|\^/| 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 > INFO, > glob_iolevel, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_dump_analytic, > glob_initial_pass, > glob_almost_1, > glob_max_opt_iter, > glob_normmax, > glob_max_iter, > glob_clock_sec, > glob_log10abserr, > glob_orig_start_sec, > glob_optimal_start, > glob_hmax, > glob_optimal_done, > days_in_year, > glob_display_flag, > glob_smallish_float, > glob_last_good_h, > glob_percent_done, > glob_h, > glob_not_yet_start_msg, > hours_in_day, > glob_max_sec, > glob_small_float, > glob_log10_relerr, > sec_in_min, > glob_log10normmin, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_abserr, > glob_disp_incr, > years_in_century, > min_in_hour, > glob_warned, > glob_max_trunc_err, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_large_float, > glob_hmin_init, > glob_clock_start_sec, > djd_debug2, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_iter, > glob_current_iter, > glob_warned2, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > djd_debug, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_tmp1_g, > array_1st_rel_error, > array_y, > array_x, > array_m1, > array_norms, > array_tmp3_g, > array_last_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_y_set_initial, > array_real_pole, > array_y_higher_work, > array_y_higher_work2, > array_complex_pole, > array_y_higher, > array_poles, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_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 INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec, glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax, glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float, glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg, hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min, glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt, glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned, glob_max_trunc_err, glob_log10_abserr, glob_look_poles, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float, glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter, glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours, array_const_0D0, array_const_1, array_y_init, array_tmp1_g, array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher_work2, array_complex_pole, array_y_higher, array_poles, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_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 > INFO, > glob_iolevel, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_dump_analytic, > glob_initial_pass, > glob_almost_1, > glob_max_opt_iter, > glob_normmax, > glob_max_iter, > glob_clock_sec, > glob_log10abserr, > glob_orig_start_sec, > glob_optimal_start, > glob_hmax, > glob_optimal_done, > days_in_year, > glob_display_flag, > glob_smallish_float, > glob_last_good_h, > glob_percent_done, > glob_h, > glob_not_yet_start_msg, > hours_in_day, > glob_max_sec, > glob_small_float, > glob_log10_relerr, > sec_in_min, > glob_log10normmin, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_abserr, > glob_disp_incr, > years_in_century, > min_in_hour, > glob_warned, > glob_max_trunc_err, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_large_float, > glob_hmin_init, > glob_clock_start_sec, > djd_debug2, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_iter, > glob_current_iter, > glob_warned2, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > djd_debug, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_tmp1_g, > array_1st_rel_error, > array_y, > array_x, > array_m1, > array_norms, > array_tmp3_g, > array_last_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_y_set_initial, > array_real_pole, > array_y_higher_work, > array_y_higher_work2, > array_complex_pole, > array_y_higher, > array_poles, > 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 INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec, glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax, glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float, glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg, hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min, glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt, glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned, glob_max_trunc_err, glob_log10_abserr, glob_look_poles, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float, glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter, glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours, array_const_0D0, array_const_1, array_y_init, array_tmp1_g, array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher_work2, array_complex_pole, array_y_higher, array_poles, 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 > INFO, > glob_iolevel, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_dump_analytic, > glob_initial_pass, > glob_almost_1, > glob_max_opt_iter, > glob_normmax, > glob_max_iter, > glob_clock_sec, > glob_log10abserr, > glob_orig_start_sec, > glob_optimal_start, > glob_hmax, > glob_optimal_done, > days_in_year, > glob_display_flag, > glob_smallish_float, > glob_last_good_h, > glob_percent_done, > glob_h, > glob_not_yet_start_msg, > hours_in_day, > glob_max_sec, > glob_small_float, > glob_log10_relerr, > sec_in_min, > glob_log10normmin, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_abserr, > glob_disp_incr, > years_in_century, > min_in_hour, > glob_warned, > glob_max_trunc_err, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_large_float, > glob_hmin_init, > glob_clock_start_sec, > djd_debug2, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_iter, > glob_current_iter, > glob_warned2, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > djd_debug, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_tmp1_g, > array_1st_rel_error, > array_y, > array_x, > array_m1, > array_norms, > array_tmp3_g, > array_last_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_y_set_initial, > array_real_pole, > array_y_higher_work, > array_y_higher_work2, > array_complex_pole, > array_y_higher, > array_poles, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec, glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax, glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float, glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg, hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min, glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt, glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned, glob_max_trunc_err, glob_log10_abserr, glob_look_poles, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float, glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter, glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours, array_const_0D0, array_const_1, array_y_init, array_tmp1_g, array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher_work2, array_complex_pole, array_y_higher, array_poles, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > glob_iolevel, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_dump_analytic, > glob_initial_pass, > glob_almost_1, > glob_max_opt_iter, > glob_normmax, > glob_max_iter, > glob_clock_sec, > glob_log10abserr, > glob_orig_start_sec, > glob_optimal_start, > glob_hmax, > glob_optimal_done, > days_in_year, > glob_display_flag, > glob_smallish_float, > glob_last_good_h, > glob_percent_done, > glob_h, > glob_not_yet_start_msg, > hours_in_day, > glob_max_sec, > glob_small_float, > glob_log10_relerr, > sec_in_min, > glob_log10normmin, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_abserr, > glob_disp_incr, > years_in_century, > min_in_hour, > glob_warned, > glob_max_trunc_err, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_large_float, > glob_hmin_init, > glob_clock_start_sec, > djd_debug2, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_iter, > glob_current_iter, > glob_warned2, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > djd_debug, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_tmp1_g, > array_1st_rel_error, > array_y, > array_x, > array_m1, > array_norms, > array_tmp3_g, > array_last_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_y_set_initial, > array_real_pole, > array_y_higher_work, > array_y_higher_work2, > array_complex_pole, > array_y_higher, > array_poles, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((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 INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec, glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax, glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float, glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg, hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min, glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt, glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned, glob_max_trunc_err, glob_log10_abserr, glob_look_poles, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float, glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter, glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours, array_const_0D0, array_const_1, array_y_init, array_tmp1_g, array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher_work2, array_complex_pole, array_y_higher, array_poles, 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 > INFO, > glob_iolevel, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_dump_analytic, > glob_initial_pass, > glob_almost_1, > glob_max_opt_iter, > glob_normmax, > glob_max_iter, > glob_clock_sec, > glob_log10abserr, > glob_orig_start_sec, > glob_optimal_start, > glob_hmax, > glob_optimal_done, > days_in_year, > glob_display_flag, > glob_smallish_float, > glob_last_good_h, > glob_percent_done, > glob_h, > glob_not_yet_start_msg, > hours_in_day, > glob_max_sec, > glob_small_float, > glob_log10_relerr, > sec_in_min, > glob_log10normmin, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_abserr, > glob_disp_incr, > years_in_century, > min_in_hour, > glob_warned, > glob_max_trunc_err, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_large_float, > glob_hmin_init, > glob_clock_start_sec, > djd_debug2, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_iter, > glob_current_iter, > glob_warned2, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > djd_debug, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_tmp1_g, > array_1st_rel_error, > array_y, > array_x, > array_m1, > array_norms, > array_tmp3_g, > array_last_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_y_set_initial, > array_real_pole, > array_y_higher_work, > array_y_higher_work2, > array_complex_pole, > array_y_higher, > array_poles, > 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 INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec, glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax, glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float, glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg, hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min, glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt, glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned, glob_max_trunc_err, glob_log10_abserr, glob_look_poles, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float, glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter, glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours, array_const_0D0, array_const_1, array_y_init, array_tmp1_g, array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher_work2, array_complex_pole, array_y_higher, array_poles, 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 > INFO, > glob_iolevel, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_dump_analytic, > glob_initial_pass, > glob_almost_1, > glob_max_opt_iter, > glob_normmax, > glob_max_iter, > glob_clock_sec, > glob_log10abserr, > glob_orig_start_sec, > glob_optimal_start, > glob_hmax, > glob_optimal_done, > days_in_year, > glob_display_flag, > glob_smallish_float, > glob_last_good_h, > glob_percent_done, > glob_h, > glob_not_yet_start_msg, > hours_in_day, > glob_max_sec, > glob_small_float, > glob_log10_relerr, > sec_in_min, > glob_log10normmin, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_abserr, > glob_disp_incr, > years_in_century, > min_in_hour, > glob_warned, > glob_max_trunc_err, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_large_float, > glob_hmin_init, > glob_clock_start_sec, > djd_debug2, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_iter, > glob_current_iter, > glob_warned2, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > djd_debug, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_tmp1_g, > array_1st_rel_error, > array_y, > array_x, > array_m1, > array_norms, > array_tmp3_g, > array_last_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_y_set_initial, > array_real_pole, > array_y_higher_work, > array_y_higher_work2, > array_complex_pole, > array_y_higher, > array_poles, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre cos $eq_no = 1 > array_tmp1_g[1] := sin(array_x[1]); > array_tmp1[1] := cos(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre sin $eq_no = 1 iii = 1 > #emit pre sin 1 $eq_no = 1 > array_tmp3[1] := sin(array_x[1]); > array_tmp3_g[1] := cos(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp2[1] + array_tmp3[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_tmp4[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 cos $eq_no = 1 > array_tmp1_g[2] := (att(1,array_tmp1,array_x,1)); > array_tmp1[2] := (-att(1,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre sin $eq_no = 1 iii = 2 > #emit pre sin 2 $eq_no = 1 > array_tmp3[2] := att(1,array_tmp3_g,array_x,1); > array_tmp3_g[2] := -att(1,array_tmp3,array_x,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp2[2] + array_tmp3[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_tmp4[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 cos $eq_no = 1 > array_tmp1_g[3] := (att(2,array_tmp1,array_x,1)); > array_tmp1[3] := (-att(2,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre sin $eq_no = 1 iii = 3 > #emit pre sin 3 $eq_no = 1 > array_tmp3[3] := att(2,array_tmp3_g,array_x,1); > array_tmp3_g[3] := -att(2,array_tmp3,array_x,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp2[3] + array_tmp3[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_tmp4[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 cos $eq_no = 1 > array_tmp1_g[4] := (att(3,array_tmp1,array_x,1)); > array_tmp1[4] := (-att(3,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre sin $eq_no = 1 iii = 4 > #emit pre sin 4 $eq_no = 1 > array_tmp3[4] := att(3,array_tmp3_g,array_x,1); > array_tmp3_g[4] := -att(3,array_tmp3,array_x,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp2[4] + array_tmp3[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_tmp4[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 cos $eq_no = 1 > array_tmp1_g[5] := (att(4,array_tmp1,array_x,1)); > array_tmp1[5] := (-att(4,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre sin $eq_no = 1 iii = 5 > #emit pre sin 5 $eq_no = 1 > array_tmp3[5] := att(4,array_tmp3_g,array_x,1); > array_tmp3_g[5] := -att(4,array_tmp3,array_x,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp2[5] + array_tmp3[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_tmp4[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 cos $eq_no = 1 > array_tmp1_g[kkk] := (att(kkk-1,array_tmp1,array_x,1)); > array_tmp1[kkk] := (-att(kkk-1,array_tmp1_g,array_x,1)); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit sin $eq_no = 1 > array_tmp3[kkk] := att(kkk-1,array_tmp3_g,array_x,1); > array_tmp3_g[kkk] := -att(kkk-1,array_tmp3,array_x,1); > #emit add $eq_no = 1 > array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[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_tmp4[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 INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec, glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax, glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float, glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg, hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min, glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt, glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned, glob_max_trunc_err, glob_log10_abserr, glob_look_poles, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float, glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter, glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours, array_const_0D0, array_const_1, array_y_init, array_tmp1_g, array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher_work2, array_complex_pole, array_y_higher, array_poles, glob_last; array_tmp1_g[1] := sin(array_x[1]); array_tmp1[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := sin(array_x[1]); array_tmp3_g[1] := cos(array_x[1]); array_tmp4[1] := array_tmp2[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[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_g[2] := att(1, array_tmp1, array_x, 1); array_tmp1[2] := -att(1, array_tmp1_g, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; array_tmp3[2] := att(1, array_tmp3_g, array_x, 1); array_tmp3_g[2] := -att(1, array_tmp3, array_x, 1); array_tmp4[2] := array_tmp2[2] + array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[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_g[3] := att(2, array_tmp1, array_x, 1); array_tmp1[3] := -att(2, array_tmp1_g, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; array_tmp3[3] := att(2, array_tmp3_g, array_x, 1); array_tmp3_g[3] := -att(2, array_tmp3, array_x, 1); array_tmp4[3] := array_tmp2[3] + array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[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_g[4] := att(3, array_tmp1, array_x, 1); array_tmp1[4] := -att(3, array_tmp1_g, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; array_tmp3[4] := att(3, array_tmp3_g, array_x, 1); array_tmp3_g[4] := -att(3, array_tmp3, array_x, 1); array_tmp4[4] := array_tmp2[4] + array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[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_g[5] := att(4, array_tmp1, array_x, 1); array_tmp1[5] := -att(4, array_tmp1_g, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; array_tmp3[5] := att(4, array_tmp3_g, array_x, 1); array_tmp3_g[5] := -att(4, array_tmp3, array_x, 1); array_tmp4[5] := array_tmp2[5] + array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[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_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1); array_tmp1[kkk] := -att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; array_tmp3[kkk] := att(kkk - 1, array_tmp3_g, array_x, 1); array_tmp3_g[kkk] := -att(kkk - 1, array_tmp3, array_x, 1); array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[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_tmp4[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) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 2.0 + sin(x) - cos(x); > end; exact_soln_y := proc(x) 2.0 + sin(x) - cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > INFO, > glob_iolevel, > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > #Top Generate Globals Decl > glob_start, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_relerr, > glob_dump_analytic, > glob_initial_pass, > glob_almost_1, > glob_max_opt_iter, > glob_normmax, > glob_max_iter, > glob_clock_sec, > glob_log10abserr, > glob_orig_start_sec, > glob_optimal_start, > glob_hmax, > glob_optimal_done, > days_in_year, > glob_display_flag, > glob_smallish_float, > glob_last_good_h, > glob_percent_done, > glob_h, > glob_not_yet_start_msg, > hours_in_day, > glob_max_sec, > glob_small_float, > glob_log10_relerr, > sec_in_min, > glob_log10normmin, > glob_subiter_method, > glob_curr_iter_when_opt, > glob_abserr, > glob_disp_incr, > years_in_century, > min_in_hour, > glob_warned, > glob_max_trunc_err, > glob_log10_abserr, > glob_look_poles, > glob_not_yet_finished, > glob_html_log, > MAX_UNCHANGED, > glob_large_float, > glob_hmin_init, > glob_clock_start_sec, > djd_debug2, > glob_optimal_expect_sec, > glob_max_minutes, > glob_log10relerr, > glob_iter, > glob_current_iter, > glob_warned2, > glob_hmin, > glob_reached_optimal_h, > centuries_in_millinium, > djd_debug, > glob_dump, > glob_optimal_clock_start_sec, > glob_max_hours, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_tmp1_g, > array_1st_rel_error, > array_y, > array_x, > array_m1, > array_norms, > array_tmp3_g, > array_last_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_type_pole, > array_pole, > array_y_set_initial, > array_real_pole, > array_y_higher_work, > array_y_higher_work2, > array_complex_pole, > array_y_higher, > array_poles, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > glob_iolevel := 5; > DEBUGL := 3; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > ALWAYS := 1; > glob_start := 0; > glob_unchanged_h_cnt := 0; > glob_no_eqs := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_initial_pass := true; > glob_almost_1 := 0.9990; > glob_max_opt_iter := 10; > glob_normmax := 0.0; > glob_max_iter := 1000; > glob_clock_sec := 0.0; > glob_log10abserr := 0.0; > glob_orig_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_hmax := 1.0; > glob_optimal_done := false; > days_in_year := 365.0; > glob_display_flag := true; > glob_smallish_float := 0.1e-100; > glob_last_good_h := 0.1; > glob_percent_done := 0.0; > glob_h := 0.1; > glob_not_yet_start_msg := true; > hours_in_day := 24.0; > glob_max_sec := 10000.0; > glob_small_float := 0.1e-50; > glob_log10_relerr := 0.1e-10; > sec_in_min := 60.0; > glob_log10normmin := 0.1; > glob_subiter_method := 3; > glob_curr_iter_when_opt := 0; > glob_abserr := 0.1e-10; > glob_disp_incr := 0.1; > years_in_century := 100.0; > min_in_hour := 60.0; > glob_warned := false; > glob_max_trunc_err := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_look_poles := false; > glob_not_yet_finished := true; > glob_html_log := true; > MAX_UNCHANGED := 10; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_clock_start_sec := 0.0; > djd_debug2 := true; > glob_optimal_expect_sec := 0.1; > glob_max_minutes := 0.0; > glob_log10relerr := 0.0; > glob_iter := 0; > glob_current_iter := 0; > glob_warned2 := false; > glob_hmin := 0.00000000001; > glob_reached_optimal_h := false; > centuries_in_millinium := 10.0; > djd_debug := true; > glob_dump := false; > glob_optimal_clock_start_sec := 0.0; > glob_max_hours := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 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/addpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"Digits := 32;"); > 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 := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 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,"2.0 + sin(x) - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > max_terms := 30; > Digits := 32; > #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_y_init:= Array(1..(max_terms + 1),[]); > array_tmp1_g:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_tmp3_g:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > 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_tmp1_g[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_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_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_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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 > ; > 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 <=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 <=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 <=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[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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_tmp3_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > 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)) / (convfp(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)) / (convfp(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)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_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 ) = cos ( x ) + sin ( x ) ;"); > 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,"2012-06-13T11:49:31-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"add") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 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," 090 ") > ; > logitem_str(html_log_file,"add diffeq.mxt") > ; > logitem_str(html_log_file,"add maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > 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, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err, glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec, glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax, glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float, glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg, hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min, glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt, glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned, glob_max_trunc_err, glob_log10_abserr, glob_look_poles, glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float, glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec, glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter, glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium, djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours, array_const_0D0, array_const_1, array_y_init, array_tmp1_g, array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_type_pole, array_pole, array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher_work2, array_complex_pole, array_y_higher, array_poles, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; glob_iolevel := 5; DEBUGL := 3; glob_max_terms := 30; DEBUGMASSIVE := 4; ALWAYS := 1; glob_start := 0; glob_unchanged_h_cnt := 0; glob_no_eqs := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_initial_pass := true; glob_almost_1 := 0.9990; glob_max_opt_iter := 10; glob_normmax := 0.; glob_max_iter := 1000; glob_clock_sec := 0.; glob_log10abserr := 0.; glob_orig_start_sec := 0.; glob_optimal_start := 0.; glob_hmax := 1.0; glob_optimal_done := false; days_in_year := 365.0; glob_display_flag := true; glob_smallish_float := 0.1*10^(-100); glob_last_good_h := 0.1; glob_percent_done := 0.; glob_h := 0.1; glob_not_yet_start_msg := true; hours_in_day := 24.0; glob_max_sec := 10000.0; glob_small_float := 0.1*10^(-50); glob_log10_relerr := 0.1*10^(-10); sec_in_min := 60.0; glob_log10normmin := 0.1; glob_subiter_method := 3; glob_curr_iter_when_opt := 0; glob_abserr := 0.1*10^(-10); glob_disp_incr := 0.1; years_in_century := 100.0; min_in_hour := 60.0; glob_warned := false; glob_max_trunc_err := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_look_poles := false; glob_not_yet_finished := true; glob_html_log := true; MAX_UNCHANGED := 10; glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_clock_start_sec := 0.; djd_debug2 := true; glob_optimal_expect_sec := 0.1; glob_max_minutes := 0.; glob_log10relerr := 0.; glob_iter := 0; glob_current_iter := 0; glob_warned2 := false; glob_hmin := 0.1*10^(-10); glob_reached_optimal_h := false; centuries_in_millinium := 10.0; djd_debug := true; glob_dump := false; glob_optimal_clock_start_sec := 0.; glob_max_hours := 0.; 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/addpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "Digits := 32;"); 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 := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 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, "2.0 + sin(x) - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; max_terms := 30; Digits := 32; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(1 .. max_terms + 1, []); array_tmp1_g := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_tmp3_g := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); 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_tmp1_g[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_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_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_tmp3_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; 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; 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 <= 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 <= 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 <= 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[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; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_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_tmp3_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3_g[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_h := 0.0001; 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)/convfp(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)/convfp(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)/convfp(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 ) = cos ( x ) + sin ( x ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-13T11:49:31-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "add"); logitem_str(html_log_file, "diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "add diffeq.mxt"); logitem_str(html_log_file, "add maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/addpostode.ode################# diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK max_terms := 30; Digits := 32; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 2.0 + sin(x) - cos(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 = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0001 y[1] (analytic) = 1.0001000049998333291667500013888 y[1] (numeric) = 1.000100004999833329166750049999 absolute error = 4.86102e-26 relative error = 4.8605339223059099067186492115008e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0002 y[1] (analytic) = 1.000200019998666600002666755553 y[1] (numeric) = 1.0002000199986666000026668527684 absolute error = 9.72154e-26 relative error = 9.7195958864437536295280861070034e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0003 y[1] (analytic) = 1.0003000449954996625202510124566 y[1] (numeric) = 1.0003000449954996625202511582724 absolute error = 1.458158e-25 relative error = 1.4577206182236653150737335276307e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0004 y[1] (analytic) = 1.0004000799893322667520056885638 y[1] (numeric) = 1.0004000799893322667520058829752 absolute error = 1.944114e-25 relative error = 1.9433365099498302674058493001738e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0005 y[1] (analytic) = 1.0005001249791640627604383665053 y[1] (numeric) = 1.0005001249791640627604386095075 absolute error = 2.430022e-25 relative error = 2.4288072928032932292935385826422e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0006 y[1] (analytic) = 1.0006001799639946006480647944453 y[1] (numeric) = 1.0006001799639946006480650860333 absolute error = 2.915880e-25 relative error = 2.9141309969631670966814256530008e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0007 y[1] (analytic) = 1.0007002449428233305674133850473 y[1] (numeric) = 1.0007002449428233305674137252163 absolute error = 3.401690e-25 relative error = 3.3993096506080711554056021922066e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0008 y[1] (analytic) = 1.0008003199146496027310307139413 y[1] (numeric) = 1.0008003199146496027310311026863 absolute error = 3.887450e-25 relative error = 3.8843412843148671972292457803534e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0009 y[1] (analytic) = 1.0009004048784726674214880175891 y[1] (numeric) = 1.0009004048784726674214884549055 absolute error = 4.373164e-25 relative error = 4.3692299240612065274300422517635e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 1.0010004998332916750013886904514 y[1] (numeric) = 1.0010004998332916750013891763341 absolute error = 4.858827e-25 relative error = 4.8539706032206750234944115171851e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.23 NO POLE x[1] = 0.0011 y[1] (analytic) = 1.0011006047781056759233767813522 y[1] (numeric) = 1.0011006047781056759233773157964 absolute error = 5.344442e-25 relative error = 5.3385663483687511820148092736736e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0012 y[1] (analytic) = 1.0012007197119136207401464889448 y[1] (numeric) = 1.0012007197119136207401470719457 absolute error = 5.830009e-25 relative error = 5.8230171884789814555834535821231e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0013 y[1] (analytic) = 1.0013008446337143601144526561763 y[1] (numeric) = 1.001300844633714360114453287729 absolute error = 6.315527e-25 relative error = 6.3073221538230915315739893883306e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0014 y[1] (analytic) = 1.0014009795425066448291222636518 y[1] (numeric) = 1.0014009795425066448291229437514 absolute error = 6.800996e-25 relative error = 6.7914812736722681801974191064948e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0015 y[1] (analytic) = 1.0015011244372891257970669217975 y[1] (numeric) = 1.0015011244372891257970676504391 absolute error = 7.286416e-25 relative error = 7.2754945772966554719040381186675e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0016 y[1] (analytic) = 1.0016012793170603540712963617235 y[1] (numeric) = 1.0016012793170603540712971389023 absolute error = 7.771788e-25 relative error = 7.7593630923666318426960461702743e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0017 y[1] (analytic) = 1.0017014441808187808549329246854 y[1] (numeric) = 1.0017014441808187808549337503965 absolute error = 8.257111e-25 relative error = 8.2430858495492947160031721845095e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0018 y[1] (analytic) = 1.0018016190275627575112270500446 y[1] (numeric) = 1.0018016190275627575112279242831 absolute error = 8.742385e-25 relative error = 8.7266628781116684412229736514124e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0019 y[1] (analytic) = 1.0019018038562905355735737616272 y[1] (numeric) = 1.0019018038562905355735746843883 absolute error = 9.227611e-25 relative error = 9.2100952054215263687533231570253e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 1.0020019986660002667555301523823 y[1] (numeric) = 1.0020019986660002667555311236612 absolute error = 9.712789e-25 relative error = 9.6933828604443605402676771631850e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0021 y[1] (analytic) = 1.0021022034556900029608338672377 y[1] (numeric) = 1.0021022034556900029608348870294 absolute error = 1.0197917e-24 relative error = 1.0176523876340245711104895044408e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0022 y[1] (analytic) = 1.0022024182243576962934225840542 y[1] (numeric) = 1.0022024182243576962934236523538 absolute error = 1.0682996e-24 relative error = 1.0659519280473792281987468207424e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0023 y[1] (analytic) = 1.0023026429710011990674544925777 y[1] (numeric) = 1.0023026429710011990674556093804 absolute error = 1.1168027e-24 relative error = 1.1142370099809380002244610889870e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0024 y[1] (analytic) = 1.0024028776946182638173297712897 y[1] (numeric) = 1.0024028776946182638173309365906 absolute error = 1.1653009e-24 relative error = 1.1625075365705490021980496132884e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0025 y[1] (analytic) = 1.0025031223942065433077130620547 y[1] (numeric) = 1.0025031223942065433077142758489 absolute error = 1.2137942e-24 relative error = 1.2107635107421731317732662563235e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.0MB, time=0.49 NO POLE x[1] = 0.0026 y[1] (analytic) = 1.0026033770687635905435569424651 y[1] (numeric) = 1.0026033770687635905435582047478 absolute error = 1.2622827e-24 relative error = 1.2590050351620013476873054939724e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0027 y[1] (analytic) = 1.0027036417172868587801263957835 y[1] (numeric) = 1.0027036417172868587801277065498 absolute error = 1.3107663e-24 relative error = 1.3072320129954925093382021648242e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0028 y[1] (analytic) = 1.0028039163387737015330242783816 y[1] (numeric) = 1.0028039163387737015330256376267 absolute error = 1.3592451e-24 relative error = 1.3554445468886771216276043790605e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0029 y[1] (analytic) = 1.0029042009322213725882177845759 y[1] (numeric) = 1.0029042009322213725882191922949 absolute error = 1.4077190e-24 relative error = 1.4036425400267487410193833735232e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 1.0030044954966270260120659087596 y[1] (numeric) = 1.0030044954966270260120673649476 absolute error = 1.4561880e-24 relative error = 1.4518259953351295535816189303175e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0031 y[1] (analytic) = 1.0031048000309877161613479047306 y[1] (numeric) = 1.0031048000309877161613494093827 absolute error = 1.5046521e-24 relative error = 1.4999949157391317271212447784043e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0032 y[1] (analytic) = 1.0032051145343003976932927421156 y[1] (numeric) = 1.0032051145343003976932942952269 absolute error = 1.5531113e-24 relative error = 1.5481493041639570540472776304482e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0033 y[1] (analytic) = 1.003305439005561925575609559789 y[1] (numeric) = 1.0033054390055619255756111613546 absolute error = 1.6015656e-24 relative error = 1.5962891635346965944986449733833e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0034 y[1] (analytic) = 1.0034057734437690550965191161878 y[1] (numeric) = 1.003405773443769055096520766203 absolute error = 1.6500152e-24 relative error = 1.6444146960974876154374968698825e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0035 y[1] (analytic) = 1.0035061178479184418747862364213 y[1] (numeric) = 1.003506117847918441874787934881 absolute error = 1.6984597e-24 relative error = 1.6925255061149531687624729494435e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0036 y[1] (analytic) = 1.0036064722170066418697532560743 y[1] (numeric) = 1.0036064722170066418697550029737 absolute error = 1.7468994e-24 relative error = 1.7406218954935889330274981202086e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0037 y[1] (analytic) = 1.0037068365500301113913744616058 y[1] (numeric) = 1.0037068365500301113913762569401 absolute error = 1.7953343e-24 relative error = 1.7887038671281491727504004429417e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0038 y[1] (analytic) = 1.0038072108459852071102515272413 y[1] (numeric) = 1.0038072108459852071102533710056 absolute error = 1.8437643e-24 relative error = 1.8367713242925587581744792475737e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0039 y[1] (analytic) = 1.0039075951038681860676699482581 y[1] (numeric) = 1.0039075951038681860676718404474 absolute error = 1.8921893e-24 relative error = 1.8848241703004814226695714615256e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 1.004007989322675205685636470564 y[1] (numeric) = 1.0040079893226752056856384111735 absolute error = 1.9406095e-24 relative error = 1.9328626073077125291927415782765e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0041 y[1] (analytic) = 1.0041083935014023237769175164691 y[1] (numeric) = 1.004108393501402323776919505494 absolute error = 1.9890249e-24 relative error = 1.9808866382085692181477237270246e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=0.76 NO POLE x[1] = 0.0042 y[1] (analytic) = 1.0042088076390454985550786065498 y[1] (numeric) = 1.0042088076390454985550806439851 absolute error = 2.0374353e-24 relative error = 2.0288960667354942860171291229854e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0043 y[1] (analytic) = 1.0043092317346005886445247775044 y[1] (numeric) = 1.0043092317346005886445268633453 absolute error = 2.0858409e-24 relative error = 2.0768910949841847854866986032764e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0044 y[1] (analytic) = 1.0044096657870633530905419959013 y[1] (numeric) = 1.0044096657870633530905441301429 absolute error = 2.1342416e-24 relative error = 2.1248716262876576490600407654745e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0045 y[1] (analytic) = 1.0045101097954294513693395677172 y[1] (numeric) = 1.0045101097954294513693417503546 absolute error = 2.1826374e-24 relative error = 2.1728376635696564496715787124016e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0046 y[1] (analytic) = 1.0046105637586944433980935435669 y[1] (numeric) = 1.0046105637586944433980957745952 absolute error = 2.2310283e-24 relative error = 2.2207892097538094138089821713690e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0047 y[1] (analytic) = 1.004711027675853789544991119523 y[1] (numeric) = 1.0047110276758537895449933989374 absolute error = 2.2794144e-24 relative error = 2.2687263672947352723970966863840e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0048 y[1] (analytic) = 1.004811501545902850639276033426 y[1] (numeric) = 1.0048115015459028506392783612216 absolute error = 2.3277956e-24 relative error = 2.3166490395648195167013957747722e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0049 y[1] (analytic) = 1.0049119853678368879812949565833 y[1] (numeric) = 1.0049119853678368879812973327551 absolute error = 2.3761718e-24 relative error = 2.3645571299761428000638217703796e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 1.005012479140651063352544880757 y[1] (numeric) = 1.0050124791406510633525473053002 absolute error = 2.4245432e-24 relative error = 2.4124508404842266878958354583017e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0051 y[1] (analytic) = 1.0051129828633404390257215003412 y[1] (numeric) = 1.0051129828633404390257239732509 absolute error = 2.4729097e-24 relative error = 2.4603300744909665820441893652441e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0052 y[1] (analytic) = 1.0052134965348999777747685896263 y[1] (numeric) = 1.0052134965348999777747711108976 absolute error = 2.5212713e-24 relative error = 2.5081948349192942377157261531945e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0053 y[1] (analytic) = 1.0053140201543245428849283750511 y[1] (numeric) = 1.0053140201543245428849309446792 absolute error = 2.5696281e-24 relative error = 2.5560452241634305360505907423823e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0054 y[1] (analytic) = 1.0054145537206088981627929023424 y[1] (numeric) = 1.0054145537206088981627955203223 absolute error = 2.6179799e-24 relative error = 2.6038810461933110176053496012684e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0055 y[1] (analytic) = 1.0055150972327477079463563984402 y[1] (numeric) = 1.0055150972327477079463590647671 absolute error = 2.6663269e-24 relative error = 2.6517025028643824731183508198138e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0056 y[1] (analytic) = 1.0056156506897355371150686281098 y[1] (numeric) = 1.0056156506897355371150713427788 absolute error = 2.7146690e-24 relative error = 2.6995094976276993767017544823160e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.1MB, time=1.04 x[1] = 0.0057 y[1] (analytic) = 1.0057162140905668510998892451388 y[1] (numeric) = 1.0057162140905668510998920081449 absolute error = 2.7630061e-24 relative error = 2.7473019339739763953127846515709e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0058 y[1] (analytic) = 1.0058167874342360158933431380187 y[1] (numeric) = 1.0058167874342360158933459493572 absolute error = 2.8113385e-24 relative error = 2.7950801131203187480464252104891e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0059 y[1] (analytic) = 1.0059173707197372980595767700121 y[1] (numeric) = 1.0059173707197372980595796296781 absolute error = 2.8596660e-24 relative error = 2.8428438391056904171331251484060e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 1.0060179639460648647444155135024 y[1] (numeric) = 1.0060179639460648647444184214908 absolute error = 2.9079884e-24 relative error = 2.8905929160484698063462300079470e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0061 y[1] (analytic) = 1.0061185671122127836854219785267 y[1] (numeric) = 1.0061185671122127836854249348327 absolute error = 2.9563060e-24 relative error = 2.9383276451057503201437819000168e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0062 y[1] (analytic) = 1.0062191802171750232219553353926 y[1] (numeric) = 1.0062191802171750232219583400114 absolute error = 3.0046188e-24 relative error = 2.9860480291694548596492164640963e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0063 y[1] (analytic) = 1.006319803259945452305231631276 y[1] (numeric) = 1.0063198032599454523052346842026 absolute error = 3.0529266e-24 relative error = 3.0337538723874138820455128576675e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0064 y[1] (analytic) = 1.0064204362395178405083851007001 y[1] (numeric) = 1.0064204362395178405083882019297 absolute error = 3.1012296e-24 relative error = 3.0814453764350417639887143332797e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0065 y[1] (analytic) = 1.0065210791548858580365304697964 y[1] (numeric) = 1.006521079154885858036533619324 absolute error = 3.1495276e-24 relative error = 3.1291223454996745285410979083873e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0066 y[1] (analytic) = 1.0066217320050430757368262542443 y[1] (numeric) = 1.0066217320050430757368294520651 absolute error = 3.1978208e-24 relative error = 3.1767849812167369666325779523033e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0067 y[1] (analytic) = 1.0067223947889829651085390507921 y[1] (numeric) = 1.0067223947889829651085422969011 absolute error = 3.2461090e-24 relative error = 3.2244330878130612256780379932068e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0068 y[1] (analytic) = 1.0068230675056988983131088222552 y[1] (numeric) = 1.0068230675056988983131121166475 absolute error = 3.2943923e-24 relative error = 3.2720667675617720431479513956361e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0069 y[1] (analytic) = 1.0069237501541841481842151758934 y[1] (numeric) = 1.0069237501541841481842185185642 absolute error = 3.3426708e-24 relative error = 3.3196861226961396261962593352700e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 1.0070244427334318882378446350663 y[1] (numeric) = 1.0070244427334318882378480260106 absolute error = 3.3909443e-24 relative error = 3.3672909575022226072174373499894e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0071 y[1] (analytic) = 1.0071251452424351926823589040641 y[1] (numeric) = 1.0071251452424351926823623432772 absolute error = 3.4392131e-24 relative error = 3.4148815728080272764005401538998e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0072 y[1] (analytic) = 1.0072258576801870364285641260168 y[1] (numeric) = 1.0072258576801870364285676134936 absolute error = 3.4874768e-24 relative error = 3.4624575743441038803149483019611e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.1MB, time=1.32 NO POLE x[1] = 0.0073 y[1] (analytic) = 1.0073265800456802950997811337764 y[1] (numeric) = 1.0073265800456802950997846695121 absolute error = 3.5357357e-24 relative error = 3.5100192629084217000056000082211e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0074 y[1] (analytic) = 1.0074273123379077450419166936762 y[1] (numeric) = 1.007427312337907745041920277666 absolute error = 3.5839898e-24 relative error = 3.5575666413914641599185324174869e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0075 y[1] (analytic) = 1.0075280545558620633335357420632 y[1] (numeric) = 1.0075280545558620633335393743022 absolute error = 3.6322390e-24 relative error = 3.6050996134307758842370029276822e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0076 y[1] (analytic) = 1.0076288066985358277959346145041 y[1] (numeric) = 1.0076288066985358277959382949872 absolute error = 3.6804831e-24 relative error = 3.6526179834605834733361562064693e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0077 y[1] (analytic) = 1.0077295687649215170032152675632 y[1] (numeric) = 1.0077295687649215170032189962856 absolute error = 3.7287224e-24 relative error = 3.7001220521592326908535343503408e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0078 y[1] (analytic) = 1.0078303407540115102923604930541 y[1] (numeric) = 1.007830340754011510292364270011 absolute error = 3.7769569e-24 relative error = 3.7476118224167150492711572825662e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0079 y[1] (analytic) = 1.007931122664798087773310124661 y[1] (numeric) = 1.0079311226647980877733139498473 absolute error = 3.8251863e-24 relative error = 3.7950869994835157196485590419871e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 1.0080319144962734303390382368304 y[1] (numeric) = 1.0080319144962734303390421102414 absolute error = 3.8734110e-24 relative error = 3.8425479831514992402899781298343e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0081 y[1] (analytic) = 1.0081327162474296196756313358339 y[1] (numeric) = 1.0081327162474296196756352574646 absolute error = 3.9216307e-24 relative error = 3.8899944787006596317967226908494e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0082 y[1] (analytic) = 1.0082335279172586382723675428982 y[1] (numeric) = 1.0082335279172586382723715127437 absolute error = 3.9698455e-24 relative error = 3.9374265882633770512891511645463e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0083 y[1] (analytic) = 1.0083343495047523694317967693042 y[1] (numeric) = 1.0083343495047523694318007873596 absolute error = 4.0180554e-24 relative error = 3.9848443147587749094012900671788e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0084 y[1] (analytic) = 1.008435181008902597279821883353 y[1] (numeric) = 1.0084351810089025972798259496135 absolute error = 4.0662605e-24 relative error = 4.0322477602693856453802734652284e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0085 y[1] (analytic) = 1.008536022428701006775780869099 y[1] (numeric) = 1.0085360224287010067757849835595 absolute error = 4.1144605e-24 relative error = 4.0796366302234623299789758463700e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0086 y[1] (analytic) = 1.0086368737631391837225299767469 y[1] (numeric) = 1.0086368737631391837225341394027 absolute error = 4.1626558e-24 relative error = 4.1270113241740627371017876885884e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0087 y[1] (analytic) = 1.0087377350112086147765278646163 y[1] (numeric) = 1.0087377350112086147765320754623 absolute error = 4.2108460e-24 relative error = 4.1743714484451313586481840846821e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0088 y[1] (analytic) = 1.0088386061719006874579207325672 y[1] (numeric) = 1.0088386061719006874579249915986 absolute error = 4.2590314e-24 relative error = 4.2217173033862701853173339487744e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=1.59 NO POLE x[1] = 0.0089 y[1] (analytic) = 1.0089394872442066901606284467914 y[1] (numeric) = 1.0089394872442066901606327540032 absolute error = 4.3072118e-24 relative error = 4.2690486936581457718159360419483e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 1.0090403782271178121624316558638 y[1] (numeric) = 1.0090403782271178121624360112513 absolute error = 4.3553875e-24 relative error = 4.3163659195208899914468367421745e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0091 y[1] (analytic) = 1.0091412791196251436350598979574 y[1] (numeric) = 1.0091412791196251436350643015155 absolute error = 4.4035581e-24 relative error = 4.3636685874565195726670050447588e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0092 y[1] (analytic) = 1.0092421899207196756542806991162 y[1] (numeric) = 1.0092421899207196756542851508401 absolute error = 4.4517239e-24 relative error = 4.4109569976951737436306478597600e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0093 y[1] (analytic) = 1.0093431106293923002099896624904 y[1] (numeric) = 1.0093431106293923002099941623751 absolute error = 4.4998847e-24 relative error = 4.4582309549762753761504382608126e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0094 y[1] (analytic) = 1.009444041244633810216301548428 y[1] (numeric) = 1.0094440412446338102163060964687 absolute error = 4.5480407e-24 relative error = 4.5054906603760957293701385697042e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0095 y[1] (analytic) = 1.0095449817654348995216423453262 y[1] (numeric) = 1.0095449817654348995216469415179 absolute error = 4.5961917e-24 relative error = 4.5527359186734216843594385783790e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0096 y[1] (analytic) = 1.0096459321907861629188423311378 y[1] (numeric) = 1.0096459321907861629188469754757 absolute error = 4.6443379e-24 relative error = 4.5999669309046351505521057590580e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0097 y[1] (analytic) = 1.0097468925196780961552301254352 y[1] (numeric) = 1.0097468925196780961552348179143 absolute error = 4.6924791e-24 relative error = 4.6471835018878775863119096310582e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0098 y[1] (analytic) = 1.0098478627511010959427277319283 y[1] (numeric) = 1.0098478627511010959427324725438 absolute error = 4.7406155e-24 relative error = 4.6943858326196482617709079858280e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0099 y[1] (analytic) = 1.009948842884045459967946571337 y[1] (numeric) = 1.009948842884045459967951360084 absolute error = 4.7887470e-24 relative error = 4.7415738269723499372676662674370e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 1.0100498329175013869022845045169 y[1] (numeric) = 1.0100498329175013869022893413903 absolute error = 4.8368734e-24 relative error = 4.7887472898528413596483444004998e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0101 y[1] (analytic) = 1.0101508328504589764120238457363 y[1] (numeric) = 1.0101508328504589764120287307313 absolute error = 4.8849950e-24 relative error = 4.8359065212226245930932180017549e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0102 y[1] (analytic) = 1.0102518426819082291684303660054 y[1] (numeric) = 1.0102518426819082291684352991172 absolute error = 4.9331118e-24 relative error = 4.8830515239686214621644333826998e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0103 y[1] (analytic) = 1.0103528624108390468578532863555 y[1] (numeric) = 1.0103528624108390468578582675791 absolute error = 4.9812236e-24 relative error = 4.9301821030269805718200149664149e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0104 y[1] (analytic) = 1.0104538920362412321918262609664 y[1] (numeric) = 1.0104538920362412321918312902969 absolute error = 5.0293305e-24 relative error = 4.9772983603091674512903349146570e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=1.86 NO POLE x[1] = 0.0105 y[1] (analytic) = 1.0105549315571044889171693500432 y[1] (numeric) = 1.0105549315571044889171744274756 absolute error = 5.0774324e-24 relative error = 5.0244001997758636384196159123735e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0106 y[1] (analytic) = 1.0106559809724184218260919823391 y[1] (numeric) = 1.0106559809724184218260971078687 absolute error = 5.1255296e-24 relative error = 5.0714879212097391630207714429519e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0107 y[1] (analytic) = 1.0107570402811725367662969072259 y[1] (numeric) = 1.0107570402811725367663020808476 absolute error = 5.1736217e-24 relative error = 5.1185611317243965790232673483226e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0108 y[1] (analytic) = 1.0108581094823562406510851362074 y[1] (numeric) = 1.0108581094823562406510903579163 absolute error = 5.2217089e-24 relative error = 5.1656200321466985834525079925402e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0109 y[1] (analytic) = 1.0109591885749588414694618737786 y[1] (numeric) = 1.0109591885749588414694671435698 absolute error = 5.2697912e-24 relative error = 5.2126646253923085033731270961752e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 1.0110602775579695482962434375271 y[1] (numeric) = 1.0110602775579695482962487553958 absolute error = 5.3178687e-24 relative error = 5.2596950132828236404569762027071e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0111 y[1] (analytic) = 1.0111613764303774713021651673767 y[1] (numeric) = 1.0111613764303774713021705333179 absolute error = 5.3659412e-24 relative error = 5.3067110009116004234088580311839e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0112 y[1] (analytic) = 1.0112624851911716217639903238713 y[1] (numeric) = 1.01126248519117162176399573788 absolute error = 5.4140087e-24 relative error = 5.3537125912235556542745653970402e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0113 y[1] (analytic) = 1.0113636038393409120746199753988 y[1] (numeric) = 1.0113636038393409120746254374702 absolute error = 5.4620714e-24 relative error = 5.4006999849162769888793256568268e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0114 y[1] (analytic) = 1.0114647323738741557532038742542 y[1] (numeric) = 1.0114647323738741557532093843834 absolute error = 5.5101292e-24 relative error = 5.4476730860085547937316521083312e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0115 y[1] (analytic) = 1.0115658707937600674552523214391 y[1] (numeric) = 1.0115658707937600674552578796212 absolute error = 5.5581821e-24 relative error = 5.4946318974152228114081307306712e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0116 y[1] (analytic) = 1.0116670190979872629827490200985 y[1] (numeric) = 1.0116670190979872629827546263285 absolute error = 5.6062300e-24 relative error = 5.5415763232042223010130692898020e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0117 y[1] (analytic) = 1.0117681772855442592942649174923 y[1] (numeric) = 1.0117681772855442592942705717653 absolute error = 5.6542730e-24 relative error = 5.5885064651566265469186034300878e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0118 y[1] (analytic) = 1.0118693453554194745150730354014 y[1] (numeric) = 1.0118693453554194745150787377125 absolute error = 5.7023111e-24 relative error = 5.6354223261868469373940371248968e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0119 y[1] (analytic) = 1.0119705233066012279472642888665 y[1] (numeric) = 1.0119705233066012279472700392107 absolute error = 5.7503442e-24 relative error = 5.6823238103920469056387926472532e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.2MB, time=2.15 x[1] = 0.012 y[1] (analytic) = 1.0120717111380777400798642931584 y[1] (numeric) = 1.0120717111380777400798700915309 absolute error = 5.7983725e-24 relative error = 5.7292111183304514637703368159672e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0121 y[1] (analytic) = 1.0121729088488371325989511588799 y[1] (numeric) = 1.0121729088488371325989570052757 absolute error = 5.8463958e-24 relative error = 5.7760840552917124441110422873197e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0122 y[1] (analytic) = 1.0122741164378674283977742750962 y[1] (numeric) = 1.0122741164378674283977801695104 absolute error = 5.8944142e-24 relative error = 5.8229427230067819339257778151707e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0123 y[1] (analytic) = 1.012375333904156551586874080394 y[1] (numeric) = 1.0123753339041565515868800228217 absolute error = 5.9424277e-24 relative error = 5.8697871243893627296261671090703e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0124 y[1] (analytic) = 1.0124765612466923275042028217678 y[1] (numeric) = 1.012476561246692327504208812204 absolute error = 5.9904362e-24 relative error = 5.9166171635852970041879600113046e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0125 y[1] (analytic) = 1.0125777984644624827252463012317 y[1] (numeric) = 1.0125777984644624827252523396716 absolute error = 6.0384399e-24 relative error = 5.9634330410533147836079769207139e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0126 y[1] (analytic) = 1.0126790455564546450731466100564 y[1] (numeric) = 1.0126790455564546450731526964952 absolute error = 6.0864388e-24 relative error = 6.0102347596770672291314262773740e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0127 y[1] (analytic) = 1.0127803025216563436288258505295 y[1] (numeric) = 1.0127803025216563436288319849621 absolute error = 6.1344326e-24 relative error = 6.0570220261257767201044603560046e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0128 y[1] (analytic) = 1.0128815693590550087411108451371 y[1] (numeric) = 1.0128815693590550087411170275585 absolute error = 6.1824214e-24 relative error = 6.1037949420998911015927227674090e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0129 y[1] (analytic) = 1.0129828460676379720368588330676 y[1] (numeric) = 1.012982846067637972036865063473 absolute error = 6.2304054e-24 relative error = 6.1505537079785742198921172924969e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 1.0130841326463924664310841539349 y[1] (numeric) = 1.0130841326463924664310904323194 absolute error = 6.2783845e-24 relative error = 6.1972982279364268171512392370201e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0131 y[1] (analytic) = 1.0131854290943056261370859186194 y[1] (numeric) = 1.013185429094305626137092244978 absolute error = 6.3263586e-24 relative error = 6.2440284061873860520518282296673e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0132 y[1] (analytic) = 1.0132867354103644866765766671269 y[1] (numeric) = 1.0132867354103644866765830414545 absolute error = 6.3743276e-24 relative error = 6.2907441469847150493970872422234e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0133 y[1] (analytic) = 1.0133880515935559848898120133623 y[1] (numeric) = 1.0133880515935559848898184356543 absolute error = 6.4222920e-24 relative error = 6.3374459466942846649214406230784e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0134 y[1] (analytic) = 1.01348937764286695894572127672 y[1] (numeric) = 1.0134893776428669589457277469712 absolute error = 6.4702512e-24 relative error = 6.3841332161253148426884317351696e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0135 y[1] (analytic) = 1.0135907135572841483520391003845 y[1] (numeric) = 1.0135907135572841483520456185902 absolute error = 6.5182057e-24 relative error = 6.4308064515743185419434750826425e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.2MB, time=2.43 NO POLE x[1] = 0.0136 y[1] (analytic) = 1.0136920593357941939654380562461 y[1] (numeric) = 1.0136920593357941939654446224013 absolute error = 6.5661552e-24 relative error = 6.4774653599460669549527016239849e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0137 y[1] (analytic) = 1.0137934149773836380016622363247 y[1] (numeric) = 1.0137934149773836380016688504244 absolute error = 6.6140997e-24 relative error = 6.5241099441818248861032218609441e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0138 y[1] (analytic) = 1.0138947804810389240456618306043 y[1] (numeric) = 1.0138947804810389240456684926436 absolute error = 6.6620393e-24 relative error = 6.5707403058522681743063732744354e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0139 y[1] (analytic) = 1.0139961558457463970617286911751 y[1] (numeric) = 1.0139961558457463970617354011491 absolute error = 6.7099740e-24 relative error = 6.6173564478687738477092996836127e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 1.0140975410704923034036328825821 y[1] (numeric) = 1.0140975410704923034036396404859 absolute error = 6.7579038e-24 relative error = 6.6639583731425715235919836022964e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0141 y[1] (analytic) = 1.0141989361542627908247602182789 y[1] (numeric) = 1.0141989361542627908247670241075 absolute error = 6.8058286e-24 relative error = 6.7105459859847579728126425144147e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0142 y[1] (analytic) = 1.0143003410960439084882507830851 y[1] (numeric) = 1.0143003410960439084882576368337 absolute error = 6.8537486e-24 relative error = 6.7571194865160947770921355453026e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0143 y[1] (analytic) = 1.0144017558948216069771384415473 y[1] (numeric) = 1.0144017558948216069771453432109 absolute error = 6.9016636e-24 relative error = 6.8036786804572526688867413975130e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0144 y[1] (analytic) = 1.0145031805495817383044913320994 y[1] (numeric) = 1.0145031805495817383044982816731 absolute error = 6.9495737e-24 relative error = 6.8502236693188504032497711726939e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0145 y[1] (analytic) = 1.0146046150593100559235533469241 y[1] (numeric) = 1.0146046150593100559235603444028 absolute error = 6.9974787e-24 relative error = 6.8967542588902506807681083871758e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0146 y[1] (analytic) = 1.0147060594229922147378865974112 y[1] (numeric) = 1.0147060594229922147378936427901 absolute error = 7.0453789e-24 relative error = 6.9432707477930320793188870866909e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0147 y[1] (analytic) = 1.0148075136396137711115148651146 y[1] (numeric) = 1.0148075136396137711115219583888 absolute error = 7.0932742e-24 relative error = 6.9897730403669615978072571392523e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0148 y[1] (analytic) = 1.014908977708160182879068038103 y[1] (numeric) = 1.0149089777081601828790751792676 absolute error = 7.1411646e-24 relative error = 7.0362611395220716671729370856257e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0149 y[1] (analytic) = 1.0150104516276168093559275326052 y[1] (numeric) = 1.0150104516276168093559347216551 absolute error = 7.1890499e-24 relative error = 7.0827348511259383586606126191982e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.015 y[1] (analytic) = 1.0151119353969689113483726998476 y[1] (numeric) = 1.015111935396968911348379936778 absolute error = 7.2369304e-24 relative error = 7.1291944736813004085031265928695e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0151 y[1] (analytic) = 1.0152134290152016511637282179834 y[1] (numeric) = 1.0152134290152016511637355027894 absolute error = 7.2848060e-24 relative error = 7.1756399115667316741018375026521e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.2MB, time=2.70 NO POLE x[1] = 0.0152 y[1] (analytic) = 1.0153149324813000926205124690109 y[1] (numeric) = 1.0153149324813000926205198016875 absolute error = 7.3326766e-24 relative error = 7.2220710692000504583164075809004e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0153 y[1] (analytic) = 1.0154164457942492010585869005792 y[1] (numeric) = 1.0154164457942492010585942811216 absolute error = 7.3805424e-24 relative error = 7.2684881464835928442655833010796e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0154 y[1] (analytic) = 1.0155179689530338433493063725821 y[1] (numeric) = 1.0155179689530338433493138009852 absolute error = 7.4284031e-24 relative error = 7.3148908508811943135446496186245e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0155 y[1] (analytic) = 1.0156195019566387879056704884352 y[1] (numeric) = 1.0156195019566387879056779646941 absolute error = 7.4762589e-24 relative error = 7.3612793822850341412416835399136e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0156 y[1] (analytic) = 1.0157210448040487046924759109381 y[1] (numeric) = 1.0157210448040487046924834350478 absolute error = 7.5241097e-24 relative error = 7.4076536451516954903272454516157e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0157 y[1] (analytic) = 1.0158225974942481652364696626172 y[1] (numeric) = 1.0158225974942481652364772345729 absolute error = 7.5719557e-24 relative error = 7.4540138393041352438792795835754e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0158 y[1] (analytic) = 1.015924160026221642636503410451 y[1] (numeric) = 1.0159241600262216426365110302476 absolute error = 7.6197966e-24 relative error = 7.5003596723236981085547627581159e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0159 y[1] (analytic) = 1.0160257323989535115736887348718 y[1] (numeric) = 1.0160257323989535115736964025044 absolute error = 7.6676326e-24 relative error = 7.5466913440231856131171187942134e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 1.0161273146114280483215533829469 y[1] (numeric) = 1.0161273146114280483215610984106 absolute error = 7.7154637e-24 relative error = 7.5930088573107891217322359992633e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0161 y[1] (analytic) = 1.0162289066626294307561985056346 y[1] (numeric) = 1.0162289066626294307562062689245 absolute error = 7.7632899e-24 relative error = 7.6393122150945457317497592265212e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0162 y[1] (analytic) = 1.016330508551541738366456879015 y[1] (numeric) = 1.0163305085515417383664646901261 absolute error = 7.8111111e-24 relative error = 7.6856013218891487674733069920540e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0163 y[1] (analytic) = 1.0164321202771489522640521093928 y[1] (numeric) = 1.0164321202771489522640599683201 absolute error = 7.8589273e-24 relative error = 7.7318761806318346349606760931793e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0164 y[1] (analytic) = 1.0165337418384349551937588221717 y[1] (numeric) = 1.0165337418384349551937667289104 absolute error = 7.9067387e-24 relative error = 7.7781369910067137264402598024600e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0165 y[1] (analytic) = 1.0166353732343835315435638343986 y[1] (numeric) = 1.0166353732343835315435717889436 absolute error = 7.9545450e-24 relative error = 7.8243834608006437843142933282545e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0166 y[1] (analytic) = 1.0167370144639783673548283108745 y[1] (numeric) = 1.016737014463978367354836313221 absolute error = 8.0023465e-24 relative error = 7.8706158880414326001802900162067e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0167 y[1] (analytic) = 1.0168386655262030503324509037332 y[1] (numeric) = 1.0168386655262030503324589538763 absolute error = 8.0501431e-24 relative error = 7.9168341772626611390197169386694e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.2MB, time=2.98 NO POLE x[1] = 0.0168 y[1] (analytic) = 1.0169403264200410698550318753835 y[1] (numeric) = 1.0169403264200410698550399733182 absolute error = 8.0979347e-24 relative error = 7.9630382330370847161179251977604e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0169 y[1] (analytic) = 1.0170419971444758169850382047146 y[1] (numeric) = 1.0170419971444758169850463504359 absolute error = 8.1457213e-24 relative error = 8.0092280583009791215706059384227e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 1.017143677698490584478969676463 y[1] (numeric) = 1.017143677698490584478977869966 absolute error = 8.1935030e-24 relative error = 8.0554037543049843128911520168645e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0171 y[1] (analytic) = 1.0172453680810685667975259536392 y[1] (numeric) = 1.017245368081068566797534194919 absolute error = 8.2412798e-24 relative error = 8.1015653239555647800898989245632e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0172 y[1] (analytic) = 1.0173470682911928601157746329124 y[1] (numeric) = 1.017347068291192860115782921964 absolute error = 8.2890516e-24 relative error = 8.1477126718641550591054897631010e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0173 y[1] (analytic) = 1.0174487783278464623333202828506 y[1] (numeric) = 1.0174487783278464623333286196691 absolute error = 8.3368185e-24 relative error = 8.1938458992514280743733281328847e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0174 y[1] (analytic) = 1.017550498190012273084474464917 y[1] (numeric) = 1.0175504981900122730844828494974 absolute error = 8.3845804e-24 relative error = 8.2399649107481499529200124966481e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0175 y[1] (analytic) = 1.0176522278766730937484267371178 y[1] (numeric) = 1.0176522278766730937484351694552 absolute error = 8.4323374e-24 relative error = 8.2860698075550180531323215647922e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0176 y[1] (analytic) = 1.017753967386811627459416640202 y[1] (numeric) = 1.0177539673868116274594251202915 absolute error = 8.4800895e-24 relative error = 8.3321605925776984968822067931473e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0177 y[1] (analytic) = 1.0178557167194104791169066663106 y[1] (numeric) = 1.0178557167194104791169151941472 absolute error = 8.5278366e-24 relative error = 8.3782371704759463010500233182592e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0178 y[1] (analytic) = 1.0179574758734521553957562099735 y[1] (numeric) = 1.0179574758734521553957647855522 absolute error = 8.5755787e-24 relative error = 8.4242995441845715661476913743461e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0179 y[1] (analytic) = 1.018059244847919064756396501352 y[1] (numeric) = 1.018059244847919064756405124668 absolute error = 8.6233160e-24 relative error = 8.4703479130904394787569550158006e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 1.0181610236417935174550065216268 y[1] (numeric) = 1.0181610236417935174550151926751 absolute error = 8.6710483e-24 relative error = 8.5163820836365302372728068187144e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0181 y[1] (analytic) = 1.0182628122540577255536899004273 y[1] (numeric) = 1.0182628122540577255536986192028 absolute error = 8.7187755e-24 relative error = 8.5624019605506870191249184299763e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0182 y[1] (analytic) = 1.0183646106836938029306527952017 y[1] (numeric) = 1.0183646106836938029306615616995 absolute error = 8.7664978e-24 relative error = 8.6084077431898237045775491896484e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0183 y[1] (analytic) = 1.0184664189296837652903827524271 y[1] (numeric) = 1.0184664189296837652903915666423 absolute error = 8.8142152e-24 memory used=45.7MB, alloc=4.2MB, time=3.25 relative error = 8.6543994344584716071077063748379e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0184 y[1] (analytic) = 1.0185682369910095301738285505558 y[1] (numeric) = 1.0185682369910095301738374124835 absolute error = 8.8619277e-24 relative error = 8.7003770372610003911105761061644e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0185 y[1] (analytic) = 1.0186700648666529169685810245975 y[1] (numeric) = 1.0186700648666529169685899342328 absolute error = 8.9096353e-24 relative error = 8.7463405545016177540685799037688e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0186 y[1] (analytic) = 1.0187719025555956469190548722349 y[1] (numeric) = 1.0187719025555956469190638295727 absolute error = 8.9573378e-24 relative error = 8.7922897927695713624877603834518e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0187 y[1] (analytic) = 1.0188737500568193431366714413706 y[1] (numeric) = 1.018873750056819343136680446406 absolute error = 9.0050354e-24 relative error = 8.8382249513227893679385686243575e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0188 y[1] (analytic) = 1.018975607369305530610042499005 y[1] (numeric) = 1.0189756073693055306100515517331 absolute error = 9.0527281e-24 relative error = 8.8841460330649855637239325341478e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0189 y[1] (analytic) = 1.0190774744920356362151549813417 y[1] (numeric) = 1.0190774744920356362151640817575 absolute error = 9.1004158e-24 relative error = 8.9300529427717442794425733978619e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 1.0191793514239909887255567250185 y[1] (numeric) = 1.0191793514239909887255658731171 absolute error = 9.1480986e-24 relative error = 8.9759457814940364439912534558794e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0191 y[1] (analytic) = 1.0192812381641528188225431793642 y[1] (numeric) = 1.0192812381641528188225523751406 absolute error = 9.1957764e-24 relative error = 9.0218244540267325954148095749108e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0192 y[1] (analytic) = 1.0193831347115022591053450995768 y[1] (numeric) = 1.0193831347115022591053543430259 absolute error = 9.2434491e-24 relative error = 9.0676888652037663471319873360501e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0193 y[1] (analytic) = 1.0194850410650203441013172207221 y[1] (numeric) = 1.0194850410650203441013265118393 absolute error = 9.2911172e-24 relative error = 9.1135395084305455004522195215984e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0194 y[1] (analytic) = 1.0195869572236880102761279124532 y[1] (numeric) = 1.0195869572236880102761372512334 absolute error = 9.3387802e-24 relative error = 9.1593758961268836929857384725675e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0195 y[1] (analytic) = 1.0196888831864860960439498143438 y[1] (numeric) = 1.019688883186486096043959200782 absolute error = 9.3864382e-24 relative error = 9.2051981293232933456933933772398e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0196 y[1] (analytic) = 1.0197908189523953417776514517387 y[1] (numeric) = 1.0197908189523953417776608858299 absolute error = 9.4340912e-24 relative error = 9.2510062109515725978360404017753e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0197 y[1] (analytic) = 1.0198927645203963898189898320166 y[1] (numeric) = 1.0198927645203963898189993137558 absolute error = 9.4817392e-24 relative error = 9.2968001439433477226074493812211e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0198 y[1] (analytic) = 1.0199947198894697844888040211637 y[1] (numeric) = 1.019994719889469784488813550546 absolute error = 9.5293823e-24 relative error = 9.3425800292697960084203045568078e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=49.5MB, alloc=4.2MB, time=3.53 x[1] = 0.0199 y[1] (analytic) = 1.0200966850585959720972097005572 y[1] (numeric) = 1.0200966850585959720972192775777 absolute error = 9.5770205e-24 relative error = 9.3883458698327999638311963712576e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 1.0201986600267553009537947038555 y[1] (numeric) = 1.0201986600267553009538043285093 absolute error = 9.6246538e-24 relative error = 9.4340976685340753904253097732977e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0201 y[1] (analytic) = 1.0203006447929280213778155338939 y[1] (numeric) = 1.0203006447929280213778252061759 absolute error = 9.6722820e-24 relative error = 9.4798352322545167444790142267013e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0202 y[1] (analytic) = 1.0204026393560942857083948594832 y[1] (numeric) = 1.0204026393560942857084045793885 absolute error = 9.7199053e-24 relative error = 9.5255587599553463693074175236787e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0203 y[1] (analytic) = 1.0205046437152341483147199920105 y[1] (numeric) = 1.0205046437152341483147297595341 absolute error = 9.7675236e-24 relative error = 9.5712681565470370640540827855969e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0204 y[1] (analytic) = 1.0206066578693275656062423417382 y[1] (numeric) = 1.0206066578693275656062521568753 absolute error = 9.8151371e-24 relative error = 9.6169636209218929549860629571541e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0205 y[1] (analytic) = 1.020708681817354396042877853702 y[1] (numeric) = 1.0207086818173543960428877164474 absolute error = 9.8627454e-24 relative error = 9.6626447640668148923966019854134e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0206 y[1] (analytic) = 1.0208107155582944001452084231018 y[1] (numeric) = 1.0208107155582944001452183334506 absolute error = 9.9103488e-24 relative error = 9.7083118828547012664723406726445e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0207 y[1] (analytic) = 1.0209127590911272405046842900886 y[1] (numeric) = 1.0209127590911272405046942480359 absolute error = 9.9579473e-24 relative error = 9.7539649801860768862977010118351e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0208 y[1] (analytic) = 1.0210148124148324817938274138409 y[1] (numeric) = 1.0210148124148324817938374193818 absolute error = 1.00055409e-23 relative error = 9.7996040589612973485679661140164e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0209 y[1] (analytic) = 1.0211168755283895907764358258313 y[1] (numeric) = 1.0211168755283895907764458789608 absolute error = 1.00531295e-23 relative error = 9.8452290241485662107286695002099e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 1.0212189484307779363177889621797 y[1] (numeric) = 1.0212189484307779363177990628929 absolute error = 1.01007132e-23 relative error = 9.8908399765994592243219882807946e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0211 y[1] (analytic) = 1.0213210311209767893948539749922 y[1] (numeric) = 1.0213210311209767893948641232841 absolute error = 1.01482919e-23 relative error = 9.9364368213014128907467359214348e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0212 y[1] (analytic) = 1.0214231235979653231064930225829 y[1] (numeric) = 1.0214231235979653231065032184485 absolute error = 1.01958656e-23 relative error = 9.9820195611834591763413595022067e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0213 y[1] (analytic) = 1.0215252258607226126836715384766 y[1] (numeric) = 1.021525225860722612683681781911 absolute error = 1.02434344e-23 relative error = 1.0027588297067287792165910923546e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0214 y[1] (analytic) = 1.021627337908227635499667479091 y[1] (numeric) = 1.0216273379082276354996777700891 absolute error = 1.02909981e-23 relative error = 1.0073142836086122957701440209579e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.2MB, time=3.81 NO POLE x[1] = 0.0215 y[1] (analytic) = 1.0217294597394592710802815499949 y[1] (numeric) = 1.0217294597394592710802918885519 absolute error = 1.03385570e-23 relative error = 1.0118683474817618715072473224764e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0216 y[1] (analytic) = 1.0218315913533963011140484106423 y[1] (numeric) = 1.0218315913533963011140587967531 absolute error = 1.03861108e-23 relative error = 1.0164209922540950106158265882345e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0217 y[1] (analytic) = 1.0219337327490174094624488574779 y[1] (numeric) = 1.0219337327490174094624592911376 absolute error = 1.04336597e-23 relative error = 1.0209722377921017870030349423392e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0218 y[1] (analytic) = 1.0220358839253011821701229853144 y[1] (numeric) = 1.022035883925301182170133466518 absolute error = 1.04812036e-23 relative error = 1.0255220746012527351056849230889e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0219 y[1] (analytic) = 1.0221380448812261074750843268771 y[1] (numeric) = 1.0221380448812261074750948556196 absolute error = 1.05287425e-23 relative error = 1.0300705029743271939489920545317e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 1.0222402156157705758189349704154 y[1] (numeric) = 1.0222402156157705758189455466919 absolute error = 1.05762765e-23 relative error = 1.0346175329865231001115747775839e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0221 y[1] (analytic) = 1.0223423961279128798570816552785 y[1] (numeric) = 1.022342396127912879857092279084 absolute error = 1.06238055e-23 relative error = 1.0391631551461919888763756596659e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0222 y[1] (analytic) = 1.0224445864166312144689528453525 y[1] (numeric) = 1.022444586416631214468963516682 absolute error = 1.06713295e-23 relative error = 1.0437073697460596959848372030869e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0223 y[1] (analytic) = 1.0225467864809036767682167802575 y[1] (numeric) = 1.0225467864809036767682274991062 absolute error = 1.07188487e-23 relative error = 1.0482501966378412989934877049665e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0224 y[1] (analytic) = 1.0226489963197082661130005042031 y[1] (numeric) = 1.0226489963197082661130112705659 absolute error = 1.07663628e-23 relative error = 1.0527916067727834749865178147914e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0225 y[1] (analytic) = 1.0227512159320228841161098723978 y[1] (numeric) = 1.0227512159320228841161206862697 absolute error = 1.08138719e-23 relative error = 1.0573316102240394240664483116812e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0226 y[1] (analytic) = 1.0228534453168253346552505349128 y[1] (numeric) = 1.0228534453168253346552613962889 absolute error = 1.08613761e-23 relative error = 1.0618702170608347641819376184260e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0227 y[1] (analytic) = 1.0229556844730933238832498978965 y[1] (numeric) = 1.0229556844730933238832608067718 absolute error = 1.09088753e-23 relative error = 1.0664074177972794470542591785902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0228 y[1] (analytic) = 1.0230579333998044602382800620375 y[1] (numeric) = 1.023057933399804460238291018407 absolute error = 1.09563695e-23 relative error = 1.0709432127259914682566030577880e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0229 y[1] (analytic) = 1.0231601920959362544540817381744 y[1] (numeric) = 1.0231601920959362544540927420332 absolute error = 1.10038588e-23 relative error = 1.0754776119132112463615335774598e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 1.0232624605604661195701891399502 y[1] (numeric) = 1.0232624605604661195702001912932 absolute error = 1.10513430e-23 relative error = 1.0800105961032623556886057476781e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.2MB, time=4.09 NO POLE x[1] = 0.0231 y[1] (analytic) = 1.0233647387923713709421558534077 y[1] (numeric) = 1.02336473879237137094216695223 absolute error = 1.10988223e-23 relative error = 1.0845421851350127542893397416667e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0232 y[1] (analytic) = 1.0234670267906292262517816834262 y[1] (numeric) = 1.023467026790629226251792829723 absolute error = 1.11462968e-23 relative error = 1.0890723890687881718803558869278e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0233 y[1] (analytic) = 1.0235693245542168055173404768949 y[1] (numeric) = 1.023569324554216805517351670661 absolute error = 1.11937661e-23 relative error = 1.0936011691123207728571403970393e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0234 y[1] (analytic) = 1.0236716320821111311038089225209 y[1] (numeric) = 1.0236716320821111311038201637514 absolute error = 1.12412305e-23 relative error = 1.0981285548702510320831207594031e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0235 y[1] (analytic) = 1.0237739493732891277330963271718 y[1] (numeric) = 1.0237739493732891277331076158617 absolute error = 1.12886899e-23 relative error = 1.1026545368643591552679389992966e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0236 y[1] (analytic) = 1.0238762764267276224942753686475 y[1] (numeric) = 1.0238762764267276224942867047919 absolute error = 1.13361444e-23 relative error = 1.1071791251539224884313804554791e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0237 y[1] (analytic) = 1.0239786132414033448538138247812 y[1] (numeric) = 1.0239786132414033448538252083752 absolute error = 1.13835940e-23 relative error = 1.1117023200284665920687380407238e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0238 y[1] (analytic) = 1.0240809598162929266658072787665 y[1] (numeric) = 1.0240809598162929266658187098049 absolute error = 1.14310384e-23 relative error = 1.1162240924829402757523743312888e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0239 y[1] (analytic) = 1.024183316150372902182212800607 y[1] (numeric) = 1.0241833161503729021822242790849 absolute error = 1.14784779e-23 relative error = 1.1207444721072476454249925774980e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 1.0242856822426197080630836045889 y[1] (numeric) = 1.0242856822426197080630951305015 absolute error = 1.15259126e-23 relative error = 1.1252634689537609934768040294905e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0241 y[1] (analytic) = 1.0243880580920096833868046826723 y[1] (numeric) = 1.0243880580920096833868162560144 absolute error = 1.15733421e-23 relative error = 1.1297810442613039557916281913024e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0242 y[1] (analytic) = 1.0244904436975190696603294136978 y[1] (numeric) = 1.0244904436975190696603410344644 absolute error = 1.16207666e-23 relative error = 1.1342972178499922423258499959025e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0243 y[1] (analytic) = 1.0245928390581240108294171483089 y[1] (numeric) = 1.0245928390581240108294288164952 absolute error = 1.16681863e-23 relative error = 1.1388120095321178390797682297622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0244 y[1] (analytic) = 1.0246952441728005532888717694864 y[1] (numeric) = 1.0246952441728005532888834850874 absolute error = 1.17156010e-23 relative error = 1.1433254000761544846963492215763e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0245 y[1] (analytic) = 1.0247976590405246458927812285911 y[1] (numeric) = 1.0247976590405246458927929916017 absolute error = 1.17630106e-23 relative error = 1.1478373800163845774674415551732e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0246 y[1] (analytic) = 1.0249000836602721399647580568145 y[1] (numeric) = 1.0249000836602721399647698672298 absolute error = 1.18104153e-23 relative error = 1.1523479691621185481134212777331e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.2MB, time=4.36 NO POLE x[1] = 0.0247 y[1] (analytic) = 1.0250025180310187893081808519346 y[1] (numeric) = 1.0250025180310187893081927097496 absolute error = 1.18578150e-23 relative error = 1.1568571580466260781955374952407e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0248 y[1] (analytic) = 1.025104962151740250216436740273 y[1] (numeric) = 1.0251049621517402502164486454828 absolute error = 1.19052098e-23 relative error = 1.1613649567172558383100699246071e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0249 y[1] (analytic) = 1.025207416021412081483164813753 y[1] (numeric) = 1.0252074160214120814831767663525 absolute error = 1.19525995e-23 relative error = 1.1658713459550669771408706546039e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 1.0253098796390097444125005419541 y[1] (numeric) = 1.0253098796390097444125125419384 absolute error = 1.19999843e-23 relative error = 1.1703763455614944977588702116615e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0251 y[1] (analytic) = 1.0254123530035086028293211590628 y[1] (numeric) = 1.0254123530035086028293332064269 absolute error = 1.20473641e-23 relative error = 1.1748799460736336700803265611922e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0252 y[1] (analytic) = 1.0255148361138839230894920256147 y[1] (numeric) = 1.0255148361138839230895041203536 absolute error = 1.20947389e-23 relative error = 1.1793821477836594986020132073682e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0253 y[1] (analytic) = 1.0256173289691108740901139649276 y[1] (numeric) = 1.0256173289691108740901261070363 absolute error = 1.21421087e-23 relative error = 1.1838829509837280738218726155111e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0254 y[1] (analytic) = 1.0257198315681645272797715741219 y[1] (numeric) = 1.0257198315681645272797837635955 absolute error = 1.21894736e-23 relative error = 1.1883823657152274507947884002712e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0255 y[1] (analytic) = 1.0258223439100198566687825096263 y[1] (numeric) = 1.0258223439100198566687947464597 absolute error = 1.22368334e-23 relative error = 1.1928803727707997233085349023289e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0256 y[1] (analytic) = 1.0259248659936517388394477470656 y[1] (numeric) = 1.0259248659936517388394600312539 absolute error = 1.22841883e-23 relative error = 1.1973769919400718198914110791610e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0257 y[1] (analytic) = 1.02602739781803495295630281543 y[1] (numeric) = 1.0260273978180349529563151469682 absolute error = 1.23315382e-23 relative error = 1.2018722137658732714644522667927e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0258 y[1] (analytic) = 1.0261299393821441807763700054205 y[1] (numeric) = 1.0261299393821441807763823843036 absolute error = 1.23788831e-23 relative error = 1.2063660385402654531509536761920e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0259 y[1] (analytic) = 1.0262324906849540066594115518703 y[1] (numeric) = 1.0262324906849540066594239780934 absolute error = 1.24262231e-23 relative error = 1.2108584762996712715274002279270e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 1.0263350517254389175781837901389 y[1] (numeric) = 1.0263350517254389175781962636969 absolute error = 1.24735580e-23 relative error = 1.2153495078463788805637746047534e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0261 y[1] (analytic) = 1.0264376225025733031286922863756 y[1] (numeric) = 1.0264376225025733031287048072636 absolute error = 1.25208880e-23 relative error = 1.2198391529601799880354504643572e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0262 memory used=64.8MB, alloc=4.2MB, time=4.64 y[1] (analytic) = 1.0265402030153314555404479415512 y[1] (numeric) = 1.0265402030153314555404605097641 absolute error = 1.25682129e-23 relative error = 1.2243273924472194091123607915054e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0263 y[1] (analytic) = 1.0266427932626875696867240691541 y[1] (numeric) = 1.026642793262687569686736684687 absolute error = 1.26155329e-23 relative error = 1.2288142460833558611460872137723e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0264 y[1] (analytic) = 1.0267453932436157430948144464493 y[1] (numeric) = 1.0267453932436157430948271092972 absolute error = 1.26628479e-23 relative error = 1.2332997044181027808610472914094e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0265 y[1] (analytic) = 1.0268480029570899759562923391966 y[1] (numeric) = 1.0268480029570899759563050493545 absolute error = 1.27101579e-23 relative error = 1.2377837677433875588252761290699e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0266 y[1] (analytic) = 1.0269506224020841711372704997266 y[1] (numeric) = 1.0269506224020841711372832571895 absolute error = 1.27574629e-23 relative error = 1.2422664363511182815254284020857e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0267 y[1] (analytic) = 1.0270532515775721341886621382709 y[1] (numeric) = 1.0270532515775721341886749430338 absolute error = 1.28047629e-23 relative error = 1.2467477105331837015260280041137e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0268 y[1] (analytic) = 1.0271558904825275733564428674442 y[1] (numeric) = 1.0271558904825275733564557195022 absolute error = 1.28520580e-23 relative error = 1.2512276003170737620970047822352e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0269 y[1] (analytic) = 1.0272585391159240995919136197766 y[1] (numeric) = 1.0272585391159240995919265191246 absolute error = 1.28993480e-23 relative error = 1.2557060865224245194303538023358e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 1.0273611974767352265619645381911 y[1] (numeric) = 1.0273611974767352265619774848243 absolute error = 1.29466332e-23 relative error = 1.2601831986450100249254303720137e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0271 y[1] (analytic) = 1.0274638655639343706593398393274 y[1] (numeric) = 1.0274638655639343706593528332406 absolute error = 1.29939132e-23 relative error = 1.2646588980399961610670177052588e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0272 y[1] (analytic) = 1.0275665433764948510129036496045 y[1] (numeric) = 1.0275665433764948510129166907928 absolute error = 1.30411883e-23 relative error = 1.2691332142001998595668253665638e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0273 y[1] (analytic) = 1.0276692309133898894979068139245 y[1] (numeric) = 1.0276692309133898894979199023829 absolute error = 1.30884584e-23 relative error = 1.2736061376837185546921672628202e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0274 y[1] (analytic) = 1.0277719281735926107462546769114 y[1] (numeric) = 1.0277719281735926107462678126348 absolute error = 1.31357234e-23 relative error = 1.2780776590525200279926418565691e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0275 y[1] (analytic) = 1.0278746351560760421567758365828 y[1] (numeric) = 1.0278746351560760421567890195664 absolute error = 1.31829836e-23 relative error = 1.2825478077876929167375042849664e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0276 y[1] (analytic) = 1.0279773518598131139054918703543 y[1] (numeric) = 1.0279773518598131139055051005929 absolute error = 1.32302386e-23 relative error = 1.2870165452637548398368190568659e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0277 y[1] (analytic) = 1.0280800782837766589558880332692 y[1] (numeric) = 1.028080078283776658955901310758 absolute error = 1.32774888e-23 relative error = 1.2914839106857073158170131122482e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=68.6MB, alloc=4.2MB, time=4.92 x[1] = 0.0278 y[1] (analytic) = 1.0281828144269394130691849283565 y[1] (numeric) = 1.0281828144269394130691982530905 absolute error = 1.33247340e-23 relative error = 1.2959498848875992949430981114398e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0279 y[1] (analytic) = 1.0282855602882740148146111490094 y[1] (numeric) = 1.0282855602882740148146245209835 absolute error = 1.33719741e-23 relative error = 1.3004144584361607714725077491929e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 1.0283883158667530055796768932843 y[1] (numeric) = 1.0283883158667530055796903124935 absolute error = 1.34192092e-23 relative error = 1.3048776413498955231188701143953e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0281 y[1] (analytic) = 1.0284910811613488295804485500176 y[1] (numeric) = 1.0284910811613488295804620164569 absolute error = 1.34664393e-23 relative error = 1.3093394339204188148068280323195e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0282 y[1] (analytic) = 1.0285938561710338338718242566562 y[1] (numeric) = 1.0285938561710338338718377703207 absolute error = 1.35136645e-23 relative error = 1.3137998461613363704272541657967e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0283 y[1] (analytic) = 1.0286966408947802683578104287003 y[1] (numeric) = 1.0286966408947802683578239895849 absolute error = 1.35608846e-23 relative error = 1.3182588589192319948193751637737e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0284 y[1] (analytic) = 1.0287994353315602858017992606542 y[1] (numeric) = 1.0287994353315602858018128687539 absolute error = 1.36080997e-23 relative error = 1.3227164822086432669202930807078e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0285 y[1] (analytic) = 1.0289022394803459418368471983842 y[1] (numeric) = 1.0289022394803459418368608536941 absolute error = 1.36553099e-23 relative error = 1.3271727260402025103670154845183e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0286 y[1] (analytic) = 1.0290050533401091949759543827795 y[1] (numeric) = 1.0290050533401091949759680852945 absolute error = 1.37025150e-23 relative error = 1.3316275712662620119600581818641e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0287 y[1] (analytic) = 1.0291078769098219066223450646132 y[1] (numeric) = 1.0291078769098219066223588143285 absolute error = 1.37497153e-23 relative error = 1.3360810473326940062343752555270e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0288 y[1] (analytic) = 1.0292107101884558410797489905024 y[1] (numeric) = 1.0292107101884558410797627874128 absolute error = 1.37969104e-23 relative error = 1.3405331156604158386507267302032e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0289 y[1] (analytic) = 1.0293135531749826655626837598611 y[1] (numeric) = 1.0293135531749826655626976039617 absolute error = 1.38441006e-23 relative error = 1.3449838056923468378165913797846e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 1.0294164058683739502067381527475 y[1] (numeric) = 1.0294164058683739502067520440333 absolute error = 1.38912858e-23 relative error = 1.3494331080027692403676812939450e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0291 y[1] (analytic) = 1.0295192682676011680788564284991 y[1] (numeric) = 1.029519268267601168078870366965 absolute error = 1.39384659e-23 relative error = 1.3538810131698281721095174077625e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0292 y[1] (analytic) = 1.0296221403716356951876235950546 y[1] (numeric) = 1.0296221403716356951876375806956 absolute error = 1.39856410e-23 relative error = 1.3583275312001323161620731542600e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0293 y[1] (analytic) = 1.0297250221794488104935516488596 y[1] (numeric) = 1.0297250221794488104935656816708 absolute error = 1.40328112e-23 relative error = 1.3627726720963881413956591640389e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=5.20 NO POLE x[1] = 0.0294 y[1] (analytic) = 1.029827913690011695919366785253 y[1] (numeric) = 1.0298279136900116959193808652294 absolute error = 1.40799764e-23 relative error = 1.3672164264366804698423530962425e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0295 y[1] (analytic) = 1.0299308149022954363602975792312 y[1] (numeric) = 1.0299308149022954363603117063677 absolute error = 1.41271365e-23 relative error = 1.3716587848029552577584905347988e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0296 y[1] (analytic) = 1.0300337258152710196943641364868 y[1] (numeric) = 1.0300337258152710196943783107785 absolute error = 1.41742917e-23 relative error = 1.3760997669062784714482446161819e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0297 y[1] (analytic) = 1.0301366464279093367926682146204 y[1] (numeric) = 1.0301366464279093367926824360622 absolute error = 1.42214418e-23 relative error = 1.3805393536201354793626368730781e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0298 y[1] (analytic) = 1.0302395767391811815296843144206 y[1] (numeric) = 1.0302395767391811815296985830075 absolute error = 1.42685869e-23 relative error = 1.3849775549451913644438758876414e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0299 y[1] (analytic) = 1.0303425167480572507935517411109 y[1] (numeric) = 1.030342516748057250793566056838 absolute error = 1.43157271e-23 relative error = 1.3894143808782112782650817887744e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 1.0304454664535081444963676354597 y[1] (numeric) = 1.0304454664535081444963819983219 absolute error = 1.43628622e-23 relative error = 1.3938498122984392440598350973899e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0301 y[1] (analytic) = 1.0305484258545043655844809746505 y[1] (numeric) = 1.0305484258545043655844953846429 absolute error = 1.44099924e-23 relative error = 1.3982838689071407097560603863009e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0302 y[1] (analytic) = 1.0306513949500163200487875428104 y[1] (numeric) = 1.0306513949500163200488019999279 absolute error = 1.44571175e-23 relative error = 1.4027165315873976323266309482376e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0303 y[1] (analytic) = 1.0307543737390143169350258710918 y[1] (numeric) = 1.0307543737390143169350403753294 absolute error = 1.45042376e-23 relative error = 1.4071478103349241110798748171065e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0304 y[1] (analytic) = 1.030857362220468568354074147207 y[1] (numeric) = 1.0308573622204685683540886985598 absolute error = 1.45513528e-23 relative error = 1.4115777151415362177160552858863e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0305 y[1] (analytic) = 1.0309603603933491894922480943109 y[1] (numeric) = 1.0309603603933491894922626927738 absolute error = 1.45984629e-23 relative error = 1.4160062268960710558594649518526e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0306 y[1] (analytic) = 1.0310633682566261986215998191285 y[1] (numeric) = 1.0310633682566261986216144646966 absolute error = 1.46455681e-23 relative error = 1.4204333652899979519690796882331e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0307 y[1] (analytic) = 1.0311663858092695171102176292269 y[1] (numeric) = 1.0311663858092695171102323218951 absolute error = 1.46926682e-23 relative error = 1.4248591112159896049328084104666e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0308 y[1] (analytic) = 1.031269413050248969432526819325 y[1] (numeric) = 1.0312694130502489694325415590882 absolute error = 1.47397632e-23 relative error = 1.4292834649680238105330151535648e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0309 y[1] (analytic) = 1.0313724499785342831795914265408 y[1] (numeric) = 1.031372449978534283179606213394 absolute error = 1.47868532e-23 relative error = 1.4337064365358756057234960871036e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=5.48 NO POLE x[1] = 0.031 y[1] (analytic) = 1.0314754965930950890694169544723 y[1] (numeric) = 1.0314754965930950890694317884107 absolute error = 1.48339384e-23 relative error = 1.4381280456002740744715460698740e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0311 y[1] (analytic) = 1.0315785528929009209572540660092 y[1] (numeric) = 1.0315785528929009209572689470277 absolute error = 1.48810185e-23 relative error = 1.4425482633647731434380448170780e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0312 y[1] (analytic) = 1.0316816188769212158459032447712 y[1] (numeric) = 1.0316816188769212158459181728647 absolute error = 1.49280935e-23 relative error = 1.4469670901232669438141487708941e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0313 y[1] (analytic) = 1.0317846945441253138960204250715 y[1] (numeric) = 1.0317846945441253138960354002351 absolute error = 1.49751636e-23 relative error = 1.4513845455535173199292094098398e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0314 y[1] (analytic) = 1.0318877798934824584364235903022 y[1] (numeric) = 1.0318877798934824584364386125308 absolute error = 1.50222286e-23 relative error = 1.4558006105616138821256092605842e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0315 y[1] (analytic) = 1.0319908749239617959744003396368 y[1] (numeric) = 1.0319908749239617959744154089255 absolute error = 1.50692887e-23 relative error = 1.4602153048214037253665766142519e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0316 y[1] (analytic) = 1.0320939796345323762060164229494 y[1] (numeric) = 1.0320939796345323762060315392931 absolute error = 1.51163437e-23 relative error = 1.4646286092428078473635277632750e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0317 y[1] (analytic) = 1.0321970940241631520264252438448 y[1] (numeric) = 1.0321970940241631520264404072386 absolute error = 1.51633938e-23 relative error = 1.4690405434957592992550409196530e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0318 y[1] (analytic) = 1.0323002180918229795401783306991 y[1] (numeric) = 1.0323002180918229795401935411378 absolute error = 1.52104387e-23 relative error = 1.4734510788069051165668356589554e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0319 y[1] (analytic) = 1.0324033518364806180715367756048 y[1] (numeric) = 1.0324033518364806180715520330835 absolute error = 1.52574787e-23 relative error = 1.4778602445313048477610972457122e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 1.0325064952571047301747836411203 y[1] (numeric) = 1.0325064952571047301747989456339 absolute error = 1.53045136e-23 relative error = 1.4822680215865391532120894575582e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0321 y[1] (analytic) = 1.032609648352663881644537334718 y[1] (numeric) = 1.0326096483526638816445526862615 absolute error = 1.53515435e-23 relative error = 1.4866744199505132149594354879031e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0322 y[1] (analytic) = 1.0327128111221265415260659508296 y[1] (numeric) = 1.0327128111221265415260813493981 absolute error = 1.53985685e-23 relative error = 1.4910794495972410510554797202729e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0323 y[1] (analytic) = 1.0328159835644610821256025803852 y[1] (numeric) = 1.0328159835644610821256180259737 absolute error = 1.54455885e-23 relative error = 1.4954831011323127349727534106434e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0324 y[1] (analytic) = 1.0329191656786357790206615877419 y[1] (numeric) = 1.0329191656786357790206770803453 absolute error = 1.54926034e-23 relative error = 1.4998853651651667502649615235805e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0325 y[1] (analytic) = 1.0330223574636188110703558549003 y[1] (numeric) = 1.0330223574636188110703713945136 absolute error = 1.55396133e-23 relative error = 1.5042862516697541295240200503780e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=5.76 NO POLE x[1] = 0.0326 y[1] (analytic) = 1.0331255589183782604257149929048 y[1] (numeric) = 1.0331255589183782604257305795229 absolute error = 1.55866181e-23 relative error = 1.5086857512574050599870663397157e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0327 y[1] (analytic) = 1.0332287700418821125400045203243 y[1] (numeric) = 1.0332287700418821125400201539423 absolute error = 1.56336180e-23 relative error = 1.5130838835784923512200482820400e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0328 y[1] (analytic) = 1.0333319908330982561790460087115 y[1] (numeric) = 1.0333319908330982561790616893244 absolute error = 1.56806129e-23 relative error = 1.5174806392433370089131876450478e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0329 y[1] (analytic) = 1.033435221290994483431538194936 y[1] (numeric) = 1.0334352212909944834315539225387 absolute error = 1.57276027e-23 relative error = 1.5218760088661062549107336533740e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 1.0335384614145384897193790602884 y[1] (numeric) = 1.0335384614145384897193948348758 absolute error = 1.57745874e-23 relative error = 1.5262699927403111342030877551577e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0331 y[1] (analytic) = 1.0336417112026978738079888762527 y[1] (numeric) = 1.0336417112026978738080046978199 absolute error = 1.58215672e-23 relative error = 1.5306626105085052467784363391290e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0332 y[1] (analytic) = 1.0337449706544401378166342168439 y[1] (numeric) = 1.0337449706544401378166500853859 absolute error = 1.58685420e-23 relative error = 1.5350538527847919250601678285941e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0333 y[1] (analytic) = 1.0338482397687326872287529374064 y[1] (numeric) = 1.0338482397687326872287688529182 absolute error = 1.59155118e-23 relative error = 1.5394437198597184943261397439043e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0334 y[1] (analytic) = 1.0339515185445428309022801197714 y[1] (numeric) = 1.0339515185445428309022960822478 absolute error = 1.59624764e-23 relative error = 1.5438321926805442799878572605533e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0335 y[1] (analytic) = 1.0340548069808377810799749836681 y[1] (numeric) = 1.0340548069808377810799909931043 absolute error = 1.60094362e-23 relative error = 1.5482193102262396013974192846999e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0336 y[1] (analytic) = 1.0341581050765846533997487642886 y[1] (numeric) = 1.0341581050765846533997648206795 absolute error = 1.60563909e-23 relative error = 1.5526050437723874734376229123002e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0337 y[1] (analytic) = 1.0342614128307504669049935558994 y[1] (numeric) = 1.03426141283075046690500965924 absolute error = 1.61033406e-23 relative error = 1.5569894032810829901271739609233e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0338 y[1] (analytic) = 1.0343647302423021440549121213991 y[1] (numeric) = 1.0343647302423021440549282716844 absolute error = 1.61502853e-23 relative error = 1.5613723890427664934657983753618e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0339 y[1] (analytic) = 1.0344680573102065107348486677179 y[1] (numeric) = 1.0344680573102065107348648649428 absolute error = 1.61972249e-23 relative error = 1.5657539916810528617138917841727e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 1.0345713940334302962666205869552 y[1] (numeric) = 1.0345713940334302962666368311148 absolute error = 1.62441596e-23 relative error = 1.5701342308209132133468736117670e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0341 y[1] (analytic) = 1.0346747404109401334188511631534 y[1] (numeric) = 1.0346747404109401334188674542425 absolute error = 1.62910891e-23 relative error = 1.5745130777552077725967765893931e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.3MB, time=6.04 NO POLE x[1] = 0.0342 y[1] (analytic) = 1.0347780964417025584173032446024 y[1] (numeric) = 1.034778096441702558417319582616 absolute error = 1.63380136e-23 relative error = 1.5788905521078985070370418694779e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0343 y[1] (analytic) = 1.0348814621246840109552138815736 y[1] (numeric) = 1.0348814621246840109552302665068 absolute error = 1.63849332e-23 relative error = 1.5832666638322602032866577089826e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0344 y[1] (analytic) = 1.0349848374588508342036299293793 y[1] (numeric) = 1.034984837458850834203646361227 absolute error = 1.64318477e-23 relative error = 1.5876413938917536257553452816254e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0345 y[1] (analytic) = 1.0350882224431692748217446166531 y[1] (numeric) = 1.0350882224431692748217610954102 absolute error = 1.64787571e-23 relative error = 1.5920147425795634075193722502868e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0346 y[1] (analytic) = 1.0351916170766054829672350787494 y[1] (numeric) = 1.035191617076605482967251604411 absolute error = 1.65256616e-23 relative error = 1.5963867295089465775527839113898e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0347 y[1] (analytic) = 1.0352950213581255123066008561585 y[1] (numeric) = 1.0352950213581255123066174287195 absolute error = 1.65725610e-23 relative error = 1.6007573356490893034944099004223e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0348 y[1] (analytic) = 1.0353984352866953200255033578324 y[1] (numeric) = 1.0353984352866953200255199772878 absolute error = 1.66194554e-23 relative error = 1.6051265709512277986586863293505e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0349 y[1] (analytic) = 1.0355018588612807668391062893198 y[1] (numeric) = 1.0355018588612807668391229556646 absolute error = 1.66663448e-23 relative error = 1.6094944357055643237602350155742e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 1.035605292080847617002417045606 y[1] (numeric) = 1.0356052920808476170024337588351 absolute error = 1.67132291e-23 relative error = 1.6138609205460908270450605639829e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0351 y[1] (analytic) = 1.035708734944361538320629068554 y[1] (numeric) = 1.0357087349443615383206458286624 absolute error = 1.67601084e-23 relative error = 1.6182260354210835223479468898272e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0352 y[1] (analytic) = 1.0358121874507881021594651688438 y[1] (numeric) = 1.0358121874507881021594819758266 absolute error = 1.68069828e-23 relative error = 1.6225897902749389333634434880353e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0353 y[1] (analytic) = 1.0359156495990927834555218123074 y[1] (numeric) = 1.0359156495990927834555386661593 absolute error = 1.68538519e-23 relative error = 1.6269521467816968076670271206542e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0354 y[1] (analytic) = 1.0360191213882409607266143705527 y[1] (numeric) = 1.0360191213882409607266312712689 absolute error = 1.69007162e-23 relative error = 1.6313131535017850447940757961063e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0355 y[1] (analytic) = 1.0361226028171979160821233357783 y[1] (numeric) = 1.0361226028171979160821402833537 absolute error = 1.69475754e-23 relative error = 1.6356727817653876556869816278365e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0356 y[1] (analytic) = 1.0362260938849288352333414996702 y[1] (numeric) = 1.0362260938849288352333584940997 absolute error = 1.69944295e-23 relative error = 1.6400310318654456515647459210659e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=87.7MB, alloc=4.3MB, time=6.31 x[1] = 0.0357 y[1] (analytic) = 1.0363295945903988075038220962801 y[1] (numeric) = 1.0363295945903988075038391375588 absolute error = 1.70412787e-23 relative error = 1.6443879233937570357125587250242e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0358 y[1] (analytic) = 1.036433104932572825839727908782 y[1] (numeric) = 1.0364331049325728258397449969048 absolute error = 1.70881228e-23 relative error = 1.6487434373404833598934129254161e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0359 y[1] (analytic) = 1.0365366249104157868201813400013 y[1] (numeric) = 1.0365366249104157868201984749632 absolute error = 1.71349619e-23 relative error = 1.6530975836460110093460396145673e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 1.0366401545228924906676154466153 y[1] (numeric) = 1.0366401545228924906676326284112 absolute error = 1.71817959e-23 relative error = 1.6574503529537518346854374219903e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0361 y[1] (analytic) = 1.0367436937689676412581259369198 y[1] (numeric) = 1.0367436937689676412581431655448 absolute error = 1.72286250e-23 relative error = 1.6618017648477059186184687192227e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0362 y[1] (analytic) = 1.0368472426476058461318241320603 y[1] (numeric) = 1.0368472426476058461318414075092 absolute error = 1.72754489e-23 relative error = 1.6661517906810329923334605341591e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0363 y[1] (analytic) = 1.0369508011577716165031908906212 y[1] (numeric) = 1.0369508011577716165032082128891 absolute error = 1.73222679e-23 relative error = 1.6705004596803840475618691876837e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0364 y[1] (analytic) = 1.0370543692984293672714314964735 y[1] (numeric) = 1.0370543692984293672714488655553 absolute error = 1.73690818e-23 relative error = 1.6748477528473497466570979130188e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0365 y[1] (analytic) = 1.0371579470685434170308315097732 y[1] (numeric) = 1.0371579470685434170308489256639 absolute error = 1.74158907e-23 relative error = 1.6791936801164021040936446352851e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0366 y[1] (analytic) = 1.0372615344670779880811135810104 y[1] (numeric) = 1.0372615344670779880811310437049 absolute error = 1.74626945e-23 relative error = 1.6835382321365985887181301521602e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0367 y[1] (analytic) = 1.037365131492997206437795228003 y[1] (numeric) = 1.0373651314929972064378127374963 absolute error = 1.75094933e-23 relative error = 1.6878814188404402573980489447255e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0368 y[1] (analytic) = 1.0374687381452651018425475757333 y[1] (numeric) = 1.0374687381452651018425651320204 absolute error = 1.75562871e-23 relative error = 1.6922232405177099597827775524796e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0369 y[1] (analytic) = 1.0375723544228456077735550589224 y[1] (numeric) = 1.0375723544228456077735726619982 absolute error = 1.76030758e-23 relative error = 1.6965636878202862142730984381206e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 1.0376759803247025614558760872396 y[1] (numeric) = 1.0376759803247025614558937370992 absolute error = 1.76498596e-23 relative error = 1.7009027803146339673820117342879e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0371 y[1] (analytic) = 1.0377796158497997038718046730438 y[1] (numeric) = 1.037779615849799703871822369682 absolute error = 1.76966382e-23 relative error = 1.7052404893797101006796236548852e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0372 y[1] (analytic) = 1.0378832609971006797712330215512 y[1] (numeric) = 1.0378832609971006797712507649629 absolute error = 1.77434117e-23 relative error = 1.7095768249459768584428466799352e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=6.59 NO POLE x[1] = 0.0373 y[1] (analytic) = 1.0379869157655690376820150833279 y[1] (numeric) = 1.0379869157655690376820328735082 absolute error = 1.77901803e-23 relative error = 1.7139118065740570415275949581285e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0374 y[1] (analytic) = 1.0380905801541682299203310690031 y[1] (numeric) = 1.038090580154168229920348905947 absolute error = 1.78369439e-23 relative error = 1.7182454249176417189641968012142e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0375 y[1] (analytic) = 1.0381942541618616126010529260984 y[1] (numeric) = 1.0381942541618616126010708098008 absolute error = 1.78837024e-23 relative error = 1.7225776706342479915137106974581e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0376 y[1] (analytic) = 1.0382979377876124456481107778703 y[1] (numeric) = 1.0382979377876124456481287083262 absolute error = 1.79304559e-23 relative error = 1.7269085536475118033977578001719e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0377 y[1] (analytic) = 1.0384016310303838928048603240627 y[1] (numeric) = 1.038401631030383892804878301267 absolute error = 1.79772043e-23 relative error = 1.7312380646168286384605923520062e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0378 y[1] (analytic) = 1.038505333889139021644451203464 y[1] (numeric) = 1.0385053338891390216444692274117 absolute error = 1.80239477e-23 relative error = 1.7355662134638651441201353868471e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0379 y[1] (analytic) = 1.0386090463628408035801963181678 y[1] (numeric) = 1.0386090463628408035802143888539 absolute error = 1.80706861e-23 relative error = 1.7398930004781566533389761589457e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 1.0387127684504521138759421194306 y[1] (numeric) = 1.0387127684504521138759602368499 absolute error = 1.81174193e-23 relative error = 1.7442184066946148597290401486659e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0381 y[1] (analytic) = 1.0388165001509357316564398550246 y[1] (numeric) = 1.0388165001509357316564580191721 absolute error = 1.81641475e-23 relative error = 1.7485424516611764115473476023247e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0382 y[1] (analytic) = 1.0389202414632543399177177779819 y[1] (numeric) = 1.0389202414632543399177359888527 absolute error = 1.82108708e-23 relative error = 1.7528651452926862497740691949678e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0383 y[1] (analytic) = 1.0390239923863705255374543166255 y[1] (numeric) = 1.0390239923863705255374725742145 absolute error = 1.82575890e-23 relative error = 1.7571864686268716503798808513516e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0384 y[1] (analytic) = 1.0391277529192467792853522057837 y[1] (numeric) = 1.0391277529192467792853705100858 absolute error = 1.83043021e-23 relative error = 1.7615064219560376970149939027026e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0385 y[1] (analytic) = 1.0392315230608454958335135790846 y[1] (numeric) = 1.0392315230608454958335319300947 absolute error = 1.83510101e-23 relative error = 1.7658250055724661673688726407541e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0386 y[1] (analytic) = 1.0393353028101289737668160222261 y[1] (numeric) = 1.0393353028101289737668344199393 absolute error = 1.83977132e-23 relative error = 1.7701422390114835957802699834120e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0387 y[1] (analytic) = 1.0394390921660594155932895871192 y[1] (numeric) = 1.0394390921660594155933080315303 absolute error = 1.84444111e-23 relative error = 1.7744580936978407638778260094695e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0388 y[1] (analytic) = 1.0395428911275989277544947667979 y[1] (numeric) = 1.039542891127598927754513257902 absolute error = 1.84911041e-23 relative error = 1.7787725987854699529429016255055e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=6.87 NO POLE x[1] = 0.0389 y[1] (analytic) = 1.0396466996937095206359014309964 y[1] (numeric) = 1.0396466996937095206359199687883 absolute error = 1.85377919e-23 relative error = 1.7830857257048400977691912524745e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 1.0397505178633531085772687222844 y[1] (numeric) = 1.0397505178633531085772873067591 absolute error = 1.85844747e-23 relative error = 1.7873974939863817517136539566786e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0391 y[1] (analytic) = 1.0398543456354915098830259126617 y[1] (numeric) = 1.0398543456354915098830445438142 absolute error = 1.86311525e-23 relative error = 1.7917079039193559737147003514942e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0392 y[1] (analytic) = 1.0399581830090864468326542205048 y[1] (numeric) = 1.0399581830090864468326728983301 absolute error = 1.86778253e-23 relative error = 1.7960169557930009455203656120386e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0393 y[1] (analytic) = 1.040062029983099545691069587764 y[1] (numeric) = 1.040062029983099545691088312257 absolute error = 1.87244930e-23 relative error = 1.8003246402817207972916026966741e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0394 y[1] (analytic) = 1.0401658865564923367190064173048 y[1] (numeric) = 1.0401658865564923367190251884604 absolute error = 1.87711556e-23 relative error = 1.8046309576775878818299764402753e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0395 y[1] (analytic) = 1.0402697527282262541834022702924 y[1] (numeric) = 1.0402697527282262541834210881057 absolute error = 1.88178133e-23 relative error = 1.8089359274984334692642656477940e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0396 y[1] (analytic) = 1.0403736284972626363677835235138 y[1] (numeric) = 1.0403736284972626363678023879797 absolute error = 1.88644659e-23 relative error = 1.8132395308066610571032245472986e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0397 y[1] (analytic) = 1.0404775138625627255826519865337 y[1] (numeric) = 1.040477513862562725582670897647 absolute error = 1.89111133e-23 relative error = 1.8175417582833010511346536013664e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0398 y[1] (analytic) = 1.0405814088230876681758724785803 y[1] (numeric) = 1.0405814088230876681758914363361 absolute error = 1.89577558e-23 relative error = 1.8218426390532472308387476286987e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0399 y[1] (analytic) = 1.040685313377798514543061365059 y[1] (numeric) = 1.0406853133777985145430803694522 absolute error = 1.90043932e-23 relative error = 1.8261421541845918284854233111085e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 1.0407892275256562191379760535868 y[1] (numeric) = 1.0407892275256562191379951046124 absolute error = 1.90510256e-23 relative error = 1.8304403135773595640870270813679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0401 y[1] (analytic) = 1.0408931512656216404829054494465 y[1] (numeric) = 1.0408931512656216404829245470994 absolute error = 1.90976529e-23 relative error = 1.8347371079134462664373596948991e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0402 y[1] (analytic) = 1.0409970845966555411790613703548 y[1] (numeric) = 1.04099708459665554117908051463 absolute error = 1.91442752e-23 relative error = 1.8390325470909110062113918749430e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0403 y[1] (analytic) = 1.0411010275177185879169709204418 y[1] (numeric) = 1.0411010275177185879169901113343 absolute error = 1.91908925e-23 relative error = 1.8433266313987370020359216568641e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0404 y[1] (analytic) = 1.0412049800277713514868698233371 y[1] (numeric) = 1.0412049800277713514868890608417 absolute error = 1.92375046e-23 relative error = 1.8476193419173706927925696080515e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.3MB, time=7.14 NO POLE x[1] = 0.0405 y[1] (analytic) = 1.0413089421257743067890967142584 y[1] (numeric) = 1.0413089421257743067891159983701 absolute error = 1.92841117e-23 relative error = 1.8519106981480979308685422299162e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0406 y[1] (analytic) = 1.0414129138106878328444883909999 y[1] (numeric) = 1.0414129138106878328445077217137 absolute error = 1.93307138e-23 relative error = 1.8562007003798316421342979513031e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0407 y[1] (analytic) = 1.041516895081472212804776023715 y[1] (numeric) = 1.0415168950814722128047954010258 absolute error = 1.93773108e-23 relative error = 1.8604893393000809810459451625593e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0408 y[1] (analytic) = 1.0416208859370876339629823233904 y[1] (numeric) = 1.0416208859370876339630017472931 absolute error = 1.94239027e-23 relative error = 1.8647766152005879699620100085744e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0409 y[1] (analytic) = 1.0417248863764941877638196689072 y[1] (numeric) = 1.0417248863764941877638391393968 absolute error = 1.94704896e-23 relative error = 1.8690625379725341589720334228120e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.041 y[1] (analytic) = 1.0418288963986518698140891925851 y[1] (numeric) = 1.0418288963986518698141087096566 absolute error = 1.95170715e-23 relative error = 1.8733471079047385844661383387473e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0411 y[1] (analytic) = 1.0419329160025205798930808241058 y[1] (numeric) = 1.0419329160025205798931003877541 absolute error = 1.95636483e-23 relative error = 1.8776303156884500256824947956838e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0412 y[1] (analytic) = 1.0420369451870601219629742927114 y[1] (numeric) = 1.0420369451870601219629939029314 absolute error = 1.96102200e-23 relative error = 1.8819121616153151667042232909378e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0413 y[1] (analytic) = 1.0421409839512302041792410875737 y[1] (numeric) = 1.0421409839512302041792607443604 absolute error = 1.96567867e-23 relative error = 1.8861926555725873176972091174546e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0414 y[1] (analytic) = 1.0422450322939904389010473762312 y[1] (numeric) = 1.0422450322939904389010670795795 absolute error = 1.97033483e-23 relative error = 1.8904717882543184616888296335012e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0415 y[1] (analytic) = 1.0423490902143003427016578809887 y[1] (numeric) = 1.0423490902143003427016776308935 absolute error = 1.97499048e-23 relative error = 1.8947495599520833466343344473621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0416 y[1] (analytic) = 1.0424531577111193363788407131755 y[1] (numeric) = 1.0424531577111193363788605096318 absolute error = 1.97964563e-23 relative error = 1.8990259805501897529818424170930e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0417 y[1] (analytic) = 1.0425572347834067449652731651598 y[1] (numeric) = 1.0425572347834067449652930081625 absolute error = 1.98430027e-23 relative error = 1.9033010407454917021664036461661e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0418 y[1] (analytic) = 1.0426613214301217977389484600126 y[1] (numeric) = 1.0426613214301217977389683495567 absolute error = 1.98895441e-23 relative error = 1.9075747504203337749284171511009e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0419 y[1] (analytic) = 1.0427654176502236282335834587195 y[1] (numeric) = 1.0427654176502236282336033948 absolute error = 1.99360805e-23 relative error = 1.9118471098633220549131236568974e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 1.0428695234426712742490273248348 y[1] (numeric) = 1.0428695234426712742490473074465 absolute error = 1.99826117e-23 relative error = 1.9161181001851844882990208757716e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.3MB, time=7.42 NO POLE x[1] = 0.0421 y[1] (analytic) = 1.0429736388064236778616711464741 y[1] (numeric) = 1.042973638806423677861691175612 absolute error = 2.00291379e-23 relative error = 1.9203877408561632840602122390532e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0422 y[1] (analytic) = 1.043077763740439685434858515542 y[1] (numeric) = 1.043077763740439685434878591201 absolute error = 2.00756590e-23 relative error = 1.9246560225777800423420613143124e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0423 y[1] (analytic) = 1.0431818982436780476292970640898 y[1] (numeric) = 1.0431818982436780476293171862648 absolute error = 2.01221750e-23 relative error = 1.9289229456414166252899711339589e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0424 y[1] (analytic) = 1.0432860423150974194134709576996 y[1] (numeric) = 1.0432860423150974194134911263857 absolute error = 2.01686861e-23 relative error = 1.9331885295086285484035149139458e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0425 y[1] (analytic) = 1.0433901959536563600740543457916 y[1] (numeric) = 1.0433901959536563600740745609835 absolute error = 2.02151919e-23 relative error = 1.9374527361284393475139329294665e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0426 y[1] (analytic) = 1.0434943591583133332263257687473 y[1] (numeric) = 1.0434943591583133332263460304401 absolute error = 2.02616928e-23 relative error = 1.9417156041306405668193070199897e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0427 y[1] (analytic) = 1.0435985319280267068245835217493 y[1] (numeric) = 1.0435985319280267068246038299379 absolute error = 2.03081886e-23 relative error = 1.9459771146363191524538967433188e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0428 y[1] (analytic) = 1.0437027142617547531725619752291 y[1] (numeric) = 1.0437027142617547531725823299084 absolute error = 2.03546793e-23 relative error = 1.9502372679367355993128979814601e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0429 y[1] (analytic) = 1.0438069061584556489338488518209 y[1] (numeric) = 1.0438069061584556489338692529859 absolute error = 2.04011650e-23 relative error = 1.9544960739034419228789527726852e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 1.0439111076170874751423034597174 y[1] (numeric) = 1.0439111076170874751423239073631 absolute error = 2.04476457e-23 relative error = 1.9587535328247807674711224375526e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0431 y[1] (analytic) = 1.0440153186366082172124758823224 y[1] (numeric) = 1.0440153186366082172124963764437 absolute error = 2.04941213e-23 relative error = 1.9630096354106673515592065194704e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0432 y[1] (analytic) = 1.0441195392159757649500271240966 y[1] (numeric) = 1.0441195392159757649500476646884 absolute error = 2.05405918e-23 relative error = 1.9672643819522647303403420843470e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0433 y[1] (analytic) = 1.0442237693541479125621502124922 y[1] (numeric) = 1.0442237693541479125621707995494 absolute error = 2.05870572e-23 relative error = 1.9715177727407113792720968150628e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0434 y[1] (analytic) = 1.0443280090500823586679922558726 y[1] (numeric) = 1.04432800905008235866801288939 absolute error = 2.06335174e-23 relative error = 1.9757697984915855956005079486805e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0435 y[1] (analytic) = 1.0444322583027367063090774573116 y[1] (numeric) = 1.0444322583027367063090981372843 absolute error = 2.06799727e-23 relative error = 1.9800204882225833348121306575766e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=106.8MB, alloc=4.3MB, time=7.69 x[1] = 0.0436 y[1] (analytic) = 1.0445365171110684629597310841704 y[1] (numeric) = 1.0445365171110684629597518105933 absolute error = 2.07264229e-23 relative error = 1.9842698230717865851826787974405e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0437 y[1] (analytic) = 1.0446407854740350405375043933448 y[1] (numeric) = 1.0446407854740350405375251662129 absolute error = 2.07728681e-23 relative error = 1.9885178129029041097136775810989e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0438 y[1] (analytic) = 1.0447450633905937554136005120815 y[1] (numeric) = 1.0447450633905937554136213313897 absolute error = 2.08193082e-23 relative error = 1.9927644484323719177336639807279e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0439 y[1] (analytic) = 1.0448493508597018284233012742574 y[1] (numeric) = 1.0448493508597018284233221400006 absolute error = 2.08657432e-23 relative error = 1.9970097299511810805852982641651e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 1.0449536478803163848763950120176 y[1] (numeric) = 1.0449536478803163848764159241908 absolute error = 2.09121732e-23 relative error = 2.0012536673201003779683842119062e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0441 y[1] (analytic) = 1.0450579544513944545676053026694 y[1] (numeric) = 1.0450579544513944545676262612675 absolute error = 2.09585981e-23 relative error = 2.0054962512583585517840631849622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0442 y[1] (analytic) = 1.045162270571892971787020670726 y[1] (numeric) = 1.045162270571892971787041675744 absolute error = 2.10050180e-23 relative error = 2.0097374916247648830673160878688e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0443 y[1] (analytic) = 1.0452665962407687753305252449973 y[1] (numeric) = 1.04526659624076877533054629643 absolute error = 2.10514327e-23 relative error = 2.0139773695734720821255465536685e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0444 y[1] (analytic) = 1.0453709314569786085102303706217 y[1] (numeric) = 1.0453709314569786085102514684641 absolute error = 2.10978424e-23 relative error = 2.0182159045301772450707103693046e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0445 y[1] (analytic) = 1.045475276219479119164907175937 y[1] (numeric) = 1.045475276219479119164928320184 absolute error = 2.11442470e-23 relative error = 2.0224530872178308479339718955977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0446 y[1] (analytic) = 1.0455796305272268596704200940838 y[1] (numeric) = 1.0455796305272268596704412847302 absolute error = 2.11906464e-23 relative error = 2.0266889083631776293449883473705e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0447 y[1] (analytic) = 1.0456839943791782869501613392377 y[1] (numeric) = 1.0456839943791782869501825762786 absolute error = 2.12370409e-23 relative error = 2.0309233969492297167338955675496e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0448 y[1] (analytic) = 1.0457883677742897624854863373674 y[1] (numeric) = 1.0457883677742897624855076207976 absolute error = 2.12834302e-23 relative error = 2.0351565245745357750440485215262e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0449 y[1] (analytic) = 1.0458927507115175523261501114119 y[1] (numeric) = 1.0458927507115175523261714412264 absolute error = 2.13298145e-23 relative error = 2.0393883106551215896277181819584e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 1.0459971431898178271007446207744 y[1] (numeric) = 1.0459971431898178271007659969682 absolute error = 2.13761938e-23 relative error = 2.0436187554788423818980528497146e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0451 y[1] (analytic) = 1.0461015452081466620271370550281 y[1] (numeric) = 1.046101545208146662027158477596 absolute error = 2.14225679e-23 relative error = 2.0478478402149260832224286731853e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.3MB, time=7.96 NO POLE x[1] = 0.0452 y[1] (analytic) = 1.0462059567654600369229090817279 y[1] (numeric) = 1.0462059567654600369229305506649 absolute error = 2.14689370e-23 relative error = 2.0520755842735979869467799683832e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0453 y[1] (analytic) = 1.046310377860713836215797048227 y[1] (numeric) = 1.0463103778607138362158185635279 absolute error = 2.15153009e-23 relative error = 2.0563019688278523534055353081166e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0454 y[1] (analytic) = 1.0464148084928638489541331373898 y[1] (numeric) = 1.0464148084928638489541546990496 absolute error = 2.15616598e-23 relative error = 2.0605270132840481796382030875322e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0455 y[1] (analytic) = 1.0465192486608657688172874771006 y[1] (numeric) = 1.0465192486608657688173090851143 absolute error = 2.16080137e-23 relative error = 2.0647507179299170705546345382584e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0456 y[1] (analytic) = 1.0466236983636751941261112034611 y[1] (numeric) = 1.0466236983636751941261328578235 absolute error = 2.16543624e-23 relative error = 2.0689730639441013491445268743300e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0457 y[1] (analytic) = 1.0467281576002476278533804775726 y[1] (numeric) = 1.0467281576002476278534021782787 absolute error = 2.17007061e-23 relative error = 2.0731940707271622358452781712187e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0458 y[1] (analytic) = 1.0468326263695384776342414558004 y[1] (numeric) = 1.0468326263695384776342632028451 absolute error = 2.17470447e-23 relative error = 2.0774137290141315228396838462527e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0459 y[1] (analytic) = 1.046937104670503055776656213413 y[1] (numeric) = 1.0469371046705030557766780067912 absolute error = 2.17933782e-23 relative error = 2.0816320390955017263232598149844e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 1.0470415925020965792718496214939 y[1] (numeric) = 1.0470415925020965792718714612006 absolute error = 2.18397067e-23 relative error = 2.0858490108124590592132781595448e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0461 y[1] (analytic) = 1.0471460898632741698047571770209 y[1] (numeric) = 1.047146089863274169804779063051 absolute error = 2.18860301e-23 relative error = 2.0900646349028203145645181145421e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0462 y[1] (analytic) = 1.0472505967529908537644737860077 y[1] (numeric) = 1.0472505967529908537644957183561 absolute error = 2.19323484e-23 relative error = 2.0942789116570024222649960412007e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0463 y[1] (analytic) = 1.0473551131702015622547034996046 y[1] (numeric) = 1.0473551131702015622547254782662 absolute error = 2.19786616e-23 relative error = 2.0984918413653969627595258689502e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0464 y[1] (analytic) = 1.0474596391138611311042102030524 y[1] (numeric) = 1.0474596391138611311042322280221 absolute error = 2.20249697e-23 relative error = 2.1027034243183701417352791392645e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0465 y[1] (analytic) = 1.0475641745829243008772692573861 y[1] (numeric) = 1.0475641745829243008772913286589 absolute error = 2.20712728e-23 relative error = 2.1069136703522173159972654588490e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0466 y[1] (analytic) = 1.0476687195763457168841200937839 y[1] (numeric) = 1.0476687195763457168841422113547 absolute error = 2.21175708e-23 relative error = 2.1111225702093941671292951565702e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0467 y[1] (analytic) = 1.0477732740930799291914197604554 y[1] (numeric) = 1.0477732740930799291914419243191 absolute error = 2.21638637e-23 relative error = 2.1153301241801909349186460151270e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.3MB, time=8.25 NO POLE x[1] = 0.0468 y[1] (analytic) = 1.0478778381320813926326974219668 y[1] (numeric) = 1.0478778381320813926327196321183 absolute error = 2.22101515e-23 relative error = 2.1195363325548723833784834428845e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0469 y[1] (analytic) = 1.0479824116923044668188098108967 y[1] (numeric) = 1.0479824116923044668188320673309 absolute error = 2.22564342e-23 relative error = 2.1237411956236777755448493818883e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 1.0480869947727034161483976317188 y[1] (numeric) = 1.0480869947727034161484199344307 absolute error = 2.23027119e-23 relative error = 2.1279447232180135640481809556465e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0471 y[1] (analytic) = 1.048191587372232409818342916807 y[1] (numeric) = 1.0481915873722324098183652657915 absolute error = 2.23489845e-23 relative error = 2.1321469060849711046777053829033e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0472 y[1] (analytic) = 1.0482961894898455218342273344576 y[1] (numeric) = 1.0482961894898455218342497297096 absolute error = 2.23952520e-23 relative error = 2.1363477445147133166472054005152e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0473 y[1] (analytic) = 1.048400801124496731020791448825 y[1] (numeric) = 1.0484008011244967310208138903394 absolute error = 2.24415144e-23 relative error = 2.1405472387973775176218556220945e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0474 y[1] (analytic) = 1.0485054222751399210323949316653 y[1] (numeric) = 1.048505422275139921032417419437 absolute error = 2.24877717e-23 relative error = 2.1447453892230753986263791615582e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0475 y[1] (analytic) = 1.0486100529407288803634777257841 y[1] (numeric) = 1.0486100529407288803635002598081 absolute error = 2.25340240e-23 relative error = 2.1489422056183264634038139211621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0476 y[1] (analytic) = 1.0487146931202173023590221600837 y[1] (numeric) = 1.0487146931202173023590447403548 absolute error = 2.25802711e-23 relative error = 2.1531376691993726055302429030780e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0477 y[1] (analytic) = 1.048819342812558785225016016104 y[1] (numeric) = 1.0488193428125587852250386426171 absolute error = 2.26265131e-23 relative error = 2.1573317897936335937233082431036e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0478 y[1] (analytic) = 1.0489240020167068320389165459543 y[1] (numeric) = 1.0489240020167068320389392187043 absolute error = 2.26727500e-23 relative error = 2.1615245676911183619760402693735e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0479 y[1] (analytic) = 1.0490286707316148507601154415298 y[1] (numeric) = 1.0490286707316148507601381605117 absolute error = 2.27189819e-23 relative error = 2.1657160127144380168076189512212e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 1.0491333489562361542404047549093 y[1] (numeric) = 1.0491333489562361542404275201179 absolute error = 2.27652086e-23 relative error = 2.1699061060873429885981161347032e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0481 y[1] (analytic) = 1.0492380366895239602344437698279 y[1] (numeric) = 1.0492380366895239602344665812582 absolute error = 2.28114303e-23 relative error = 2.1740948671640698100537156072313e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0482 y[1] (analytic) = 1.0493427339304313914102268241225 y[1] (numeric) = 1.0493427339304313914102496817694 absolute error = 2.28576469e-23 relative error = 2.1782822867018966443823494590428e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0483 y[1] (analytic) = 1.0494474406779114753595520830424 y[1] (numeric) = 1.0494474406779114753595749869009 absolute error = 2.29038585e-23 relative error = 2.1824683745195277662537377435909e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.3MB, time=8.53 NO POLE x[1] = 0.0484 y[1] (analytic) = 1.0495521569309171446084912633233 y[1] (numeric) = 1.0495521569309171446085142133881 absolute error = 2.29500648e-23 relative error = 2.1866531023203454195359158123357e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0485 y[1] (analytic) = 1.0496568826884012366278603079168 y[1] (numeric) = 1.0496568826884012366278833041831 absolute error = 2.29962663e-23 relative error = 2.1908365180344956112387758724552e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0486 y[1] (analytic) = 1.0497616179493164938436910112751 y[1] (numeric) = 1.0497616179493164938437140537376 absolute error = 2.30424625e-23 relative error = 2.1950185743133649580855832093459e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0487 y[1] (analytic) = 1.0498663627126155636477035950802 y[1] (numeric) = 1.0498663627126155636477266837339 absolute error = 2.30886537e-23 relative error = 2.1991993000274985010304282396666e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0488 y[1] (analytic) = 1.0499711169772509984077802343195 y[1] (numeric) = 1.0499711169772509984078033691592 absolute error = 2.31348397e-23 relative error = 2.2033786764156529317349238744936e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0489 y[1] (analytic) = 1.050075880742175255478439533597 y[1] (numeric) = 1.0500758807421752554784627146176 absolute error = 2.31810206e-23 relative error = 2.2075567132935250663297148961757e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 1.0501806540063406972113119535802 y[1] (numeric) = 1.0501806540063406972113351807767 absolute error = 2.32271965e-23 relative error = 2.2117334204729847061805058707677e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0491 y[1] (analytic) = 1.0502854367686995909656161874748 y[1] (numeric) = 1.0502854367686995909656394608421 absolute error = 2.32733673e-23 relative error = 2.2159087887196331840729284854116e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0492 y[1] (analytic) = 1.0503902290282041091186364874238 y[1] (numeric) = 1.0503902290282041091186598069569 absolute error = 2.33195331e-23 relative error = 2.2200828278433886133103909557936e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0493 y[1] (analytic) = 1.0504950307838063290762009407261 y[1] (numeric) = 1.0504950307838063290762243064197 absolute error = 2.33656936e-23 relative error = 2.2242555095730576222850164131920e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0494 y[1] (analytic) = 1.0505998420344582332831606957689 y[1] (numeric) = 1.050599842034458233283184107618 absolute error = 2.34118491e-23 relative error = 2.2284268627590487942492825663879e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0495 y[1] (analytic) = 1.050704662779111709233870137571 y[1] (numeric) = 1.0507046627791117092338935955706 absolute error = 2.34579996e-23 relative error = 2.2325968876880814894519998147278e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0496 y[1] (analytic) = 1.0508094930167185494826680128308 y[1] (numeric) = 1.0508094930167185494826915169756 absolute error = 2.35041448e-23 relative error = 2.2367655560974309968184286901714e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0497 y[1] (analytic) = 1.050914332746230451654359504373 y[1] (numeric) = 1.0509143327462304516543830546581 absolute error = 2.35502851e-23 relative error = 2.2409329063444037464811157271463e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0498 y[1] (analytic) = 1.0510191819665990184546992548934 y[1] (numeric) = 1.0510191819665990184547228513135 absolute error = 2.35964201e-23 relative error = 2.2450989006544968148337142709178e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0499 y[1] (analytic) = 1.0511240406767757576808753398911 y[1] (numeric) = 1.0511240406767757576808989824412 absolute error = 2.36425501e-23 relative error = 2.2492635678637441729855456147682e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.3MB, time=8.80 NO POLE x[1] = 0.05 y[1] (analytic) = 1.051228908875712082231994189689 y[1] (numeric) = 1.051228908875712082232017878364 absolute error = 2.36886750e-23 relative error = 2.2534268987460596339893489508424e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0501 y[1] (analytic) = 1.0513337865623593101195664604333 y[1] (numeric) = 1.0513337865623593101195901952281 absolute error = 2.37347948e-23 relative error = 2.2575888935908541868801426534154e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0502 y[1] (analytic) = 1.0514386737356686644779938539701 y[1] (numeric) = 1.0514386737356686644780176348797 absolute error = 2.37809096e-23 relative error = 2.2617495621982906845142229223382e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0503 y[1] (analytic) = 1.0515435703945912735750568864925 y[1] (numeric) = 1.0515435703945912735750807135117 absolute error = 2.38270192e-23 relative error = 2.2659088858352223359924510224894e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0504 y[1] (analytic) = 1.0516484765380781708224036058538 y[1] (numeric) = 1.0516484765380781708224274789775 absolute error = 2.38731237e-23 relative error = 2.2700668743027081309921164188287e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0505 y[1] (analytic) = 1.0517533921650802947860392574427 y[1] (numeric) = 1.0517533921650802947860631766658 absolute error = 2.39192231e-23 relative error = 2.2742235278900536311334889175003e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0506 y[1] (analytic) = 1.0518583172745484891968168985142 y[1] (numeric) = 1.0518583172745484891968408638317 absolute error = 2.39653175e-23 relative error = 2.2783788563935217970607985800360e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0507 y[1] (analytic) = 1.0519632518654335029609289608726 y[1] (numeric) = 1.0519632518654335029609529722793 absolute error = 2.40114067e-23 relative error = 2.2825328410874493634895305843377e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0508 y[1] (analytic) = 1.0520681959366859901703997618004 y[1] (numeric) = 1.0520681959366859901704238192912 absolute error = 2.40574908e-23 relative error = 2.2866854917689948187570403397451e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0509 y[1] (analytic) = 1.0521731494872565101135789631296 y[1] (numeric) = 1.0521731494872565101136030666995 absolute error = 2.41035699e-23 relative error = 2.2908368182314970353884458535517e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 1.0522781125160955272856359783499 y[1] (numeric) = 1.0522781125160955272856601279936 absolute error = 2.41496437e-23 relative error = 2.2949867922517118567028432640799e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0511 y[1] (analytic) = 1.052383085022153411399055327647 y[1] (numeric) = 1.0523830850221534113990795233596 absolute error = 2.41957126e-23 relative error = 2.2991354521334465447691366881778e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0512 y[1] (analytic) = 1.0524880670043804373941329407705 y[1] (numeric) = 1.0524880670043804373941571825468 absolute error = 2.42417763e-23 relative error = 2.3032827696562479069195334477429e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0513 y[1] (analytic) = 1.0525930584617267854494734076211 y[1] (numeric) = 1.052593058461726785449497695456 absolute error = 2.42878349e-23 relative error = 2.3074287546124005868934150720031e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0514 y[1] (analytic) = 1.0526980593931425409924881764565 y[1] (numeric) = 1.0526980593931425409925125103448 absolute error = 2.43338883e-23 relative error = 2.3115733977915714582899045128541e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=125.8MB, alloc=4.3MB, time=9.09 x[1] = 0.0515 y[1] (analytic) = 1.0528030697975776947098946996078 y[1] (numeric) = 1.0528030697975776947099190795445 absolute error = 2.43799367e-23 relative error = 2.3157167184825484186269282510842e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0516 y[1] (analytic) = 1.0529080896739821425582165266044 y[1] (numeric) = 1.0529080896739821425582409525844 absolute error = 2.44259800e-23 relative error = 2.3198587074739974363558530213203e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0517 y[1] (analytic) = 1.0530131190213056857742843445996 y[1] (numeric) = 1.0530131190213056857743088166177 absolute error = 2.44720181e-23 relative error = 2.3239993555583476068647484048100e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0518 y[1] (analytic) = 1.0531181578384980308857379659933 y[1] (numeric) = 1.0531181578384980308857624840445 absolute error = 2.45180512e-23 relative error = 2.3281386820186220561938978721885e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0519 y[1] (analytic) = 1.0532232061245087897215292631474 y[1] (numeric) = 1.0532232061245087897215538272265 absolute error = 2.45640791e-23 relative error = 2.3322766681515855763936570019196e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 1.0533282638782874794224260500869 y[1] (numeric) = 1.053328263878287479422450660189 absolute error = 2.46101021e-23 relative error = 2.3364133427301356047678978520112e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0521 y[1] (analytic) = 1.0534333310987835224515169110843 y[1] (numeric) = 1.0534333310987835224515415672041 absolute error = 2.46561198e-23 relative error = 2.3405486680663917193818083123478e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0522 y[1] (analytic) = 1.053538407784946246604716976019 y[1] (numeric) = 1.0535384077849462466047416781515 absolute error = 2.47021325e-23 relative error = 2.3446826729303568108117402370260e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0523 y[1] (analytic) = 1.0536434939357248850212746424102 y[1] (numeric) = 1.0536434939357248850212993905502 absolute error = 2.47481400e-23 relative error = 2.3488153386262643937077230028520e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0524 y[1] (analytic) = 1.0537485895500685761942792440151 y[1] (numeric) = 1.0537485895500685761943040381576 absolute error = 2.47941425e-23 relative error = 2.3529466844256129935723719195799e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0525 y[1] (analytic) = 1.0538536946269263639811696658896 y[1] (numeric) = 1.0538536946269263639811945060294 absolute error = 2.48401398e-23 relative error = 2.3570766916363690993406969563801e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0526 y[1] (analytic) = 1.053958809165247197614243905805 y[1] (numeric) = 1.053958809165247197614268791937 absolute error = 2.48861320e-23 relative error = 2.3612053700381543370254151970878e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0527 y[1] (analytic) = 1.0540639331639799317111695819162 y[1] (numeric) = 1.0540639331639799317111945140353 absolute error = 2.49321191e-23 relative error = 2.3653327199196871695954088686859e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0528 y[1] (analytic) = 1.0541690666220733262854953865766 y[1] (numeric) = 1.0541690666220733262855203646776 absolute error = 2.49781010e-23 relative error = 2.3694587320835146997536688903949e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0529 y[1] (analytic) = 1.0542742095384760467571634861931 y[1] (numeric) = 1.0542742095384760467571885102711 absolute error = 2.50240780e-23 relative error = 2.3735834352767347030149120082527e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 1.054379361912136663963022867019 y[1] (numeric) = 1.0543793619121366639630479370688 absolute error = 2.50700498e-23 relative error = 2.3777068013295514899149025736244e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.3MB, time=9.37 x[1] = 0.0531 y[1] (analytic) = 1.0544845237420036541673436267759 y[1] (numeric) = 1.0544845237420036541673687427924 absolute error = 2.51160165e-23 relative error = 2.3818288400167199960946496180628e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0532 y[1] (analytic) = 1.0545896950270253990723322120025 y[1] (numeric) = 1.0545896950270253990723573739806 absolute error = 2.51619781e-23 relative error = 2.3859495516268237015162877933947e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0533 y[1] (analytic) = 1.0546948757661501858286476010239 y[1] (numeric) = 1.0546948757661501858286728089583 absolute error = 2.52079344e-23 relative error = 2.3900689174855886682156691358308e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0534 y[1] (analytic) = 1.0548000659583262070459184324358 y[1] (numeric) = 1.0548000659583262070459436863215 absolute error = 2.52538857e-23 relative error = 2.3941869663286263502453552482452e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0535 y[1] (analytic) = 1.0549052656025015608032610790001 y[1] (numeric) = 1.0549052656025015608032863788321 absolute error = 2.52998320e-23 relative error = 2.3983036984416020318267168666990e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0536 y[1] (analytic) = 1.0550104746976242506597986668446 y[1] (numeric) = 1.0550104746976242506598240126177 absolute error = 2.53457731e-23 relative error = 2.4024190951529967265264317245258e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0537 y[1] (analytic) = 1.055115693242642185665181039863 y[1] (numeric) = 1.055115693242642185665206431572 absolute error = 2.53917090e-23 relative error = 2.4065331567540940128633447340347e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0538 y[1] (analytic) = 1.0552209212365031803701056692096 y[1] (numeric) = 1.0552209212365031803701311068495 absolute error = 2.54376399e-23 relative error = 2.4106459024895267190357982859637e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0539 y[1] (analytic) = 1.0553261586781549548368395077837 y[1] (numeric) = 1.0553261586781549548368649913494 absolute error = 2.54835657e-23 relative error = 2.4147573231691091623300076601164e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 1.055431405566545134649741789598 y[1] (numeric) = 1.0554314055665451346497673190845 absolute error = 2.55294865e-23 relative error = 2.4188674285560058988285107545318e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0541 y[1] (analytic) = 1.0555366619006212509257877739268 y[1] (numeric) = 1.0555366619006212509258133493287 absolute error = 2.55754019e-23 relative error = 2.4229761810403060560945230252449e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0542 y[1] (analytic) = 1.0556419276793307403250934341263 y[1] (numeric) = 1.0556419276793307403251190554386 absolute error = 2.56213123e-23 relative error = 2.4270836188104600438085700532699e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0543 y[1] (analytic) = 1.0557472029016209450614410910258 y[1] (numeric) = 1.0557472029016209450614667582434 absolute error = 2.56672176e-23 relative error = 2.4311897326799530704296655861911e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0544 y[1] (analytic) = 1.0558524875664391129128059907807 y[1] (numeric) = 1.0558524875664391129128317038985 absolute error = 2.57131178e-23 relative error = 2.4352945229370416122779157571676e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0545 y[1] (analytic) = 1.0559577816727323972318838270838 y[1] (numeric) = 1.0559577816727323972319095860967 absolute error = 2.57590129e-23 relative error = 2.4393979898699547936492232275290e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0546 y[1] (analytic) = 1.0560630852194478569566192076298 y[1] (numeric) = 1.0560630852194478569566450125327 absolute error = 2.58049029e-23 relative error = 2.4435001337668943632961497431650e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.3MB, time=9.64 NO POLE x[1] = 0.0547 y[1] (analytic) = 1.0561683982055324566207350647272 y[1] (numeric) = 1.0561683982055324566207609155148 absolute error = 2.58507876e-23 relative error = 2.4476009359796604772119776023168e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0548 y[1] (analytic) = 1.0562737206299330663642630099517 y[1] (numeric) = 1.056273720629933066364288906619 absolute error = 2.58966673e-23 relative error = 2.4517004252037936088619215488518e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0549 y[1] (analytic) = 1.0563790524915964619440746327377 y[1] (numeric) = 1.0563790524915964619441005752797 absolute error = 2.59425420e-23 relative error = 2.4557986017245806727195405249111e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 1.0564843937894693247444137428009 y[1] (numeric) = 1.0564843937894693247444397312123 absolute error = 2.59884114e-23 relative error = 2.4598954374312162792823323969540e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0551 y[1] (analytic) = 1.0565897445224982417874295562864 y[1] (numeric) = 1.0565897445224982417874555905621 absolute error = 2.60342757e-23 relative error = 2.4639909515462503486470986046373e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0552 y[1] (analytic) = 1.0566951046896297057437108255389 y[1] (numeric) = 1.0566951046896297057437369056739 absolute error = 2.60801350e-23 relative error = 2.4680851538211869690084923120493e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0553 y[1] (analytic) = 1.0568004742898101149428209123883 y[1] (numeric) = 1.0568004742898101149428470383773 absolute error = 2.61259890e-23 relative error = 2.4721780161536318585899886498080e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0554 y[1] (analytic) = 1.0569058533219857733838338048445 y[1] (numeric) = 1.0569058533219857733838599766825 absolute error = 2.61718380e-23 relative error = 2.4762695672219694182081350858868e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0555 y[1] (analytic) = 1.0570112417851028907458710770986 y[1] (numeric) = 1.0570112417851028907458972947805 absolute error = 2.62176819e-23 relative error = 2.4803597978506856320344300745174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0556 y[1] (analytic) = 1.0571166396781075823986397927226 y[1] (numeric) = 1.0571166396781075823986660562433 absolute error = 2.62635207e-23 relative error = 2.4844487083277065822463849306507e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0557 y[1] (analytic) = 1.0572220469999458694129713509636 y[1] (numeric) = 1.0572220469999458694129976603179 absolute error = 2.63093543e-23 relative error = 2.4885362894821798073325572319301e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0558 y[1] (analytic) = 1.0573274637495636785713612760266 y[1] (numeric) = 1.0573274637495636785713876312094 absolute error = 2.63551828e-23 relative error = 2.4926225510626131077194737627457e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0559 y[1] (analytic) = 1.0574328899259068423785099492409 y[1] (numeric) = 1.057432889925906842378536350247 absolute error = 2.64010061e-23 relative error = 2.4967074838999843679340779488810e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 1.0575383255279210990718642840042 y[1] (numeric) = 1.0575383255279210990718907308285 absolute error = 2.64468243e-23 relative error = 2.5007910977408592876589239316424e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0561 y[1] (analytic) = 1.0576437705545520926321603433994 y[1] (numeric) = 1.0576437705545520926321868360369 absolute error = 2.64926375e-23 relative error = 2.5048734023280042702472174837864e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0562 y[1] (analytic) = 1.0577492250047453727939669003787 y[1] (numeric) = 1.0577492250047453727939934388241 absolute error = 2.65384454e-23 relative error = 2.5089543695842406088203662536016e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.3MB, time=9.92 NO POLE x[1] = 0.0563 y[1] (analytic) = 1.0578546888774463950562299404085 y[1] (numeric) = 1.0578546888774463950562565246568 absolute error = 2.65842483e-23 relative error = 2.5130340281622378662043686623227e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0564 y[1] (analytic) = 1.0579601621716005206928181064718 y[1] (numeric) = 1.0579601621716005206928447365178 absolute error = 2.66300460e-23 relative error = 2.5171123594425686970974312384331e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0565 y[1] (analytic) = 1.0580656448861530167630690863205 y[1] (numeric) = 1.058065644886153016763095762159 absolute error = 2.66758385e-23 relative error = 2.5211893637157359959722290314701e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0566 y[1] (analytic) = 1.0581711370200490561223369418728 y[1] (numeric) = 1.0581711370200490561223636634988 absolute error = 2.67216260e-23 relative error = 2.5252650601727486156946841656769e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0567 y[1] (analytic) = 1.0582766385722337174325403806516 y[1] (numeric) = 1.05827663857223371743256714806 absolute error = 2.67674084e-23 relative error = 2.5293394396490747155668302259901e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0568 y[1] (analytic) = 1.0583821495416519851727119691563 y[1] (numeric) = 1.0583821495416519851727387823419 absolute error = 2.68131856e-23 relative error = 2.5334124929839232331137028156244e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0569 y[1] (analytic) = 1.0584876699272487496495482880633 y[1] (numeric) = 1.0584876699272487496495751470209 absolute error = 2.68589576e-23 relative error = 2.5374842204676840021986890833034e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 1.0585931997279688070079610291504 y[1] (numeric) = 1.058593199727968807007987933875 absolute error = 2.69047246e-23 relative error = 2.5415546412837170511985748730725e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0571 y[1] (analytic) = 1.0586987389427568592416290338394 y[1] (numeric) = 1.0586987389427568592416559843258 absolute error = 2.69504864e-23 relative error = 2.5456237368255895295677286244518e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0572 y[1] (analytic) = 1.0588042875705575142035512732498 y[1] (numeric) = 1.0588042875705575142035782694929 absolute error = 2.69962431e-23 relative error = 2.5496915168282222361011345256161e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0573 y[1] (analytic) = 1.0589098456103152856166007696603 y[1] (numeric) = 1.0589098456103152856166278116551 absolute error = 2.70419948e-23 relative error = 2.5537579910227413763570013957294e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0574 y[1] (analytic) = 1.0590154130609745930840794592717 y[1] (numeric) = 1.0590154130609745930841065470129 absolute error = 2.70877412e-23 relative error = 2.5578231313655467782922058993426e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0575 y[1] (analytic) = 1.0591209899214797621002739961643 y[1] (numeric) = 1.0591209899214797621003011296467 absolute error = 2.71334824e-23 relative error = 2.5618869475914739189496050087069e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0576 y[1] (analytic) = 1.0592265761907750240610124973466 y[1] (numeric) = 1.0592265761907750240610396765652 absolute error = 2.71792186e-23 relative error = 2.5659494588724149706797698743537e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0577 y[1] (analytic) = 1.0593321718678045162742222287886 y[1] (numeric) = 1.0593321718678045162742494537382 absolute error = 2.72249496e-23 relative error = 2.5700106466130661427786913205766e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0578 y[1] (analytic) = 1.0594377769515122819704882323329 y[1] (numeric) = 1.0594377769515122819705155030085 absolute error = 2.72706756e-23 relative error = 2.5740705299814986737496890526207e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.3MB, time=10.20 NO POLE x[1] = 0.0579 y[1] (analytic) = 1.0595433914408422703136128933811 y[1] (numeric) = 1.0595433914408422703136402097774 absolute error = 2.73163963e-23 relative error = 2.5781290809480890082710130073811e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 1.0596490153347383364111764492458 y[1] (numeric) = 1.0596490153347383364112038113578 absolute error = 2.73621120e-23 relative error = 2.5821863281169975364176901779664e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0581 y[1] (analytic) = 1.059754648632144241325098438067 y[1] (numeric) = 1.0597546486321442413251258458895 absolute error = 2.74078225e-23 relative error = 2.5862422529003353360686596898555e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0582 y[1] (analytic) = 1.0598602913320036520822000881835 y[1] (numeric) = 1.0598602913320036520822275417114 absolute error = 2.74535279e-23 relative error = 2.5902968650233278537229219173042e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0583 y[1] (analytic) = 1.0599659434332601416847676478563 y[1] (numeric) = 1.0599659434332601416847951470844 absolute error = 2.74992281e-23 relative error = 2.5943501553388791135131577325691e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0584 y[1] (analytic) = 1.0600716049348571891211166552364 y[1] (numeric) = 1.0600716049348571891211442001596 absolute error = 2.75449232e-23 relative error = 2.5984021335702763388086934857383e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0585 y[1] (analytic) = 1.0601772758357381793761571484734 y[1] (numeric) = 1.0601772758357381793761847390865 absolute error = 2.75906131e-23 relative error = 2.6024527905722473092009545716139e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0586 y[1] (analytic) = 1.0602829561348464034419598158572 y[1] (numeric) = 1.0602829561348464034419874521552 absolute error = 2.76362980e-23 relative error = 2.6065021454975859860147546089076e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0587 y[1] (analytic) = 1.0603886458311250583283230858888 y[1] (numeric) = 1.0603886458311250583283507678665 absolute error = 2.76819777e-23 relative error = 2.6105501797695186839444555409070e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0588 y[1] (analytic) = 1.0604943449235172470733411571733 y[1] (numeric) = 1.0604943449235172470733688848255 absolute error = 2.77276522e-23 relative error = 2.6145968936778928021742312779849e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0589 y[1] (analytic) = 1.0606000534109659787539729680301 y[1] (numeric) = 1.0606000534109659787540007413517 absolute error = 2.77733216e-23 relative error = 2.6186422969411515816990325258327e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 1.0607057712924141684966121057147 y[1] (numeric) = 1.0607057712924141684966399247005 absolute error = 2.78189858e-23 relative error = 2.6226863804185801331352533883960e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0591 y[1] (analytic) = 1.0608114985668046374876576551456 y[1] (numeric) = 1.0608114985668046374876855197907 absolute error = 2.78646451e-23 relative error = 2.6267291726801755720607377680687e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0592 y[1] (analytic) = 1.0609172352330801129840859870323 y[1] (numeric) = 1.0609172352330801129841138973314 absolute error = 2.79102991e-23 relative error = 2.6307706363039899930130272868070e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0593 y[1] (analytic) = 1.0610229812901832283240234852957 y[1] (numeric) = 1.0610229812901832283240514412436 absolute error = 2.79559479e-23 relative error = 2.6348107810074116590169573532592e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0594 y[1] (analytic) = 1.0611287367370565229373202136787 y[1] (numeric) = 1.0611287367370565229373482152703 absolute error = 2.80015916e-23 relative error = 2.6388496165040418593517855893747e-21 % h = 0.0001 memory used=144.9MB, alloc=4.3MB, time=10.49 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0595 y[1] (analytic) = 1.0612345015726424423561245214385 y[1] (numeric) = 1.0612345015726424423561525686687 absolute error = 2.80472302e-23 relative error = 2.6428871430807079005007424892634e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0596 y[1] (analytic) = 1.0613402757958833382254585880169 y[1] (numeric) = 1.0613402757958833382254866808804 absolute error = 2.80928635e-23 relative error = 2.6469233421801107231126282107429e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0597 y[1] (analytic) = 1.0614460594057214683137949065803 y[1] (numeric) = 1.0614460594057214683138230450722 absolute error = 2.81384919e-23 relative error = 2.6509582517790942456639853367938e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0598 y[1] (analytic) = 1.0615518524010989965236337063273 y[1] (numeric) = 1.0615518524010989965236618904423 absolute error = 2.81841150e-23 relative error = 2.6549918344780820366487381876265e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0599 y[1] (analytic) = 1.0616576547809579929020813134538 y[1] (numeric) = 1.0616576547809579929021095431869 absolute error = 2.82297331e-23 relative error = 2.6590241188271166187839207540134e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 1.0617634665442404336514294506742 y[1] (numeric) = 1.06176346654424043365145772602 absolute error = 2.82753458e-23 relative error = 2.6630550674368915941401485544574e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0601 y[1] (analytic) = 1.0618692876898882011397354751883 y[1] (numeric) = 1.0618692876898882011397637961419 absolute error = 2.83209536e-23 relative error = 2.6670847276892845238937382139791e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0602 y[1] (analytic) = 1.0619751182168430839114035549935 y[1] (numeric) = 1.0619751182168430839114319215496 absolute error = 2.83665561e-23 relative error = 2.6711130621996245359456724234708e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0603 y[1] (analytic) = 1.0620809581240467766977667834305 y[1] (numeric) = 1.0620809581240467766977951955841 absolute error = 2.84121536e-23 relative error = 2.6751400995065740491708037909634e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0604 y[1] (analytic) = 1.0621868074104408804276702318624 y[1] (numeric) = 1.0621868074104408804276986896082 absolute error = 2.84577458e-23 relative error = 2.6791658116502673012907705722961e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0605 y[1] (analytic) = 1.0622926660749669022380549403762 y[1] (numeric) = 1.0622926660749669022380834437092 absolute error = 2.85033330e-23 relative error = 2.6831902271636783949651367491035e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0606 y[1] (analytic) = 1.0623985341165662554845428464056 y[1] (numeric) = 1.0623985341165662554845713953206 absolute error = 2.85489150e-23 relative error = 2.6872133275051767011611511356095e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0607 y[1] (analytic) = 1.0625044115341802597520226511655 y[1] (numeric) = 1.0625044115341802597520512456573 absolute error = 2.85944918e-23 relative error = 2.6912351129640583942037820535055e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0608 y[1] (analytic) = 1.062610298326750140865236623794 y[1] (numeric) = 1.0626102983267501408652652638576 absolute error = 2.86400636e-23 relative error = 2.6952556026511657730668005954027e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0609 y[1] (analytic) = 1.0627161944932170308993683430971 y[1] (numeric) = 1.0627161944932170308993970287271 absolute error = 2.86856300e-23 relative error = 2.6992747592107095694454867921307e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=148.7MB, alloc=4.3MB, time=10.76 x[1] = 0.061 y[1] (analytic) = 1.0628221000325219681906313767867 y[1] (numeric) = 1.0628221000325219681906601079782 absolute error = 2.87311915e-23 relative error = 2.7032926299820859982849005140933e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0611 y[1] (analytic) = 1.0629280149436058973468588981111 y[1] (numeric) = 1.0629280149436058973468876748588 absolute error = 2.87767477e-23 relative error = 2.7073091776141362420259123712113e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0612 y[1] (analytic) = 1.0630339392254096692580942397665 y[1] (numeric) = 1.0630339392254096692581230620653 absolute error = 2.88222988e-23 relative error = 2.7113244212128971913877973093623e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0613 y[1] (analytic) = 1.0631398728768740411071823849887 y[1] (numeric) = 1.0631398728768740411072112528335 absolute error = 2.88678448e-23 relative error = 2.7153383610646768013982108924316e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0614 y[1] (analytic) = 1.0632458158969396763803623957155 y[1] (numeric) = 1.0632458158969396763803913091011 absolute error = 2.89133856e-23 relative error = 2.7193509880505912970024564957747e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0615 y[1] (analytic) = 1.0633517682845471448778607777152 y[1] (numeric) = 1.0633517682845471448778897366365 absolute error = 2.89589213e-23 relative error = 2.7233623118639278264604804449485e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0616 y[1] (analytic) = 1.0634577300386369227244857825761 y[1] (numeric) = 1.0634577300386369227245147870278 absolute error = 2.90044517e-23 relative error = 2.7273723139843298958988106384977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0617 y[1] (analytic) = 1.0635637011581493923802226464488 y[1] (numeric) = 1.0635637011581493923802516964259 absolute error = 2.90499771e-23 relative error = 2.7313810229106660258874396999562e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0618 y[1] (analytic) = 1.0636696816420248426508297654386 y[1] (numeric) = 1.0636696816420248426508588609358 absolute error = 2.90954972e-23 relative error = 2.7353884107220432148589905152418e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0619 y[1] (analytic) = 1.0637756714892034686984358075377 y[1] (numeric) = 1.06377567148920346869846494855 absolute error = 2.91410123e-23 relative error = 2.7393945059116497744895156704684e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 1.0638816706986253720521377609965 y[1] (numeric) = 1.0638816706986253720521669475187 absolute error = 2.91865222e-23 relative error = 2.7433992899636964798552662193794e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0621 y[1] (analytic) = 1.0639876792692305606185999190228 y[1] (numeric) = 1.0639876792692305606186291510497 absolute error = 2.92320269e-23 relative error = 2.7474027631670678526977940894389e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0622 y[1] (analytic) = 1.0640936971999589486926538007067 y[1] (numeric) = 1.0640936971999589486926830782332 absolute error = 2.92775265e-23 relative error = 2.7514049352082873598000192016902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0623 y[1] (analytic) = 1.0641997244897503569678990080635 y[1] (numeric) = 1.0641997244897503569679283310844 absolute error = 2.93230209e-23 relative error = 2.7554057969766387830215908744454e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0624 y[1] (analytic) = 1.0643057611375445125473050190886 y[1] (numeric) = 1.0643057611375445125473343875988 absolute error = 2.93685102e-23 relative error = 2.7594053581567138910675436681305e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0625 y[1] (analytic) = 1.0644118071422810489538139167194 y[1] (numeric) = 1.0644118071422810489538433307137 absolute error = 2.94139943e-23 relative error = 2.7634036096396101285803573843740e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.3MB, time=11.04 NO POLE x[1] = 0.0626 y[1] (analytic) = 1.0645178625028995061409440535966 y[1] (numeric) = 1.0645178625028995061409735130699 absolute error = 2.94594733e-23 relative error = 2.7674005611079878944526544940377e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0627 y[1] (analytic) = 1.0646239272183393305033946525204 y[1] (numeric) = 1.0646239272183393305034241574675 absolute error = 2.95049471e-23 relative error = 2.7713962034547577929629215156065e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0628 y[1] (analytic) = 1.0647300012875398748876513424946 y[1] (numeric) = 1.0647300012875398748876808929104 absolute error = 2.95504158e-23 relative error = 2.7753905463606491816464638449944e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0629 y[1] (analytic) = 1.0648360847094403986025926302533 y[1] (numeric) = 1.0648360847094403986026222261325 absolute error = 2.95958792e-23 relative error = 2.7793835713292685630727238436021e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 1.0649421774829800674300973071622 y[1] (numeric) = 1.0649421774829800674301269484998 absolute error = 2.96413376e-23 relative error = 2.7833753068225836703127974219703e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0631 y[1] (analytic) = 1.0650482796070979536356527913924 y[1] (numeric) = 1.0650482796070979536356824781832 absolute error = 2.96867908e-23 relative error = 2.7873657343450774841775645496925e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0632 y[1] (analytic) = 1.0651543910807330359789644052557 y[1] (numeric) = 1.0651543910807330359789941374945 absolute error = 2.97322388e-23 relative error = 2.7913548541853079100971387680485e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0633 y[1] (analytic) = 1.0652605119028241997245655875989 y[1] (numeric) = 1.0652605119028241997245953652806 absolute error = 2.97776817e-23 relative error = 2.7953426760191779844987232601138e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0634 y[1] (analytic) = 1.0653666420723102366524290411499 y[1] (numeric) = 1.0653666420723102366524588642692 absolute error = 2.98231193e-23 relative error = 2.7993291813595003140973547375141e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0635 y[1] (analytic) = 1.0654727815881298450685788147086 y[1] (numeric) = 1.0654727815881298450686086832605 absolute error = 2.98685519e-23 relative error = 2.8033143986540629769884940439490e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0636 y[1] (analytic) = 1.0655789304492216298157033200786 y[1] (numeric) = 1.0655789304492216298157332340578 absolute error = 2.99139792e-23 relative error = 2.8072983000319843808105127234100e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0637 y[1] (analytic) = 1.0656850886545241022837692836306 y[1] (numeric) = 1.0656850886545241022837992430321 absolute error = 2.99594015e-23 relative error = 2.8112809139353828356646284351767e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0638 y[1] (analytic) = 1.0657912562029756804206366323946 y[1] (numeric) = 1.0657912562029756804206666372132 absolute error = 3.00048186e-23 relative error = 2.8152622218816272920811647197106e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0639 y[1] (analytic) = 1.0658974330935146887426743145721 y[1] (numeric) = 1.0658974330935146887427043648026 absolute error = 3.00502305e-23 relative error = 2.8192422241590663826259163703394e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 1.0660036193250793583453770543635 y[1] (numeric) = 1.0660036193250793583454071500008 absolute error = 3.00956373e-23 relative error = 2.8232209304368498128582342782102e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0641 y[1] (analytic) = 1.0661098148966078269139830410047 y[1] (numeric) = 1.0661098148966078269140131820435 absolute error = 3.01410388e-23 relative error = 2.8271983222406691549703104600554e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.3MB, time=11.31 NO POLE x[1] = 0.0642 y[1] (analytic) = 1.0662160198070381387340925519051 y[1] (numeric) = 1.0662160198070381387341227383404 absolute error = 3.01864353e-23 relative error = 2.8311744279984732242111933994043e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0643 y[1] (analytic) = 1.0663222340553082447022875097838 y[1] (numeric) = 1.0663222340553082447023177416104 absolute error = 3.02318266e-23 relative error = 2.8351492292368283044371629170080e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0644 y[1] (analytic) = 1.0664284576403560023367519736941 y[1] (numeric) = 1.0664284576403560023367822509068 absolute error = 3.02772127e-23 relative error = 2.8391227262439328556655484092799e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0645 y[1] (analytic) = 1.0665346905611191757878935638331 y[1] (numeric) = 1.0665346905611191757879238864267 absolute error = 3.03225936e-23 relative error = 2.8430949193079551141380806536433e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0646 y[1] (analytic) = 1.0666409328165354358489658200287 y[1] (numeric) = 1.0666409328165354358489961879981 absolute error = 3.03679694e-23 relative error = 2.8470658180922592527448071475236e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0647 y[1] (analytic) = 1.0667471844055423599666914937985 y[1] (numeric) = 1.0667471844055423599667219071385 absolute error = 3.04133400e-23 relative error = 2.8510354135078592061766442213837e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0648 y[1] (analytic) = 1.0668534453270774322518867738733 y[1] (numeric) = 1.0668534453270774322519172325787 absolute error = 3.04587054e-23 relative error = 2.8550037058428327227488169235622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0649 y[1] (analytic) = 1.0669597155800780434900864450803 y[1] (numeric) = 1.0669597155800780434901169491459 absolute error = 3.05040656e-23 relative error = 2.8589706953852272413353914360729e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 1.0670659951634814911521699804788 y[1] (numeric) = 1.0670659951634814911522005298995 absolute error = 3.05494207e-23 relative error = 2.8629363917945514603298867065271e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0651 y[1] (analytic) = 1.0671722840762249794049885666427 y[1] (numeric) = 1.0671722840762249794050191614134 absolute error = 3.05947707e-23 relative error = 2.8669007953559919720683489664045e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0652 y[1] (analytic) = 1.0672785823172456191219930619832 y[1] (numeric) = 1.0672785823172456191220237020987 absolute error = 3.06401155e-23 relative error = 2.8708638969850807008755192671482e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0653 y[1] (analytic) = 1.0673848898854804278938628880051 y[1] (numeric) = 1.0673848898854804278938935734601 absolute error = 3.06854550e-23 relative error = 2.8748256876010525196996220709816e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0654 y[1] (analytic) = 1.0674912067798663300391358533912 y[1] (numeric) = 1.0674912067798663300391665841807 absolute error = 3.07307895e-23 relative error = 2.8787861955978788406728629465115e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0655 y[1] (analytic) = 1.0675975329993401566148389108086 y[1] (numeric) = 1.0675975329993401566148696869273 absolute error = 3.07761187e-23 relative error = 2.8827453931573502057528438302618e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0656 y[1] (analytic) = 1.0677038685428386454271198463287 y[1] (numeric) = 1.0677038685428386454271506677715 absolute error = 3.08214428e-23 relative error = 2.8867032993018864770629136928939e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0657 y[1] (analytic) = 1.0678102134092984410418799013575 y[1] (numeric) = 1.0678102134092984410419107681194 absolute error = 3.08667619e-23 relative error = 2.8906599236814542432691091381753e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.3MB, time=11.59 NO POLE x[1] = 0.0658 y[1] (analytic) = 1.0679165675976560947954073269679 y[1] (numeric) = 1.0679165675976560947954382390435 absolute error = 3.09120756e-23 relative error = 2.8946152291221225770416941285446e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0659 y[1] (analytic) = 1.0680229311068480648050118705272 y[1] (numeric) = 1.0680229311068480648050428279113 absolute error = 3.09573841e-23 relative error = 2.8985692346434212343470798281396e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 1.0681293039358107159796601945154 y[1] (numeric) = 1.068129303935810715979691197203 absolute error = 3.10026876e-23 relative error = 2.9025219592573885665232583824523e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0661 y[1] (analytic) = 1.0682356860834803200306122274274 y[1] (numeric) = 1.0682356860834803200306432754133 absolute error = 3.10479859e-23 relative error = 2.9064733845236533988057657366446e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0662 y[1] (analytic) = 1.0683420775487930554820584466505 y[1] (numeric) = 1.0683420775487930554820895399295 absolute error = 3.10932790e-23 relative error = 2.9104235107298687710488218472645e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0663 y[1] (analytic) = 1.0684484783306850076817580932143 y[1] (numeric) = 1.0684484783306850076817892317812 absolute error = 3.11385669e-23 relative error = 2.9143723381636571164331311360844e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0664 y[1] (analytic) = 1.0685548884280921688116783183038 y[1] (numeric) = 1.0685548884280921688117095021535 absolute error = 3.11838497e-23 relative error = 2.9183198764710438672339699896129e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0665 y[1] (analytic) = 1.0686613078399504378986342614313 y[1] (numeric) = 1.0686613078399504378986654905586 absolute error = 3.12291273e-23 relative error = 2.9222661165792926904603290798466e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0666 y[1] (analytic) = 1.0687677365651956208249300601592 y[1] (numeric) = 1.0687677365651956208249613345588 absolute error = 3.12743996e-23 relative error = 2.9262110494193645168744616508924e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0667 y[1] (analytic) = 1.0688741746027634303390007912677 y[1] (numeric) = 1.0688741746027634303390321109346 absolute error = 3.13196669e-23 relative error = 2.9301547033484690589836625071140e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0668 y[1] (analytic) = 1.0689806219515894860660553432624 y[1] (numeric) = 1.0689806219515894860660867081914 absolute error = 3.13649290e-23 relative error = 2.9340970599390726341938558793119e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0669 y[1] (analytic) = 1.0690870786106093145187202201126 y[1] (numeric) = 1.0690870786106093145187516302985 absolute error = 3.14101859e-23 relative error = 2.9380381194786142180228405628781e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 1.0691935445787583491076842761166 y[1] (numeric) = 1.0691935445787583491077157315542 absolute error = 3.14554376e-23 relative error = 2.9419778822545020321924645360836e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0671 y[1] (analytic) = 1.0693000198549719301523443817856 y[1] (numeric) = 1.0693000198549719301523758824698 absolute error = 3.15006842e-23 relative error = 2.9459163579060258161406808532069e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0672 y[1] (analytic) = 1.0694065044381853048914520206413 y[1] (numeric) = 1.0694065044381853048914835665668 absolute error = 3.15459255e-23 relative error = 2.9498535280157764333564232732665e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0673 y[1] (analytic) = 1.069512998327333627493760816819 y[1] (numeric) = 1.0695129983273336274937924079806 absolute error = 3.15911616e-23 relative error = 2.9537894022239133180851899468960e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.3MB, time=11.86 NO POLE x[1] = 0.0674 y[1] (analytic) = 1.0696195015213519590686749933714 y[1] (numeric) = 1.0696195015213519590687066297641 absolute error = 3.16363927e-23 relative error = 2.9577239995159594593703259417589e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0675 y[1] (analytic) = 1.0697260140191752676768987611662 y[1] (numeric) = 1.0697260140191752676769304427847 absolute error = 3.16816185e-23 relative error = 2.9616572921290193365870477033494e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0676 y[1] (analytic) = 1.0698325358197384283410866382691 y[1] (numeric) = 1.0698325358197384283411183651083 absolute error = 3.17268392e-23 relative error = 2.9655892990476238310452542547742e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0677 y[1] (analytic) = 1.0699390669219762230564946997096 y[1] (numeric) = 1.0699390669219762230565264717641 absolute error = 3.17720545e-23 relative error = 2.9695199925171936595202771921004e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0678 y[1] (analytic) = 1.0700456073248233408016327575183 y[1] (numeric) = 1.0700456073248233408016645747831 absolute error = 3.18172648e-23 relative error = 2.9734494102120585864619829906187e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0679 y[1] (analytic) = 1.0701521570272143775489174709341 y[1] (numeric) = 1.070152157027214377548949333404 absolute error = 3.18624699e-23 relative error = 2.9773775337248350971567004724310e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 1.0702587160280838362753263866704 y[1] (numeric) = 1.0702587160280838362753582943403 absolute error = 3.19076699e-23 relative error = 2.9813043726861585644031954633584e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0681 y[1] (analytic) = 1.0703652843263661269730529091368 y[1] (numeric) = 1.0703652843263661269730848620014 absolute error = 3.19528646e-23 relative error = 2.9852299086950974734481959107526e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0682 y[1] (analytic) = 1.070471861920995566660162200508 y[1] (numeric) = 1.0704718619209955666601941985622 absolute error = 3.19980542e-23 relative error = 2.9891541607248303651660894047341e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0683 y[1] (analytic) = 1.0705784488109063793912480105347 y[1] (numeric) = 1.0705784488109063793912800537732 absolute error = 3.20432385e-23 relative error = 2.9930771103780847615050144370929e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0684 y[1] (analytic) = 1.0706850449950326962680904359881 y[1] (numeric) = 1.0706850449950326962681225244058 absolute error = 3.20884177e-23 relative error = 2.9969987766242564854426019063862e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0685 y[1] (analytic) = 1.0707916504723085554503146096339 y[1] (numeric) = 1.0707916504723085554503467432257 absolute error = 3.21335918e-23 relative error = 3.0009191597475010256537636296920e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0686 y[1] (analytic) = 1.070898265241667902166050318627 y[1] (numeric) = 1.0708982652416679021660824973876 absolute error = 3.21787606e-23 relative error = 3.0048382413560330549822708968158e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0687 y[1] (analytic) = 1.071004889302044588722592552221 y[1] (numeric) = 1.0710048893020445887226247761452 absolute error = 3.22239242e-23 relative error = 3.0087560310765505030545788734843e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0688 y[1] (analytic) = 1.0711115226523723745170629786866 y[1] (numeric) = 1.0711115226523723745170952477693 absolute error = 3.22690827e-23 relative error = 3.0126725385320013973255815064183e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=167.8MB, alloc=4.3MB, time=12.14 x[1] = 0.0689 y[1] (analytic) = 1.0712181652915849260470723513317 y[1] (numeric) = 1.0712181652915849260471046655676 absolute error = 3.23142359e-23 relative error = 3.0165877453360851898564218957346e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 1.0713248172186158169213838435158 y[1] (numeric) = 1.0713248172186158169214162028998 absolute error = 3.23593840e-23 relative error = 3.0205016704468543640605838874220e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0691 y[1] (analytic) = 1.0714314784323985278705773125542 y[1] (numeric) = 1.0714314784323985278706097170811 absolute error = 3.24045269e-23 relative error = 3.0244143048149717577434202720604e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0692 y[1] (analytic) = 1.0715381489318664467577144924028 y[1] (numeric) = 1.0715381489318664467577469420675 absolute error = 3.24496647e-23 relative error = 3.0283256580595438860650207515380e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0693 y[1] (analytic) = 1.0716448287159528685890051150189 y[1] (numeric) = 1.0716448287159528685890376098162 absolute error = 3.24947973e-23 relative error = 3.0322357211330302218532766095178e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0694 y[1] (analytic) = 1.0717515177835909955244739602901 y[1] (numeric) = 1.0717515177835909955245065002147 absolute error = 3.25399246e-23 relative error = 3.0361444849915752631020630978141e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0695 y[1] (analytic) = 1.0718582161337139368886288344249 y[1] (numeric) = 1.0718582161337139368886614194716 absolute error = 3.25850467e-23 relative error = 3.0400519592541917728623657482032e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0696 y[1] (analytic) = 1.0719649237652547091811294766991 y[1] (numeric) = 1.0719649237652547091811621068628 absolute error = 3.26301637e-23 relative error = 3.0439581535361457797030630011835e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0697 y[1] (analytic) = 1.0720716406771462360874573944504 y[1] (numeric) = 1.0720716406771462360874900697259 absolute error = 3.26752755e-23 relative error = 3.0478630587934879068603892933818e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0698 y[1] (analytic) = 1.0721783668683213484895866262142 y[1] (numeric) = 1.0721783668683213484896193465964 absolute error = 3.27203822e-23 relative error = 3.0517666846395647542082359861447e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0699 y[1] (analytic) = 1.0722851023377127844766554328955 y[1] (numeric) = 1.0722851023377127844766881983791 absolute error = 3.27654836e-23 relative error = 3.0556690127063441279443495560689e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 1.0723918470842531893556389168682 y[1] (numeric) = 1.072391847084253189355671727448 absolute error = 3.28105798e-23 relative error = 3.0595700526080383983101773976057e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0701 y[1] (analytic) = 1.0724986011068751156620225688965 y[1] (numeric) = 1.0724986011068751156620554245674 absolute error = 3.28556709e-23 relative error = 3.0634698139551151818299036682214e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0702 y[1] (analytic) = 1.0726053644045110231704767427717 y[1] (numeric) = 1.0726053644045110231705096435284 absolute error = 3.29007567e-23 relative error = 3.0673682783850181447254188535116e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0703 y[1] (analytic) = 1.0727121369760932789055320575559 y[1] (numeric) = 1.0727121369760932789055650033932 absolute error = 3.29458373e-23 relative error = 3.0712654555090802395311479751950e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0704 y[1] (analytic) = 1.0728189188205541571522557273279 y[1] (numeric) = 1.0728189188205541571522887182407 absolute error = 3.29909128e-23 relative error = 3.0751613549348908538674855067866e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.3MB, time=12.42 NO POLE x[1] = 0.0705 y[1] (analytic) = 1.0729257099368258394669288183241 y[1] (numeric) = 1.0729257099368258394669618543072 absolute error = 3.30359831e-23 relative error = 3.0790559676256772484174094007947e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0706 y[1] (analytic) = 1.0730325103238404146877244333665 y[1] (numeric) = 1.0730325103238404146877575144147 absolute error = 3.30810482e-23 relative error = 3.0829492938677285949263993449337e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0707 y[1] (analytic) = 1.0731393199805298789453868234719 y[1] (numeric) = 1.07313931998052987894541994958 absolute error = 3.31261081e-23 relative error = 3.0868413339473025500997741830568e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0708 y[1] (analytic) = 1.0732461389058261356739114265358 y[1] (numeric) = 1.0732461389058261356739445976986 absolute error = 3.31711628e-23 relative error = 3.0907320881506252354081708091934e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0709 y[1] (analytic) = 1.0733529670986609956212258329835 y[1] (numeric) = 1.0733529670986609956212590491958 absolute error = 3.32162123e-23 relative error = 3.0946215567638912169129604298176e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 1.0734598045579661768598716782817 y[1] (numeric) = 1.0734598045579661768599049395384 absolute error = 3.32612567e-23 relative error = 3.0985097493889360026473951357333e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0711 y[1] (analytic) = 1.0735666512826733047976874622046 y[1] (numeric) = 1.0735666512826733047977207685005 absolute error = 3.33062959e-23 relative error = 3.1023966569943641851949678812460e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0712 y[1] (analytic) = 1.0736735072717139121884922947465 y[1] (numeric) = 1.0736735072717139121885256460762 absolute error = 3.33513297e-23 relative error = 3.1062822612386391819921594756768e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0713 y[1] (analytic) = 1.0737803725240194391427705685741 y[1] (numeric) = 1.0737803725240194391428039649326 absolute error = 3.33963585e-23 relative error = 3.1101665996649566647163406771620e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0714 y[1] (analytic) = 1.0738872470385212331383575579137 y[1] (numeric) = 1.0738872470385212331383909992957 absolute error = 3.34413820e-23 relative error = 3.1140496446178981094048269733349e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0715 y[1] (analytic) = 1.0739941308141505490311259437632 y[1] (numeric) = 1.0739941308141505490311594301636 absolute error = 3.34864004e-23 relative error = 3.1179314150083245116335758756915e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0716 y[1] (analytic) = 1.074101023849838549065673265325 y[1] (numeric) = 1.0741010238498385490657067967385 absolute error = 3.35314135e-23 relative error = 3.1218118924992066698948769545065e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0717 y[1] (analytic) = 1.0742079261445163028860102975506 y[1] (numeric) = 1.0742079261445163028860438739721 absolute error = 3.35764215e-23 relative error = 3.1256910959976352649279374733935e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0718 y[1] (analytic) = 1.074314837697114787546250354692 y[1] (numeric) = 1.0743148376971147875462839761163 absolute error = 3.36214243e-23 relative error = 3.1295690164784824245765071279786e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0719 y[1] (analytic) = 1.0744217585065648875212995197517 y[1] (numeric) = 1.0744217585065648875213331861735 absolute error = 3.36664218e-23 relative error = 3.1334456449202943815726833435245e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 1.0745286885717973947175477997241 y[1] (numeric) = 1.0745286885717973947175815111383 absolute error = 3.37114142e-23 relative error = 3.1373210002245077570967330644410e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.3MB, time=12.71 NO POLE x[1] = 0.0721 y[1] (analytic) = 1.0746356278917430084835612065234 y[1] (numeric) = 1.0746356278917430084835949629248 absolute error = 3.37564014e-23 relative error = 3.1411950733686789029566330416177e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0722 y[1] (analytic) = 1.0747425764653323356207747634888 y[1] (numeric) = 1.0747425764653323356208085648721 absolute error = 3.38013833e-23 relative error = 3.1450678553340369658823227076085e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0723 y[1] (analytic) = 1.0748495342914958903941864373609 y[1] (numeric) = 1.0748495342914958903942202837211 absolute error = 3.38463602e-23 relative error = 3.1489393743199939958156794548756e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0724 y[1] (analytic) = 1.0749565013691640945430519956235 y[1] (numeric) = 1.0749565013691640945430858869553 absolute error = 3.38913318e-23 relative error = 3.1528096026986080786101770336029e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0725 y[1] (analytic) = 1.0750634776972672772915807891016 y[1] (numeric) = 1.0750634776972672772916147253997 absolute error = 3.39362981e-23 relative error = 3.1566785407583438429846959201628e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0726 y[1] (analytic) = 1.0751704632747356753596324597104 y[1] (numeric) = 1.0751704632747356753596664409696 absolute error = 3.39812592e-23 relative error = 3.1605461980884841381313519187857e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0727 y[1] (analytic) = 1.0752774581004994329734145732479 y[1] (numeric) = 1.0752774581004994329734485994631 absolute error = 3.40262152e-23 relative error = 3.1644125842745773710681355294121e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0728 y[1] (analytic) = 1.0753844621734886018761811771242 y[1] (numeric) = 1.0753844621734886018762152482901 absolute error = 3.40711659e-23 relative error = 3.1682776810014388461264105818950e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0729 y[1] (analytic) = 1.0754914754926331413389322829193 y[1] (numeric) = 1.0754914754926331413389663990309 absolute error = 3.41161116e-23 relative error = 3.1721415164516278104192227569969e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 1.0755984980568629181711142736652 y[1] (numeric) = 1.0755984980568629181711484347172 absolute error = 3.41610520e-23 relative error = 3.1760040630136721712433323777730e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0731 y[1] (analytic) = 1.0757055298651077067313212357416 y[1] (numeric) = 1.0757055298651077067313554417287 absolute error = 3.42059871e-23 relative error = 3.1798653209758430129405161155688e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0732 y[1] (analytic) = 1.0758125709162971889379972152815 y[1] (numeric) = 1.0758125709162971889380314661985 absolute error = 3.42509170e-23 relative error = 3.1837252999216782318605778610279e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0733 y[1] (analytic) = 1.0759196212093609542801393989777 y[1] (numeric) = 1.0759196212093609542801736948195 absolute error = 3.42958418e-23 relative error = 3.1875840094309836644734043699111e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0734 y[1] (analytic) = 1.0760266807432284998280022191841 y[1] (numeric) = 1.0760266807432284998280365599455 absolute error = 3.43407614e-23 relative error = 3.1914414404929344000034626935605e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0735 y[1] (analytic) = 1.076133749516829230243802383204 y[1] (numeric) = 1.0761337495168292302438367688797 absolute error = 3.43856757e-23 relative error = 3.1952975841003726472753927132397e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0736 y[1] (analytic) = 1.0762408275290924577924248266591 y[1] (numeric) = 1.0762408275290924577924592572439 absolute error = 3.44305848e-23 relative error = 3.1991524498330080238307078453322e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.3MB, time=12.99 NO POLE x[1] = 0.0737 y[1] (analytic) = 1.0763479147789474023521295908318 y[1] (numeric) = 1.0763479147789474023521640663204 absolute error = 3.44754886e-23 relative error = 3.2030060286854671920117129091342e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0738 y[1] (analytic) = 1.0764550112653231914252596238732 y[1] (numeric) = 1.0764550112653231914252941442607 absolute error = 3.45203875e-23 relative error = 3.2068583581048015633036669078409e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0739 y[1] (analytic) = 1.076562116987148860148949505772 y[1] (numeric) = 1.076562116987148860148984071053 absolute error = 3.45652810e-23 relative error = 3.2107093919237929820418285774017e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 1.0766692319433533513058350969725 y[1] (numeric) = 1.0766692319433533513058697071419 absolute error = 3.46101694e-23 relative error = 3.2145591582969039495563992711140e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0741 y[1] (analytic) = 1.0767763561328655153347641105409 y[1] (numeric) = 1.0767763561328655153347987655933 absolute error = 3.46550524e-23 relative error = 3.2184076296455980240058326313780e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0742 y[1] (analytic) = 1.0768834895546141103415076077666 y[1] (numeric) = 1.0768834895546141103415423076969 absolute error = 3.46999303e-23 relative error = 3.2222548341187279563551925905140e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0743 y[1] (analytic) = 1.0769906322075278021094724170966 y[1] (numeric) = 1.0769906322075278021095071618996 absolute error = 3.47448030e-23 relative error = 3.2261007627134999994413830157601e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0744 y[1] (analytic) = 1.0770977840905351641104144762918 y[1] (numeric) = 1.0770977840905351641104492659623 absolute error = 3.47896705e-23 relative error = 3.2299454157149917242059448109152e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0745 y[1] (analytic) = 1.077204945202564677515153097701 y[1] (numeric) = 1.0772049452025646775151879322337 absolute error = 3.48345327e-23 relative error = 3.2337887841249639062802553781769e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0746 y[1] (analytic) = 1.0773121155425447312042861565433 y[1] (numeric) = 1.0773121155425447312043210359331 absolute error = 3.48793898e-23 relative error = 3.2376308867959221091508952512099e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0747 y[1] (analytic) = 1.0774192951094036217789062020936 y[1] (numeric) = 1.0774192951094036217789411263353 absolute error = 3.49242417e-23 relative error = 3.2414717147286389135204836367315e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0748 y[1] (analytic) = 1.0775264839020695535713174916627 y[1] (numeric) = 1.077526483902069553571352460751 absolute error = 3.49690883e-23 relative error = 3.2453112589275483463539671680658e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0749 y[1] (analytic) = 1.0776336819194706386557539472649 y[1] (numeric) = 1.0776336819194706386557889611947 absolute error = 3.50139298e-23 relative error = 3.2491495382395183312638704062421e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 1.0777408891605348968590980348673 y[1] (numeric) = 1.0777408891605348968591330936333 absolute error = 3.50587660e-23 relative error = 3.2529865343893268043370809315300e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0751 y[1] (analytic) = 1.0778481056241902557716005661117 y[1] (numeric) = 1.0778481056241902557716356697087 absolute error = 3.51035970e-23 relative error = 3.2568222569423390900116857800917e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0752 y[1] (analytic) = 1.0779553313093645507576014224032 y[1] (numeric) = 1.077955331309364550757636570826 absolute error = 3.51484228e-23 relative error = 3.2606567061833737551383009971744e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.3MB, time=13.27 NO POLE x[1] = 0.0753 y[1] (analytic) = 1.078062566214985524966251201258 y[1] (numeric) = 1.0780625662149855249662863945013 absolute error = 3.51932433e-23 relative error = 3.2644898731213174606046035261033e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0754 y[1] (analytic) = 1.0781698103399808293422337848026 y[1] (numeric) = 1.0781698103399808293422690228614 absolute error = 3.52380588e-23 relative error = 3.2683217858686223542867474207714e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0755 y[1] (analytic) = 1.0782770636832780226364898303188 y[1] (numeric) = 1.0782770636832780226365251131878 absolute error = 3.52828690e-23 relative error = 3.2721524168823112273022942353192e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0756 y[1] (analytic) = 1.0783843262438045714169411827244 y[1] (numeric) = 1.0783843262438045714169765103984 absolute error = 3.53276740e-23 relative error = 3.2759817757229723192398762690374e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0757 y[1] (analytic) = 1.0784915980204878500792162088857 y[1] (numeric) = 1.0784915980204878500792515813594 absolute error = 3.53724737e-23 relative error = 3.2798098534030524245541152281940e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0758 y[1] (analytic) = 1.078598879012255140857376053652 y[1] (numeric) = 1.0785988790122551408574114709202 absolute error = 3.54172682e-23 relative error = 3.2836366594812292311066028538563e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0759 y[1] (analytic) = 1.0787061692180336338346418175061 y[1] (numeric) = 1.0787061692180336338346772795636 absolute error = 3.54620575e-23 relative error = 3.2874621942420936240102203632119e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 1.0788134686367504269541226557232 y[1] (numeric) = 1.0788134686367504269541581625648 absolute error = 3.55068416e-23 relative error = 3.2912864579702039302489970176037e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0761 y[1] (analytic) = 1.0789207772673325260295447989308 y[1] (numeric) = 1.0789207772673325260295803505513 absolute error = 3.55516205e-23 relative error = 3.2951094509500858995263255463096e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0762 y[1] (analytic) = 1.0790280951087068447559814949627 y[1] (numeric) = 1.0790280951087068447560170913568 absolute error = 3.55963941e-23 relative error = 3.2989311641986334026574070440624e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0763 y[1] (analytic) = 1.0791354221598002047205838718988 y[1] (numeric) = 1.0791354221598002047206195130614 absolute error = 3.56411626e-23 relative error = 3.3027516165364272655079610590123e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0764 y[1] (analytic) = 1.0792427584195393354133127221855 y[1] (numeric) = 1.0792427584195393354133484081113 absolute error = 3.56859258e-23 relative error = 3.3065707897136183408946033869256e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0765 y[1] (analytic) = 1.0793501038868508742376712077262 y[1] (numeric) = 1.07935010388685087423770693841 absolute error = 3.57306838e-23 relative error = 3.3103886932822008479450510327888e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0766 y[1] (analytic) = 1.0794574585606613665214384858379 y[1] (numeric) = 1.0794574585606613665214742612745 absolute error = 3.57754366e-23 relative error = 3.3142053275265370505563176425283e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0767 y[1] (analytic) = 1.0795648224398972655274042559645 y[1] (numeric) = 1.0795648224398972655274400761487 absolute error = 3.58201842e-23 relative error = 3.3180206927309565208343817365758e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=186.9MB, alloc=4.3MB, time=13.56 x[1] = 0.0768 y[1] (analytic) = 1.0796721955234849324641042270395 y[1] (numeric) = 1.0796721955234849324641400919662 absolute error = 3.58649267e-23 relative error = 3.3218347984418266276467081847809e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0769 y[1] (analytic) = 1.0797795778103506364965565053925 y[1] (numeric) = 1.0797795778103506364965924150563 absolute error = 3.59096638e-23 relative error = 3.3256476171571999797819907511198e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 1.079886969299420554756998903089 y[1] (numeric) = 1.0798869692994205547570348574847 absolute error = 3.59543957e-23 relative error = 3.3294591676872910658951524698614e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0771 y[1] (analytic) = 1.0799943699896207723556271665998 y[1] (numeric) = 1.0799943699896207723556631657222 absolute error = 3.59991224e-23 relative error = 3.3332694503162981881330236572261e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0772 y[1] (analytic) = 1.08010177987987728239133412569 y[1] (numeric) = 1.080101779879877282391370169534 absolute error = 3.60438440e-23 relative error = 3.3370784745867736050215049965703e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0773 y[1] (analytic) = 1.0802091989691159859624497624212 y[1] (numeric) = 1.0802091989691159859624858509815 absolute error = 3.60885603e-23 relative error = 3.3408862222651558598570083614496e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0774 y[1] (analytic) = 1.0803166272562626921774822001589 y[1] (numeric) = 1.0803166272562626921775183334302 absolute error = 3.61332713e-23 relative error = 3.3446926936383068792866897036748e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0775 y[1] (analytic) = 1.0804240647402431181658596124787 y[1] (numeric) = 1.0804240647402431181658957904557 absolute error = 3.61779770e-23 relative error = 3.3484978889930551208825930359117e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0776 y[1] (analytic) = 1.0805315114199828890886730518627 y[1] (numeric) = 1.0805315114199828890887092745405 absolute error = 3.62226778e-23 relative error = 3.3523018456350141423806342705629e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0777 y[1] (analytic) = 1.0806389672944075381494201980808 y[1] (numeric) = 1.0806389672944075381494564654539 absolute error = 3.62673731e-23 relative error = 3.3561045083171959446231629536151e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0778 y[1] (analytic) = 1.0807464323624425066047500261452 y[1] (numeric) = 1.0807464323624425066047863382084 absolute error = 3.63120632e-23 relative error = 3.3599059050904433444411485909406e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0779 y[1] (analytic) = 1.0808539066230131437752083937359 y[1] (numeric) = 1.080853906623013143775244750484 absolute error = 3.63567481e-23 relative error = 3.3637060362386911960951806435550e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 1.080961390075044707055984547986 y[1] (numeric) = 1.0809613900750447070560209494139 absolute error = 3.64014279e-23 relative error = 3.3675049112968656358967062533438e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0781 y[1] (analytic) = 1.0810688827174623619276585515214 y[1] (numeric) = 1.0810688827174623619276949976237 absolute error = 3.64461023e-23 relative error = 3.3713025027957629656123292293704e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0782 y[1] (analytic) = 1.0811763845491911819669496276449 y[1] (numeric) = 1.0811763845491911819669861184164 absolute error = 3.64907715e-23 relative error = 3.3750988295231071977973730276927e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0783 y[1] (analytic) = 1.0812838955691561488574654245611 y[1] (numeric) = 1.0812838955691561488575019599966 absolute error = 3.65354355e-23 relative error = 3.3788938917627010112513767505187e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=190.7MB, alloc=4.3MB, time=13.84 x[1] = 0.0784 y[1] (analytic) = 1.081391415776282152400452198531 y[1] (numeric) = 1.0813914157762821524004887786252 absolute error = 3.65800942e-23 relative error = 3.3826876805509686115303595432523e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0785 y[1] (analytic) = 1.0814989451694939905255459158503 y[1] (numeric) = 1.0814989451694939905255825405981 absolute error = 3.66247478e-23 relative error = 3.3864802146672569843147089204483e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0786 y[1] (analytic) = 1.0816064837477163693015242735447 y[1] (numeric) = 1.0816064837477163693015609429409 absolute error = 3.66693962e-23 relative error = 3.3902714851470047209206632059075e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0787 y[1] (analytic) = 1.0817140315098739029470596386726 y[1] (numeric) = 1.0817140315098739029470963527119 absolute error = 3.67140393e-23 relative error = 3.3940614830292948514093629354551e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0788 y[1] (analytic) = 1.0818215884548911138414729061297 y[1] (numeric) = 1.0818215884548911138415096648068 absolute error = 3.67586771e-23 relative error = 3.3978502086005221536984409073361e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0789 y[1] (analytic) = 1.0819291545816924325354882748466 y[1] (numeric) = 1.0819291545816924325355250781564 absolute error = 3.68033098e-23 relative error = 3.4016376806325463921720679481103e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 1.0820367298892021977619889422729 y[1] (numeric) = 1.0820367298892021977620257902101 absolute error = 3.68479372e-23 relative error = 3.4054238809225205152648131873478e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0791 y[1] (analytic) = 1.0821443143763446564467737170393 y[1] (numeric) = 1.0821443143763446564468106095986 absolute error = 3.68925593e-23 relative error = 3.4092088097567386762952448938244e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0792 y[1] (analytic) = 1.0822519080420439637193145496904 y[1] (numeric) = 1.0822519080420439637193514868666 absolute error = 3.69371762e-23 relative error = 3.4129924766614541908822879248053e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0793 y[1] (analytic) = 1.0823595108852241829235149813813 y[1] (numeric) = 1.0823595108852241829235519631693 absolute error = 3.69817880e-23 relative error = 3.4167748911592121907258010387947e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0794 y[1] (analytic) = 1.0824671229048092856284695104297 y[1] (numeric) = 1.0824671229048092856285065368241 absolute error = 3.70263944e-23 relative error = 3.4205560258162271886804362128889e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0795 y[1] (analytic) = 1.0825747440997231516392238766154 y[1] (numeric) = 1.0825747440997231516392609476111 absolute error = 3.70709957e-23 relative error = 3.4243359086331266110894410788235e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0796 y[1] (analytic) = 1.0826823744688895690075362631217 y[1] (numeric) = 1.0826823744688895690075733787134 absolute error = 3.71155917e-23 relative error = 3.4281145214178880310689255195884e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0797 y[1] (analytic) = 1.0827900140112322340426394160082 y[1] (numeric) = 1.0827900140112322340426765761906 absolute error = 3.71601824e-23 relative error = 3.4318918644566038520645179110274e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0798 y[1] (analytic) = 1.0828976627256747513220036811095 y[1] (numeric) = 1.0828976627256747513220408858776 absolute error = 3.72047681e-23 relative error = 3.4356679657387814208223265416594e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0799 y[1] (analytic) = 1.0830053206111406337021009582524 y[1] (numeric) = 1.0830053206111406337021382076008 absolute error = 3.72493484e-23 relative error = 3.4394427886079236938448577955204e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.3MB, time=14.12 NO POLE x[1] = 0.08 y[1] (analytic) = 1.083112987666553302329169572681 y[1] (numeric) = 1.0831129876665533023292068666045 absolute error = 3.72939235e-23 relative error = 3.4432163518180700847434946568235e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0801 y[1] (analytic) = 1.083220663890836086649980063586 y[1] (numeric) = 1.0832206638908360866500174020794 absolute error = 3.73384934e-23 relative error = 3.4469886556524246392368886637376e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0802 y[1] (analytic) = 1.0833283492829122244226018896282 y[1] (numeric) = 1.0833283492829122244226392726862 absolute error = 3.73830580e-23 relative error = 3.4507596911633463584595319847090e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0803 y[1] (analytic) = 1.0834360438417048617271710513483 y[1] (numeric) = 1.0834360438417048617272084789657 absolute error = 3.74276174e-23 relative error = 3.4545294678666193791347675738006e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0804 y[1] (analytic) = 1.0835437475661370529766586303569 y[1] (numeric) = 1.0835437475661370529766961025284 absolute error = 3.74721715e-23 relative error = 3.4582979768163706408155193891455e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0805 y[1] (analytic) = 1.0836514604551317609276402451957 y[1] (numeric) = 1.0836514604551317609276777619162 absolute error = 3.75167205e-23 relative error = 3.4620652367545411255659065548828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0806 y[1] (analytic) = 1.083759182507611856691066423763 y[1] (numeric) = 1.0837591825076118566911039850272 absolute error = 3.75612642e-23 relative error = 3.4658312295071313865112918402158e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0807 y[1] (analytic) = 1.0838669137225001197430338921948 y[1] (numeric) = 1.0838669137225001197430714979975 absolute error = 3.76058027e-23 relative error = 3.4695959645861211930237972476812e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0808 y[1] (analytic) = 1.0839746540987192379355577800952 y[1] (numeric) = 1.0839746540987192379355954304312 absolute error = 3.76503360e-23 relative error = 3.4733594422744801584469421781328e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0809 y[1] (analytic) = 1.0840824036351918075073447420074 y[1] (numeric) = 1.0840824036351918075073824368713 absolute error = 3.76948639e-23 relative error = 3.4771216444063623618901337940493e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 1.0841901623308403330945669950168 y[1] (numeric) = 1.0841901623308403330946047344035 absolute error = 3.77393867e-23 relative error = 3.4808825989405940039358259968531e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0811 y[1] (analytic) = 1.0842979301845872277416372723815 y[1] (numeric) = 1.0842979301845872277416750562857 absolute error = 3.77839042e-23 relative error = 3.4846422877121784604347000850358e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0812 y[1] (analytic) = 1.0844057071953548129119846930783 y[1] (numeric) = 1.0844057071953548129120225214948 absolute error = 3.78284165e-23 relative error = 3.4884007202283417436291301641315e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0813 y[1] (analytic) = 1.0845134933620653184988315471598 y[1] (numeric) = 1.0845134933620653184988694200834 absolute error = 3.78729236e-23 relative error = 3.4921578967718852888970719821583e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0814 y[1] (analytic) = 1.0846212886836408828359709968133 y[1] (numeric) = 1.0846212886836408828360089142387 absolute error = 3.79174254e-23 relative error = 3.4959138084057689984257606760542e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0815 y[1] (analytic) = 1.0847290931590035527085456930135 y[1] (numeric) = 1.0847290931590035527085836549354 absolute error = 3.79619219e-23 relative error = 3.4996684554154760577504955515993e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.3MB, time=14.41 NO POLE x[1] = 0.0816 y[1] (analytic) = 1.0848369067870752833638273076623 y[1] (numeric) = 1.0848369067870752833638653140755 absolute error = 3.80064132e-23 relative error = 3.5034218473044308992100622031569e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0817 y[1] (analytic) = 1.0849447295667779385219969811074 y[1] (numeric) = 1.0849447295667779385220350320065 absolute error = 3.80508991e-23 relative error = 3.5071739659211811973853798297887e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0818 y[1] (analytic) = 1.0850525614970332903869266849307 y[1] (numeric) = 1.0850525614970332903869647803106 absolute error = 3.80953799e-23 relative error = 3.5109248392022858649979227798221e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0819 y[1] (analytic) = 1.0851604025767630196569614999015 y[1] (numeric) = 1.085160402576763019656999639757 absolute error = 3.81398555e-23 relative error = 3.5146744582123682636645262820568e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 1.0852682528048887155357028089837 y[1] (numeric) = 1.0852682528048887155357409933095 absolute error = 3.81843258e-23 relative error = 3.5184228140196818182719541416379e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0821 y[1] (analytic) = 1.0853761121803318757427924052904 y[1] (numeric) = 1.0853761121803318757428306340814 absolute error = 3.82287910e-23 relative error = 3.5221699253362971477294264046883e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0822 y[1] (analytic) = 1.0854839807020139065246975148793 y[1] (numeric) = 1.0854839807020139065247357881302 absolute error = 3.82732509e-23 relative error = 3.5259157740170040035093566878604e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0823 y[1] (analytic) = 1.0855918583688561226654967342783 y[1] (numeric) = 1.0855918583688561226655350519838 absolute error = 3.83177055e-23 relative error = 3.5296603603470128136833362620319e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0824 y[1] (analytic) = 1.0856997451797797474976668826363 y[1] (numeric) = 1.0856997451797797474977052447911 absolute error = 3.83621548e-23 relative error = 3.5334036846114996349872208964323e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0825 y[1] (analytic) = 1.0858076411337059129128707683887 y[1] (numeric) = 1.0858076411337059129129091749877 absolute error = 3.84065990e-23 relative error = 3.5371457655150749637392833371637e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0826 y[1] (analytic) = 1.0859155462295556593727458703327 y[1] (numeric) = 1.0859155462295556593727843213706 absolute error = 3.84510379e-23 relative error = 3.5408865849197166252140975760195e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0827 y[1] (analytic) = 1.0860234604662499359196939330013 y[1] (numeric) = 1.0860234604662499359197324284729 absolute error = 3.84954716e-23 relative error = 3.5446261523184022964128911754343e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0828 y[1] (analytic) = 1.0861313838427096001876714762307 y[1] (numeric) = 1.0861313838427096001877100161306 absolute error = 3.85398999e-23 relative error = 3.5483644495794476213700904840875e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0829 y[1] (analytic) = 1.086239316357855418412981218811 y[1] (numeric) = 1.0862393163578554184130198031341 absolute error = 3.85843231e-23 relative error = 3.5521015046088252893092931382089e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 1.0863472580106080654450644161152 y[1] (numeric) = 1.0863472580106080654451030448562 absolute error = 3.86287410e-23 relative error = 3.5558372992756975736917470047272e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0831 y[1] (analytic) = 1.0864552087998881247572941115952 y[1] (numeric) = 1.0864552087998881247573327847488 absolute error = 3.86731536e-23 relative error = 3.5595718338650006829097386451136e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.3MB, time=14.68 NO POLE x[1] = 0.0832 y[1] (analytic) = 1.0865631687246160884577693020388 y[1] (numeric) = 1.0865631687246160884578080195999 absolute error = 3.87175611e-23 relative error = 3.5633051270682974014100353963041e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0833 y[1] (analytic) = 1.0866711377837123573001100164806 y[1] (numeric) = 1.0866711377837123573001487784438 absolute error = 3.87619632e-23 relative error = 3.5670371515577199924981806752380e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0834 y[1] (analytic) = 1.0867791159760972406942533086559 y[1] (numeric) = 1.086779115976097240694292115016 absolute error = 3.88063601e-23 relative error = 3.5707679260238482594032735830898e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0835 y[1] (analytic) = 1.0868871033006909567172501628929 y[1] (numeric) = 1.0868871033006909567172890136446 absolute error = 3.88507517e-23 relative error = 3.5744974415481503275483467446822e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0836 y[1] (analytic) = 1.0869950997564136321240633133328 y[1] (numeric) = 1.086995099756413632124102208471 absolute error = 3.88951382e-23 relative error = 3.5782257168147372566805239866752e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0837 y[1] (analytic) = 1.0871031053421853023583659763717 y[1] (numeric) = 1.0871031053421853023584049158911 absolute error = 3.89395194e-23 relative error = 3.5819527337053355401681648130741e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0838 y[1] (analytic) = 1.0872111200569259115633414962144 y[1] (numeric) = 1.0872111200569259115633804801096 absolute error = 3.89838952e-23 relative error = 3.5856784833067950811289539751825e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0839 y[1] (analytic) = 1.0873191438995553125924839034335 y[1] (numeric) = 1.0873191438995553125925229316994 absolute error = 3.90282659e-23 relative error = 3.5894029934973134821044226780992e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 1.0874271768689932670203993864259 y[1] (numeric) = 1.0874271768689932670204384590573 absolute error = 3.90726314e-23 relative error = 3.5931262553600163810306737569657e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0841 y[1] (analytic) = 1.0875352189641594451536086756576 y[1] (numeric) = 1.0875352189641594451536477926491 absolute error = 3.91169915e-23 relative error = 3.5968482507865458258841563940082e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0842 y[1] (analytic) = 1.0876432701839734260413503405892 y[1] (numeric) = 1.0876432701839734260413895019355 absolute error = 3.91613463e-23 relative error = 3.6005689892583907473154243862962e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0843 y[1] (analytic) = 1.0877513305273546974863849991746 y[1] (numeric) = 1.0877513305273546974864242048706 absolute error = 3.92056960e-23 relative error = 3.6042884894466288852933082348520e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0844 y[1] (analytic) = 1.0878593999932226560558004398248 y[1] (numeric) = 1.0878593999932226560558396898653 absolute error = 3.92500405e-23 relative error = 3.6080067424379039264141052698808e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0845 y[1] (analytic) = 1.0879674785804966070918176557277 y[1] (numeric) = 1.0879674785804966070918569501073 absolute error = 3.92943796e-23 relative error = 3.6117237301310275277419044769328e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0846 y[1] (analytic) = 1.0880755662880957647225977914166 y[1] (numeric) = 1.0880755662880957647226371301301 absolute error = 3.93387135e-23 relative error = 3.6154394711942343173047895600623e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0847 y[1] (analytic) = 1.08818366311493925187305000148 y[1] (numeric) = 1.0881836631149392518730893845222 absolute error = 3.93830422e-23 relative error = 3.6191539659091694622739600462839e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.3MB, time=14.97 NO POLE x[1] = 0.0848 y[1] (analytic) = 1.0882917690599461002756402213037 y[1] (numeric) = 1.0882917690599461002756796486692 absolute error = 3.94273655e-23 relative error = 3.6228671961800192938631561309724e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0849 y[1] (analytic) = 1.0883998841220352504812008497363 y[1] (numeric) = 1.08839988412203525048124032142 absolute error = 3.94716837e-23 relative error = 3.6265791898572358724873419484826e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 1.0885080083001255518697413435729 y[1] (numeric) = 1.0885080083001255518697808595694 absolute error = 3.95159965e-23 relative error = 3.6302899196589624303574208856140e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0851 y[1] (analytic) = 1.0886161415931357626612597237449 y[1] (numeric) = 1.0886161415931357626612992840491 absolute error = 3.95603042e-23 relative error = 3.6339994134301054667207657286080e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0852 y[1] (analytic) = 1.0887242839999845499265549931121 y[1] (numeric) = 1.0887242839999845499265945977187 absolute error = 3.96046066e-23 relative error = 3.6377076530792769593907685248854e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0853 y[1] (analytic) = 1.088832435519590489598040465745 y[1] (numeric) = 1.0888324355195904895980801146486 absolute error = 3.96489036e-23 relative error = 3.6414146297065035445250403435122e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0854 y[1] (analytic) = 1.0889405961508720664805580075917 y[1] (numeric) = 1.0889405961508720664805977007872 absolute error = 3.96931955e-23 relative error = 3.6451203711483754408899510085840e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0855 y[1] (analytic) = 1.0890487658927476742621931884208 y[1] (numeric) = 1.0890487658927476742622329259029 absolute error = 3.97374821e-23 relative error = 3.6488248593188754895222709871761e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0856 y[1] (analytic) = 1.0891569447441356155250913449314 y[1] (numeric) = 1.0891569447441356155251311266947 absolute error = 3.97817633e-23 relative error = 3.6525280853206622580255299126993e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0857 y[1] (analytic) = 1.0892651327039541017562745549221 y[1] (numeric) = 1.0892651327039541017563143809616 absolute error = 3.98260395e-23 relative error = 3.6562300861625136770477303440099e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0858 y[1] (analytic) = 1.089373329771121253358459522413 y[1] (numeric) = 1.0893733297711212533584993927233 absolute error = 3.98703103e-23 relative error = 3.6599308254018669431834888244220e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0859 y[1] (analytic) = 1.0894815359445550996608763736082 y[1] (numeric) = 1.089481535944555099660916288184 absolute error = 3.99145758e-23 relative error = 3.6636303125041025179486679350505e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.086 y[1] (analytic) = 1.0895897512231735789300883635951 y[1] (numeric) = 1.0895897512231735789301283224312 absolute error = 3.99588361e-23 relative error = 3.6673285569309188195890166113753e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0861 y[1] (analytic) = 1.0896979756058945383808124936697 y[1] (numeric) = 1.0896979756058945383808524967609 absolute error = 4.00030912e-23 relative error = 3.6710255589634785396087929904951e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0862 y[1] (analytic) = 1.0898062090916357341867410391808 y[1] (numeric) = 1.0898062090916357341867810865216 absolute error = 4.00473408e-23 relative error = 3.6747212913550800081145694006412e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=209.8MB, alloc=4.3MB, time=15.25 x[1] = 0.0863 y[1] (analytic) = 1.089914451679314831491363987783 y[1] (numeric) = 1.0899144516793148314914040793683 absolute error = 4.00915853e-23 relative error = 3.6784157910951467847975418807697e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0864 y[1] (analytic) = 1.0900227033678494044187923879938 y[1] (numeric) = 1.0900227033678494044188325238184 absolute error = 4.01358246e-23 relative error = 3.6821090492878829324845781650283e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0865 y[1] (analytic) = 1.0901309641561569360845826079432 y[1] (numeric) = 1.0901309641561569360846227880018 absolute error = 4.01800586e-23 relative error = 3.6858010570411029989926471475335e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0866 y[1] (analytic) = 1.0902392340431548186065615042088 y[1] (numeric) = 1.0902392340431548186066017284961 absolute error = 4.02242873e-23 relative error = 3.6894918146385297394176155730373e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0867 y[1] (analytic) = 1.0903475130277603531156525006289 y[1] (numeric) = 1.0903475130277603531156927691396 absolute error = 4.02685107e-23 relative error = 3.6931813223638507830219144569339e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0868 y[1] (analytic) = 1.0904558011088907497667025769839 y[1] (numeric) = 1.0904558011088907497667428897128 absolute error = 4.03127289e-23 relative error = 3.6968695896711957595344860647354e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0869 y[1] (analytic) = 1.0905640982854631277493101674392 y[1] (numeric) = 1.090564098285463127749350524381 absolute error = 4.03569418e-23 relative error = 3.7005566076718835249614161126290e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 1.0906724045563945152986539686397 y[1] (numeric) = 1.0906724045563945152986943697892 absolute error = 4.04011495e-23 relative error = 3.7042423858181524625738852865137e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0871 y[1] (analytic) = 1.0907807199206018497063226573496 y[1] (numeric) = 1.0907807199206018497063631027015 absolute error = 4.04453519e-23 relative error = 3.7079269152230730100297821156171e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0872 y[1] (analytic) = 1.0908890443770019773311455175269 y[1] (numeric) = 1.0908890443770019773311860070759 absolute error = 4.04895490e-23 relative error = 3.7116101961701575370862462350004e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0873 y[1] (analytic) = 1.0909973779245116536100239767264 y[1] (numeric) = 1.0909973779245116536100645104673 absolute error = 4.05337409e-23 relative error = 3.7152922381088080556416763271715e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0874 y[1] (analytic) = 1.0911057205620475430687640517216 y[1] (numeric) = 1.0911057205620475430688046296491 absolute error = 4.05779275e-23 relative error = 3.7189730321547213083425566120779e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0875 y[1] (analytic) = 1.0912140722885262193329097032376 y[1] (numeric) = 1.0912140722885262193329503253464 absolute error = 4.06221088e-23 relative error = 3.7226525785913042419133534374056e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0876 y[1] (analytic) = 1.0913224331028641651385770996866 y[1] (numeric) = 1.0913224331028641651386177659715 absolute error = 4.06662849e-23 relative error = 3.7263308868651232832235984093207e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0877 y[1] (analytic) = 1.0914308030039777723432897897978 y[1] (numeric) = 1.0914308030039777723433305002535 absolute error = 4.07104557e-23 relative error = 3.7300079480945003872534268199137e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0878 y[1] (analytic) = 1.0915391819907833419368147840331 y[1] (numeric) = 1.0915391819907833419368555386543 absolute error = 4.07546212e-23 relative error = 3.7336837625627369247800465715845e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.3MB, time=15.53 NO POLE x[1] = 0.0879 y[1] (analytic) = 1.0916475700621970840519995446803 y[1] (numeric) = 1.0916475700621970840520403434617 absolute error = 4.07987814e-23 relative error = 3.7373583305530989363006123006372e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 1.0917559672171351179756098845156 y[1] (numeric) = 1.091755967217135117975650727452 absolute error = 4.08429364e-23 relative error = 3.7410316615083731883353081998935e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0881 y[1] (analytic) = 1.0918643734545134721591687739272 y[1] (numeric) = 1.0918643734545134721592096610133 absolute error = 4.08870861e-23 relative error = 3.7447037465503801157068606053247e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0882 y[1] (analytic) = 1.0919727887732480842297960563906 y[1] (numeric) = 1.0919727887732480842298369876212 absolute error = 4.09312306e-23 relative error = 3.7483745951200173363182830017664e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0883 y[1] (analytic) = 1.0920812131722548010010490721888 y[1] (numeric) = 1.0920812131722548010010900475586 absolute error = 4.09753698e-23 relative error = 3.7520441983408539537504666393405e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0884 y[1] (analytic) = 1.0921896466504493784837641902673 y[1] (numeric) = 1.092189646650449378483805209771 absolute error = 4.10195037e-23 relative error = 3.7557125564959797301205333723448e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0885 y[1] (analytic) = 1.0922980892067474818968992481169 y[1] (numeric) = 1.0922980892067474818969403117493 absolute error = 4.10636324e-23 relative error = 3.7593796790234590604209383468483e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0886 y[1] (analytic) = 1.0924065408400646856783768995751 y[1] (numeric) = 1.0924065408400646856784180073309 absolute error = 4.11077558e-23 relative error = 3.7630455570494829854495500992372e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0887 y[1] (analytic) = 1.0925150015493164734959288704379 y[1] (numeric) = 1.0925150015493164734959700223118 absolute error = 4.11518739e-23 relative error = 3.7667101908570352355987798715136e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0888 y[1] (analytic) = 1.0926234713334182382579411217732 y[1] (numeric) = 1.0926234713334182382579823177599 absolute error = 4.11959867e-23 relative error = 3.7703735807290640593780822369097e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0889 y[1] (analytic) = 1.092731950191285282124299920828 y[1] (numeric) = 1.0927319501912852821243411609223 absolute error = 4.12400943e-23 relative error = 3.7740357360998573433063331448546e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 1.0928404381218328165172388194208 y[1] (numeric) = 1.0928404381218328165172801036173 absolute error = 4.12841965e-23 relative error = 3.7776966389486335776762145602630e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0891 y[1] (analytic) = 1.0929489351239759621321865397095 y[1] (numeric) = 1.0929489351239759621322278680031 absolute error = 4.13282936e-23 relative error = 3.7813563170096347753283726457960e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0892 y[1] (analytic) = 1.0930574411966297489486157672292 y[1] (numeric) = 1.0930574411966297489486571396145 absolute error = 4.13723853e-23 relative error = 3.7850147431142674059108593546073e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0893 y[1] (analytic) = 1.0931659563387091162408928510873 y[1] (numeric) = 1.093165956338709116240934267559 absolute error = 4.14164717e-23 relative error = 3.7886719266957690365379392462876e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0894 y[1] (analytic) = 1.0932744805491289125891284112113 y[1] (numeric) = 1.0932744805491289125891698717642 absolute error = 4.14605529e-23 relative error = 3.7923278771837088126493835825268e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.3MB, time=15.80 NO POLE x[1] = 0.0895 y[1] (analytic) = 1.0933830138268038958900288525388 y[1] (numeric) = 1.0933830138268038958900703571676 absolute error = 4.15046288e-23 relative error = 3.7959825857121367308113647977207e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0896 y[1] (analytic) = 1.0934915561706487333677487860411 y[1] (numeric) = 1.0934915561706487333677903347405 absolute error = 4.15486994e-23 relative error = 3.7996360525637172093275576338604e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0897 y[1] (analytic) = 1.0936001075795780015847443564727 y[1] (numeric) = 1.0936001075795780015847859492375 absolute error = 4.15927648e-23 relative error = 3.8032882871651893273581530939853e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0898 y[1] (analytic) = 1.0937086680525061864526274767378 y[1] (numeric) = 1.0937086680525061864526691135627 absolute error = 4.16368249e-23 relative error = 3.8069392806532206584982377353800e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0899 y[1] (analytic) = 1.093817237588347683243020968765 y[1] (numeric) = 1.0938172375883476832430626496447 absolute error = 4.16808797e-23 relative error = 3.8105890333103689885082525420979e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 1.093925816186016796598414610782 y[1] (numeric) = 1.0939258161860167965984563357113 absolute error = 4.17249293e-23 relative error = 3.8142375545605441206949968470341e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0901 y[1] (analytic) = 1.0940344038444277405430220908818 y[1] (numeric) = 1.0940344038444277405430638598554 absolute error = 4.17689736e-23 relative error = 3.8178848355430301168225069057149e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0902 y[1] (analytic) = 1.0941430005624946384936388667717 y[1] (numeric) = 1.0941430005624946384936806797842 absolute error = 4.18130125e-23 relative error = 3.8215308674007048221751255305650e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0903 y[1] (analytic) = 1.0942516063391315232705009315955 y[1] (numeric) = 1.0942516063391315232705427886417 absolute error = 4.18570462e-23 relative error = 3.8251756686960369411583536539785e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0904 y[1] (analytic) = 1.0943602211732523371081444857231 y[1] (numeric) = 1.0943602211732523371081863867976 absolute error = 4.19010745e-23 relative error = 3.8288192214331665857599896388030e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0905 y[1] (analytic) = 1.0944688450637709316662665143953 y[1] (numeric) = 1.0944688450637709316663084594929 absolute error = 4.19450976e-23 relative error = 3.8324615441708624942659612033807e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0906 y[1] (analytic) = 1.0945774780096010680405862711183 y[1] (numeric) = 1.0945774780096010680406282602337 absolute error = 4.19891154e-23 relative error = 3.8361026280527666015592854898578e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0907 y[1] (analytic) = 1.0946861200096564167737076666972 y[1] (numeric) = 1.0946861200096564167737496998251 absolute error = 4.20331279e-23 relative error = 3.8397424733611510908474089513856e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0908 y[1] (analytic) = 1.0947947710628505578659825638008 y[1] (numeric) = 1.0947947710628505578660246409361 absolute error = 4.20771353e-23 relative error = 3.8433810986465164198875165064439e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0909 y[1] (analytic) = 1.0949034311680969807863749769496 y[1] (numeric) = 1.0949034311680969807864170980868 absolute error = 4.21211372e-23 relative error = 3.8470184676527219783259138292340e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 1.0950121003243090844833261778163 y[1] (numeric) = 1.0950121003243090844833683429501 absolute error = 4.21651338e-23 relative error = 3.8506545989320097306311504471844e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.3MB, time=16.09 NO POLE x[1] = 0.0911 y[1] (analytic) = 1.0951207785304001773956207057327 y[1] (numeric) = 1.095120778530400177395662914858 absolute error = 4.22091253e-23 relative error = 3.8542895110293343001624254622170e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0912 y[1] (analytic) = 1.0952294657852834774632532832932 y[1] (numeric) = 1.0952294657852834774632955364046 absolute error = 4.22531114e-23 relative error = 3.8579231768298314288987728793720e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0913 y[1] (analytic) = 1.095338162087872112138296636945 y[1] (numeric) = 1.0953381620878721121383389340374 absolute error = 4.22970924e-23 relative error = 3.8615556240070789674348805460541e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0914 y[1] (analytic) = 1.0954468674370791183957702224592 y[1] (numeric) = 1.0954468674370791183958125635271 absolute error = 4.23410679e-23 relative error = 3.8651868163228838317419187848782e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0915 y[1] (analytic) = 1.0955555818318174427445098551706 y[1] (numeric) = 1.0955555818318174427445522402088 absolute error = 4.23850382e-23 relative error = 3.8688167814480338249573950426135e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0916 y[1] (analytic) = 1.0956643052709999412380382448811 y[1] (numeric) = 1.0956643052709999412380806738843 absolute error = 4.24290032e-23 relative error = 3.8724455105348781935517585364615e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0917 y[1] (analytic) = 1.0957730377535393794854364353149 y[1] (numeric) = 1.0957730377535393794854789082778 absolute error = 4.24729629e-23 relative error = 3.8760730038653308767507727145206e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0918 y[1] (analytic) = 1.0958817792783484326622161480189 y[1] (numeric) = 1.0958817792783484326622586649362 absolute error = 4.25169173e-23 relative error = 3.8796992617212698371720326040802e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0919 y[1] (analytic) = 1.0959905298443396855211930305984 y[1] (numeric) = 1.0959905298443396855212355914649 absolute error = 4.25608665e-23 relative error = 3.8833242935087034746100914583351e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 1.09609928945042563240336080918 y[1] (numeric) = 1.0960992894504256324034034139903 absolute error = 4.26048103e-23 relative error = 3.8869480812601995514836473334115e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0921 y[1] (analytic) = 1.0962080580955186772487663449923 y[1] (numeric) = 1.0962080580955186772488089937412 absolute error = 4.26487489e-23 relative error = 3.8905706435049557338589869647165e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0922 y[1] (analytic) = 1.0963168357785311336073855949569 y[1] (numeric) = 1.096316835778531133607428287639 absolute error = 4.26926821e-23 relative error = 3.8941919622790890711097138459757e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0923 y[1] (analytic) = 1.0964256224983752246500004761788 y[1] (numeric) = 1.096425622498375224650043212789 absolute error = 4.27366102e-23 relative error = 3.8978120652286498977385164550112e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0924 y[1] (analytic) = 1.0965344182539630831790766342305 y[1] (numeric) = 1.0965344182539630831791194147634 absolute error = 4.27805329e-23 relative error = 3.9014309252709481057146281841191e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0925 y[1] (analytic) = 1.0966432230442067516396421151175 y[1] (numeric) = 1.0966432230442067516396849395678 absolute error = 4.28244503e-23 relative error = 3.9050485518090604099136741317366e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0926 y[1] (analytic) = 1.0967520368680181821301669408191 y[1] (numeric) = 1.0967520368680181821302098091815 absolute error = 4.28683624e-23 relative error = 3.9086649451245766912595512321799e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.3MB, time=16.37 NO POLE x[1] = 0.0927 y[1] (analytic) = 1.0968608597243092364134435882948 y[1] (numeric) = 1.0968608597243092364134865005641 absolute error = 4.29122693e-23 relative error = 3.9122801146159773557449932481052e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0928 y[1] (analytic) = 1.0969696916119916859274683718474 y[1] (numeric) = 1.0969696916119916859275113280182 absolute error = 4.29561708e-23 relative error = 3.9158940423300222276798716939464e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0929 y[1] (analytic) = 1.0970785325299772117963237287336 y[1] (numeric) = 1.0970785325299772117963667288007 absolute error = 4.30000671e-23 relative error = 3.9195067467811417740184629078284e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 1.0971873824771774048410614079145 y[1] (numeric) = 1.0971873824771774048411044518726 absolute error = 4.30439581e-23 relative error = 3.9231182191338549583402159738535e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0931 y[1] (analytic) = 1.0972962414525037655905865618359 y[1] (numeric) = 1.0972962414525037655906296496796 absolute error = 4.30878437e-23 relative error = 3.9267284505562619435525816873176e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0932 y[1] (analytic) = 1.0974051094548677042925427411296 y[1] (numeric) = 1.0974051094548677042925858728538 absolute error = 4.31317242e-23 relative error = 3.9303374686696637372145370837272e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0933 y[1] (analytic) = 1.097513986483180540924197792129 y[1] (numeric) = 1.0975139864831805409242409677284 absolute error = 4.31755994e-23 relative error = 3.9339452555269707546745529734669e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0934 y[1] (analytic) = 1.0976228725363535052033306570867 y[1] (numeric) = 1.0976228725363535052033738765558 absolute error = 4.32194691e-23 relative error = 3.9375517931882894417344109785910e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0935 y[1] (analytic) = 1.0977317676132977365991190769872 y[1] (numeric) = 1.0977317676132977365991623403208 absolute error = 4.32633336e-23 relative error = 3.9411571092693879062202245381884e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0936 y[1] (analytic) = 1.0978406717129242843430281968468 y[1] (numeric) = 1.0978406717129242843430715040398 absolute error = 4.33071930e-23 relative error = 3.9447612131575729673486487067253e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0937 y[1] (analytic) = 1.09794958483414410743970007339 y[1] (numeric) = 1.0979495848341441074397434244369 absolute error = 4.33510469e-23 relative error = 3.9483640686970699540514603072017e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0938 y[1] (analytic) = 1.0980585069758680746778440849931 y[1] (numeric) = 1.0980585069758680746778874798886 absolute error = 4.33948955e-23 relative error = 3.9519656943884216371839496492043e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0939 y[1] (analytic) = 1.0981674381370069646411282437887 y[1] (numeric) = 1.0981674381370069646411716825275 absolute error = 4.34387388e-23 relative error = 3.9555660905127473798776704735835e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 1.0982763783164714657190714098198 y[1] (numeric) = 1.0982763783164714657191148923966 absolute error = 4.34825768e-23 relative error = 3.9591652573511302161340515126523e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0941 y[1] (analytic) = 1.0983853275131721761179364071355 y[1] (numeric) = 1.0983853275131721761179799335451 absolute error = 4.35264096e-23 relative error = 3.9627632042888899434606010177039e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0942 memory used=228.8MB, alloc=4.3MB, time=16.64 y[1] (analytic) = 1.0984942857260196038716240417195 y[1] (numeric) = 1.0984942857260196038716676119565 absolute error = 4.35702370e-23 relative error = 3.9663599133975876322950504812263e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0943 y[1] (analytic) = 1.0986032529539241668525680211417 y[1] (numeric) = 1.0986032529539241668526116352008 absolute error = 4.36140591e-23 relative error = 3.9699553940633734882447244746934e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0944 y[1] (analytic) = 1.0987122291957961927826307758246 y[1] (numeric) = 1.0987122291957961927826744337007 absolute error = 4.36578761e-23 relative error = 3.9735496647703136685532183806566e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0945 y[1] (analytic) = 1.0988212144505459192440001818166 y[1] (numeric) = 1.0988212144505459192440438835042 absolute error = 4.37016876e-23 relative error = 3.9771426893912466737684094962234e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0946 y[1] (analytic) = 1.0989302087170834936900871849596 y[1] (numeric) = 1.0989302087170834936901309304535 absolute error = 4.37454939e-23 relative error = 3.9807344955117304414893303674323e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0947 y[1] (analytic) = 1.0990392119943189734564243263472 y[1] (numeric) = 1.099039211994318973456468115642 absolute error = 4.37892948e-23 relative error = 3.9843250652121728450701577250219e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0948 y[1] (analytic) = 1.0991482242811623257715651689591 y[1] (numeric) = 1.0991482242811623257716090020496 absolute error = 4.38330905e-23 relative error = 3.9879144169719813035390961209568e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0949 y[1] (analytic) = 1.0992572455765234277679846253674 y[1] (numeric) = 1.0992572455765234277680285022483 absolute error = 4.38768809e-23 relative error = 3.9915025419721525442914780991494e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 1.0993662758793120664929801864023 y[1] (numeric) = 1.0993662758793120664930241070683 absolute error = 4.39206660e-23 relative error = 3.9950894404934057561984602338948e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0951 y[1] (analytic) = 1.0994753151884379389195740506702 y[1] (numeric) = 1.0994753151884379389196180151159 absolute error = 4.39644457e-23 relative error = 3.9986751037211762276316022268199e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0952 y[1] (analytic) = 1.099584363502810651957416154814 y[1] (numeric) = 1.0995843635028106519574601630342 absolute error = 4.40082202e-23 relative error = 4.0022595501275069208105801001551e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0953 y[1] (analytic) = 1.0996934208213397224636881044083 y[1] (numeric) = 1.0996934208213397224637321563976 absolute error = 4.40519893e-23 relative error = 4.0058427618034144623573447498288e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0954 y[1] (analytic) = 1.0998024871429345772540080053777 y[1] (numeric) = 1.0998024871429345772540521011309 absolute error = 4.40957532e-23 relative error = 4.0094247572172607455609410282610e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0955 y[1] (analytic) = 1.099911562466504553113336195832 y[1] (numeric) = 1.0999115624665045531133803353438 absolute error = 4.41395118e-23 relative error = 4.0130055275552368906969415520613e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0956 y[1] (analytic) = 1.1000206467909588968068818782074 y[1] (numeric) = 1.1000206467909588968069260614725 absolute error = 4.41832651e-23 relative error = 4.0165850730978428396257039159492e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0957 y[1] (analytic) = 1.1001297401152067650910106516052 y[1] (numeric) = 1.1001297401152067650910548786183 absolute error = 4.42270131e-23 relative error = 4.0201633941255419385585363952874e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=232.7MB, alloc=4.3MB, time=16.92 x[1] = 0.0958 y[1] (analytic) = 1.1002388424381572247241529442193 y[1] (numeric) = 1.1002388424381572247241972149751 absolute error = 4.42707558e-23 relative error = 4.0237404909187609225387036293957e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0959 y[1] (analytic) = 1.1003479537587192524777133457425 y[1] (numeric) = 1.1003479537587192524777576602357 absolute error = 4.43144932e-23 relative error = 4.0273163637578898999399975177896e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 1.1004570740758017351469808396437 y[1] (numeric) = 1.1004570740758017351470251978689 absolute error = 4.43582252e-23 relative error = 4.0308910038361491488043853444717e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0961 y[1] (analytic) = 1.1005662033883134695620399352054 y[1] (numeric) = 1.1005662033883134695620843371574 absolute error = 4.44019520e-23 relative error = 4.0344644296090229108315475622402e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0962 y[1] (analytic) = 1.1006753416951631625986826992144 y[1] (numeric) = 1.1006753416951631625987271448879 absolute error = 4.44456735e-23 relative error = 4.0380366322687569722003220556046e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0963 y[1] (analytic) = 1.1007844889952594311893216871945 y[1] (numeric) = 1.1007844889952594311893661765841 absolute error = 4.44893896e-23 relative error = 4.0416076030111644486914959268282e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0964 y[1] (analytic) = 1.1008936452875108023339037740729 y[1] (numeric) = 1.1008936452875108023339483071734 absolute error = 4.45331005e-23 relative error = 4.0451773602862134893704176326080e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0965 y[1] (analytic) = 1.1010028105708257131108248841725 y[1] (numeric) = 1.1010028105708257131108694609784 absolute error = 4.45768059e-23 relative error = 4.0487458771234850413201710805511e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0966 y[1] (analytic) = 1.1011119848441125106878456204178 y[1] (numeric) = 1.101111984844112510687890240924 absolute error = 4.46205062e-23 relative error = 4.0523131901354292580120621852174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0967 y[1] (analytic) = 1.1012211681062794523330077926492 y[1] (numeric) = 1.1012211681062794523330524568503 absolute error = 4.46642011e-23 relative error = 4.0558792723542555188199865495625e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0968 y[1] (analytic) = 1.1013303603562347054255518449328 y[1] (numeric) = 1.1013303603562347054255965528235 absolute error = 4.47078907e-23 relative error = 4.0594441331426522329216844786037e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0969 y[1] (analytic) = 1.1014395615928863474668351817592 y[1] (numeric) = 1.1014395615928863474668799333342 absolute error = 4.47515750e-23 relative error = 4.0630077727806420799758472746500e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 1.1015487718151423660912513930206 y[1] (numeric) = 1.1015487718151423660912961882746 absolute error = 4.47952540e-23 relative error = 4.0665701915482109436126255126671e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0971 y[1] (analytic) = 1.1016579910219106590771503776581 y[1] (numeric) = 1.1016579910219106590771952165857 absolute error = 4.48389276e-23 relative error = 4.0701313806480805883061111786462e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0972 y[1] (analytic) = 1.1017672192120990343577593658687 y[1] (numeric) = 1.1017672192120990343578042484646 absolute error = 4.48825959e-23 relative error = 4.0736913494391903835653963525516e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0973 y[1] (analytic) = 1.1018764563846152100321048397643 y[1] (numeric) = 1.1018764563846152100321497660232 absolute error = 4.49262589e-23 relative error = 4.0772500982014154199577910982009e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.3MB, time=17.21 NO POLE x[1] = 0.0974 y[1] (analytic) = 1.101985702538366814375935352372 y[1] (numeric) = 1.1019857025383668143759803222887 absolute error = 4.49699167e-23 relative error = 4.0808076362891218281614645139962e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0975 y[1] (analytic) = 1.102094957672261385852645244868 y[1] (numeric) = 1.1020949576722613858526902584371 absolute error = 4.50135691e-23 relative error = 4.0843639458321555802639396483076e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0976 y[1] (analytic) = 1.1022042217852063731241992619339 y[1] (numeric) = 1.1022042217852063731242443191501 absolute error = 4.50572162e-23 relative error = 4.0879190361857087462299306090197e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0977 y[1] (analytic) = 1.1023134948761091350620580651283 y[1] (numeric) = 1.1023134948761091350621031659864 absolute error = 4.51008581e-23 relative error = 4.0914729167013383234687631750502e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0978 y[1] (analytic) = 1.1024227769438769407581046441634 y[1] (numeric) = 1.1024227769438769407581497886579 absolute error = 4.51444945e-23 relative error = 4.0950255604432466856822136077795e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0979 y[1] (analytic) = 1.1025320679874169695355716259763 y[1] (numeric) = 1.102532067987416969535616814102 absolute error = 4.51881257e-23 relative error = 4.0985769949065758323028793212848e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 1.1026413680056363109599694814882 y[1] (numeric) = 1.1026413680056363109600147132398 absolute error = 4.52317516e-23 relative error = 4.1021272112991131087689844081421e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0981 y[1] (analytic) = 1.1027506769974419648500156299402 y[1] (numeric) = 1.1027506769974419648500609053123 absolute error = 4.52753721e-23 relative error = 4.1056762008322053961760415851297e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0982 y[1] (analytic) = 1.1028599949617408412885644406962 y[1] (numeric) = 1.1028599949617408412886097596837 absolute error = 4.53189875e-23 relative error = 4.1092239909900943073487117128357e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0983 y[1] (analytic) = 1.1029693218974397606335381324066 y[1] (numeric) = 1.102969321897439760633583495004 absolute error = 4.53625974e-23 relative error = 4.1127705457811515918433213903521e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0984 y[1] (analytic) = 1.1030786578034454535288585694187 y[1] (numeric) = 1.1030786578034454535289039756207 absolute error = 4.54062020e-23 relative error = 4.1163158836213116196806544465524e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0985 y[1] (analytic) = 1.103188002678664560915379955329 y[1] (numeric) = 1.1031880026786645609154254051303 absolute error = 4.54498013e-23 relative error = 4.1198600047900058822579140942956e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0986 y[1] (analytic) = 1.1032973565220036340418224235656 y[1] (numeric) = 1.1032973565220036340418679169608 absolute error = 4.54933952e-23 relative error = 4.1234029005028891787889870720731e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0987 y[1] (analytic) = 1.1034067193323691344757065248914 y[1] (numeric) = 1.1034067193323691344757520618753 absolute error = 4.55369839e-23 relative error = 4.1269445891676965571107170733170e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0988 y[1] (analytic) = 1.1035160911086674341142886117205 y[1] (numeric) = 1.1035160911086674341143341922877 absolute error = 4.55805672e-23 relative error = 4.1304850529371671732604545026252e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0989 y[1] (analytic) = 1.1036254718498048151954971191357 y[1] (numeric) = 1.103625471849804815195542743281 absolute error = 4.56241453e-23 relative error = 4.1340243102153685568967230462421e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.3MB, time=17.50 NO POLE x[1] = 0.099 y[1] (analytic) = 1.103734861554687470308869742501 y[1] (numeric) = 1.103734861554687470308915410219 absolute error = 4.56677180e-23 relative error = 4.1375623431585586301673763016828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0991 y[1] (analytic) = 1.1038442602222215024064915115563 y[1] (numeric) = 1.1038442602222215024065372228417 absolute error = 4.57112854e-23 relative error = 4.1410991611078891897343772233815e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0992 y[1] (analytic) = 1.1039536678513129248139337608879 y[1] (numeric) = 1.1039536678513129248139795157353 absolute error = 4.57548474e-23 relative error = 4.1446347552841806577318444284373e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0993 y[1] (analytic) = 1.1040630844408676612411939966634 y[1] (numeric) = 1.1040630844408676612412397950676 absolute error = 4.57984042e-23 relative error = 4.1481691440841675411137354668763e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0994 y[1] (analytic) = 1.1041725099897915457936366595229 y[1] (numeric) = 1.1041725099897915457936825014785 absolute error = 4.58419556e-23 relative error = 4.1517023096711422954251331329925e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0995 y[1] (analytic) = 1.104281944496990322982934783516 y[1] (numeric) = 1.1042819444969903229829806690178 absolute error = 4.58855018e-23 relative error = 4.1552342704381742366559716265367e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0996 y[1] (analytic) = 1.1043913879613696477380125509762 y[1] (numeric) = 1.1043913879613696477380584800188 absolute error = 4.59290426e-23 relative error = 4.1587650085520719012118861103914e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0997 y[1] (analytic) = 1.104500840381835085415988743222 y[1] (numeric) = 1.1045008403818350854160347158002 absolute error = 4.59725782e-23 relative error = 4.1622945424022401901254659409760e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0998 y[1] (analytic) = 1.1046103017572921118131210869776 y[1] (numeric) = 1.1046103017572921118131671030858 absolute error = 4.60161082e-23 relative error = 4.1658228360530699297236097133603e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0999 y[1] (analytic) = 1.1047197720866461131757514963997 y[1] (numeric) = 1.1047197720866461131757975560329 absolute error = 4.60596332e-23 relative error = 4.1693499441039623511634359547636e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 1.1048292513688023862112522106067 y[1] (numeric) = 1.1048292513688023862112983137594 absolute error = 4.61031527e-23 relative error = 4.1728758215698558108159626101366e-21 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ; Iterations = 1000 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 17 Seconds Expected Time Remaining = 29 Minutes 4 Seconds Optimized Time Remaining = 29 Minutes 3 Seconds Time to Timeout = 14 Minutes 42 Seconds Percent Done = 1.001 % > quit memory used=242.9MB, alloc=4.3MB, time=17.68