|\^/| 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 > DEBUGMASSIVE, > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_current_iter, > glob_start, > glob_max_sec, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_disp_incr, > glob_clock_sec, > djd_debug2, > glob_dump_analytic, > glob_large_float, > glob_not_yet_start_msg, > glob_initial_pass, > glob_display_flag, > glob_max_opt_iter, > glob_subiter_method, > glob_warned, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > djd_debug, > glob_iter, > glob_no_eqs, > glob_hmax, > glob_optimal_done, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin, > glob_h, > hours_in_day, > glob_log10relerr, > glob_orig_start_sec, > glob_max_trunc_err, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > min_in_hour, > glob_html_log, > glob_smallish_float, > glob_log10_abserr, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_m1, > array_norms, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_y, > array_x, > array_last_rel_error, > array_pole, > array_complex_pole, > array_real_pole, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > 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 DEBUGMASSIVE, INFO, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, glob_current_iter, glob_start, glob_max_sec, glob_small_float, glob_max_hours, glob_log10_relerr, glob_disp_incr, glob_clock_sec, djd_debug2, glob_dump_analytic, glob_large_float, glob_not_yet_start_msg, glob_initial_pass, glob_display_flag, glob_max_opt_iter, glob_subiter_method, glob_warned, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_optimal_expect_sec, glob_log10normmin, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, sec_in_min, glob_log10abserr, glob_optimal_start, djd_debug, glob_iter, glob_no_eqs, glob_hmax, glob_optimal_done, years_in_century, glob_normmax, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_abserr, glob_hmin, glob_h, hours_in_day, glob_log10relerr, glob_orig_start_sec, glob_max_trunc_err, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_percent_done, glob_max_minutes, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, min_in_hour, glob_html_log, glob_smallish_float, glob_log10_abserr, glob_dump, array_const_0D0, array_const_1, array_y_init, array_m1, array_norms, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_y, array_x, array_last_rel_error, array_pole, array_complex_pole, array_real_pole, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher, 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 > DEBUGMASSIVE, > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_current_iter, > glob_start, > glob_max_sec, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_disp_incr, > glob_clock_sec, > djd_debug2, > glob_dump_analytic, > glob_large_float, > glob_not_yet_start_msg, > glob_initial_pass, > glob_display_flag, > glob_max_opt_iter, > glob_subiter_method, > glob_warned, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > djd_debug, > glob_iter, > glob_no_eqs, > glob_hmax, > glob_optimal_done, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin, > glob_h, > hours_in_day, > glob_log10relerr, > glob_orig_start_sec, > glob_max_trunc_err, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > min_in_hour, > glob_html_log, > glob_smallish_float, > glob_log10_abserr, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_m1, > array_norms, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_y, > array_x, > array_last_rel_error, > array_pole, > array_complex_pole, > array_real_pole, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > 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 DEBUGMASSIVE, INFO, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, glob_current_iter, glob_start, glob_max_sec, glob_small_float, glob_max_hours, glob_log10_relerr, glob_disp_incr, glob_clock_sec, djd_debug2, glob_dump_analytic, glob_large_float, glob_not_yet_start_msg, glob_initial_pass, glob_display_flag, glob_max_opt_iter, glob_subiter_method, glob_warned, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_optimal_expect_sec, glob_log10normmin, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, sec_in_min, glob_log10abserr, glob_optimal_start, djd_debug, glob_iter, glob_no_eqs, glob_hmax, glob_optimal_done, years_in_century, glob_normmax, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_abserr, glob_hmin, glob_h, hours_in_day, glob_log10relerr, glob_orig_start_sec, glob_max_trunc_err, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_percent_done, glob_max_minutes, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, min_in_hour, glob_html_log, glob_smallish_float, glob_log10_abserr, glob_dump, array_const_0D0, array_const_1, array_y_init, array_m1, array_norms, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_y, array_x, array_last_rel_error, array_pole, array_complex_pole, array_real_pole, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher, 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 > DEBUGMASSIVE, > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_current_iter, > glob_start, > glob_max_sec, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_disp_incr, > glob_clock_sec, > djd_debug2, > glob_dump_analytic, > glob_large_float, > glob_not_yet_start_msg, > glob_initial_pass, > glob_display_flag, > glob_max_opt_iter, > glob_subiter_method, > glob_warned, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > djd_debug, > glob_iter, > glob_no_eqs, > glob_hmax, > glob_optimal_done, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin, > glob_h, > hours_in_day, > glob_log10relerr, > glob_orig_start_sec, > glob_max_trunc_err, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > min_in_hour, > glob_html_log, > glob_smallish_float, > glob_log10_abserr, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_m1, > array_norms, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_y, > array_x, > array_last_rel_error, > array_pole, > array_complex_pole, > array_real_pole, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > 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 DEBUGMASSIVE, INFO, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, glob_current_iter, glob_start, glob_max_sec, glob_small_float, glob_max_hours, glob_log10_relerr, glob_disp_incr, glob_clock_sec, djd_debug2, glob_dump_analytic, glob_large_float, glob_not_yet_start_msg, glob_initial_pass, glob_display_flag, glob_max_opt_iter, glob_subiter_method, glob_warned, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_optimal_expect_sec, glob_log10normmin, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, sec_in_min, glob_log10abserr, glob_optimal_start, djd_debug, glob_iter, glob_no_eqs, glob_hmax, glob_optimal_done, years_in_century, glob_normmax, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_abserr, glob_hmin, glob_h, hours_in_day, glob_log10relerr, glob_orig_start_sec, glob_max_trunc_err, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_percent_done, glob_max_minutes, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, min_in_hour, glob_html_log, glob_smallish_float, glob_log10_abserr, glob_dump, array_const_0D0, array_const_1, array_y_init, array_m1, array_norms, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_y, array_x, array_last_rel_error, array_pole, array_complex_pole, array_real_pole, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher, 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 > DEBUGMASSIVE, > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_current_iter, > glob_start, > glob_max_sec, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_disp_incr, > glob_clock_sec, > djd_debug2, > glob_dump_analytic, > glob_large_float, > glob_not_yet_start_msg, > glob_initial_pass, > glob_display_flag, > glob_max_opt_iter, > glob_subiter_method, > glob_warned, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > djd_debug, > glob_iter, > glob_no_eqs, > glob_hmax, > glob_optimal_done, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin, > glob_h, > hours_in_day, > glob_log10relerr, > glob_orig_start_sec, > glob_max_trunc_err, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > min_in_hour, > glob_html_log, > glob_smallish_float, > glob_log10_abserr, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_m1, > array_norms, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_y, > array_x, > array_last_rel_error, > array_pole, > array_complex_pole, > array_real_pole, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > 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 DEBUGMASSIVE, INFO, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, glob_current_iter, glob_start, glob_max_sec, glob_small_float, glob_max_hours, glob_log10_relerr, glob_disp_incr, glob_clock_sec, djd_debug2, glob_dump_analytic, glob_large_float, glob_not_yet_start_msg, glob_initial_pass, glob_display_flag, glob_max_opt_iter, glob_subiter_method, glob_warned, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_optimal_expect_sec, glob_log10normmin, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, sec_in_min, glob_log10abserr, glob_optimal_start, djd_debug, glob_iter, glob_no_eqs, glob_hmax, glob_optimal_done, years_in_century, glob_normmax, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_abserr, glob_hmin, glob_h, hours_in_day, glob_log10relerr, glob_orig_start_sec, glob_max_trunc_err, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_percent_done, glob_max_minutes, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, min_in_hour, glob_html_log, glob_smallish_float, glob_log10_abserr, glob_dump, array_const_0D0, array_const_1, array_y_init, array_m1, array_norms, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_y, array_x, array_last_rel_error, array_pole, array_complex_pole, array_real_pole, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher, 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 > DEBUGMASSIVE, > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_current_iter, > glob_start, > glob_max_sec, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_disp_incr, > glob_clock_sec, > djd_debug2, > glob_dump_analytic, > glob_large_float, > glob_not_yet_start_msg, > glob_initial_pass, > glob_display_flag, > glob_max_opt_iter, > glob_subiter_method, > glob_warned, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > djd_debug, > glob_iter, > glob_no_eqs, > glob_hmax, > glob_optimal_done, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin, > glob_h, > hours_in_day, > glob_log10relerr, > glob_orig_start_sec, > glob_max_trunc_err, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > min_in_hour, > glob_html_log, > glob_smallish_float, > glob_log10_abserr, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_m1, > array_norms, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_y, > array_x, > array_last_rel_error, > array_pole, > array_complex_pole, > array_real_pole, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > 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 DEBUGMASSIVE, INFO, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, glob_current_iter, glob_start, glob_max_sec, glob_small_float, glob_max_hours, glob_log10_relerr, glob_disp_incr, glob_clock_sec, djd_debug2, glob_dump_analytic, glob_large_float, glob_not_yet_start_msg, glob_initial_pass, glob_display_flag, glob_max_opt_iter, glob_subiter_method, glob_warned, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_optimal_expect_sec, glob_log10normmin, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, sec_in_min, glob_log10abserr, glob_optimal_start, djd_debug, glob_iter, glob_no_eqs, glob_hmax, glob_optimal_done, years_in_century, glob_normmax, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_abserr, glob_hmin, glob_h, hours_in_day, glob_log10relerr, glob_orig_start_sec, glob_max_trunc_err, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_percent_done, glob_max_minutes, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, min_in_hour, glob_html_log, glob_smallish_float, glob_log10_abserr, glob_dump, array_const_0D0, array_const_1, array_y_init, array_m1, array_norms, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_y, array_x, array_last_rel_error, array_pole, array_complex_pole, array_real_pole, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher, 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 > DEBUGMASSIVE, > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_current_iter, > glob_start, > glob_max_sec, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_disp_incr, > glob_clock_sec, > djd_debug2, > glob_dump_analytic, > glob_large_float, > glob_not_yet_start_msg, > glob_initial_pass, > glob_display_flag, > glob_max_opt_iter, > glob_subiter_method, > glob_warned, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > djd_debug, > glob_iter, > glob_no_eqs, > glob_hmax, > glob_optimal_done, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin, > glob_h, > hours_in_day, > glob_log10relerr, > glob_orig_start_sec, > glob_max_trunc_err, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > min_in_hour, > glob_html_log, > glob_smallish_float, > glob_log10_abserr, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_m1, > array_norms, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_y, > array_x, > array_last_rel_error, > array_pole, > array_complex_pole, > array_real_pole, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre tan $eq_no = 1 > array_tmp1_a1[1] := sin(array_x[1]); > array_tmp1_a2[1] := cos(array_x[1]); > array_tmp1[1] := (array_tmp1_a1[1] / array_tmp1_a2[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre tan $eq_no = 1 > array_tmp1_a1[2] := att(1,array_tmp1_a2,array_x,1); > array_tmp1_a2[2] := -att(1,array_tmp1_a1,array_x,1); > array_tmp1[2] := (array_tmp1_a1[2] - ats(2,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre tan $eq_no = 1 > array_tmp1_a1[3] := att(2,array_tmp1_a2,array_x,1); > array_tmp1_a2[3] := -att(2,array_tmp1_a1,array_x,1); > array_tmp1[3] := (array_tmp1_a1[3] - ats(3,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre tan $eq_no = 1 > array_tmp1_a1[4] := att(3,array_tmp1_a2,array_x,1); > array_tmp1_a2[4] := -att(3,array_tmp1_a1,array_x,1); > array_tmp1[4] := (array_tmp1_a1[4] - ats(4,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre tan $eq_no = 1 > array_tmp1_a1[5] := att(4,array_tmp1_a2,array_x,1); > array_tmp1_a2[5] := -att(4,array_tmp1_a1,array_x,1); > array_tmp1[5] := (array_tmp1_a1[5] - ats(5,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit tan $eq_no = 1 > array_tmp1_a1[kkk] := att(kkk-1 ,array_tmp1_a2,array_x,1); > array_tmp1_a2[kkk] := -att(kkk-1,array_tmp1_a1,array_x,1); > array_tmp1[kkk] := (array_tmp1_a1[kkk] - ats(kkk ,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGMASSIVE, INFO, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, glob_current_iter, glob_start, glob_max_sec, glob_small_float, glob_max_hours, glob_log10_relerr, glob_disp_incr, glob_clock_sec, djd_debug2, glob_dump_analytic, glob_large_float, glob_not_yet_start_msg, glob_initial_pass, glob_display_flag, glob_max_opt_iter, glob_subiter_method, glob_warned, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_optimal_expect_sec, glob_log10normmin, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, sec_in_min, glob_log10abserr, glob_optimal_start, djd_debug, glob_iter, glob_no_eqs, glob_hmax, glob_optimal_done, years_in_century, glob_normmax, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_abserr, glob_hmin, glob_h, hours_in_day, glob_log10relerr, glob_orig_start_sec, glob_max_trunc_err, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_percent_done, glob_max_minutes, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, min_in_hour, glob_html_log, glob_smallish_float, glob_log10_abserr, glob_dump, array_const_0D0, array_const_1, array_y_init, array_m1, array_norms, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_y, array_x, array_last_rel_error, array_pole, array_complex_pole, array_real_pole, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; array_tmp1_a1[1] := sin(array_x[1]); array_tmp1_a2[1] := cos(array_x[1]); array_tmp1[1] := array_tmp1_a1[1]/array_tmp1_a2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1_a1[2] := att(1, array_tmp1_a2, array_x, 1); array_tmp1_a2[2] := -att(1, array_tmp1_a1, array_x, 1); array_tmp1[2] := ( array_tmp1_a1[2] - ats(2, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1_a1[3] := att(2, array_tmp1_a2, array_x, 1); array_tmp1_a2[3] := -att(2, array_tmp1_a1, array_x, 1); array_tmp1[3] := ( array_tmp1_a1[3] - ats(3, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1_a1[4] := att(3, array_tmp1_a2, array_x, 1); array_tmp1_a2[4] := -att(3, array_tmp1_a1, array_x, 1); array_tmp1[4] := ( array_tmp1_a1[4] - ats(4, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1_a1[5] := att(4, array_tmp1_a2, array_x, 1); array_tmp1_a2[5] := -att(4, array_tmp1_a1, array_x, 1); array_tmp1[5] := ( array_tmp1_a1[5] - ats(5, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1_a1[kkk] := att(kkk - 1, array_tmp1_a2, array_x, 1); array_tmp1_a2[kkk] := -att(kkk - 1, array_tmp1_a1, array_x, 1); array_tmp1[kkk] := ( array_tmp1_a1[kkk] - ats(kkk, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > 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 - log(abs(cos((x)))) > end; exact_soln_y := proc(x) 2.0 - log(abs(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 > DEBUGMASSIVE, > INFO, > glob_iolevel, > glob_max_terms, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_current_iter, > glob_start, > glob_max_sec, > glob_small_float, > glob_max_hours, > glob_log10_relerr, > glob_disp_incr, > glob_clock_sec, > djd_debug2, > glob_dump_analytic, > glob_large_float, > glob_not_yet_start_msg, > glob_initial_pass, > glob_display_flag, > glob_max_opt_iter, > glob_subiter_method, > glob_warned, > glob_clock_start_sec, > glob_almost_1, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_max_rel_trunc_err, > glob_last_good_h, > days_in_year, > sec_in_min, > glob_log10abserr, > glob_optimal_start, > djd_debug, > glob_iter, > glob_no_eqs, > glob_hmax, > glob_optimal_done, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_abserr, > glob_hmin, > glob_h, > hours_in_day, > glob_log10relerr, > glob_orig_start_sec, > glob_max_trunc_err, > glob_look_poles, > glob_hmin_init, > glob_not_yet_finished, > glob_percent_done, > glob_max_minutes, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > min_in_hour, > glob_html_log, > glob_smallish_float, > glob_log10_abserr, > glob_dump, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y_init, > array_m1, > array_norms, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_a1, > array_tmp1_a2, > array_type_pole, > array_y, > array_x, > array_last_rel_error, > array_pole, > array_complex_pole, > array_real_pole, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > INFO := 2; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGL := 3; > ALWAYS := 1; > glob_current_iter := 0; > glob_start := 0; > glob_max_sec := 10000.0; > glob_small_float := 0.1e-50; > glob_max_hours := 0.0; > glob_log10_relerr := 0.1e-10; > glob_disp_incr := 0.1; > glob_clock_sec := 0.0; > djd_debug2 := true; > glob_dump_analytic := false; > glob_large_float := 9.0e100; > glob_not_yet_start_msg := true; > glob_initial_pass := true; > glob_display_flag := true; > glob_max_opt_iter := 10; > glob_subiter_method := 3; > glob_warned := false; > glob_clock_start_sec := 0.0; > glob_almost_1 := 0.9990; > centuries_in_millinium := 10.0; > glob_optimal_expect_sec := 0.1; > glob_log10normmin := 0.1; > glob_curr_iter_when_opt := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_last_good_h := 0.1; > days_in_year := 365.0; > sec_in_min := 60.0; > glob_log10abserr := 0.0; > glob_optimal_start := 0.0; > djd_debug := true; > glob_iter := 0; > glob_no_eqs := 0; > glob_hmax := 1.0; > glob_optimal_done := false; > years_in_century := 100.0; > glob_normmax := 0.0; > MAX_UNCHANGED := 10; > glob_unchanged_h_cnt := 0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_h := 0.1; > hours_in_day := 24.0; > glob_log10relerr := 0.0; > glob_orig_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_look_poles := false; > glob_hmin_init := 0.001; > glob_not_yet_finished := true; > glob_percent_done := 0.0; > glob_max_minutes := 0.0; > glob_warned2 := false; > glob_optimal_clock_start_sec := 0.0; > glob_reached_optimal_h := false; > min_in_hour := 60.0; > glob_html_log := true; > glob_smallish_float := 0.1e-100; > glob_log10_abserr := 0.1e-10; > glob_dump := false; > #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/tanpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > 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 := 10;"); > 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 - log(abs(cos((x))))"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_1st_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_tmp1_a1:= Array(1..(max_terms + 1),[]); > array_tmp1_a2:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 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_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_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_a1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_a2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[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_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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_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 <=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 <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_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 <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_a2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_a1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_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 := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #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 ) = tan ( 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,"2012-06-13T20:04:55-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tan") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( 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,"tan diffeq.mxt") > ; > logitem_str(html_log_file,"tan 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 DEBUGMASSIVE, INFO, glob_iolevel, glob_max_terms, DEBUGL, ALWAYS, glob_current_iter, glob_start, glob_max_sec, glob_small_float, glob_max_hours, glob_log10_relerr, glob_disp_incr, glob_clock_sec, djd_debug2, glob_dump_analytic, glob_large_float, glob_not_yet_start_msg, glob_initial_pass, glob_display_flag, glob_max_opt_iter, glob_subiter_method, glob_warned, glob_clock_start_sec, glob_almost_1, centuries_in_millinium, glob_optimal_expect_sec, glob_log10normmin, glob_curr_iter_when_opt, glob_max_rel_trunc_err, glob_last_good_h, days_in_year, sec_in_min, glob_log10abserr, glob_optimal_start, djd_debug, glob_iter, glob_no_eqs, glob_hmax, glob_optimal_done, years_in_century, glob_normmax, MAX_UNCHANGED, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_abserr, glob_hmin, glob_h, hours_in_day, glob_log10relerr, glob_orig_start_sec, glob_max_trunc_err, glob_look_poles, glob_hmin_init, glob_not_yet_finished, glob_percent_done, glob_max_minutes, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, min_in_hour, glob_html_log, glob_smallish_float, glob_log10_abserr, glob_dump, array_const_0D0, array_const_1, array_y_init, array_m1, array_norms, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp1_a1, array_tmp1_a2, array_type_pole, array_y, array_x, array_last_rel_error, array_pole, array_complex_pole, array_real_pole, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; INFO := 2; glob_iolevel := 5; glob_max_terms := 30; DEBUGL := 3; ALWAYS := 1; glob_current_iter := 0; glob_start := 0; glob_max_sec := 10000.0; glob_small_float := 0.1*10^(-50); glob_max_hours := 0.; glob_log10_relerr := 0.1*10^(-10); glob_disp_incr := 0.1; glob_clock_sec := 0.; djd_debug2 := true; glob_dump_analytic := false; glob_large_float := 0.90*10^101; glob_not_yet_start_msg := true; glob_initial_pass := true; glob_display_flag := true; glob_max_opt_iter := 10; glob_subiter_method := 3; glob_warned := false; glob_clock_start_sec := 0.; glob_almost_1 := 0.9990; centuries_in_millinium := 10.0; glob_optimal_expect_sec := 0.1; glob_log10normmin := 0.1; glob_curr_iter_when_opt := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_last_good_h := 0.1; days_in_year := 365.0; sec_in_min := 60.0; glob_log10abserr := 0.; glob_optimal_start := 0.; djd_debug := true; glob_iter := 0; glob_no_eqs := 0; glob_hmax := 1.0; glob_optimal_done := false; years_in_century := 100.0; glob_normmax := 0.; MAX_UNCHANGED := 10; glob_unchanged_h_cnt := 0; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_h := 0.1; hours_in_day := 24.0; glob_log10relerr := 0.; glob_orig_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_look_poles := false; glob_hmin_init := 0.001; glob_not_yet_finished := true; glob_percent_done := 0.; glob_max_minutes := 0.; glob_warned2 := false; glob_optimal_clock_start_sec := 0.; glob_reached_optimal_h := false; min_in_hour := 60.0; glob_html_log := true; glob_smallish_float := 0.1*10^(-100); glob_log10_abserr := 0.1*10^(-10); glob_dump := false; 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/tanpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); 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 := 10;"); 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\t- log(abs(cos((x))))"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_1st_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_tmp1_a1 := Array(1 .. max_terms + 1, []); array_tmp1_a2 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); 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_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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_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 <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_a2[term] := 0.; term := term + 1 end do; array_tmp1_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_a1[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_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 := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; 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 ) = tan ( 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, "2012-06-13T20:04:55-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tan"); logitem_str(html_log_file, "diff ( y , x , 1 ) = tan ( 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, "tan diffeq.mxt"); logitem_str(html_log_file, "tan 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/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #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 - log(abs(cos((x)))) end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0001 y[1] (analytic) = 2.0000000050000000083333333555556 y[1] (numeric) = 2.0000000050000000083333341333333 absolute error = 7.777777e-25 relative error = 3.8888884902777787581018510187113e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0002 y[1] (analytic) = 2.0000000200000001333333347555556 y[1] (numeric) = 2.0000000200000001333333363111112 absolute error = 1.5555556e-24 relative error = 7.7777779222222202592592637283949e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0003 y[1] (analytic) = 2.0000000450000006750000162000004 y[1] (numeric) = 2.0000000450000006750000185333342 absolute error = 2.3333338e-24 relative error = 1.1666668737499949468750343546865e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0004 y[1] (analytic) = 2.00000008000000213333342435556 y[1] (numeric) = 2.0000000800000021333334274666722 absolute error = 3.1111122e-24 relative error = 1.5555560377777568296298823901103e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0005 y[1] (analytic) = 2.0000001250000052083336805555819 y[1] (numeric) = 2.0000001250000052083336844444731 absolute error = 3.8888912e-24 relative error = 1.9444454784721525318300289953603e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0006 y[1] (analytic) = 2.0000001800000108000010368001133 y[1] (numeric) = 2.0000001800000108000010414667841 absolute error = 4.6666708e-24 relative error = 2.3333351899998203000049373994313e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0007 y[1] (analytic) = 2.0000002450000200083359477559444 y[1] (numeric) = 2.0000002450000200083359532003956 absolute error = 5.4444512e-24 relative error = 2.7222252665273776167974128676987e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.16 NO POLE x[1] = 0.0008 y[1] (analytic) = 2.0000003200000341333391587566874 y[1] (numeric) = 2.0000003200000341333391649789197 absolute error = 6.2222323e-24 relative error = 3.1111156522214425481863325946785e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0009 y[1] (analytic) = 2.0000004050000546750118098029039 y[1] (numeric) = 2.0000004050000546750118168029185 absolute error = 7.0000146e-24 relative error = 3.5000065912485695907138024286813e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 2.0000005000000833333555555623016 y[1] (numeric) = 2.0000005000000833333555633400995 absolute error = 7.7777979e-24 relative error = 3.8888979777753435187051696937461e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0011 y[1] (analytic) = 2.0000006050001220083727013700163 y[1] (numeric) = 2.0000006050001220083727099255988 absolute error = 8.5555825e-24 relative error = 4.2777899559682773565004566812043e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0012 y[1] (analytic) = 2.0000007200001728000663552290067 y[1] (numeric) = 2.0000007200001728000663645623753 absolute error = 9.3333686e-24 relative error = 4.6666826199938536006795068894508e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0013 y[1] (analytic) = 2.000000845000238008440595810585 y[1] (numeric) = 2.0000008450002380084406059217412 absolute error = 1.01111562e-23 relative error = 5.0555759640185535672853629630650e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0014 y[1] (analytic) = 2.0000009800003201335006564551128 y[1] (numeric) = 2.0000009800003201335006673440583 absolute error = 1.08889455e-23 relative error = 5.4444700822087882390604444417164e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0015 y[1] (analytic) = 2.0000011250004218752531251728935 y[1] (numeric) = 2.0000011250004218752531368396301 absolute error = 1.16667366e-23 relative error = 5.8333650187309464876706763617612e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0016 y[1] (analytic) = 2.0000012800005461337061606452957 y[1] (numeric) = 2.0000012800005461337061730898253 absolute error = 1.24445296e-23 relative error = 6.2222608177513775459378222361264e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0017 y[1] (analytic) = 2.0000014450006960088697242261428 y[1] (numeric) = 2.0000014450006960088697374484676 absolute error = 1.32223248e-23 relative error = 6.6111576234363163550889051424536e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.36 NO POLE x[1] = 0.0018 y[1] (analytic) = 2.0000016200008748007558279434108 y[1] (numeric) = 2.0000016200008748007558419435329 absolute error = 1.40001221e-23 relative error = 7.0000553799520804119462565527646e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0019 y[1] (analytic) = 2.0000018050010860093787985012735 y[1] (numeric) = 2.0000018050010860093788132791952 absolute error = 1.47779217e-23 relative error = 7.3889541814648389912125188215790e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 2.0000020000013333347555572825419 y[1] (numeric) = 2.0000020000013333347555728382658 absolute error = 1.55557239e-23 relative error = 7.7778541721406426177116966213565e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0021 y[1] (analytic) = 2.0000022050016206769059163515457 y[1] (numeric) = 2.0000022050016206769059326850744 absolute error = 1.63335287e-23 relative error = 8.1667553461456130385687414306108e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0022 y[1] (analytic) = 2.0000024200019521358528904575052 y[1] (numeric) = 2.0000024200019521358529075688413 absolute error = 1.71113361e-23 relative error = 8.5556576976458349454713996496043e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0023 y[1] (analytic) = 2.0000026450023320116230250384485 y[1] (numeric) = 2.000002645002332011623042927595 absolute error = 1.78891465e-23 relative error = 8.9445614208070915720233042544165e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0024 y[1] (analytic) = 2.0000028800027648042467402257295 y[1] (numeric) = 2.0000028800027648042467588926893 absolute error = 1.86669598e-23 relative error = 9.3334664597953952907783563945617e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0025 y[1] (analytic) = 2.000003125003255213758690849204 y[1] (numeric) = 2.0000031250032552137587102939802 absolute error = 1.94447762e-23 relative error = 9.7223729087765058356797455232334e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0026 y[1] (analytic) = 2.0000033800038081401981424431265 y[1] (numeric) = 2.0000033800038081401981626657225 absolute error = 2.02225960e-23 relative error = 1.0111280911916006274301707568535e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0027 y[1] (analytic) = 2.0000036450044286836093632528312 y[1] (numeric) = 2.0000036450044286836093842532504 absolute error = 2.10004192e-23 relative error = 1.0500190463379629479925091984652e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0028 y[1] (analytic) = 2.0000039200051221440420322422631 y[1] (numeric) = 2.0000039200051221440420540205089 absolute error = 2.17782458e-23 relative error = 1.0889101557333059853870197642804e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=0.55 NO POLE x[1] = 0.0029 y[1] (analytic) = 2.0000042050058940215516631024294 y[1] (numeric) = 2.0000042050058940215516856585056 absolute error = 2.25560762e-23 relative error = 1.1278014387941512923037832397740e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 2.0000045000067500162000442608434 y[1] (numeric) = 2.0000045000067500162000675947538 absolute error = 2.33339104e-23 relative error = 1.1666928949370487936695634354078e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0031 y[1] (analytic) = 2.0000048050076960280556948920349 y[1] (numeric) = 2.0000048050076960280557190037834 absolute error = 2.41117485e-23 relative error = 1.2055845285785309839015851390372e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0032 y[1] (analytic) = 2.0000051200087381571943369292052 y[1] (numeric) = 2.0000051200087381571943618187958 absolute error = 2.48895906e-23 relative error = 1.2444763441351217991283510140801e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0033 y[1] (analytic) = 2.0000054450098827036993830771068 y[1] (numeric) = 2.0000054450098827036994087445437 absolute error = 2.56674369e-23 relative error = 1.2833683510233227644286091674345e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0034 y[1] (analytic) = 2.0000057800111361676624408262308 y[1] (numeric) = 2.0000057800111361676624672715183 absolute error = 2.64452875e-23 relative error = 1.3222605536596374660382303706943e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0035 y[1] (analytic) = 2.0000061250125052491838324683876 y[1] (numeric) = 2.0000061250125052491838596915302 absolute error = 2.72231426e-23 relative error = 1.3611529614605447486015195955886e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0036 y[1] (analytic) = 2.0000064800139968483731311137695 y[1] (numeric) = 2.0000064800139968483731591147718 absolute error = 2.80010023e-23 relative error = 1.4000455788425264373730771989091e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0037 y[1] (analytic) = 2.0000068450156180653497127095862 y[1] (numeric) = 2.0000068450156180653497414884529 absolute error = 2.87788667e-23 relative error = 1.4389384102220542979566353640028e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0038 y[1] (analytic) = 2.0000072200173762002433240603665 y[1] (numeric) = 2.0000072200173762002433536171024 absolute error = 2.95567359e-23 relative error = 1.4778314600155897960332788984621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0039 y[1] (analytic) = 2.000007605019278753194666850024 y[1] (numeric) = 2.0000076050192787531946971846342 absolute error = 3.03346102e-23 relative error = 1.5167247426395458321381770945151e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.0MB, time=0.74 x[1] = 0.004 y[1] (analytic) = 2.0000080000213334243559976657853 y[1] (numeric) = 2.0000080000213334243560287782748 absolute error = 3.11124895e-23 relative error = 1.5556182525103966262551250683083e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0041 y[1] (analytic) = 2.0000084050235481138917440240819 y[1] (numeric) = 2.000008405023548113891775914456 absolute error = 3.18903741e-23 relative error = 1.5945120040445291277298439253983e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0042 y[1] (analytic) = 2.0000088200259309219791363985129 y[1] (numeric) = 2.000008820025930921979169066777 absolute error = 3.26682641e-23 relative error = 1.6334060016583548248605943959154e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0043 y[1] (analytic) = 2.0000092450284901488088562499832 y[1] (numeric) = 2.0000092450284901488088896961428 absolute error = 3.34461596e-23 relative error = 1.6723002497682734046716941131554e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0044 y[1] (analytic) = 2.000009680031234294585700059129 y[1] (numeric) = 2.0000096800312342945857342831898 absolute error = 3.42240608e-23 relative error = 1.7111947577906483126829972289593e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0045 y[1] (analytic) = 2.0000101250341720595292593611437 y[1] (numeric) = 2.0000101250341720595292943631114 absolute error = 3.50019677e-23 relative error = 1.7500895251418768875309161425409e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0046 y[1] (analytic) = 2.0000105800373123438746167831183 y[1] (numeric) = 2.0000105800373123438746525629988 absolute error = 3.57798805e-23 relative error = 1.7889845612382954458494396032598e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0047 y[1] (analytic) = 2.0000110450406642478730580840161 y[1] (numeric) = 2.0000110450406642478730946418155 absolute error = 3.65577994e-23 relative error = 1.8278798754962228919394027860695e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0048 y[1] (analytic) = 2.0000115200442370717928001974024 y[1] (numeric) = 2.0000115200442370717928375331268 absolute error = 3.73357244e-23 relative error = 1.8667754673320178273926119124502e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0049 y[1] (analytic) = 2.0000120050480403159197352770522 y[1] (numeric) = 2.0000120050480403159197733907079 absolute error = 3.81136557e-23 relative error = 1.9056713461619701360198544158800e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 2.0000125000520836805581907455634 y[1] (numeric) = 2.0000125000520836805582296371569 absolute error = 3.88915935e-23 relative error = 1.9445675214023511185012329665572e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0051 y[1] (analytic) = 2.0000130050563770660317053461044 y[1] (numeric) = 2.0000130050563770660317450156422 absolute error = 3.96695378e-23 relative error = 1.9834639924694780269816487127895e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.0MB, time=0.93 NO POLE x[1] = 0.0052 y[1] (analytic) = 2.0000135200609305726838211974274 y[1] (numeric) = 2.0000135200609305726838616449162 absolute error = 4.04474888e-23 relative error = 2.0223607687795912500556329242569e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0053 y[1] (analytic) = 2.000014045065754500878891852283 y[1] (numeric) = 2.0000140450657545008789330777298 absolute error = 4.12254468e-23 relative error = 2.0612578647488763099764868250681e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0054 y[1] (analytic) = 2.0000145800708593510029063593734 y[1] (numeric) = 2.000014580070859351002948362785 absolute error = 4.20034116e-23 relative error = 2.1001552697936753843949909867173e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0055 y[1] (analytic) = 2.0000151250762558234643293289828 y[1] (numeric) = 2.0000151250762558234643721103664 absolute error = 4.27813836e-23 relative error = 2.1390530033301046919818749272418e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0056 y[1] (analytic) = 2.0000156800819548186949570024303 y[1] (numeric) = 2.0000156800819548186950005617931 absolute error = 4.35593628e-23 relative error = 2.1779510647744053763418120066480e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0057 y[1] (analytic) = 2.0000162450879674371507893254888 y[1] (numeric) = 2.0000162450879674371508336628382 absolute error = 4.43373494e-23 relative error = 2.2168494635427270912707232147870e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0058 y[1] (analytic) = 2.0000168200943049793129180259189 y[1] (numeric) = 2.0000168200943049793129631412624 absolute error = 4.51153435e-23 relative error = 2.2557482040512397852143042687759e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0059 y[1] (analytic) = 2.0000174051009789456884306952691 y[1] (numeric) = 2.0000174051009789456884765886143 absolute error = 4.58933452e-23 relative error = 2.2946472907160970110940982533885e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 2.0000180001080010368113308750952 y[1] (numeric) = 2.0000180001080010368113775464498 absolute error = 4.66713546e-23 relative error = 2.3335467279534356860454957291793e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0061 y[1] (analytic) = 2.0000186051153831532434741477562 y[1] (numeric) = 2.0000186051153831532435215971282 absolute error = 4.74493720e-23 relative error = 2.3724465301792828264446946458148e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0062 y[1] (analytic) = 2.0000192201231373955755202319455 y[1] (numeric) = 2.0000192201231373955755684593429 absolute error = 4.82273974e-23 relative error = 2.4113466968097801819750562435195e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=1.12 NO POLE x[1] = 0.0063 y[1] (analytic) = 2.0000198451312760644279010831186 y[1] (numeric) = 2.0000198451312760644279500885495 absolute error = 4.90054309e-23 relative error = 2.4502472322610084833800324321474e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0064 y[1] (analytic) = 2.0000204801398116604518049989831 y[1] (numeric) = 2.0000204801398116604518547824559 absolute error = 4.97834728e-23 relative error = 2.4891481509489283149267002402200e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0065 y[1] (analytic) = 2.0000211251487568843301767302178 y[1] (numeric) = 2.0000211251487568843302272917408 absolute error = 5.05615230e-23 relative error = 2.5280494472896806231426989376480e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0066 y[1] (analytic) = 2.0000217801581246367787335965899 y[1] (numeric) = 2.0000217801581246367787849361717 absolute error = 5.13395818e-23 relative error = 2.5669511356991831279151414902229e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0067 y[1] (analytic) = 2.0000224451679280185469976086452 y[1] (numeric) = 2.0000224451679280185470497262946 absolute error = 5.21176494e-23 relative error = 2.6058532255933778939174863577441e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0068 y[1] (analytic) = 2.0000231201781803304193435951451 y[1] (numeric) = 2.0000231201781803304193964908708 absolute error = 5.28957257e-23 relative error = 2.6447557113883546273536962142952e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0069 y[1] (analytic) = 2.0000238051888950732160633364283 y[1] (numeric) = 2.0000238051888950732161170102393 absolute error = 5.36738110e-23 relative error = 2.6836586074999592871592728919464e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 2.0000245002000859477944457038803 y[1] (numeric) = 2.0000245002000859477945001557856 absolute error = 5.44519053e-23 relative error = 2.7225619133441883432625292954099e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0071 y[1] (analytic) = 2.0000252052117668550498728056917 y[1] (numeric) = 2.0000252052117668550499280357007 absolute error = 5.52300090e-23 relative error = 2.7614656483367733879751097832175e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0072 y[1] (analytic) = 2.000025920223951895916932139094 y[1] (numeric) = 2.0000259202239518959169881472159 absolute error = 5.60081219e-23 relative error = 2.8003698018937933932363043115669e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0073 y[1] (analytic) = 2.0000266452366553713705447492595 y[1] (numeric) = 2.0000266452366553713706015355038 absolute error = 5.67862443e-23 relative error = 2.8392743884309953606558008974349e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=1.33 NO POLE x[1] = 0.0074 y[1] (analytic) = 2.0000273802498917824271093950598 y[1] (numeric) = 2.0000273802498917824271669594361 absolute error = 5.75643763e-23 relative error = 2.8781794123642280419677518384023e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0075 y[1] (analytic) = 2.0000281252636758301456627218753 y[1] (numeric) = 2.0000281252636758301457210643934 absolute error = 5.83425181e-23 relative error = 2.9170848831092488871079276922670e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0076 y[1] (analytic) = 2.0000288802780224156290554416542 y[1] (numeric) = 2.000028880278022415629114562324 absolute error = 5.91206698e-23 relative error = 2.9559908050818587658563536601587e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0077 y[1] (analytic) = 2.0000296452929466400251445204202 y[1] (numeric) = 2.0000296452929466400252044192517 absolute error = 5.98988315e-23 relative error = 2.9948971826978369278660853466234e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0078 y[1] (analytic) = 2.0000304203084638045280013734322 y[1] (numeric) = 2.0000304203084638045280620504355 absolute error = 6.06770033e-23 relative error = 3.0338040203729407624127119547904e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0079 y[1] (analytic) = 2.0000312053245894103791360682009 y[1] (numeric) = 2.0000312053245894103791975233863 absolute error = 6.14551854e-23 relative error = 3.0727113275228275460502492279176e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 2.0000320003413391588687375355708 y[1] (numeric) = 2.0000320003413391588687997689487 absolute error = 6.22333779e-23 relative error = 3.1116191085632042641133466618021e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0081 y[1] (analytic) = 2.0000328053587289513369297890785 y[1] (numeric) = 2.0000328053587289513369928006594 absolute error = 6.30115809e-23 relative error = 3.1505273679097551708165286535639e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0082 y[1] (analytic) = 2.0000336203767748891750441528004 y[1] (numeric) = 2.000033620376774889175107942595 absolute error = 6.37897946e-23 relative error = 3.1894361149780574994775632849319e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0083 y[1] (analytic) = 2.0000344453954932738269074979069 y[1] (numeric) = 2.0000344453954932738269720659259 absolute error = 6.45680190e-23 relative error = 3.2283453491838292459045206682884e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0084 y[1] (analytic) = 2.0000352804149006067901464881408 y[1] (numeric) = 2.0000352804149006067902118343953 absolute error = 6.53462545e-23 relative error = 3.2672550899424203560272672560053e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0085 y[1] (analytic) = 2.0000361254350135896175078344438 y[1] (numeric) = 2.0000361254350135896175739589448 absolute error = 6.61245010e-23 relative error = 3.3061653316695832937524847032340e-21 % h = 0.0001 memory used=30.5MB, alloc=4.1MB, time=1.52 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0086 y[1] (analytic) = 2.0000369804558491239181945589531 y[1] (numeric) = 2.0000369804558491239182614617118 absolute error = 6.69027587e-23 relative error = 3.3450760837807858921532658698138e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0087 y[1] (analytic) = 2.0000378454774243113592182685971 y[1] (numeric) = 2.0000378454774243113592859496249 absolute error = 6.76810278e-23 relative error = 3.3839873556914630118215094395542e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0088 y[1] (analytic) = 2.0000387204997564536667674385195 y[1] (numeric) = 2.0000387204997564536668358978278 absolute error = 6.84593083e-23 relative error = 3.4228991468172096493850015912852e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0089 y[1] (analytic) = 2.0000396055228630526275917055641 y[1] (numeric) = 2.0000396055228630526276609431645 absolute error = 6.92376004e-23 relative error = 3.4618114665734065246004108602952e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 2.0000405005467618100904021720563 y[1] (numeric) = 2.0000405005467618100904721879606 absolute error = 7.00159043e-23 relative error = 3.5007243243754002140341687964851e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0091 y[1] (analytic) = 2.0000414055714706279672877201194 y[1] (numeric) = 2.0000414055714706279673585143394 absolute error = 7.07942200e-23 relative error = 3.5396377196387096844034427693786e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0092 y[1] (analytic) = 2.0000423205970076082351473367653 y[1] (numeric) = 2.000042320597007608235218909313 absolute error = 7.15725477e-23 relative error = 3.5785516617786254800126583741016e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0093 y[1] (analytic) = 2.0000432456233910529371384500049 y[1] (numeric) = 2.0000432456233910529372108008925 absolute error = 7.23508876e-23 relative error = 3.6174661602104028312757656434286e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0094 y[1] (analytic) = 2.0000441806506394641841412762234 y[1] (numeric) = 2.0000441806506394641842144054631 absolute error = 7.31292397e-23 relative error = 3.6563812143494820628625779550389e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0095 y[1] (analytic) = 2.0000451256787715441562391790695 y[1] (numeric) = 2.0000451256787715441563130866737 absolute error = 7.39076042e-23 relative error = 3.6952968336110604815149654374839e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0096 y[1] (analytic) = 2.0000460807078061951042150401104 y[1] (numeric) = 2.0000460807078061951042897260916 absolute error = 7.46859812e-23 relative error = 3.7342130224104141085084769154774e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=1.72 NO POLE x[1] = 0.0097 y[1] (analytic) = 2.0000470457377625193510636415074 y[1] (numeric) = 2.0000470457377625193511391058782 absolute error = 7.54643708e-23 relative error = 3.7731297851627916401635249195958e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0098 y[1] (analytic) = 2.0000480207686598192935200609682 y[1] (numeric) = 2.0000480207686598192935963037415 absolute error = 7.62427733e-23 relative error = 3.8120471362831741095327274933957e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0099 y[1] (analytic) = 2.0000490058005175974036040792374 y[1] (numeric) = 2.0000490058005175974036811004261 absolute error = 7.70211887e-23 relative error = 3.8509650751868625790627681289706e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 2.0000500008333555562301806003859 y[1] (numeric) = 2.000050000833355556230258400003 absolute error = 7.77996171e-23 relative error = 3.8898836062890147164372677184892e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0101 y[1] (analytic) = 2.0000510058671935984005360851658 y[1] (numeric) = 2.0000510058671935984006146632246 absolute error = 7.85780588e-23 relative error = 3.9288027440045047306285238180543e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0102 y[1] (analytic) = 2.000052020902051826621970997699 y[1] (numeric) = 2.0000520209020518266220503542127 absolute error = 7.93565137e-23 relative error = 3.9677224827486780503376572947432e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0103 y[1] (analytic) = 2.0000530459379505436834082657689 y[1] (numeric) = 2.0000530459379505436834884007511 absolute error = 8.01349822e-23 relative error = 4.0066428419362083309448912083560e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0104 y[1] (analytic) = 2.0000540809749102524570177549906 y[1] (numeric) = 2.0000540809749102524570986684548 absolute error = 8.09134642e-23 relative error = 4.0455638159823850157239932751759e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0105 y[1] (analytic) = 2.0000551260129516558998567571337 y[1] (numeric) = 2.0000551260129516558999384490936 absolute error = 8.16919599e-23 relative error = 4.0844854143020751670951571847715e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0106 y[1] (analytic) = 2.0000561810520956570555264928787 y[1] (numeric) = 2.0000561810520956570556089633481 absolute error = 8.24704694e-23 relative error = 4.1234076413102459593449610358146e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0107 y[1] (analytic) = 2.0000572460923633590558446292871 y[1] (numeric) = 2.0000572460923633590559278782801 absolute error = 8.32489930e-23 relative error = 4.1623305114215481672590456152928e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=1.91 NO POLE x[1] = 0.0108 y[1] (analytic) = 2.0000583211337760651225338122706 y[1] (numeric) = 2.0000583211337760651226178398013 absolute error = 8.40275307e-23 relative error = 4.2012540240510180443294402188092e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0109 y[1] (analytic) = 2.0000594061763552785689262143457 y[1] (numeric) = 2.0000594061763552785690110204284 absolute error = 8.48060827e-23 relative error = 4.2401781886133747141134683590370e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 2.0000605012201227028016840979645 y[1] (numeric) = 2.0000605012201227028017696826135 absolute error = 8.55846490e-23 relative error = 4.2791030045235977994434972331602e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0111 y[1] (analytic) = 2.0000616062651002413225363947132 y[1] (numeric) = 2.0000616062651002413226227579429 absolute error = 8.63632297e-23 relative error = 4.3180284761964925239021491078898e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0112 y[1] (analytic) = 2.0000627213113099977300313006741 y[1] (numeric) = 2.0000627213113099977301184424993 absolute error = 8.71418252e-23 relative error = 4.3569546230463621876534078983317e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0113 y[1] (analytic) = 2.0000638463587742757213048882499 y[1] (numeric) = 2.0000638463587742757213928086853 absolute error = 8.79204354e-23 relative error = 4.3958814394882426270260567521877e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0114 y[1] (analytic) = 2.0000649814075155790938657347492 y[1] (numeric) = 2.0000649814075155790939544338098 absolute error = 8.86990606e-23 relative error = 4.4348089399365101261533063425412e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0115 y[1] (analytic) = 2.0000661264575566117473955680385 y[1] (numeric) = 2.0000661264575566117474850457393 absolute error = 8.94777008e-23 relative error = 4.4737371238059816027216673822256e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0116 y[1] (analytic) = 2.0000672815089202776855659295659 y[1] (numeric) = 2.000067281508920277685656185922 absolute error = 9.02563561e-23 relative error = 4.5126659955112843868686767118690e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0117 y[1] (analytic) = 2.0000684465616296810178708550651 y[1] (numeric) = 2.0000684465616296810179618900919 absolute error = 9.10350268e-23 relative error = 4.5515955694666705582325253930389e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0118 y[1] (analytic) = 2.000069621615708125961475573253 y[1] (numeric) = 2.000069621615708125961567386966 absolute error = 9.18137130e-23 relative error = 4.5905258500866835233359201785174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0119 memory used=41.9MB, alloc=4.1MB, time=2.11 y[1] (analytic) = 2.0000708066711791168430812228331 y[1] (numeric) = 2.0000708066711791168431738152478 absolute error = 9.25924147e-23 relative error = 4.6294568367860098893032897307934e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 2.0000720017280663581008055881231 y[1] (numeric) = 2.0000720017280663581008989592551 absolute error = 9.33711320e-23 relative error = 4.6683885339791341651136152716221e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0121 y[1] (analytic) = 2.0000732067863937542860798536264 y[1] (numeric) = 2.0000732067863937542861740034917 absolute error = 9.41498653e-23 relative error = 4.7073209610799576887021076805036e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0122 y[1] (analytic) = 2.00007442184618541006556137787 y[1] (numeric) = 2.0000744218461854100656563064845 absolute error = 9.49286145e-23 relative error = 4.7462541125032412069111141108205e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0123 y[1] (analytic) = 2.0000756469074656302230624868336 y[1] (numeric) = 2.0000756469074656302231581942134 absolute error = 9.57073798e-23 relative error = 4.7851879976631675649955687641580e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0124 y[1] (analytic) = 2.0000768819702589196614952872982 y[1] (numeric) = 2.0000768819702589196615917734595 absolute error = 9.64861613e-23 relative error = 4.8241226209740644452052556499881e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0125 y[1] (analytic) = 2.0000781270345899834048325004452 y[1] (numeric) = 2.0000781270345899834049297654044 absolute error = 9.72649592e-23 relative error = 4.8630579918500288187818222352662e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0126 y[1] (analytic) = 2.0000793821004837266000843160394 y[1] (numeric) = 2.000079382100483726600182359813 absolute error = 9.80437736e-23 relative error = 4.9019941147053079134149733879566e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0127 y[1] (analytic) = 2.000080647167965254519291267531 y[1] (numeric) = 2.0000806471679652545193900901357 absolute error = 9.88226047e-23 relative error = 4.9409309989539113155562922810278e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0128 y[1] (analytic) = 2.0000819222370598725615331284175 y[1] (numeric) = 2.00008192223705987256163272987 absolute error = 9.96014525e-23 relative error = 4.9798686440102091847604655391651e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0129 y[1] (analytic) = 2.0000832073077930862549538302049 y[1] (numeric) = 2.0000832073077930862550542105222 absolute error = 1.003803173e-22 relative error = 5.0188070642879238395428693006343e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 2.0000845023801906012588024023147 y[1] (numeric) = 2.0000845023801906012589035615137 absolute error = 1.011591990e-22 relative error = 5.0577462542015599351915048598364e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=2.31 NO POLE x[1] = 0.0131 y[1] (analytic) = 2.0000858074542783233654899342813 y[1] (numeric) = 2.0000858074542783233655918723792 absolute error = 1.019380979e-22 relative error = 5.0966862281647528962987802312702e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0132 y[1] (analytic) = 2.0000871225300823585026625605928 y[1] (numeric) = 2.0000871225300823585027652776068 absolute error = 1.027170140e-22 relative error = 5.1356269855917280062801271225371e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0133 y[1] (analytic) = 2.0000884476076290127352904685241 y[1] (numeric) = 2.0000884476076290127353939644717 absolute error = 1.034959476e-22 relative error = 5.1745685408960226978223514565139e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0134 y[1] (analytic) = 2.0000897826869447922677729293207 y[1] (numeric) = 2.0000897826869447922678772042195 absolute error = 1.042748988e-22 relative error = 5.2135108984915587348618063115479e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0135 y[1] (analytic) = 2.0000911277680564034460593530894 y[1] (numeric) = 2.0000911277680564034461644069571 absolute error = 1.050538677e-22 relative error = 5.2524540627922194783408813701007e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0136 y[1] (analytic) = 2.0000924828509907527597863677569 y[1] (numeric) = 2.0000924828509907527598922006113 absolute error = 1.058328544e-22 relative error = 5.2913980382118496460157392055120e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0137 y[1] (analytic) = 2.0000938479357749468444309224601 y[1] (numeric) = 2.0000938479357749468445375343191 absolute error = 1.066118590e-22 relative error = 5.3303428291642550722652293986888e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0138 y[1] (analytic) = 2.0000952230224362924834794157341 y[1] (numeric) = 2.0000952230224362924835868066158 absolute error = 1.073908817e-22 relative error = 5.3692884450629644216786377133019e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0139 y[1] (analytic) = 2.0000966081110022966106128488667 y[1] (numeric) = 2.0000966081110022966107210187894 absolute error = 1.081699227e-22 relative error = 5.4082348953214531455320888809872e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 2.000098003201500666311908004791 y[1] (numeric) = 2.0000980032015006663120169537731 absolute error = 1.089489821e-22 relative error = 5.4471821843533879876237433622810e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0141 y[1] (analytic) = 2.0000994082939593088280546528909 y[1] (numeric) = 2.0000994082939593088281643809508 absolute error = 1.097280599e-22 relative error = 5.4861303115726440560345715730017e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=2.50 NO POLE x[1] = 0.0142 y[1] (analytic) = 2.0001008233884063315565887800953 y[1] (numeric) = 2.0001008233884063315566992872516 absolute error = 1.105071563e-22 relative error = 5.5250792863925661325588925188072e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0143 y[1] (analytic) = 2.0001022484848700420541418486428 y[1] (numeric) = 2.0001022484848700420542531349143 absolute error = 1.112862715e-22 relative error = 5.5640291182264442749904224778970e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0144 y[1] (analytic) = 2.0001036835833789480387060808976 y[1] (numeric) = 2.0001036835833789480388181463031 absolute error = 1.120654055e-22 relative error = 5.6029798064880317180081404270382e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0145 y[1] (analytic) = 2.0001051286839617573919157716026 y[1] (numeric) = 2.0001051286839617573920286161612 absolute error = 1.128445586e-22 relative error = 5.6419313655902664672865686090388e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0146 y[1] (analytic) = 2.0001065837866473781613446279581 y[1] (numeric) = 2.000106583786647378161458251689 absolute error = 1.136237309e-22 relative error = 5.6808837999465489750516913455164e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0147 y[1] (analytic) = 2.0001080488914649185628191379159 y[1] (numeric) = 2.0001080488914649185629335408383 absolute error = 1.144029224e-22 relative error = 5.7198371089705079160098531364670e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0148 y[1] (analytic) = 2.000109523998443686982747967083 y[1] (numeric) = 2.0001095239984436869828631492163 absolute error = 1.151821333e-22 relative error = 5.7587913020751969989954697166737e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0149 y[1] (analytic) = 2.0001110091076131919804673846302 y[1] (numeric) = 2.0001110091076131919805833459941 absolute error = 1.159613639e-22 relative error = 5.7977463936733353604992676318445e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.015 y[1] (analytic) = 2.0001125042190031422906027186064 y[1] (numeric) = 2.0001125042190031422907194592204 absolute error = 1.167406140e-22 relative error = 5.8367023731789758560795369048071e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0151 y[1] (analytic) = 2.000114009332643446825445841057 y[1] (numeric) = 2.0001140093326434468255633609411 absolute error = 1.175198841e-22 relative error = 5.8756592650041782941770017991314e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0152 y[1] (analytic) = 2.0001155244485642146773486833546 y[1] (numeric) = 2.0001155244485642146774669825286 absolute error = 1.182991740e-22 relative error = 5.9146170585629205105897040747425e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0153 y[1] (analytic) = 2.0001170495667957551211327821453 memory used=53.4MB, alloc=4.1MB, time=2.70 y[1] (numeric) = 2.0001170495667957551212518606293 absolute error = 1.190784840e-22 relative error = 5.9535757682677192792399520276636e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0154 y[1] (analytic) = 2.0001185846873685776165148563237 y[1] (numeric) = 2.000118584687368577616634714138 absolute error = 1.198578143e-22 relative error = 5.9925354035313135530358499607772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0155 y[1] (analytic) = 2.0001201298103133918105484154472 y[1] (numeric) = 2.000120129810313391810669052612 absolute error = 1.206371648e-22 relative error = 6.0314959587672836484711297632231e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0156 y[1] (analytic) = 2.0001216849356611075400814000045 y[1] (numeric) = 2.0001216849356611075402028165404 absolute error = 1.214165359e-22 relative error = 6.0704574533876755149904896823237e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0157 y[1] (analytic) = 2.0001232500634428348342298539589 y[1] (numeric) = 2.0001232500634428348343520498864 absolute error = 1.221959275e-22 relative error = 6.1094198818059842479735300638981e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0158 y[1] (analytic) = 2.0001248251936898839168676299835 y[1] (numeric) = 2.0001248251936898839169906053234 absolute error = 1.229753399e-22 relative error = 6.1483832584344431405162027117744e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0159 y[1] (analytic) = 2.000126410326433765209132127815 y[1] (numeric) = 2.0001264103264337652092558825882 absolute error = 1.237547732e-22 relative error = 6.1873475876858407315835953619827e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 2.0001280054617061893319460661503 y[1] (numeric) = 2.0001280054617061893320706003778 absolute error = 1.245342275e-22 relative error = 6.2263128739729199528754789742667e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0161 y[1] (analytic) = 2.0001296105995390671085552885156 y[1] (numeric) = 2.0001296105995390671086806022185 absolute error = 1.253137029e-22 relative error = 6.2652791217083778886690500481397e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0162 y[1] (analytic) = 2.0001312257399645095670826035393 y[1] (numeric) = 2.0001312257399645095672086967389 absolute error = 1.260931996e-22 relative error = 6.3042463403045374928369900208062e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0163 y[1] (analytic) = 2.0001328508830148279430976600637 y[1] (numeric) = 2.0001328508830148279432245327813 absolute error = 1.268727176e-22 relative error = 6.3432145291743233525287970907924e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0164 y[1] (analytic) = 2.0001344860287225336822028575313 y[1] (numeric) = 2.0001344860287225336823305097886 absolute error = 1.276522573e-22 relative error = 6.3821837077292849164387335583486e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=2.89 NO POLE x[1] = 0.0165 y[1] (analytic) = 2.0001361311771203384426352920878 y[1] (numeric) = 2.0001361311771203384427637239064 absolute error = 1.284318186e-22 relative error = 6.4211538703825770013479149801193e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0166 y[1] (analytic) = 2.0001377863282411540978847388415 y[1] (numeric) = 2.0001377863282411540980139502433 absolute error = 1.292114018e-22 relative error = 6.4601250315459622560366545134815e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0167 y[1] (analytic) = 2.0001394514821180927393276707269 y[1] (numeric) = 2.0001394514821180927394576617337 absolute error = 1.299910068e-22 relative error = 6.4990971856325170101028714231637e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0168 y[1] (analytic) = 2.0001411266387844666788773144188 y[1] (numeric) = 2.0001411266387844666790080850527 absolute error = 1.307706339e-22 relative error = 6.5380703470538919463466885991834e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0169 y[1] (analytic) = 2.0001428117982737884516497437489 y[1] (numeric) = 2.0001428117982737884517812940322 absolute error = 1.315502833e-22 relative error = 6.5770445252220131345590410242202e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 2.0001445069606197708186460110779 y[1] (numeric) = 2.0001445069606197708187783410329 absolute error = 1.323299550e-22 relative error = 6.6160197195494637192352698469392e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0171 y[1] (analytic) = 2.0001462121258563267694503170785 y[1] (numeric) = 2.0001462121258563267695834267276 absolute error = 1.331096491e-22 relative error = 6.6549959344484295416222777065180e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0172 y[1] (analytic) = 2.0001479272940175695249442193897 y[1] (numeric) = 2.0001479272940175695250781087556 absolute error = 1.338893659e-22 relative error = 6.6939731843303079222090214149580e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0173 y[1] (analytic) = 2.0001496524651378125400368806036 y[1] (numeric) = 2.000149652465137812540171549709 absolute error = 1.346691054e-22 relative error = 6.7329514686075348135768705279543e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0174 y[1] (analytic) = 2.0001513876392515695064113560483 y[1] (numeric) = 2.000151387639251569506546804916 absolute error = 1.354488677e-22 relative error = 6.7719307916921353577633009697297e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0175 y[1] (analytic) = 2.0001531328163935543552869218348 y[1] (numeric) = 2.0001531328163935543554231504879 absolute error = 1.362286531e-22 relative error = 6.8109111679953192819649483578963e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.1MB, time=3.10 NO POLE x[1] = 0.0176 y[1] (analytic) = 2.0001548879965986812601974436382 y[1] (numeric) = 2.0001548879965986812603344520998 absolute error = 1.370084616e-22 relative error = 6.8498925969293727356856428981848e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0177 y[1] (analytic) = 2.0001566531799020646397857866848 y[1] (numeric) = 2.0001566531799020646399235749781 absolute error = 1.377882933e-22 relative error = 6.8888750829061573256380368195683e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0178 y[1] (analytic) = 2.0001584283663390191606142674206 y[1] (numeric) = 2.0001584283663390191607528355691 absolute error = 1.385681485e-22 relative error = 6.9278586403366918996956922651574e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0179 y[1] (analytic) = 2.0001602135559450597399911473407 y[1] (numeric) = 2.0001602135559450597401304953678 absolute error = 1.393480271e-22 relative error = 6.9668432636335106949755694406994e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 2.0001620087487559015488131694577 y[1] (numeric) = 2.0001620087487559015489532973872 absolute error = 1.401279295e-22 relative error = 7.0058289722071074413779546732655e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0181 y[1] (analytic) = 2.0001638139448074600144241378959 y[1] (numeric) = 2.0001638139448074600145650457516 absolute error = 1.409078557e-22 relative error = 7.0448157654695083268948145579541e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0182 y[1] (analytic) = 2.0001656291441358508234895410948 y[1] (numeric) = 2.0001656291441358508236312289005 absolute error = 1.416878057e-22 relative error = 7.0838036428327055983391130253952e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0183 y[1] (analytic) = 2.0001674543467773899248872191121 y[1] (numeric) = 2.000167454346777389925029686892 absolute error = 1.424677799e-22 relative error = 7.1227926237069831679076271050621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0184 y[1] (analytic) = 2.0001692895527685935326140755185 y[1] (numeric) = 2.0001692895527685935327573232967 absolute error = 1.432477782e-22 relative error = 7.1617827025046335707188782119003e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0185 y[1] (analytic) = 2.0001711347621461781287088343774 y[1] (numeric) = 2.0001711347621461781288528621782 absolute error = 1.440278008e-22 relative error = 7.2007738886366498783831446147870e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0186 y[1] (analytic) = 2.0001729899749470604661908428077 y[1] (numeric) = 2.0001729899749470604663356506557 absolute error = 1.448078480e-22 relative error = 7.2397661965135212753573723404879e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0187 y[1] (analytic) = 2.0001748551912083575720149196299 y[1] (numeric) = 2.0001748551912083575721605075495 absolute error = 1.455879196e-22 relative error = 7.2787596155478318563051770388098e-21 % h = 0.0001 memory used=64.8MB, alloc=4.1MB, time=3.30 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0188 y[1] (analytic) = 2.0001767304109673867500422505962 y[1] (numeric) = 2.0001767304109673867501886186123 absolute error = 1.463680161e-22 relative error = 7.3177541701490756228398929297997e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0189 y[1] (analytic) = 2.0001786156342616655840273307134 y[1] (numeric) = 2.0001786156342616655841744788508 absolute error = 1.471481374e-22 relative error = 7.3567498547292965552750624034588e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 2.0001805108611289119406209541629 y[1] (numeric) = 2.0001805108611289119407688824466 absolute error = 1.479282837e-22 relative error = 7.3957466786991683613512082240612e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0191 y[1] (analytic) = 2.0001824160916070439723892523321 y[1] (numeric) = 2.0001824160916070439725379607871 absolute error = 1.487084550e-22 relative error = 7.4347446414702032960504506906137e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0192 y[1] (analytic) = 2.0001843313257341801208487804677 y[1] (numeric) = 2.0001843313257341801209982691195 absolute error = 1.494886518e-22 relative error = 7.4737437674515740426904974187953e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0193 y[1] (analytic) = 2.0001862565635486391195176534707 y[1] (numeric) = 2.0001862565635486391196679223446 absolute error = 1.502688739e-22 relative error = 7.5127440460555805942864746383021e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0194 y[1] (analytic) = 2.0001881918050889399969827313484 y[1] (numeric) = 2.0001881918050889399971337804699 absolute error = 1.510491215e-22 relative error = 7.5517454866926435278567351372198e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0195 y[1] (analytic) = 2.0001901370503938020799828548483 y[1] (numeric) = 2.000190137050393802080134684243 absolute error = 1.518293947e-22 relative error = 7.5907480937735837575142322003756e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0196 y[1] (analytic) = 2.0001920922995021449965081317967 y[1] (numeric) = 2.0001920922995021449966607414904 absolute error = 1.526096937e-22 relative error = 7.6297518767086861111010807143871e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0197 y[1] (analytic) = 2.00019405755245308867891527467 y[1] (numeric) = 2.0001940575524530886790686646887 absolute error = 1.533900187e-22 relative error = 7.6687568449081596259851870855195e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0198 y[1] (analytic) = 2.0001960328092859533670589899286 y[1] (numeric) = 2.0001960328092859533672131602983 absolute error = 1.541703697e-22 relative error = 7.7077629977831171269975549416508e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=3.49 NO POLE x[1] = 0.0199 y[1] (analytic) = 2.0001980180700402596114394196458 y[1] (numeric) = 2.0001980180700402596115943703927 absolute error = 1.549507469e-22 relative error = 7.7467703447436443734662050323855e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 2.0002000133347557282763656359674 y[1] (numeric) = 2.0002000133347557282765213671179 absolute error = 1.557311505e-22 relative error = 7.7857788951997501640545435755581e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0201 y[1] (analytic) = 2.0002020186034722805431351889412 y[1] (numeric) = 2.0002020186034722805432917005216 absolute error = 1.565115804e-22 relative error = 7.8247886435628808332204586956184e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0202 y[1] (analytic) = 2.0002040338762300379132297082546 y[1] (numeric) = 2.0002040338762300379133870002916 absolute error = 1.572920370e-22 relative error = 7.8637996092419150572985150082796e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0203 y[1] (analytic) = 2.0002060591530693222115265594281 y[1] (numeric) = 2.0002060591530693222116846319484 absolute error = 1.580725203e-22 relative error = 7.9028117916476734137756307934376e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0204 y[1] (analytic) = 2.0002080944340306555895265550067 y[1] (numeric) = 2.0002080944340306555896854080372 absolute error = 1.588530305e-22 relative error = 7.9418252001898980425704424619065e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0205 y[1] (analytic) = 2.0002101397191547605285977213023 y[1] (numeric) = 2.0002101397191547605287573548699 absolute error = 1.596335676e-22 relative error = 7.9808398342793027108847059671402e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0206 y[1] (analytic) = 2.0002121950084825598432351212356 y[1] (numeric) = 2.0002121950084825598433955353675 absolute error = 1.604141319e-22 relative error = 8.0198557083249715383422220547212e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0207 y[1] (analytic) = 2.0002142603020551766843367338354 y[1] (numeric) = 2.0002142603020551766844979285587 absolute error = 1.611947233e-22 relative error = 8.0588728167380307284998536509825e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0208 y[1] (analytic) = 2.0002163355999139345424953909493 y[1] (numeric) = 2.0002163355999139345426573662915 absolute error = 1.619753422e-22 relative error = 8.0978911789268845468922771056828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0209 y[1] (analytic) = 2.0002184209021003572513067717293 y[1] (numeric) = 2.0002184209021003572514695277179 absolute error = 1.627559886e-22 relative error = 8.1369107943019992114351952433201e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.1MB, time=3.69 NO POLE x[1] = 0.021 y[1] (analytic) = 2.0002205162086561689906934554522 y[1] (numeric) = 2.0002205162086561689908569921148 absolute error = 1.635366626e-22 relative error = 8.1759316672732504961353323843121e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0211 y[1] (analytic) = 2.000222621519623294290245033242 y[1] (numeric) = 2.0002226215196232942904093506066 absolute error = 1.643173646e-22 relative error = 8.2149538172487844466983273181079e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0212 y[1] (analytic) = 2.0002247368350438580325742792631 y[1] (numeric) = 2.0002247368350438580327393773575 absolute error = 1.650980944e-22 relative error = 8.2539772336399938445257907247134e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0213 y[1] (analytic) = 2.0002268621549601854566893819531 y[1] (numeric) = 2.0002268621549601854568552608053 absolute error = 1.658788522e-22 relative error = 8.2930019258560056692092715001661e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0214 y[1] (analytic) = 2.0002289974794148021613822358714 y[1] (numeric) = 2.0002289974794148021615488955096 absolute error = 1.666596382e-22 relative error = 8.3320279033058645790312490380453e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0215 y[1] (analytic) = 2.0002311428084504341086327947392 y[1] (numeric) = 2.0002311428084504341088002351917 absolute error = 1.674404525e-22 relative error = 8.3710551703991102112055429034314e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0216 y[1] (analytic) = 2.0002332981421100076270294862496 y[1] (numeric) = 2.0002332981421100076271977075449 absolute error = 1.682212953e-22 relative error = 8.4100837365446372726346269217701e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0217 y[1] (analytic) = 2.0002354634804366494152056892306 y[1] (numeric) = 2.0002354634804366494153746913973 absolute error = 1.690021667e-22 relative error = 8.4491136061518454182771288881238e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0218 y[1] (analytic) = 2.0002376388234736865452922737457 y[1] (numeric) = 2.0002376388234736865454620568125 absolute error = 1.697830668e-22 relative error = 8.4881447836300719200315099993225e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0219 y[1] (analytic) = 2.0002398241712646464663862047189 y[1] (numeric) = 2.0002398241712646464665567687147 absolute error = 1.705639958e-22 relative error = 8.5271772783879919381410532611368e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 2.0002420195238532570080352096754 y[1] (numeric) = 2.0002420195238532570082065546291 absolute error = 1.713449537e-22 relative error = 8.5662110898354057726508403030652e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0221 y[1] (analytic) = 2.0002442248812834463837385111898 y[1] (numeric) = 2.0002442248812834463839106371305 absolute error = 1.721259407e-22 relative error = 8.6052462273808515433329101425569e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.1MB, time=3.88 NO POLE x[1] = 0.0222 y[1] (analytic) = 2.0002464402435993431944636246382 y[1] (numeric) = 2.0002464402435993431946365315952 absolute error = 1.729069570e-22 relative error = 8.6442827004327818785105849119317e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0223 y[1] (analytic) = 2.0002486656108452764321792218528 y[1] (numeric) = 2.0002486656108452764323529098555 absolute error = 1.736880027e-22 relative error = 8.6833205134001850118184438760393e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0224 y[1] (analytic) = 2.0002509009830657754834040612797 y[1] (numeric) = 2.0002509009830657754835785303576 absolute error = 1.744690779e-22 relative error = 8.7223596706919850536180310371173e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0225 y[1] (analytic) = 2.0002531463603055701327719852438 y[1] (numeric) = 2.0002531463603055701329472354265 absolute error = 1.752501827e-22 relative error = 8.7614001767170417509577545482482e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0226 y[1] (analytic) = 2.0002554017426095905666129849279 y[1] (numeric) = 2.0002554017426095905667890162452 absolute error = 1.760313173e-22 relative error = 8.8004420408835118247053728678448e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0227 y[1] (analytic) = 2.0002576671300229673765503336751 y[1] (numeric) = 2.0002576671300229673767271461569 absolute error = 1.768124818e-22 relative error = 8.8394852676001085891227501465136e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0228 y[1] (analytic) = 2.0002599425225910315631137892265 y[1] (numeric) = 2.000259942522591031563291382903 absolute error = 1.775936765e-22 relative error = 8.8785298712741805813791106194752e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0229 y[1] (analytic) = 2.00026222792035931453936886551 y[1] (numeric) = 2.0002622279203593145395472404113 absolute error = 1.783749013e-22 relative error = 8.9175758463155871046362333059960e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 2.0002645233233735481345621745959 y[1] (numeric) = 2.0002645233233735481347413307522 absolute error = 1.791561563e-22 relative error = 8.9566231971328449029532809556089e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0231 y[1] (analytic) = 2.0002668287316796645977828394417 y[1] (numeric) = 2.0002668287316796645979627768836 absolute error = 1.799374419e-22 relative error = 8.9956719431324038183855725821193e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0232 y[1] (analytic) = 2.0002691441453237966016399780485 y[1] (numeric) = 2.0002691441453237966018206968065 absolute error = 1.807187580e-22 relative error = 9.0347220787239419048295712415333e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.1MB, time=4.08 NO POLE x[1] = 0.0233 y[1] (analytic) = 2.0002714695643522772459562596539 y[1] (numeric) = 2.0002714695643522772461377597587 absolute error = 1.815001048e-22 relative error = 9.0737736133150810831823973055875e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0234 y[1] (analytic) = 2.0002738049888116400614775335913 y[1] (numeric) = 2.0002738049888116400616598150738 absolute error = 1.822814825e-22 relative error = 9.1128265563133531029615017962981e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0235 y[1] (analytic) = 2.0002761504187486190135985314466 y[1] (numeric) = 2.0002761504187486190137815943377 absolute error = 1.830628911e-22 relative error = 9.1518809071275796138265242224612e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0236 y[1] (analytic) = 2.0002785058542101485061046431455 y[1] (numeric) = 2.0002785058542101485062884874764 absolute error = 1.838443309e-22 relative error = 9.1909366801644497067304740261595e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0237 y[1] (analytic) = 2.0002808712952433633849297676094 y[1] (numeric) = 2.0002808712952433633851143934114 absolute error = 1.846258020e-22 relative error = 9.2299938798319416428074716489942e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0238 y[1] (analytic) = 2.000283246741895598941930238619 y[1] (numeric) = 2.0002832467418955989421156459234 absolute error = 1.854073044e-22 relative error = 9.2690525055386734663372702658986e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0239 y[1] (analytic) = 2.0002856321942143909186748265271 y[1] (numeric) = 2.0002856321942143909188610153654 absolute error = 1.861888383e-22 relative error = 9.3081125666917906388568664505442e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 2.0002880276522474755102508164671 y[1] (numeric) = 2.0002880276522474755104377868709 absolute error = 1.869704038e-22 relative error = 9.3471740676990660761418444926155e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0241 y[1] (analytic) = 2.0002904331160427893690861637038 y[1] (numeric) = 2.0002904331160427893692739157049 absolute error = 1.877520011e-22 relative error = 9.3862370179674777631432487866592e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0242 y[1] (analytic) = 2.0002928485856484696087877267776 y[1] (numeric) = 2.000292848585648469608976260408 absolute error = 1.885336304e-22 relative error = 9.4253014269039103436979352071460e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0243 y[1] (analytic) = 2.0002952740611128538079955790952 y[1] (numeric) = 2.0002952740611128538081848943869 absolute error = 1.893152917e-22 relative error = 9.4643672939166307829719434793241e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.1MB, time=4.28 NO POLE x[1] = 0.0244 y[1] (analytic) = 2.0002977095424844800142533996224 y[1] (numeric) = 2.0002977095424844800144434966076 absolute error = 1.900969852e-22 relative error = 9.5034346284123720941862383782667e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0245 y[1] (analytic) = 2.0003001550298120867478949433388 y[1] (numeric) = 2.0003001550298120867480858220499 absolute error = 1.908787111e-22 relative error = 9.5425034397977727795860031345489e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0246 y[1] (analytic) = 2.0003026105231446130059465921148 y[1] (numeric) = 2.0003026105231446130061382525841 absolute error = 1.916604693e-22 relative error = 9.5815737224816455760983046533861e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0247 y[1] (analytic) = 2.0003050760225311982660459866754 y[1] (numeric) = 2.0003050760225311982662384289355 absolute error = 1.924422601e-22 relative error = 9.6206454908697313774140883938126e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0248 y[1] (analytic) = 2.0003075515280211824903767403183 y[1] (numeric) = 2.000307551528021182490569964402 absolute error = 1.932240837e-22 relative error = 9.6597187543684195594949879012704e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0249 y[1] (analytic) = 2.0003100370396641061296192350557 y[1] (numeric) = 2.0003100370396641061298132409958 absolute error = 1.940059401e-22 relative error = 9.6987935123855532725077642082001e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 2.0003125325575097101269175008517 y[1] (numeric) = 2.0003125325575097101271122886812 absolute error = 1.947878295e-22 relative error = 9.7378697743273664821798348719635e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0251 y[1] (analytic) = 2.0003150380816079359218621786316 y[1] (numeric) = 2.0003150380816079359220577483836 absolute error = 1.955697520e-22 relative error = 9.7769475446007837747749869552931e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0252 y[1] (analytic) = 2.0003175536120089254544895677399 y[1] (numeric) = 2.0003175536120089254546859194477 absolute error = 1.963517078e-22 relative error = 9.8160268326118637853800688566902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0253 y[1] (analytic) = 2.0003200791487630211692967585292 y[1] (numeric) = 2.0003200791487630211694938922261 absolute error = 1.971336969e-22 relative error = 9.8551076377681676082685544601430e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0254 y[1] (analytic) = 2.0003226146919207660192728507611 y[1] (numeric) = 2.0003226146919207660194707664807 absolute error = 1.979157196e-22 relative error = 9.8941899744747896419678200250856e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0255 y[1] (analytic) = 2.0003251602415329034699462585083 y[1] (numeric) = 2.0003251602415329034701449562842 absolute error = 1.986977759e-22 relative error = 9.9332738421391387827897266477522e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.1MB, time=4.49 NO POLE x[1] = 0.0256 y[1] (analytic) = 2.0003277157976503775034481022438 y[1] (numeric) = 2.0003277157976503775036475821098 absolute error = 1.994798660e-22 relative error = 9.9723592501669377107562295024692e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0257 y[1] (analytic) = 2.0003302813603243326225916888115 y[1] (numeric) = 2.0003302813603243326227919508015 absolute error = 2.002619900e-22 relative error = 1.0011446202964635482778950193323e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0258 y[1] (analytic) = 2.0003328569296061138549680799705 y[1] (numeric) = 2.0003328569296061138551691241185 absolute error = 2.010441480e-22 relative error = 1.0050534704938607222865879415700e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0259 y[1] (analytic) = 2.0003354425055472667570577502118 y[1] (numeric) = 2.000335442505547266757259576552 absolute error = 2.018263402e-22 relative error = 1.0089624765494315416524039710130e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 2.0003380380881995374183583345463 y[1] (numeric) = 2.0003380380881995374185609431131 absolute error = 2.026085668e-22 relative error = 1.0128716394037122189346770468395e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0261 y[1] (analytic) = 2.0003406436776148724655284669679 y[1] (numeric) = 2.0003406436776148724657318577957 absolute error = 2.033908278e-22 relative error = 1.0167809589973991745482919875469e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0262 y[1] (analytic) = 2.0003432592738454190665477102953 y[1] (numeric) = 2.0003432592738454190667518834187 absolute error = 2.041731234e-22 relative error = 1.0206904362710123241613839542935e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0263 y[1] (analytic) = 2.0003458848769435249348925781027 y[1] (numeric) = 2.0003458848769435249350975335564 absolute error = 2.049554537e-22 relative error = 1.0246000716651478867468810517430e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0264 y[1] (analytic) = 2.0003485204869617383337286494489 y[1] (numeric) = 2.0003485204869617383339343872678 absolute error = 2.057378189e-22 relative error = 1.0285098661203073990829680936216e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0265 y[1] (analytic) = 2.000351166103952808080118777119 y[1] (numeric) = 2.000351166103952808080325297338 absolute error = 2.065202190e-22 relative error = 1.0324198195771577142357537784085e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0266 y[1] (analytic) = 2.000353821727969683549247390095 y[1] (numeric) = 2.0003538217279696835494546927492 absolute error = 2.073026542e-22 relative error = 1.0363299329761838301498736206086e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.1MB, time=4.69 NO POLE x[1] = 0.0267 y[1] (analytic) = 2.0003564873590655146786608909741 y[1] (numeric) = 2.0003564873590655146788689760988 absolute error = 2.080851247e-22 relative error = 1.0402402072578604408482713933288e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0268 y[1] (analytic) = 2.0003591629972936519725241490578 y[1] (numeric) = 2.0003591629972936519727330166884 absolute error = 2.088676306e-22 relative error = 1.0441506428627416620745617683839e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0269 y[1] (analytic) = 2.0003618486427076465058930898346 y[1] (numeric) = 2.0003618486427076465061027400066 absolute error = 2.096501720e-22 relative error = 1.0480612402313738923583220885045e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 2.0003645442953612499290033815852 y[1] (numeric) = 2.0003645442953612499292138143343 absolute error = 2.104327491e-22 relative error = 1.0519720003042046695563887095335e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0271 y[1] (analytic) = 2.0003672499553084144715752198396 y[1] (numeric) = 2.0003672499553084144717864352015 absolute error = 2.112153619e-22 relative error = 1.0558829230218546529204746656153e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0272 y[1] (analytic) = 2.0003699656226032929471342104192 y[1] (numeric) = 2.0003699656226032929473462084299 absolute error = 2.119980107e-22 relative error = 1.0597940098246619892823265520202e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0273 y[1] (analytic) = 2.0003726912973002387573483517996 y[1] (numeric) = 2.0003726912973002387575611324951 absolute error = 2.127806955e-22 relative error = 1.0637052606532310293573923588156e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0274 y[1] (analytic) = 2.0003754269794538058963811175323 y[1] (numeric) = 2.0003754269794538058965946809488 absolute error = 2.135634165e-22 relative error = 1.0676166764479733130927730285076e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0275 y[1] (analytic) = 2.0003781726691187489552606394665 y[1] (numeric) = 2.0003781726691187489554749856404 absolute error = 2.143461739e-22 relative error = 1.0715282581492897596149822763968e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0276 y[1] (analytic) = 2.0003809283663500231262649925151 y[1] (numeric) = 2.0003809283663500231264801214828 absolute error = 2.151289677e-22 relative error = 1.0754400056977610461609613413694e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0277 y[1] (analytic) = 2.000383694071202784207323581711 y[1] (numeric) = 2.000383694071202784207539493509 absolute error = 2.159117980e-22 relative error = 1.0793519195338667553594193608983e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=95.3MB, alloc=4.1MB, time=4.89 x[1] = 0.0278 y[1] (analytic) = 2.0003864697837323886064346323034 y[1] (numeric) = 2.0003864697837323886066513269686 absolute error = 2.166946652e-22 relative error = 1.0832640015977887103656470653768e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0279 y[1] (analytic) = 2.0003892555039943933460987836472 y[1] (numeric) = 2.0003892555039943933463162612163 absolute error = 2.174775691e-22 relative error = 1.0871762508302761629273542769657e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 2.0003920512320445560677687876376 y[1] (numeric) = 2.0003920512320445560679870481477 absolute error = 2.182605101e-22 relative error = 1.0910886691714907310094728971456e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0281 y[1] (analytic) = 2.0003948569679388350363153124513 y[1] (numeric) = 2.0003948569679388350365343559395 absolute error = 2.190434882e-22 relative error = 1.0950012565619723626004480453812e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0282 y[1] (analytic) = 2.0003976727117333891445088523514 y[1] (numeric) = 2.0003976727117333891447286788549 absolute error = 2.198265035e-22 relative error = 1.0989140134421563178235990896175e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0283 y[1] (analytic) = 2.0004004984634845779175177443209 y[1] (numeric) = 2.0004004984634845779177383538772 absolute error = 2.206095563e-22 relative error = 1.1028269412522695345867808901925e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0284 y[1] (analytic) = 2.0004033342232489615174222922907 y[1] (numeric) = 2.0004033342232489615176436849372 absolute error = 2.213926465e-22 relative error = 1.1067400394329283973923069545941e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0285 y[1] (analytic) = 2.0004061799910833007477449997293 y[1] (numeric) = 2.0004061799910833007479671755037 absolute error = 2.221757744e-22 relative error = 1.1106533094243406914158096432637e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0286 y[1] (analytic) = 2.0004090357670445570579969113676 y[1] (numeric) = 2.0004090357670445570582198703077 absolute error = 2.229589401e-22 relative error = 1.1145667516669047836289584542746e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0287 y[1] (analytic) = 2.0004119015511898925482400648312 y[1] (numeric) = 2.0004119015511898925484638069749 absolute error = 2.237421437e-22 relative error = 1.1184803666010108019827625991846e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0288 y[1] (analytic) = 2.0004147773435766699736660529582 y[1] (numeric) = 2.0004147773435766699738905783436 absolute error = 2.245253854e-22 relative error = 1.1223941551669369385836313389639e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0289 y[1] (analytic) = 2.0004176631442624527491906975816 y[1] (numeric) = 2.0004176631442624527494160062468 absolute error = 2.253086652e-22 relative error = 1.1263081173051590019110097039964e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.2MB, time=5.09 NO POLE x[1] = 0.029 y[1] (analytic) = 2.0004205589533050049540648355588 y[1] (numeric) = 2.0004205589533050049542909275422 absolute error = 2.260919834e-22 relative error = 1.1302222544558320161578687058619e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0291 y[1] (analytic) = 2.0004234647707622913365012178336 y[1] (numeric) = 2.0004234647707622913367280931737 absolute error = 2.268753401e-22 relative error = 1.1341365670593085489247460026543e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0292 y[1] (analytic) = 2.0004263805966924773183175223183 y[1] (numeric) = 2.0004263805966924773185451810536 absolute error = 2.276587353e-22 relative error = 1.1380510550560393512926413785598e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0293 y[1] (analytic) = 2.0004293064311539289995954813863 y[1] (numeric) = 2.0004293064311539289998239235556 absolute error = 2.284421693e-22 relative error = 1.1419657198861477752657138389321e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0294 y[1] (analytic) = 2.0004322422742052131633561247699 y[1] (numeric) = 2.000432242274205213163585350412 absolute error = 2.292256421e-22 relative error = 1.1458805614900669934197501175403e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0295 y[1] (analytic) = 2.0004351881259050972802511386572 y[1] (numeric) = 2.0004351881259050972804811478112 absolute error = 2.300091540e-22 relative error = 1.1497955813078983269129667766069e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0296 y[1] (analytic) = 2.0004381439863125495132703417897 y[1] (numeric) = 2.0004381439863125495135011344946 absolute error = 2.307927049e-22 relative error = 1.1537107787801667508898289865961e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0297 y[1] (analytic) = 2.0004411098554867387224652793598 y[1] (numeric) = 2.0004411098554867387226968556549 absolute error = 2.315762951e-22 relative error = 1.1576261553469536181694257949975e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0298 y[1] (analytic) = 2.0004440857334870344696889355145 y[1] (numeric) = 2.0004440857334870344699212954392 absolute error = 2.323599247e-22 relative error = 1.1615417114485477931550171498973e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0299 y[1] (analytic) = 2.0004470716203730070233515652713 y[1] (numeric) = 2.0004470716203730070235847088652 absolute error = 2.331435939e-22 relative error = 1.1654574480251178104831228482490e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 2.000450067516204427363192646657 y[1] (numeric) = 2.0004500675162044273634265739597 absolute error = 2.339273027e-22 relative error = 1.1693733650170455825417042676229e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.2MB, time=5.28 NO POLE x[1] = 0.0301 y[1] (analytic) = 2.0004530734210412671850689538811 y[1] (numeric) = 2.0004530734210412671853036649324 absolute error = 2.347110513e-22 relative error = 1.1732894633644808910596871718002e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0302 y[1] (analytic) = 2.0004560893349436989057587523606 y[1] (numeric) = 2.0004560893349436989059942472005 absolute error = 2.354948399e-22 relative error = 1.1772057440075618444274692049488e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0303 y[1] (analytic) = 2.0004591152579720956677821164137 y[1] (numeric) = 2.0004591152579720956680183950822 absolute error = 2.362786685e-22 relative error = 1.1811222068866443336682222803967e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0304 y[1] (analytic) = 2.0004621511901870313442373704422 y[1] (numeric) = 2.0004621511901870313444744329796 absolute error = 2.370625374e-22 relative error = 1.1850388534417320142721051651266e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0305 y[1] (analytic) = 2.0004651971316492805436536544293 y[1] (numeric) = 2.0004651971316492805438915008758 absolute error = 2.378464465e-22 relative error = 1.1889556831132787958819203521509e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0306 y[1] (analytic) = 2.0004682530824198186148596145755 y[1] (numeric) = 2.0004682530824198186150982449717 absolute error = 2.386303962e-22 relative error = 1.1928726978411507181330480817526e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0307 y[1] (analytic) = 2.0004713190425598216518682199055 y[1] (numeric) = 2.0004713190425598216521076342919 absolute error = 2.394143864e-22 relative error = 1.1967898970657848433897604267725e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0308 y[1] (analytic) = 2.0004743950121306664987777056748 y[1] (numeric) = 2.0004743950121306664990179040922 absolute error = 2.401984174e-22 relative error = 1.2007072822271412378645560170203e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0309 y[1] (analytic) = 2.0004774809911939307546886444137 y[1] (numeric) = 2.0004774809911939307549296269029 absolute error = 2.409824892e-22 relative error = 1.2046248532655229673502529300899e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 2.0004805769798113927786371454431 y[1] (numeric) = 2.0004805769798113927788789120452 absolute error = 2.417666021e-22 relative error = 1.2085426116208669353635487748699e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0311 y[1] (analytic) = 2.0004836829780450316945441837061 y[1] (numeric) = 2.0004836829780450316947867344622 absolute error = 2.425507561e-22 relative error = 1.2124605572334575913187670119980e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0312 memory used=106.8MB, alloc=4.2MB, time=5.48 y[1] (analytic) = 2.0004867989859570273961810587543 y[1] (numeric) = 2.0004867989859570273964243937057 absolute error = 2.433349514e-22 relative error = 1.2163786910433301852716652842847e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0313 y[1] (analytic) = 2.0004899250036097605521509847379 y[1] (numeric) = 2.000489925003609760552395103926 absolute error = 2.441191881e-22 relative error = 1.2202970134906303114617254893975e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0314 y[1] (analytic) = 2.0004930610310658126108868122465 y[1] (numeric) = 2.0004930610310658126111317157128 absolute error = 2.449034663e-22 relative error = 1.2242155250154945425749368444692e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0315 y[1] (analytic) = 2.0004962070683879658056648828518 y[1] (numeric) = 2.000496207068387965805910570638 absolute error = 2.456877862e-22 relative error = 1.2281342265579263847658921565553e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0316 y[1] (analytic) = 2.0004993631156392031596350172075 y[1] (numeric) = 2.0004993631156392031598814893554 absolute error = 2.464721479e-22 relative error = 1.2320531185580419298137035703791e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0317 y[1] (analytic) = 2.0005025291728827084908666375615 y[1] (numeric) = 2.0005025291728827084911138941131 absolute error = 2.472565516e-22 relative error = 1.2359722019558225602755321388142e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0318 y[1] (analytic) = 2.0005057052401818664174110255416 y[1] (numeric) = 2.0005057052401818664176590665389 absolute error = 2.480409973e-22 relative error = 1.2398914766914901404758543384878e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0319 y[1] (analytic) = 2.0005088913176002623623797160754 y[1] (numeric) = 2.0005088913176002623626285415606 absolute error = 2.488254852e-22 relative error = 1.2438109437050061668284237253472e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 2.0005120874052016825590390283112 y[1] (numeric) = 2.0005120874052016825592886383267 absolute error = 2.496100155e-22 relative error = 1.2477306039363197608636079725868e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0321 y[1] (analytic) = 2.0005152935030501140559207344063 y[1] (numeric) = 2.0005152935030501140561711289946 absolute error = 2.503945883e-22 relative error = 1.2516504578254964104554529020500e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0322 y[1] (analytic) = 2.0005185096112097447219488670544 y[1] (numeric) = 2.000518509611209744722200046258 absolute error = 2.511792036e-22 relative error = 1.2555705053127219389137893149860e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0323 y[1] (analytic) = 2.0005217357297449632515826666239 y[1] (numeric) = 2.0005217357297449632518346304857 absolute error = 2.519638618e-22 relative error = 1.2594907483376545119809107975489e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.2MB, time=5.68 NO POLE x[1] = 0.0324 y[1] (analytic) = 2.000524971858720359169975668786 y[1] (numeric) = 2.0005249718587203591702284173488 absolute error = 2.527485628e-22 relative error = 1.2634111863405893433790305142020e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0325 y[1] (analytic) = 2.0005282179982007228381509335079 y[1] (numeric) = 2.0005282179982007228384044668147 absolute error = 2.535333068e-22 relative error = 1.2673318202614227165081062525288e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0326 y[1] (analytic) = 2.0005314741482510454581924162958 y[1] (numeric) = 2.0005314741482510454584467343898 absolute error = 2.543180940e-22 relative error = 1.2712526510400383060615699467790e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0327 y[1] (analytic) = 2.0005347403089365190784524825708 y[1] (numeric) = 2.0005347403089365190787075854952 absolute error = 2.551029244e-22 relative error = 1.2751736786165744277491178282614e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0328 y[1] (analytic) = 2.0005380164803225365987755660642 y[1] (numeric) = 2.0005380164803225365990314538626 absolute error = 2.558877984e-22 relative error = 1.2790949049306253676876652483352e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0329 y[1] (analytic) = 2.0005413026624746917757379721242 y[1] (numeric) = 2.00054130266247469177599464484 absolute error = 2.566727158e-22 relative error = 1.2830163289225778518587047844243e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 2.0005445988554587792279038268238 y[1] (numeric) = 2.0005445988554587792281612845008 absolute error = 2.574576770e-22 relative error = 1.2869379525320023033972448670418e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0331 y[1] (analytic) = 2.0005479050593407944410971727688 y[1] (numeric) = 2.0005479050593407944413554154508 absolute error = 2.582426820e-22 relative error = 1.2908597756989974980868878448365e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0332 y[1] (analytic) = 2.0005512212741869337736902125006 y[1] (numeric) = 2.0005512212741869337739492402315 absolute error = 2.590277309e-22 relative error = 1.2947817988635182006487746178381e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0333 y[1] (analytic) = 2.0005545475000635944619077003975 y[1] (numeric) = 2.0005545475000635944621675132214 absolute error = 2.598128239e-22 relative error = 1.2987040229653710102680827559145e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0334 y[1] (analytic) = 2.000557883737037374625147483977 y[1] (numeric) = 2.0005578837370373746254080819382 absolute error = 2.605979612e-22 relative error = 1.3026264489443496006822502176288e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.2MB, time=5.89 NO POLE x[1] = 0.0335 y[1] (analytic) = 2.0005612299851750732713171955056 y[1] (numeric) = 2.0005612299851750732715785786484 absolute error = 2.613831428e-22 relative error = 1.3065490767405152074901033169586e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0336 y[1] (analytic) = 2.0005645862445436903021870948259 y[1] (numeric) = 2.0005645862445436903024492631948 absolute error = 2.621683689e-22 relative error = 1.3104719072936405382080813914483e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0337 y[1] (analytic) = 2.0005679525152104265187590643123 y[1] (numeric) = 2.000567952515210426519022017952 absolute error = 2.629536397e-22 relative error = 1.3143949415434852580070129868228e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0338 y[1] (analytic) = 2.0005713287972426836266517568713 y[1] (numeric) = 2.0005713287972426836269154958265 absolute error = 2.637389552e-22 relative error = 1.3183181794300815235703308010145e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0339 y[1] (analytic) = 2.0005747150907080642415018979024 y[1] (numeric) = 2.000574715090708064241766422218 absolute error = 2.645243156e-22 relative error = 1.3222416218931678450302351585892e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 2.0005781113956743718943817421411 y[1] (numeric) = 2.0005781113956743718946470518622 absolute error = 2.653097211e-22 relative error = 1.3261652698724695732787947848044e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0341 y[1] (analytic) = 2.0005815177122096110372326863071 y[1] (numeric) = 2.0005815177122096110374987814787 absolute error = 2.660951716e-22 relative error = 1.3300891228081348625195582324574e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0342 y[1] (analytic) = 2.0005849340403819870483150384822 y[1] (numeric) = 2.0005849340403819870485819191497 absolute error = 2.668806675e-22 relative error = 1.3340131826395778990387853442370e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0343 y[1] (analytic) = 2.0005883603802599062376739451489 y[1] (numeric) = 2.0005883603802599062379416113577 absolute error = 2.676662088e-22 relative error = 1.3379374493067809466684744882341e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0344 y[1] (analytic) = 2.0005917967319119758526214768183 y[1] (numeric) = 2.0005917967319119758528899286141 absolute error = 2.684517958e-22 relative error = 1.3418619242492760815566753705152e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0345 y[1] (analytic) = 2.0005952430954070040832348731843 y[1] (numeric) = 2.0005952430954070040835041106127 absolute error = 2.692374284e-22 relative error = 1.3457866069071736424695899764794e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0346 y[1] (analytic) = 2.0005986994708140000678709487381 y[1] (numeric) = 2.000598699470814000068140971845 absolute error = 2.700231069e-22 relative error = 1.3497114987199823878072231077294e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.2MB, time=6.09 NO POLE x[1] = 0.0347 y[1] (analytic) = 2.0006021658582021738986966597859 y[1] (numeric) = 2.0006021658582021738989674686172 absolute error = 2.708088313e-22 relative error = 1.3536365996276456731369751375784e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0348 y[1] (analytic) = 2.000605642257640936627235833809 y[1] (numeric) = 2.0006056422576409366275074284109 absolute error = 2.715946019e-22 relative error = 1.3575619110696462175140442346577e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0349 y[1] (analytic) = 2.0006091286691999002699320621142 y[1] (numeric) = 2.0006091286691999002702044425328 absolute error = 2.723804186e-22 relative error = 1.3614874324860586890022245583456e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 2.0006126250929488778137277567206 y[1] (numeric) = 2.0006126250929488778140009230024 absolute error = 2.731662818e-22 relative error = 1.3654131658161891178134976733256e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0351 y[1] (analytic) = 2.0006161315289578832216593724353 y[1] (numeric) = 2.0006161315289578832219333246268 absolute error = 2.739521915e-22 relative error = 1.3693391109999388895424453937200e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0352 y[1] (analytic) = 2.0006196479772971314384687950697 y[1] (numeric) = 2.0006196479772971314387435332176 absolute error = 2.747381479e-22 relative error = 1.3732652689768930335436244794734e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0353 y[1] (analytic) = 2.0006231744380370383962308967542 y[1] (numeric) = 2.0006231744380370383965064209052 absolute error = 2.755241510e-22 relative error = 1.3771916396869343935968454059970e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0354 y[1] (analytic) = 2.0006267109112482210199972593092 y[1] (numeric) = 2.0006267109112482210202735695103 absolute error = 2.763102011e-22 relative error = 1.3811182245694692713778544205627e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0355 y[1] (analytic) = 2.0006302573970014972334560666357 y[1] (numeric) = 2.0006302573970014972337331629338 absolute error = 2.770962981e-22 relative error = 1.3850450230645167394904795562345e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0356 y[1] (analytic) = 2.0006338138953678859646081670881 y[1] (numeric) = 2.0006338138953678859648860495305 absolute error = 2.778824424e-22 relative error = 1.3889720371113007093156129734205e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0357 y[1] (analytic) = 2.0006373804064186071514593067989 y[1] (numeric) = 2.0006373804064186071517379754328 absolute error = 2.786686339e-22 relative error = 1.3928992661498206238399384957345e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.2MB, time=6.29 NO POLE x[1] = 0.0358 y[1] (analytic) = 2.0006409569302250817477285349229 y[1] (numeric) = 2.0006409569302250817480079897959 absolute error = 2.794548730e-22 relative error = 1.3968267121192718187717834062615e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0359 y[1] (analytic) = 2.0006445434668589317285727817768 y[1] (numeric) = 2.0006445434668589317288530229364 absolute error = 2.802411596e-22 relative error = 1.4007543744596339866285032838866e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 2.0006481400163919800963276108466 y[1] (numeric) = 2.0006481400163919800966086383406 absolute error = 2.810274940e-22 relative error = 1.4046822546102356991373627663679e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0361 y[1] (analytic) = 2.0006517465788962508862641456441 y[1] (numeric) = 2.0006517465788962508865459595204 absolute error = 2.818138763e-22 relative error = 1.4086103530107137135312908028505e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0362 y[1] (analytic) = 2.0006553631544439691723621723923 y[1] (numeric) = 2.0006553631544439691726447726988 absolute error = 2.826003065e-22 relative error = 1.4125386696008581470297918514045e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0363 y[1] (analytic) = 2.0006589897431075610730994195233 y[1] (numeric) = 2.0006589897431075610733828063081 absolute error = 2.833867848e-22 relative error = 1.4164672053201229036211999417294e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0364 y[1] (analytic) = 2.000662626344959653757257014977 y[1] (numeric) = 2.0006626263449596537575411882884 absolute error = 2.841733114e-22 relative error = 1.4203959611079477930218485663775e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0365 y[1] (analytic) = 2.0006662729600730754497411222889 y[1] (numeric) = 2.0006662729600730754500260821753 absolute error = 2.849598864e-22 relative error = 1.4243249374039249944964602860123e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0366 y[1] (analytic) = 2.0006699295885208554374207564596 y[1] (numeric) = 2.0006699295885208554377065029696 absolute error = 2.857465100e-22 relative error = 1.4282541351474687230134192474453e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0367 y[1] (analytic) = 2.0006735962303762240749817806016 y[1] (numeric) = 2.0006735962303762240752683137838 absolute error = 2.865331822e-22 relative error = 1.4321835542783156521365291822108e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0368 y[1] (analytic) = 2.0006772728857126127907970843601 y[1] (numeric) = 2.0006772728857126127910844042633 absolute error = 2.873199032e-22 relative error = 1.4361131957358570068973386630063e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=125.8MB, alloc=4.2MB, time=6.49 x[1] = 0.0369 y[1] (analytic) = 2.00068095955460365409281294511 y[1] (numeric) = 2.0006809595546036540931010517831 absolute error = 2.881066731e-22 relative error = 1.4400430599596399002342821723860e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 2.0006846562371231815744515729312 y[1] (numeric) = 2.0006846562371231815747404664233 absolute error = 2.888934921e-22 relative error = 1.4439731478890296907762545456561e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0371 y[1] (analytic) = 2.0006883629333452299205298403692 y[1] (numeric) = 2.0006883629333452299208195207295 absolute error = 2.896803603e-22 relative error = 1.4479034599635493917355982102961e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0372 y[1] (analytic) = 2.0006920796433440349131941979893 y[1] (numeric) = 2.0006920796433440349134846652671 absolute error = 2.904672778e-22 relative error = 1.4518339966227113045858148524868e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0373 y[1] (analytic) = 2.0006958063671940334378717767367 y[1] (numeric) = 2.0006958063671940334381630309816 absolute error = 2.912542449e-22 relative error = 1.4557647593056692129107400849320e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0374 y[1] (analytic) = 2.0006995431049698634892376781171 y[1] (numeric) = 2.0006995431049698634895297193786 absolute error = 2.920412615e-22 relative error = 1.4596957474522579708781968385321e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0375 y[1] (analytic) = 2.0007032898567463641771984532138 y[1] (numeric) = 2.0007032898567463641774912815417 absolute error = 2.928283279e-22 relative error = 1.4636269625016060646687087173062e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0376 y[1] (analytic) = 2.0007070466225985757328917715635 y[1] (numeric) = 2.0007070466225985757331853870077 absolute error = 2.936154442e-22 relative error = 1.4675584048931770630194868889897e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0377 y[1] (analytic) = 2.0007108134026017395147022809116 y[1] (numeric) = 2.0007108134026017395149966835221 absolute error = 2.944026105e-22 relative error = 1.4714900750664236731446295185819e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0378 y[1] (analytic) = 2.000714590196831298014293658874 y[1] (numeric) = 2.000714590196831298014588848701 absolute error = 2.951898270e-22 relative error = 1.4754219739606091330330739103989e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0379 y[1] (analytic) = 2.0007183770053628948626568575328 y[1] (numeric) = 2.0007183770053628948629528346266 absolute error = 2.959770938e-22 relative error = 1.4793541020151615169006130149467e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 2.000722173828272374836174541998 y[1] (numeric) = 2.0007221738282723748364713064089 absolute error = 2.967644109e-22 relative error = 1.4832864591696784288605922313947e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.2MB, time=6.69 NO POLE x[1] = 0.0381 y[1] (analytic) = 2.000725980665635783862701723968 y[1] (numeric) = 2.0007259806656357838629992757467 absolute error = 2.975517787e-22 relative error = 1.4872190473630245875214618882286e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0382 y[1] (analytic) = 2.0007297975175293690276625913273 y[1] (numeric) = 2.0007297975175293690279609305244 absolute error = 2.983391971e-22 relative error = 1.4911518660349542020873438789360e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0383 y[1] (analytic) = 2.0007336243840295785801635348186 y[1] (numeric) = 2.000733624384029578580462661485 absolute error = 2.991266664e-22 relative error = 1.4950849166244847242728901110262e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0384 y[1] (analytic) = 2.000737461265213061939122372834 y[1] (numeric) = 2.0007374612652130619394222870205 absolute error = 2.999141865e-22 relative error = 1.4990181985713520828880128413934e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0385 y[1] (analytic) = 2.000741308161156669699413775368 y[1] (numeric) = 2.0007413081611566696997144771258 absolute error = 3.007017578e-22 relative error = 1.5029517138143625048214633663223e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0386 y[1] (analytic) = 2.0007451650719374536380308881827 y[1] (numeric) = 2.0007451650719374536383323775631 absolute error = 3.014893804e-22 relative error = 1.5068854627928582283403973850152e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0387 y[1] (analytic) = 2.0007490319976326667202631582332 y[1] (numeric) = 2.0007490319976326667205654352875 absolute error = 3.022770543e-22 relative error = 1.5108194454463575185440243272013e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0388 y[1] (analytic) = 2.0007529089383197631058903614082 y[1] (numeric) = 2.000752908938319763106193426188 absolute error = 3.030647798e-22 relative error = 1.5147536632138068603369192832076e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0389 y[1] (analytic) = 2.000756795894076398155392833642 y[1] (numeric) = 2.0007567958940763981556966861988 absolute error = 3.038525568e-22 relative error = 1.5186881155348902862235008427782e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 2.0007606928649804284361779064556 y[1] (numeric) = 2.0007606928649804284364825468412 absolute error = 3.046403856e-22 relative error = 1.5226228038485279651727613042343e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0391 y[1] (analytic) = 2.00076459985110991172882254799 y[1] (numeric) = 2.0007645998511099117291279762563 absolute error = 3.054282663e-22 relative error = 1.5265577285940031700687873443233e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.2MB, time=6.89 NO POLE x[1] = 0.0392 y[1] (analytic) = 2.0007685168525431070333322105956 y[1] (numeric) = 2.0007685168525431070336384267946 absolute error = 3.062161990e-22 relative error = 1.5304928902105878779669085990805e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0393 y[1] (analytic) = 2.0007724438693584745754158860444 y[1] (numeric) = 2.0007724438693584745757228902284 absolute error = 3.070041840e-22 relative error = 1.5344282901371566733143964086713e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0394 y[1] (analytic) = 2.0007763809016346758127773694369 y[1] (numeric) = 2.0007763809016346758130851616581 absolute error = 3.077922212e-22 relative error = 1.5383639278133410084858895788568e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0395 y[1] (analytic) = 2.0007803279494505734414227328737 y[1] (numeric) = 2.0007803279494505734417313131846 absolute error = 3.085803109e-22 relative error = 1.5422998046779888025307884068664e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0396 y[1] (analytic) = 2.0007842850128852314019840099703 y[1] (numeric) = 2.0007842850128852314022933784235 absolute error = 3.093684532e-22 relative error = 1.5462359211703206637059629404036e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0397 y[1] (analytic) = 2.000788252092017914886059092292 y[1] (numeric) = 2.0007882520920179148863692489402 absolute error = 3.101566482e-22 relative error = 1.5501722777295457546944624413879e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0398 y[1] (analytic) = 2.0007922291869280903425678387896 y[1] (numeric) = 2.0007922291869280903428787836857 absolute error = 3.109448961e-22 relative error = 1.5541088752946637897786100367401e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0399 y[1] (analytic) = 2.0007962162976954254841243993217 y[1] (numeric) = 2.0007962162976954254844361325187 absolute error = 3.117331970e-22 relative error = 1.5580457143048579806771779591991e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 2.0008002134243997892934257533484 y[1] (numeric) = 2.0008002134243997892937382748994 absolute error = 3.125215510e-22 relative error = 1.5619827951993000066906034889623e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0401 y[1] (analytic) = 2.0008042205671212520296564648873 y[1] (numeric) = 2.0008042205671212520299697748456 absolute error = 3.133099583e-22 relative error = 1.5659201189169490164217023366553e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0402 y[1] (analytic) = 2.0008082377259400852349096548233 y[1] (numeric) = 2.0008082377259400852352237532422 absolute error = 3.140984189e-22 relative error = 1.5698576853971525198474645793782e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0403 y[1] (analytic) = 2.0008122649009367617406241916678 y[1] (numeric) = 2.0008122649009367617409390786008 absolute error = 3.148869330e-22 relative error = 1.5737954955788444640257438124611e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.2MB, time=7.09 NO POLE x[1] = 0.0404 y[1] (analytic) = 2.0008163020921919556740381018647 y[1] (numeric) = 2.0008163020921919556743537773656 absolute error = 3.156755009e-22 relative error = 1.5777335509007391416235653600204e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0405 y[1] (analytic) = 2.0008203492997865424646582007452 y[1] (numeric) = 2.0008203492997865424649746648677 absolute error = 3.164641225e-22 relative error = 1.5816718508023511033045208402703e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0406 y[1] (analytic) = 2.0008244065238015988507459452319 y[1] (numeric) = 2.00082440652380159885106319803 absolute error = 3.172527981e-22 relative error = 1.5856103967223672195862141399273e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0407 y[1] (analytic) = 2.0008284737643184028858195094027 y[1] (numeric) = 2.0008284737643184028861375509304 absolute error = 3.180415277e-22 relative error = 1.5895491886000756162073768656950e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0408 y[1] (analytic) = 2.0008325510214184339451720840192 y[1] (numeric) = 2.0008325510214184339454909143308 absolute error = 3.188303116e-22 relative error = 1.5934882278741325703516448688109e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0409 y[1] (analytic) = 2.0008366382951833727324064011348 y[1] (numeric) = 2.0008366382951833727327260202845 absolute error = 3.196191497e-22 relative error = 1.5974275139840107019904822586079e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.041 y[1] (analytic) = 2.0008407355856951012859854848946 y[1] (numeric) = 2.000840735585695101286305892937 absolute error = 3.204080424e-22 relative error = 1.6013670488681285090475438592306e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0411 y[1] (analytic) = 2.0008448428930357029857996296469 y[1] (numeric) = 2.0008448428930357029861208266366 absolute error = 3.211969897e-22 relative error = 1.6053068324657248382286426921450e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0412 y[1] (analytic) = 2.0008489602172874625597496064837 y[1] (numeric) = 2.0008489602172874625600715924755 absolute error = 3.219859918e-22 relative error = 1.6092468657156064553300543783730e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0413 y[1] (analytic) = 2.0008530875585328660903460993358 y[1] (numeric) = 2.0008530875585328660906688743845 absolute error = 3.227750487e-22 relative error = 1.6131871485569904605276755071304e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0414 y[1] (analytic) = 2.0008572249168546010213253717464 y[1] (numeric) = 2.0008572249168546010216489359071 absolute error = 3.235641607e-22 relative error = 1.6171276824284435019370122098184e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.2MB, time=7.29 NO POLE x[1] = 0.0415 y[1] (analytic) = 2.0008613722923355561642811654528 y[1] (numeric) = 2.0008613722923355561646055187805 absolute error = 3.243533277e-22 relative error = 1.6210684667693729899177626815724e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0416 y[1] (analytic) = 2.0008655296850588217053128319065 y[1] (numeric) = 2.0008655296850588217056379744566 absolute error = 3.251425501e-22 relative error = 1.6250095035181011928263142114846e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0417 y[1] (analytic) = 2.0008696970951076892116896978673 y[1] (numeric) = 2.0008696970951076892120156296953 absolute error = 3.259318280e-22 relative error = 1.6289507931135778774440694587219e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0418 y[1] (analytic) = 2.0008738745225656516385316662068 y[1] (numeric) = 2.0008738745225656516388583873682 absolute error = 3.267211614e-22 relative error = 1.6328923354949591153722629989906e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0419 y[1] (analytic) = 2.0008780619675164033355060530617 y[1] (numeric) = 2.0008780619675164033358335636122 absolute error = 3.275105505e-22 relative error = 1.6368341316009542313316655290791e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 2.0008822594300438400535406624792 y[1] (numeric) = 2.0008822594300438400538689624747 absolute error = 3.282999955e-22 relative error = 1.6407761823702562549759238254818e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0421 y[1] (analytic) = 2.0008864669102320589515530997003 y[1] (numeric) = 2.0008864669102320589518821891967 absolute error = 3.290894964e-22 relative error = 1.6447184877419849090562684270160e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0422 y[1] (analytic) = 2.0008906844081653586031963242281 y[1] (numeric) = 2.0008906844081653586035262032815 absolute error = 3.298790534e-22 relative error = 1.6486610486548068069573205513364e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0423 y[1] (analytic) = 2.0008949119239282390036204438325 y[1] (numeric) = 2.0008949119239282390039511124991 absolute error = 3.306686666e-22 relative error = 1.6526038655475957781243184453085e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0424 y[1] (analytic) = 2.000899149457605401576250750645 y[1] (numeric) = 2.0008991494576054015765822089813 absolute error = 3.314583363e-22 relative error = 1.6565469398587640522585983542390e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0425 y[1] (analytic) = 2.0009033970092817491795820005001 y[1] (numeric) = 2.0009033970092817491799142485625 absolute error = 3.322480624e-22 relative error = 1.6604902710276061097562250894296e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=144.9MB, alloc=4.2MB, time=7.48 x[1] = 0.0426 y[1] (analytic) = 2.0009076545790423861139889366817 y[1] (numeric) = 2.0009076545790423861143219745269 absolute error = 3.330378452e-22 relative error = 1.6644338604925053907018047208268e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0427 y[1] (analytic) = 2.0009119221669726181285530592377 y[1] (numeric) = 2.0009119221669726181288868869225 absolute error = 3.338276848e-22 relative error = 1.6683777086922802621755449512577e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0428 y[1] (analytic) = 2.0009161997731579524279056410268 y[1] (numeric) = 2.0009161997731579524282402586081 absolute error = 3.346175813e-22 relative error = 1.6723218160657367384780207615284e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0429 y[1] (analytic) = 2.0009204873976840976790869916653 y[1] (numeric) = 2.0009204873976840976794223992001 absolute error = 3.354075348e-22 relative error = 1.6762661830516684571899882625272e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 2.0009247850406369640184219705438 y[1] (numeric) = 2.0009247850406369640187581680894 absolute error = 3.361975456e-22 relative error = 1.6802108110883944764202804948386e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0431 y[1] (analytic) = 2.0009290927021026630584117500889 y[1] (numeric) = 2.0009290927021026630587487377026 absolute error = 3.369876137e-22 relative error = 1.6841557001149093183079764426487e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0432 y[1] (analytic) = 2.0009334103821675078946418304427 y[1] (numeric) = 2.0009334103821675078949796081819 absolute error = 3.377777392e-22 relative error = 1.6881008505699660964044030295525e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0433 y[1] (analytic) = 2.0009377380809180131127063067414 y[1] (numeric) = 2.0009377380809180131130448746638 absolute error = 3.385679224e-22 relative error = 1.6920462638918367874928323406917e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0434 y[1] (analytic) = 2.0009420757984408947951483901743 y[1] (numeric) = 2.0009420757984408947954877483375 absolute error = 3.393581632e-22 relative error = 1.6959919395197138219228662603549e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0435 y[1] (analytic) = 2.0009464235348230705284171840057 y[1] (numeric) = 2.0009464235348230705287573324677 absolute error = 3.401484620e-22 relative error = 1.6999378793916032821415611752290e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0436 y[1] (analytic) = 2.0009507812901516594098407157495 y[1] (numeric) = 2.0009507812901516594101816545682 absolute error = 3.409388187e-22 relative error = 1.7038840829466735423368756970192e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0437 y[1] (analytic) = 2.000955149064513982054615226684 y[1] (numeric) = 2.0009551490645139820549569559176 absolute error = 3.417292336e-22 relative error = 1.7078305516231343826289139302146e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.2MB, time=7.68 NO POLE x[1] = 0.0438 y[1] (analytic) = 2.0009595268579975606028107199014 y[1] (numeric) = 2.0009595268579975606031532396081 absolute error = 3.425197067e-22 relative error = 1.7117772853598935138410740375794e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0439 y[1] (analytic) = 2.0009639146706901187263927680865 y[1] (numeric) = 2.0009639146706901187267360783248 absolute error = 3.433102383e-22 relative error = 1.7157242855951277666032153865745e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 2.0009683125026795816362605822236 y[1] (numeric) = 2.0009683125026795816366046830521 absolute error = 3.441008285e-22 relative error = 1.7196715527674764213372841951820e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0441 y[1] (analytic) = 2.0009727203540540760893013424323 y[1] (numeric) = 2.0009727203540540760896462339096 absolute error = 3.448914773e-22 relative error = 1.7236190868158090814389230829614e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0442 y[1] (analytic) = 2.0009771382249019303954607921357 y[1] (numeric) = 2.0009771382249019303958064743206 absolute error = 3.456821849e-22 relative error = 1.7275668886784986705075115801929e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0443 y[1] (analytic) = 2.000981566115311674424830096769 y[1] (numeric) = 2.0009815661153116744251765697206 absolute error = 3.464729516e-22 relative error = 1.7315149597936556456485372764272e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0444 y[1] (analytic) = 2.0009860040253720396147489682373 y[1] (numeric) = 2.0009860040253720396150962320145 absolute error = 3.472637772e-22 relative error = 1.7354632991006006838742869197947e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0445 y[1] (analytic) = 2.0009904519551719589769250563336 y[1] (numeric) = 2.0009904519551719589772731109958 absolute error = 3.480546622e-22 relative error = 1.7394119090369224952275445759816e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0446 y[1] (analytic) = 2.0009949099048005671045696083353 y[1] (numeric) = 2.0009949099048005671049184539418 absolute error = 3.488456065e-22 relative error = 1.7433607890416707548990702401846e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0447 y[1] (analytic) = 2.0009993778743472001795493979936 y[1] (numeric) = 2.0009993778743472001798990346039 absolute error = 3.496366103e-22 relative error = 1.7473099400531419785987464662589e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0448 y[1] (analytic) = 2.0010038558639013959795549251388 y[1] (numeric) = 2.0010038558639013959799053528125 absolute error = 3.504276737e-22 relative error = 1.7512593625098661251731877445372e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.2MB, time=7.87 NO POLE x[1] = 0.0449 y[1] (analytic) = 2.0010083438735528938852848871242 y[1] (numeric) = 2.0010083438735528938856361059212 absolute error = 3.512187970e-22 relative error = 1.7552090578498562752577157238052e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 2.0010128419033916348876469233352 y[1] (numeric) = 2.0010128419033916348879989333153 absolute error = 3.520099801e-22 relative error = 1.7591590255121158674839557728871e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0451 y[1] (analytic) = 2.0010173499535077615949746339921 y[1] (numeric) = 2.0010173499535077615953274352153 absolute error = 3.528012232e-22 relative error = 1.7631092664348816847336180801922e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0452 y[1] (analytic) = 2.0010218680239916182402608744789 y[1] (numeric) = 2.0010218680239916182406144670055 absolute error = 3.535925266e-22 relative error = 1.7670597820561176277465804500737e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0453 y[1] (analytic) = 2.0010263961149337506884073264339 y[1] (numeric) = 2.0010263961149337506887617103241 absolute error = 3.543838902e-22 relative error = 1.7710105718147913489455563743443e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0454 y[1] (analytic) = 2.0010309342264249064434903468366 y[1] (numeric) = 2.001030934226424906443845522151 absolute error = 3.551753144e-22 relative error = 1.7749616376485784388451818974471e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0455 y[1] (analytic) = 2.0010354823585560346560430963354 y[1] (numeric) = 2.0010354823585560346563990631345 absolute error = 3.559667991e-22 relative error = 1.7789129789964214219030396263197e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0456 y[1] (analytic) = 2.0010400405114182861303539480548 y[1] (numeric) = 2.0010400405114182861307107063993 absolute error = 3.567583445e-22 relative error = 1.7828645967964791166816732564094e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0457 y[1] (analytic) = 2.0010446086851030133317811781318 y[1] (numeric) = 2.0010446086851030133321387280827 absolute error = 3.575499509e-22 relative error = 1.7868164924866315807420944615094e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0458 y[1] (analytic) = 2.001049186879701770394083939228 y[1] (numeric) = 2.0010491868797017703944422808461 absolute error = 3.583416181e-22 relative error = 1.7907686650060473001426412512027e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0459 y[1] (analytic) = 2.0010537750953063131267695182689 y[1] (numeric) = 2.0010537750953063131271286516154 absolute error = 3.591333465e-22 relative error = 1.7947211162923154063240600603303e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 2.0010583733320085990224568796665 y[1] (numeric) = 2.0010583733320085990228168048028 absolute error = 3.599251363e-22 relative error = 1.7986738472835269038226420967757e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.2MB, time=8.07 NO POLE x[1] = 0.0461 y[1] (analytic) = 2.0010629815899007872642564952805 y[1] (numeric) = 2.0010629815899007872646172122679 absolute error = 3.607169874e-22 relative error = 1.8026268574185516840886997137028e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0462 y[1] (analytic) = 2.0010675998690752387331664623784 y[1] (numeric) = 2.0010675998690752387335279712784 absolute error = 3.615089000e-22 relative error = 1.8065801476354552312668361943746e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0463 y[1] (analytic) = 2.0010722281696245160154849108579 y[1] (numeric) = 2.0010722281696245160158472117323 absolute error = 3.623008744e-22 relative error = 1.8105337193720171374652678533221e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0464 y[1] (analytic) = 2.0010768664916413834102387009971 y[1] (numeric) = 2.0010768664916413834106017939077 absolute error = 3.630929106e-22 relative error = 1.8144875725668015491627655455280e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0465 y[1] (analytic) = 2.0010815148352188069366284129998 y[1] (numeric) = 2.0010815148352188069369922980085 absolute error = 3.638850087e-22 relative error = 1.8184417076580935755153859548599e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0466 y[1] (analytic) = 2.0010861732004499543414896296079 y[1] (numeric) = 2.0010861732004499543418543067768 absolute error = 3.646771689e-22 relative error = 1.8223961255838934727548092214622e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0467 y[1] (analytic) = 2.0010908415874281951067705130551 y[1] (numeric) = 2.0010908415874281951071359824464 absolute error = 3.654693913e-22 relative error = 1.8263508267824559145995430847237e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0468 y[1] (analytic) = 2.0010955199962471004570256776378 y[1] (numeric) = 2.0010955199962471004573919393139 absolute error = 3.662616761e-22 relative error = 1.8303058121917483248606131796182e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0469 y[1] (analytic) = 2.0011002084270004433669263591836 y[1] (numeric) = 2.0011002084270004433672934132071 absolute error = 3.670540235e-22 relative error = 1.8342610827497199002915556158715e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 2.0011049068797821985687868826991 y[1] (numeric) = 2.0011049068797821985691547291325 absolute error = 3.678464334e-22 relative error = 1.8382166378951297842987243736638e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0471 y[1] (analytic) = 2.0011096153546865425601074294825 y[1] (numeric) = 2.0011096153546865425604760683886 absolute error = 3.686389061e-22 relative error = 1.8421724790656239051656507952421e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.2MB, time=8.27 NO POLE x[1] = 0.0472 y[1] (analytic) = 2.001114333851807853611133104989 y[1] (numeric) = 2.0011143338518078536115025364308 absolute error = 3.694314418e-22 relative error = 1.8461286071991035774624182506570e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0473 y[1] (analytic) = 2.0011190623712407117724293087402 y[1] (numeric) = 2.0011190623712407117727995327807 absolute error = 3.702240405e-22 relative error = 1.8500850222340109413771278517293e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0474 y[1] (analytic) = 2.0011238009130798988824734075697 y[1] (numeric) = 2.0011238009130798988828444242721 absolute error = 3.710167024e-22 relative error = 1.8540417251082175771005782534826e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0475 y[1] (analytic) = 2.0011285494774203985752627135033 y[1] (numeric) = 2.0011285494774203985756345229309 absolute error = 3.718094276e-22 relative error = 1.8579987162598585825936821717259e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0476 y[1] (analytic) = 2.0011333080643573962879387675714 y[1] (numeric) = 2.0011333080643573962883113697876 absolute error = 3.726022162e-22 relative error = 1.8619559961270552996495060692726e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0477 y[1] (analytic) = 2.0011380766739862792684279308561 y[1] (numeric) = 2.0011380766739862792688013259246 absolute error = 3.733950685e-22 relative error = 1.8659135661473465752574417550094e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0478 y[1] (analytic) = 2.0011428553064026365830982840788 y[1] (numeric) = 2.0011428553064026365834724720633 absolute error = 3.741879845e-22 relative error = 1.8698714262591045579915942204596e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0479 y[1] (analytic) = 2.0011476439617022591244328370341 y[1] (numeric) = 2.0011476439617022591248078179984 absolute error = 3.749809643e-22 relative error = 1.8738295769004055752625443888258e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 2.0011524426399811396187190491822 y[1] (numeric) = 2.0011524426399811396190948231903 absolute error = 3.757740081e-22 relative error = 1.8777880190090241429154590413015e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0481 y[1] (analytic) = 2.0011572513413354726337546627119 y[1] (numeric) = 2.0011572513413354726341312298281 absolute error = 3.765671162e-22 relative error = 1.8817467540224269373715105526917e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0482 y[1] (analytic) = 2.0011620700658616545865698493915 y[1] (numeric) = 2.0011620700658616545869472096799 absolute error = 3.773602884e-22 relative error = 1.8857057808795088231948229052281e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=164.0MB, alloc=4.2MB, time=8.46 x[1] = 0.0483 y[1] (analytic) = 2.0011668988136562837511656725245 y[1] (numeric) = 2.0011668988136562837515438260496 absolute error = 3.781535251e-22 relative error = 1.8896651015174158232378827928581e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0484 y[1] (analytic) = 2.0011717375848161602662688653343 y[1] (numeric) = 2.0011717375848161602666478121606 absolute error = 3.789468263e-22 relative error = 1.8936247158744365500086051186298e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0485 y[1] (analytic) = 2.0011765863794382861431029271004 y[1] (numeric) = 2.0011765863794382861434826672927 absolute error = 3.797401923e-22 relative error = 1.8975846253879685068088675061286e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0486 y[1] (analytic) = 2.0011814451976198652731755383747 y[1] (numeric) = 2.0011814451976198652735560719977 absolute error = 3.805336230e-22 relative error = 1.9015448294965661981659964058949e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0487 y[1] (analytic) = 2.0011863140394583034360822966071 y[1] (numeric) = 2.0011863140394583034364636237257 absolute error = 3.813271186e-22 relative error = 1.9055053291378905525154442194883e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0488 y[1] (analytic) = 2.0011911929050512083073267735138 y[1] (numeric) = 2.0011911929050512083077088941933 absolute error = 3.821206795e-22 relative error = 1.9094661262489882951755678979420e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0489 y[1] (analytic) = 2.0011960817944963894661568955252 y[1] (numeric) = 2.0011960817944963894665398098307 absolute error = 3.829143055e-22 relative error = 1.9134272197686704256480725333335e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 2.001200980707891858403417648649 y[1] (numeric) = 2.0012009807078918584038013566459 absolute error = 3.837079969e-22 relative error = 1.9173886111342481017486955352031e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0491 y[1] (analytic) = 2.0012058896453358285294201090934 y[1] (numeric) = 2.0012058896453358285298046108473 absolute error = 3.845017539e-22 relative error = 1.9213503012833097911326825639013e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0492 y[1] (analytic) = 2.0012108086069267151818268009925 y[1] (numeric) = 2.001210808606926715182212096569 absolute error = 3.852955765e-22 relative error = 1.9253122901540298577268199721854e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0493 y[1] (analytic) = 2.0012157375927631356335533825811 y[1] (numeric) = 2.0012157375927631356339394720459 absolute error = 3.860894648e-22 relative error = 1.9292745781842695711009149067134e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0494 y[1] (analytic) = 2.0012206766029439091006866621693 y[1] (numeric) = 2.0012206766029439091010735455884 absolute error = 3.868834191e-22 relative error = 1.9332371668112659582696011683493e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.2MB, time=8.67 NO POLE x[1] = 0.0495 y[1] (analytic) = 2.00122562563756805675041894527 y[1] (numeric) = 2.0012256256375680567508066227093 absolute error = 3.876774393e-22 relative error = 1.9372000554734567348421717354140e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0496 y[1] (analytic) = 2.0012305846967348017089987142329 y[1] (numeric) = 2.0012305846967348017093871857588 absolute error = 3.884715259e-22 relative error = 1.9411632466074304260633745096785e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0497 y[1] (analytic) = 2.0012355537805435690696976417461 y[1] (numeric) = 2.0012355537805435690700869074248 absolute error = 3.892656787e-22 relative error = 1.9451267391519022412298066168102e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0498 y[1] (analytic) = 2.0012405328890939859007939395632 y[1] (numeric) = 2.0012405328890939859011839994612 absolute error = 3.900598980e-22 relative error = 1.9490905345440381714998824553748e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0499 y[1] (analytic) = 2.0012455220224858812535720438232 y[1] (numeric) = 2.0012455220224858812539628980071 absolute error = 3.908541839e-22 relative error = 1.9530546332216022045073389806469e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 2.0012505211808192861703386383269 y[1] (numeric) = 2.0012505211808192861707302868634 absolute error = 3.916485365e-22 relative error = 1.9570190356223438629435855918752e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0501 y[1] (analytic) = 2.0012555303641944336924550171416 y[1] (numeric) = 2.0012555303641944336928474600976 absolute error = 3.924429560e-22 relative error = 1.9609837426836844949796114221584e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0502 y[1] (analytic) = 2.0012605495727117588683857879052 y[1] (numeric) = 2.0012605495727117588687790253478 absolute error = 3.932374426e-22 relative error = 1.9649487553430259231284382638493e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0503 y[1] (analytic) = 2.001265578806471898761763917206 y[1] (numeric) = 2.0012655788064718987621579492023 absolute error = 3.940319963e-22 relative error = 1.9689140735383827846034841271575e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0504 y[1] (analytic) = 2.0012706180655756924594721194147 y[1] (numeric) = 2.0012706180655756924598669460319 absolute error = 3.948266172e-22 relative error = 1.9728796977074427061236155194178e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0505 y[1] (analytic) = 2.001275667350124181079740590351 y[1] (numeric) = 2.0012756673501241810801362116566 absolute error = 3.956213056e-22 relative error = 1.9768456292872412878463985205848e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.2MB, time=8.87 NO POLE x[1] = 0.0506 y[1] (analytic) = 2.0012807266602186077802610871676 y[1] (numeric) = 2.0012807266602186077806575032292 absolute error = 3.964160616e-22 relative error = 1.9808118687154293543933735611648e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0507 y[1] (analytic) = 2.0012857959959604177663173558388 y[1] (numeric) = 2.001285795995960417766714566724 absolute error = 3.972108852e-22 relative error = 1.9847784159299642956276632991892e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0508 y[1] (analytic) = 2.0012908753574512582989319076414 y[1] (numeric) = 2.0012908753574512582993299134182 absolute error = 3.980057768e-22 relative error = 1.9887452728675038303852047845258e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0509 y[1] (analytic) = 2.001295964744792978703029146023 y[1] (numeric) = 2.0012959647447929787034279467592 absolute error = 3.988007362e-22 relative error = 1.9927124384666184072991367902211e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 2.0013010641580876303756148452488 y[1] (numeric) = 2.0013010641580876303760144410126 absolute error = 3.995957638e-22 relative error = 1.9966799146639286470055035440424e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0511 y[1] (analytic) = 2.0013061735974374667939719822287 y[1] (numeric) = 2.0013061735974374667943723730883 absolute error = 4.003908596e-22 relative error = 2.0006477013973304250283727229010e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0512 y[1] (analytic) = 2.0013112930629449435238729229218 y[1] (numeric) = 2.0013112930629449435242741089457 absolute error = 4.011860239e-22 relative error = 2.0046158001037270775423579076766e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0513 y[1] (analytic) = 2.0013164225547127182278079647245 y[1] (numeric) = 2.0013164225547127182282099459811 absolute error = 4.019812566e-22 relative error = 2.0085842102213124162125527830038e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0514 y[1] (analytic) = 2.0013215620728436506732302362464 y[1] (numeric) = 2.0013215620728436506736330128044 absolute error = 4.027765580e-22 relative error = 2.0125529331869549393150167754835e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0515 y[1] (analytic) = 2.0013267116174408027408169558843 y[1] (numeric) = 2.0013267116174408027412205278125 absolute error = 4.035719282e-22 relative error = 2.0165219694381608922850222141414e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0516 y[1] (analytic) = 2.0013318711886074384327470506061 y[1] (numeric) = 2.0013318711886074384331514179734 absolute error = 4.043673673e-22 relative error = 2.0204913194124215832617507146840e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0517 y[1] (analytic) = 2.0013370407864470238809951363587 y[1] (numeric) = 2.0013370407864470238814002992342 absolute error = 4.051628755e-22 relative error = 2.0244609840468793223020251420731e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.2MB, time=9.06 NO POLE x[1] = 0.0518 y[1] (analytic) = 2.0013422204110632273556418615178 y[1] (numeric) = 2.0013422204110632273560478199708 absolute error = 4.059584530e-22 relative error = 2.0284309642786562616739774098985e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0519 y[1] (analytic) = 2.0013474100625599192732006148006 y[1] (numeric) = 2.0013474100625599192736073689004 absolute error = 4.067540998e-22 relative error = 2.0324012600455275984496867454725e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 2.0013526097410411722049605990636 y[1] (numeric) = 2.0013526097410411722053681488796 absolute error = 4.075498160e-22 relative error = 2.0363718717849207356180045369473e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0521 y[1] (analytic) = 2.0013578194466112608853462724117 y[1] (numeric) = 2.0013578194466112608857546180136 absolute error = 4.083456019e-22 relative error = 2.0403428009335695552783704548391e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0522 y[1] (analytic) = 2.0013630391793746622202931580487 y[1] (numeric) = 2.0013630391793746622207022995062 absolute error = 4.091414575e-22 relative error = 2.0443140474292040017384303086990e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0523 y[1] (analytic) = 2.0013682689394360552956400242991 y[1] (numeric) = 2.0013682689394360552960499616821 absolute error = 4.099373830e-22 relative error = 2.0482856122088604256554012264932e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0524 y[1] (analytic) = 2.0013735087269003213855374362368 y[1] (numeric) = 2.0013735087269003213859481696154 absolute error = 4.107333786e-22 relative error = 2.0522574962095547866317596169280e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0525 y[1] (analytic) = 2.0013787585418725439608726803583 y[1] (numeric) = 2.0013787585418725439612842098026 absolute error = 4.115294443e-22 relative error = 2.0562296993689715087078159998223e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0526 y[1] (analytic) = 2.0013840183844580086977110637393 y[1] (numeric) = 2.0013840183844580086981233893197 absolute error = 4.123255804e-22 relative error = 2.0602022231237477363443433488919e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0527 y[1] (analytic) = 2.0013892882547622034857535891194 y[1] (numeric) = 2.0013892882547622034861667109063 absolute error = 4.131217869e-22 relative error = 2.0641750674115360866495669539055e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0528 y[1] (analytic) = 2.0013945681528908184368110073592 y[1] (numeric) = 2.0013945681528908184372249254232 absolute error = 4.139180640e-22 relative error = 2.0681482331692823521154394257421e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.2MB, time=9.26 NO POLE x[1] = 0.0529 y[1] (analytic) = 2.0013998580789497458932942487194 y[1] (numeric) = 2.0013998580789497458937089631312 absolute error = 4.147144118e-22 relative error = 2.0721217208342614545544548824645e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 2.0014051580330450804367212344132 y[1] (numeric) = 2.0014051580330450804371367452437 absolute error = 4.155108305e-22 relative error = 2.0760955313433819261559235141991e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0531 y[1] (analytic) = 2.0014104680152831188962400698865 y[1] (numeric) = 2.0014104680152831188966563772066 absolute error = 4.163073201e-22 relative error = 2.0800696646342363629542746836600e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0532 y[1] (analytic) = 2.0014157880257703603571686212819 y[1] (numeric) = 2.0014157880257703603575857251629 absolute error = 4.171038810e-22 relative error = 2.0840441226429924774627843429421e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0533 y[1] (analytic) = 2.0014211180646135061695504765492 y[1] (numeric) = 2.0014211180646135061699683770622 absolute error = 4.179005130e-22 relative error = 2.0880189043079167597972564184387e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0534 y[1] (analytic) = 2.0014264581319194599567272926613 y[1] (numeric) = 2.0014264581319194599571459898778 absolute error = 4.186972165e-22 relative error = 2.0919940115651380480359471087268e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0535 y[1] (analytic) = 2.0014318082277953276239275304055 y[1] (numeric) = 2.001431808227795327624347024397 absolute error = 4.194939915e-22 relative error = 2.0959694443521844705957889903468e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0536 y[1] (analytic) = 2.0014371683523484173668715782145 y[1] (numeric) = 2.0014371683523484173672918690528 absolute error = 4.202908383e-22 relative error = 2.0999452041054968710245697132481e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0537 y[1] (analytic) = 2.0014425385056862396803932665127 y[1] (numeric) = 2.0014425385056862396808143542695 absolute error = 4.210877568e-22 relative error = 2.1039212902629313228594010521926e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0538 y[1] (analytic) = 2.0014479186879165073670777740474 y[1] (numeric) = 2.0014479186879165073674996587948 absolute error = 4.218847474e-22 relative error = 2.1078977047605304576574328919000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0539 y[1] (analytic) = 2.0014533088991471355459159276863 y[1] (numeric) = 2.0014533088991471355463386094963 absolute error = 4.226818100e-22 relative error = 2.1118744470361204850624759747983e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=183.1MB, alloc=4.2MB, time=9.46 x[1] = 0.054 y[1] (analytic) = 2.0014587091394862416609748971576 y[1] (numeric) = 2.0014587091394862416613983761024 absolute error = 4.234789448e-22 relative error = 2.1158515180264295044409156832852e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0541 y[1] (analytic) = 2.0014641194090421454900852862177 y[1] (numeric) = 2.0014641194090421454905095623698 absolute error = 4.242761521e-22 relative error = 2.1198289191677987962129812245141e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0542 y[1] (analytic) = 2.001469539707923369153544621731 y[1] (numeric) = 2.0014695397079233691539696951629 absolute error = 4.250734319e-22 relative error = 2.1238066503976444682827597355625e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0543 y[1] (analytic) = 2.0014749700362386371228372421501 y[1] (numeric) = 2.0014749700362386371232631129344 absolute error = 4.258707843e-22 relative error = 2.1277847121530038329386485406353e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0544 y[1] (analytic) = 2.0014804103940968762293705868878 y[1] (numeric) = 2.0014804103940968762297972550973 absolute error = 4.266682095e-22 relative error = 2.1317631053705286175208939940520e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0545 y[1] (analytic) = 2.0014858607816072156732278880752 y[1] (numeric) = 2.0014858607816072156736553537828 absolute error = 4.274657076e-22 relative error = 2.1357418304872205164996971385024e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0546 y[1] (analytic) = 2.0014913211988789870319372662023 y[1] (numeric) = 2.0014913211988789870323655294811 absolute error = 4.282632788e-22 relative error = 2.1397208884396928529954075375141e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0547 y[1] (analytic) = 2.0014967916460217242692572311409 y[1] (numeric) = 2.0014967916460217242696862920641 absolute error = 4.290609232e-22 relative error = 2.1437002796649115631854065200672e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0548 y[1] (analytic) = 2.0015022721231451637439785900525 y[1] (numeric) = 2.0015022721231451637444084486934 absolute error = 4.298586409e-22 relative error = 2.1476800045998267016525703196140e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0549 y[1] (analytic) = 2.0015077626303592442187427636862 y[1] (numeric) = 2.0015077626303592442191734201184 absolute error = 4.306564322e-22 relative error = 2.1516600646806191040953223997685e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 2.0015132631677741068688765125758 y[1] (numeric) = 2.0015132631677741068693079668729 absolute error = 4.314542971e-22 relative error = 2.1556404598445767816624065340461e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0551 y[1] (analytic) = 2.0015187737355000952912430746456 y[1] (numeric) = 2.0015187737355000952916753268812 absolute error = 4.322522356e-22 relative error = 2.1596211900289772645268610996605e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.3MB, time=9.65 NO POLE x[1] = 0.0552 y[1] (analytic) = 2.0015242943336477555131097157398 y[1] (numeric) = 2.0015242943336477555135427659879 absolute error = 4.330502481e-22 relative error = 2.1636022571695644694844142727545e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0553 y[1] (analytic) = 2.0015298249623278360010316945928 y[1] (numeric) = 2.0015298249623278360014655429274 absolute error = 4.338483346e-22 relative error = 2.1675836612035784014191971176759e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0554 y[1] (analytic) = 2.0015353656216512876697526437581 y[1] (numeric) = 2.0015353656216512876701872902535 absolute error = 4.346464954e-22 relative error = 2.1715654035670978866833200010711e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0555 y[1] (analytic) = 2.0015409163117292638911213680206 y[1] (numeric) = 2.001540916311729263891556812751 absolute error = 4.354447304e-22 relative error = 2.1755474836977143185948890943448e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0556 y[1] (analytic) = 2.0015464770326731205030250618149 y[1] (numeric) = 2.0015464770326731205034613048548 absolute error = 4.362430399e-22 relative error = 2.1795299030314687800468728723772e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0557 y[1] (analytic) = 2.0015520477845944158183389471805 y[1] (numeric) = 2.0015520477845944158187759886045 absolute error = 4.370414240e-22 relative error = 2.1835126620051505253323661103924e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0558 y[1] (analytic) = 2.0015576285676049106338923337827 y[1] (numeric) = 2.0015576285676049106343301736654 absolute error = 4.378398827e-22 relative error = 2.1874957605559217325306197490315e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0559 y[1] (analytic) = 2.0015632193818165682394511025336 y[1] (numeric) = 2.00156321938181656823988974095 absolute error = 4.386384164e-22 relative error = 2.1914792006193719591184073479351e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 2.0015688202273415544267166143509 y[1] (numeric) = 2.0015688202273415544271560513759 absolute error = 4.394370250e-22 relative error = 2.1954629816330172614645525241618e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0561 y[1] (analytic) = 2.0015744311042922374983410455917 y[1] (numeric) = 2.0015744311042922374987812813005 absolute error = 4.402357088e-22 relative error = 2.1994471050327954255111490463801e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0562 y[1] (analytic) = 2.0015800520127811882769591517065 y[1] (numeric) = 2.0015800520127811882774001861744 absolute error = 4.410344679e-22 relative error = 2.2034315712554061396253307181215e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.3MB, time=9.85 NO POLE x[1] = 0.0563 y[1] (analytic) = 2.0015856829529211801142364606559 y[1] (numeric) = 2.0015856829529211801146782939583 absolute error = 4.418333024e-22 relative error = 2.2074163807375327625190783989243e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0564 y[1] (analytic) = 2.0015913239248251888999338976398 y[1] (numeric) = 2.0015913239248251889003765298522 absolute error = 4.426322124e-22 relative error = 2.2114015339158422993736556918717e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0565 y[1] (analytic) = 2.0015969749286063930709888426887 y[1] (numeric) = 2.0015969749286063930714322738869 absolute error = 4.434311982e-22 relative error = 2.2153870322261875275737689431343e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0566 y[1] (analytic) = 2.0016026359643781736206126226726 y[1] (numeric) = 2.0016026359643781736210568529323 absolute error = 4.442302597e-22 relative error = 2.2193728751059948720152202753623e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0567 y[1] (analytic) = 2.0016083070322541141074044392816 y[1] (numeric) = 2.0016083070322541141078494686787 absolute error = 4.450293971e-22 relative error = 2.2233590634914803653762084035608e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0568 y[1] (analytic) = 2.0016139881323480006644817345394 y[1] (numeric) = 2.0016139881323480006649275631502 absolute error = 4.458286108e-22 relative error = 2.2273455993180315759970731628033e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0569 y[1] (analytic) = 2.0016196792647738220086269954123 y[1] (numeric) = 2.0016196792647738220090736233129 absolute error = 4.466279006e-22 relative error = 2.2313324815234300914839513511031e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 2.0016253804296457694494509990761 y[1] (numeric) = 2.001625380429645769449898426343 absolute error = 4.474272669e-22 relative error = 2.2353197120430219276864637902238e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0571 y[1] (analytic) = 2.0016310916270782368985725004127 y[1] (numeric) = 2.0016310916270782368990207271223 absolute error = 4.482267096e-22 relative error = 2.2393072903141566622056825372256e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0572 y[1] (analytic) = 2.0016368128571858208788143633035 y[1] (numeric) = 2.0016368128571858208792633895326 absolute error = 4.490262291e-22 relative error = 2.2432952182721343490418787701226e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0573 y[1] (analytic) = 2.0016425441200833205334161372964 y[1] (numeric) = 2.0016425441200833205338659631218 absolute error = 4.498258254e-22 relative error = 2.2472834958538624744768238086935e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0574 y[1] (analytic) = 2.0016482854158857376352630812203 y[1] (numeric) = 2.0016482854158857376357137067189 absolute error = 4.506254986e-22 relative error = 2.2512721234958258574893607649943e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.3MB, time=10.05 NO POLE x[1] = 0.0575 y[1] (analytic) = 2.0016540367447082765961316353282 y[1] (numeric) = 2.001654036744708276596583060577 absolute error = 4.514252488e-22 relative error = 2.2552611016344926410287435478462e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0576 y[1] (analytic) = 2.0016597981066663444759513435502 y[1] (numeric) = 2.0016597981066663444764035686265 absolute error = 4.522250763e-22 relative error = 2.2592504317054850572536007668819e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0577 y[1] (analytic) = 2.0016655695018755509920832274422 y[1] (numeric) = 2.0016655695018755509925362524234 absolute error = 4.530249812e-22 relative error = 2.2632401141452291827306631196408e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0578 y[1] (analytic) = 2.0016713509304517085286146134172 y[1] (numeric) = 2.0016713509304517085290684383807 absolute error = 4.538249635e-22 relative error = 2.2672301488905518052887157419838e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0579 y[1] (analytic) = 2.0016771423925108321456704148508 y[1] (numeric) = 2.0016771423925108321461250398742 absolute error = 4.546250234e-22 relative error = 2.2712205368774308244980215232079e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 2.001682943888169139588740870654 y[1] (numeric) = 2.0016829438881691395891962958152 absolute error = 4.554251612e-22 relative error = 2.2752112795414011555910608322280e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0581 y[1] (analytic) = 2.0016887554175430512980257419107 y[1] (numeric) = 2.0016887554175430512984819672875 absolute error = 4.562253768e-22 relative error = 2.2792023763196565917990479275189e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0582 y[1] (analytic) = 2.0016945769807491904177949681771 y[1] (numeric) = 2.0016945769807491904182519938477 absolute error = 4.570256706e-22 relative error = 2.2831938291472692188065910159876e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0583 y[1] (analytic) = 2.0017004085779043828057657850484 y[1] (numeric) = 2.0017004085779043828062236110909 absolute error = 4.578260425e-22 relative error = 2.2871856374614004653890530577712e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0584 y[1] (analytic) = 2.0017062502091256570424963045944 y[1] (numeric) = 2.0017062502091256570429549310871 absolute error = 4.586264927e-22 relative error = 2.2911778021979278611505437934443e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0585 y[1] (analytic) = 2.0017121018745302444407955602742 y[1] (numeric) = 2.0017121018745302444412549872955 absolute error = 4.594270213e-22 relative error = 2.2951703237931337937692423477082e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.3MB, time=10.24 NO POLE x[1] = 0.0586 y[1] (analytic) = 2.0017179635742355790551500179402 y[1] (numeric) = 2.0017179635742355790556102455688 absolute error = 4.602276286e-22 relative error = 2.2991632036824254078950525068763e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0587 y[1] (analytic) = 2.0017238353083592976911665545445 y[1] (numeric) = 2.0017238353083592976916275828592 absolute error = 4.610283147e-22 relative error = 2.3031564423020422779643109353792e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0588 y[1] (analytic) = 2.0017297170770192399150319061647 y[1] (numeric) = 2.0017297170770192399154937352443 absolute error = 4.618290796e-22 relative error = 2.3071500395886389578843162350301e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0589 y[1] (analytic) = 2.0017356088803334480629885869679 y[1] (numeric) = 2.0017356088803334480634512168914 absolute error = 4.626299235e-22 relative error = 2.3111439964779917311689516533629e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 2.0017415107184201672508272807356 y[1] (numeric) = 2.0017415107184201672512907115822 absolute error = 4.634308466e-22 relative error = 2.3151383139058538808614495808853e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0591 y[1] (analytic) = 2.0017474225913978453833957065744 y[1] (numeric) = 2.0017474225913978453838599384234 absolute error = 4.642318490e-22 relative error = 2.3191329923083921150124352179835e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0592 y[1] (analytic) = 2.0017533444993851331641239604399 y[1] (numeric) = 2.0017533444993851331645889933708 absolute error = 4.650329309e-22 relative error = 2.3231280326213180029397736812992e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0593 y[1] (analytic) = 2.0017592764425008841045663341056 y[1] (numeric) = 2.0017592764425008841050321681979 absolute error = 4.658340923e-22 relative error = 2.3271234347811988471529202979793e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0594 y[1] (analytic) = 2.0017652184208641545339596132087 y[1] (numeric) = 2.0017652184208641545344262485421 absolute error = 4.666353334e-22 relative error = 2.3311191997237088015435788010920e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0595 y[1] (analytic) = 2.0017711704345942036087978560114 y[1] (numeric) = 2.0017711704345942036092652926658 absolute error = 4.674366544e-22 relative error = 2.3351153283844988203751791730244e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0596 y[1] (analytic) = 2.0017771324838104933224236545152 y[1] (numeric) = 2.0017771324838104933228918925706 absolute error = 4.682380554e-22 relative error = 2.3391118211996404981656514884439e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=202.1MB, alloc=4.3MB, time=10.44 x[1] = 0.0597 y[1] (analytic) = 2.0017831045686326885146358795717 y[1] (numeric) = 2.0017831045686326885151049191081 absolute error = 4.690395364e-22 relative error = 2.3431086781056334727095484041919e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0598 y[1] (analytic) = 2.0017890866891806568813139116333 y[1] (numeric) = 2.0017890866891806568817837527311 absolute error = 4.698410978e-22 relative error = 2.3471059010371785059043873487534e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0599 y[1] (analytic) = 2.0017950788455744689840583587944 y[1] (numeric) = 2.001795078845574468984529001534 absolute error = 4.706427396e-22 relative error = 2.3511034899307345159609053465562e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 2.0018010810379343982598482637709 y[1] (numeric) = 2.0018010810379343982603197082329 absolute error = 4.714444620e-22 relative error = 2.3551014457218492449278695098136e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0601 y[1] (analytic) = 2.0018070932663809210307148014737 y[1] (numeric) = 2.0018070932663809210311870477387 absolute error = 4.722462650e-22 relative error = 2.3590997683469497182485972965182e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0602 y[1] (analytic) = 2.0018131155310347165134314688314 y[1] (numeric) = 2.0018131155310347165139045169803 absolute error = 4.730481489e-22 relative error = 2.3630984592410928827407445337687e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0603 y[1] (analytic) = 2.0018191478320166668292207685231 y[1] (numeric) = 2.0018191478320166668296946186369 absolute error = 4.738501138e-22 relative error = 2.3670975188402148959537581003082e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0604 y[1] (analytic) = 2.001825190169447857013477388282 y[1] (numeric) = 2.0018251901694478570139520404417 absolute error = 4.746521597e-22 relative error = 2.3710969470806902492549703787936e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0605 y[1] (analytic) = 2.0018312425434495750255078774352 y[1] (numeric) = 2.0018312425434495750259833317221 absolute error = 4.754542869e-22 relative error = 2.3750967453975097282797110304215e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0606 y[1] (analytic) = 2.0018373049541433117582868223487 y[1] (numeric) = 2.0018373049541433117587630788442 absolute error = 4.762564955e-22 relative error = 2.3790969142265522449600412670354e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0607 y[1] (analytic) = 2.0018433774016507610482295224474 y[1] (numeric) = 2.001843377401650761048706581233 absolute error = 4.770587856e-22 relative error = 2.3830974540036790770106907068817e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0608 y[1] (analytic) = 2.0018494598860938196849811684839 y[1] (numeric) = 2.0018494598860938196854590296412 absolute error = 4.778611573e-22 relative error = 2.3870983651647338440784357683938e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.3MB, time=10.63 NO POLE x[1] = 0.0609 y[1] (analytic) = 2.001855552407594587421222524733 y[1] (numeric) = 2.0018555524075945874217011883438 absolute error = 4.786636108e-22 relative error = 2.3910996486450790257755215267481e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.061 y[1] (analytic) = 2.0018616549662753669824921167912 y[1] (numeric) = 2.0018616549662753669829715829376 absolute error = 4.794661464e-22 relative error = 2.3951013058795883237898090476924e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0611 y[1] (analytic) = 2.0018677675622586640770249266639 y[1] (numeric) = 2.0018677675622586640775051954279 absolute error = 4.802687640e-22 relative error = 2.3991033363049715177048621010936e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0612 y[1] (analytic) = 2.0018738901956671874056075968241 y[1] (numeric) = 2.0018738901956671874060886682879 absolute error = 4.810714638e-22 relative error = 2.4031057408565287090328822423753e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0613 y[1] (analytic) = 2.0018800228666238486714501449323 y[1] (numeric) = 2.0018800228666238486719320191784 absolute error = 4.818742461e-22 relative error = 2.4071085209690665215040272363005e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0614 y[1] (analytic) = 2.0018861655752517625900741909081 y[1] (numeric) = 2.0018861655752517625905568680189 absolute error = 4.826771108e-22 relative error = 2.4111116760792458738701087871165e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0615 y[1] (analytic) = 2.001892318321674246899217698046 y[1] (numeric) = 2.0018923183216742468997011781041 absolute error = 4.834800581e-22 relative error = 2.4151152071223041850815897053744e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0616 y[1] (analytic) = 2.0018984811060148223687562298738 y[1] (numeric) = 2.0018984811060148223692405129621 absolute error = 4.842830883e-22 relative error = 2.4191191155329806739974784835541e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0617 y[1] (analytic) = 2.0019046539283972128106407244523 y[1] (numeric) = 2.0019046539283972128111258106536 absolute error = 4.850862013e-22 relative error = 2.4231234007478871614618402784584e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0618 y[1] (analytic) = 2.0019108367889453450888517878183 y[1] (numeric) = 2.0019108367889453450893376772157 absolute error = 4.858893974e-22 relative error = 2.4271280642017208261984434083022e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0619 y[1] (analytic) = 2.001917029687783349129370508277 y[1] (numeric) = 2.0019170296877833491298572009537 absolute error = 4.866926767e-22 relative error = 2.4311331063301061164753145171584e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.3MB, time=10.83 NO POLE x[1] = 0.062 y[1] (analytic) = 2.0019232326250355579301657932514 y[1] (numeric) = 2.0019232326250355579306532892908 absolute error = 4.874960394e-22 relative error = 2.4351385280681691152239294370995e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0621 y[1] (analytic) = 2.0019294456008265075711982304001 y[1] (numeric) = 2.0019294456008265075716865298856 absolute error = 4.882994855e-22 relative error = 2.4391443293519754544263472230166e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0622 y[1] (analytic) = 2.0019356686152809372244404747165 y[1] (numeric) = 2.0019356686152809372249295777318 absolute error = 4.891030153e-22 relative error = 2.4431505116161285475595298611334e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0623 y[1] (analytic) = 2.0019419016685237891639141633276 y[1] (numeric) = 2.0019419016685237891644040699563 absolute error = 4.899066287e-22 relative error = 2.4471570742971412935182862163512e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0624 y[1] (analytic) = 2.0019481447606802087757433597104 y[1] (numeric) = 2.0019481447606802087762340700365 absolute error = 4.907103261e-22 relative error = 2.4511640193290880975152566359262e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0625 y[1] (analytic) = 2.0019543978918755445682245290501 y[1] (numeric) = 2.0019543978918755445687160431577 absolute error = 4.915141076e-22 relative error = 2.4551713471474708710632772651395e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0626 y[1] (analytic) = 2.001960661062235348181913046464 y[1] (numeric) = 2.0019606610622353481824053644373 absolute error = 4.923179733e-22 relative error = 2.4591790581877733186246734764859e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0627 y[1] (analytic) = 2.0019669342718853743997262398202 y[1] (numeric) = 2.0019669342718853744002193617434 absolute error = 4.931219232e-22 relative error = 2.4631871523859521642113944450846e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0628 y[1] (analytic) = 2.0019732175209515811570629688817 y[1] (numeric) = 2.0019732175209515811575568948393 absolute error = 4.939259576e-22 relative error = 2.4671956311764736935113643274658e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0629 y[1] (analytic) = 2.0019795108095601295519397425107 y[1] (numeric) = 2.0019795108095601295524344725874 absolute error = 4.947300767e-22 relative error = 2.4712044954942677552570579028350e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 2.0019858141378373838551433756696 y[1] (numeric) = 2.00198581413783738385563890995 absolute error = 4.955342804e-22 relative error = 2.4752137447757274732306475604014e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0631 y[1] (analytic) = 2.0019921275059099115204001879573 y[1] (numeric) = 2.0019921275059099115208965265264 absolute error = 4.963385691e-22 relative error = 2.4792233809547525351990925868678e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.3MB, time=11.02 NO POLE x[1] = 0.0632 y[1] (analytic) = 2.0019984509139044831945617454262 y[1] (numeric) = 2.0019984509139044831950588883689 absolute error = 4.971429427e-22 relative error = 2.4832334034677009164279713410837e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0633 y[1] (analytic) = 2.0020047843619480727278071474221 y[1] (numeric) = 2.0020047843619480727283050948237 absolute error = 4.979474016e-22 relative error = 2.4872438142484213439465107392688e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0634 y[1] (analytic) = 2.0020111278501678571838618601986 y[1] (numeric) = 2.0020111278501678571843606121443 absolute error = 4.987519457e-22 relative error = 2.4912546127332365242109729214367e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0635 y[1] (analytic) = 2.0020174813786912168502330990542 y[1] (numeric) = 2.0020174813786912168507326556295 absolute error = 4.995565753e-22 relative error = 2.4952658003564479154007176878768e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0636 y[1] (analytic) = 2.0020238449476457352484617607492 y[1] (numeric) = 2.0020238449476457352489621220397 absolute error = 5.003612905e-22 relative error = 2.4992773775533366984007913169060e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0637 y[1] (analytic) = 2.0020302185571591991443909079575 y[1] (numeric) = 2.0020302185571591991448920740488 absolute error = 5.011660913e-22 relative error = 2.5032893442596725649051084225129e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0638 y[1] (analytic) = 2.0020366022073595985584508075132 y[1] (numeric) = 2.0020366022073595985589527784912 absolute error = 5.019709780e-22 relative error = 2.5073017019096871265029383239178e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0639 y[1] (analytic) = 2.0020429958983751267759605242168 y[1] (numeric) = 2.0020429958983751267764633001675 absolute error = 5.027759507e-22 relative error = 2.5113144509386011271769578136783e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 2.0020493996303341803574460719639 y[1] (numeric) = 2.0020493996303341803579496529735 absolute error = 5.035810096e-22 relative error = 2.5153275922811048698749023548894e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0641 y[1] (analytic) = 2.0020558134033653591489751239676 y[1] (numeric) = 2.0020558134033653591494795101223 absolute error = 5.043861547e-22 relative error = 2.5193411258728904686851995325405e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0642 y[1] (analytic) = 2.0020622372175974662925082838437 y[1] (numeric) = 2.00206223721759746629301347523 absolute error = 5.051913863e-22 relative error = 2.5233550531480926853317285025111e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.3MB, time=11.23 NO POLE x[1] = 0.0643 y[1] (analytic) = 2.0020686710731595082362669193353 y[1] (numeric) = 2.0020686710731595082367729160397 absolute error = 5.059967044e-22 relative error = 2.5273693740423646534668035144377e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0644 y[1] (analytic) = 2.0020751149701806947451175604522 y[1] (numeric) = 2.0020751149701806947456243625614 absolute error = 5.068021092e-22 relative error = 2.5313840894903107143818948181166e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0645 y[1] (analytic) = 2.0020815689087904389109728638062 y[1] (numeric) = 2.0020815689087904389114804714071 absolute error = 5.076076009e-22 relative error = 2.5353992004265100191112005194866e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0646 y[1] (analytic) = 2.0020880328891183571632091449254 y[1] (numeric) = 2.0020880328891183571637175581049 absolute error = 5.084131795e-22 relative error = 2.5394147067865594072667838849668e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0647 y[1] (analytic) = 2.0020945069112942692791004803324 y[1] (numeric) = 2.0020945069112942692796096991776 absolute error = 5.092188452e-22 relative error = 2.5434306095049971937983263341643e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0648 y[1] (analytic) = 2.0021009909754481983942693811761 y[1] (numeric) = 2.0021009909754481983947794057743 absolute error = 5.100245982e-22 relative error = 2.5474469095163363870107472965860e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0649 y[1] (analytic) = 2.0021074850817103710131540402091 y[1] (numeric) = 2.0021074850817103710136648706478 absolute error = 5.108304387e-22 relative error = 2.5514636077550646397906919249469e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 2.0021139892302112170194921539039 y[1] (numeric) = 2.0021139892302112170200037902706 absolute error = 5.116363667e-22 relative error = 2.5554807041567000793910627297632e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0651 y[1] (analytic) = 2.0021205034210813696868213215062 y[1] (numeric) = 2.0021205034210813696873337638886 absolute error = 5.124423824e-22 relative error = 2.5594981996556892521758612174679e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0652 y[1] (analytic) = 2.002127027654451665688996022826 y[1] (numeric) = 2.0021270276544516656895092713119 absolute error = 5.132484859e-22 relative error = 2.5635160946869844246958227569738e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0653 y[1] (analytic) = 2.002133561930453145110721176569 y[1] (numeric) = 2.0021335619304531451112352312463 absolute error = 5.140546773e-22 relative error = 2.5675343896855188633128222079518e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=221.2MB, alloc=4.3MB, time=11.43 x[1] = 0.0654 y[1] (analytic) = 2.0021401062492170514581022810142 y[1] (numeric) = 2.0021401062492170514586171419711 absolute error = 5.148609569e-22 relative error = 2.5715530860851379010425149851572e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0655 y[1] (analytic) = 2.0021466606108748316692121388485 y[1] (numeric) = 2.0021466606108748316697278061732 absolute error = 5.156673247e-22 relative error = 2.5755721838212630116498462973028e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0656 y[1] (analytic) = 2.0021532250155581361246741679671 y[1] (numeric) = 2.002153225015558136125190641748 absolute error = 5.164737809e-22 relative error = 2.5795916838282276629636690201393e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0657 y[1] (analytic) = 2.002159799463398818658262300058 y[1] (numeric) = 2.0021597994633988186587795803836 absolute error = 5.172803256e-22 relative error = 2.5836115865408790194798821091898e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0658 y[1] (analytic) = 2.0021663839545289365675174687851 y[1] (numeric) = 2.0021663839545289365680355557441 absolute error = 5.180869590e-22 relative error = 2.5876318928935040864923818276926e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0659 y[1] (analytic) = 2.002172978489080750624380689393 y[1] (numeric) = 2.0021729784890807506248995830742 absolute error = 5.188936812e-22 relative error = 2.5916526033209067710283424805150e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 2.0021795830671867250858427315552 y[1] (numeric) = 2.0021795830671867250863624320476 absolute error = 5.197004924e-22 relative error = 2.5956737187573274656878290500397e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0661 y[1] (analytic) = 2.0021861976889795277046103872932 y[1] (numeric) = 2.0021861976889795277051308946859 absolute error = 5.205073927e-22 relative error = 2.5996952396375266798518504355769e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0662 y[1] (analytic) = 2.002192822354592029739789335795 y[1] (numeric) = 2.0021928223545920297403106501771 absolute error = 5.213143821e-22 relative error = 2.6037171658967932536501343439727e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0663 y[1] (analytic) = 2.0021994570641573059675836069654 y[1] (numeric) = 2.0021994570641573059681057284264 absolute error = 5.221214610e-22 relative error = 2.6077394994682063082034213932763e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0664 y[1] (analytic) = 2.0022061018178086346920116455437 y[1] (numeric) = 2.002206101817808634692534574173 absolute error = 5.229286293e-22 relative error = 2.6117622397875603559252089851683e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0665 y[1] (analytic) = 2.0022127566156794977556389776253 y[1] (numeric) = 2.0022127566156794977561627135127 absolute error = 5.237358874e-22 relative error = 2.6157853887878809246755885895120e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.3MB, time=11.64 NO POLE x[1] = 0.0666 y[1] (analytic) = 2.0022194214579035805503274814304 y[1] (numeric) = 2.0022194214579035805508520246656 absolute error = 5.245432352e-22 relative error = 2.6198089459049254239115461310517e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0667 y[1] (analytic) = 2.0022260963446147720280012641605 y[1] (numeric) = 2.0022260963446147720285266148334 absolute error = 5.253506729e-22 relative error = 2.6238329120727774288116526079277e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0668 y[1] (analytic) = 2.0022327812759471647114291467921 y[1] (numeric) = 2.0022327812759471647119553049928 absolute error = 5.261582007e-22 relative error = 2.6278572882254944122043669386915e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0669 y[1] (analytic) = 2.0022394762520350547050237586556 y[1] (numeric) = 2.0022394762520350547055507244743 absolute error = 5.269658187e-22 relative error = 2.6318820747976669386680290291742e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 2.0022461812730129417056572436521 y[1] (numeric) = 2.0022461812730129417061850171792 absolute error = 5.277735271e-22 relative error = 2.6359072727233051475654053560311e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0671 y[1] (analytic) = 2.0022528963390155290134935799638 y[1] (numeric) = 2.0022528963390155290140221612898 absolute error = 5.285813260e-22 relative error = 2.6399328824369555349618126184582e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0672 y[1] (analytic) = 2.0022596214501777235428375151157 y[1] (numeric) = 2.0022596214501777235433669043312 absolute error = 5.293892155e-22 relative error = 2.6439589043731450244775638657371e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0673 y[1] (analytic) = 2.0022663566066346358330001182503 y[1] (numeric) = 2.002266356606634635833530315446 absolute error = 5.301971957e-22 relative error = 2.6479853389663809434777348466811e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0674 y[1] (analytic) = 2.0022731018085215800591809514785 y[1] (numeric) = 2.0022731018085215800597119567455 absolute error = 5.310052670e-22 relative error = 2.6520121881494481083283565195830e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0675 y[1] (analytic) = 2.0022798570559740740433668621753 y[1] (numeric) = 2.0022798570559740740438986756045 absolute error = 5.318134292e-22 relative error = 2.6560394508585073635466045886041e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0676 y[1] (analytic) = 2.0022866223491278392652473980872 y[1] (numeric) = 2.00228662234912783926578001977 absolute error = 5.326216828e-22 relative error = 2.6600671295257230714135867229107e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.3MB, time=11.83 NO POLE x[1] = 0.0677 y[1] (analytic) = 2.0022933976881188008731468471281 y[1] (numeric) = 2.0022933976881188008736802771557 absolute error = 5.334300276e-22 relative error = 2.6640952230872217123319726731779e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0678 y[1] (analytic) = 2.0023001830730830876949729037347 y[1] (numeric) = 2.0023001830730830876955071421987 absolute error = 5.342384640e-22 relative error = 2.6681237334756839899891064815420e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0679 y[1] (analytic) = 2.0023069785041570322491819636645 y[1] (numeric) = 2.0023069785041570322497170106565 absolute error = 5.350469920e-22 relative error = 2.6721526606260548350853385905186e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 2.0023137839814771707557610491142 y[1] (numeric) = 2.0023137839814771707562969047259 absolute error = 5.358556117e-22 relative error = 2.6761820049726883677611511371288e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0681 y[1] (analytic) = 2.0023205995051802431472263660449 y[1] (numeric) = 2.0023205995051802431477630303683 absolute error = 5.366643234e-22 relative error = 2.6802117679487599215282247678000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0682 y[1] (analytic) = 2.002327425075403193079638495601 y[1] (numeric) = 2.002327425075403193080175968728 absolute error = 5.374731270e-22 relative error = 2.6842419489897360747820061372268e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0683 y[1] (analytic) = 2.0023342606922831679436342215121 y[1] (numeric) = 2.002334260692283167944172503535 absolute error = 5.382820229e-22 relative error = 2.6882725500281627118394266518210e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0684 y[1] (analytic) = 2.0023411063559575188754749953727 y[1] (numeric) = 2.0023411063559575188760140863838 absolute error = 5.390910111e-22 relative error = 2.6923035709988836940990493370592e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0685 y[1] (analytic) = 2.0023479620665638007681120416934 y[1] (numeric) = 2.0023479620665638007686519417851 absolute error = 5.399000917e-22 relative error = 2.6963350123361434486953432039375e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0686 y[1] (analytic) = 2.0023548278242397722822681046245 y[1] (numeric) = 2.0023548278242397722828088138896 absolute error = 5.407092651e-22 relative error = 2.7003668759724023783472654946721e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0687 y[1] (analytic) = 2.0023617036291233958575358382532 y[1] (numeric) = 2.0023617036291233958580773567843 absolute error = 5.415185311e-22 relative error = 2.7043991608436186797045390508917e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0688 y[1] (analytic) = 2.0023685894813528377234928423779 y[1] (numeric) = 2.002368589481352837724035170268 absolute error = 5.423278901e-22 relative error = 2.7084318688822024036119200144967e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.3MB, time=12.04 NO POLE x[1] = 0.0689 y[1] (analytic) = 2.0023754853810664679108333456695 y[1] (numeric) = 2.0023754853810664679113764830116 absolute error = 5.431373421e-22 relative error = 2.7124650000228955775042944516414e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 2.0023823913284028602625165381279 y[1] (numeric) = 2.0023823913284028602630604850152 absolute error = 5.439468873e-22 relative error = 2.7164985551992372193077165503402e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0691 y[1] (analytic) = 2.002389307323500792444931554749 y[1] (numeric) = 2.0023893073235007924454763112748 absolute error = 5.447565258e-22 relative error = 2.7205325348453359320227909397294e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0692 y[1] (analytic) = 2.002396233366499245959079112317 y[1] (numeric) = 2.0023962333664992459596246785748 absolute error = 5.455662578e-22 relative error = 2.7245669398946818089442358111669e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0693 y[1] (analytic) = 2.0024031694575374061517698012428 y[1] (numeric) = 2.0024031694575374061523161773262 absolute error = 5.463760834e-22 relative error = 2.7286017707813379031740738890880e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0694 y[1] (analytic) = 2.0024101155967546622268390343691 y[1] (numeric) = 2.0024101155967546622273862203719 absolute error = 5.471860028e-22 relative error = 2.7326370284387452333187417282770e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0695 y[1] (analytic) = 2.0024170717842906072563786546687 y[1] (numeric) = 2.0024170717842906072569266506848 absolute error = 5.479960161e-22 relative error = 2.7366727133009211625040421458212e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0696 y[1] (analytic) = 2.0024240380202850381919852037631 y[1] (numeric) = 2.0024240380202850381925340098864 absolute error = 5.488061233e-22 relative error = 2.7407088253024680363958098529912e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0697 y[1] (analytic) = 2.0024310143048779558760248531922 y[1] (numeric) = 2.002431014304877955876574469517 absolute error = 5.496163248e-22 relative error = 2.7447453663755467799098083581246e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0698 y[1] (analytic) = 2.0024380006382095650529150003701 y[1] (numeric) = 2.0024380006382095650534654269907 absolute error = 5.504266206e-22 relative error = 2.7487823364547121162433507153486e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0699 y[1] (analytic) = 2.0024449970204202743804225311623 y[1] (numeric) = 2.0024449970204202743809737681731 absolute error = 5.512370108e-22 relative error = 2.7528197359738948503420844565231e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.3MB, time=12.26 NO POLE x[1] = 0.07 y[1] (analytic) = 2.0024520034516506964409787510246 y[1] (numeric) = 2.0024520034516506964415307985202 absolute error = 5.520474956e-22 relative error = 2.7568575658663931334127772810023e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0701 y[1] (analytic) = 2.0024590199320416477530109866468 y[1] (numeric) = 2.002459019932041647753563844722 absolute error = 5.528580752e-22 relative error = 2.7608958270654776900917342099761e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0702 y[1] (analytic) = 2.0024660464617341487822908600457 y[1] (numeric) = 2.0024660464617341487828445287954 absolute error = 5.536687497e-22 relative error = 2.7649345200050075220934437219555e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0703 y[1] (analytic) = 2.0024730830408694239532992370563 y[1] (numeric) = 2.0024730830408694239538537165754 absolute error = 5.544795191e-22 relative error = 2.7689736446194386335242120333756e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0704 y[1] (analytic) = 2.0024801296695889016606078521725 y[1] (numeric) = 2.0024801296695889016611631425563 absolute error = 5.552903838e-22 relative error = 2.7730132028407364711580151176981e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0705 y[1] (analytic) = 2.002487186348034214280277611692 y[1] (numeric) = 2.0024871863480342142808337130357 absolute error = 5.561013437e-22 relative error = 2.7770531941039299482316405041760e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0706 y[1] (analytic) = 2.0024942530763471981812735771213 y[1] (numeric) = 2.0024942530763471981818304895204 absolute error = 5.569123991e-22 relative error = 2.7810936198415503239126058255985e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0707 y[1] (analytic) = 2.0025013298546698937368966308022 y[1] (numeric) = 2.0025013298546698937374543543523 absolute error = 5.577235501e-22 relative error = 2.7851344804873432418675391294168e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0708 y[1] (analytic) = 2.0025084166831445453362318257224 y[1] (numeric) = 2.0025084166831445453367903605192 absolute error = 5.585347968e-22 relative error = 2.7891757764750336921016624286510e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0709 y[1] (analytic) = 2.0025155135619136013956134214757 y[1] (numeric) = 2.0025155135619136013961727676151 absolute error = 5.593461394e-22 relative error = 2.7932175087376978987647507296476e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 2.0025226204911197143701066083408 y[1] (numeric) = 2.0025226204911197143706667659188 absolute error = 5.601575780e-22 relative error = 2.7972596777090141563866741741614e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0711 y[1] (analytic) = 2.0025297374709057407650059214513 y[1] (numeric) = 2.0025297374709057407655668905641 absolute error = 5.609691128e-22 relative error = 2.8013022843220083840855549843576e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.3MB, time=12.46 NO POLE x[1] = 0.0712 y[1] (analytic) = 2.0025368645014147411473503470304 y[1] (numeric) = 2.0025368645014147411479121277743 absolute error = 5.617807439e-22 relative error = 2.8053453290103120408900327709114e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0713 y[1] (analytic) = 2.0025440015827899801574551226684 y[1] (numeric) = 2.0025440015827899801580177151398 absolute error = 5.625924714e-22 relative error = 2.8093888122075357833193468016789e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0714 y[1] (analytic) = 2.0025511487151749265204602336236 y[1] (numeric) = 2.0025511487151749265210236379191 absolute error = 5.634042955e-22 relative error = 2.8134327348466324669305286306980e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0715 y[1] (analytic) = 2.0025583058987132530578956071306 y[1] (numeric) = 2.002558305898713253058459823347 absolute error = 5.642162164e-22 relative error = 2.8174770978605269582728313770016e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0716 y[1] (analytic) = 2.002565473133548836699263006701 y[1] (numeric) = 2.0025654731335488366998280349351 absolute error = 5.650282341e-22 relative error = 2.8215219011833971794316781352332e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0717 y[1] (analytic) = 2.0025726504198257584936346284071 y[1] (numeric) = 2.002572650419825758494200468756 absolute error = 5.658403489e-22 relative error = 2.8255671462474802747615458294514e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0718 y[1] (analytic) = 2.0025798377576883036212684011403 y[1] (numeric) = 2.0025798377576883036218350537011 absolute error = 5.666525608e-22 relative error = 2.8296128329869105002225068948788e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0719 y[1] (analytic) = 2.0025870351472809614052399928393 y[1] (numeric) = 2.0025870351472809614058074577093 absolute error = 5.674648700e-22 relative error = 2.8336589623345164539791388770187e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 2.0025942425887484253230915246866 y[1] (numeric) = 2.0025942425887484253236598019633 absolute error = 5.682772767e-22 relative error = 2.8377055352230985464936636420955e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0721 y[1] (analytic) = 2.0026014600822355930184969952738 y[1] (numeric) = 2.0026014600822355930190660850547 absolute error = 5.690897809e-22 relative error = 2.8417525515867279921529860709877e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0722 y[1] (analytic) = 2.0026086876278875663129444167399 y[1] (numeric) = 2.0026086876278875663135143191228 absolute error = 5.699023829e-22 relative error = 2.8458000128575081706481947687289e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.3MB, time=12.67 NO POLE x[1] = 0.0723 y[1] (analytic) = 2.0026159252258496512174346648897 y[1] (numeric) = 2.0026159252258496512180053799725 absolute error = 5.707150828e-22 relative error = 2.8498479194688131931065297543743e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0724 y[1] (analytic) = 2.0026231728762673579441970453018 y[1] (numeric) = 2.0026231728762673579447685731824 absolute error = 5.715278806e-22 relative error = 2.8538962713546509659847602928706e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0725 y[1] (analytic) = 2.0026304305792864009184215774388 y[1] (numeric) = 2.0026304305792864009189939182154 absolute error = 5.723407766e-22 relative error = 2.8579450699470452400984586820904e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0726 y[1] (analytic) = 2.0026376983350526987900079987758 y[1] (numeric) = 2.0026376983350526987905811525467 absolute error = 5.731537709e-22 relative error = 2.8619943156793012095840353171743e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0727 y[1] (analytic) = 2.0026449761437123744453314909659 y[1] (numeric) = 2.0026449761437123744459054578295 absolute error = 5.739668636e-22 relative error = 2.8660440089847028434080226973761e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0728 y[1] (analytic) = 2.0026522640054117550190251300631 y[1] (numeric) = 2.002652264005411755019599910118 absolute error = 5.747800549e-22 relative error = 2.8700941507958506737415077701302e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0729 y[1] (analytic) = 2.0026595619202973719057790628288 y[1] (numeric) = 2.0026595619202973719063546561737 absolute error = 5.755933449e-22 relative error = 2.8741447415459806889656466009283e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 2.0026668698885159607721564111478 y[1] (numeric) = 2.0026668698885159607727328178816 absolute error = 5.764067338e-22 relative error = 2.8781957821676417363835410790539e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0731 y[1] (analytic) = 2.0026741879102144615684259065849 y[1] (numeric) = 2.0026741879102144615690031268066 absolute error = 5.772202217e-22 relative error = 2.8822472730940216838245297818506e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0732 y[1] (analytic) = 2.0026815159855400185404112571153 y[1] (numeric) = 2.0026815159855400185409892909241 absolute error = 5.780338088e-22 relative error = 2.8862992152576175437869526368155e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0733 y[1] (analytic) = 2.002688854114639980241357248065 y[1] (numeric) = 2.0026888541146399802419360955602 absolute error = 5.788474952e-22 relative error = 2.8903516090915689235883505896421e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=247.9MB, alloc=4.3MB, time=12.88 x[1] = 0.0734 y[1] (analytic) = 2.0026962022976618995438125792997 y[1] (numeric) = 2.0026962022976618995443922405806 absolute error = 5.796612809e-22 relative error = 2.8944044545296671372109720394554e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0735 y[1] (analytic) = 2.0027035605347535336515294407052 y[1] (numeric) = 2.0027035605347535336521099158715 absolute error = 5.804751663e-22 relative error = 2.8984577535029894659869694833689e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0736 y[1] (analytic) = 2.0027109288260628441113798280041 y[1] (numeric) = 2.0027109288260628441119611171555 absolute error = 5.812891514e-22 relative error = 2.9025115059452769363092227523476e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0737 y[1] (analytic) = 2.0027183071717379968252886009563 y[1] (numeric) = 2.0027183071717379968258707041927 absolute error = 5.821032364e-22 relative error = 2.9065657127888990864677642102109e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0738 y[1] (analytic) = 2.0027256955719273620621832859944 y[1] (numeric) = 2.0027256955719273620627662034158 absolute error = 5.829174214e-22 relative error = 2.9106203744668770364314494506991e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0739 y[1] (analytic) = 2.002733094026779514469960625348 y[1] (numeric) = 2.0027330940267795144705443570546 absolute error = 5.837317066e-22 relative error = 2.9146754919115279799181845610602e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 2.0027405025364432330874698747138 y[1] (numeric) = 2.0027405025364432330880544208058 absolute error = 5.845460920e-22 relative error = 2.9187310650565084896596614679795e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0741 y[1] (analytic) = 2.0027479211010675013565128515301 y[1] (numeric) = 2.002747921101067501357098212108 absolute error = 5.853605779e-22 relative error = 2.9227870953334027758941276453539e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0742 y[1] (analytic) = 2.0027553497208015071338607359206 y[1] (numeric) = 2.0027553497208015071344469110849 absolute error = 5.861751643e-22 relative error = 2.9268435826758222451574132818980e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0743 y[1] (analytic) = 2.0027627883957946427032876263702 y[1] (numeric) = 2.0027627883957946427038746162217 absolute error = 5.869898515e-22 relative error = 2.9309005285152947791425671503629e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0744 y[1] (analytic) = 2.0027702371261965047876208522039 y[1] (numeric) = 2.0027702371261965047882086568434 absolute error = 5.878046395e-22 relative error = 2.9349579327853864882373839544394e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0745 y[1] (analytic) = 2.0027776959121568945608080449384 y[1] (numeric) = 2.002777695912156894561396664467 absolute error = 5.886195286e-22 relative error = 2.9390157969175687657229036583186e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.3MB, time=13.08 NO POLE x[1] = 0.0746 y[1] (analytic) = 2.0027851647538258176600009705825 y[1] (numeric) = 2.0027851647538258176605904051013 absolute error = 5.894345188e-22 relative error = 2.9430741208453622958931386713544e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0747 y[1] (analytic) = 2.0027926436513534841976561249617 y[1] (numeric) = 2.002792643651353484198246374572 absolute error = 5.902496103e-22 relative error = 2.9471329055008790111720221758185e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0748 y[1] (analytic) = 2.0028001326048903087736520941494 y[1] (numeric) = 2.0028001326048903087742431589526 absolute error = 5.910648032e-22 relative error = 2.9511921513169005864333253451989e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0749 y[1] (analytic) = 2.0028076316145869104874236820858 y[1] (numeric) = 2.0028076316145869104880155621835 absolute error = 5.918800977e-22 relative error = 2.9552518592254858899758175980889e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 2.0028151406805941129501128074729 y[1] (numeric) = 2.0028151406805941129507055029669 absolute error = 5.926954940e-22 relative error = 2.9593120301586643957023244418547e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0751 y[1] (analytic) = 2.0028226598030629442967361720329 y[1] (numeric) = 2.002822659803062944297329683025 absolute error = 5.935109921e-22 relative error = 2.9633726640498454752901156733075e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0752 y[1] (analytic) = 2.0028301889821446371983697022231 y[1] (numeric) = 2.0028301889821446371989640288154 absolute error = 5.943265923e-22 relative error = 2.9674337623303043822933978946760e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0753 y[1] (analytic) = 2.002837728217990628874349766502 y[1] (numeric) = 2.0028377282179906288749449087965 absolute error = 5.951422945e-22 relative error = 2.9714953244341130493870034131194e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0754 y[1] (analytic) = 2.0028452775107525611044911702444 y[1] (numeric) = 2.0028452775107525611050871283435 absolute error = 5.959580991e-22 relative error = 2.9755573522917848744057887534294e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0755 y[1] (analytic) = 2.0028528368605822802413219304072 y[1] (numeric) = 2.0028528368605822802419187044134 absolute error = 5.967740062e-22 relative error = 2.9796198463359251814684662374391e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0756 y[1] (analytic) = 2.0028604062676318372223348320489 y[1] (numeric) = 2.0028604062676318372229324220647 absolute error = 5.975900158e-22 relative error = 2.9836828064998312662274267367784e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.3MB, time=13.28 NO POLE x[1] = 0.0757 y[1] (analytic) = 2.0028679857320534875822557688096 y[1] (numeric) = 2.0028679857320534875828541749377 absolute error = 5.984061281e-22 relative error = 2.9877462337153539101569521189938e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0758 y[1] (analytic) = 2.0028755752539996914653288694623 y[1] (numeric) = 2.0028755752539996914659280918057 absolute error = 5.992223434e-22 relative error = 2.9918101294135963239783883716016e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0759 y[1] (analytic) = 2.0028831748336231136376184126476 y[1] (numeric) = 2.0028831748336231136382184513092 absolute error = 6.000386616e-22 relative error = 2.9958744930285034073854861057752e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 2.0028907844710766234993275319063 y[1] (numeric) = 2.0028907844710766234999283869894 absolute error = 6.008550831e-22 relative error = 2.9999393264904047366039772016906e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0761 y[1] (analytic) = 2.0028984041665132950971337131315 y[1] (numeric) = 2.0028984041665132950977353847392 absolute error = 6.016716077e-22 relative error = 3.0040046287339261821002839788965e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0762 y[1] (analytic) = 2.0029060339200864071365410865581 y[1] (numeric) = 2.0029060339200864071371435747939 absolute error = 6.024882358e-22 relative error = 3.0080704016893414148979608801649e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0763 y[1] (analytic) = 2.0029136737319494429942495154176 y[1] (numeric) = 2.0029136737319494429948528203852 absolute error = 6.033049676e-22 relative error = 3.0121366462883336957112516448284e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0764 y[1] (analytic) = 2.0029213236022560907305404833834 y[1] (numeric) = 2.0029213236022560907311446051865 absolute error = 6.041218031e-22 relative error = 3.0162033624640148454169265395055e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0765 y[1] (analytic) = 2.002928983531160243101679782938 y[1] (numeric) = 2.0029289835311602431022847216805 absolute error = 6.049387425e-22 relative error = 3.0202705511480195899783300162887e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0766 y[1] (analytic) = 2.0029366535188159975723370067955 y[1] (numeric) = 2.0029366535188159975729427625814 absolute error = 6.057557859e-22 relative error = 3.0243382127726857036772197168651e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0767 y[1] (analytic) = 2.0029443335653776563280218445154 y[1] (numeric) = 2.0029443335653776563286284174488 absolute error = 6.065729334e-22 relative error = 3.0284063477703285309870403635740e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0768 y[1] (analytic) = 2.0029520236709997262875371864474 y[1] (numeric) = 2.0029520236709997262881445766327 absolute error = 6.073901853e-22 relative error = 3.0324749575717671263938873265670e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.3MB, time=13.48 NO POLE x[1] = 0.0769 y[1] (analytic) = 2.0029597238358369191154490371492 y[1] (numeric) = 2.0029597238358369191160572446908 absolute error = 6.082075416e-22 relative error = 3.0365440421099992249242077759065e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 2.0029674340600441512345732404228 y[1] (numeric) = 2.0029674340600441512351822654253 absolute error = 6.090250025e-22 relative error = 3.0406136023165261992055962531093e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0771 y[1] (analytic) = 2.002975154343776543838479018117 y[1] (numeric) = 2.0029751543437765438390888606851 absolute error = 6.098425681e-22 relative error = 3.0446836386235618685225225088852e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0772 y[1] (analytic) = 2.0029828846871894229040093248478 y[1] (numeric) = 2.0029828846871894229046199850865 absolute error = 6.106602387e-22 relative error = 3.0487541524618082524730989797685e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0773 y[1] (analytic) = 2.0029906250904383192038180207909 y[1] (numeric) = 2.0029906250904383192044294988052 absolute error = 6.114780143e-22 relative error = 3.0528251437641689536988294434842e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0774 y[1] (analytic) = 2.0029983755536789683189238647022 y[1] (numeric) = 2.0029983755536789683195361605972 absolute error = 6.122958950e-22 relative error = 3.0568966129627841745389099249935e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0775 y[1] (analytic) = 2.003006136077067310651281329328 y[1] (numeric) = 2.0030061360770673106518944432091 absolute error = 6.131138811e-22 relative error = 3.0609685614882706405138929197101e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0776 y[1] (analytic) = 2.0030139066607594914363682413667 y[1] (numeric) = 2.0030139066607594914369821733393 absolute error = 6.139319726e-22 relative error = 3.0650409892734639230687612471224e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0777 y[1] (analytic) = 2.0030216873049118607557902481483 y[1] (numeric) = 2.003021687304911860756404998318 absolute error = 6.147501697e-22 relative error = 3.0691138972496760444302398803222e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0778 y[1] (analytic) = 2.0030294780096809735499021132008 y[1] (numeric) = 2.0030294780096809735505176816734 absolute error = 6.155684726e-22 relative error = 3.0731872863481885088697470159858e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0779 y[1] (analytic) = 2.0030372787752235896304458428754 y[1] (numeric) = 2.0030372787752235896310622297568 absolute error = 6.163868814e-22 relative error = 3.0772611570010104223528773086988e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.3MB, time=13.68 NO POLE x[1] = 0.078 y[1] (analytic) = 2.0030450896016966736932056462047 y[1] (numeric) = 2.0030450896016966736938228516009 absolute error = 6.172053962e-22 relative error = 3.0813355096401280626972328450903e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0781 y[1] (analytic) = 2.0030529104892573953306797301723 y[1] (numeric) = 2.0030529104892573953312977541895 absolute error = 6.180240172e-22 relative error = 3.0854103451967427914735952725972e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0782 y[1] (analytic) = 2.0030607414380631290447689325751 y[1] (numeric) = 2.0030607414380631290453877753196 absolute error = 6.188427445e-22 relative error = 3.0894856641027893037039839645101e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0783 y[1] (analytic) = 2.0030685824482714542594821946604 y[1] (numeric) = 2.0030685824482714542601018562387 absolute error = 6.196615783e-22 relative error = 3.0935614672894134097187277900049e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0784 y[1] (analytic) = 2.0030764335200401553336588757265 y[1] (numeric) = 2.0030764335200401553342793562452 absolute error = 6.204805187e-22 relative error = 3.0976377551884980819523061466922e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0785 y[1] (analytic) = 2.0030842946535272215737079118746 y[1] (numeric) = 2.0030842946535272215743292114405 absolute error = 6.212995659e-22 relative error = 3.1017145287311334297365019167659e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0786 y[1] (analytic) = 2.0030921658488908472463638211063 y[1] (numeric) = 2.0030921658488908472469859398263 absolute error = 6.221187200e-22 relative error = 3.1057917883491505631332196410409e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0787 y[1] (analytic) = 2.0031000471062894315914595569612 y[1] (numeric) = 2.0031000471062894315920824949423 absolute error = 6.229379811e-22 relative error = 3.1098695344743575530738947631435e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0788 y[1] (analytic) = 2.0031079384258815788347162128934 y[1] (numeric) = 2.0031079384258815788353399702428 absolute error = 6.237573494e-22 relative error = 3.1139477680377636285615061918810e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0789 y[1] (analytic) = 2.003115839807826098200549579589 y[1] (numeric) = 2.003115839807826098201174156414 absolute error = 6.245768250e-22 relative error = 3.1180264894711248034440729439771e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 2.0031237512522820039248935574283 y[1] (numeric) = 2.0031237512522820039255189538364 absolute error = 6.253964081e-22 relative error = 3.1221056997053942463153347046341e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0791 memory used=267.0MB, alloc=4.3MB, time=13.88 y[1] (analytic) = 2.0031316727594085152680404263009 y[1] (numeric) = 2.0031316727594085152686666423998 absolute error = 6.262160989e-22 relative error = 3.1261853996714940799871917384680e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0792 y[1] (analytic) = 2.0031396043293650565274979749841 y[1] (numeric) = 2.0031396043293650565281250108815 absolute error = 6.270358974e-22 relative error = 3.1302655893018826745904144444537e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0793 y[1] (analytic) = 2.003147545962311257050863492297 y[1] (numeric) = 2.0031475459623112570514913481008 absolute error = 6.278558038e-22 relative error = 3.1343462695274317905216375463472e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0794 y[1] (analytic) = 2.0031554976584069512487146222484 y[1] (numeric) = 2.0031554976584069512493432980667 absolute error = 6.286758183e-22 relative error = 3.1384274412789820263624801904868e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0795 y[1] (analytic) = 2.0031634594178121786075170853968 y[1] (numeric) = 2.0031634594178121786081465813379 absolute error = 6.294959411e-22 relative error = 3.1425091054873427702348945419421e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0796 y[1] (analytic) = 2.003171431240687183702549268645 y[1] (numeric) = 2.0031714312406871837031795848172 absolute error = 6.303161722e-22 relative error = 3.1465912620848753562648733949980e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0797 y[1] (analytic) = 2.0031794131271924162108436856946 y[1] (numeric) = 2.0031794131271924162114748222063 absolute error = 6.311365117e-22 relative error = 3.1506739115031321323305985536297e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0798 y[1] (analytic) = 2.003187405077488530924145310389 y[1] (numeric) = 2.0031874050774885309247772673489 absolute error = 6.319569599e-22 relative error = 3.1547570551720509197052059835575e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0799 y[1] (analytic) = 2.0031954070917363877618867851763 y[1] (numeric) = 2.0031954070917363877625195626932 absolute error = 6.327775169e-22 relative error = 3.1588406935231253579151877507497e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 2.0032034191700970517841805069258 y[1] (numeric) = 2.0032034191700970517848141051087 absolute error = 6.335981829e-22 relative error = 3.1629248274870260751234616025156e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0801 y[1] (analytic) = 2.0032114413127317932048275923358 y[1] (numeric) = 2.0032114413127317932054620112937 absolute error = 6.344189579e-22 relative error = 3.1670094569959953884952851796112e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0802 y[1] (analytic) = 2.0032194735198020874043437251726 y[1] (numeric) = 2.0032194735198020874049789650147 absolute error = 6.352398421e-22 relative error = 3.1710945829806529723216452118661e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.3MB, time=14.08 NO POLE x[1] = 0.0803 y[1] (analytic) = 2.0032275157914696149430018875844 y[1] (numeric) = 2.00322751579146961494363794842 absolute error = 6.360608356e-22 relative error = 3.1751802058723925550131713339955e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0804 y[1] (analytic) = 2.0032355681278962615738919777356 y[1] (numeric) = 2.0032355681278962615745288596743 absolute error = 6.368819387e-22 relative error = 3.1792663271009691468377660297388e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0805 y[1] (analytic) = 2.0032436305292441182559973160116 y[1] (numeric) = 2.0032436305292441182566350191631 absolute error = 6.377031515e-22 relative error = 3.1833529470977173038187263000819e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0806 y[1] (analytic) = 2.0032517029956754811672880420455 y[1] (numeric) = 2.0032517029956754811679265665194 absolute error = 6.385244739e-22 relative error = 3.1874400652955711699652109720331e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0807 y[1] (analytic) = 2.0032597855273528517178314048212 y[1] (numeric) = 2.0032597855273528517184707507276 absolute error = 6.393459064e-22 relative error = 3.1915276841225756321173059967958e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0808 y[1] (analytic) = 2.0032678781244389365629189481134 y[1] (numeric) = 2.0032678781244389365635591155624 absolute error = 6.401674490e-22 relative error = 3.1956158035107978543384094355294e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0809 y[1] (analytic) = 2.0032759807870966476162105935229 y[1] (numeric) = 2.0032759807870966476168515826246 absolute error = 6.409891017e-22 relative error = 3.1997044233922893514577901163560e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 2.0032840935154891020628956233724 y[1] (numeric) = 2.0032840935154891020635374342373 absolute error = 6.418108649e-22 relative error = 3.2037935456958072805574699621834e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0811 y[1] (analytic) = 2.0032922163097796223728705657309 y[1] (numeric) = 2.0032922163097796223735131984694 absolute error = 6.426327385e-22 relative error = 3.2078831698541692746368103666793e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0812 y[1] (analytic) = 2.0033003491701317363139339838343 y[1] (numeric) = 2.0033003491701317363145774385572 absolute error = 6.434547229e-22 relative error = 3.2119732977960667274121073995515e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0813 y[1] (analytic) = 2.0033084920967091769649981721782 y[1] (numeric) = 2.0033084920967091769656424489962 absolute error = 6.442768180e-22 relative error = 3.2160639289542716640987583017922e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=274.6MB, alloc=4.3MB, time=14.28 x[1] = 0.0814 y[1] (analytic) = 2.0033166450896758827293177615559 y[1] (numeric) = 2.0033166450896758827299628605801 absolute error = 6.450990242e-22 relative error = 3.2201550652574095454579313186505e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0815 y[1] (analytic) = 2.0033248081491959973477352353237 y[1] (numeric) = 2.003324808149195997348381156665 absolute error = 6.459213413e-22 relative error = 3.2242467056390364917085548523658e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0816 y[1] (analytic) = 2.003332981275433869911943359172 y[1] (numeric) = 2.0033329812754338699125901029418 absolute error = 6.467437698e-22 relative error = 3.2283388525268861115312697754961e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0817 y[1] (analytic) = 2.0033411644685540548777645266912 y[1] (numeric) = 2.0033411644685540548784120930009 absolute error = 6.475663097e-22 relative error = 3.2324315058528049647853338851884e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0818 y[1] (analytic) = 2.0033493577287213120784470230166 y[1] (numeric) = 2.0033493577287213120790954119777 absolute error = 6.483889611e-22 relative error = 3.2365246660477878391249552117953e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0819 y[1] (analytic) = 2.0033575610561006067379782088457 y[1] (numeric) = 2.0033575610561006067386274205699 absolute error = 6.492117242e-22 relative error = 3.2406183340419675313537449335785e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 2.0033657744508571094844146271212 y[1] (numeric) = 2.0033657744508571094850646617203 absolute error = 6.500345991e-22 relative error = 3.2447125102662846512787753561658e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0821 y[1] (analytic) = 2.0033739979131561963632290346761 y[1] (numeric) = 2.0033739979131561963638798922621 absolute error = 6.508575860e-22 relative error = 3.2488071956508136600826681051951e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0822 y[1] (analytic) = 2.0033822314431634488506743611416 y[1] (numeric) = 2.0033822314431634488513260418266 absolute error = 6.516806850e-22 relative error = 3.2529023906264408500663111501434e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0823 y[1] (analytic) = 2.0033904750410446538671645974205 y[1] (numeric) = 2.0033904750410446538678171013168 absolute error = 6.525038963e-22 relative error = 3.2569980961231821971693311053790e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0824 y[1] (analytic) = 2.0033987287069658037906726160316 y[1] (numeric) = 2.0033987287069658037913259432516 absolute error = 6.533272200e-22 relative error = 3.2610943125718695365346349998509e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0825 y[1] (analytic) = 2.0034069924410930964701449256347 y[1] (numeric) = 2.003406992441093096470799076291 absolute error = 6.541506563e-22 relative error = 3.2651910409024602092442723156771e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.3MB, time=14.48 NO POLE x[1] = 0.0826 y[1] (analytic) = 2.0034152662435929352389333620479 y[1] (numeric) = 2.0034152662435929352395883362532 absolute error = 6.549742053e-22 relative error = 3.2692882815457314536386421335540e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0827 y[1] (analytic) = 2.0034235501146319289282437180715 y[1] (numeric) = 2.0034235501146319289288995159387 absolute error = 6.557978672e-22 relative error = 3.2733860354315818263350759947616e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0828 y[1] (analytic) = 2.0034318440543768918806013144376 y[1] (numeric) = 2.0034318440543768918812579360796 absolute error = 6.566216420e-22 relative error = 3.2774843024915903205754609039242e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0829 y[1] (analytic) = 2.003440148062994843963333514205 y[1] (numeric) = 2.0034401480629948439639909597349 absolute error = 6.574455299e-22 relative error = 3.2815830836556027655748069163575e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 2.0034484621406530105820691829242 y[1] (numeric) = 2.0034484621406530105827274524554 absolute error = 6.582695312e-22 relative error = 3.2856823803525717455600569695442e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0831 y[1] (analytic) = 2.0034567862875188226942550968995 y[1] (numeric) = 2.0034567862875188226949141905454 absolute error = 6.590936459e-22 relative error = 3.2897821925139970037206733682633e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0832 y[1] (analytic) = 2.0034651205037599168226893018771 y[1] (numeric) = 2.0034651205037599168233492197512 absolute error = 6.599178741e-22 relative error = 3.2938825205704973867544527319033e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0833 y[1] (analytic) = 2.003473464789544135069071424493 y[1] (numeric) = 2.0034734647895441350697321667091 absolute error = 6.607422161e-22 relative error = 3.2979833659509335911314497331956e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0834 y[1] (analytic) = 2.0034818191450395251275699388168 y[1] (numeric) = 2.0034818191450395251282315054887 absolute error = 6.615666719e-22 relative error = 3.3020847285867320361417164012617e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0835 y[1] (analytic) = 2.0034901835704143402984063903289 y[1] (numeric) = 2.0034901835704143402990687815707 absolute error = 6.623912418e-22 relative error = 3.3061866099066898926784762844366e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0836 y[1] (analytic) = 2.003498558065837039501456579675 y[1] (numeric) = 2.0034985580658370395021197956008 absolute error = 6.632159258e-22 relative error = 3.3102890098421824627526298647545e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.3MB, time=14.69 NO POLE x[1] = 0.0837 y[1] (analytic) = 2.0035069426314762872898687085409 y[1] (numeric) = 2.003506942631476287290532749265 absolute error = 6.640407241e-22 relative error = 3.3143919293228184331630440057142e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0838 y[1] (analytic) = 2.0035153372675009538636984899967 y[1] (numeric) = 2.0035153372675009538643633556337 absolute error = 6.648656370e-22 relative error = 3.3184953697772962559518986172013e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0839 y[1] (analytic) = 2.0035237419740801150835612256616 y[1] (numeric) = 2.0035237419740801150842269163259 absolute error = 6.656906643e-22 relative error = 3.3225993301386699475711183694499e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 2.0035321567513830524843008520412 y[1] (numeric) = 2.0035321567513830524849673678476 absolute error = 6.665158064e-22 relative error = 3.3267038123347051160464571718022e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0841 y[1] (analytic) = 2.003540581599579253288675958397 y[1] (numeric) = 2.0035405815995792532893432994605 absolute error = 6.673410635e-22 relative error = 3.3308088172948846981597499893048e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0842 y[1] (analytic) = 2.0035490165188384104210627785062 y[1] (numeric) = 2.0035490165188384104217309449418 absolute error = 6.681664356e-22 relative error = 3.3349143449504298737733098391589e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0843 y[1] (analytic) = 2.0035574615093304225211751586748 y[1] (numeric) = 2.0035574615093304225218441505976 absolute error = 6.689919228e-22 relative error = 3.3390203957316576961578709133376e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0844 y[1] (analytic) = 2.0035659165712253939578015043707 y[1] (numeric) = 2.0035659165712253939584713218961 absolute error = 6.698175254e-22 relative error = 3.3431269710670806694344141423542e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0845 y[1] (analytic) = 2.0035743817046936348425587078457 y[1] (numeric) = 2.0035743817046936348432293510892 absolute error = 6.706432435e-22 relative error = 3.3472340713869536424090815940096e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0846 y[1] (analytic) = 2.0035828569099056610436630591175 y[1] (numeric) = 2.0035828569099056610443345281947 absolute error = 6.714690772e-22 relative error = 3.3513416971215066224830304141459e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0847 y[1] (analytic) = 2.0035913421870321941997181426876 y[1] (numeric) = 2.0035913421870321942003904377142 absolute error = 6.722950266e-22 relative error = 3.3554498487009447519714576813649e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0848 y[1] (analytic) = 2.0035998375362441617335197223723 y[1] (numeric) = 2.0035998375362441617341928434643 absolute error = 6.731210920e-22 relative error = 3.3595585275536515995420767630521e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.3MB, time=14.91 NO POLE x[1] = 0.0849 y[1] (analytic) = 2.0036083429577126968658776166291 y[1] (numeric) = 2.0036083429577126968665515639025 absolute error = 6.739472734e-22 relative error = 3.3636677336106702551765431685535e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 2.0036168584516091386294545667602 y[1] (numeric) = 2.0036168584516091386301293403313 absolute error = 6.747735711e-22 relative error = 3.3677774683003195805838081253728e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0851 y[1] (analytic) = 2.0036253840181050318826221003833 y[1] (numeric) = 2.0036253840181050318832977003684 absolute error = 6.755999851e-22 relative error = 3.3718877315535905913216359672065e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0852 y[1] (analytic) = 2.0036339196573721273233333925562 y[1] (numeric) = 2.0036339196573721273240098190718 absolute error = 6.764265156e-22 relative error = 3.3759985242996441148991692163099e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0853 y[1] (analytic) = 2.0036424653695823815030131269512 y[1] (numeric) = 2.003642465369582381503690380114 absolute error = 6.772531628e-22 relative error = 3.3801098474676074270721424358094e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0854 y[1] (analytic) = 2.0036510211549079568404643594739 y[1] (numeric) = 2.0036510211549079568411424394006 absolute error = 6.780799267e-22 relative error = 3.3842217009883963874189679120116e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0855 y[1] (analytic) = 2.0036595870135212216357923867252 y[1] (numeric) = 2.0036595870135212216364712935328 absolute error = 6.789068076e-22 relative error = 3.3883340862901705986462861754886e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0856 y[1] (analytic) = 2.00366816294559475008434562171 y[1] (numeric) = 2.0036681629455947500850253555156 absolute error = 6.797338056e-22 relative error = 3.3924470038028781750261849552469e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0857 y[1] (analytic) = 2.003676748951301322290673479196 y[1] (numeric) = 2.0036767489513013222913540401169 absolute error = 6.805609209e-22 relative error = 3.3965604544555245537221998332260e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0858 y[1] (analytic) = 2.0036853450308139242825012731324 y[1] (numeric) = 2.0036853450308139242831826612859 absolute error = 6.813881535e-22 relative error = 3.4006744381789206904403032309189e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0859 y[1] (analytic) = 2.0036939511843057480247221285378 y[1] (numeric) = 2.0036939511843057480254043440414 absolute error = 6.822155036e-22 relative error = 3.4047889559020173059434295090644e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.3MB, time=15.12 NO POLE x[1] = 0.086 y[1] (analytic) = 2.0037025674119501914334059102733 y[1] (numeric) = 2.0037025674119501914340889532447 absolute error = 6.830429714e-22 relative error = 3.4089040085537312889504251540407e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0861 y[1] (analytic) = 2.0037111937139208583898251711167 y[1] (numeric) = 2.0037111937139208583905090416738 absolute error = 6.838705571e-22 relative error = 3.4130195970629456475584635888382e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0862 y[1] (analytic) = 2.0037198300903915587544981215589 y[1] (numeric) = 2.0037198300903915587551828198196 absolute error = 6.846982607e-22 relative error = 3.4171357213603659228498827412939e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0863 y[1] (analytic) = 2.0037284765415363083812486237443 y[1] (numeric) = 2.0037284765415363083819341498268 absolute error = 6.855260825e-22 relative error = 3.4212523828738897527840112161114e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0864 y[1] (analytic) = 2.0037371330675293291312832119837 y[1] (numeric) = 2.0037371330675293291319695660062 absolute error = 6.863540225e-22 relative error = 3.4253695815341697768158759792293e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0865 y[1] (analytic) = 2.0037457996685450488872851422665 y[1] (numeric) = 2.0037457996685450488879723243474 absolute error = 6.871820809e-22 relative error = 3.4294873182699724443184606033762e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0866 y[1] (analytic) = 2.0037544763447581015675254732064 y[1] (numeric) = 2.0037544763447581015682134834643 absolute error = 6.880102579e-22 relative error = 3.4336055940100301260050517283341e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0867 y[1] (analytic) = 2.0037631630963433271399911808548 y[1] (numeric) = 2.0037631630963433271406800194085 absolute error = 6.888385537e-22 relative error = 3.4377244096830410653580688211908e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0868 y[1] (analytic) = 2.0037718599234757716365303098209 y[1] (numeric) = 2.0037718599234757716372199767892 absolute error = 6.896669683e-22 relative error = 3.4418437652195517099841123290861e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0869 y[1] (analytic) = 2.0037805668263306871670141631392 y[1] (numeric) = 2.003780566826330687167704658641 absolute error = 6.904955018e-22 relative error = 3.4459636610491482728616789219140e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 2.0037892838050835319335165333294 y[1] (numeric) = 2.0037892838050835319342078574838 absolute error = 6.913241544e-22 relative error = 3.4500840981004458784869307500532e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=293.7MB, alloc=4.3MB, time=15.32 x[1] = 0.0871 y[1] (analytic) = 2.0037980108599099702445099770956 y[1] (numeric) = 2.003798010859909970245202130022 absolute error = 6.921529264e-22 relative error = 3.4542050778010776716609475168297e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0872 y[1] (analytic) = 2.0038067479909858725290791361162 y[1] (numeric) = 2.003806747990985872529772117934 absolute error = 6.929818178e-22 relative error = 3.4583266000814834050100777741586e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0873 y[1] (analytic) = 2.0038154951984873153511511063764 y[1] (numeric) = 2.0038154951984873153518449172052 absolute error = 6.938108288e-22 relative error = 3.4624486658701817553168750224847e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0874 y[1] (analytic) = 2.0038242524825905814237428585011 y[1] (numeric) = 2.0038242524825905814244374984607 absolute error = 6.946399596e-22 relative error = 3.4665712760956569919397056279128e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0875 y[1] (analytic) = 2.0038330198434721596232257115475 y[1] (numeric) = 2.0038330198434721596239211807577 absolute error = 6.954692102e-22 relative error = 3.4706944306882717721875514948806e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0876 y[1] (analytic) = 2.0038417972813087450036068627192 y[1] (numeric) = 2.0038417972813087450043031613002 absolute error = 6.962985810e-22 relative error = 3.4748181315745373047985129161654e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0877 y[1] (analytic) = 2.0038505847962772388108279754689 y[1] (numeric) = 2.0038505847962772388115251035407 absolute error = 6.971280718e-22 relative error = 3.4789423776866775459710002856305e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0878 y[1] (analytic) = 2.0038593823885547484970808284559 y[1] (numeric) = 2.0038593823885547484977787861389 absolute error = 6.979576830e-22 relative error = 3.4830671709511389813642329508923e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0879 y[1] (analytic) = 2.0038681900583185877351400278334 y[1] (numeric) = 2.003868190058318587735838815248 absolute error = 6.987874146e-22 relative error = 3.4871925112981766817609565429686e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 2.0038770078057462764327127853365 y[1] (numeric) = 2.0038770078057462764334124026034 absolute error = 6.996172669e-22 relative error = 3.4913184001551264863802047217474e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0881 y[1] (analytic) = 2.0038858356310155407468057646523 y[1] (numeric) = 2.0038858356310155407475062118922 absolute error = 7.004472399e-22 relative error = 3.4954448374521894785211035125638e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0882 y[1] (analytic) = 2.0038946735343043130981089985497 y[1] (numeric) = 2.0038946735343043130988102758836 absolute error = 7.012773339e-22 relative error = 3.4995718246166342696349456542143e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.3MB, time=15.52 NO POLE x[1] = 0.0883 y[1] (analytic) = 2.0039035215157907321853968792551 y[1] (numeric) = 2.003903521515790732186098986804 absolute error = 7.021075489e-22 relative error = 3.5036993615786078260670226480266e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0884 y[1] (analytic) = 2.0039123795756531429999462245589 y[1] (numeric) = 2.0039123795756531430006491624441 absolute error = 7.029378852e-22 relative error = 3.5078274497653113721501255974908e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0885 y[1] (analytic) = 2.0039212477140700968399714221448 y[1] (numeric) = 2.0039212477140700968406751904876 absolute error = 7.037683428e-22 relative error = 3.5119560891068376278131019537885e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0886 y[1] (analytic) = 2.0039301259312203513250766546321 y[1] (numeric) = 2.003930125931220351325781253554 absolute error = 7.045989219e-22 relative error = 3.5160852805313008754607705155740e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0887 y[1] (analytic) = 2.0039390142272828704107252078298 y[1] (numeric) = 2.0039390142272828704114306374524 absolute error = 7.054296226e-22 relative error = 3.5202150244677632813310782178366e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0888 y[1] (analytic) = 2.0039479126024368244027258646991 y[1] (numeric) = 2.0039479126024368244034321251443 absolute error = 7.062604452e-22 relative error = 3.5243453223432908249707573338649e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0889 y[1] (analytic) = 2.0039568210568615899717363875283 y[1] (numeric) = 2.003956821056861589972443478918 absolute error = 7.070913897e-22 relative error = 3.5284761740878673525890179575994e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 2.003965739590736750167784090823 y[1] (numeric) = 2.0039657395907367501684920132793 absolute error = 7.079224563e-22 relative error = 3.5326075806294804515122812749519e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0891 y[1] (analytic) = 2.0039746682042420944348035074221 y[1] (numeric) = 2.0039746682042420944355122610672 absolute error = 7.087536451e-22 relative error = 3.5367395423970743069245389314509e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0892 y[1] (analytic) = 2.0039836068975576186251911503486 y[1] (numeric) = 2.003983606897557618625900735305 absolute error = 7.095849564e-22 relative error = 3.5408720608175790162806854661867e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0893 y[1] (analytic) = 2.0039925556708635250143773729112 y[1] (numeric) = 2.0039925556708635250150877893013 absolute error = 7.104163901e-22 relative error = 3.5450051353218651846358299728602e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.3MB, time=15.73 NO POLE x[1] = 0.0894 y[1] (analytic) = 2.004001514524340222315415329572 y[1] (numeric) = 2.0040015145243402223161265775186 absolute error = 7.112479466e-22 relative error = 3.5491387678358030369455677975630e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0895 y[1] (analytic) = 2.0040104834581683256935870401029 y[1] (numeric) = 2.0040104834581683256942991197288 absolute error = 7.120796259e-22 relative error = 3.5532729582892121417951348778481e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0896 y[1] (analytic) = 2.0040194624725286567810265595516 y[1] (numeric) = 2.0040194624725286567817394709798 absolute error = 7.129114282e-22 relative error = 3.5574077076098889274662285240812e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0897 y[1] (analytic) = 2.0040284515676022436913602565456 y[1] (numeric) = 2.0040284515676022436920739998992 absolute error = 7.137433536e-22 relative error = 3.5615430162265995658693806621776e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0898 y[1] (analytic) = 2.0040374507435703210343642024621 y[1] (numeric) = 2.0040374507435703210350787778644 absolute error = 7.145754023e-22 relative error = 3.5656788850670764694168864618687e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0899 y[1] (analytic) = 2.0040464600006143299306386739975 y[1] (numeric) = 2.0040464600006143299313540815719 absolute error = 7.154075744e-22 relative error = 3.5698153145600261960021692625374e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 2.0040554793389159180262997716708 y[1] (numeric) = 2.0040554793389159180270160115409 absolute error = 7.162398701e-22 relative error = 3.5739523056331169928425626452275e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0901 y[1] (analytic) = 2.0040645087586569395076881568007 y[1] (numeric) = 2.0040645087586569395084052290903 absolute error = 7.170722896e-22 relative error = 3.5780898592139815981039398404877e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0902 y[1] (analytic) = 2.0040735482600194551160949094971 y[1] (numeric) = 2.00407354826001945511681281433 absolute error = 7.179048329e-22 relative error = 3.5822279752322498264811579006540e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0903 y[1] (analytic) = 2.0040825978431857321625045102116 y[1] (numeric) = 2.0040825978431857321632232477118 absolute error = 7.187375002e-22 relative error = 3.5863666546154967716257457323879e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0904 y[1] (analytic) = 2.0040916575083382445423549473956 y[1] (numeric) = 2.0040916575083382445430745176874 absolute error = 7.195702918e-22 relative error = 3.5905058987902410764788680964925e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0905 y[1] (analytic) = 2.0041007272556596727503149538163 y[1] (numeric) = 2.004100727255659672751035357024 absolute error = 7.204032077e-22 relative error = 3.5946457076860259303322264118511e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.3MB, time=15.95 NO POLE x[1] = 0.0906 y[1] (analytic) = 2.0041098070853329038950783740836 y[1] (numeric) = 2.0041098070853329038957996103316 absolute error = 7.212362480e-22 relative error = 3.5987860817313515262632876849346e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0907 y[1] (analytic) = 2.0041188969975410317141756659462 y[1] (numeric) = 2.0041188969975410317148977353591 absolute error = 7.220694129e-22 relative error = 3.6029270218536637466189600409229e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0908 y[1] (analytic) = 2.0041279969924673565888025379158 y[1] (numeric) = 2.0041279969924673565895254406184 absolute error = 7.229027026e-22 relative error = 3.6070685289803726847435292458128e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0909 y[1] (analytic) = 2.0041371070702953855586657257829 y[1] (numeric) = 2.0041371070702953855593894619001 absolute error = 7.237361172e-22 relative error = 3.6112106035398847381805509610239e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 2.0041462272312088323368459105899 y[1] (numeric) = 2.0041462272312088323375704802468 absolute error = 7.245696569e-22 relative error = 3.6153532464595450885734514263124e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0911 y[1] (analytic) = 2.0041553574753916173246777806308 y[1] (numeric) = 2.0041553574753916173254031839525 absolute error = 7.254033217e-22 relative error = 3.6194964576687363688681931309880e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0912 y[1] (analytic) = 2.0041644978030278676266472400492 y[1] (numeric) = 2.0041644978030278676273734771613 absolute error = 7.262371121e-22 relative error = 3.6236402395916286433221959945863e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0913 y[1] (analytic) = 2.0041736482143019170653057666114 y[1] (numeric) = 2.0041736482143019170660328376392 absolute error = 7.270710278e-22 relative error = 3.6277845906606585656102017159708e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0914 y[1] (analytic) = 2.0041828087093983061962019212297 y[1] (numeric) = 2.0041828087093983061969298262989 absolute error = 7.279050692e-22 relative error = 3.6319295128009676826820663270365e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0915 y[1] (analytic) = 2.0041919792885017823228300118211 y[1] (numeric) = 2.0041919792885017823235587510575 absolute error = 7.287392364e-22 relative error = 3.6360750064407806314159184513200e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0916 y[1] (analytic) = 2.0042011599517972995115959140826 y[1] (numeric) = 2.0042011599517972995123254876122 absolute error = 7.295735296e-22 relative error = 3.6402210725072469701941714867510e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=309.0MB, alloc=4.3MB, time=16.16 NO POLE x[1] = 0.0917 y[1] (analytic) = 2.0042103506994700186068000517725 y[1] (numeric) = 2.0042103506994700186075304597214 absolute error = 7.304079489e-22 relative error = 3.6443677114285304679107482265642e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0918 y[1] (analytic) = 2.0042195515317053072456375390869 y[1] (numeric) = 2.0042195515317053072463687815814 absolute error = 7.312424945e-22 relative error = 3.6485149241317151741896426833057e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0919 y[1] (analytic) = 2.0042287624486887398732154877262 y[1] (numeric) = 2.0042287624486887398739475648927 absolute error = 7.320771665e-22 relative error = 3.6526627110449038506510461245196e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 2.0042379834506060977575874812476 y[1] (numeric) = 2.0042379834506060977583203932125 absolute error = 7.329119649e-22 relative error = 3.6568110720972294000105912402714e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0921 y[1] (analytic) = 2.0042472145376433690048052193022 y[1] (numeric) = 2.0042472145376433690055389661924 absolute error = 7.337468902e-22 relative error = 3.6609600097125090111694685474507e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0922 y[1] (analytic) = 2.0042564557099867485739873343626 y[1] (numeric) = 2.0042564557099867485747219163049 absolute error = 7.345819423e-22 relative error = 3.6651095233208670426209808576773e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0923 y[1] (analytic) = 2.0042657069678226382924053835428 y[1] (numeric) = 2.0042657069678226382931408006641 absolute error = 7.354171213e-22 relative error = 3.6692596133502907325739326602905e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0924 y[1] (analytic) = 2.0042749683113376468705870181225 y[1] (numeric) = 2.00427496831133764687132327055 absolute error = 7.362524275e-22 relative error = 3.6734102812266071703254874098445e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0925 y[1] (analytic) = 2.0042842397407185899174363333864 y[1] (numeric) = 2.0042842397407185899181734212474 absolute error = 7.370878610e-22 relative error = 3.6775615273777352749547568006594e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0926 y[1] (analytic) = 2.0042935212561524899553714013932 y[1] (numeric) = 2.0042935212561524899561093248152 absolute error = 7.379234220e-22 relative error = 3.6817133527304955836337032018588e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0927 y[1] (analytic) = 2.0043028128578265764354789892937 y[1] (numeric) = 2.0043028128578265764362177484042 absolute error = 7.387591105e-22 relative error = 3.6858657572138188449982104728431e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0928 y[1] (analytic) = 2.0043121145459282857526864658175 y[1] (numeric) = 2.0043121145459282857534260607443 absolute error = 7.395949268e-22 relative error = 3.6900187422533905782930982575752e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.3MB, time=16.37 NO POLE x[1] = 0.0929 y[1] (analytic) = 2.0043214263206452612609508985543 y[1] (numeric) = 2.0043214263206452612616913294253 absolute error = 7.404308710e-22 relative error = 3.6941723082770064421142146817575e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 2.0043307481821653532884653446555 y[1] (numeric) = 2.0043307481821653532892066115987 absolute error = 7.412669432e-22 relative error = 3.6983264557124346697988522082938e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0931 y[1] (analytic) = 2.0043400801306766191528823375874 y[1] (numeric) = 2.004340080130676619153624440731 absolute error = 7.421031436e-22 relative error = 3.7024811854863333752241735870034e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0932 y[1] (analytic) = 2.0043494221663673231765545725697 y[1] (numeric) = 2.0043494221663673231772975120421 absolute error = 7.429394724e-22 relative error = 3.7066364985253238982158993995397e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0933 y[1] (analytic) = 2.004358774289425936701792793335 y[1] (numeric) = 2.0043587742894259367025365692647 absolute error = 7.437759297e-22 relative error = 3.7107923952570780799230461799248e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0934 y[1] (analytic) = 2.0043681365000411381061408828492 y[1] (numeric) = 2.0043681365000411381068854953648 absolute error = 7.446125156e-22 relative error = 3.7149488761092402119408899636668e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0935 y[1] (analytic) = 2.0043775087984018128176681606358 y[1] (numeric) = 2.0043775087984018128184136098662 absolute error = 7.454492304e-22 relative error = 3.7191059425072430384911577344065e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0936 y[1] (analytic) = 2.0043868911846970533302788893499 y[1] (numeric) = 2.004386891184697053331025175424 absolute error = 7.462860741e-22 relative error = 3.7232635943797559916022002863834e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0937 y[1] (analytic) = 2.0043962836591161592190389932499 y[1] (numeric) = 2.0043962836591161592197861162967 absolute error = 7.471230468e-22 relative error = 3.7274218321543335441324215694795e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0938 y[1] (analytic) = 2.0044056862218486371555199912196 y[1] (numeric) = 2.0044056862218486371562679513684 absolute error = 7.479601488e-22 relative error = 3.7315806572563045087828538987780e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0939 y[1] (analytic) = 2.0044150988730842009231601469959 y[1] (numeric) = 2.0044150988730842009239089443761 absolute error = 7.487973802e-22 relative error = 3.7357400701131539601028422871132e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.3MB, time=16.58 NO POLE x[1] = 0.094 y[1] (analytic) = 2.0044245216130127714326428392592 y[1] (numeric) = 2.0044245216130127714333924740003 absolute error = 7.496347411e-22 relative error = 3.7399000711523392366749869630361e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0941 y[1] (analytic) = 2.0044339544418244767372921542483 y[1] (numeric) = 2.00443395444182447673804262648 absolute error = 7.504722317e-22 relative error = 3.7440606613001838809643144906948e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0942 y[1] (analytic) = 2.0044433973597096520484857035643 y[1] (numeric) = 2.0044433973597096520492370134164 absolute error = 7.513098521e-22 relative error = 3.7482218409840826379688890380185e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0943 y[1] (analytic) = 2.0044528503668588397510846698298 y[1] (numeric) = 2.0044528503668588397518368174323 absolute error = 7.521476025e-22 relative error = 3.7523836111302916913808952436712e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0944 y[1] (analytic) = 2.004462313463462789418881082875 y[1] (numeric) = 2.0044623134634627894196340683581 absolute error = 7.529854831e-22 relative error = 3.7565459726650299585494882825180e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0945 y[1] (analytic) = 2.0044717866497124578300623291235 y[1] (numeric) = 2.0044717866497124578308161526174 absolute error = 7.538234939e-22 relative error = 3.7607089255167099472554439714835e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0946 y[1] (analytic) = 2.0044812699257990089826928968539 y[1] (numeric) = 2.0044812699257990089834475584891 absolute error = 7.546616352e-22 relative error = 3.7648724711103722452892600623646e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0947 y[1] (analytic) = 2.0044907632919138141102133600182 y[1] (numeric) = 2.0044907632919138141109688599253 absolute error = 7.554999071e-22 relative error = 3.7690366098732509587976939294244e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0948 y[1] (analytic) = 2.0045002667482484516969566032986 y[1] (numeric) = 2.0045002667482484516977129416084 absolute error = 7.563383098e-22 relative error = 3.7732013427314296686455665703707e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0949 y[1] (analytic) = 2.0045097802949947074936812910887 y[1] (numeric) = 2.004509780294994707494438467932 absolute error = 7.571768433e-22 relative error = 3.7773666696132042938703306010453e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 2.0045193039323445745331225830883 y[1] (numeric) = 2.0045193039323445745338805985961 absolute error = 7.580155078e-22 relative error = 3.7815325914445976302710865711329e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=320.4MB, alloc=4.3MB, time=16.80 x[1] = 0.0951 y[1] (analytic) = 2.0045288376604902531455600992036 y[1] (numeric) = 2.0045288376604902531463189535071 absolute error = 7.588543035e-22 relative error = 3.7856991091515949276730418585565e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0952 y[1] (analytic) = 2.0045383814796241509744031364481 y[1] (numeric) = 2.0045383814796241509751628296787 absolute error = 7.596932306e-22 relative error = 3.7898662236601438414515626508789e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0953 y[1] (analytic) = 2.004547935389938882991793140542 y[1] (numeric) = 2.0045479353899388829925536728312 absolute error = 7.605322892e-22 relative error = 3.7940339353972887883063889674188e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0954 y[1] (analytic) = 2.0045574993916272715142234349118 y[1] (numeric) = 2.0045574993916272715149848063912 absolute error = 7.613714794e-22 relative error = 3.7982022447900460141471231036558e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0955 y[1] (analytic) = 2.0045670734848823462181762097936 y[1] (numeric) = 2.004567073484882346218938420595 absolute error = 7.622108014e-22 relative error = 3.8023711527642644034667091255490e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0956 y[1] (analytic) = 2.004576657669897344155776774149 y[1] (numeric) = 2.0045766576698973441565398244044 absolute error = 7.630502554e-22 relative error = 3.8065406602457550822813914760582e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0957 y[1] (analytic) = 2.0045862519468657097704650731029 y[1] (numeric) = 2.0045862519468657097712289629443 absolute error = 7.638898414e-22 relative error = 3.8107107671625792492381266617325e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0958 y[1] (analytic) = 2.0045958563159810949126844736169 y[1] (numeric) = 2.0045958563159810949134492031766 absolute error = 7.647295597e-22 relative error = 3.8148814749393403787354484846460e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0959 y[1] (analytic) = 2.0046054707774373588555878211158 y[1] (numeric) = 2.0046054707774373588563533905263 absolute error = 7.655694105e-22 relative error = 3.8190527845017432232622244373575e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 2.0046150953314285683107607697867 y[1] (numeric) = 2.0046150953314285683115271791804 absolute error = 7.664093937e-22 relative error = 3.8232246952789079506125174259213e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0961 y[1] (analytic) = 2.0046247299781489974439623892726 y[1] (numeric) = 2.0046247299781489974447296387822 absolute error = 7.672495096e-22 relative error = 3.8273972086953314529798167780747e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0962 y[1] (analytic) = 2.0046343747177931278908830504884 y[1] (numeric) = 2.0046343747177931278916511402468 absolute error = 7.680897584e-22 relative error = 3.8315703256766189479691573096063e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.3MB, time=17.00 NO POLE x[1] = 0.0963 y[1] (analytic) = 2.0046440295505556487729195932871 y[1] (numeric) = 2.0046440295505556487736885234273 absolute error = 7.689301402e-22 relative error = 3.8357440466494959179957345022999e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0964 y[1] (analytic) = 2.0046536944766314567129677787082 y[1] (numeric) = 2.0046536944766314567137375493633 absolute error = 7.697706551e-22 relative error = 3.8399183720406593642180337427887e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0965 y[1] (analytic) = 2.0046633694962156558512320285447 y[1] (numeric) = 2.004663369496215655852002639848 absolute error = 7.706113033e-22 relative error = 3.8440933027756146526413980267004e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0966 y[1] (analytic) = 2.0046730546095035578610524549665 y[1] (numeric) = 2.0046730546095035578618239070514 absolute error = 7.714520849e-22 relative error = 3.8482688392809945211407082570748e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0967 y[1] (analytic) = 2.0046827498166906819647491829412 y[1] (numeric) = 2.0046827498166906819655214759414 absolute error = 7.722930002e-22 relative error = 3.8524449829810672350019387731473e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0968 y[1] (analytic) = 2.0046924551179727549494839681983 y[1] (numeric) = 2.0046924551179727549502571022475 absolute error = 7.731340492e-22 relative error = 3.8566217338035642525851368670188e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0969 y[1] (analytic) = 2.0047021705135457111831391134826 y[1] (numeric) = 2.0047021705135457111839130887147 absolute error = 7.739752321e-22 relative error = 3.8607990926738524876329076902045e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 2.0047118960036056926302136858497 y[1] (numeric) = 2.0047118960036056926309885023988 absolute error = 7.748165491e-22 relative error = 3.8649770605172605214574673022456e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0971 y[1] (analytic) = 2.004721631588349048867737037756 y[1] (numeric) = 2.0047216315883490488685126957563 absolute error = 7.756580003e-22 relative error = 3.8691556377602561822222941690932e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0972 y[1] (analytic) = 2.0047313772679723371011996347005 y[1] (numeric) = 2.0047313772679723371019761342862 absolute error = 7.764995857e-22 relative error = 3.8733348243304586212144184311315e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0973 y[1] (analytic) = 2.004741133042672322180501192179 y[1] (numeric) = 2.0047411330426723221812785334847 absolute error = 7.773413057e-22 relative error = 3.8775146221507380258775681849754e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.3MB, time=17.20 NO POLE x[1] = 0.0974 y[1] (analytic) = 2.0047508989126459766159161247141 y[1] (numeric) = 2.0047508989126459766166943078744 absolute error = 7.781831603e-22 relative error = 3.8816950311486463029743432656819e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0975 y[1] (analytic) = 2.004760674878090480594076309726 y[1] (numeric) = 2.0047606748780904805948553348758 absolute error = 7.790251498e-22 relative error = 3.8858760527481542314578348648892e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0976 y[1] (analytic) = 2.0047704609392032219939711690156 y[1] (numeric) = 2.0047704609392032219947510362898 absolute error = 7.798672742e-22 relative error = 3.8900576868767536043717136565289e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0977 y[1] (analytic) = 2.0047802570961817964029650706301 y[1] (numeric) = 2.0047802570961817964037457801639 absolute error = 7.807095338e-22 relative error = 3.8942399349583404279462339906810e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0978 y[1] (analytic) = 2.0047900633492240071328320538892 y[1] (numeric) = 2.0047900633492240071336136058178 absolute error = 7.815519286e-22 relative error = 3.8984227969203462524153053500349e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0979 y[1] (analytic) = 2.0047998796985278652358078803487 y[1] (numeric) = 2.0047998796985278652365902748076 absolute error = 7.823944589e-22 relative error = 3.9026062741865921523414905687191e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 2.0048097061442915895206594134848 y[1] (numeric) = 2.0048097061442915895214426506095 absolute error = 7.832371247e-22 relative error = 3.9067903666844493060665085223364e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0981 y[1] (analytic) = 2.0048195426867136065687713298828 y[1] (numeric) = 2.004819542686713606569555409809 absolute error = 7.840799262e-22 relative error = 3.9109750753388656867020280559477e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0982 y[1] (analytic) = 2.0048293893259925507502501647196 y[1] (numeric) = 2.0048293893259925507510350875832 absolute error = 7.849228636e-22 relative error = 3.9151604010747504431447007417226e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0983 y[1] (analytic) = 2.0048392460623272642400456943308 y[1] (numeric) = 2.0048392460623272642408314602678 absolute error = 7.857659370e-22 relative error = 3.9193463443181807429309589813820e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0984 y[1] (analytic) = 2.0048491128959167970340896586558 y[1] (numeric) = 2.0048491128959167970348762678024 absolute error = 7.866091466e-22 relative error = 3.9235329059939953056197905665960e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0985 y[1] (analytic) = 2.0048589898269604069654518263601 y[1] (numeric) = 2.0048589898269604069662392788525 absolute error = 7.874524924e-22 relative error = 3.9277200860294175029437611202160e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.3MB, time=17.40 NO POLE x[1] = 0.0986 y[1] (analytic) = 2.0048688768556575597205134054336 y[1] (numeric) = 2.0048688768556575597213017014084 absolute error = 7.882959748e-22 relative error = 3.9319078863467943291682184784368e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0987 y[1] (analytic) = 2.0048787739822079288551578020707 y[1] (numeric) = 2.0048787739822079288559469416644 absolute error = 7.891395937e-22 relative error = 3.9360963063744976859712943699881e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0988 y[1] (analytic) = 2.0048886812068113958109787306362 y[1] (numeric) = 2.0048886812068113958117687139856 absolute error = 7.899833494e-22 relative error = 3.9402853475360131914388964968429e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0989 y[1] (analytic) = 2.0048985985296680499315056775296 y[1] (numeric) = 2.0048985985296680499322965047717 absolute error = 7.908272421e-22 relative error = 3.9444750107559991485660737883066e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 2.0049085259509781884784467217598 y[1] (numeric) = 2.0049085259509781884792383930317 absolute error = 7.916712719e-22 relative error = 3.9486652964602988205980501016778e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0991 y[1] (analytic) = 2.0049184634709423166479487150456 y[1] (numeric) = 2.0049184634709423166487412304845 absolute error = 7.925154389e-22 relative error = 3.9528562050747261443149717843126e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0992 y[1] (analytic) = 2.004928411089761147586874824263 y[1] (numeric) = 2.0049284110897611475876681840062 absolute error = 7.933597432e-22 relative error = 3.9570477370250657064825164169759e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0993 y[1] (analytic) = 2.0049383688076356024090994390597 y[1] (numeric) = 2.0049383688076356024098936432448 absolute error = 7.942041851e-22 relative error = 3.9612398937346096177539416087540e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0994 y[1] (analytic) = 2.0049483366247668102118204474644 y[1] (numeric) = 2.0049483366247668102126154962292 absolute error = 7.950487648e-22 relative error = 3.9654326761278347851781701896232e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0995 y[1] (analytic) = 2.0049583145413561080918888823185 y[1] (numeric) = 2.0049583145413561080926847758007 absolute error = 7.958934822e-22 relative error = 3.9696260836328882759925813590070e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0996 y[1] (analytic) = 2.004968302557605041162155941361 y[1] (numeric) = 2.0049683025576050411629526796986 absolute error = 7.967383376e-22 relative error = 3.9738201176729515545797244638120e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.3MB, time=17.61 NO POLE x[1] = 0.0997 y[1] (analytic) = 2.004978300673715362567837383804 y[1] (numeric) = 2.0049783006737153625686349671352 absolute error = 7.975833312e-22 relative error = 3.9780147791723981904191442809105e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0998 y[1] (analytic) = 2.0049883088898890335028953062349 y[1] (numeric) = 2.0049883088898890335036937346979 absolute error = 7.984284630e-22 relative error = 3.9822100680580502075079047100895e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0999 y[1] (analytic) = 2.0049983272063282232264373006866 y[1] (numeric) = 2.0049983272063282232272365744199 absolute error = 7.992737333e-22 relative error = 3.9864059857529706237507275702457e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 2.0050083556232353090791329977213 y[1] (numeric) = 2.0050083556232353090799331168635 absolute error = 8.001191422e-22 relative error = 3.9906025326826708396093165902071e-20 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 1000 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 17 Seconds Expected Time Remaining = 14 Minutes 23 Seconds Optimized Time Remaining = 14 Minutes 22 Seconds Time to Timeout = 14 Minutes 42 Seconds Percent Done = 2.002 % > quit memory used=336.9MB, alloc=4.3MB, time=17.67