done := false; > djd_debug2 := true; > glob_subiter_method := 3; > glob_normmax := 0.0; > glob_display_flag := true; > glob_percent_done := 0.0; > glob_log10abserr := 0.0; > glob_warned := false; > glob_no_eqs := 0; > glob_max_iter := 1000; > glob_last_good_h := 0.1; > glob_initial_pass := true; > glob_clock_sec := 0.0; > djd_debug := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/nonlinear1postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 0.5 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.01;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"1.0/(1.0 - x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_m1:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y:= 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_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > 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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_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_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 > ; > 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_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_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_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 0.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.01; > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = y * y;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-18T00:44:30-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"nonlinear1") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 092 ") > ; > logitem_str(html_log_file,"nonlinear1 diffeq.mxt") > ; > logitem_str(html_log_file,"nonlinear1 maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr, glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium, glob_log10_relerr, glob_large_float, glob_hmin, glob_dump, glob_log10normmin, glob_max_minutes, glob_log10relerr, glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1, glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr, glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec, MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr, glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished, years_in_century, glob_html_log, glob_warned2, glob_max_hours, glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err, glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax, glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned, glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass, glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1, array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole, array_y_init, array_pole, array_real_pole, array_poles, array_y_higher, array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2, array_y_set_initial, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; INFO := 2; ALWAYS := 1; DEBUGMASSIVE := 4; DEBUGL := 3; glob_iolevel := 5; glob_iter := 0; glob_smallish_float := 0.1*10^(-100); glob_optimal_start := 0.; glob_disp_incr := 0.1; glob_reached_optimal_h := false; days_in_year := 365.0; glob_relerr := 0.1*10^(-10); centuries_in_millinium := 10.0; glob_log10_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmin := 0.1*10^(-10); glob_dump := false; glob_log10normmin := 0.1; glob_max_minutes := 0.; glob_log10relerr := 0.; glob_curr_iter_when_opt := 0; glob_unchanged_h_cnt := 0; glob_almost_1 := 0.9990; glob_optimal_expect_sec := 0.1; glob_current_iter := 0; glob_max_sec := 10000.0; glob_log10_abserr := 0.1*10^(-10); glob_dump_analytic := false; glob_not_yet_start_msg := true; glob_clock_start_sec := 0.; MAX_UNCHANGED := 10; glob_orig_start_sec := 0.; glob_small_float := 0.1*10^(-50); glob_abserr := 0.1*10^(-10); glob_hmax := 1.0; min_in_hour := 60.0; glob_look_poles := false; glob_not_yet_finished := true; years_in_century := 100.0; glob_html_log := true; glob_warned2 := false; glob_max_hours := 0.; glob_hmin_init := 0.001; hours_in_day := 24.0; sec_in_min := 60.0; glob_max_opt_iter := 10; glob_start := 0; glob_optimal_clock_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_max_rel_trunc_err := 0.1*10^(-10); glob_h := 0.1; glob_optimal_done := false; djd_debug2 := true; glob_subiter_method := 3; glob_normmax := 0.; glob_display_flag := true; glob_percent_done := 0.; glob_log10abserr := 0.; glob_warned := false; glob_no_eqs := 0; glob_max_iter := 1000; glob_last_good_h := 0.1; glob_initial_pass := true; glob_clock_sec := 0.; djd_debug := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/nonlinear1postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 0.5 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.01;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "1.0/(1.0 - x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_m1 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y := 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_1st_rel_error := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_m1[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_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 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_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 0.5; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = y * y;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-18T00:44:30-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "nonlinear1"); logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 092 "); logitem_str(html_log_file, "nonlinear1 diffeq.mxt"); logitem_str(html_log_file, "nonlinear1 maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 0.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0/(1.0 - x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 1.001001001001001001001001001001 y[1] (numeric) = 1.0010010010010010365484123685393 absolute error = 3.55474113675383e-17 relative error = 3.5511863956170761700000000000000e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 1.0020040080160320641282565130261 y[1] (numeric) = 1.0020040080160321355447439290729 absolute error = 7.14164874160468e-17 relative error = 7.1273654441214706399999999999997e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 1.0030090270812437311935807422267 y[1] (numeric) = 1.0030090270812438388036152524857 absolute error = 1.076100345102590e-16 relative error = 1.0728720440672822300000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 1.0040160642570281124497991967871 y[1] (numeric) = 1.0040160642570282565806845368025 absolute error = 1.441308853400154e-16 relative error = 1.4355436179865533840000000000001e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 1.0050251256281407035175879396985 y[1] (numeric) = 1.0050251256281408844994871299519 absolute error = 1.809818991902534e-16 relative error = 1.8007698969430213300000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 1.006036217303822937625754527163 y[1] (numeric) = 1.0060362173038231557917167411861 absolute error = 2.181659622140231e-16 relative error = 2.1685696644073896140000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 1.0070493454179254783484390735146 y[1] (numeric) = 1.0070493454179257340344267820808 absolute error = 2.556859877085662e-16 relative error = 2.5389618579460623660000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 1.0080645161290322580645161290323 y[1] (numeric) = 1.0080645161290325516094325235274 absolute error = 2.935449163944951e-16 relative error = 2.9119655706333913919999999999999e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 1.0090817356205852674066599394551 y[1] (numeric) = 1.0090817356205855991523766375663 absolute error = 3.317457166981112e-16 relative error = 3.2876000524782819920000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.14 NO POLE x[1] = 0.01 y[1] (analytic) = 1.010101010101010101010101010101 y[1] (numeric) = 1.0101010101010104713014860469996 absolute error = 3.702913850368986e-16 relative error = 3.6658847118652961400000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 1.0111223458038422649140546006067 y[1] (numeric) = 1.0111223458038426740990007088414 absolute error = 4.091849461082347e-16 relative error = 4.0468391170104411829999999999999e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 1.0121457489878542510121457489879 y[1] (numeric) = 1.0121457489878546994415989303429 absolute error = 4.484294531813550e-16 relative error = 4.4304829974317873999999999999998e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 1.0131712259371833839918946301925 y[1] (numeric) = 1.013171225937183872019883022806 absolute error = 4.880279883926135e-16 relative error = 4.8168362454350952450000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 1.0141987829614604462474645030426 y[1] (numeric) = 1.0141987829614609742311275471202 absolute error = 5.279836630440776e-16 relative error = 5.2059189176146051360000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.015 y[1] (analytic) = 1.0152284263959390862944162436548 y[1] (numeric) = 1.0152284263959396545940341491555 absolute error = 5.682996179055007e-16 relative error = 5.5977512363691818950000000000001e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 1.016260162601626016260162601626 y[1] (numeric) = 1.0162601626016266252391861213375 absolute error = 6.089790235197115e-16 relative error = 5.9923535914339611600000000000001e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 1.0172939979654120040691759918616 y[1] (numeric) = 1.0172939979654126540942565033261 absolute error = 6.500250805114645e-16 relative error = 6.3897465414276960350000000000003e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 1.0183299389002036659877800407332 y[1] (numeric) = 1.0183299389002043574287999405253 absolute error = 6.914410198997921e-16 relative error = 6.7899508154159584220000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 1.0193679918450560652395514780836 y[1] (numeric) = 1.0193679918450567984696548919875 absolute error = 7.332301034139039e-16 relative error = 7.1929873144903972589999999999999e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 1.0204081632653061224489795918367 y[1] (numeric) = 1.0204081632653068978446034045113 absolute error = 7.753956238126746e-16 relative error = 7.5988771133642110800000000000003e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 1.0214504596527068437180796731359 y[1] (numeric) = 1.0214504596527076616589848809025 absolute error = 8.179409052077666e-16 relative error = 8.0076414619840350139999999999996e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 1.0224948875255623721881390593047 y[1] (numeric) = 1.0224948875255632330574424497371 absolute error = 8.608693033904324e-16 relative error = 8.4193017871584288720000000000000e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 1.0235414534288638689866939611054 y[1] (numeric) = 1.0235414534288647731709001231455 absolute error = 9.041842061620401e-16 relative error = 8.8338796942031317770000000000002e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 1.0245901639344262295081967213115 y[1] (numeric) = 1.0245901639344271773972303896829 absolute error = 9.478890336683714e-16 relative error = 9.2513969686033048639999999999998e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.29 NO POLE x[1] = 0.025 y[1] (analytic) = 1.025641025641025641025641025641 y[1] (numeric) = 1.0256410256410266330128797633778 absolute error = 9.919872387377368e-16 relative error = 9.6718755776929338000000000000002e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 1.0266940451745379876796714579055 y[1] (numeric) = 1.0266940451745390241619786808612 absolute error = 1.0364823072229557e-15 relative error = 1.0095337672351588518000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 1.0277492291880781089414182939363 y[1] (numeric) = 1.0277492291880791903191766411863 absolute error = 1.0813777583472500e-15 relative error = 1.0521805588718742500000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 1.0288065843621399176954732510288 y[1] (numeric) = 1.0288065843621410443726183051293 absolute error = 1.1266771450541005e-15 relative error = 1.0951301849925856860000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 1.029866117404737384140061791967 y[1] (numeric) = 1.0298661174047385565241161530801 absolute error = 1.1723840543611131e-15 relative error = 1.1383849167846408201000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 1.0309278350515463917525773195876 y[1] (numeric) = 1.0309278350515476102546850375356 absolute error = 1.2185021077179480e-15 relative error = 1.1819470444864095600000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 1.0319917440660474716202270381837 y[1] (numeric) = 1.0319917440660487366551884065443 absolute error = 1.2650349613683606e-15 relative error = 1.2258188775659414214000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 1.0330578512396694214876033057851 y[1] (numeric) = 1.033057851239670733473910022191 absolute error = 1.3119863067164059e-15 relative error = 1.2700027449014809112000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 1.0341261633919338159255429162358 y[1] (numeric) = 1.0341261633919351752854136130943 absolute error = 1.3593598706968585e-15 relative error = 1.3145009949638621695000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 1.0351966873706004140786749482402 y[1] (numeric) = 1.0351966873706018212380910981422 absolute error = 1.4071594161499020e-15 relative error = 1.3593159960008053320000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 1.0362694300518134715025906735751 y[1] (numeric) = 1.0362694300518149268913328737149 absolute error = 1.4553887422001398e-15 relative error = 1.4044501362231349070000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 1.037344398340248962655601659751 y[1] (numeric) = 1.0373443983402504667072862997332 absolute error = 1.5040516846399822e-15 relative error = 1.4499058239929428408000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 1.0384215991692627206645898234683 y[1] (numeric) = 1.0384215991692642738167061409341 absolute error = 1.5531521163174658e-15 relative error = 1.4956854880137195654000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 1.039501039501039501039501039501 y[1] (numeric) = 1.0395010395010411037334485680602 absolute error = 1.6026939475285592e-15 relative error = 1.5417915775224739504000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 1.0405827263267429760665972944849 y[1] (numeric) = 1.0405827263267446287477237084976 absolute error = 1.6526811264140127e-15 relative error = 1.5882265624838662047000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 1.0416666666666666666666666666667 y[1] (numeric) = 1.0416666666666683697843060274757 absolute error = 1.7031176393608090e-15 relative error = 1.6349929337863766399999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=0.44 NO POLE x[1] = 0.041 y[1] (analytic) = 1.0427528675703858185610010427529 y[1] (numeric) = 1.042752867570387572568512451026 absolute error = 1.7540075114082731e-15 relative error = 1.6820932034405339028999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 1.0438413361169102296450939457202 y[1] (numeric) = 1.0438413361169120349999006046197 absolute error = 1.8053548066588995e-15 relative error = 1.7295299047792257210000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 1.0449320794148380355276907001045 y[1] (numeric) = 1.044932079414839892691319394062 absolute error = 1.8571636286939575e-15 relative error = 1.7773055926601173275000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 1.0460251046025104602510460251046 y[1] (numeric) = 1.0460251046025123696891670190394 absolute error = 1.9094381209939348e-15 relative error = 1.8254228436702016688000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 1.0471204188481675392670157068063 y[1] (numeric) = 1.0471204188481695014494830706858 absolute error = 1.9621824673638795e-15 relative error = 1.8738842563325049225000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 1.0482180293501048218029350104822 y[1] (numeric) = 1.0482180293501068372038273741866 absolute error = 2.0154008923637044e-15 relative error = 1.9226924513149739976000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 1.0493179433368310598111227701994 y[1] (numeric) = 1.049317943336833128908784513715 absolute error = 2.0690976617435156e-15 relative error = 1.9718500716415703667999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 1.0504201680672268907563025210084 y[1] (numeric) = 1.0504201680672290140333854050379 absolute error = 2.1232770828840295e-15 relative error = 2.0213597829055960840000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 1.0515247108307045215562565720294 y[1] (numeric) = 1.0515247108307066994997618141721 absolute error = 2.1779435052421427e-15 relative error = 2.0712242734852777077000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 1.0526315789473684210526315789474 y[1] (numeric) = 1.0526315789473706541539523806685 absolute error = 2.2331013208017211e-15 relative error = 2.1214462547616350449999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 1.0537407797681770284510010537408 y[1] (numeric) = 1.0537407797681793172059655834151 absolute error = 2.2887549645296743e-15 relative error = 2.1720284613386609107000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 1.0548523206751054852320675105485 y[1] (numeric) = 1.0548523206751078301409823479306 absolute error = 2.3449089148373821e-15 relative error = 2.2229736512658382308000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 1.0559662090813093980992608236536 y[1] (numeric) = 1.0559662090813117996669548711967 absolute error = 2.4015676940475431e-15 relative error = 2.2742846062630233157000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 1.0570824524312896405919661733615 y[1] (numeric) = 1.0570824524312920993278350398749 absolute error = 2.4587358688665134e-15 relative error = 2.3259641319477216764000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 1.0582010582010582010582010582011 y[1] (numeric) = 1.0582010582010607174762519204074 absolute error = 2.5164180508622063e-15 relative error = 2.3780150580647849534999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 1.0593220338983050847457627118644 y[1] (numeric) = 1.0593220338983076593646596594884 absolute error = 2.5746188969476240e-15 relative error = 2.4304402387185570560000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.0MB, time=0.60 NO POLE x[1] = 0.057 y[1] (analytic) = 1.0604453870625662778366914103924 y[1] (numeric) = 1.0604453870625689111798012804859 absolute error = 2.6333431098700935e-15 relative error = 2.4832425526074981704999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 1.0615711252653927813163481953291 y[1] (numeric) = 1.0615711252653954739117869016101 absolute error = 2.6925954387062810e-15 relative error = 2.5364249032613167020000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 1.0626992561105207226354941551541 y[1] (numeric) = 1.0626992561105234750161735182114 absolute error = 2.7523806793630573e-15 relative error = 2.5899902192806369193000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 1.0638297872340425531914893617021 y[1] (numeric) = 1.0638297872340453658951644459934 absolute error = 2.8127036750842913e-15 relative error = 2.6439414545792338220000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.061 y[1] (analytic) = 1.0649627263045793397231096911608 y[1] (numeric) = 1.0649627263045822132924266548072 absolute error = 2.8735693169636464e-15 relative error = 2.6982815886288639696000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 1.0660980810234541577825159914712 y[1] (numeric) = 1.0660980810234570927650604549301 absolute error = 2.9349825444634589e-15 relative error = 2.7530136267067244482000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 1.0672358591248665955176093916756 y[1] (numeric) = 1.067235859124869592465955331451 absolute error = 2.9969483459397754e-15 relative error = 2.8081406001455695497999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 1.0683760683760683760683760683761 y[1] (numeric) = 1.0683760683760714355401352420059 absolute error = 3.0594717591736298e-15 relative error = 2.8636655665865174927999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 1.069518716577540106951871657754 y[1] (numeric) = 1.0695187165775432295097435663942 absolute error = 3.1225578719086402e-15 relative error = 2.9195916102345785870000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 1.0706638115631691648822269807281 y[1] (numeric) = 1.0706638115631723510940493757356 absolute error = 3.1862118223950075e-15 relative error = 2.9759218421169370049999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 1.0718113612004287245444801714898 y[1] (numeric) = 1.0718113612004319749832801114897 absolute error = 3.2504387999399999e-15 relative error = 3.0326594003440199067000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 1.0729613733905579399141630901288 y[1] (numeric) = 1.0729613733905612551582085551335 absolute error = 3.3152440454650047e-15 relative error = 3.0898074503733843803999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 1.0741138560687432867883995703545 y[1] (numeric) = 1.074113856068746667421251639591 absolute error = 3.3806328520692365e-15 relative error = 3.1473691852764591814999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 1.0752688172043010752688172043011 y[1] (numeric) = 1.0752688172043045218793828044863 absolute error = 3.4466105656001852e-15 relative error = 3.2053478260081722359999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 1.0764262648008611410118406889128 y[1] (numeric) = 1.0764262648008646541944259198058 absolute error = 3.5131825852308930e-15 relative error = 3.2637466216794995970000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 1.0775862068965517241379310344828 y[1] (numeric) = 1.0775862068965553044922950786324 absolute error = 3.5803543640441496e-15 relative error = 3.3225688498329708287999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.0MB, time=0.76 NO POLE x[1] = 0.073 y[1] (analytic) = 1.0787486515641855447680690399137 y[1] (numeric) = 1.0787486515641891928994786636094 absolute error = 3.6481314096236957e-15 relative error = 3.3818178167211659139000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 1.0799136069114470842332613390929 y[1] (numeric) = 1.0799136069114508007525459916181 absolute error = 3.7165192846525252e-15 relative error = 3.4414968575882383351999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 1.0810810810810810810810810810811 y[1] (numeric) = 1.0810810810810848666046885994623 absolute error = 3.7855236075183812e-15 relative error = 3.5016093369545026099999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 1.0822510822510822510822510822511 y[1] (numeric) = 1.0822510822510861062323040087889 absolute error = 3.8551500529265378e-15 relative error = 3.5621586489041209271999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 1.0834236186348862405200433369447 y[1] (numeric) = 1.0834236186348901659243958569094 absolute error = 3.9254043525199647e-15 relative error = 3.6231482173759274181000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 1.0845986984815618221258134490239 y[1] (numeric) = 1.0845986984815658184181089559942 absolute error = 3.9962922955069703e-15 relative error = 3.6845814964574266165999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 1.0857763300760043431053203040174 y[1] (numeric) = 1.0857763300760084109250496004405 absolute error = 4.0678197292964231e-15 relative error = 3.7464619706820056750999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 1.0869565217391304347826086956522 y[1] (numeric) = 1.086956521739134574775168836301 absolute error = 4.1399925601406488e-15 relative error = 3.8087931553293968959999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 1.0881392818280739934711643090316 y[1] (numeric) = 1.0881392818280782062879180951382 absolute error = 4.2128167537861066e-15 relative error = 3.8715785967294319653999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 1.0893246187363834422657952069717 y[1] (numeric) = 1.0893246187363877285641313389168 absolute error = 4.2862983361319451e-15 relative error = 3.9348218725691256017999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 1.0905125408942202835332606324973 y[1] (numeric) = 1.0905125408942246439766545290405 absolute error = 4.3604433938965432e-15 relative error = 3.9985265922031301143999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 1.0917030567685589519650655021834 y[1] (numeric) = 1.0917030567685633872231407943244 absolute error = 4.4352580752921410e-15 relative error = 4.0626963969676011560000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 1.0928961748633879781420765027322 y[1] (numeric) = 1.0928961748633924888906672103991 absolute error = 4.5107485907076669e-15 relative error = 4.1273349604975152135000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.086 y[1] (analytic) = 1.0940919037199124726477024070022 y[1] (numeric) = 1.0940919037199170595689158068729 absolute error = 4.5869212133998707e-15 relative error = 4.1924459890474818198000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 1.0952902519167579408543263964951 y[1] (numeric) = 1.0952902519167626046366065893671 absolute error = 4.6637822801928720e-15 relative error = 4.2580332218160921359999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 1.0964912280701754385964912280702 y[1] (numeric) = 1.0964912280701801799346834143053 absolute error = 4.7413381921862351e-15 relative error = 4.3241004312738464111999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=0.92 NO POLE x[1] = 0.089 y[1] (analytic) = 1.0976948408342480790340285400659 y[1] (numeric) = 1.0976948408342528986294440117507 absolute error = 4.8195954154716848e-15 relative error = 4.3906514234947048527999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 1.0989010989010989010989010989011 y[1] (numeric) = 1.098901098901103799659382957478 absolute error = 4.8985604818585769e-15 relative error = 4.4576900384913049790000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 1.10011001100110011001100110011 y[1] (numeric) = 1.1001100110011050882509907083499 absolute error = 4.9782399896082399e-15 relative error = 4.5252201505538900691000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 1.1013215859030837004405286343612 y[1] (numeric) = 1.1013215859030887590811328116685 absolute error = 5.0586406041773073e-15 relative error = 4.5932456685929950284000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 1.1025358324145534729878721058434 y[1] (numeric) = 1.1025358324145586127569310760022 absolute error = 5.1397690589701588e-15 relative error = 4.6617705364859340316000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 1.1037527593818984547461368653422 y[1] (numeric) = 1.1037527593819036763782929659352 absolute error = 5.2216321561005930e-15 relative error = 4.7307987334271372579999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 1.1049723756906077348066298342541 y[1] (numeric) = 1.1049723756906130390433969971093 absolute error = 5.3042367671628552e-15 relative error = 4.8003342742823839560000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 1.1061946902654867256637168141593 y[1] (numeric) = 1.1061946902654921132535508263027 absolute error = 5.3875898340121434e-15 relative error = 4.8703812099469776336000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 1.1074197120708748615725359911406 y[1] (numeric) = 1.1074197120708803332709055458641 absolute error = 5.4716983695547235e-15 relative error = 4.9409436277079153205000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 1.1086474501108647450110864745011 y[1] (numeric) = 1.1086474501108703015805450222787 absolute error = 5.5565694585477776e-15 relative error = 5.0120256516100953952000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 1.1098779134295227524972253052164 y[1] (numeric) = 1.1098779134295283947074837143366 absolute error = 5.6422102584091202e-15 relative error = 5.0836314428266173002000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 1.1111111111111111111111111111111 y[1] (numeric) = 1.1111111111111168397391111480237 absolute error = 5.7286280000369126e-15 relative error = 5.1557652000332213400000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 1.112347052280311457174638487208 y[1] (numeric) = 1.1123470522803172730046271267188 absolute error = 5.8158299886395108e-15 relative error = 5.2284311597869202092000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 1.113585746102449888641425389755 y[1] (numeric) = 1.113585746102455792465029965338 absolute error = 5.9038236045755830e-15 relative error = 5.3016335969088735340000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 1.1148272017837235228539576365663 y[1] (numeric) = 1.1148272017837295154702618412022 absolute error = 5.9926163042046359e-15 relative error = 5.3753768248715584023000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 1.1160714285714285714285714285714 y[1] (numeric) = 1.1160714285714346536441921766604 absolute error = 6.0822156207480890e-15 relative error = 5.4496651961902877440000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=1.07 NO POLE x[1] = 0.105 y[1] (analytic) = 1.1173184357541899441340782122905 y[1] (numeric) = 1.1173184357541961167632433733318 absolute error = 6.1726291651610413e-15 relative error = 5.5245031028191319635000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 1.1185682326621923937360178970917 y[1] (numeric) = 1.1185682326621986576006449119647 absolute error = 6.2638646270148730e-15 relative error = 5.5998949765512964620000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 1.1198208286674132138857782754759 y[1] (numeric) = 1.1198208286674195698155536663062 absolute error = 6.3559297753908303e-15 relative error = 5.6758452894240114579000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 1.1210762331838565022421524663677 y[1] (numeric) = 1.1210762331838629510746122511097 absolute error = 6.4488324597847420e-15 relative error = 5.7523585541279898640000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 1.1223344556677890011223344556678 y[1] (numeric) = 1.1223344556677955437029454786863 absolute error = 6.5425806110230185e-15 relative error = 5.8294393244215094834999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 1.1235955056179775280898876404494 y[1] (numeric) = 1.1235955056179841652721298305363 absolute error = 6.6371822421900869e-15 relative error = 5.9070921955491773410000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 1.1248593925759280089988751406074 y[1] (numeric) = 1.124859392575934741644324708025 absolute error = 6.7326454495674176e-15 relative error = 5.9853218046654342464000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 1.1261261261261261261261261261261 y[1] (numeric) = 1.126126126126132955104539710427 absolute error = 6.8289784135843009e-15 relative error = 6.0641328312628591992000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 1.1273957158962795941375422773393 y[1] (numeric) = 1.1273957158962865203269420578715 absolute error = 6.9261893997805322e-15 relative error = 6.1435299976053320614000000000003e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 1.1286681715575620767494356659142 y[1] (numeric) = 1.1286681715575691010361954470847 absolute error = 7.0242867597811705e-15 relative error = 6.2235180691661170630000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 1.1299435028248587570621468926554 y[1] (numeric) = 1.1299435028248658803410791761884 absolute error = 7.1232789322835330e-15 relative error = 6.3041018550709267049999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 1.1312217194570135746606334841629 y[1] (numeric) = 1.1312217194570207978350775407583 absolute error = 7.2231744440565954e-15 relative error = 6.3852862085460303336000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 1.1325028312570781426953567383918 y[1] (numeric) = 1.132502831257085466677267691357 absolute error = 7.3239819109529652e-15 relative error = 6.4670760273714682716000000000003e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 1.1337868480725623582766439909297 y[1] (numeric) = 1.1337868480725697839866829245328 absolute error = 7.4257100389336031e-15 relative error = 6.5494762543394379342000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 1.1350737797956867196367763904654 y[1] (numeric) = 1.1350737797956942480044014959309 absolute error = 7.5283676251054655e-15 relative error = 6.6324918777179151054999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 1.1363636363636363636363636363636 y[1] (numeric) = 1.1363636363636439955999224086102 absolute error = 7.6319635587722466e-15 relative error = 6.7161279317195770080000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.1MB, time=1.23 x[1] = 0.121 y[1] (analytic) = 1.1376564277588168373151308304892 y[1] (numeric) = 1.1376564277588245738219533288887 absolute error = 7.7365068224983995e-15 relative error = 6.8003894969760931605000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 1.1389521640091116173120728929385 y[1] (numeric) = 1.1389521640091194593185660795594 absolute error = 7.8420064931866209e-15 relative error = 6.8852817010178531502000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 1.1402508551881413911060433295325 y[1] (numeric) = 1.1402508551881493395777864985151 absolute error = 7.9484717431689826e-15 relative error = 6.9708097187591977402000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 1.1415525114155251141552511415525 y[1] (numeric) = 1.1415525114155331700670924534524 absolute error = 8.0559118413118999e-15 relative error = 7.0569787729892243124000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 1.1428571428571428571428571428571 y[1] (numeric) = 1.1428571428571510214790112779852 absolute error = 8.1643361541351281e-15 relative error = 7.1437941348682370875000000000003e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 1.1441647597254004576659038901602 y[1] (numeric) = 1.1441647597254087314200508351401 absolute error = 8.2737541469449799e-15 relative error = 7.2312611244299124325999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 1.145475372279495990836197021764 y[1] (numeric) = 1.1454753722795043750115820037263 absolute error = 8.3841753849819623e-15 relative error = 7.3193851110892530879000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 1.146788990825688073394495412844 y[1] (numeric) = 1.1467889908256965690040299958754 absolute error = 8.4956095345830314e-15 relative error = 7.4081715141564033808000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 1.1481056257175660160734787600459 y[1] (numeric) = 1.1481056257175746241398431187152 absolute error = 8.6080663643586693e-15 relative error = 7.4976258033564009603000000000002e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 1.1494252873563218390804597701149 y[1] (numeric) = 1.1494252873563305606362061551033 absolute error = 8.7215557463849884e-15 relative error = 7.5877534993549399080000000000003e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 1.1507479861910241657077100115075 y[1] (numeric) = 1.1507479861910330017953674225796 absolute error = 8.8360876574110721e-15 relative error = 7.6785601742902216548999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 1.1520737327188940092165898617512 y[1] (numeric) = 1.1520737327189029608887699435163 absolute error = 8.9516721800817651e-15 relative error = 7.7700514523109721067999999999997e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 1.1534025374855824682814302191465 y[1] (numeric) = 1.1534025374855915366009343952736 absolute error = 9.0683195041761271e-15 relative error = 7.8622330101207021956999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 1.1547344110854503464203233256351 y[1] (numeric) = 1.1547344110854595324602511874051 absolute error = 9.1860399278617700e-15 relative error = 7.9551105775282928200000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 1.1560693641618497109826589595376 y[1] (numeric) = 1.156069364161859015826517924838 absolute error = 9.3048438589653004e-15 relative error = 8.0486899380049848459999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 1.1574074074074074074074074074074 y[1] (numeric) = 1.1574074074074168321492236664996 absolute error = 9.4247418162590922e-15 relative error = 8.1429769292478556608000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 1.158748551564310544611819235226 y[1] (numeric) = 1.1587485515643200903562499998443 absolute error = 9.5457444307646183e-15 relative error = 8.2379774437498655928999999999997e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=1.39 NO POLE x[1] = 0.138 y[1] (analytic) = 1.1600928074245939675174013921114 y[1] (numeric) = 1.1600928074246036353798484646857 absolute error = 9.6678624470725743e-15 relative error = 8.3336974293765590465999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 1.1614401858304297328687572590012 y[1] (numeric) = 1.1614401858304395239754819390297 absolute error = 9.7911067246800285e-15 relative error = 8.4301428899495045384999999999997e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 1.1627906976744186046511627906977 y[1] (numeric) = 1.1627906976744285201394021355375 absolute error = 9.9154882393448398e-15 relative error = 8.5273198858365622279999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 1.1641443538998835855646100116414 y[1] (numeric) = 1.1641443538998936265826944692256 absolute error = 1.00410180844575842e-14 relative error = 8.6252345345490648278000000000003e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 1.1655011655011655011655011655012 y[1] (numeric) = 1.1655011655011756688729735967392 absolute error = 1.01677074724312380e-14 relative error = 8.7238930113460022039999999999997e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.143 y[1] (analytic) = 1.1668611435239206534422403733956 y[1] (numeric) = 1.1668611435239309490099764822641 absolute error = 1.02955677361088685e-14 relative error = 8.8233015498453003044999999999997e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 1.1682242990654205607476635514019 y[1] (numeric) = 1.1682242990654309853579937409866 absolute error = 1.04246103301895847e-14 relative error = 8.9234664426422845031999999999998e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 1.1695906432748538011695906432749 y[1] (numeric) = 1.1695906432748643560164233162834 absolute error = 1.05548468326730085e-14 relative error = 9.0243940419354222674999999999996e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 1.1709601873536299765807962529274 y[1] (numeric) = 1.1709601873536406628697425754544 absolute error = 1.06862889463225270e-14 relative error = 9.1260907601594380580000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 1.1723329425556858147713950762016 y[1] (numeric) = 1.1723329425556966337198952237942 absolute error = 1.08189485001475926e-14 relative error = 9.2285630706258964878000000000003e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.148 y[1] (analytic) = 1.1737089201877934272300469483568 y[1] (numeric) = 1.173708920187804380067497853698 absolute error = 1.09528374509053412e-14 relative error = 9.3318175081713507024000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 1.1750881316098707403055229142186 y[1] (numeric) = 1.1750881316098818282734075360218 absolute error = 1.10879678846218032e-14 relative error = 9.4358606698131545231999999999997e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 1.1764705882352941176470588235294 y[1] (numeric) = 1.1764705882353053419990769565147 absolute error = 1.12243520181329853e-14 relative error = 9.5406992154130375050000000000001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 1.1778563015312131919905771495878 y[1] (numeric) = 1.177856301531224553992777795694 absolute error = 1.13620022006461062e-14 relative error = 9.6463398683485441637999999999996e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 1.1792452830188679245283018867925 y[1] (numeric) = 1.1792452830188794254592172080673 absolute error = 1.15009309153212748e-14 relative error = 9.7527894161924410303999999999996e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.153 y[1] (analytic) = 1.180637544273907910271546635183 y[1] (numeric) = 1.1806375442739195514223275090831 absolute error = 1.16411507808739001e-14 relative error = 9.8600547114001933847000000000000e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=1.56 NO POLE x[1] = 0.154 y[1] (analytic) = 1.1820330969267139479905437352246 y[1] (numeric) = 1.1820330969267257306650969333562 absolute error = 1.17826745531981316e-14 relative error = 9.9681426720056193335999999999999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 1.183431952662721893491124260355 y[1] (numeric) = 1.1834319526627338190062512719851 absolute error = 1.19255151270116301e-14 relative error = 1.0077060282324827434500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.156 y[1] (analytic) = 1.1848341232227488151658767772512 y[1] (numeric) = 1.1848341232227608848514142992248 absolute error = 1.20696855375219736e-14 relative error = 1.0186814593668545718400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 1.1862396204033214709371293001186 y[1] (numeric) = 1.1862396204033336861360914151285 absolute error = 1.22151989621150099e-14 relative error = 1.0297412725062953345700000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 1.1876484560570071258907363420428 y[1] (numeric) = 1.1876484560570194879594584075129 absolute error = 1.23620687220654701e-14 relative error = 1.0408861863979125824200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.159 y[1] (analytic) = 1.1890606420927467300832342449465 y[1] (numeric) = 1.1890606420927592403915185151102 absolute error = 1.25103082842701637e-14 relative error = 1.0521169267071207671700000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 1.1904761904761904761904761904762 y[1] (numeric) = 1.1904761904762031361217391945551 absolute error = 1.26599312630040789e-14 relative error = 1.0634342260923426276000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 1.1918951132300357568533969010727 y[1] (numeric) = 1.1918951132300485678048186007932 absolute error = 1.28109514216997205e-14 relative error = 1.0748388242806065499500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.162 y[1] (analytic) = 1.1933174224343675417661097852029 y[1] (numeric) = 1.1933174224343805051487845352208 absolute error = 1.29633826747500179e-14 relative error = 1.0863314681440515000200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 1.1947431302270011947431302270012 y[1] (numeric) = 1.1947431302270143119822195621467 absolute error = 1.31172390893351455e-14 relative error = 1.0979129117773516783500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 1.1961722488038277511961722488038 y[1] (numeric) = 1.1961722488038410237310595224044 absolute error = 1.32725348872736006e-14 relative error = 1.1095839165760730101600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.165 y[1] (analytic) = 1.1976047904191616766467065868263 y[1] (numeric) = 1.1976047904191751059311534847161 absolute error = 1.34292844468978898e-14 relative error = 1.1213452513159737983000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 1.1990407673860911270983213429257 y[1] (numeric) = 1.199040767386104714600626298107 absolute error = 1.35875023049551813e-14 relative error = 1.1331976922332621204200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 1.2004801920768307322929171668667 y[1] (numeric) = 1.2004801920768444794960757001514 absolute error = 1.37472031585332847e-14 relative error = 1.1451420231058226155100000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 1.2019230769230769230769230769231 y[1] (numeric) = 1.2019230769230908314787900892485 absolute error = 1.39084018670123254e-14 relative error = 1.1571790353354254732800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.169 y[1] (analytic) = 1.2033694344163658243080625752106 y[1] (numeric) = 1.2033694344163798954215166177015 absolute error = 1.40711134540424909e-14 relative error = 1.1693095280309309937900000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=1.72 NO POLE x[1] = 0.17 y[1] (analytic) = 1.2048192771084337349397590361446 y[1] (numeric) = 1.204819277108447970292868584368 absolute error = 1.42353531095482234e-14 relative error = 1.1815343080925025422000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 1.2062726176115802171290711700844 y[1] (numeric) = 1.2062726176115946182652629293339 absolute error = 1.44011361917592495e-14 relative error = 1.1938541902968417835500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 1.2077294685990338164251207729469 y[1] (numeric) = 1.2077294685990483849033500417814 absolute error = 1.45684782292688345e-14 relative error = 1.2062699973834594966000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 1.2091898428053204353083434099154 y[1] (numeric) = 1.2091898428053351727032665295785 absolute error = 1.47373949231196631e-14 relative error = 1.2187825601419961383700000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 1.2106537530266343825665859564165 y[1] (numeric) = 1.2106537530266492904687348741637 absolute error = 1.49079021489177472e-14 relative error = 1.2313927175006059187200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.175 y[1] (analytic) = 1.2121212121212121212121212121212 y[1] (numeric) = 1.2121212121212272012280801868951 absolute error = 1.50800159589747739e-14 relative error = 1.2441013166154188467500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.176 y[1] (analytic) = 1.2135922330097087378640776699029 y[1] (numeric) = 1.2135922330097239916166621492127 absolute error = 1.52537525844793098e-14 relative error = 1.2569092129610951275200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.177 y[1] (analytic) = 1.2150668286755771567436208991495 y[1] (numeric) = 1.2150668286755925858720585964353 absolute error = 1.54291284376972858e-14 relative error = 1.2698172704224866213400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 1.216545012165450121654501216545 y[1] (numeric) = 1.2165450121654657278146154187382 absolute error = 1.56061601142021932e-14 relative error = 1.2828263613874202810400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.179 y[1] (analytic) = 1.2180267965895249695493300852619 y[1] (numeric) = 1.218026796589540754413725220689 absolute error = 1.57848643951354271e-14 relative error = 1.2959373668406185649100000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.18 y[1] (analytic) = 1.2195121951219512195121951219512 y[1] (numeric) = 1.219512195121967184770444619175 absolute error = 1.59652582494972238e-14 relative error = 1.3091511764587723516000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 1.2210012210012210012210012210012 y[1] (numeric) = 1.2210012210012371485798376896429 absolute error = 1.61473588364686417e-14 relative error = 1.3224686887067817552300000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 1.2224938875305623471882640586797 y[1] (numeric) = 1.222493887530578678371771823725 absolute error = 1.63311835077650453e-14 relative error = 1.3358908109351807055400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 1.2239902080783353733170134638923 y[1] (numeric) = 1.2239902080783518900668234854509 absolute error = 1.65167498100215586e-14 relative error = 1.3494184594787613376200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 1.2254901960784313725490196078431 y[1] (numeric) = 1.2254901960784480766245068188038 absolute error = 1.67040754872109607e-14 relative error = 1.3630525597564143931200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 1.2269938650306748466257668711656 y[1] (numeric) = 1.2269938650306917398042499656705 absolute error = 1.68931784830945049e-14 relative error = 1.3767940463722021493500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=1.87 NO POLE x[1] = 0.186 y[1] (analytic) = 1.2285012285012285012285012285012 y[1] (numeric) = 1.2285012285012455853054449346523 absolute error = 1.70840769437061511e-14 relative error = 1.3906438632176806995400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 1.2300123001230012300123001230012 y[1] (numeric) = 1.2300123001230185068015199937085 absolute error = 1.72767892198707073e-14 relative error = 1.4046029635754885034900000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.188 y[1] (analytic) = 1.2315270935960591133004926108374 y[1] (numeric) = 1.2315270935960765846343623672218 absolute error = 1.74713338697563844e-14 relative error = 1.4186723102242184132800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.189 y[1] (analytic) = 1.2330456226880394574599260172626 y[1] (numeric) = 1.2330456226880571251895874795418 absolute error = 1.76677296614622792e-14 relative error = 1.4328528755445908431200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 1.2345679012345679012345679012346 y[1] (numeric) = 1.2345679012345857672301435425391 absolute error = 1.78659955756413045e-14 relative error = 1.4471456416269456645000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 1.23609394313967861557478368356 y[1] (numeric) = 1.2360939431396966817255918426575 absolute error = 1.80661508081590975e-14 relative error = 1.4615516003800709877499999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 1.2376237623762376237623762376238 y[1] (numeric) = 1.2376237623762558919771490270676 absolute error = 1.82682147727894438e-14 relative error = 1.4760717536413870590400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.193 y[1] (analytic) = 1.2391573729863692688971499380421 y[1] (numeric) = 1.2391573729863877411042538848063 absolute error = 1.84722071039467642e-14 relative error = 1.4907071132885038709400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 1.2406947890818858560794044665012 y[1] (numeric) = 1.2406947890819045342270639227214 absolute error = 1.86781476594562202e-14 relative error = 1.5054587013521713481200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.195 y[1] (analytic) = 1.2422360248447204968944099378882 y[1] (numeric) = 1.242236024844739382950933299891 absolute error = 1.88860565233620028e-14 relative error = 1.5203275501306412254000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 1.2437810945273631840796019900498 y[1] (numeric) = 1.2437810945273822800336107644285 absolute error = 1.90959540087743787e-14 relative error = 1.5353147023054600474799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 1.24533001245330012453300124533 y[1] (numeric) = 1.245330012453319432393662001407 absolute error = 1.93078606607560770e-14 relative error = 1.5504212110587129831000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 1.2468827930174563591022443890274 y[1] (numeric) = 1.2468827930174758808995036376367 absolute error = 1.95217972592486093e-14 relative error = 1.5656481401917384658600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 1.2484394506866416978776529338327 y[1] (numeric) = 1.2484394506866614356624749729593 absolute error = 1.97377848220391266e-14 relative error = 1.5809965642453340406600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2 y[1] (analytic) = 1.25 y[1] (numeric) = 1.2500000000000199558446077684241 absolute error = 1.99558446077684241e-14 relative error = 1.5964675686214739280000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 1.2515644555694618272841051314143 y[1] (numeric) = 1.2515644555694820032822241121314 absolute error = 2.01759981189807171e-14 relative error = 1.6120622497065592962900000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=2.03 NO POLE x[1] = 0.202 y[1] (analytic) = 1.2531328320802005012531328320802 y[1] (numeric) = 1.2531328320802208995202380479007 absolute error = 2.03982671052158205e-14 relative error = 1.6277817149962224759000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.203 y[1] (analytic) = 1.2547051442910915934755332496863 y[1] (numeric) = 1.2547051442911122161490993940609 absolute error = 2.06226735661443746e-14 relative error = 1.6436270832217066556200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.204 y[1] (analytic) = 1.2562814070351758793969849246231 y[1] (numeric) = 1.2562814070351967286367396713946 absolute error = 2.08492397547467715e-14 relative error = 1.6595994844778430114000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.205 y[1] (analytic) = 1.2578616352201257861635220125786 y[1] (numeric) = 1.2578616352201468641517025490243 absolute error = 2.10779881805364457e-14 relative error = 1.6757000603526474331500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.206 y[1] (analytic) = 1.2594458438287153652392947103275 y[1] (numeric) = 1.2594458438287366741809075385317 absolute error = 2.13089416128282042e-14 relative error = 1.6919299640585594134799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.207 y[1] (analytic) = 1.2610340479192938209331651954603 y[1] (numeric) = 1.2610340479193153630562492477442 absolute error = 2.15421230840522839e-14 relative error = 1.7082903605653461132700000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.208 y[1] (analytic) = 1.2626262626262626262626262626263 y[1] (numeric) = 1.2626262626262844038185193774574 absolute error = 2.17775558931148311e-14 relative error = 1.7247824267346946231199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.209 y[1] (analytic) = 1.2642225031605562579013906447535 y[1] (numeric) = 1.2642225031605782731649994502697 absolute error = 2.20152636088055162e-14 relative error = 1.7414073514565163314200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.21 y[1] (analytic) = 1.2658227848101265822784810126582 y[1] (numeric) = 1.2658227848101488375485542656598 absolute error = 2.22552700732530016e-14 relative error = 1.7581663357869871264000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.211 y[1] (analytic) = 1.2674271229404309252217997465146 y[1] (numeric) = 1.2674271229404534228212051755114 absolute error = 2.24975994054289968e-14 relative error = 1.7750605930883478475200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.212 y[1] (analytic) = 1.2690355329949238578680203045685 y[1] (numeric) = 1.2690355329949466001440250062156 absolute error = 2.27422760047016471e-14 relative error = 1.7920913491704897914800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.213 y[1] (analytic) = 1.2706480304955527318932655654384 y[1] (numeric) = 1.2706480304955757212178200044491 absolute error = 2.29893245544390107e-14 relative error = 1.8092598424343501420900000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.214 y[1] (analytic) = 1.2722646310432569974554707379135 y[1] (numeric) = 1.2722646310432802362254964013114 absolute error = 2.32387700256633979e-14 relative error = 1.8265673240171430749400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.215 y[1] (analytic) = 1.2738853503184713375796178343949 y[1] (numeric) = 1.2738853503184948282172985917467 absolute error = 2.34906376807573518e-14 relative error = 1.8440150579394521163000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.216 y[1] (analytic) = 1.2755102040816326530612244897959 y[1] (numeric) = 1.2755102040816563980143017118654 absolute error = 2.37449530772220695e-14 relative error = 1.8616043212542102488000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.217 y[1] (analytic) = 1.2771392081736909323116219667944 y[1] (numeric) = 1.2771392081737149340536934558659 absolute error = 2.40017420714890715e-14 relative error = 1.8793364041975942984500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=53.4MB, alloc=4.1MB, time=2.19 x[1] = 0.218 y[1] (analytic) = 1.278772378516624040920716112532 y[1] (numeric) = 1.2787723785166483019515388984749 absolute error = 2.42610308227859429e-14 relative error = 1.8972126103418607347800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.219 y[1] (analytic) = 1.2804097311139564660691421254802 y[1] (numeric) = 1.2804097311139809889149391824626 absolute error = 2.45228457970569824e-14 relative error = 1.9152342567501503254399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.22 y[1] (analytic) = 1.2820512820512820512820512820513 y[1] (numeric) = 1.2820512820513068384958222216624 absolute error = 2.47872137709396111e-14 relative error = 1.9334026741332896658000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.221 y[1] (analytic) = 1.2836970474967907573812580231065 y[1] (numeric) = 1.2836970474968158115430938205113 absolute error = 2.50541618357974048e-14 relative error = 1.9517192070086178339200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.222 y[1] (analytic) = 1.2853470437017994858611825192802 y[1] (numeric) = 1.2853470437018248095785843299102 absolute error = 2.53237174018106300e-14 relative error = 1.9701852138608670140000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.223 y[1] (analytic) = 1.2870012870012870012870012870013 y[1] (numeric) = 1.2870012870013125971952034121796 absolute error = 2.55959082021251783e-14 relative error = 1.9888020673051263539100000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.224 y[1] (analytic) = 1.2886597938144329896907216494845 y[1] (numeric) = 1.2886597938144588604530187102922 absolute error = 2.58707622970608077e-14 relative error = 2.0075711542519186775200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.225 y[1] (analytic) = 1.2903225806451612903225806451613 y[1] (numeric) = 1.2903225806451874386306590247777 absolute error = 2.61483080783796164e-14 relative error = 2.0264938760744202710000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.226 y[1] (analytic) = 1.2919896640826873385012919896641 y[1] (numeric) = 1.2919896640827137670755656053536 absolute error = 2.64285742736156895e-14 relative error = 2.0455716487778543673000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.227 y[1] (analytic) = 1.2936610608020698576972833117723 y[1] (numeric) = 1.2936610608020965692872337786468 absolute error = 2.67115899504668745e-14 relative error = 2.0648059031710893988500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.228 y[1] (analytic) = 1.2953367875647668393782383419689 y[1] (numeric) = 1.2953367875647938367627595916272 absolute error = 2.69973845212496583e-14 relative error = 2.0841980850404736207600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.229 y[1] (analytic) = 1.2970168612191958495460440985733 y[1] (numeric) = 1.2970168612192231355337915167087 absolute error = 2.72859877474181354e-14 relative error = 2.1037496553259382393400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.23 y[1] (analytic) = 1.2987012987012987012987012987013 y[1] (numeric) = 1.2987012987013262787284454467736 absolute error = 2.75774297441480723e-14 relative error = 2.1234620902994015671000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.231 y[1] (analytic) = 1.3003901170351105331599479843953 y[1] (numeric) = 1.3003901170351384049009329714866 absolute error = 2.78717409849870913e-14 relative error = 2.1433368817455073209700000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.232 y[1] (analytic) = 1.3020833333333333333333333333333 y[1] (numeric) = 1.302083333333361502285639905348 absolute error = 2.81689523065720147e-14 relative error = 2.1633755371447307289600000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.233 y[1] (analytic) = 1.3037809647979139504563233376793 y[1] (numeric) = 1.3037809647979424195512367521059 absolute error = 2.84690949134144266e-14 relative error = 2.1835795798588865202199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.234 y[1] (analytic) = 1.3054830287206266318537859007833 y[1] (numeric) = 1.3054830287206554040541686563131 absolute error = 2.87722003827555298e-14 relative error = 2.2039505493190735826800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=2.35 NO POLE x[1] = 0.235 y[1] (analytic) = 1.307189542483660130718954248366 y[1] (numeric) = 1.3071895424836892090196237397566 absolute error = 2.90783006694913906e-14 relative error = 2.2244900012160913809000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.236 y[1] (analytic) = 1.3089005235602094240837696335079 y[1] (numeric) = 1.3089005235602388115118808031948 absolute error = 2.93874281111696869e-14 relative error = 2.2451995076933640791599999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.237 y[1] (analytic) = 1.3106159895150720838794233289646 y[1] (numeric) = 1.3106159895151017834948563880556 absolute error = 2.96996154330590910e-14 relative error = 2.2660806575424086433000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.238 y[1] (analytic) = 1.3123359580052493438320209973753 y[1] (numeric) = 1.3123359580052793587277742898136 absolute error = 3.00148957532924383e-14 relative error = 2.2871350564008837984600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.239 y[1] (analytic) = 1.3140604467805519053876478318003 y[1] (numeric) = 1.314060446780582238690235916656 absolute error = 3.03333025880848557e-14 relative error = 2.3083643269532575187699999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.24 y[1] (analytic) = 1.3157894736842105263157894736842 y[1] (numeric) = 1.3157894736842411811856465017237 absolute error = 3.06548698570280395e-14 relative error = 2.3297701091341310020000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.241 y[1] (analytic) = 1.3175230566534914361001317523057 y[1] (numeric) = 1.3175230566535224157320202142019 absolute error = 3.09796318884618962e-14 relative error = 2.3513540603342579215799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.242 y[1] (analytic) = 1.3192612137203166226912928759894 y[1] (numeric) = 1.3192612137203479303147178007693 absolute error = 3.13076234249247799e-14 relative error = 2.3731178556092983164200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.243 y[1] (analytic) = 1.321003963011889035667107001321 y[1] (numeric) = 1.3210039630119206745467356849008 absolute error = 3.16388796286835798e-14 relative error = 2.3950631878913469908600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.244 y[1] (analytic) = 1.3227513227513227513227513227513 y[1] (numeric) = 1.3227513227513547247588386676871 absolute error = 3.19734360873449358e-14 relative error = 2.4171917682032771464800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.245 y[1] (analytic) = 1.3245033112582781456953642384106 y[1] (numeric) = 1.3245033112583104570241837872894 absolute error = 3.23113288195488788e-14 relative error = 2.4395053258759403494000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.246 y[1] (analytic) = 1.3262599469496021220159151193634 y[1] (numeric) = 1.3262599469496347746101958655821 absolute error = 3.26525942807462187e-14 relative error = 2.4620056087682648899800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.247 y[1] (analytic) = 1.3280212483399734395750332005312 y[1] (numeric) = 1.3280212483400064368444022615537 absolute error = 3.29972693690610225e-14 relative error = 2.4846943834902949942500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.248 y[1] (analytic) = 1.3297872340425531914893617021277 y[1] (numeric) = 1.3297872340425865368807929416783 absolute error = 3.33453914312395506e-14 relative error = 2.5075734356292142051199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.249 y[1] (analytic) = 1.3315579227696404793608521970706 y[1] (numeric) = 1.3315579227696741763591208841135 absolute error = 3.36969982686870429e-14 relative error = 2.5306445699783969217899999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.25 y[1] (analytic) = 1.3333333333333333333333333333333 y[1] (numeric) = 1.3333333333333673854614769271024 absolute error = 3.40521281435937691e-14 relative error = 2.5539096107695326825000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.1MB, time=2.51 NO POLE x[1] = 0.251 y[1] (analytic) = 1.3351134846461949265687583444593 y[1] (numeric) = 1.3351134846462293373885434962432 absolute error = 3.44108197851517839e-14 relative error = 2.5773704019078686141100000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.252 y[1] (analytic) = 1.3368983957219251336898395721925 y[1] (numeric) = 1.3368983957219599068022354360461 absolute error = 3.47731123958638536e-14 relative error = 2.6010288072106162492800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.253 y[1] (analytic) = 1.3386880856760374832663989290495 y[1] (numeric) = 1.3386880856760726223120568750919 absolute error = 3.51390456579460424e-14 relative error = 2.6248867106485693672800000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.254 y[1] (analytic) = 1.3404825737265415549597855227882 y[1] (numeric) = 1.3404825737265770636195253482669 absolute error = 3.55086597398254787e-14 relative error = 2.6489460165909807110200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.255 y[1] (analytic) = 1.3422818791946308724832214765101 y[1] (numeric) = 1.3422818791946667544785242113533 absolute error = 3.58819953027348432e-14 relative error = 2.6732086500537458183999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.256 y[1] (analytic) = 1.3440860215053763440860215053763 y[1] (numeric) = 1.3440860215054126031795289105268 absolute error = 3.62590935074051505e-14 relative error = 2.6976765569509431972000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.257 y[1] (analytic) = 1.3458950201884253028263795423957 y[1] (numeric) = 1.3458950201884619428224004008179 absolute error = 3.66399960208584222e-14 relative error = 2.7223517043497807694600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.258 y[1] (analytic) = 1.3477088948787061994609164420485 y[1] (numeric) = 1.3477088948787432242059397439288 absolute error = 3.70247450233018803e-14 relative error = 2.7472360807289995182600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.259 y[1] (analytic) = 1.3495276653171390013495276653171 y[1] (numeric) = 1.3495276653171764147327427906305 absolute error = 3.74133832151253134e-14 relative error = 2.7723316962407857229400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.26 y[1] (analytic) = 1.3513513513513513513513513513514 y[1] (numeric) = 1.3513513513513891573051753546544 absolute error = 3.78059538240033030e-14 relative error = 2.7976405829762444219999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.261 y[1] (analytic) = 1.3531799729364005412719891745602 y[1] (numeric) = 1.3531799729364387437726012785844 absolute error = 3.82025006121040242e-14 relative error = 2.8231647952344873883800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.262 y[1] (analytic) = 1.3550135501355013550135501355014 y[1] (numeric) = 1.3550135501355399580814335418653 absolute error = 3.86030678834063639e-14 relative error = 2.8489064097953896558199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.263 y[1] (analytic) = 1.3568521031207598371777476255088 y[1] (numeric) = 1.3568521031207988448782387526448 absolute error = 3.90077004911271360e-14 relative error = 2.8748675261960699232000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.264 y[1] (analytic) = 1.3586956521739130434782608695652 y[1] (numeric) = 1.3586956521739524599221061297626 absolute error = 3.94164438452601974e-14 relative error = 2.9010502670111505286400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.265 y[1] (analytic) = 1.3605442176870748299319727891156 y[1] (numeric) = 1.3605442176871146592758930184233 absolute error = 3.98293439202293077e-14 relative error = 2.9274567781368541159500000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.266 y[1] (analytic) = 1.3623978201634877384196185286104 y[1] (numeric) = 1.3623978201635279848668811852135 absolute error = 4.02464472626566031e-14 relative error = 2.9540892290789946675399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.1MB, time=2.67 NO POLE x[1] = 0.267 y[1] (analytic) = 1.3642564802182810368349249658936 y[1] (numeric) = 1.364256480218321704635924214486 absolute error = 4.06678009992485924e-14 relative error = 2.9809498132449218229200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.268 y[1] (analytic) = 1.3661202185792349726775956284153 y[1] (numeric) = 1.3661202185792760661304404300277 absolute error = 4.10934528448016124e-14 relative error = 3.0080407482394780276800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.269 y[1] (analytic) = 1.3679890560875512995896032831737 y[1] (numeric) = 1.3679890560875928230407136118946 absolute error = 4.15234511103287209e-14 relative error = 3.0353642761650294977900000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.27 y[1] (analytic) = 1.369863013698630136986301369863 y[1] (numeric) = 1.3698630136986720948310126798977 absolute error = 4.19578447113100347e-14 relative error = 3.0629226639256325331000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.271 y[1] (analytic) = 1.3717421124828532235939643347051 y[1] (numeric) = 1.3717421124828956202771404032657 absolute error = 4.23966831760685606e-14 relative error = 3.0907182035353980677399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.272 y[1] (analytic) = 1.3736263736263736263736263736264 y[1] (numeric) = 1.3736263736264164663902806472278 absolute error = 4.28400166542736014e-14 relative error = 3.1187532124311181819199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.273 y[1] (analytic) = 1.3755158184319119669876203576341 y[1] (numeric) = 1.3755158184319552548835459314921 absolute error = 4.32878959255738580e-14 relative error = 3.1470300337892194766000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.274 y[1] (analytic) = 1.3774104683195592286501377410468 y[1] (numeric) = 1.377410468319602969022546103433 absolute error = 4.37403724083623862e-14 relative error = 3.1755510368471092381200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.275 y[1] (analytic) = 1.3793103448275862068965517241379 y[1] (numeric) = 1.3793103448276304043947203997438 absolute error = 4.41974981686756059e-14 relative error = 3.2043186172289814277500000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.276 y[1] (analytic) = 1.3812154696132596685082872928177 y[1] (numeric) = 1.3812154696133043278342165214179 absolute error = 4.46593259292286002e-14 relative error = 3.2333351972761506544800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.277 y[1] (analytic) = 1.3831258644536652835408022130014 y[1] (numeric) = 1.3831258644537104094498808019838 absolute error = 4.51259090785889824e-14 relative error = 3.2626032263819834275200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.278 y[1] (analytic) = 1.3850415512465373961218836565097 y[1] (numeric) = 1.3850415512465829934235641481591 absolute error = 4.55973016804916494e-14 relative error = 3.2921251813314970866800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.279 y[1] (analytic) = 1.3869625520110957004160887656033 y[1] (numeric) = 1.3869625520111417739745720623874 absolute error = 4.60735584832967841e-14 relative error = 3.3219035666456981336100000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.28 y[1] (analytic) = 1.3888888888888888888888888888889 y[1] (numeric) = 1.3888888888889354436238184823985 absolute error = 4.65547349295935096e-14 relative error = 3.3519409149307326912000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.281 y[1] (analytic) = 1.3908205841446453407510431154381 y[1] (numeric) = 1.3908205841446923816382090670828 absolute error = 4.70408871659516447e-14 relative error = 3.3822397872319232539300000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.282 y[1] (analytic) = 1.3927576601671309192200557103064 y[1] (numeric) = 1.3927576601671784512921085343575 absolute error = 4.75320720528240511e-14 relative error = 3.4128027733927668689800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=2.83 NO POLE x[1] = 0.283 y[1] (analytic) = 1.3947001394700139470013947001395 y[1] (numeric) = 1.3947001394700619753485693022523 absolute error = 4.80283471746021128e-14 relative error = 3.4436324924189714877599999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.284 y[1] (analytic) = 1.3966480446927374301675977653631 y[1] (numeric) = 1.3966480446927859599384475922934 absolute error = 4.85297708498269303e-14 relative error = 3.4747315928476082094800000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.285 y[1] (analytic) = 1.3986013986013986013986013986014 y[1] (numeric) = 1.3986013986014476378007429574633 absolute error = 4.90364021415588619e-14 relative error = 3.5061027531214586258500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.286 y[1] (analytic) = 1.4005602240896358543417366946779 y[1] (numeric) = 1.4005602240896854026426046027706 absolute error = 4.95483008679080927e-14 relative error = 3.5377486819686378187799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.287 y[1] (analytic) = 1.4025245441795231416549789621318 y[1] (numeric) = 1.4025245441795732071825916910912 absolute error = 5.00655276127289594e-14 relative error = 3.5696721187875748052200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.288 y[1] (analytic) = 1.4044943820224719101123595505618 y[1] (numeric) = 1.4044943820225224982560960313722 absolute error = 5.05881437364808104e-14 relative error = 3.6018758340374337004800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.289 y[1] (analytic) = 1.4064697609001406469760900140647 y[1] (numeric) = 1.4064697609001917631874772722972 absolute error = 5.11162113872582325e-14 relative error = 3.6343626296340603307500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.29 y[1] (analytic) = 1.4084507042253521126760563380282 y[1] (numeric) = 1.4084507042254037624695683315538 absolute error = 5.16497935119935256e-14 relative error = 3.6671353393515403175999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.291 y[1] (analytic) = 1.4104372355430183356840620592384 y[1] (numeric) = 1.4104372355430705246379298936008 absolute error = 5.21889538678343624e-14 relative error = 3.7001968292294562941599999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.292 y[1] (analytic) = 1.4124293785310734463276836158192 y[1] (numeric) = 1.4124293785311261800847173154407 absolute error = 5.27337570336996215e-14 relative error = 3.7335499979859332022000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.293 y[1] (analytic) = 1.4144271570014144271570014144272 y[1] (numeric) = 1.4144271570014677114254234308683 absolute error = 5.32842684220164411e-14 relative error = 3.7671977774365623857699999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.294 y[1] (analytic) = 1.416430594900849858356940509915 y[1] (numeric) = 1.4164305949009036989112311515095 absolute error = 5.38405542906415945e-14 relative error = 3.8011431329192965717000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.295 y[1] (analytic) = 1.4184397163120567375886524822695 y[1] (numeric) = 1.418439716312111140270407452615 absolute error = 5.44026817549703455e-14 relative error = 3.8353890637254093577500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.296 y[1] (analytic) = 1.4204545454545454545454545454545 y[1] (numeric) = 1.4204545454546004252642547814589 absolute error = 5.49707188002360044e-14 relative error = 3.8699386035366147097600000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.297 y[1] (analytic) = 1.4224751066856330014224751066856 y[1] (numeric) = 1.4224751066856885461567691101455 absolute error = 5.55447342940034599e-14 relative error = 3.9047948208684432309700000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.298 y[1] (analytic) = 1.4245014245014245014245014245014 y[1] (numeric) = 1.4245014245014806262225002845296 absolute error = 5.61247979988600282e-14 relative error = 3.9399608195199739796400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=72.4MB, alloc=4.1MB, time=2.99 x[1] = 0.299 y[1] (analytic) = 1.4265335235378031383737517831669 y[1] (numeric) = 1.4265335235378598493543370901865 absolute error = 5.67109805853070196e-14 relative error = 3.9754397390300220739600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3 y[1] (analytic) = 1.4285714285714285714285714285714 y[1] (numeric) = 1.4285714285714858747822162840588 absolute error = 5.73033536448554874e-14 relative error = 4.0112347551398841180000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.301 y[1] (analytic) = 1.4306151645207439198855507868383 y[1] (numeric) = 1.4306151645208018218752541165287 absolute error = 5.79019897033296904e-14 relative error = 4.0473490802627453589600000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.302 y[1] (analytic) = 1.4326647564469914040114613180516 y[1] (numeric) = 1.4326647564470499109736956999149 absolute error = 5.85069622343818633e-14 relative error = 4.0837859639598540583399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.303 y[1] (analytic) = 1.4347202295552367288378766140603 y[1] (numeric) = 1.4347202295552958471835498360207 absolute error = 5.91183456732219604e-14 relative error = 4.1205486934235706398799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304 y[1] (analytic) = 1.4367816091954022988505747126437 y[1] (numeric) = 1.4367816091954620350660052787468 absolute error = 5.97362154305661031e-14 relative error = 4.1576405939674007757599999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.305 y[1] (analytic) = 1.4388489208633093525179856115108 y[1] (numeric) = 1.4388489208633697131658924190467 absolute error = 6.03606479068075359e-14 relative error = 4.1950650295231237450500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.306 y[1] (analytic) = 1.440922190201729106628242074928 y[1] (numeric) = 1.4409221902017900983487484888919 absolute error = 6.09917205064139639e-14 relative error = 4.2328254031451290946599999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.307 y[1] (analytic) = 1.4430014430014430014430014430014 y[1] (numeric) = 1.4430014430015046309546539982218 absolute error = 6.16295116525552204e-14 relative error = 4.2709251575220767737200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.308 y[1] (analytic) = 1.445086705202312138728323699422 y[1] (numeric) = 1.4450867052023744128291256647075 absolute error = 6.22741008019652855e-14 relative error = 4.3093677754959977565999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.309 y[1] (analytic) = 1.4471780028943560057887120115774 y[1] (numeric) = 1.4471780028944189313571720543339 absolute error = 6.29255684600427565e-14 relative error = 4.3481567805889544741500000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.31 y[1] (analytic) = 1.4492753623188405797101449275362 y[1] (numeric) = 1.4492753623189041637063411214793 absolute error = 6.35839961961939431e-14 relative error = 4.3872957375373820739000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.311 y[1] (analytic) = 1.4513788098693759071117561683599 y[1] (numeric) = 1.4513788098694401565784155912058 absolute error = 6.42494666594228459e-14 relative error = 4.4267882528342340825100000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.312 y[1] (analytic) = 1.4534883720930232558139534883721 y[1] (numeric) = 1.4534883720930881778775476607245 absolute error = 6.49220635941723524e-14 relative error = 4.4666379752790578451200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.313 y[1] (analytic) = 1.4556040756914119359534206695779 y[1] (numeric) = 1.4556040756914775378252770906491 absolute error = 6.56018718564210712e-14 relative error = 4.5068485965361275914399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.314 y[1] (analytic) = 1.4577259475218658892128279883382 y[1] (numeric) = 1.4577259475219321781902580286438 absolute error = 6.62889774300403056e-14 relative error = 4.5474238517007649641600000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.315 y[1] (analytic) = 1.459854014598540145985401459854 y[1] (numeric) = 1.4598540145986071294528448756125 absolute error = 6.69834674434157585e-14 relative error = 4.5883675198739794572500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.1MB, time=3.15 NO POLE x[1] = 0.316 y[1] (analytic) = 1.4619883040935672514619883040936 y[1] (numeric) = 1.4619883040936349368921746427372 absolute error = 6.76854301863386436e-14 relative error = 4.6296834247455632222399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.317 y[1] (analytic) = 1.4641288433382137628111273792094 y[1] (numeric) = 1.4641288433382821577662545501802 absolute error = 6.83949551271709708e-14 relative error = 4.6713754351857773056399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.318 y[1] (analytic) = 1.4662756598240469208211143695015 y[1] (numeric) = 1.4662756598241160329540446593652 absolute error = 6.91121329302898637e-14 relative error = 4.7134474658457687043399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.319 y[1] (analytic) = 1.4684287812041116005873715124816 y[1] (numeric) = 1.4684287812041814376428453283422 absolute error = 6.98370554738158606e-14 relative error = 4.7559034777668601068600000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.32 y[1] (analytic) = 1.4705882352941176470588235294118 y[1] (numeric) = 1.4705882352941882168746911596577 absolute error = 7.05698158676302459e-14 relative error = 4.7987474789988567211999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.321 y[1] (analytic) = 1.4727540500736377025036818851252 y[1] (numeric) = 1.4727540500737090130121535716821 absolute error = 7.13105084716865569e-14 relative error = 4.8419835252275172135099999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.322 y[1] (analytic) = 1.4749262536873156342182890855457 y[1] (numeric) = 1.4749262536873876934472037070533 absolute error = 7.20592289146215076e-14 relative error = 4.8856157204113382152800000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.323 y[1] (analytic) = 1.477104874446085672082717872969 y[1] (numeric) = 1.4771048744461584881568305436448 absolute error = 7.28160741126706758e-14 relative error = 4.9296482174278047516599999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.324 y[1] (analytic) = 1.4792899408284023668639053254438 y[1] (numeric) = 1.4792899408284759480061942198456 absolute error = 7.35811422888944018e-14 relative error = 4.9740852187292615616800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.325 y[1] (analytic) = 1.4814814814814814814814814814815 y[1] (numeric) = 1.4814814814815558360144742009327 absolute error = 7.43545329927194512e-14 relative error = 5.0189309770085629559999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.326 y[1] (analytic) = 1.4836795252225519287833827893175 y[1] (numeric) = 1.4836795252226270651305025914225 absolute error = 7.51363471198021050e-14 relative error = 5.0641897958746618770000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.327 y[1] (analytic) = 1.4858841010401188707280832095097 y[1] (numeric) = 1.4858841010401947974150154279573 absolute error = 7.59266869322184476e-14 relative error = 5.1098660305383015234799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.328 y[1] (analytic) = 1.4880952380952380952380952380952 y[1] (numeric) = 1.4880952380953148208941742258336 absolute error = 7.67256560789877384e-14 relative error = 5.1559640885079760204800000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.329 y[1] (analytic) = 1.4903129657228017883755588673621 y[1] (numeric) = 1.4903129657228793217351758022259 absolute error = 7.75333596169348638e-14 relative error = 5.2024884302963293609800000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.33 y[1] (analytic) = 1.4925373134328358208955223880597 y[1] (numeric) = 1.4925373134329141707995542860477 absolute error = 7.83499040318979880e-14 relative error = 5.2494435701371651960000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.331 y[1] (analytic) = 1.4947683109118086696562032884903 y[1] (numeric) = 1.4947683109118878450534635761277 absolute error = 7.91753972602876374e-14 relative error = 5.2968340767132429420599999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.1MB, time=3.31 NO POLE x[1] = 0.332 y[1] (analytic) = 1.4970059880239520958083832335329 y[1] (numeric) = 1.4970059880240321057570942371087 absolute error = 8.00099487110035758e-14 relative error = 5.3446645738950388634400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.333 y[1] (analytic) = 1.4992503748125937031484257871064 y[1] (numeric) = 1.4992503748126745568177135030607 absolute error = 8.08536692877159543e-14 relative error = 5.3929397414906541518100000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.334 y[1] (analytic) = 1.5015015015015015015015015015015 y[1] (numeric) = 1.5015015015015832081729130188475 absolute error = 8.17066714115173460e-14 relative error = 5.4416643160070552436000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.335 y[1] (analytic) = 1.5037593984962406015037593984962 y[1] (numeric) = 1.503759398496323170572803350901 absolute error = 8.25690690439524048e-14 relative error = 5.4908430914228349192000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.336 y[1] (analytic) = 1.5060240963855421686746987951807 y[1] (numeric) = 1.5060240963856256096524092272025 absolute error = 8.34409777104320218e-14 relative error = 5.5404809199726862475200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.337 y[1] (analytic) = 1.5082956259426847662141779788839 y[1] (numeric) = 1.5082956259427690887287020178722 absolute error = 8.43225145240389883e-14 relative error = 5.5905827129437849242899999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.338 y[1] (analytic) = 1.5105740181268882175226586102719 y[1] (numeric) = 1.5105740181269734313208683425844 absolute error = 8.52137982097323125e-14 relative error = 5.6411534414842790875000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.339 y[1] (analytic) = 1.5128593040847201210287443267776 y[1] (numeric) = 1.5128593040848062359778732842555 absolute error = 8.61149491289574779e-14 relative error = 5.6921981374240892891900000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.34 y[1] (analytic) = 1.5151515151515151515151515151515 y[1] (numeric) = 1.5151515151516021776044561852299 absolute error = 8.70260893046700784e-14 relative error = 5.7437218941082251744000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.341 y[1] (analytic) = 1.517450682852807283763277693475 y[1] (numeric) = 1.5174506828528952311057244738845 absolute error = 8.79473424467804095e-14 relative error = 5.7957298672428289860499999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.342 y[1] (analytic) = 1.5197568389057750759878419452888 y[1] (numeric) = 1.5197568389058639548218199720373 absolute error = 8.88788339780267485e-14 relative error = 5.8482272757541600512999999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.343 y[1] (analytic) = 1.52207001522070015220700152207 y[1] (numeric) = 1.522070015220789972898061807278 absolute error = 8.98206910602852080e-14 relative error = 5.9012194026607381656000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.344 y[1] (analytic) = 1.524390243902439024390243902439 y[1] (numeric) = 1.5243902439025297974328652266465 absolute error = 9.07730426213242075e-14 relative error = 5.9547115959588680120000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.345 y[1] (analytic) = 1.5267175572519083969465648854962 y[1] (numeric) = 1.5267175572520001329659468972621 absolute error = 9.17360193820117659e-14 relative error = 6.0087092695217706664499999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.346 y[1] (analytic) = 1.5290519877675840978593272171254 y[1] (numeric) = 1.5290519877676768076132112011087 absolute error = 9.27097538839839833e-14 relative error = 6.0632179040125525078199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.347 y[1] (analytic) = 1.531393568147013782542113323124 y[1] (numeric) = 1.5313935681471074769226311063714 absolute error = 9.36943805177832474e-14 relative error = 6.1182430478112460552200000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.1MB, time=3.47 NO POLE x[1] = 0.348 y[1] (analytic) = 1.5337423312883435582822085889571 y[1] (numeric) = 1.5337423312884382483177600638286 absolute error = 9.46900355514748715e-14 relative error = 6.1737903179561616217999999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.349 y[1] (analytic) = 1.5360983102918586789554531490015 y[1] (numeric) = 1.5360983102919543758126129000495 absolute error = 9.56968571597510480e-14 relative error = 6.2298654010997932248000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.35 y[1] (analytic) = 1.5384615384615384615384615384615 y[1] (numeric) = 1.5384615384616351765239150696363 absolute error = 9.67149854535311748e-14 relative error = 6.2864740544795263620000000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.351 y[1] (analytic) = 1.5408320493066255778120184899846 y[1] (numeric) = 1.5408320493067233223745285577869 absolute error = 9.77445625100678023e-14 relative error = 6.3436221069034003692700000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.352 y[1] (analytic) = 1.5432098765432098765432098765432 y[1] (numeric) = 1.543209876543308662275613444172 absolute error = 9.87857324035676288e-14 relative error = 6.4013154597511823462400000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.353 y[1] (analytic) = 1.5455950540958268933539412673879 y[1] (numeric) = 1.5455950540959267319951776045539 absolute error = 9.98386412363371660e-14 relative error = 6.4595600879910146402000000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.354 y[1] (analytic) = 1.5479876160990712074303405572755 y[1] (numeric) = 1.5479876160991721108675110201672 absolute error = 1.009034371704628917e-13 relative error = 6.5183620412119028038200000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.355 y[1] (analytic) = 1.5503875968992248062015503875969 y[1] (numeric) = 1.5503875968993267864720104235009 absolute error = 1.019802704600359040e-13 relative error = 6.5777274446723158080000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.356 y[1] (analytic) = 1.5527950310559006211180124223602 y[1] (numeric) = 1.5527950310560036904114963536567 absolute error = 1.030692934839312965e-13 relative error = 6.6376625003651754946000000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.357 y[1] (analytic) = 1.5552099533437013996889580093313 y[1] (numeric) = 1.5552099533438055703497371620118 absolute error = 1.041706607791526805e-13 relative error = 6.6981734880995173561499999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.358 y[1] (analytic) = 1.5576323987538940809968847352025 y[1] (numeric) = 1.5576323987539993655259594876986 absolute error = 1.052845290747524961e-13 relative error = 6.7592667665991102496200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.359 y[1] (analytic) = 1.56006240249609984399375975039 y[1] (numeric) = 1.5600624024962062550510860893551 absolute error = 1.064110573263389651e-13 relative error = 6.8209487746183276629100000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.36 y[1] (analytic) = 1.5625 y[1] (numeric) = 1.5625000000001075504067511807682 absolute error = 1.075504067511807682e-13 relative error = 6.8832260320755691648000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.361 y[1] (analytic) = 1.5649452269170579029733959311424 y[1] (numeric) = 1.5649452269171666057142598518932 absolute error = 1.087027408639207508e-13 relative error = 6.9461051412045359761200000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.362 y[1] (analytic) = 1.5673981191222570532915360501567 y[1] (numeric) = 1.5673981191223669215170489603508 absolute error = 1.098682255129101941e-13 relative error = 7.0095927877236703835800000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.363 y[1] (analytic) = 1.5698587127158555729984301412873 y[1] (numeric) = 1.5698587127159666200273473167155 absolute error = 1.110470289171754282e-13 relative error = 7.0736957420240747763399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.1MB, time=3.63 NO POLE x[1] = 0.364 y[1] (analytic) = 1.5723270440251572327044025157233 y[1] (numeric) = 1.5723270440252694720261065445266 absolute error = 1.122393217040288033e-13 relative error = 7.1384208603762318898799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.365 y[1] (analytic) = 1.5748031496062992125984251968504 y[1] (numeric) = 1.5748031496064126578753725331339 absolute error = 1.134452769473362835e-13 relative error = 7.2037750861558540022500000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.366 y[1] (analytic) = 1.5772870662460567823343848580442 y[1] (numeric) = 1.5772870662461714474045913122265 absolute error = 1.146650702064541823e-13 relative error = 7.2697654510891951578199999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.367 y[1] (analytic) = 1.5797788309636650868878357030016 y[1] (numeric) = 1.5797788309637809857674015508182 absolute error = 1.158988795658478166e-13 relative error = 7.3363990765181667907799999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.368 y[1] (analytic) = 1.5822784810126582278481012658228 y[1] (numeric) = 1.5822784810127753747337766709425 absolute error = 1.171468856754051197e-13 relative error = 7.4036831746856035650399999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.369 y[1] (analytic) = 1.5847860538827258320126782884311 y[1] (numeric) = 1.5847860538828442412844697469577 absolute error = 1.184092717914585266e-13 relative error = 7.4716250500410330284599999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.37 y[1] (analytic) = 1.5873015873015873015873015873016 y[1] (numeric) = 1.5873015873017069878111201160222 absolute error = 1.196862238185287206e-13 relative error = 7.5402321005673093977999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.371 y[1] (analytic) = 1.5898251192368839427662957074722 y[1] (numeric) = 1.5898251192370049206966475115833 absolute error = 1.209779303518041111e-13 relative error = 7.6095118191284785881899999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.372 y[1] (analytic) = 1.5923566878980891719745222929936 y[1] (numeric) = 1.5923566878982114565572426631991 absolute error = 1.222845827203702055e-13 relative error = 7.6794717948392489054000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.373 y[1] (analytic) = 1.5948963317384370015948963317384 y[1] (numeric) = 1.5948963317385606079699275350679 absolute error = 1.236063750312033295e-13 relative error = 7.7501197144564487596500000000002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.374 y[1] (analytic) = 1.5974440894568690095846645367412 y[1] (numeric) = 1.5974440894569939530888784801977 absolute error = 1.249435042139434565e-13 relative error = 7.8214633637928603769000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.375 y[1] (analytic) = 1.6 y[1] (numeric) = 1.600000000000126296170066461212 absolute error = 1.262961700664612120e-13 relative error = 7.8935106291538257500000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.376 y[1] (analytic) = 1.6025641025641025641025641025641 y[1] (numeric) = 1.6025641025642302286778653370023 absolute error = 1.276645753012344382e-13 relative error = 7.9662694987970289436800000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.377 y[1] (analytic) = 1.6051364365971107544141252006421 y[1] (numeric) = 1.6051364365972398033397177506674 absolute error = 1.290489255925500253e-13 relative error = 8.0397480644158665761899999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.378 y[1] (analytic) = 1.6077170418006430868167202572347 y[1] (numeric) = 1.6077170418007735362463448042829 absolute error = 1.304494296245470482e-13 relative error = 8.1139545226468263980400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.379 y[1] (analytic) = 1.6103059581320450885668276972625 y[1] (numeric) = 1.610305958132176954865967814845 absolute error = 1.318662991401175825e-13 relative error = 8.1888971766013018732499999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=91.5MB, alloc=4.2MB, time=3.79 x[1] = 0.38 y[1] (analytic) = 1.6129032258064516129032258064516 y[1] (numeric) = 1.6129032258065849126522164883759 absolute error = 1.332997489906819243e-13 relative error = 8.2645844374222793066000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.381 y[1] (analytic) = 1.6155088852988691437802907915994 y[1] (numeric) = 1.6155088852990038937774776468853 absolute error = 1.347499971868552859e-13 relative error = 8.3410248258663421972099999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.382 y[1] (analytic) = 1.6181229773462783171521035598706 y[1] (numeric) = 1.6181229773464145344170535832778 absolute error = 1.362172649500234072e-13 relative error = 8.4182269739114465649599999999997e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.383 y[1] (analytic) = 1.6207455429497568881685575364668 y[1] (numeric) = 1.6207455429498945899453223813548 absolute error = 1.377017767648448880e-13 relative error = 8.4961996263909295895999999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.384 y[1] (analytic) = 1.6233766233766233766233766233766 y[1] (numeric) = 1.6233766233767625803838093218038 absolute error = 1.392037604326984272e-13 relative error = 8.5749516426542231155200000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.385 y[1] (analytic) = 1.6260162601626016260162601626016 y[1] (numeric) = 1.6260162601627423494633862561432 absolute error = 1.407234471260935416e-13 relative error = 8.6544919982547528084000000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.386 y[1] (analytic) = 1.6286644951140065146579804560261 y[1] (numeric) = 1.6286644951141487757294245197588 absolute error = 1.422610714440637327e-13 relative error = 8.7348297866655131877799999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.387 y[1] (analytic) = 1.6313213703099510603588907014682 y[1] (numeric) = 1.6313213703100948772303592629436 absolute error = 1.438168714685614754e-13 relative error = 8.8159742210228184420199999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.388 y[1] (analytic) = 1.6339869281045751633986928104575 y[1] (numeric) = 1.6339869281047205544875146852734 absolute error = 1.453910888218748159e-13 relative error = 8.8979346358987387330800000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.389 y[1] (analytic) = 1.6366612111292962356792144026187 y[1] (numeric) = 1.6366612111294432196479394884112 absolute error = 1.469839687250857925e-13 relative error = 8.9807204891027419217499999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.39 y[1] (analytic) = 1.6393442622950819672131147540984 y[1] (numeric) = 1.6393442622952305629731723454224 absolute error = 1.485957600575913240e-13 relative error = 9.0643413635130707639999999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.391 y[1] (analytic) = 1.6420361247947454844006568144499 y[1] (numeric) = 1.6420361247948957111160745221055 absolute error = 1.502267154177076556e-13 relative error = 9.1488069689383962260400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.392 y[1] (analytic) = 1.6447368421052631578947368421053 y[1] (numeric) = 1.644736842105415034985921222012 absolute error = 1.518770911843799067e-13 relative error = 9.2341271440102983273599999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.393 y[1] (analytic) = 1.6474464579901153212520593080725 y[1] (numeric) = 1.6474464579902688683996393268024 absolute error = 1.535471475800187299e-13 relative error = 9.3203118581071369049299999999999e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.394 y[1] (analytic) = 1.650165016501650165016501650165 y[1] (numeric) = 1.6501650165018054021652361367284 absolute error = 1.552371487344865634e-13 relative error = 9.4073712133098857420400000000001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.395 y[1] (analytic) = 1.6528925619834710743801652892562 y[1] (numeric) = 1.6528925619836280217429155457058 absolute error = 1.569473627502564496e-13 relative error = 9.4953154463905152008000000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.396 y[1] (analytic) = 1.6556291390728476821192052980132 y[1] (numeric) = 1.6556291390730063601809740649009 absolute error = 1.586780617687668877e-13 relative error = 9.5841549308335200170800000000003e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.2MB, time=3.94 NO POLE x[1] = 0.397 y[1] (analytic) = 1.658374792703150912106135986733 y[1] (numeric) = 1.6583747927033113416281739834309 absolute error = 1.604295220379966979e-13 relative error = 9.6739001788912008833700000000000e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.398 y[1] (analytic) = 1.661129568106312292358803986711 y[1] (numeric) = 1.66112956810647449438278527111 absolute error = 1.622020239812843990e-13 relative error = 9.7645618436733208197999999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.399 y[1] (analytic) = 1.6638935108153078202995008319468 y[1] (numeric) = 1.6638935108154718161517682490774 absolute error = 1.639958522674171306e-13 relative error = 9.8561507212717695490599999999997e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4 y[1] (analytic) = 1.6666666666666666666666666666667 y[1] (numeric) = 1.6666666666668324779625486813681 absolute error = 1.658112958820147014e-13 relative error = 9.9486777529208820839999999999998e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.401 y[1] (analytic) = 1.669449081803005008347245409015 y[1] (numeric) = 1.6694490818031726569954456439171 absolute error = 1.676486482002349021e-13 relative error = 1.0042154027194070635790000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.402 y[1] (analytic) = 1.6722408026755852842809364548495 y[1] (numeric) = 1.6722408026757547924879972816433 absolute error = 1.695082070608267938e-13 relative error = 1.0136590782237442269240000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.403 y[1] (analytic) = 1.6750418760469011725293132328308 y[1] (numeric) = 1.675041876047072562804154792101 absolute error = 1.713902748415592702e-13 relative error = 1.0231999408041088430940000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.404 y[1] (analytic) = 1.6778523489932885906040268456376 y[1] (numeric) = 1.6778523489934618857625628984268 absolute error = 1.732951585360527892e-13 relative error = 1.0328391448748746236320000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.405 y[1] (analytic) = 1.6806722689075630252100840336134 y[1] (numeric) = 1.6806722689077382483799160763995 absolute error = 1.752231698320427861e-13 relative error = 1.0425778605006545772950000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.406 y[1] (analytic) = 1.6835016835016835016835016835017 y[1] (numeric) = 1.6835016835018606763086927874074 absolute error = 1.771746251911039057e-13 relative error = 1.0524172736351571998580000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.407 y[1] (analytic) = 1.6863406408094435075885328836425 y[1] (numeric) = 1.6863406408096226574344627484821 absolute error = 1.791498459298648396e-13 relative error = 1.0623585863640984988280000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.408 y[1] (analytic) = 1.6891891891891891891891891891892 y[1] (numeric) = 1.6891891891893703383474919333947 absolute error = 1.811491583027442055e-13 relative error = 1.0724030171522456965600000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.409 y[1] (analytic) = 1.692047377326565143824027072758 y[1] (numeric) = 1.6920473773267483167176133113473 absolute error = 1.831728935862385893e-13 relative error = 1.0825518010946700627630000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.41 y[1] (analytic) = 1.694915254237288135593220338983 y[1] (numeric) = 1.694915254237473356981385133536 absolute error = 1.852213881647945530e-13 relative error = 1.0928061901722878627000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.411 y[1] (analytic) = 1.697792869269949066213921901528 y[1] (numeric) = 1.6977928692701363611975401986523 absolute error = 1.872949836182971243e-13 relative error = 1.1031674535117700621270000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.412 y[1] (analytic) = 1.7006802721088435374149659863946 y[1] (numeric) = 1.7006802721090329314417771943997 absolute error = 1.893940268112080051e-13 relative error = 1.1136368776499030699880000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.2MB, time=4.11 NO POLE x[1] = 0.413 y[1] (analytic) = 1.7035775127768313458262350936968 y[1] (numeric) = 1.7035775127770228646962184811746 absolute error = 1.915188699833874778e-13 relative error = 1.1242157668024844946860000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.414 y[1] (analytic) = 1.7064846416382252559726962457338 y[1] (numeric) = 1.7064846416384189258435388804824 absolute error = 1.936698708426347486e-13 relative error = 1.1349054431378396267960000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.415 y[1] (analytic) = 1.7094017094017094017094017094017 y[1] (numeric) = 1.7094017094019052491020606916462 absolute error = 1.958473926589822445e-13 relative error = 1.1457072470550461303250000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.416 y[1] (analytic) = 1.7123287671232876712328767123288 y[1] (numeric) = 1.7123287671234857230372374925047 absolute error = 1.980518043607801759e-13 relative error = 1.1566225374669562272560000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.417 y[1] (analytic) = 1.7152658662092624356775300171527 y[1] (numeric) = 1.7152658662094627191581626256463 absolute error = 2.002834806326084936e-13 relative error = 1.1676526920881075176880000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.418 y[1] (analytic) = 1.718213058419243986254295532646 y[1] (numeric) = 1.71821305841944652905631058685 absolute error = 2.025428020150542040e-13 relative error = 1.1787991077276154672800000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.419 y[1] (analytic) = 1.7211703958691910499139414802065 y[1] (numeric) = 1.7211703958693958800689478730683 absolute error = 2.048301550063928618e-13 relative error = 1.1900632005871425270580000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.42 y[1] (analytic) = 1.7241379310344827586206896551724 y[1] (numeric) = 1.7241379310346899045528558691098 absolute error = 2.071459321662139374e-13 relative error = 1.2014464065640408369200000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.421 y[1] (analytic) = 1.7271157167530224525043177892919 y[1] (numeric) = 1.7271157167532319430365388199429 absolute error = 2.094905322210306510e-13 relative error = 1.2129501815597674692900000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.422 y[1] (analytic) = 1.7301038062283737024221453287197 y[1] (numeric) = 1.7301038062285855667823172445085 absolute error = 2.118643601719157888e-13 relative error = 1.2245760017936732592640000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.423 y[1] (analytic) = 1.7331022530329289428076256499133 y[1] (numeric) = 1.7331022530331432106350298558695 absolute error = 2.142678274042059562e-13 relative error = 1.2363253641222683672740000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.424 y[1] (analytic) = 1.7361111111111111111111111111111 y[1] (numeric) = 1.736111111111327812462910428801 absolute error = 2.167013517993176899e-13 relative error = 1.2481997863640698938240000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.425 y[1] (analytic) = 1.7391304347826086956521739130435 y[1] (numeric) = 1.7391304347828278610100226328829 absolute error = 2.191653578487198394e-13 relative error = 1.2602008076301390765500000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.426 y[1] (analytic) = 1.7421602787456445993031358885017 y[1] (numeric) = 1.742160278745866259579905996142 absolute error = 2.216602767701076403e-13 relative error = 1.2723299886604178553220000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.427 y[1] (analytic) = 1.7452006980802792321116928446771 y[1] (numeric) = 1.7452006980805034186583186696192 absolute error = 2.241865466258249421e-13 relative error = 1.2845889121659769182330000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.428 y[1] (analytic) = 1.7482517482517482517482517482517 y[1] (numeric) = 1.7482517482519749963606953303682 absolute error = 2.267446124435821165e-13 relative error = 1.2969791831772897063800000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.2MB, time=4.26 NO POLE x[1] = 0.429 y[1] (analytic) = 1.7513134851138353765323992994746 y[1] (numeric) = 1.7513134851140647114587388177357 absolute error = 2.293349263395182611e-13 relative error = 1.3095024293986492708810000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.43 y[1] (analytic) = 1.7543859649122807017543859649123 y[1] (numeric) = 1.754385964912512659702029622344 absolute error = 2.319579476436574317e-13 relative error = 1.3221603015688473606900000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.431 y[1] (analytic) = 1.7574692442882249560632688927944 y[1] (numeric) = 1.757469244288459570206296702575 absolute error = 2.346141430278097806e-13 relative error = 1.3349544738282376516140000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.432 y[1] (analytic) = 1.7605633802816901408450704225352 y[1] (numeric) = 1.7605633802819274448317063921875 absolute error = 2.373039866359696523e-13 relative error = 1.3478866440923076250640000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.433 y[1] (analytic) = 1.7636684303350970017636684303351 y[1] (numeric) = 1.763668430335337029723885694224 absolute error = 2.400279602172638889e-13 relative error = 1.3609585344318862500630000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.434 y[1] (analytic) = 1.7667844522968197879858657243816 y[1] (numeric) = 1.7667844522970625745391272292134 absolute error = 2.427865532615048318e-13 relative error = 1.3741718914601173479880000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.435 y[1] (analytic) = 1.7699115044247787610619469026549 y[1] (numeric) = 1.7699115044250243413250843064219 absolute error = 2.455802631374037670e-13 relative error = 1.3875284867263312835500000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.436 y[1] (analytic) = 1.7730496453900709219858156028369 y[1] (numeric) = 1.7730496453903193315810491046957 absolute error = 2.484095952335018588e-13 relative error = 1.4010301171169504836320000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.437 y[1] (analytic) = 1.7761989342806394316163410301954 y[1] (numeric) = 1.7761989342808907066794429071358 absolute error = 2.512750631018769404e-13 relative error = 1.4146786052635671744520000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.438 y[1] (analytic) = 1.7793594306049822064056939501779 y[1] (numeric) = 1.7793594306052363835942986360725 absolute error = 2.541771886046858946e-13 relative error = 1.4284757999583347276520000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.439 y[1] (analytic) = 1.78253119429590017825311942959 y[1] (numeric) = 1.7825311942961572947551830333383 absolute error = 2.571165020636037483e-13 relative error = 1.4424235765768170279630000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.44 y[1] (analytic) = 1.7857142857142857142857142857143 y[1] (numeric) = 1.7857142857145458078281265077512 absolute error = 2.600935424122220369e-13 relative error = 1.4565238375084434066400000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.441 y[1] (analytic) = 1.7889087656529516994633273703041 y[1] (numeric) = 1.7889087656532148083206788407634 absolute error = 2.631088573514704593e-13 relative error = 1.4707785125947198674870000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.442 y[1] (analytic) = 1.7921146953405017921146953405018 y[1] (numeric) = 1.7921146953407679551182034678494 absolute error = 2.661630035081273476e-13 relative error = 1.4851895595753505996080000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.443 y[1] (analytic) = 1.7953321364452423698384201077199 y[1] (numeric) = 1.7953321364455116263850165937369 absolute error = 2.692565465964860170e-13 relative error = 1.4997589645424271146900000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.444 y[1] (analytic) = 1.7985611510791366906474820143885 y[1] (numeric) = 1.7985611510794090807090652600284 absolute error = 2.723900615832456399e-13 relative error = 1.5144887424028457578440000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=106.8MB, alloc=4.2MB, time=4.43 x[1] = 0.445 y[1] (analytic) = 1.8018018018018018018018018018018 y[1] (numeric) = 1.8018018018020773659346574987123 absolute error = 2.755641328556969105e-13 relative error = 1.5293809373491178532750000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.446 y[1] (analytic) = 1.8050541516245487364620938628159 y[1] (numeric) = 1.8050541516248275158164871372412 absolute error = 2.787793543932744253e-13 relative error = 1.5444376233387403161620000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.447 y[1] (analytic) = 1.8083182640144665461121157323689 y[1] (numeric) = 1.8083182640147485824420582817806 absolute error = 2.820363299425494117e-13 relative error = 1.5596609045822982467010000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.448 y[1] (analytic) = 1.8115942028985507246376811594203 y[1] (numeric) = 1.8115942028988360603108768976008 absolute error = 2.853356731957381805e-13 relative error = 1.5750529160404747563600000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.449 y[1] (analytic) = 1.814882032667876588021778584392 y[1] (numeric) = 1.8148820326681652660297513878665 absolute error = 2.886780079728034745e-13 relative error = 1.5906158239301471444950000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.45 y[1] (analytic) = 1.8181818181818181818181818181818 y[1] (numeric) = 1.818181818182110245786589045901 absolute error = 2.920639684072277192e-13 relative error = 1.6063518262397524556000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.451 y[1] (analytic) = 1.8214936247723132969034608378871 y[1] (numeric) = 1.8214936247726087911025963769578 absolute error = 2.954941991355390707e-13 relative error = 1.6222631532541094981430000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.452 y[1] (analytic) = 1.8248175182481751824817518248175 y[1] (numeric) = 1.8248175182484741518372424979052 absolute error = 2.989693554906730877e-13 relative error = 1.6383520680888885205960000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.453 y[1] (analytic) = 1.8281535648994515539305301645338 y[1] (numeric) = 1.8281535648997540440342294193707 absolute error = 3.024901036992548369e-13 relative error = 1.6546208672349239578430000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.454 y[1] (analytic) = 1.8315018315018315018315018315018 y[1] (numeric) = 1.8315018315021375589525847197823 absolute error = 3.060571210828882805e-13 relative error = 1.6710718811125700115300000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.455 y[1] (analytic) = 1.8348623853211009174311926605505 y[1] (numeric) = 1.8348623853214105885274562024277 absolute error = 3.096710962635418772e-13 relative error = 1.6877074746363032307400000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.456 y[1] (analytic) = 1.8382352941176470588235294117647 y[1] (numeric) = 1.8382352941179603915529025332385 absolute error = 3.133327293731214738e-13 relative error = 1.7045300477897808174720000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.457 y[1] (analytic) = 1.8416206261510128913443830570902 y[1] (numeric) = 1.8416206261513299340766503808479 absolute error = 3.170427322673237577e-13 relative error = 1.7215420362115680043110000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.458 y[1] (analytic) = 1.8450184501845018450184501845018 y[1] (numeric) = 1.8450184501848226468471940503029 absolute error = 3.208018287438658011e-13 relative error = 1.7387459117917526419620000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.459 y[1] (analytic) = 1.8484288354898336414048059149723 y[1] (numeric) = 1.8484288354901582521595711035077 absolute error = 3.246107547651885354e-13 relative error = 1.7561441832796699765140000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.46 y[1] (analytic) = 1.8518518518518518518518518518519 y[1] (numeric) = 1.8518518518521803221105375862234 absolute error = 3.284702586857343715e-13 relative error = 1.7737393969029656061000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.461 y[1] (analytic) = 1.8552875695732838589981447124304 y[1] (numeric) = 1.8552875695736162400996286140466 absolute error = 3.323811014839016162e-13 relative error = 1.7915341369982297113180000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.2MB, time=4.59 NO POLE x[1] = 0.462 y[1] (analytic) = 1.8587360594795539033457249070632 y[1] (numeric) = 1.8587360594798902474027236878994 absolute error = 3.363440569987808362e-13 relative error = 1.8095310266534408987560000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.463 y[1] (analytic) = 1.8621973929236499068901303538175 y[1] (numeric) = 1.8621973929239902668023021347034 absolute error = 3.403599121717808859e-13 relative error = 1.8277327283624633572830000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.464 y[1] (analytic) = 1.8656716417910447761194029850746 y[1] (numeric) = 1.8656716417913892055866962400222 absolute error = 3.444294672932549476e-13 relative error = 1.8461419446918465191360000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.465 y[1] (analytic) = 1.869158878504672897196261682243 y[1] (numeric) = 1.8691588785050214507325159218798 absolute error = 3.485535362542396368e-13 relative error = 1.8647614189601820568800000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.466 y[1] (analytic) = 1.8726591760299625468164794007491 y[1] (numeric) = 1.8726591760303152797632828237476 absolute error = 3.527329468034229985e-13 relative error = 1.8835939359302788119900000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.467 y[1] (analytic) = 1.8761726078799249530956848030019 y[1] (numeric) = 1.8761726078802819216364942630692 absolute error = 3.569685408094600673e-13 relative error = 1.9026423225144221587090000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.468 y[1] (analytic) = 1.8796992481203007518796992481203 y[1] (numeric) = 1.8796992481206620130542280057086 absolute error = 3.612611745287575883e-13 relative error = 1.9219094484929903697560000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.469 y[1] (analytic) = 1.8832391713747645951035781544256 y[1] (numeric) = 1.8832391713751302068224570069206 absolute error = 3.656117188788524950e-13 relative error = 1.9413982272467067484500000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.47 y[1] (analytic) = 1.8867924528301886792452830188679 y[1] (numeric) = 1.8867924528305587003050005306898 absolute error = 3.700210597175118219e-13 relative error = 1.9611116165028126560700000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.471 y[1] (analytic) = 1.8903591682419659735349716446125 y[1] (numeric) = 1.8903591682423404636330993295041 absolute error = 3.744900981276848916e-13 relative error = 1.9810526190954530765640000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.472 y[1] (analytic) = 1.8939393939393939393939393939394 y[1] (numeric) = 1.8939393939397729591446478358035 absolute error = 3.790197507084418641e-13 relative error = 2.0012242837405730424480000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.473 y[1] (analytic) = 1.8975332068311195445920303605313 y[1] (numeric) = 1.8975332068315031555419023965992 absolute error = 3.836109498720360679e-13 relative error = 2.0216297058256300778330000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.474 y[1] (analytic) = 1.9011406844106463878326996197719 y[1] (numeric) = 1.9011406844110346524768468507319 absolute error = 3.882646441472309600e-13 relative error = 2.0422720282144348496000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.475 y[1] (analytic) = 1.9047619047619047619047619047619 y[1] (numeric) = 1.9047619047622977437032509408359 absolute error = 3.929817984890360740e-13 relative error = 2.0631544420674393885000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.476 y[1] (analytic) = 1.9083969465648854961832061068702 y[1] (numeric) = 1.9083969465652832595778011067963 absolute error = 3.977633945949999261e-13 relative error = 2.0842801876777996127640000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.477 y[1] (analytic) = 1.9120458891013384321223709369025 y[1] (numeric) = 1.912045889101741042553599148462 absolute error = 4.026104312282115595e-13 relative error = 2.1056525553235464561850000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.2MB, time=4.75 NO POLE x[1] = 0.478 y[1] (analytic) = 1.9157088122605363984674329501916 y[1] (numeric) = 1.915708812260943922391980116403 absolute error = 4.075239245471662114e-13 relative error = 2.1272748861362076235080000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.479 y[1] (analytic) = 1.9193857965451055662188099808061 y[1] (numeric) = 1.9193857965455180711272526353073 absolute error = 4.125049084426545012e-13 relative error = 2.1491505729862299512520000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.48 y[1] (analytic) = 1.9230769230769230769230769230769 y[1] (numeric) = 1.9230769230773406313579587616301 absolute error = 4.175544348818385532e-13 relative error = 2.1712830613855604766400000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.481 y[1] (analytic) = 1.9267822736030828516377649325626 y[1] (numeric) = 1.9267822736035055252120246151592 absolute error = 4.226735742596825966e-13 relative error = 2.1936758504077526763540000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.482 y[1] (analytic) = 1.9305019305019305019305019305019 y[1] (numeric) = 1.9305019305023583653462598403218 absolute error = 4.278634157579098199e-13 relative error = 2.2163324936259728670820000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.483 y[1] (analytic) = 1.9342359767891682785299806576402 y[1] (numeric) = 1.9342359767896014035976923192571 absolute error = 4.331250677116616169e-13 relative error = 2.2392566000692905593730000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.484 y[1] (analytic) = 1.9379844961240310077519379844961 y[1] (numeric) = 1.9379844961244694674099220243261 absolute error = 4.384596579840398300e-13 relative error = 2.2624518351976455228000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.485 y[1] (analytic) = 1.9417475728155339805825242718447 y[1] (numeric) = 1.9417475728159778489168729890408 absolute error = 4.438683343487171961e-13 relative error = 2.2859219218958935599150000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.486 y[1] (analytic) = 1.9455252918287937743190661478599 y[1] (numeric) = 1.9455252918292431265839469537825 absolute error = 4.493522648808059226e-13 relative error = 2.3096706414873424421640000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.487 y[1] (analytic) = 1.9493177387914230019493177387914 y[1] (numeric) = 1.9493177387918779145876739179612 absolute error = 4.549126383561791698e-13 relative error = 2.3337018347671991410740000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.488 y[1] (analytic) = 1.953125 y[1] (numeric) = 1.9531250000004605506646594452094 absolute error = 4.605506646594452094e-13 relative error = 2.3580194030563594721280000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.489 y[1] (analytic) = 1.9569471624266144814090019569472 y[1] (numeric) = 1.9569471624270807489842027360911 absolute error = 4.662675752007791439e-13 relative error = 2.3826273092759814253290000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.49 y[1] (analytic) = 1.960784313725490196078431372549 y[1] (numeric) = 1.9607843137259622607017731948937 absolute error = 4.720646233418223447e-13 relative error = 2.4075295790432939579700000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.491 y[1] (analytic) = 1.9646365422396856581532416502947 y[1] (numeric) = 1.9646365422401636012380725154686 absolute error = 4.779430848308651739e-13 relative error = 2.4327303017891037351510000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.492 y[1] (analytic) = 1.968503937007874015748031496063 y[1] (numeric) = 1.9685039370083579200062790301829 absolute error = 4.839042582475341199e-13 relative error = 2.4582336318974733290920000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.493 y[1] (analytic) = 1.972386587771203155818540433925 y[1] (numeric) = 1.9723865877716931052839976441158 absolute error = 4.899494654572101908e-13 relative error = 2.4840437898680556673560000000001e-11 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.2MB, time=4.91 NO POLE x[1] = 0.494 y[1] (analytic) = 1.9762845849802371541501976284585 y[1] (numeric) = 1.9762845849807332342022730397469 absolute error = 4.960800520754112884e-13 relative error = 2.5101650635015811193040000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.495 y[1] (analytic) = 1.980198019801980198019801980198 y[1] (numeric) = 1.9801980198024824954077443575242 absolute error = 5.022973879423773262e-13 relative error = 2.5366018091090054973100000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.496 y[1] (analytic) = 1.984126984126984126984126984127 y[1] (numeric) = 1.9841269841274927298517350871889 absolute error = 5.086028676081030619e-13 relative error = 2.5633584527448394319760000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.497 y[1] (analytic) = 1.9880715705765407554671968190855 y[1] (numeric) = 1.988071570577055753378024889089 absolute error = 5.149979108280700035e-13 relative error = 2.5904394914651921176050000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.498 y[1] (analytic) = 1.9920318725099601593625498007968 y[1] (numeric) = 1.9920318725104816433256197361038 absolute error = 5.214839630699353070e-13 relative error = 2.6178494946110752411400000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.499 y[1] (analytic) = 1.9960079840319361277445109780439 y[1] (numeric) = 1.9960079840324641902405424203802 absolute error = 5.280624960314423363e-13 relative error = 2.6455931051175261048630000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5 y[1] (analytic) = 2 y[1] (numeric) = 2.0000000000005347350081698244918 absolute error = 5.347350081698244918e-13 relative error = 2.6736750408491224590000000000000e-11 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.501 y[1] (analytic) = 2.0040080160320641282565130260521 y[1] (numeric) = 2.0040080160326056312817560071046 absolute error = 5.415030252429810525e-13 relative error = 2.7021000959624754519750000000000e-11 % h = 0.001 Finished! diff ( y , x , 1 ) = y * y; Iterations = 501 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Time to Timeout = 14 Minutes 55 Seconds Percent Done = 100.4 % > quit memory used=120.0MB, alloc=4.2MB, time=4.98