|\^/| 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 > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_small_float, > glob_max_rel_trunc_err, > glob_dump_analytic, > min_in_hour, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_warned2, > glob_warned, > glob_smallish_float, > glob_log10_abserr, > glob_hmin, > glob_initial_pass, > glob_max_opt_iter, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_abserr, > glob_orig_start_sec, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > sec_in_min, > glob_dump, > glob_unchanged_h_cnt, > glob_max_hours, > glob_log10_relerr, > glob_hmin_init, > glob_clock_start_sec, > glob_normmax, > glob_start, > glob_no_eqs, > glob_max_trunc_err, > glob_look_poles, > glob_not_yet_start_msg, > glob_clock_sec, > centuries_in_millinium, > hours_in_day, > djd_debug, > glob_optimal_start, > glob_hmax, > glob_html_log, > glob_current_iter, > glob_last_good_h, > glob_not_yet_finished, > days_in_year, > glob_subiter_method, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_large_float, > years_in_century, > glob_h, > djd_debug2, > glob_percent_done, > glob_max_minutes, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_last_rel_error, > array_type_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_y, > array_x, > array_tmp1_g, > array_norms, > array_y_init, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_poles, > array_complex_pole, > array_y_higher_work2, > 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 ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, INFO, glob_log10relerr, glob_small_float, glob_max_rel_trunc_err, glob_dump_analytic, min_in_hour, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_warned2, glob_warned, glob_smallish_float, glob_log10_abserr, glob_hmin, glob_initial_pass, glob_max_opt_iter, glob_log10normmin, glob_curr_iter_when_opt, glob_abserr, glob_orig_start_sec, glob_max_sec, glob_disp_incr, glob_optimal_done, glob_almost_1, sec_in_min, glob_dump, glob_unchanged_h_cnt, glob_max_hours, glob_log10_relerr, glob_hmin_init, glob_clock_start_sec, glob_normmax, glob_start, glob_no_eqs, glob_max_trunc_err, glob_look_poles, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, hours_in_day, djd_debug, glob_optimal_start, glob_hmax, glob_html_log, glob_current_iter, glob_last_good_h, glob_not_yet_finished, days_in_year, glob_subiter_method, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_large_float, years_in_century, glob_h, djd_debug2, glob_percent_done, glob_max_minutes, glob_max_iter, glob_relerr, glob_reached_optimal_h, array_const_1, array_const_0D0, array_pole, array_last_rel_error, array_type_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_y, array_x, array_tmp1_g, array_norms, array_y_init, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_poles, array_complex_pole, array_y_higher_work2, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_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 > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_small_float, > glob_max_rel_trunc_err, > glob_dump_analytic, > min_in_hour, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_warned2, > glob_warned, > glob_smallish_float, > glob_log10_abserr, > glob_hmin, > glob_initial_pass, > glob_max_opt_iter, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_abserr, > glob_orig_start_sec, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > sec_in_min, > glob_dump, > glob_unchanged_h_cnt, > glob_max_hours, > glob_log10_relerr, > glob_hmin_init, > glob_clock_start_sec, > glob_normmax, > glob_start, > glob_no_eqs, > glob_max_trunc_err, > glob_look_poles, > glob_not_yet_start_msg, > glob_clock_sec, > centuries_in_millinium, > hours_in_day, > djd_debug, > glob_optimal_start, > glob_hmax, > glob_html_log, > glob_current_iter, > glob_last_good_h, > glob_not_yet_finished, > days_in_year, > glob_subiter_method, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_large_float, > years_in_century, > glob_h, > djd_debug2, > glob_percent_done, > glob_max_minutes, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_last_rel_error, > array_type_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_y, > array_x, > array_tmp1_g, > array_norms, > array_y_init, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_poles, > array_complex_pole, > array_y_higher_work2, > 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 ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, INFO, glob_log10relerr, glob_small_float, glob_max_rel_trunc_err, glob_dump_analytic, min_in_hour, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_warned2, glob_warned, glob_smallish_float, glob_log10_abserr, glob_hmin, glob_initial_pass, glob_max_opt_iter, glob_log10normmin, glob_curr_iter_when_opt, glob_abserr, glob_orig_start_sec, glob_max_sec, glob_disp_incr, glob_optimal_done, glob_almost_1, sec_in_min, glob_dump, glob_unchanged_h_cnt, glob_max_hours, glob_log10_relerr, glob_hmin_init, glob_clock_start_sec, glob_normmax, glob_start, glob_no_eqs, glob_max_trunc_err, glob_look_poles, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, hours_in_day, djd_debug, glob_optimal_start, glob_hmax, glob_html_log, glob_current_iter, glob_last_good_h, glob_not_yet_finished, days_in_year, glob_subiter_method, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_large_float, years_in_century, glob_h, djd_debug2, glob_percent_done, glob_max_minutes, glob_max_iter, glob_relerr, glob_reached_optimal_h, array_const_1, array_const_0D0, array_pole, array_last_rel_error, array_type_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_y, array_x, array_tmp1_g, array_norms, array_y_init, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_poles, array_complex_pole, array_y_higher_work2, 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 > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_small_float, > glob_max_rel_trunc_err, > glob_dump_analytic, > min_in_hour, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_warned2, > glob_warned, > glob_smallish_float, > glob_log10_abserr, > glob_hmin, > glob_initial_pass, > glob_max_opt_iter, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_abserr, > glob_orig_start_sec, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > sec_in_min, > glob_dump, > glob_unchanged_h_cnt, > glob_max_hours, > glob_log10_relerr, > glob_hmin_init, > glob_clock_start_sec, > glob_normmax, > glob_start, > glob_no_eqs, > glob_max_trunc_err, > glob_look_poles, > glob_not_yet_start_msg, > glob_clock_sec, > centuries_in_millinium, > hours_in_day, > djd_debug, > glob_optimal_start, > glob_hmax, > glob_html_log, > glob_current_iter, > glob_last_good_h, > glob_not_yet_finished, > days_in_year, > glob_subiter_method, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_large_float, > years_in_century, > glob_h, > djd_debug2, > glob_percent_done, > glob_max_minutes, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_last_rel_error, > array_type_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_y, > array_x, > array_tmp1_g, > array_norms, > array_y_init, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_poles, > array_complex_pole, > array_y_higher_work2, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, INFO, glob_log10relerr, glob_small_float, glob_max_rel_trunc_err, glob_dump_analytic, min_in_hour, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_warned2, glob_warned, glob_smallish_float, glob_log10_abserr, glob_hmin, glob_initial_pass, glob_max_opt_iter, glob_log10normmin, glob_curr_iter_when_opt, glob_abserr, glob_orig_start_sec, glob_max_sec, glob_disp_incr, glob_optimal_done, glob_almost_1, sec_in_min, glob_dump, glob_unchanged_h_cnt, glob_max_hours, glob_log10_relerr, glob_hmin_init, glob_clock_start_sec, glob_normmax, glob_start, glob_no_eqs, glob_max_trunc_err, glob_look_poles, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, hours_in_day, djd_debug, glob_optimal_start, glob_hmax, glob_html_log, glob_current_iter, glob_last_good_h, glob_not_yet_finished, days_in_year, glob_subiter_method, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_large_float, years_in_century, glob_h, djd_debug2, glob_percent_done, glob_max_minutes, glob_max_iter, glob_relerr, glob_reached_optimal_h, array_const_1, array_const_0D0, array_pole, array_last_rel_error, array_type_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_y, array_x, array_tmp1_g, array_norms, array_y_init, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_poles, array_complex_pole, array_y_higher_work2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_small_float, > glob_max_rel_trunc_err, > glob_dump_analytic, > min_in_hour, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_warned2, > glob_warned, > glob_smallish_float, > glob_log10_abserr, > glob_hmin, > glob_initial_pass, > glob_max_opt_iter, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_abserr, > glob_orig_start_sec, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > sec_in_min, > glob_dump, > glob_unchanged_h_cnt, > glob_max_hours, > glob_log10_relerr, > glob_hmin_init, > glob_clock_start_sec, > glob_normmax, > glob_start, > glob_no_eqs, > glob_max_trunc_err, > glob_look_poles, > glob_not_yet_start_msg, > glob_clock_sec, > centuries_in_millinium, > hours_in_day, > djd_debug, > glob_optimal_start, > glob_hmax, > glob_html_log, > glob_current_iter, > glob_last_good_h, > glob_not_yet_finished, > days_in_year, > glob_subiter_method, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_large_float, > years_in_century, > glob_h, > djd_debug2, > glob_percent_done, > glob_max_minutes, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_last_rel_error, > array_type_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_y, > array_x, > array_tmp1_g, > array_norms, > array_y_init, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_poles, > array_complex_pole, > array_y_higher_work2, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 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 ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, INFO, glob_log10relerr, glob_small_float, glob_max_rel_trunc_err, glob_dump_analytic, min_in_hour, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_warned2, glob_warned, glob_smallish_float, glob_log10_abserr, glob_hmin, glob_initial_pass, glob_max_opt_iter, glob_log10normmin, glob_curr_iter_when_opt, glob_abserr, glob_orig_start_sec, glob_max_sec, glob_disp_incr, glob_optimal_done, glob_almost_1, sec_in_min, glob_dump, glob_unchanged_h_cnt, glob_max_hours, glob_log10_relerr, glob_hmin_init, glob_clock_start_sec, glob_normmax, glob_start, glob_no_eqs, glob_max_trunc_err, glob_look_poles, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, hours_in_day, djd_debug, glob_optimal_start, glob_hmax, glob_html_log, glob_current_iter, glob_last_good_h, glob_not_yet_finished, days_in_year, glob_subiter_method, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_large_float, years_in_century, glob_h, djd_debug2, glob_percent_done, glob_max_minutes, glob_max_iter, glob_relerr, glob_reached_optimal_h, array_const_1, array_const_0D0, array_pole, array_last_rel_error, array_type_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_y, array_x, array_tmp1_g, array_norms, array_y_init, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_poles, array_complex_pole, array_y_higher_work2, 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 > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_small_float, > glob_max_rel_trunc_err, > glob_dump_analytic, > min_in_hour, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_warned2, > glob_warned, > glob_smallish_float, > glob_log10_abserr, > glob_hmin, > glob_initial_pass, > glob_max_opt_iter, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_abserr, > glob_orig_start_sec, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > sec_in_min, > glob_dump, > glob_unchanged_h_cnt, > glob_max_hours, > glob_log10_relerr, > glob_hmin_init, > glob_clock_start_sec, > glob_normmax, > glob_start, > glob_no_eqs, > glob_max_trunc_err, > glob_look_poles, > glob_not_yet_start_msg, > glob_clock_sec, > centuries_in_millinium, > hours_in_day, > djd_debug, > glob_optimal_start, > glob_hmax, > glob_html_log, > glob_current_iter, > glob_last_good_h, > glob_not_yet_finished, > days_in_year, > glob_subiter_method, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_large_float, > years_in_century, > glob_h, > djd_debug2, > glob_percent_done, > glob_max_minutes, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_last_rel_error, > array_type_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_y, > array_x, > array_tmp1_g, > array_norms, > array_y_init, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_poles, > array_complex_pole, > array_y_higher_work2, > 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 ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, INFO, glob_log10relerr, glob_small_float, glob_max_rel_trunc_err, glob_dump_analytic, min_in_hour, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_warned2, glob_warned, glob_smallish_float, glob_log10_abserr, glob_hmin, glob_initial_pass, glob_max_opt_iter, glob_log10normmin, glob_curr_iter_when_opt, glob_abserr, glob_orig_start_sec, glob_max_sec, glob_disp_incr, glob_optimal_done, glob_almost_1, sec_in_min, glob_dump, glob_unchanged_h_cnt, glob_max_hours, glob_log10_relerr, glob_hmin_init, glob_clock_start_sec, glob_normmax, glob_start, glob_no_eqs, glob_max_trunc_err, glob_look_poles, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, hours_in_day, djd_debug, glob_optimal_start, glob_hmax, glob_html_log, glob_current_iter, glob_last_good_h, glob_not_yet_finished, days_in_year, glob_subiter_method, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_large_float, years_in_century, glob_h, djd_debug2, glob_percent_done, glob_max_minutes, glob_max_iter, glob_relerr, glob_reached_optimal_h, array_const_1, array_const_0D0, array_pole, array_last_rel_error, array_type_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_y, array_x, array_tmp1_g, array_norms, array_y_init, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_poles, array_complex_pole, array_y_higher_work2, 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 > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_small_float, > glob_max_rel_trunc_err, > glob_dump_analytic, > min_in_hour, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_warned2, > glob_warned, > glob_smallish_float, > glob_log10_abserr, > glob_hmin, > glob_initial_pass, > glob_max_opt_iter, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_abserr, > glob_orig_start_sec, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > sec_in_min, > glob_dump, > glob_unchanged_h_cnt, > glob_max_hours, > glob_log10_relerr, > glob_hmin_init, > glob_clock_start_sec, > glob_normmax, > glob_start, > glob_no_eqs, > glob_max_trunc_err, > glob_look_poles, > glob_not_yet_start_msg, > glob_clock_sec, > centuries_in_millinium, > hours_in_day, > djd_debug, > glob_optimal_start, > glob_hmax, > glob_html_log, > glob_current_iter, > glob_last_good_h, > glob_not_yet_finished, > days_in_year, > glob_subiter_method, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_large_float, > years_in_century, > glob_h, > djd_debug2, > glob_percent_done, > glob_max_minutes, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_last_rel_error, > array_type_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_y, > array_x, > array_tmp1_g, > array_norms, > array_y_init, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_poles, > array_complex_pole, > array_y_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sinh $eq_no = 1 > array_tmp1[1] := sinh(array_x[1]); > array_tmp1_g[1] := cosh(array_x[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 sinh $eq_no = 1 > array_tmp1[2] := att(1,array_tmp1_g,array_x,1); > array_tmp1_g[2] := att(1,array_tmp1,array_x,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 sinh $eq_no = 1 > array_tmp1[3] := att(2,array_tmp1_g,array_x,1); > array_tmp1_g[3] := att(2,array_tmp1,array_x,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 sinh $eq_no = 1 > array_tmp1[4] := att(3,array_tmp1_g,array_x,1); > array_tmp1_g[4] := att(3,array_tmp1,array_x,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 sinh $eq_no = 1 > array_tmp1[5] := att(4,array_tmp1_g,array_x,1); > array_tmp1_g[5] := att(4,array_tmp1,array_x,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 sinh $eq_no = 1 > array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1); > array_tmp1_g[kkk] := att(kkk-1,array_tmp1,array_x,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 ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, INFO, glob_log10relerr, glob_small_float, glob_max_rel_trunc_err, glob_dump_analytic, min_in_hour, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_warned2, glob_warned, glob_smallish_float, glob_log10_abserr, glob_hmin, glob_initial_pass, glob_max_opt_iter, glob_log10normmin, glob_curr_iter_when_opt, glob_abserr, glob_orig_start_sec, glob_max_sec, glob_disp_incr, glob_optimal_done, glob_almost_1, sec_in_min, glob_dump, glob_unchanged_h_cnt, glob_max_hours, glob_log10_relerr, glob_hmin_init, glob_clock_start_sec, glob_normmax, glob_start, glob_no_eqs, glob_max_trunc_err, glob_look_poles, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, hours_in_day, djd_debug, glob_optimal_start, glob_hmax, glob_html_log, glob_current_iter, glob_last_good_h, glob_not_yet_finished, days_in_year, glob_subiter_method, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_large_float, years_in_century, glob_h, djd_debug2, glob_percent_done, glob_max_minutes, glob_max_iter, glob_relerr, glob_reached_optimal_h, array_const_1, array_const_0D0, array_pole, array_last_rel_error, array_type_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_y, array_x, array_tmp1_g, array_norms, array_y_init, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_poles, array_complex_pole, array_y_higher_work2, glob_last; array_tmp1[1] := sinh(array_x[1]); array_tmp1_g[1] := cosh(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := att(1, array_tmp1_g, array_x, 1); array_tmp1_g[2] := att(1, array_tmp1, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := att(2, array_tmp1_g, array_x, 1); array_tmp1_g[3] := att(2, array_tmp1, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := att(3, array_tmp1_g, array_x, 1); array_tmp1_g[4] := att(3, array_tmp1, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := att(4, array_tmp1_g, array_x, 1); array_tmp1_g[5] := att(4, array_tmp1, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 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) > 1.0 + cosh(x); > end; exact_soln_y := proc(x) 1.0 + cosh(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 > ALWAYS, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_log10relerr, > glob_small_float, > glob_max_rel_trunc_err, > glob_dump_analytic, > min_in_hour, > glob_display_flag, > glob_optimal_expect_sec, > glob_log10abserr, > glob_iter, > glob_warned2, > glob_warned, > glob_smallish_float, > glob_log10_abserr, > glob_hmin, > glob_initial_pass, > glob_max_opt_iter, > glob_log10normmin, > glob_curr_iter_when_opt, > glob_abserr, > glob_orig_start_sec, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > glob_almost_1, > sec_in_min, > glob_dump, > glob_unchanged_h_cnt, > glob_max_hours, > glob_log10_relerr, > glob_hmin_init, > glob_clock_start_sec, > glob_normmax, > glob_start, > glob_no_eqs, > glob_max_trunc_err, > glob_look_poles, > glob_not_yet_start_msg, > glob_clock_sec, > centuries_in_millinium, > hours_in_day, > djd_debug, > glob_optimal_start, > glob_hmax, > glob_html_log, > glob_current_iter, > glob_last_good_h, > glob_not_yet_finished, > days_in_year, > glob_subiter_method, > MAX_UNCHANGED, > glob_optimal_clock_start_sec, > glob_large_float, > years_in_century, > glob_h, > djd_debug2, > glob_percent_done, > glob_max_minutes, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_last_rel_error, > array_type_pole, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_y, > array_x, > array_tmp1_g, > array_norms, > array_y_init, > array_real_pole, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_poles, > array_complex_pole, > array_y_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_iolevel := 5; > glob_max_terms := 30; > INFO := 2; > glob_log10relerr := 0.0; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_dump_analytic := false; > min_in_hour := 60.0; > glob_display_flag := true; > glob_optimal_expect_sec := 0.1; > glob_log10abserr := 0.0; > glob_iter := 0; > glob_warned2 := false; > glob_warned := false; > glob_smallish_float := 0.1e-100; > glob_log10_abserr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_initial_pass := true; > glob_max_opt_iter := 10; > glob_log10normmin := 0.1; > glob_curr_iter_when_opt := 0; > glob_abserr := 0.1e-10; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_disp_incr := 0.1; > glob_optimal_done := false; > glob_almost_1 := 0.9990; > sec_in_min := 60.0; > glob_dump := false; > glob_unchanged_h_cnt := 0; > glob_max_hours := 0.0; > glob_log10_relerr := 0.1e-10; > glob_hmin_init := 0.001; > glob_clock_start_sec := 0.0; > glob_normmax := 0.0; > glob_start := 0; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_look_poles := false; > glob_not_yet_start_msg := true; > glob_clock_sec := 0.0; > centuries_in_millinium := 10.0; > hours_in_day := 24.0; > djd_debug := true; > glob_optimal_start := 0.0; > glob_hmax := 1.0; > glob_html_log := true; > glob_current_iter := 0; > glob_last_good_h := 0.1; > glob_not_yet_finished := true; > days_in_year := 365.0; > glob_subiter_method := 3; > MAX_UNCHANGED := 10; > glob_optimal_clock_start_sec := 0.0; > glob_large_float := 9.0e100; > years_in_century := 100.0; > glob_h := 0.1; > djd_debug2 := true; > glob_percent_done := 0.0; > glob_max_minutes := 0.0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_reached_optimal_h := 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/sinhpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh ( 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 := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 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,"1.0 + cosh(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_m1:= 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_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_tmp1_g:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[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 <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #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_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 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 ) = sinh ( 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,"2012-06-13T19:13:32-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sinh") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh ( 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,"sinh diffeq.mxt") > ; > logitem_str(html_log_file,"sinh 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 ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_max_terms, INFO, glob_log10relerr, glob_small_float, glob_max_rel_trunc_err, glob_dump_analytic, min_in_hour, glob_display_flag, glob_optimal_expect_sec, glob_log10abserr, glob_iter, glob_warned2, glob_warned, glob_smallish_float, glob_log10_abserr, glob_hmin, glob_initial_pass, glob_max_opt_iter, glob_log10normmin, glob_curr_iter_when_opt, glob_abserr, glob_orig_start_sec, glob_max_sec, glob_disp_incr, glob_optimal_done, glob_almost_1, sec_in_min, glob_dump, glob_unchanged_h_cnt, glob_max_hours, glob_log10_relerr, glob_hmin_init, glob_clock_start_sec, glob_normmax, glob_start, glob_no_eqs, glob_max_trunc_err, glob_look_poles, glob_not_yet_start_msg, glob_clock_sec, centuries_in_millinium, hours_in_day, djd_debug, glob_optimal_start, glob_hmax, glob_html_log, glob_current_iter, glob_last_good_h, glob_not_yet_finished, days_in_year, glob_subiter_method, MAX_UNCHANGED, glob_optimal_clock_start_sec, glob_large_float, years_in_century, glob_h, djd_debug2, glob_percent_done, glob_max_minutes, glob_max_iter, glob_relerr, glob_reached_optimal_h, array_const_1, array_const_0D0, array_pole, array_last_rel_error, array_type_pole, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_y, array_x, array_tmp1_g, array_norms, array_y_init, array_real_pole, array_y_set_initial, array_y_higher_work, array_y_higher, array_poles, array_complex_pole, array_y_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; DEBUGMASSIVE := 4; DEBUGL := 3; glob_iolevel := 5; glob_max_terms := 30; INFO := 2; glob_log10relerr := 0.; glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_dump_analytic := false; min_in_hour := 60.0; glob_display_flag := true; glob_optimal_expect_sec := 0.1; glob_log10abserr := 0.; glob_iter := 0; glob_warned2 := false; glob_warned := false; glob_smallish_float := 0.1*10^(-100); glob_log10_abserr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_initial_pass := true; glob_max_opt_iter := 10; glob_log10normmin := 0.1; glob_curr_iter_when_opt := 0; glob_abserr := 0.1*10^(-10); glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_disp_incr := 0.1; glob_optimal_done := false; glob_almost_1 := 0.9990; sec_in_min := 60.0; glob_dump := false; glob_unchanged_h_cnt := 0; glob_max_hours := 0.; glob_log10_relerr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_clock_start_sec := 0.; glob_normmax := 0.; glob_start := 0; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_look_poles := false; glob_not_yet_start_msg := true; glob_clock_sec := 0.; centuries_in_millinium := 10.0; hours_in_day := 24.0; djd_debug := true; glob_optimal_start := 0.; glob_hmax := 1.0; glob_html_log := true; glob_current_iter := 0; glob_last_good_h := 0.1; glob_not_yet_finished := true; days_in_year := 365.0; glob_subiter_method := 3; MAX_UNCHANGED := 10; glob_optimal_clock_start_sec := 0.; glob_large_float := 0.90*10^101; years_in_century := 100.0; glob_h := 0.1; djd_debug2 := true; glob_percent_done := 0.; glob_max_minutes := 0.; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_reached_optimal_h := 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/sinhpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh ( 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 := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 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, "1.0 + \t cosh(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_m1 := 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_1st_rel_error := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_tmp1_g := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[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 <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; 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_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 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 ) = sinh ( 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, "2012-06-13T19:13:32-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sinh"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh ( 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, "sinh diffeq.mxt"); logitem_str(html_log_file, "sinh 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/sinhpostode.ode################# diff ( y , x , 1 ) = sinh ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 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) 1.0 + cosh(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) = 2.0000000050000000041666666680556 y[1] (numeric) = 2.0000000050000000041666667166667 absolute error = 4.86111e-26 relative error = 2.4305549939236125101273124856529e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0002 y[1] (analytic) = 2.0000000200000000666666667555556 y[1] (numeric) = 2.0000000200000000666666668527778 absolute error = 9.72222e-26 relative error = 4.8611099513889003240739981635806e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0003 y[1] (analytic) = 2.0000000450000003375000010125 y[1] (numeric) = 2.0000000450000003375000011583334 absolute error = 1.458334e-25 relative error = 7.2916698359374274609385936230329e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0004 y[1] (analytic) = 2.0000000800000010666666723555556 y[1] (numeric) = 2.0000000800000010666666725500001 absolute error = 1.944445e-25 relative error = 9.7222246111110103703730982715425e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0005 y[1] (analytic) = 2.0000001250000026041666883680557 y[1] (numeric) = 2.0000001250000026041666886111113 absolute error = 2.430556e-25 relative error = 1.2152779240451281647863462471499e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0006 y[1] (analytic) = 2.0000001800000054000000648000004 y[1] (numeric) = 2.0000001800000054000000650916672 absolute error = 2.916668e-25 relative error = 1.4583338687499478750031983748352e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0007 y[1] (analytic) = 2.000000245000010004166830068057 y[1] (numeric) = 2.0000002450000100041668304083349 absolute error = 3.402779e-25 relative error = 1.7013892915798032709829413767609e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0008 y[1] (analytic) = 2.0000003200000170666670307555597 y[1] (numeric) = 2.0000003200000170666670311444488 absolute error = 3.888891e-25 relative error = 1.9444451888887531852001912084940e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0009 y[1] (analytic) = 2.0000004050000273375007381125107 y[1] (numeric) = 2.0000004050000273375007385500109 absolute error = 4.375002e-25 relative error = 2.1875005570311073008017253579385e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 2.0000005000000416666680555555804 y[1] (numeric) = 2.0000005000000416666680560416917 absolute error = 4.861113e-25 relative error = 2.4305558923609762731731529669728e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0011 y[1] (analytic) = 2.0000006050000610041691271681087 y[1] (numeric) = 2.0000006050000610041691277028312 absolute error = 5.347225e-25 relative error = 2.6736116912323818514745937718439e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0012 y[1] (analytic) = 2.0000007200000864000041472001066 y[1] (numeric) = 2.0000007200000864000041477834403 absolute error = 5.833337e-25 relative error = 2.9166674499995920001069919773287e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0013 y[1] (analytic) = 2.0000008450001190041733705682579 y[1] (numeric) = 2.0000008450001190041733712002027 absolute error = 6.319448e-25 relative error = 3.1597226650169860202314911545071e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0014 y[1] (analytic) = 2.0000009800001600666771243559216 y[1] (numeric) = 2.0000009800001600666771250364776 absolute error = 6.805560e-25 relative error = 3.4027783326383446715007628765712e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.20 NO POLE x[1] = 0.0015 y[1] (analytic) = 2.0000011250002109375158203131356 y[1] (numeric) = 2.0000011250002109375158210423028 absolute error = 7.291672e-25 relative error = 3.6458339492180190432861174462544e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0016 y[1] (analytic) = 2.0000012800002730666899683566208 y[1] (numeric) = 2.0000012800002730666899691343991 absolute error = 7.777783e-25 relative error = 3.8888890111105019262538080673650e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0017 y[1] (analytic) = 2.0000014450003480042001910697857 y[1] (numeric) = 2.0000014450003480042001918961752 absolute error = 8.263895e-25 relative error = 4.1319445146693691843577336056172e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0018 y[1] (analytic) = 2.0000016200004374000472392027331 y[1] (numeric) = 2.0000016200004374000472400777339 absolute error = 8.750008e-25 relative error = 4.3750004562486736258712456926139e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0019 y[1] (analytic) = 2.0000018050005430042320081722677 y[1] (numeric) = 2.0000018050005430042320090958797 absolute error = 9.236120e-25 relative error = 4.6180558322033576245394756305916e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 2.0000020000006666667555555619048 y[1] (numeric) = 2.0000020000006666667555565341279 absolute error = 9.722231e-25 relative error = 4.8611106388877407418302462123460e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0021 y[1] (analytic) = 2.0000022050008103376191196218807 y[1] (numeric) = 2.000002205000810337619120642715 absolute error = 1.0208343e-24 relative error = 5.1041658726550573489888532766385e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0022 y[1] (analytic) = 2.0000024200009760668241387691656 y[1] (numeric) = 2.0000024200009760668241398386112 absolute error = 1.0694456e-24 relative error = 5.3472215298593392474312024802970e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0023 y[1] (analytic) = 2.0000026450011660043722720874779 y[1] (numeric) = 2.0000026450011660043722732055347 absolute error = 1.1180568e-24 relative error = 5.5902766068559282895519348766549e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0024 y[1] (analytic) = 2.0000028800013824002654208273004 y[1] (numeric) = 2.0000028800013824002654219939684 absolute error = 1.1666680e-24 relative error = 5.8333315999984640026357734165731e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0025 y[1] (analytic) = 2.0000031250016276045057509058998 y[1] (numeric) = 2.000003125001627604505752121179 absolute error = 1.2152792e-24 relative error = 6.0763865056411399586911817841351e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0026 y[1] (analytic) = 2.000003380001904067095716407348 y[1] (numeric) = 2.0000033800019040670957176712385 absolute error = 1.2638905e-24 relative error = 6.3194418201373076473335671810573e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0027 y[1] (analytic) = 2.000003645002214338038084082547 y[1] (numeric) = 2.0000036450022143380380853950488 absolute error = 1.3125018e-24 relative error = 6.5624970398418790947652817573486e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0028 y[1] (analytic) = 2.0000039200025610673359588492565 y[1] (numeric) = 2.0000039200025610673359602103695 absolute error = 1.3611130e-24 relative error = 6.8055516611100294863109821382207e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0029 y[1] (analytic) = 2.0000042050029470049928102921246 y[1] (numeric) = 2.000004205002947004992811701849 absolute error = 1.4097244e-24 relative error = 7.0486071802930172936547990923475e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 2.0000045000033750010125001627232 y[1] (numeric) = 2.0000045000033750010125016210589 absolute error = 1.4583357e-24 relative error = 7.2916620937479843835605327369329e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0031 y[1] (analytic) = 2.0000048050038480053993108795861 y[1] (numeric) = 2.0000048050038480053993123865331 absolute error = 1.5069470e-24 relative error = 7.5347168978281561522022835010547e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0032 y[1] (analytic) = 2.0000051200043690681579750282519 y[1] (numeric) = 2.0000051200043690681579765838103 absolute error = 1.5555584e-24 relative error = 7.7777720888864616424714248928153e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0033 y[1] (analytic) = 2.0000054450049413392937058613117 y[1] (numeric) = 2.0000054450049413392937074654814 absolute error = 1.6041697e-24 relative error = 8.0208266632795924083300347607595e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0034 y[1] (analytic) = 2.0000057800055680688122287984608 y[1] (numeric) = 2.0000057800055680688122304512419 absolute error = 1.6527811e-24 relative error = 8.2638816173591189013955908711659e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0035 y[1] (analytic) = 2.0000061250062526067198139265565 y[1] (numeric) = 2.0000061250062526067198156279489 absolute error = 1.7013924e-24 relative error = 8.5069359474820655737390539164372e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0036 y[1] (analytic) = 2.0000064800069984030233094996801 y[1] (numeric) = 2.000006480006998403023311249684 absolute error = 1.7500039e-24 relative error = 8.7499911499980560240394432316116e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.0MB, time=0.42 NO POLE x[1] = 0.0037 y[1] (analytic) = 2.0000068450078090077301764392063 y[1] (numeric) = 2.0000068450078090077301782378216 absolute error = 1.7986153e-24 relative error = 8.9930457212659055856605352728415e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0038 y[1] (analytic) = 2.0000072200086880708485238338772 y[1] (numeric) = 2.0000072200086880708485256811039 absolute error = 1.8472267e-24 relative error = 9.2361001576383089794377723401778e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0039 y[1] (analytic) = 2.0000076050096393423871454398835 y[1] (numeric) = 2.0000076050096393423871473357216 absolute error = 1.8958381e-24 relative error = 9.4791544554694966695704611231455e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 2.0000080000106666723555571809527 y[1] (numeric) = 2.0000080000106666723555591254023 absolute error = 1.9444496e-24 relative error = 9.7222091111117037436048048990935e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0041 y[1] (analytic) = 2.0000084050117740107640356484441 y[1] (numeric) = 2.0000084050117740107640376415053 absolute error = 1.9930612e-24 relative error = 9.9652641209188662749514010291107e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0042 y[1] (analytic) = 2.0000088200129654076236576014519 y[1] (numeric) = 2.0000088200129654076236596431246 absolute error = 2.0416727e-24 relative error = 1.0208318481249320185367225168762e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0043 y[1] (analytic) = 2.0000092450142450129463404669153 y[1] (numeric) = 2.0000092450142450129463425571996 absolute error = 2.0902843e-24 relative error = 1.0451373188452996402835853602136e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0044 y[1] (analytic) = 2.0000096800156170767448838397388 y[1] (numeric) = 2.0000096800156170767448859786346 absolute error = 2.1388958e-24 relative error = 1.0694427238888655933439131994221e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0045 y[1] (analytic) = 2.0000101250170859490330119829189 y[1] (numeric) = 2.0000101250170859490330141704264 absolute error = 2.1875075e-24 relative error = 1.0937482128903283796023822176357e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0046 y[1] (analytic) = 2.0000105800186560798254173276828 y[1] (numeric) = 2.0000105800186560798254195638018 absolute error = 2.2361190e-24 relative error = 1.1180535854861035300423646740925e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0047 y[1] (analytic) = 2.0000110450203320191378049736341 y[1] (numeric) = 2.0000110450203320191378072583647 absolute error = 2.2847306e-24 relative error = 1.1423589913108572533540303847373e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0048 y[1] (analytic) = 2.0000115200221184169869381889106 y[1] (numeric) = 2.0000115200221184169869405222529 absolute error = 2.3333423e-24 relative error = 1.1666644299999808149372218939682e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0049 y[1] (analytic) = 2.000012005024020023390684910352 y[1] (numeric) = 2.000012005024020023390687292306 absolute error = 2.3819540e-24 relative error = 1.1909698511891646751974549960800e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 2.0000125000260416883680652436783 y[1] (numeric) = 2.0000125000260416883680676742439 absolute error = 2.4305656e-24 relative error = 1.2152752045141478774970685458729e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0051 y[1] (analytic) = 2.00001300502818836193929996368 y[1] (numeric) = 2.0000130050281883619393024428573 absolute error = 2.4791773e-24 relative error = 1.2395805896097451894754802610307e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0052 y[1] (analytic) = 2.0000135200304650941258600144208 y[1] (numeric) = 2.0000135200304650941258625422098 absolute error = 2.5277890e-24 relative error = 1.2638859561116844827042493958109e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0053 y[1] (analytic) = 2.0000140450328770349505170094518 y[1] (numeric) = 2.0000140450328770349505195858526 absolute error = 2.5764008e-24 relative error = 1.2881913536550430013819874619402e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0054 y[1] (analytic) = 2.0000145800354294344373947320399 y[1] (numeric) = 2.0000145800354294344373973570524 absolute error = 2.6250125e-24 relative error = 1.3124966818759386168375724051543e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0055 y[1] (analytic) = 2.0000151250381276426120216354082 y[1] (numeric) = 2.0000151250381276426120243090326 absolute error = 2.6736244e-24 relative error = 1.3368020904087067279823163310345e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0056 y[1] (analytic) = 2.0000156800409771095013843429924 y[1] (numeric) = 2.0000156800409771095013870652286 absolute error = 2.7222362e-24 relative error = 1.3611074288898703793378420305655e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0057 y[1] (analytic) = 2.0000162450439833851339821487097 y[1] (numeric) = 2.0000162450439833851339849195578 absolute error = 2.7708481e-24 relative error = 1.3854127969540891681017425363009e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0058 y[1] (analytic) = 2.0000168200471521195398825172444 y[1] (numeric) = 2.0000168200471521195398853367045 absolute error = 2.8194601e-24 relative error = 1.4097181942367508685190964551810e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=4.1MB, time=0.66 x[1] = 0.0059 y[1] (analytic) = 2.0000174050504890627507775843488 y[1] (numeric) = 2.0000174050504890627507804524208 absolute error = 2.8680720e-24 relative error = 1.4340235203741126925311634708229e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 2.0000180000540000648000416571595 y[1] (numeric) = 2.0000180000540000648000445738435 absolute error = 2.9166840e-24 relative error = 1.4583288750007500663744964527962e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0061 y[1] (analytic) = 2.0000186050576910757227897145318 y[1] (numeric) = 2.0000186050576910757227926798278 absolute error = 2.9652960e-24 relative error = 1.4826342077525150010548783469237e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0062 y[1] (analytic) = 2.0000192200615681455559369073906 y[1] (numeric) = 2.0000192200615681455559399212986 absolute error = 3.0139080e-24 relative error = 1.5069395182648397390878458173683e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0063 y[1] (analytic) = 2.0000198450656374243382590590996 y[1] (numeric) = 2.0000198450656374243382621216197 absolute error = 3.0625201e-24 relative error = 1.5312448561726611425746220928505e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0064 y[1] (analytic) = 2.0000204800699051621104541658494 y[1] (numeric) = 2.0000204800699051621104572769816 absolute error = 3.1111322e-24 relative error = 1.5555501711118773209349733754571e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0065 y[1] (analytic) = 2.0000211250743777089152048970641 y[1] (numeric) = 2.0000211250743777089152080568084 absolute error = 3.1597443e-24 relative error = 1.5798554627179220270815239778880e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0066 y[1] (analytic) = 2.0000217800790615147972420958285 y[1] (numeric) = 2.0000217800790615147972453041849 absolute error = 3.2083564e-24 relative error = 1.6041607306262297916867883516884e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0067 y[1] (analytic) = 2.0000224450839631298034092793353 y[1] (numeric) = 2.0000224450839631298034125363039 absolute error = 3.2569686e-24 relative error = 1.6284660244716748145328153532590e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0068 y[1] (analytic) = 2.0000231200890892039827281393538 y[1] (numeric) = 2.0000231200890892039827314449346 absolute error = 3.3055808e-24 relative error = 1.6527712938902205895808927547587e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0069 y[1] (analytic) = 2.0000238050944464873864650427198 y[1] (numeric) = 2.0000238050944464873864683969128 absolute error = 3.3541930e-24 relative error = 1.6770765385173033037268219205756e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 2.0000245001000418300681985318487 y[1] (numeric) = 2.000024500100041830068201934654 absolute error = 3.4028053e-24 relative error = 1.7013818079877474752355110567799e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0071 y[1] (analytic) = 2.0000252051058821820838878252711 y[1] (numeric) = 2.0000252051058821820838912766887 absolute error = 3.4514176e-24 relative error = 1.7256870519375682014702103802582e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0072 y[1] (analytic) = 2.0000259201119745934919423181925 y[1] (numeric) = 2.0000259201119745934919458182225 absolute error = 3.5000300e-24 relative error = 1.7499923200015554405183932773533e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0073 y[1] (analytic) = 2.0000266451183262143532920830777 y[1] (numeric) = 2.0000266451183262143532956317201 absolute error = 3.5486424e-24 relative error = 1.7742975618157597527277267355169e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0074 y[1] (analytic) = 2.0000273801249442947314593702598 y[1] (numeric) = 2.0000273801249442947314629675145 absolute error = 3.5972547e-24 relative error = 1.7986027270163045721758410530808e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0075 y[1] (analytic) = 2.0000281251318361846926311085754 y[1] (numeric) = 2.0000281251318361846926347544426 absolute error = 3.6458672e-24 relative error = 1.8229079652365762450552550933923e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0076 y[1] (analytic) = 2.0000288801390093343057324060272 y[1] (numeric) = 2.0000288801390093343057361005069 absolute error = 3.6944797e-24 relative error = 1.8472131761133469863033707783984e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0077 y[1] (analytic) = 2.0000296451464712936425010504726 y[1] (numeric) = 2.0000296451464712936425047935648 absolute error = 3.7430922e-24 relative error = 1.8715183592820576841201101034124e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0078 y[1] (analytic) = 2.0000304201542297127775630103415 y[1] (numeric) = 2.0000304201542297127775668020462 absolute error = 3.7917047e-24 relative error = 1.8958235143781501502864680449773e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0079 y[1] (analytic) = 2.0000312051622923417885089353824 y[1] (numeric) = 2.0000312051622923417885127756997 absolute error = 3.8403173e-24 relative error = 1.9201286910362870154300500698197e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 2.0000320001706670307559716574388 y[1] (numeric) = 2.0000320001706670307559755463687 absolute error = 3.8889299e-24 relative error = 1.9444338388926523426698951136213e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0081 y[1] (analytic) = 2.0000328051793617297637046912549 y[1] (numeric) = 2.0000328051793617297637086287975 absolute error = 3.9375426e-24 relative error = 1.9687390075818699214520316259955e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.90 NO POLE x[1] = 0.0082 y[1] (analytic) = 2.000033620188384488898661735314 y[1] (numeric) = 2.0000336201883844888986657214693 absolute error = 3.9861553e-24 relative error = 1.9930441467401639963751633460241e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0083 y[1] (analytic) = 2.0000344451977434582510771727074 y[1] (numeric) = 2.0000344451977434582510812074755 absolute error = 4.0347681e-24 relative error = 2.0173493060021185643783902729933e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0084 y[1] (analytic) = 2.0000352802074468879145475720373 y[1] (numeric) = 2.0000352802074468879145516554182 absolute error = 4.0833809e-24 relative error = 2.0416544350039991000866176958959e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0085 y[1] (analytic) = 2.0000361252175031279861141883526 y[1] (numeric) = 2.0000361252175031279861183203464 absolute error = 4.1319938e-24 relative error = 2.0659595833803488566097199047353e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0086 y[1] (analytic) = 2.0000369802279206285663464641195 y[1] (numeric) = 2.0000369802279206285663506447262 absolute error = 4.1806067e-24 relative error = 2.0902647007674755871419091760246e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0087 y[1] (analytic) = 2.0000378452387079397594265302271 y[1] (numeric) = 2.0000378452387079397594307594467 absolute error = 4.2292196e-24 relative error = 2.1145697868008269627094205290514e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0088 y[1] (analytic) = 2.0000387202498737116732347070294 y[1] (numeric) = 2.0000387202498737116732389848619 absolute error = 4.2778325e-24 relative error = 2.1388748411158516994340399459394e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0089 y[1] (analytic) = 2.0000396052614266944194360054242 y[1] (numeric) = 2.0000396052614266944194403318697 absolute error = 4.3264455e-24 relative error = 2.1631799133470094587547776587868e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 2.0000405002733757381135676279698 y[1] (numeric) = 2.0000405002733757381135720030283 absolute error = 4.3750585e-24 relative error = 2.1874849531306964465597436507516e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0091 y[1] (analytic) = 2.0000414052857297928751274700404 y[1] (numeric) = 2.000041405285729792875131893712 absolute error = 4.4236716e-24 relative error = 2.2117900101013287265072751072625e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0092 y[1] (analytic) = 2.0000423202984979088276636210213 y[1] (numeric) = 2.000042320298497908827668093306 absolute error = 4.4722847e-24 relative error = 2.2360950338953479286589870956639e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0093 y[1] (analytic) = 2.0000432453116892360988648655442 y[1] (numeric) = 2.0000432453116892360988693864421 absolute error = 4.5208979e-24 relative error = 2.2604000741471255675830474009762e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0094 y[1] (analytic) = 2.0000441803253130248206521847644 y[1] (numeric) = 2.0000441803253130248206567542755 absolute error = 4.5695111e-24 relative error = 2.2847050804931497460429408259276e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0095 y[1] (analytic) = 2.0000451253393786251292712576799 y[1] (numeric) = 2.0000451253393786251292758758043 absolute error = 4.6181244e-24 relative error = 2.3090101025677464782105656695730e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0096 y[1] (analytic) = 2.0000460803538954871653859624943 y[1] (numeric) = 2.0000460803538954871653906292319 absolute error = 4.6667376e-24 relative error = 2.3333150400086033703812630518767e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0097 y[1] (analytic) = 2.0000470453688731610741728780228 y[1] (numeric) = 2.0000470453688731610741775933738 absolute error = 4.7153510e-24 relative error = 2.3576200424477201446681389582815e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0098 y[1] (analytic) = 2.0000480203843212970054167851449 y[1] (numeric) = 2.0000480203843212970054215491093 absolute error = 4.7639644e-24 relative error = 2.3819250095228091028387179816341e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0099 y[1] (analytic) = 2.0000490054002496451136071683018 y[1] (numeric) = 2.0000490054002496451136119808796 absolute error = 4.8125778e-24 relative error = 2.4062299408693275093553598718580e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 2.0000500004166680555580357170414 y[1] (numeric) = 2.0000500004166680555580405782327 absolute error = 4.8611913e-24 relative error = 2.4305348861214838404208842561571e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0101 y[1] (analytic) = 2.0000510054335864785028948276116 y[1] (numeric) = 2.0000510054335864785028997374164 absolute error = 4.9098048e-24 relative error = 2.4548397949159374853210956608545e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0102 y[1] (analytic) = 2.0000520204510149641173771046018 y[1] (numeric) = 2.0000520204510149641173820630202 absolute error = 4.9584184e-24 relative error = 2.4791447168868480903169174508347e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0103 y[1] (analytic) = 2.0000530454689636625757758626355 y[1] (numeric) = 2.0000530454689636625757808696675 absolute error = 5.0070320e-24 relative error = 2.5034496016709262357221806882613e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=19.0MB, alloc=4.1MB, time=1.14 x[1] = 0.0104 y[1] (analytic) = 2.0000540804874428240575866281129 y[1] (numeric) = 2.0000540804874428240575916837586 absolute error = 5.0556457e-24 relative error = 2.5277544989022817865658922620850e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0105 y[1] (analytic) = 2.0000551255064627987476096410061 y[1] (numeric) = 2.0000551255064627987476147452656 absolute error = 5.1042595e-24 relative error = 2.5520594082162994630183528400253e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0106 y[1] (analytic) = 2.0000561805260340368360533567072 y[1] (numeric) = 2.0000561805260340368360585095805 absolute error = 5.1528733e-24 relative error = 2.5763642792497682229236357580034e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0107 y[1] (analytic) = 2.0000572455461670885186389479304 y[1] (numeric) = 2.0000572455461670885186441494176 absolute error = 5.2014872e-24 relative error = 2.6006691616367211008446222770875e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0108 y[1] (analytic) = 2.0000583205668726039967058066694 y[1] (numeric) = 2.0000583205668726039967110567704 absolute error = 5.2501010e-24 relative error = 2.6249739550154588385686949166669e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0109 y[1] (analytic) = 2.0000594055881613334773180462106 y[1] (numeric) = 2.0000594055881613334773233449255 absolute error = 5.2987149e-24 relative error = 2.6492787590185585874348118416782e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 2.0000605006100441271733720032042 y[1] (numeric) = 2.0000605006100441271733773505332 absolute error = 5.3473290e-24 relative error = 2.6735836232798937892684725127920e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0111 y[1] (analytic) = 2.0000616056325319353037047397932 y[1] (numeric) = 2.0000616056325319353037101357363 absolute error = 5.3959431e-24 relative error = 2.6978884474378474952568428624328e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0112 y[1] (analytic) = 2.0000627206556358080932035458017 y[1] (numeric) = 2.0000627206556358080932089903589 absolute error = 5.4445572e-24 relative error = 2.7221932311278881499894254515926e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0113 y[1] (analytic) = 2.0000638456793668957729164409838 y[1] (numeric) = 2.0000638456793668957729219341551 absolute error = 5.4931713e-24 relative error = 2.7464979739854855469210666470993e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0114 y[1] (analytic) = 2.0000649807037364485801636773343 y[1] (numeric) = 2.0000649807037364485801692191199 absolute error = 5.5417856e-24 relative error = 2.7708027756428619108930312428092e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0115 y[1] (analytic) = 2.0000661257287558167586502414623 y[1] (numeric) = 2.0000661257287558167586558318622 absolute error = 5.5903999e-24 relative error = 2.7951075357386242041695200194803e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0116 y[1] (analytic) = 2.0000672807544364505585793570277 y[1] (numeric) = 2.0000672807544364505585849960419 absolute error = 5.6390142e-24 relative error = 2.8194122539082448398936358047294e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0117 y[1] (analytic) = 2.0000684457807899002367669872439 y[1] (numeric) = 2.0000684457807899002367726748724 absolute error = 5.6876285e-24 relative error = 2.8437169297871976286740770274925e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0118 y[1] (analytic) = 2.0000696208078278160567573374456 y[1] (numeric) = 2.0000696208078278160567630736885 absolute error = 5.7362429e-24 relative error = 2.8680216130092173311242963157641e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0119 y[1] (analytic) = 2.0000708058355619482889393577247 y[1] (numeric) = 2.0000708058355619482889451425821 absolute error = 5.7848574e-24 relative error = 2.8923263032096917183903219020902e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 2.0000720008640041472106642456342 y[1] (numeric) = 2.0000720008640041472106700791062 absolute error = 5.8334720e-24 relative error = 2.9166310000240084957421881265785e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0121 y[1] (analytic) = 2.0000732058931663631063639489617 y[1] (numeric) = 2.0000732058931663631063698310483 absolute error = 5.8820866e-24 relative error = 2.9409356530893853950712341066906e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0122 y[1] (analytic) = 2.0000744209230606462676706685739 y[1] (numeric) = 2.0000744209230606462676765992752 absolute error = 5.9307013e-24 relative error = 2.9652403120394406930267746935187e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0123 y[1] (analytic) = 2.0000756459536991469935373613329 y[1] (numeric) = 2.000075645953699146993543340649 absolute error = 5.9793161e-24 relative error = 2.9895449765095627200660279754030e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0124 y[1] (analytic) = 2.0000768809850941155903592430862 y[1] (numeric) = 2.000076880985094115590365271017 absolute error = 6.0279308e-24 relative error = 3.0138495461389836908788287464230e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0125 y[1] (analytic) = 2.0000781260172579023720962917301 y[1] (numeric) = 2.0000781260172579023721023682758 absolute error = 6.0765457e-24 relative error = 3.0381541705574194314913190893572e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0126 y[1] (analytic) = 2.0000793810502029576603967503501 y[1] (numeric) = 2.0000793810502029576604028755108 absolute error = 6.1251607e-24 relative error = 3.0624587994021500842405336483028e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=1.38 NO POLE x[1] = 0.0127 y[1] (analytic) = 2.0000806460839418317847216304372 y[1] (numeric) = 2.0000806460839418317847278042128 absolute error = 6.1737756e-24 relative error = 3.0867633323125968749560957448739e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0128 y[1] (analytic) = 2.0000819211184871750824702151823 y[1] (numeric) = 2.0000819211184871750824764375729 absolute error = 6.2223906e-24 relative error = 3.1110678689202442706954499387522e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0129 y[1] (analytic) = 2.0000832061538517378991065628508 y[1] (numeric) = 2.0000832061538517378991128338565 absolute error = 6.2710057e-24 relative error = 3.1353724088604829302966041707403e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 2.0000845011900483705882870102372 y[1] (numeric) = 2.000084501190048370588293329858 absolute error = 6.3196208e-24 relative error = 3.1596769017708160087547268214684e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0131 y[1] (analytic) = 2.0000858062270900235119886762015 y[1] (numeric) = 2.0000858062270900235119950444376 absolute error = 6.3682361e-24 relative error = 3.1839814472824420305270115523970e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0132 y[1] (analytic) = 2.0000871212649897470406389652895 y[1] (numeric) = 2.0000871212649897470406453821409 absolute error = 6.4168514e-24 relative error = 3.2082859450350098619484762980886e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0133 y[1] (analytic) = 2.0000884463037606915532460714368 y[1] (numeric) = 2.0000884463037606915532525369036 absolute error = 6.4654668e-24 relative error = 3.2325904446617987667836949152725e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0134 y[1] (analytic) = 2.0000897813434161074375304817592 y[1] (numeric) = 2.0000897813434161074375369958415 absolute error = 6.5140823e-24 relative error = 3.2568949457982005535685576024720e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0135 y[1] (analytic) = 2.0000911263839693450900574804302 y[1] (numeric) = 2.0000911263839693450900640431279 absolute error = 6.5626977e-24 relative error = 3.2811993480841632588725361319062e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0136 y[1] (analytic) = 2.0000924814254338549163706526461 y[1] (numeric) = 2.0000924814254338549163772639594 absolute error = 6.6113133e-24 relative error = 3.3055038011483463876072351951464e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0137 y[1] (analytic) = 2.0000938464678231873311263886824 y[1] (numeric) = 2.0000938464678231873311330486113 absolute error = 6.6599289e-24 relative error = 3.3298082046307333683523142001937e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0138 y[1] (analytic) = 2.0000952215111509927582293880398 y[1] (numeric) = 2.0000952215111509927582360965844 absolute error = 6.7085446e-24 relative error = 3.3541126081644399921866782204387e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0139 y[1] (analytic) = 2.0000966065554310216309691636839 y[1] (numeric) = 2.0000966065554310216309759208442 absolute error = 6.7571603e-24 relative error = 3.3784169613872753182609376263639e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 2.0000980016006771243921575463776 y[1] (numeric) = 2.0000980016006771243921643521537 absolute error = 6.8057761e-24 relative error = 3.4027213139322882339300178778717e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0141 y[1] (analytic) = 2.0000994066469032514942671891099 y[1] (numeric) = 2.0000994066469032514942740435019 absolute error = 6.8543920e-24 relative error = 3.4270256654348738675021012548993e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0142 y[1] (analytic) = 2.0001008216941234533995710716205 y[1] (numeric) = 2.0001008216941234533995779746284 absolute error = 6.9030079e-24 relative error = 3.4513299655329479640780806224472e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0143 y[1] (analytic) = 2.0001022467423518805802830050225 y[1] (numeric) = 2.0001022467423518805802899566465 absolute error = 6.9516240e-24 relative error = 3.4756343138569008591068639159281e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0144 y[1] (analytic) = 2.0001036817916027835186991365251 y[1] (numeric) = 2.0001036817916027835187061367651 absolute error = 7.0002400e-24 relative error = 3.4999385600497971853490893207867e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0145 y[1] (analytic) = 2.000105126841890512707340454256 y[1] (numeric) = 2.0001051268418905127073475031122 absolute error = 7.0488562e-24 relative error = 3.5242428537393655862067846382794e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0146 y[1] (analytic) = 2.0001065818932295186490962921875 y[1] (numeric) = 2.0001065818932295186491033896599 absolute error = 7.0974724e-24 relative error = 3.5485470945662235120744112943318e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0147 y[1] (analytic) = 2.0001080469456343518573688351649 y[1] (numeric) = 2.0001080469456343518573759812537 absolute error = 7.1460888e-24 relative error = 3.5728513821604760440766577619519e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0148 y[1] (analytic) = 2.0001095219991196628562186240411 y[1] (numeric) = 2.0001095219991196628562258187462 absolute error = 7.1947051e-24 relative error = 3.5971555661656245590619489707469e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0149 y[1] (analytic) = 2.0001110070537002021805110609169 y[1] (numeric) = 2.0001110070537002021805183042384 absolute error = 7.2433215e-24 memory used=26.7MB, alloc=4.1MB, time=1.62 relative error = 3.6214597462117395764323431420012e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.015 y[1] (analytic) = 2.00011250210939082037606391449 y[1] (numeric) = 2.0001125021093908203760712064281 absolute error = 7.2919381e-24 relative error = 3.6457639719314083304564664874963e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0151 y[1] (analytic) = 2.0001140071662064679997958255135 y[1] (numeric) = 2.0001140071662064679998031660681 absolute error = 7.3405546e-24 relative error = 3.6700680929684679444120130307434e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0152 y[1] (analytic) = 2.0001155222241621956198758123647 y[1] (numeric) = 2.000115522224162195619883201536 absolute error = 7.3891713e-24 relative error = 3.6943722589498814973931461561650e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0153 y[1] (analytic) = 2.0001170472832731538158737767275 y[1] (numeric) = 2.0001170472832731538158812145155 absolute error = 7.4377880e-24 relative error = 3.7186763695167879926511200046105e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0154 y[1] (analytic) = 2.0001185823435545931789120093877 y[1] (numeric) = 2.0001185823435545931789194957925 absolute error = 7.4864048e-24 relative error = 3.7429804743017391085238439645788e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0155 y[1] (analytic) = 2.0001201274050218643118176961447 y[1] (numeric) = 2.0001201274050218643118252311665 absolute error = 7.5350218e-24 relative error = 3.7672846229371338947706908722472e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0156 y[1] (analytic) = 2.00012168246769041782927642384 y[1] (numeric) = 2.0001216824676904178292840074787 absolute error = 7.5836387e-24 relative error = 3.7915886650673837918016664210502e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0157 y[1] (analytic) = 2.0001232475315758043579866865035 y[1] (numeric) = 2.0001232475315758043579943187592 absolute error = 7.6322557e-24 relative error = 3.8158927003219635937177737127564e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0158 y[1] (analytic) = 2.0001248225966936745368153916214 y[1] (numeric) = 2.0001248225966936745368230724943 absolute error = 7.6808729e-24 relative error = 3.8401967783331568860415594023288e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0159 y[1] (analytic) = 2.0001264076630597790169543665248 y[1] (numeric) = 2.0001264076630597790169620960148 absolute error = 7.7294900e-24 relative error = 3.8645007487457291430710069841460e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 2.0001280027306899684620778649013 y[1] (numeric) = 2.0001280027306899684620856430086 absolute error = 7.7781073e-24 relative error = 3.8888047611857240383228358298412e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0161 y[1] (analytic) = 2.0001296077996001935485010734325 y[1] (numeric) = 2.0001296077996001935485089001571 absolute error = 7.8267246e-24 relative error = 3.9131087152949071434218641939264e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0162 y[1] (analytic) = 2.0001312228698065049653396185568 y[1] (numeric) = 2.0001312228698065049653474938989 absolute error = 7.8753421e-24 relative error = 3.9374127107022445207837352704321e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0163 y[1] (analytic) = 2.000132847941325053414670073361 y[1] (numeric) = 2.0001328479413250534146779973207 absolute error = 7.9239597e-24 relative error = 3.9617166970463421515616265849592e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0164 y[1] (analytic) = 2.0001344830141720896116914646012 y[1] (numeric) = 2.0001344830141720896116994371784 absolute error = 7.9725772e-24 relative error = 3.9860205739693303208910582062097e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0165 y[1] (analytic) = 2.0001361280883639642848877798545 y[1] (numeric) = 2.0001361280883639642848958010494 absolute error = 8.0211949e-24 relative error = 4.0103244910966539122970756680461e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0166 y[1] (analytic) = 2.0001377831639171281761914748046 y[1] (numeric) = 2.0001377831639171281761995446172 absolute error = 8.0698126e-24 relative error = 4.0346283480704865560384418693003e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0167 y[1] (analytic) = 2.0001394482408481320411479806607 y[1] (numeric) = 2.0001394482408481320411560990911 absolute error = 8.1184304e-24 relative error = 4.0589321945228759684297211202710e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0168 y[1] (analytic) = 2.0001411233191736266490812117135 y[1] (numeric) = 2.0001411233191736266490893787618 absolute error = 8.1670483e-24 relative error = 4.0832360300892322325459346373629e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0169 y[1] (analytic) = 2.0001428083989103627832600730284 y[1] (numeric) = 2.0001428083989103627832682886947 absolute error = 8.2156663e-24 relative error = 4.1075398544049659610768231542899e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 2.0001445034800751912410659682783 y[1] (numeric) = 2.0001445034800751912410742325627 absolute error = 8.2642844e-24 relative error = 4.1318436671054883084795525839930e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0171 y[1] (analytic) = 2.0001462085626850628341613077177 y[1] (numeric) = 2.0001462085626850628341696206203 absolute error = 8.3129026e-24 relative error = 4.1561474678262109831313731945450e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=1.86 NO POLE x[1] = 0.0172 y[1] (analytic) = 2.0001479236467570283886590162993 y[1] (numeric) = 2.0001479236467570283886673778201 absolute error = 8.3615208e-24 relative error = 4.1804512062062440771538197738218e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0173 y[1] (analytic) = 2.0001496487323082387452930419353 y[1] (numeric) = 2.0001496487323082387453014520744 absolute error = 8.4101391e-24 relative error = 4.2047549318773888669960582534362e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0174 y[1] (analytic) = 2.000151383819355944759589863905 y[1] (numeric) = 2.0001513838193559447595983226625 absolute error = 8.4587575e-24 relative error = 4.2290586444750595454866263597452e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0175 y[1] (analytic) = 2.00015312890791749730204100141 y[1] (numeric) = 2.0001531289079174973020495087861 absolute error = 8.5073761e-24 relative error = 4.2533623936308429783662375995593e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0176 y[1] (analytic) = 2.0001548839980103472582765222797 y[1] (numeric) = 2.0001548839980103472582850782743 absolute error = 8.5559946e-24 relative error = 4.2776660289916383645131556696011e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0177 y[1] (analytic) = 2.0001566490896520455292395518271 y[1] (numeric) = 2.0001566490896520455292481564404 absolute error = 8.6046133e-24 relative error = 4.3019697001813779519495675658912e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0178 y[1] (analytic) = 2.0001584241828602430313617818589 y[1] (numeric) = 2.0001584241828602430313704350909 absolute error = 8.6532320e-24 relative error = 4.3262733068432666370084228188775e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0179 y[1] (analytic) = 2.0001602092776526906967399798397 y[1] (numeric) = 2.0001602092776526906967486816905 absolute error = 8.7018508e-24 relative error = 4.3505768986088506963284831978818e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 2.0001620043740472394733134982132 y[1] (numeric) = 2.0001620043740472394733222486829 absolute error = 8.7504697e-24 relative error = 4.3748804751135488699434762644184e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0181 y[1] (analytic) = 2.0001638094720618403250427838818 y[1] (numeric) = 2.0001638094720618403250515829705 absolute error = 8.7990887e-24 relative error = 4.3991840359927805733238815691285e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0182 y[1] (analytic) = 2.0001656245717145442320888878462 y[1] (numeric) = 2.000165624571714544232097735554 absolute error = 8.8477078e-24 relative error = 4.4234875808819659095289808006228e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0183 y[1] (analytic) = 2.0001674496730235021909939750074 y[1] (numeric) = 2.0001674496730235021910028713344 absolute error = 8.8963270e-24 relative error = 4.4477911094165256813588527733654e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0184 y[1] (analytic) = 2.000169284776006965214862834132 y[1] (numeric) = 2.0001692847760069652148717790782 absolute error = 8.9449462e-24 relative error = 4.4720945712361131647201120655580e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0185 y[1] (analytic) = 2.0001711298806832843335453879835 y[1] (numeric) = 2.0001711298806832843335543815491 absolute error = 8.9935656e-24 relative error = 4.4963980659677331956892450744614e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0186 y[1] (analytic) = 2.000172984987070910593820203621 y[1] (numeric) = 2.0001729849870709105938292458061 absolute error = 9.0421851e-24 relative error = 4.5207015432509946405617247607083e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0187 y[1] (analytic) = 2.0001748500951883950595790028673 y[1] (numeric) = 2.0001748500951883950595880936719 absolute error = 9.0908046e-24 relative error = 4.5450049527256920928748822290735e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0188 y[1] (analytic) = 2.0001767252050543888120121729476 y[1] (numeric) = 2.0001767252050543888120213123718 absolute error = 9.1394242e-24 relative error = 4.5693083440229729051680380070878e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0189 y[1] (analytic) = 2.0001786103166876429497952773017 y[1] (numeric) = 2.0001786103166876429498044653456 absolute error = 9.1880439e-24 relative error = 4.5936117167782630836087829740578e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 2.000180505430107008589276566571 y[1] (numeric) = 2.0001805054301070085892858032348 absolute error = 9.2366638e-24 relative error = 4.6179151206224771906522896897166e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0191 y[1] (analytic) = 2.0001824105453314368646654897624 y[1] (numeric) = 2.000182410545331436864674775046 absolute error = 9.2852836e-24 relative error = 4.6422184052045794997518205035629e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0192 y[1] (analytic) = 2.0001843256623799789282222055897 y[1] (numeric) = 2.0001843256623799789282315394933 absolute error = 9.3339036e-24 relative error = 4.6665217201464617223921577547797e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0193 y[1] (analytic) = 2.0001862507812717859504480939974 y[1] (numeric) = 2.0001862507812717859504574765211 absolute error = 9.3825237e-24 relative error = 4.6908250150880653053589932396645e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0194 y[1] (analytic) = 2.0001881859020261091202772678651 y[1] (numeric) = 2.000188185902026109120286699009 absolute error = 9.4311439e-24 relative error = 4.7151282896648203003312383239548e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.2MB, time=2.09 NO POLE x[1] = 0.0195 y[1] (analytic) = 2.0001901310246622996452690848975 y[1] (numeric) = 2.0001901310246622996452785646616 absolute error = 9.4797641e-24 relative error = 4.7394314935169104283310058841122e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0196 y[1] (analytic) = 2.0001920861491998087518016596997 y[1] (numeric) = 2.0001920861491998087518111880842 absolute error = 9.5283845e-24 relative error = 4.7637347262703106655008300132969e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0197 y[1] (analytic) = 2.0001940512756581876852663760416 y[1] (numeric) = 2.0001940512756581876852759530465 absolute error = 9.5770049e-24 relative error = 4.7880378875700086527974881011335e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0198 y[1] (analytic) = 2.0001960264040570877102633993116 y[1] (numeric) = 2.0001960264040570877102730249371 absolute error = 9.6256255e-24 relative error = 4.8123410770417856431347713235233e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0199 y[1] (analytic) = 2.000198011534416260110798189163 y[1] (numeric) = 2.0001980115344162601108078634092 absolute error = 9.6742462e-24 relative error = 4.8366442443258777300428716296710e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 2.0002000066667555561904790123542 y[1] (numeric) = 2.0002000066667555561904887352212 absolute error = 9.7228670e-24 relative error = 4.8609473890577202208028405436935e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0201 y[1] (analytic) = 2.0002020118010949272727154557849 y[1] (numeric) = 2.0002020118010949272727252272727 absolute error = 9.7714878e-24 relative error = 4.8852504608777991261274158608336e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0202 y[1] (analytic) = 2.0002040269374544247009179397301 y[1] (numeric) = 2.0002040269374544247009277598389 absolute error = 9.8201088e-24 relative error = 4.9095535594115024006173788554295e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0203 y[1] (analytic) = 2.000206052075854199838698231275 y[1] (numeric) = 2.0002060520758541998387081000048 absolute error = 9.8687298e-24 relative error = 4.9338565843044185813105896780545e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0204 y[1] (analytic) = 2.0002080872163145040700709579507 y[1] (numeric) = 2.0002080872163145040700808753016 absolute error = 9.9173509e-24 relative error = 4.9581595851869376869637758019719e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0205 y[1] (analytic) = 2.0002101323588556887996561215747 y[1] (numeric) = 2.0002101323588556887996660875469 absolute error = 9.9659722e-24 relative error = 4.9824626116892477312797260819169e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0206 y[1] (analytic) = 2.0002121875034982054528826122975 y[1] (numeric) = 2.000212187503498205452892626891 absolute error = 1.00145935e-23 relative error = 5.0067655634572446106568926113381e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0207 y[1] (analytic) = 2.0002142526502626054761927228566 y[1] (numeric) = 2.0002142526502626054762027860715 absolute error = 1.00632149e-23 relative error = 5.0310684901211694272462535175475e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0208 y[1] (analytic) = 2.0002163277991695403372476630415 y[1] (numeric) = 2.000216327799169540337257774878 absolute error = 1.01118365e-23 relative error = 5.0553714413110583158505496612815e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0209 y[1] (analytic) = 2.0002184129502397615251340743703 y[1] (numeric) = 2.0002184129502397615251442348285 absolute error = 1.01604582e-23 relative error = 5.0796743666676594121824266344649e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 2.0002205081034941205505715449809 y[1] (numeric) = 2.0002205081034941205505817540608 absolute error = 1.02090799e-23 relative error = 5.1039772158319298497750027723583e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0211 y[1] (analytic) = 2.000222613258953568946121124738 y[1] (numeric) = 2.0002226132589535689461313824398 absolute error = 1.02577018e-23 relative error = 5.1282800884283441347866366955875e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0212 y[1] (analytic) = 2.0002247284166391582663948405594 y[1] (numeric) = 2.0002247284166391582664051468831 absolute error = 1.03063237e-23 relative error = 5.1525828841034267046964111009434e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0213 y[1] (analytic) = 2.0002268535765720400882662119618 y[1] (numeric) = 2.0002268535765720400882765669075 absolute error = 1.03549457e-23 relative error = 5.1768856524871144093383638245706e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0214 y[1] (analytic) = 2.00022898873877346601108176683 y[1] (numeric) = 2.0002289887387734660110921703979 absolute error = 1.04035679e-23 relative error = 5.2011884432091332067194329354703e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0215 y[1] (analytic) = 2.0002311339032647876568735574105 y[1] (numeric) = 2.0002311339032647876568840096007 absolute error = 1.04521902e-23 relative error = 5.2254912059105510360488654486546e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0216 y[1] (analytic) = 2.0002332890700674566705726765321 y[1] (numeric) = 2.0002332890700674566705831773446 absolute error = 1.05008125e-23 relative error = 5.2497938902326509045849034276144e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=38.1MB, alloc=4.2MB, time=2.32 x[1] = 0.0217 y[1] (analytic) = 2.000235454239203024720223774055 y[1] (numeric) = 2.00023545423920302472023432349 absolute error = 1.05494350e-23 relative error = 5.2740965957992764093952399420392e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0218 y[1] (analytic) = 2.000237629410693143497200573552 y[1] (numeric) = 2.0002376294106931434972111716096 absolute error = 1.05980576e-23 relative error = 5.2983992722516589289580284915394e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0219 y[1] (analytic) = 2.0002398145845595647164223892219 y[1] (numeric) = 2.0002398145845595647164330359022 absolute error = 1.06466803e-23 relative error = 5.3227019192252532990438814891193e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 2.0002420097608241401165716430391 y[1] (numeric) = 2.0002420097608241401165823383422 absolute error = 1.06953031e-23 relative error = 5.3470045363555155047380604622181e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0221 y[1] (analytic) = 2.0002442149395088214603123821406 y[1] (numeric) = 2.0002442149395088214603231260667 absolute error = 1.07439261e-23 relative error = 5.3713071732717980645227808606537e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0222 y[1] (analytic) = 2.000246430120635660534509796453 y[1] (numeric) = 2.0002464301206356605345205890021 absolute error = 1.07925491e-23 relative error = 5.3956097296217131887497766066877e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0223 y[1] (analytic) = 2.0002486553042268091504507365609 y[1] (numeric) = 2.0002486553042268091504615777331 absolute error = 1.08411722e-23 relative error = 5.4199122550346708713449319157673e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0224 y[1] (analytic) = 2.0002508904903045191440652318204 y[1] (numeric) = 2.0002508904903045191440761216158 absolute error = 1.08897954e-23 relative error = 5.4442147491461318161457626544330e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0225 y[1] (analytic) = 2.0002531356788911423761490087182 y[1] (numeric) = 2.0002531356788911423761599471369 absolute error = 1.09384187e-23 relative error = 5.4685172115915579370502895206102e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0226 y[1] (analytic) = 2.00025539087000913073258700948 y[1] (numeric) = 2.0002553908700091307325979965222 absolute error = 1.09870422e-23 relative error = 5.4928196920000284136178325549309e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0227 y[1] (analytic) = 2.0002576560636810361245779109296 y[1] (numeric) = 2.0002576560636810361245889465954 absolute error = 1.10356658e-23 relative error = 5.5171221400132783422267805237509e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0228 y[1] (analytic) = 2.0002599312599295104888596436008 y[1] (numeric) = 2.0002599312599295104888707278903 absolute error = 1.10842895e-23 relative error = 5.5414245552667725902362041807106e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0229 y[1] (analytic) = 2.0002622164587773057879359111052 y[1] (numeric) = 2.0002622164587773057879470440185 absolute error = 1.11329133e-23 relative error = 5.5657269373959772836653600512639e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 2.0002645116602472740103037097573 y[1] (numeric) = 2.0002645116602472740103148912945 absolute error = 1.11815372e-23 relative error = 5.5900292860363598193422775399618e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0231 y[1] (analytic) = 2.0002668168643623671706818484596 y[1] (numeric) = 2.0002668168643623671706930786208 absolute error = 1.12301612e-23 relative error = 5.6143316008233888770522561854948e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0232 y[1] (analytic) = 2.0002691320711456373102404688503 y[1] (numeric) = 2.0002691320711456373102517476356 absolute error = 1.12787853e-23 relative error = 5.6386338813925344316862723409636e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0233 y[1] (analytic) = 2.0002714572806202364968315657149 y[1] (numeric) = 2.0002714572806202364968428931243 absolute error = 1.13274094e-23 relative error = 5.6629360773860532764166149217777e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0234 y[1] (analytic) = 2.0002737924928094168252205076647 y[1] (numeric) = 2.0002737924928094168252318836985 absolute error = 1.13760338e-23 relative error = 5.6872383384190614797085069442716e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0235 y[1] (analytic) = 2.0002761377077365304173185580854 y[1] (numeric) = 2.0002761377077365304173299827436 absolute error = 1.14246582e-23 relative error = 5.7115405141473895077414397957307e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0236 y[1] (analytic) = 2.0002784929254250294224163963556 y[1] (numeric) = 2.0002784929254250294224278696384 absolute error = 1.14732828e-23 relative error = 5.7358427041927657724922721951826e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0237 y[1] (analytic) = 2.0002808581458984660174186393404 y[1] (numeric) = 2.0002808581458984660174301612479 absolute error = 1.15219075e-23 relative error = 5.7601448581975100324390855493625e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0238 y[1] (analytic) = 2.0002832333691804924070793631605 y[1] (numeric) = 2.0002832333691804924070909336927 absolute error = 1.15705322e-23 relative error = 5.7844469258041793702467117533670e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0239 y[1] (analytic) = 2.0002856185952948608242386252397 y[1] (numeric) = 2.0002856185952948608242502443968 absolute error = 1.16191571e-23 relative error = 5.8087490066341523676009292286576e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.2MB, time=2.57 NO POLE x[1] = 0.024 y[1] (analytic) = 2.000288013824265423530059986634 y[1] (numeric) = 2.0002880138242654235300716544161 absolute error = 1.16677821e-23 relative error = 5.8330510503299295157688571302513e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0241 y[1] (analytic) = 2.0002904190561161328142690346431 y[1] (numeric) = 2.0002904190561161328142807510503 absolute error = 1.17164072e-23 relative error = 5.8573530565269922426898684369713e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0242 y[1] (analytic) = 2.0002928342908710409953929057077 y[1] (numeric) = 2.0002928342908710409954046707402 absolute error = 1.17650325e-23 relative error = 5.8816550748535036073630836307609e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0243 y[1] (analytic) = 2.0002952595285543004210008085954 y[1] (numeric) = 2.0002952595285543004210126222533 absolute error = 1.18136579e-23 relative error = 5.9059570549521464423484363255207e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0244 y[1] (analytic) = 2.0002976947691901634679455478764 y[1] (numeric) = 2.0002976947691901634679574101597 absolute error = 1.18622833e-23 relative error = 5.9302589464658469738558267919964e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0245 y[1] (analytic) = 2.000300140012802982542606047692 y[1] (numeric) = 2.0003001400128029825426179586009 absolute error = 1.19109089e-23 relative error = 5.9545608490152702091003063419083e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0246 y[1] (analytic) = 2.000302595259417210081130875819 y[1] (numeric) = 2.0003025952594172100811428353536 absolute error = 1.19595346e-23 relative error = 5.9788627122432844295398936598422e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0247 y[1] (analytic) = 2.000305060509057398549682768031 y[1] (numeric) = 2.0003050605090573985496947761915 absolute error = 1.20081605e-23 relative error = 6.0031645857777536456856199705790e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0248 y[1] (analytic) = 2.0003075357617482004446841527606 y[1] (numeric) = 2.0003075357617482004446962095471 absolute error = 1.20567865e-23 relative error = 6.0274664192616703320505456665316e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0249 y[1] (analytic) = 2.0003100210175143682930636760637 y[1] (numeric) = 2.0003100210175143682930757814762 absolute error = 1.21054125e-23 relative error = 6.0517681623382754145491381705997e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 2.0003125162763807546525037268886 y[1] (numeric) = 2.0003125162763807546525158809273 absolute error = 1.21540387e-23 relative error = 6.0760699146276257222968068003188e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0251 y[1] (analytic) = 2.0003150215383723121116889626536 y[1] (numeric) = 2.0003150215383723121117011653187 absolute error = 1.22026651e-23 relative error = 6.1003716757650288105184022843305e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0252 y[1] (analytic) = 2.0003175368035140932905558351341 y[1] (numeric) = 2.0003175368035140932905680864256 absolute error = 1.22512915e-23 relative error = 6.1246733454016665932826899777843e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0253 y[1] (analytic) = 2.0003200620718312508405431166613 y[1] (numeric) = 2.0003200620718312508405554165794 absolute error = 1.22999181e-23 relative error = 6.1489750231572248425009092183944e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0254 y[1] (analytic) = 2.0003225973433490374448434266379 y[1] (numeric) = 2.0003225973433490374448557751827 absolute error = 1.23485448e-23 relative error = 6.1732766586750763988710733342365e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0255 y[1] (analytic) = 2.0003251426180928058186557583695 y[1] (numeric) = 2.0003251426180928058186681555411 absolute error = 1.23971716e-23 relative error = 6.1975782515907213794314305464064e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0256 y[1] (analytic) = 2.0003276978960880087094390062171 y[1] (numeric) = 2.0003276978960880087094514520157 absolute error = 1.24457986e-23 relative error = 6.2218798515314703825809120398783e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0257 y[1] (analytic) = 2.0003302631773601988971664930719 y[1] (numeric) = 2.0003302631773601988971789874975 absolute error = 1.24944256e-23 relative error = 6.2461813581491448104791754273934e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0258 y[1] (analytic) = 2.0003328384619350291945814981551 y[1] (numeric) = 2.0003328384619350291945940412078 absolute error = 1.25430527e-23 relative error = 6.2704828210711223323847615367935e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0259 y[1] (analytic) = 2.0003354237498382524474537851455 y[1] (numeric) = 2.0003354237498382524474663768256 absolute error = 1.25916801e-23 relative error = 6.2947843399161411096121362063251e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 2.0003380190410957215348371306378 y[1] (numeric) = 2.0003380190410957215348497709454 absolute error = 1.26403076e-23 relative error = 6.3190858143362182474317603066639e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0261 y[1] (analytic) = 2.0003406243357333893693278529331 y[1] (numeric) = 2.0003406243357333893693405418682 absolute error = 1.26889351e-23 relative error = 6.3433871939753762243668041333390e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0262 y[1] (analytic) = 2.0003432396337773088973243411648 y[1] (numeric) = 2.0003432396337773088973370787276 absolute error = 1.27375628e-23 relative error = 6.3676885784521620635989061685980e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.2MB, time=2.81 NO POLE x[1] = 0.0263 y[1] (analytic) = 2.0003458649352536330992875847632 y[1] (numeric) = 2.0003458649352536330993003709539 absolute error = 1.27861907e-23 relative error = 6.3919899674018913362540310734000e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0264 y[1] (analytic) = 2.0003485002401886149900027032604 y[1] (numeric) = 2.000348500240188614990015538079 absolute error = 1.28348186e-23 relative error = 6.4162912604773017745525333288334e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0265 y[1] (analytic) = 2.0003511455486086076188414764379 y[1] (numeric) = 2.0003511455486086076188543598846 absolute error = 1.28834467e-23 relative error = 6.4405925572965517936108488728920e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0266 y[1] (analytic) = 2.000353800860540064070025874821 y[1] (numeric) = 2.0003538008605400640700388068959 absolute error = 1.29320749e-23 relative error = 6.4648938075038025116780662810058e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0267 y[1] (analytic) = 2.000356466176009537462892590521 y[1] (numeric) = 2.0003564661760095374629055712242 absolute error = 1.29807032e-23 relative error = 6.4891950107345716389201292121229e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0268 y[1] (analytic) = 2.0003591414950436809521585684287 y[1] (numeric) = 2.0003591414950436809521715977604 absolute error = 1.30293317e-23 relative error = 6.5134962166154016925397463756578e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0269 y[1] (analytic) = 2.0003618268176692477281875377622 y[1] (numeric) = 2.0003618268176692477282006157225 absolute error = 1.30779603e-23 relative error = 6.5377973747906565673262375529965e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 2.0003645221439130910172575439702 y[1] (numeric) = 2.0003645221439130910172706705593 absolute error = 1.31265891e-23 relative error = 6.5620985348867470647355498294406e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0271 y[1] (analytic) = 2.0003672274738021640818294809956 y[1] (numeric) = 2.0003672274738021640818426562135 absolute error = 1.31752179e-23 relative error = 6.5863995965573523254105171647536e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0272 y[1] (analytic) = 2.0003699428073635202208166238997 y[1] (numeric) = 2.0003699428073635202208298477466 absolute error = 1.32238469e-23 relative error = 6.6107006594197071995820018359142e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0273 y[1] (analytic) = 2.0003726681446243127698551618521 y[1] (numeric) = 2.0003726681446243127698684343282 absolute error = 1.32724761e-23 relative error = 6.6350017231091349002417666200107e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0274 y[1] (analytic) = 2.0003754034856117951015757314871 y[1] (numeric) = 2.0003754034856117951015890525925 absolute error = 1.33211054e-23 relative error = 6.6593027372703422726645635234172e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0275 y[1] (analytic) = 2.0003781488303533206258759506302 y[1] (numeric) = 2.0003781488303533206258893203649 absolute error = 1.33697347e-23 relative error = 6.6836036515483109117574854176930e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0276 y[1] (analytic) = 2.0003809041788763427901939523971 y[1] (numeric) = 2.0003809041788763427902073707613 absolute error = 1.34183642e-23 relative error = 6.7079045655597372986755073465597e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0277 y[1] (analytic) = 2.0003836695312084150797829196687 y[1] (numeric) = 2.0003836695312084150797963866626 absolute error = 1.34669939e-23 relative error = 6.7322054789399481932787560820398e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0278 y[1] (analytic) = 2.0003864448873771910179866199437 y[1] (numeric) = 2.0003864448873771910180001355674 absolute error = 1.35156237e-23 relative error = 6.7565063413339299662500029028639e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0279 y[1] (analytic) = 2.0003892302474104241665159405723 y[1] (numeric) = 2.0003892302474104241665295048259 absolute error = 1.35642536e-23 relative error = 6.7808071523772189206592594872556e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 2.0003920256113359681257264243733 y[1] (numeric) = 2.000392025611335968125740037257 absolute error = 1.36128837e-23 relative error = 6.8051079616955545181383930811556e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0281 y[1] (analytic) = 2.0003948309791817765348968056383 y[1] (numeric) = 2.0003948309791817765349104671521 absolute error = 1.36615138e-23 relative error = 6.8294086689440041628484838054965e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0282 y[1] (analytic) = 2.0003976463509759030725085465242 y[1] (numeric) = 2.0003976463509759030725222566684 absolute error = 1.37101442e-23 relative error = 6.8537094237285026007325778787965e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0283 y[1] (analytic) = 2.000400471726746501456526373839 y[1] (numeric) = 2.0004004717267465014565401326136 absolute error = 1.37587746e-23 relative error = 6.8780100757141994496620809258188e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0284 y[1] (analytic) = 2.0004033071065218254446798162207 y[1] (numeric) = 2.000403307106521825444693623626 absolute error = 1.38074053e-23 relative error = 6.9023107745066096596455357578481e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=49.5MB, alloc=4.2MB, time=3.04 x[1] = 0.0285 y[1] (analytic) = 2.0004061524903302288347457417159 y[1] (numeric) = 2.0004061524903302288347595977519 absolute error = 1.38560360e-23 relative error = 6.9266113697713088526887726132954e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0286 y[1] (analytic) = 2.0004090078782001654648318957568 y[1] (numeric) = 2.0004090078782001654648458004237 absolute error = 1.39046669e-23 relative error = 6.9509119611236123401486786413763e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0287 y[1] (analytic) = 2.0004118732701601892136614395433 y[1] (numeric) = 2.0004118732701601892136753928412 absolute error = 1.39532979e-23 relative error = 6.9752124982091501871816374089347e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0288 y[1] (analytic) = 2.00041474866623895400085848883 y[1] (numeric) = 2.0004147486662389540008724907591 absolute error = 1.40019291e-23 relative error = 6.9995130306531072225139858364362e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0289 y[1] (analytic) = 2.0004176340664652137872346531229 y[1] (numeric) = 2.0004176340664652137872487036833 absolute error = 1.40505604e-23 relative error = 7.0238135081012591861517169529081e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 2.0004205294708678225750765752876 y[1] (numeric) = 2.0004205294708678225750906744794 absolute error = 1.40991918e-23 relative error = 7.0481139301891607114329732148982e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0291 y[1] (analytic) = 2.0004234348794757344084344715726 y[1] (numeric) = 2.000423434879475734408448619396 absolute error = 1.41478234e-23 relative error = 7.0724143465417848122121206985608e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0292 y[1] (analytic) = 2.0004263502923180033734116720499 y[1] (numeric) = 2.000426350292318003373425868505 absolute error = 1.41964551e-23 relative error = 7.0967147068051280800195410067260e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0293 y[1] (analytic) = 2.0004292757094237835984551614762 y[1] (numeric) = 2.0004292757094237835984694065632 absolute error = 1.42450870e-23 relative error = 7.1210150606040208807905558289584e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0294 y[1] (analytic) = 2.0004322111308223292546471205779 y[1] (numeric) = 2.0004322111308223292546614142969 absolute error = 1.42937190e-23 relative error = 7.1453153575846081003050694089908e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0295 y[1] (analytic) = 2.0004351565565429945559974677619 y[1] (numeric) = 2.000435156556542994556011810113 absolute error = 1.43423511e-23 relative error = 7.1696155973824530534382304654939e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0296 y[1] (analytic) = 2.000438111986615233759737401256 y[1] (numeric) = 2.0004381119866152337597517922394 absolute error = 1.43909834e-23 relative error = 7.1939158296221707266351149862309e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0297 y[1] (analytic) = 2.0004410774210686011666139416817 y[1] (numeric) = 2.0004410774210686011666283812975 absolute error = 1.44396158e-23 relative error = 7.2182160039501307862307271226598e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0298 y[1] (analytic) = 2.0004440528599327511211854750613 y[1] (numeric) = 2.0004440528599327511211999633098 absolute error = 1.44882485e-23 relative error = 7.2425162199797043371213682493207e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0299 y[1] (analytic) = 2.0004470383032374380121182962647 y[1] (numeric) = 2.0004470383032374380121328331459 absolute error = 1.45368812e-23 relative error = 7.2668163273795350708908890885196e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 2.0004500337510125162724841528952 y[1] (numeric) = 2.0004500337510125162724987384093 absolute error = 1.45855141e-23 relative error = 7.2911164257629224706819491416139e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0301 y[1] (analytic) = 2.0004530392032879403800587896214 y[1] (numeric) = 2.0004530392032879403800734237685 absolute error = 1.46341471e-23 relative error = 7.3154164647765390776829960282756e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0302 y[1] (analytic) = 2.0004560546600937648576214929545 y[1] (numeric) = 2.0004560546600937648576361757348 absolute error = 1.46827803e-23 relative error = 7.3397164940445619539006093550672e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0303 y[1] (analytic) = 2.0004590801214601442732556364771 y[1] (numeric) = 2.0004590801214601442732703678907 absolute error = 1.47314136e-23 relative error = 7.3640164632138166494999838343501e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0304 y[1] (analytic) = 2.0004621155874173332406502265234 y[1] (numeric) = 2.0004621155874173332406650065705 absolute error = 1.47800471e-23 relative error = 7.3883164219083323506501419645954e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0305 y[1] (analytic) = 2.0004651610579956864194024483171 y[1] (numeric) = 2.0004651610579956864194172769978 absolute error = 1.48286807e-23 relative error = 7.4126163197750886641764309807249e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0306 y[1] (analytic) = 2.0004682165332256585153212125672 y[1] (numeric) = 2.0004682165332256585153360898816 absolute error = 1.48773144e-23 relative error = 7.4369161564496686235548237537311e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0307 y[1] (analytic) = 2.0004712820131378042807317025265 y[1] (numeric) = 2.0004712820131378042807466284748 absolute error = 1.49259483e-23 relative error = 7.4612159815558781936755897862589e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.2MB, time=3.28 NO POLE x[1] = 0.0308 y[1] (analytic) = 2.000474357497762778514780921515 y[1] (numeric) = 2.0004743574977627785147958960973 absolute error = 1.49745823e-23 relative error = 7.4855157447409304053786553476033e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0309 y[1] (analytic) = 2.0004774429871313360637442409117 y[1] (numeric) = 2.0004774429871313360637592641282 absolute error = 1.50232165e-23 relative error = 7.5098154956284809714980269848995e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 2.0004805384812743318213329486178 y[1] (numeric) = 2.0004805384812743318213480204686 absolute error = 1.50718508e-23 relative error = 7.5341151838658995986793149885379e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0311 y[1] (analytic) = 2.0004836439802227207290027979936 y[1] (numeric) = 2.0004836439802227207290179184789 absolute error = 1.51204853e-23 relative error = 7.5584148590766907972350383659058e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0312 y[1] (analytic) = 2.0004867594840075577762635572737 y[1] (numeric) = 2.0004867594840075577762787263937 absolute error = 1.51691200e-23 relative error = 7.5827145208962159711182632773891e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0313 y[1] (analytic) = 2.0004898849926599980009895594623 y[1] (numeric) = 2.0004898849926599980010047772171 absolute error = 1.52177548e-23 relative error = 7.6070141189720814303641208977379e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0314 y[1] (analytic) = 2.0004930205062112964897312527121 y[1] (numeric) = 2.0004930205062112964897465191019 absolute error = 1.52663898e-23 relative error = 7.6313137029275627247733094611835e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0315 y[1] (analytic) = 2.0004961660246928083780277511901 y[1] (numeric) = 2.000496166024692808378043066215 absolute error = 1.53150249e-23 relative error = 7.6556132224104254592621517758446e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0316 y[1] (analytic) = 2.0004993215481359888507203864334 y[1] (numeric) = 2.0004993215481359888507357500935 absolute error = 1.53636601e-23 relative error = 7.6799126770562715279594825686150e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0317 y[1] (analytic) = 2.0005024870765723931422672591975 y[1] (numeric) = 2.000502487076572393142282671493 absolute error = 1.54122955e-23 relative error = 7.7042121164881461309399765582652e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0318 y[1] (analytic) = 2.0005056626100336765370587918015 y[1] (numeric) = 2.0005056626100336765370742527326 absolute error = 1.54609311e-23 relative error = 7.7285115403414177844433601726165e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0319 y[1] (analytic) = 2.0005088481485515943697342809722 y[1] (numeric) = 2.0005088481485515943697497905391 absolute error = 1.55095669e-23 relative error = 7.7528109482514558579898441608941e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 2.0005120436921580020254994511908 y[1] (numeric) = 2.0005120436921580020255150093935 absolute error = 1.55582027e-23 relative error = 7.7771102398792262181013733675412e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0321 y[1] (analytic) = 2.0005152492408848549404450085448 y[1] (numeric) = 2.0005152492408848549404606153836 absolute error = 1.56068388e-23 relative error = 7.8014095648219468226842119506241e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0322 y[1] (analytic) = 2.0005184647947642086018661950899 y[1] (numeric) = 2.0005184647947642086018818505649 absolute error = 1.56554750e-23 relative error = 7.8257088227406666518754370697005e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0323 y[1] (analytic) = 2.0005216903538282185485833437226 y[1] (numeric) = 2.0005216903538282185485990478339 absolute error = 1.57041113e-23 relative error = 7.8500080132710011502410742008825e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0324 y[1] (analytic) = 2.0005249259181091403712634335689 y[1] (numeric) = 2.0005249259181091403712791863167 absolute error = 1.57527478e-23 relative error = 7.8743071860354484703107271070591e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0325 y[1] (analytic) = 2.0005281714876393297127426458913 y[1] (numeric) = 2.0005281714876393297127584472758 absolute error = 1.58013845e-23 relative error = 7.8986063406693856041536151959770e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0326 y[1] (analytic) = 2.0005314270624512422683499205174 y[1] (numeric) = 2.0005314270624512422683657705387 absolute error = 1.58500213e-23 relative error = 7.9229054268214726294926372483649e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0327 y[1] (analytic) = 2.0005346926425774337862315127933 y[1] (numeric) = 2.0005346926425774337862474114516 absolute error = 1.58986583e-23 relative error = 7.9472044941139694719164806542683e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0328 y[1] (analytic) = 2.0005379682280505600676765510656 y[1] (numeric) = 2.000537968228050560067692498361 absolute error = 1.59472954e-23 relative error = 7.9715034921957023132206459551272e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0329 y[1] (analytic) = 2.0005412538189033769674435946944 y[1] (numeric) = 2.0005412538189033769674595906271 absolute error = 1.59959327e-23 relative error = 7.9958024706887713228217724904570e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 2.0005445494151687403940881926011 y[1] (numeric) = 2.0005445494151687403941042371712 absolute error = 1.60445701e-23 relative error = 8.0201013792421698341030739716291e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.2MB, time=3.52 NO POLE x[1] = 0.0331 y[1] (analytic) = 2.0005478550168796063102914423544 y[1] (numeric) = 2.0005478550168796063103075355621 absolute error = 1.60932077e-23 relative error = 8.0444002674778373099615609698094e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0332 y[1] (analytic) = 2.0005511706240690307331895497972 y[1] (numeric) = 2.0005511706240690307332056916427 absolute error = 1.61418455e-23 relative error = 8.0686991350311598135844629203355e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0333 y[1] (analytic) = 2.0005544962367701697347043892184 y[1] (numeric) = 2.0005544962367701697347205797019 absolute error = 1.61904835e-23 relative error = 8.0929979815375244315507715724475e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0334 y[1] (analytic) = 2.0005578318550162794418750640725 y[1] (numeric) = 2.000557831855016279441891303194 absolute error = 1.62391215e-23 relative error = 8.1172967066602031014946488814723e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0335 y[1] (analytic) = 2.0005611774788407160371904682497 y[1] (numeric) = 2.0005611774788407160372067560095 absolute error = 1.62877598e-23 relative error = 8.1415954599930100514250896934824e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0336 y[1] (analytic) = 2.0005645331082769357589228479019 y[1] (numeric) = 2.0005645331082769357589391843001 absolute error = 1.63363982e-23 relative error = 8.1658941411993041689393973091845e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0337 y[1] (analytic) = 2.0005678987433584949014623638249 y[1] (numeric) = 2.0005678987433584949014787488617 absolute error = 1.63850368e-23 relative error = 8.1901927999005363462615870637502e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0338 y[1] (analytic) = 2.0005712743841190498156526544033 y[1] (numeric) = 2.0005712743841190498156690880788 absolute error = 1.64336755e-23 relative error = 8.2144913857463782488502518248696e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0339 y[1] (analytic) = 2.0005746600305923569091273991185 y[1] (numeric) = 2.0005746600305923569091438814329 absolute error = 1.64823144e-23 relative error = 8.2387899483581162611549309607945e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 2.000578055682812272646647882626 y[1] (numeric) = 2.0005780556828122726466644135795 absolute error = 1.65309535e-23 relative error = 8.2630884873711472211754092165891e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0341 y[1] (analytic) = 2.0005814613408127535504415594027 y[1] (numeric) = 2.0005814613408127535504581389955 absolute error = 1.65795928e-23 relative error = 8.2873870024208690875031575215868e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0342 y[1] (analytic) = 2.0005848770046278562005416189701 y[1] (numeric) = 2.0005848770046278562005582472023 absolute error = 1.66282322e-23 relative error = 8.3116854431572986018252966037895e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0343 y[1] (analytic) = 2.0005883026742917372351275516942 y[1] (numeric) = 2.000588302674291737235144228566 absolute error = 1.66768718e-23 relative error = 8.3359838592013895330750125235676e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0344 y[1] (analytic) = 2.000591738349838653350866715168 y[1] (numeric) = 2.0005917383498386533508834406796 absolute error = 1.67255116e-23 relative error = 8.3602822501885440236487100756659e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0345 y[1] (analytic) = 2.0005951840313029613032569011786 y[1] (numeric) = 2.0005951840313029613032736753301 absolute error = 1.67741515e-23 relative error = 8.3845805657690405591847570239432e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0346 y[1] (analytic) = 2.0005986397187191179069699032621 y[1] (numeric) = 2.0005986397187191179069867260536 absolute error = 1.68227915e-23 relative error = 8.4088788055785426545359032168905e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0347 y[1] (analytic) = 2.0006021054121216800361960848507 y[1] (numeric) = 2.0006021054121216800362129562824 absolute error = 1.68714317e-23 relative error = 8.4331770192376684112251955188929e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0348 y[1] (analytic) = 2.0006055811115453046249899480151 y[1] (numeric) = 2.0006055811115453046250068680872 absolute error = 1.69200721e-23 relative error = 8.4574752063818262195209978596440e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0349 y[1] (analytic) = 2.000609066817024748667616702805 y[1] (numeric) = 2.0006090668170247486676336715177 absolute error = 1.69687127e-23 relative error = 8.4817733666464256874761252724471e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 2.0006125625285948692188998371924 y[1] (numeric) = 2.0006125625285948692189168545459 absolute error = 1.70173535e-23 relative error = 8.5060714996668776530790251015667e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0351 y[1] (analytic) = 2.00061606824629062339456968762 y[1] (numeric) = 2.0006160682462906233945867536144 absolute error = 1.70659944e-23 relative error = 8.5303695550939911597720122095244e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0352 y[1] (analytic) = 2.0006195839701470683716130101584 y[1] (numeric) = 2.000619583970147068371630124794 absolute error = 1.71146356e-23 relative error = 8.5546676325324734539525366997420e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=61.0MB, alloc=4.2MB, time=3.77 x[1] = 0.0353 y[1] (analytic) = 2.0006231097001993613886235522771 y[1] (numeric) = 2.0006231097001993613886407155539 absolute error = 1.71632768e-23 relative error = 8.5789655816641942919513431257614e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0354 y[1] (analytic) = 2.0006266454364827597461536252298 y[1] (numeric) = 2.0006266454364827597461708371481 absolute error = 1.72119183e-23 relative error = 8.6032635520781158955150512364656e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0355 y[1] (analytic) = 2.000630191179032620807066677061 y[1] (numeric) = 2.0006301911790326208070839376209 absolute error = 1.72605599e-23 relative error = 8.6275614434408908025954998492672e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0356 y[1] (analytic) = 2.0006337469278844019968908662343 y[1] (numeric) = 2.000633746927884401996908175436 absolute error = 1.73092017e-23 relative error = 8.6518593053723660933755570511233e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0357 y[1] (analytic) = 2.0006373126830736608041736358884 y[1] (numeric) = 2.0006373126830736608041909937321 absolute error = 1.73578437e-23 relative error = 8.6761571375079630537102446917418e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0358 y[1] (analytic) = 2.0006408884446360547808372887227 y[1] (numeric) = 2.0006408884446360547808546952086 absolute error = 1.74064859e-23 relative error = 8.7004549394831042965816782108561e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0359 y[1] (analytic) = 2.0006444742126073415425355625169 y[1] (numeric) = 2.0006444742126073415425530176451 absolute error = 1.74551282e-23 relative error = 8.7247526609493204393992702238076e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 2.0006480699870233787690112062878 y[1] (numeric) = 2.0006480699870233787690287100585 absolute error = 1.75037707e-23 relative error = 8.7490503515261097932844349207395e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0361 y[1] (analytic) = 2.0006516757679201242044545570869 y[1] (numeric) = 2.0006516757679201242044721095002 absolute error = 1.75524133e-23 relative error = 8.7733479608651863619405451826828e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0362 y[1] (analytic) = 2.0006552915553336356578631174428 y[1] (numeric) = 2.0006552915553336356578807184989 absolute error = 1.76010561e-23 relative error = 8.7976455385858730212549783296413e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0363 y[1] (analytic) = 2.0006589173493000710034021334514 y[1] (numeric) = 2.0006589173493000710034197831505 absolute error = 1.76496991e-23 relative error = 8.8219430843236007001276339303149e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0364 y[1] (analytic) = 2.0006625531498556881807661735177 y[1] (numeric) = 2.00066255314985568818078387186 absolute error = 1.76983423e-23 relative error = 8.8462405977138017274705125908200e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0365 y[1] (analytic) = 2.0006661989570368451955417077535 y[1] (numeric) = 2.0006661989570368451955594547391 absolute error = 1.77469856e-23 relative error = 8.8705380284085592723673296689599e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0366 y[1] (analytic) = 2.000669854770880000119570688033 y[1] (numeric) = 2.0006698547708800001195884836621 absolute error = 1.77956291e-23 relative error = 8.8948354260268417408367001100390e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0367 y[1] (analytic) = 2.0006735205914217110913151287118 y[1] (numeric) = 2.0006735205914217110913329729846 absolute error = 1.78442728e-23 relative error = 8.9191327902040864837191644211254e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0368 y[1] (analytic) = 2.0006771964186986363162226880119 y[1] (numeric) = 2.0006771964186986363162405809286 absolute error = 1.78929167e-23 relative error = 8.9434301205757323004572846834819e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0369 y[1] (analytic) = 2.0006808822527475340670932500764 y[1] (numeric) = 2.0006808822527475340671111916372 absolute error = 1.79415608e-23 relative error = 8.9677274167772194512446456106688e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 2.0006845780936052626844465076978 y[1] (numeric) = 2.0006845780936052626844644979028 absolute error = 1.79902050e-23 relative error = 8.9920246284610982654297675032980e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0371 y[1] (analytic) = 2.0006882839413087805768905457233 y[1] (numeric) = 2.0006882839413087805769085845727 absolute error = 1.80388494e-23 relative error = 9.0163218052458885301599800797224e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0372 y[1] (analytic) = 2.0006919997958951462214914251416 y[1] (numeric) = 2.0006919997958951462215095126357 absolute error = 1.80874941e-23 relative error = 9.0406189967497416985717006506611e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0373 y[1] (analytic) = 2.0006957256574015181641437678537 y[1] (numeric) = 2.0006957256574015181641619039926 absolute error = 1.81361389e-23 relative error = 9.0649161026425996847132572702617e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0374 y[1] (analytic) = 2.000699461525865155019942342132 y[1] (numeric) = 2.0006994615258651550199605269158 absolute error = 1.81847838e-23 relative error = 9.0892131225601902295387239924454e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0375 y[1] (analytic) = 2.0007032074013234154735546487716 y[1] (numeric) = 2.0007032074013234154735728822006 absolute error = 1.82334290e-23 relative error = 9.1135101561030960936525240860337e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.2MB, time=4.01 NO POLE x[1] = 0.0376 y[1] (analytic) = 2.0007069632838137582795945079375 y[1] (numeric) = 2.0007069632838137582796127900118 absolute error = 1.82820743e-23 relative error = 9.1378071029418237815570132829131e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0377 y[1] (analytic) = 2.0007107291733737422629966467109 y[1] (numeric) = 2.0007107291733737422630149774307 absolute error = 1.83307198e-23 relative error = 9.1621040126943467499725508642267e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0378 y[1] (analytic) = 2.0007145050700410263193922873388 y[1] (numeric) = 2.0007145050700410263194106667043 absolute error = 1.83793655e-23 relative error = 9.1864008849961204503955441291533e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0379 y[1] (analytic) = 2.0007182909738533694154857361907 y[1] (numeric) = 2.0007182909738533694155041642021 absolute error = 1.84280114e-23 relative error = 9.2106977194826019165418524083571e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 2.000722086884848630589431973426 y[1] (numeric) = 2.0007220868848486305894504500835 absolute error = 1.84766575e-23 relative error = 9.2349945157892497764944290841008e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0381 y[1] (analytic) = 2.0007258928030647689512152433759 y[1] (numeric) = 2.0007258928030647689512337686796 absolute error = 1.85253037e-23 relative error = 9.2592912235696650008126210072402e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0382 y[1] (analytic) = 2.0007297087285398436830286456432 y[1] (numeric) = 2.0007297087285398436830472195933 absolute error = 1.85739501e-23 relative error = 9.2835878924413593642820615812816e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0383 y[1] (analytic) = 2.0007335346613120140396547269251 y[1] (numeric) = 2.0007335346613120140396733495218 absolute error = 1.86225967e-23 relative error = 9.3078845220397970998777355289516e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0384 y[1] (analytic) = 2.0007373706014195393488470735609 y[1] (numeric) = 2.0007373706014195393488657448045 absolute error = 1.86712436e-23 relative error = 9.3321811619820166124256414295731e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0385 y[1] (analytic) = 2.0007412165489007790117129048103 y[1] (numeric) = 2.0007412165489007790117316247008 absolute error = 1.87198905e-23 relative error = 9.3564776619587678462386122659380e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0386 y[1] (analytic) = 2.0007450725037941925030966668641 y[1] (numeric) = 2.0007450725037941925031154354018 absolute error = 1.87685377e-23 relative error = 9.3807741715502375862855267597518e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0387 y[1] (analytic) = 2.0007489384661383393719646275936 y[1] (numeric) = 2.0007489384661383393719834447787 absolute error = 1.88171851e-23 relative error = 9.4050706404103241813157026948367e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0388 y[1] (analytic) = 2.0007528144359718792417904720405 y[1] (numeric) = 2.0007528144359718792418093378731 absolute error = 1.88658326e-23 relative error = 9.4293670181933134799617994362261e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0389 y[1] (analytic) = 2.0007567004133335718109418986516 y[1] (numeric) = 2.0007567004133335718109608131319 absolute error = 1.89144803e-23 relative error = 9.4536633545160606279512476323943e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 2.0007605963982622768530682162631 y[1] (numeric) = 2.0007605963982622768530871793913 absolute error = 1.89631282e-23 relative error = 9.4779596490140423628485735136966e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0391 y[1] (analytic) = 2.0007645023907969542174889418374 y[1] (numeric) = 2.0007645023907969542175079536137 absolute error = 1.90117763e-23 relative error = 9.5022559013227371501855615037886e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0392 y[1] (analytic) = 2.0007684183909766638295833989564 y[1] (numeric) = 2.000768418390976663829602459381 absolute error = 1.90604246e-23 relative error = 9.5265521110776251956073185509537e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0393 y[1] (analytic) = 2.000772344398840565691181317076 y[1] (numeric) = 2.0007723443988405656912004261491 absolute error = 1.91090731e-23 relative error = 9.5508482779141884570182064463625e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0394 y[1] (analytic) = 2.0007762804144279198809544315443 y[1] (numeric) = 2.0007762804144279198809735892661 absolute error = 1.91577218e-23 relative error = 9.5751444014679106567276414073165e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0395 y[1] (analytic) = 2.000780226437778086554809084389 y[1] (numeric) = 2.0007802264377780865548282907597 absolute error = 1.92063707e-23 relative error = 9.5994404813742772935957602035289e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0396 y[1] (analytic) = 2.0007841824689305259462798258766 y[1] (numeric) = 2.0007841824689305259462990808963 absolute error = 1.92550197e-23 relative error = 9.6237364672883725331381445683041e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0397 y[1] (analytic) = 2.000788148507924798366924016848 y[1] (numeric) = 2.000788148507924798366943320517 absolute error = 1.93036690e-23 relative error = 9.6480324588065907809061672990650e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0398 y[1] (analytic) = 2.0007921245548005642067174318346 y[1] (numeric) = 2.0007921245548005642067367841531 absolute error = 1.93523185e-23 relative error = 9.6723284055839209927784486800648e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.2MB, time=4.24 NO POLE x[1] = 0.0399 y[1] (analytic) = 2.0007961106095975839344508629584 y[1] (numeric) = 2.0007961106095975839344702639266 absolute error = 1.94009682e-23 relative error = 9.6966243072558558952699892703952e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 2.00080010667235571809812772462 y[1] (numeric) = 2.0008001066723557180981471742381 absolute error = 1.94496181e-23 relative error = 9.7209201634578900521728087085345e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0401 y[1] (analytic) = 2.0008041127431149273253626589792 y[1] (numeric) = 2.0008041127431149273253821572473 absolute error = 1.94982681e-23 relative error = 9.7452159238456146160606746943786e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0402 y[1] (analytic) = 2.0008081288219152723237811422314 y[1] (numeric) = 2.0008081288219152723238006891497 absolute error = 1.95469183e-23 relative error = 9.7695116380346337645197804828233e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0403 y[1] (analytic) = 2.0008121549087969138814200916839 y[1] (numeric) = 2.0008121549087969138814396872527 absolute error = 1.95955688e-23 relative error = 9.7938073556401527637087101841697e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0404 y[1] (analytic) = 2.0008161910038001128671294736374 y[1] (numeric) = 2.0008161910038001128671491178568 absolute error = 1.96442194e-23 relative error = 9.8181029763381648387254654906721e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0405 y[1] (analytic) = 2.0008202371069652302309749120738 y[1] (numeric) = 2.0008202371069652302309946049441 absolute error = 1.96928703e-23 relative error = 9.8423985997234820889886634282298e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0406 y[1] (analytic) = 2.0008242932183327270046412981582 y[1] (numeric) = 2.0008242932183327270046610396794 absolute error = 1.97415212e-23 relative error = 9.8666940754931036695369894417291e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0407 y[1] (analytic) = 2.0008283593379431643018374005551 y[1] (numeric) = 2.0008283593379431643018571907275 absolute error = 1.97901724e-23 relative error = 9.8909895532210455301268862645599e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0408 y[1] (analytic) = 2.0008324354658372033187014765666 y[1] (numeric) = 2.0008324354658372033187213153905 absolute error = 1.98388239e-23 relative error = 9.9152850325425134115904191613651e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0409 y[1] (analytic) = 2.0008365216020556053342078840939 y[1] (numeric) = 2.0008365216020556053342277715694 absolute error = 1.98874755e-23 relative error = 9.9395804131345220970215683172433e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.041 y[1] (analytic) = 2.0008406177466392317105746944272 y[1] (numeric) = 2.0008406177466392317105946305545 absolute error = 1.99361273e-23 relative error = 9.9638757446118855299024307201754e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0411 y[1] (analytic) = 2.0008447238996290438936723058683 y[1] (numeric) = 2.0008447238996290438936922906476 absolute error = 1.99847793e-23 relative error = 9.9881710266101200343292498198740e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0412 y[1] (analytic) = 2.0008488400610661034134330581898 y[1] (numeric) = 2.0008488400610661034134530916214 absolute error = 2.00334316e-23 relative error = 1.0012466308743531918666456139298e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0413 y[1] (analytic) = 2.0008529662309915718842618479347 y[1] (numeric) = 2.0008529662309915718842819300187 absolute error = 2.00820840e-23 relative error = 1.0036761490689962416077953048621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0414 y[1] (analytic) = 2.0008571024094467110054477445606 y[1] (numeric) = 2.0008571024094467110054678752972 absolute error = 2.01307366e-23 relative error = 1.0061056622063824654308764772911e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0415 y[1] (analytic) = 2.0008612485964728825615766074333 y[1] (numeric) = 2.0008612485964728825615967868226 absolute error = 2.01793893e-23 relative error = 1.0085351652522164909344550493213e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0416 y[1] (analytic) = 2.0008654047921115484229447036724 y[1] (numeric) = 2.0008654047921115484229649317148 absolute error = 2.02280424e-23 relative error = 1.0109646731635943700586314161561e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0417 y[1] (analytic) = 2.0008695709964042705459733268555 y[1] (numeric) = 2.0008695709964042705459936035511 absolute error = 2.02766956e-23 relative error = 1.0133941709105255273377746405073e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0418 y[1] (analytic) = 2.0008737472093927109736244165818 y[1] (numeric) = 2.0008737472093927109736447419309 absolute error = 2.03253491e-23 relative error = 1.0158236684522273999288051394708e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0419 y[1] (analytic) = 2.0008779334311186318358171789029 y[1] (numeric) = 2.0008779334311186318358375529056 absolute error = 2.03740027e-23 relative error = 1.0182531557566096125403704047881e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 2.0008821296616238953498457076217 y[1] (numeric) = 2.0008821296616238953498661302782 absolute error = 2.04226565e-23 relative error = 1.0206826377850526432847648556797e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=72.4MB, alloc=4.3MB, time=4.48 x[1] = 0.0421 y[1] (analytic) = 2.000886335900950463820797606466 y[1] (numeric) = 2.0008863359009504638208180777766 absolute error = 2.04713106e-23 relative error = 1.0231121194988953040137539692025e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0422 y[1] (analytic) = 2.0008905521491403996419736121398 y[1] (numeric) = 2.0008905521491403996419941321046 absolute error = 2.05199648e-23 relative error = 1.0255415908661106603539816509907e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0423 y[1] (analytic) = 2.0008947784062358652953082182564 y[1] (numeric) = 2.0008947784062358652953287868757 absolute error = 2.05686193e-23 relative error = 1.0279710618458125068846221742426e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0424 y[1] (analytic) = 2.0008990146722791233517913001583 y[1] (numeric) = 2.0008990146722791233518119174323 absolute error = 2.06172740e-23 relative error = 1.0304005274037699319570808394786e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0425 y[1] (analytic) = 2.0009032609473125364718907406274 y[1] (numeric) = 2.0009032609473125364719114065563 absolute error = 2.06659289e-23 relative error = 1.0328299875035373798100527798711e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0426 y[1] (analytic) = 2.00090751723137856740597605649 y[1] (numeric) = 2.0009075172313785674059967710739 absolute error = 2.07145839e-23 relative error = 1.0352594371109372740428133289794e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0427 y[1] (analytic) = 2.0009117835245197789947430261208 y[1] (numeric) = 2.00091178352451977899476378936 absolute error = 2.07632392e-23 relative error = 1.0376888861849996186228380815599e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0428 y[1] (analytic) = 2.0009160598267788341696393178504 y[1] (numeric) = 2.000916059826778834169660129745 absolute error = 2.08118946e-23 relative error = 1.0401183246938257413981604629837e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0429 y[1] (analytic) = 2.0009203461381984959532911192798 y[1] (numeric) = 2.0009203461381984959533119798301 absolute error = 2.08605503e-23 relative error = 1.0425477625964034588559819792372e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 2.0009246424588216274599307675074 y[1] (numeric) = 2.0009246424588216274599516767136 absolute error = 2.09092062e-23 relative error = 1.0449771948585667239718462208634e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0431 y[1] (analytic) = 2.0009289487886911918958253802715 y[1] (numeric) = 2.0009289487886911918958463381338 absolute error = 2.09578623e-23 relative error = 1.0474066214438712909929141456462e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0432 y[1] (analytic) = 2.0009332651278502525597064880134 y[1] (numeric) = 2.000933265127850252559727494532 absolute error = 2.10065186e-23 relative error = 1.0498360423158731367503318066092e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0433 y[1] (analytic) = 2.0009375914763419728432006668647 y[1] (numeric) = 2.0009375914763419728432217220399 absolute error = 2.10551752e-23 relative error = 1.0522654624357855815147085379974e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0434 y[1] (analytic) = 2.0009419278342096162312611725647 y[1] (numeric) = 2.0009419278342096162312822763966 absolute error = 2.11038319e-23 relative error = 1.0546948717718399809302082544402e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0435 y[1] (analytic) = 2.0009462742014965463026005753094 y[1] (numeric) = 2.0009462742014965463026217277982 absolute error = 2.11524888e-23 relative error = 1.0571242752852609122664431656772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0436 y[1] (analytic) = 2.0009506305782462267301243955396 y[1] (numeric) = 2.0009506305782462267301455966856 absolute error = 2.12011460e-23 relative error = 1.0595536779372298074714474141170e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0437 y[1] (analytic) = 2.0009549969645022212813657406702 y[1] (numeric) = 2.0009549969645022212813869904736 absolute error = 2.12498034e-23 relative error = 1.0619830746936574107210719487646e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0438 y[1] (analytic) = 2.0009593733603081938189209427658 y[1] (numeric) = 2.0009593733603081938189422412267 absolute error = 2.12984609e-23 relative error = 1.0644124605204982684431073522733e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0439 y[1] (analytic) = 2.0009637597657079083008861971669 y[1] (numeric) = 2.0009637597657079083009075442856 absolute error = 2.13471187e-23 relative error = 1.0668418453765262632569661731792e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 2.0009681561807452287812952020716 y[1] (numeric) = 2.0009681561807452287813165978483 absolute error = 2.13957767e-23 relative error = 1.0692712242276854744447574246188e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0441 y[1] (analytic) = 2.0009725626054641194105577990759 y[1] (numeric) = 2.0009725626054641194105792435108 absolute error = 2.14444349e-23 relative error = 1.0717005970375338618675674334427e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0442 y[1] (analytic) = 2.0009769790399086444358996146784 y[1] (numeric) = 2.0009769790399086444359211077718 absolute error = 2.14930934e-23 relative error = 1.0741299687671883650384197254468e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0443 y[1] (analytic) = 2.000981405484122968201802702753 y[1] (numeric) = 2.0009814054841229682018242445051 absolute error = 2.15417521e-23 relative error = 1.0765593343826265589876012862173e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=4.72 NO POLE x[1] = 0.0444 y[1] (analytic) = 2.0009858419381513551504471879938 y[1] (numeric) = 2.0009858419381513551504687784048 absolute error = 2.15904110e-23 relative error = 1.0789886938474070365373685373166e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0445 y[1] (analytic) = 2.0009902884020381698221539103376 y[1] (numeric) = 2.0009902884020381698221755494076 absolute error = 2.16390700e-23 relative error = 1.0814180421275631246493973912227e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0446 y[1] (analytic) = 2.0009947448758278768558280703671 y[1] (numeric) = 2.0009947448758278768558497580964 absolute error = 2.16877293e-23 relative error = 1.0838473891817160326820155052867e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0447 y[1] (analytic) = 2.0009992113595650409894038757006 y[1] (numeric) = 2.0009992113595650409894256120894 absolute error = 2.17363888e-23 relative error = 1.0862767299758884627867972003518e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0448 y[1] (analytic) = 2.0010036878532943270602901883717 y[1] (numeric) = 2.0010036878532943270603119734203 absolute error = 2.17850486e-23 relative error = 1.0887060694711320075064793589842e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0449 y[1] (analytic) = 2.0010081743570605000058171732038 y[1] (numeric) = 2.0010081743570605000058390069123 absolute error = 2.18337085e-23 relative error = 1.0911353976360111807049718259747e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 2.0010126708709084248636839471835 y[1] (numeric) = 2.0010126708709084248637058295521 absolute error = 2.18823686e-23 relative error = 1.0935647194315892426175083356755e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0451 y[1] (analytic) = 2.0010171773948830667724072298382 y[1] (numeric) = 2.0010171773948830667724291608671 absolute error = 2.19310289e-23 relative error = 1.0959940348214264801213401241485e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0452 y[1] (analytic) = 2.0010216939290294909717709946215 y[1] (numeric) = 2.0010216939290294909717929743111 absolute error = 2.19796896e-23 relative error = 1.0984233537639775656250950932760e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0453 y[1] (analytic) = 2.0010262204733928628032771213118 y[1] (numeric) = 2.0010262204733928628032991496622 absolute error = 2.20283504e-23 relative error = 1.1008526612304281585953038715383e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0454 y[1] (analytic) = 2.0010307570280184477105970494271 y[1] (numeric) = 2.0010307570280184477106191264385 absolute error = 2.20770114e-23 relative error = 1.1032819621817975644602070419665e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0455 y[1] (analytic) = 2.0010353035929516112400244326624 y[1] (numeric) = 2.0010353035929516112400465583351 absolute error = 2.21256727e-23 relative error = 1.1057112615790600701263371010621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0456 y[1] (analytic) = 2.0010398601682378190409287943533 y[1] (numeric) = 2.0010398601682378190409509686875 absolute error = 2.21743342e-23 relative error = 1.1081405543883412946801068343987e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0457 y[1] (analytic) = 2.0010444267539226368662101839694 y[1] (numeric) = 2.0010444267539226368662324069653 absolute error = 2.22229959e-23 relative error = 1.1105698405732028746926802272980e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0458 y[1] (analytic) = 2.0010490033500517305727548346444 y[1] (numeric) = 2.0010490033500517305727771063022 absolute error = 2.22716578e-23 relative error = 1.1129991200972067008815872557611e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0459 y[1] (analytic) = 2.0010535899566708661218918217447 y[1] (numeric) = 2.0010535899566708661219141420646 absolute error = 2.23203199e-23 relative error = 1.1154283929239149193242962386153e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 2.0010581865738259095798507224835 y[1] (numeric) = 2.0010581865738259095798730914658 absolute error = 2.23689823e-23 relative error = 1.1178576640142458651955551897891e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0461 y[1] (analytic) = 2.0010627932015628271182202765834 y[1] (numeric) = 2.0010627932015628271182426942283 absolute error = 2.24176449e-23 relative error = 1.1202869283343832576778787165029e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0462 y[1] (analytic) = 2.0010674098399276850144080479927 y[1] (numeric) = 2.0010674098399276850144305143003 absolute error = 2.24663076e-23 relative error = 1.1227161808505570425238853828620e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0463 y[1] (analytic) = 2.0010720364889666496521010876594 y[1] (numeric) = 2.0010720364889666496521236026301 absolute error = 2.25149707e-23 relative error = 1.1251454365183290210819186464077e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0464 y[1] (analytic) = 2.0010766731487259875217275973694 y[1] (numeric) = 2.0010766731487259875217501610033 absolute error = 2.25636339e-23 relative error = 1.1275746803092638630576392901218e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0465 y[1] (analytic) = 2.0010813198192520652209195946501 y[1] (numeric) = 2.0010813198192520652209422069475 absolute error = 2.26122974e-23 relative error = 1.1300039221815562574071587356436e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0466 y[1] (analytic) = 2.0010859765005913494549765787478 y[1] (numeric) = 2.001085976500591349454999239709 absolute error = 2.26609612e-23 relative error = 1.1324331620987352095747373847434e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=4.96 NO POLE x[1] = 0.0467 y[1] (analytic) = 2.0010906431927904070373301976811 y[1] (numeric) = 2.0010906431927904070373529073062 absolute error = 2.27096251e-23 relative error = 1.1348623900297800842271997561285e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0468 y[1] (analytic) = 2.001095319895895904890009916375 y[1] (numeric) = 2.0010953198958959048900326746643 absolute error = 2.27582893e-23 relative error = 1.1372916159328165909422367006203e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0469 y[1] (analytic) = 2.0011000066099546100441096858824 y[1] (numeric) = 2.001100006609954610044132492836 absolute error = 2.28069536e-23 relative error = 1.1397208297768712443421477783664e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 2.0011047033350133896402556136946 y[1] (numeric) = 2.0011047033350133896402784693129 absolute error = 2.28556183e-23 relative error = 1.1421500465172633405371972594464e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0471 y[1] (analytic) = 2.0011094100711192109290746351487 y[1] (numeric) = 2.0011094100711192109290975394318 absolute error = 2.29042831e-23 relative error = 1.1445792511258034745906980149243e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0472 y[1] (analytic) = 2.0011141268183191412716641859337 y[1] (numeric) = 2.0011141268183191412716871388819 absolute error = 2.29529482e-23 relative error = 1.1470084535605247270394871502017e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0473 y[1] (analytic) = 2.0011188535766603481400628757022 y[1] (numeric) = 2.0011188535766603481400858773157 absolute error = 2.30016135e-23 relative error = 1.1494376487877528808054056662706e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0474 y[1] (analytic) = 2.0011235903461900991177221627911 y[1] (numeric) = 2.0011235903461900991177452130701 absolute error = 2.30502790e-23 relative error = 1.1518668367710537586575608774289e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0475 y[1] (analytic) = 2.0011283371269557618999790300563 y[1] (numeric) = 2.0011283371269557619000021290011 absolute error = 2.30989448e-23 relative error = 1.1542960224711742058595698969556e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0476 y[1] (analytic) = 2.0011330939190048042945296618269 y[1] (numeric) = 2.0011330939190048042945528094377 absolute error = 2.31476108e-23 relative error = 1.1567252008544760911443193474293e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0477 y[1] (analytic) = 2.001137860722384794221904121982 y[1] (numeric) = 2.0011378607223847942219273182591 absolute error = 2.31962771e-23 relative error = 1.1591543768816829561082343228142e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0478 y[1] (analytic) = 2.0011426375371433997159420331571 y[1] (numeric) = 2.0011426375371433997159652781006 absolute error = 2.32449435e-23 relative error = 1.1615835405220357952874465573822e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0479 y[1] (analytic) = 2.001147424363328388924269257082 y[1] (numeric) = 2.0011474243633283889242925506922 absolute error = 2.32936102e-23 relative error = 1.1640127017334036956948437570109e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 2.0011522212009876301087755760583 y[1] (numeric) = 2.0011522212009876301087989183354 absolute error = 2.33422771e-23 relative error = 1.1664418554821970316304840093676e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0481 y[1] (analytic) = 2.0011570280501690916460933755782 y[1] (numeric) = 2.0011570280501690916461167665225 absolute error = 2.33909443e-23 relative error = 1.1688710067290925274360562225158e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0482 y[1] (analytic) = 2.0011618449109208420280773280915 y[1] (numeric) = 2.0011618449109208420281007677032 absolute error = 2.34396117e-23 relative error = 1.1713001504405249297233269561964e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0483 y[1] (analytic) = 2.0011666717832910498622850779242 y[1] (numeric) = 2.0011666717832910498623085662036 absolute error = 2.34882794e-23 relative error = 1.1737292915771473744209785087974e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0484 y[1] (analytic) = 2.0011715086673279838724589273549 y[1] (numeric) = 2.0011715086673279838724824643022 absolute error = 2.35369473e-23 relative error = 1.1761584251054190850791356567813e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0485 y[1] (analytic) = 2.0011763555630800128990085238523 y[1] (numeric) = 2.0011763555630800128990321094677 absolute error = 2.35856154e-23 relative error = 1.1785875509889086744614041960695e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0486 y[1] (analytic) = 2.0011812124705956058994945484798 y[1] (numeric) = 2.0011812124705956058995181827636 absolute error = 2.36342838e-23 relative error = 1.1810166741882337553311899631868e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0487 y[1] (analytic) = 2.0011860793899233319491134054716 y[1] (numeric) = 2.001186079389923331949137088424 absolute error = 2.36829524e-23 relative error = 1.1834457896698905002280733145762e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0488 y[1] (analytic) = 2.001190956321111860241182912985 y[1] (numeric) = 2.0011909563211118602412066446062 absolute error = 2.37316212e-23 relative error = 1.1858748973974483151139043275238e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=83.9MB, alloc=4.3MB, time=5.20 x[1] = 0.0489 y[1] (analytic) = 2.0011958432642099600876289950339 y[1] (numeric) = 2.0011958432642099600876527753241 absolute error = 2.37802902e-23 relative error = 1.1883039973344768977177451927936e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 2.0012007402192665009194733746086 y[1] (numeric) = 2.0012007402192665009194972035681 absolute error = 2.38289595e-23 relative error = 1.1907330944415461893406981929612e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0491 y[1] (analytic) = 2.0012056471863304522873222679864 y[1] (numeric) = 2.0012056471863304522873461456154 absolute error = 2.38776290e-23 relative error = 1.1931621836852020189516321194977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0492 y[1] (analytic) = 2.0012105641654508838618560802379 y[1] (numeric) = 2.0012105641654508838618800065367 absolute error = 2.39262988e-23 relative error = 1.1955912700259903123501005386063e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0493 y[1] (analytic) = 2.0012154911566769654343201019346 y[1] (numeric) = 2.0012154911566769654343440769034 absolute error = 2.39749688e-23 relative error = 1.1980203484304818462347917488683e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0494 y[1] (analytic) = 2.0012204281600579669170162070612 y[1] (numeric) = 2.0012204281600579669170402307003 absolute error = 2.40236391e-23 relative error = 1.2004494238591984360007708508696e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0495 y[1] (analytic) = 2.0012253751756432583437955521397 y[1] (numeric) = 2.0012253751756432583438196244493 absolute error = 2.40723096e-23 relative error = 1.2028784912787359106917850087017e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0496 y[1] (analytic) = 2.0012303322034823098705522765677 y[1] (numeric) = 2.001230332203482309870576397548 absolute error = 2.41209803e-23 relative error = 1.2053075506526658199226104223229e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0497 y[1] (analytic) = 2.001235299243624691775718204178 y[1] (numeric) = 2.0012352992436246917757423738293 absolute error = 2.41696513e-23 relative error = 1.2077366069414736729504548627723e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0498 y[1] (analytic) = 2.0012402762961200744607585460237 y[1] (numeric) = 2.0012402762961200744607827643461 absolute error = 2.42183224e-23 relative error = 1.2101656501148918799684031257259e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0499 y[1] (analytic) = 2.0012452633610182284506686043925 y[1] (numeric) = 2.0012452633610182284506928713863 absolute error = 2.42669938e-23 relative error = 1.2125946901303077378679441025043e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 2.0012502604383690243944714780576 y[1] (numeric) = 2.0012502604383690243944957937232 absolute error = 2.43156656e-23 relative error = 1.2150237319481328796977980972194e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0501 y[1] (analytic) = 2.0012552675282224330657167687685 y[1] (numeric) = 2.001255267528222433065741133106 absolute error = 2.43643375e-23 relative error = 1.2174527605412738887169234108662e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0502 y[1] (analytic) = 2.0012602846306285253629802889864 y[1] (numeric) = 2.001260284630628525363004701996 absolute error = 2.44130096e-23 relative error = 1.2198817808701927706934217434370e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0503 y[1] (analytic) = 2.0012653117456374723103647708706 y[1] (numeric) = 2.0012653117456374723103892325526 absolute error = 2.44616820e-23 relative error = 1.2223107978953017820432715469372e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0504 y[1] (analytic) = 2.00127034887329954505800157652 y[1] (numeric) = 2.0012703488732995450580260868747 absolute error = 2.45103547e-23 relative error = 1.2247398115801370379034086172664e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0505 y[1] (analytic) = 2.0012753960136651148825534094749 y[1] (numeric) = 2.0012753960136651148825779685025 absolute error = 2.45590276e-23 relative error = 1.2271688168914212730054927329620e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0506 y[1] (analytic) = 2.0012804531667846531877180274838 y[1] (numeric) = 2.0012804531667846531877426351846 absolute error = 2.46077008e-23 relative error = 1.2295978187895297222656747390403e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0507 y[1] (analytic) = 2.0012855203327087315047329565412 y[1] (numeric) = 2.0012855203327087315047576129154 absolute error = 2.46563742e-23 relative error = 1.2320268122412108004056347508141e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0508 y[1] (analytic) = 2.0012905975114880214928812061998 y[1] (numeric) = 2.0012905975114880214929059112477 absolute error = 2.47050479e-23 relative error = 1.2344558022068149676660019377902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0509 y[1] (analytic) = 2.0012956847031732949399979861643 y[1] (numeric) = 2.0012956847031732949400227398861 absolute error = 2.47537218e-23 relative error = 1.2368847836531164233588041683250e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 2.00130078190781542376297842417 y[1] (numeric) = 2.0013007819078154237630032265659 absolute error = 2.48023959e-23 relative error = 1.2393137565436905992633002643238e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0511 y[1] (analytic) = 2.0013058891254653800082862851519 y[1] (numeric) = 2.0013058891254653800083111362222 absolute error = 2.48510703e-23 relative error = 1.2417427258388506530947920224376e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=5.44 NO POLE x[1] = 0.0512 y[1] (analytic) = 2.0013110063561742358524636917104 y[1] (numeric) = 2.0013110063561742358524885914553 absolute error = 2.48997449e-23 relative error = 1.2441716865054096945738101285761e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0513 y[1] (analytic) = 2.0013161335999931636026418458763 y[1] (numeric) = 2.0013161335999931636026667942961 absolute error = 2.49484198e-23 relative error = 1.2466006435036558695223151933239e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0514 y[1] (analytic) = 2.0013212708569734356970527521834 y[1] (numeric) = 2.0013212708569734356970777492783 absolute error = 2.49970949e-23 relative error = 1.2490295918004283337414884826759e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0515 y[1] (analytic) = 2.0013264181271664247055419420505 y[1] (numeric) = 2.0013264181271664247055669878208 absolute error = 2.50457703e-23 relative error = 1.2514585363559901262765313971515e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0516 y[1] (analytic) = 2.0013315754106236033300821994809 y[1] (numeric) = 2.0013315754106236033301072939269 absolute error = 2.50944460e-23 relative error = 1.2538874771338798299671158760866e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0517 y[1] (analytic) = 2.0013367427073965444052882880822 y[1] (numeric) = 2.001336742707396544405313431204 absolute error = 2.51431218e-23 relative error = 1.2563164041043154531047576741480e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0518 y[1] (analytic) = 2.0013419200175369208989326794128 y[1] (numeric) = 2.0013419200175369208989578712107 absolute error = 2.51917979e-23 relative error = 1.2587453272242083865232623147984e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0519 y[1] (analytic) = 2.0013471073410965059124622826604 y[1] (numeric) = 2.0013471073410965059124875231347 absolute error = 2.52404743e-23 relative error = 1.2611742464570978947065284582431e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 2.0013523046781271726815161756566 y[1] (numeric) = 2.0013523046781271726815414648075 absolute error = 2.52891509e-23 relative error = 1.2636031567699018992451155063592e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0521 y[1] (analytic) = 2.0013575120286808945764443372338 y[1] (numeric) = 2.0013575120286808945764696750617 absolute error = 2.53378279e-23 relative error = 1.2660320681194160714869164424871e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0522 y[1] (analytic) = 2.0013627293928097451028273809294 y[1] (numeric) = 2.0013627293928097451028527674345 absolute error = 2.53865051e-23 relative error = 1.2684609704759502241707115074419e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0523 y[1] (analytic) = 2.0013679567705658979019972900416 y[1] (numeric) = 2.0013679567705658979020227252241 absolute error = 2.54351825e-23 relative error = 1.2708898638030835000358274539783e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0524 y[1] (analytic) = 2.0013731941620016267515591540434 y[1] (numeric) = 2.0013731941620016267515846379036 absolute error = 2.54838602e-23 relative error = 1.2733187530609647461036479082194e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0525 y[1] (analytic) = 2.0013784415671693055659139063591 y[1] (numeric) = 2.0013784415671693055659394388972 absolute error = 2.55325381e-23 relative error = 1.2757476332165782037577145556224e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0526 y[1] (analytic) = 2.0013836989861214083967820635086 y[1] (numeric) = 2.0013836989861214083968076447248 absolute error = 2.55812162e-23 relative error = 1.2781765042335039472603826594555e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0527 y[1] (analytic) = 2.0013889664189105094337284656251 y[1] (numeric) = 2.0013889664189105094337540955198 absolute error = 2.56298947e-23 relative error = 1.2806053760683823763659255204850e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0528 y[1] (analytic) = 2.0013942438655892830046880183516 y[1] (numeric) = 2.0013942438655892830047136969249 absolute error = 2.56785733e-23 relative error = 1.2830342336951647350098493455208e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0529 y[1] (analytic) = 2.0013995313262105035764924361198 y[1] (numeric) = 2.0013995313262105035765181633721 absolute error = 2.57272523e-23 relative error = 1.2854630920669824207167932055232e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 2.0014048288008270457553979868197 y[1] (numeric) = 2.0014048288008270457554237627512 absolute error = 2.57759315e-23 relative error = 1.2878919411543566544814848882368e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0531 y[1] (analytic) = 2.0014101362894918842876142378621 y[1] (numeric) = 2.0014101362894918842876400624731 absolute error = 2.58246110e-23 relative error = 1.2903207859173461307729242812645e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0532 y[1] (analytic) = 2.0014154537922580940598338036415 y[1] (numeric) = 2.0014154537922580940598596769322 absolute error = 2.58732907e-23 relative error = 1.2927496213230290517368385274302e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0533 y[1] (analytic) = 2.0014207813091788500997630944031 y[1] (numeric) = 2.0014207813091788500997890163737 absolute error = 2.59219706e-23 relative error = 1.2951784473349875829929098575776e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0534 y[1] (analytic) = 2.0014261188403074275766540665205 y[1] (numeric) = 2.0014261188403074275766800371714 absolute error = 2.59706509e-23 relative error = 1.2976072739096787232273957616264e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=5.69 NO POLE x[1] = 0.0535 y[1] (analytic) = 2.0014314663856972018018369741888 y[1] (numeric) = 2.0014314663856972018018629935202 absolute error = 2.60193314e-23 relative error = 1.3000360910177574461363308585908e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0536 y[1] (analytic) = 2.001436823945401648229254122538 y[1] (numeric) = 2.0014368239454016482292801905501 absolute error = 2.60680121e-23 relative error = 1.3024648986228068104657081466767e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0537 y[1] (analytic) = 2.0014421915194743424559946221732 y[1] (numeric) = 2.0014421915194743424560207388663 absolute error = 2.61166931e-23 relative error = 1.3048937016848073441769050340815e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0538 y[1] (analytic) = 2.0014475691079689602228301451457 y[1] (numeric) = 2.0014475691079689602228563105201 absolute error = 2.61653744e-23 relative error = 1.3073225001673025335099475978264e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0539 y[1] (analytic) = 2.0014529567109392774147516823614 y[1] (numeric) = 2.0014529567109392774147778964173 absolute error = 2.62140559e-23 relative error = 1.3097512890374658223936113698552e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 2.001458354328439170061507302431 y[1] (numeric) = 2.0014583543284391700615335651686 absolute error = 2.62627376e-23 relative error = 1.3121800682588815272495052623810e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0541 y[1] (analytic) = 2.0014637619605226143381409119678 y[1] (numeric) = 2.0014637619605226143381672233874 absolute error = 2.63114196e-23 relative error = 1.3146088427914775907301035837476e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0542 y[1] (analytic) = 2.0014691796072436865655320173388 y[1] (numeric) = 2.0014691796072436865655583774408 absolute error = 2.63601020e-23 relative error = 1.3170376175951282144355463725249e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0543 y[1] (analytic) = 2.0014746072686565632109364878741 y[1] (numeric) = 2.0014746072686565632109628966586 absolute error = 2.64087845e-23 relative error = 1.3194663776443888192230633980877e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0544 y[1] (analytic) = 2.0014800449448155208885283205393 y[1] (numeric) = 2.0014800449448155208885547780067 absolute error = 2.64574674e-23 relative error = 1.3218951378917935175439361698622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0545 y[1] (analytic) = 2.0014854926357749363599424060786 y[1] (numeric) = 2.0014854926357749363599689122291 absolute error = 2.65061505e-23 relative error = 1.3243238883082686188118814721936e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0546 y[1] (analytic) = 2.0014909503415892865348182966307 y[1] (numeric) = 2.0014909503415892865348448514645 absolute error = 2.65548338e-23 relative error = 1.3267526288574002875708261678309e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0547 y[1] (analytic) = 2.0014964180623131484713449748261 y[1] (numeric) = 2.0014964180623131484713715783435 absolute error = 2.66035174e-23 relative error = 1.3291813644990368023174881430593e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0548 y[1] (analytic) = 2.0015018957980011993768066243695 y[1] (numeric) = 2.0015018957980011993768332765708 absolute error = 2.66522013e-23 relative error = 1.3316100951967240315456961268613e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0549 y[1] (analytic) = 2.0015073835487082166081294021129 y[1] (numeric) = 2.0015073835487082166081561029984 absolute error = 2.67008855e-23 relative error = 1.3340388209140080587403273736119e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 2.0015128813144890776724292116254 y[1] (numeric) = 2.0015128813144890776724559611954 absolute error = 2.67495700e-23 relative error = 1.3364675416144351835917749329064e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0551 y[1] (analytic) = 2.001518389095398760227560478265 y[1] (numeric) = 2.0015183890953987602275872765197 absolute error = 2.67982547e-23 relative error = 1.3388962522653450162533375669948e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0552 y[1] (analytic) = 2.0015239068914923420826659257572 y[1] (numeric) = 2.0015239068914923420826927726969 absolute error = 2.68469397e-23 relative error = 1.3413249578265187464882089215508e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0553 y[1] (analytic) = 2.0015294347028250011987273542872 y[1] (numeric) = 2.0015294347028250011987542499121 absolute error = 2.68956249e-23 relative error = 1.3437536532653240696899011224472e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0554 y[1] (analytic) = 2.00153497252945201568911742011 y[1] (numeric) = 2.0015349725294520156891443644204 absolute error = 2.69443104e-23 relative error = 1.3461823435415152190140422025865e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0555 y[1] (analytic) = 2.0015405203714287638201524166848 y[1] (numeric) = 2.001540520371428763820179409681 absolute error = 2.69929962e-23 relative error = 1.3486110286186397429345844306214e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0556 y[1] (analytic) = 2.0015460782288107240116460573384 y[1] (numeric) = 2.0015460782288107240116730990207 absolute error = 2.70416823e-23 relative error = 1.3510397084602454134152229273972e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0557 y[1] (analytic) = 2.0015516461016534748374642594639 y[1] (numeric) = 2.0015516461016534748374913498326 absolute error = 2.70903687e-23 relative error = 1.3534683830298802271237364973829e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=5.93 NO POLE x[1] = 0.0558 y[1] (analytic) = 2.00155722399001269502608093026 y[1] (numeric) = 2.0015572239900126950261080693153 absolute error = 2.71390553e-23 relative error = 1.3558970472949824377964281266263e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0559 y[1] (analytic) = 2.0015628118939441634611347540157 y[1] (numeric) = 2.0015628118939441634611619417579 absolute error = 2.71877422e-23 relative error = 1.3583257062152383599865273755966e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 2.0015684098135037591819869809478 y[1] (numeric) = 2.0015684098135037591820142173771 absolute error = 2.72364293e-23 relative error = 1.3607543547581146985823628574846e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0561 y[1] (analytic) = 2.0015740177487474613842802175944 y[1] (numeric) = 2.0015740177487474613843075027111 absolute error = 2.72851167e-23 relative error = 1.3631829978832704795911070197422e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0562 y[1] (analytic) = 2.0015796356997313494204982187722 y[1] (numeric) = 2.0015796356997313494205255525766 absolute error = 2.73338044e-23 relative error = 1.3656116355542549909433343791051e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0563 y[1] (analytic) = 2.0015852636665116028005266811016 y[1] (numeric) = 2.0015852636665116028005540635939 absolute error = 2.73824923e-23 relative error = 1.3680402627385777728852397582072e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0564 y[1] (analytic) = 2.001590901649144501192215038106 y[1] (numeric) = 2.0015909016491445011922424692865 absolute error = 2.74311805e-23 relative error = 1.3704688843958567034070466055551e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0565 y[1] (analytic) = 2.001596549647686424421939256891 y[1] (numeric) = 2.00159654964768642442196673676 absolute error = 2.74798690e-23 relative error = 1.3728975004896418448061814046186e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0566 y[1] (analytic) = 2.0016022076621938524751656364083 y[1] (numeric) = 2.0016022076621938524751931649661 absolute error = 2.75285578e-23 relative error = 1.3753261109834834950090359533997e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0567 y[1] (analytic) = 2.0016078756927233654970156073111 y[1] (numeric) = 2.0016078756927233654970431845579 absolute error = 2.75772468e-23 relative error = 1.3777547108449486490325282039838e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0568 y[1] (analytic) = 2.0016135537393316437928315334057 y[1] (numeric) = 2.0016135537393316437928591593418 absolute error = 2.76259361e-23 relative error = 1.3801833050335999640156740696733e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0569 y[1] (analytic) = 2.0016192418020754678287435147052 y[1] (numeric) = 2.001619241802075467828771189331 absolute error = 2.76746258e-23 relative error = 1.3826118985089436970884172951641e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 2.0016249398810117182322371920918 y[1] (numeric) = 2.0016249398810117182322649154075 absolute error = 2.77233157e-23 relative error = 1.3850404812426066129261224501812e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0571 y[1] (analytic) = 2.0016306479761973757927225535915 y[1] (numeric) = 2.0016306479761973757927503255973 absolute error = 2.77720058e-23 relative error = 1.3874690531981829469232344550345e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0572 y[1] (analytic) = 2.001636366087689521462103742269 y[1] (numeric) = 2.0016363660876895214621315629652 absolute error = 2.78206962e-23 relative error = 1.3898976193351797560612369776842e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0573 y[1] (analytic) = 2.0016420942155453363553498657473 y[1] (numeric) = 2.0016420942155453363553777351342 absolute error = 2.78693869e-23 relative error = 1.3923261796171491711734866770512e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0574 y[1] (analytic) = 2.0016478323598221017510668073576 y[1] (numeric) = 2.0016478323598221017510947254355 absolute error = 2.79180779e-23 relative error = 1.3947547340076435684327309560563e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0575 y[1] (analytic) = 2.0016535805205771990920700389261 y[1] (numeric) = 2.0016535805205771990920980056953 absolute error = 2.79667692e-23 relative error = 1.3971832824702155705651078035916e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0576 y[1] (analytic) = 2.0016593386978681099859584352026 y[1] (numeric) = 2.0016593386978681099859864506633 absolute error = 2.80154607e-23 relative error = 1.3996118199725629559058065744489e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0577 y[1] (analytic) = 2.0016651068917524162056890899365 y[1] (numeric) = 2.0016651068917524162057171540891 absolute error = 2.80641526e-23 relative error = 1.4020403564699634247908123745524e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0578 y[1] (analytic) = 2.0016708851022877996901531336077 y[1] (numeric) = 2.0016708851022877996901812464524 absolute error = 2.81128447e-23 relative error = 1.4044688819342746089518375482927e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0579 y[1] (analytic) = 2.0016766733295320425447525528153 y[1] (numeric) = 2.0016766733295320425447807143523 absolute error = 2.81615370e-23 relative error = 1.4068973963290934686017493381077e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=99.1MB, alloc=4.3MB, time=6.17 x[1] = 0.058 y[1] (analytic) = 2.0016824715735430270419780113322 y[1] (numeric) = 2.0016824715735430270420062215619 absolute error = 2.82102297e-23 relative error = 1.4093259096096120790347941258912e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0581 y[1] (analytic) = 2.0016882798343787356219876728309 y[1] (numeric) = 2.0016882798343787356220159317535 absolute error = 2.82589226e-23 relative error = 1.4117544117477755081150315769538e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0582 y[1] (analytic) = 2.0016940981120972508931870252851 y[1] (numeric) = 2.0016940981120972508932153329009 absolute error = 2.83076158e-23 relative error = 1.4141829077029501157006287234417e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0583 y[1] (analytic) = 2.0016999264067567556328097070544 y[1] (numeric) = 2.0016999264067567556328380633638 absolute error = 2.83563094e-23 relative error = 1.4166114024344444832403519882955e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0584 y[1] (analytic) = 2.0017057647184155327874993346574 y[1] (numeric) = 2.0017057647184155327875277396605 absolute error = 2.84050031e-23 relative error = 1.4190398809185522772482702682547e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0585 y[1] (analytic) = 2.0017116130471319654738923322379 y[1] (numeric) = 2.0017116130471319654739207859352 absolute error = 2.84536973e-23 relative error = 1.4214683631018148078196991582566e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0586 y[1] (analytic) = 2.0017174713929645369792017627327 y[1] (numeric) = 2.0017174713929645369792302651244 absolute error = 2.85023917e-23 relative error = 1.4238968339605699729322756600586e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0587 y[1] (analytic) = 2.0017233397559718307618021607434 y[1] (numeric) = 2.0017233397559718307618307118298 absolute error = 2.85510864e-23 relative error = 1.4263252984541128202661029501798e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0588 y[1] (analytic) = 2.0017292181362125304518153671212 y[1] (numeric) = 2.0017292181362125304518439669025 absolute error = 2.85997813e-23 relative error = 1.4287537515503187485115715387316e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0589 y[1] (analytic) = 2.0017351065337454198516973652681 y[1] (numeric) = 2.0017351065337454198517260137446 absolute error = 2.86484765e-23 relative error = 1.4311821982084541893091789848202e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 2.0017410049486293829368261191625 y[1] (numeric) = 2.0017410049486293829368548163345 absolute error = 2.86971720e-23 relative error = 1.4336106383920758335679552965536e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0591 y[1] (analytic) = 2.001746913380923403856090413113 y[1] (numeric) = 2.0017469133809234038561191589808 absolute error = 2.87458678e-23 relative error = 1.4360390720647406381681566141855e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0592 y[1] (analytic) = 2.001752831830686566932479693248 y[1] (numeric) = 2.0017528318306865669325084878119 absolute error = 2.87945639e-23 relative error = 1.4384674991900058271749258465328e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0593 y[1] (analytic) = 2.0017587602979780566636749107462 y[1] (numeric) = 2.0017587602979780566637037540065 absolute error = 2.88432603e-23 relative error = 1.4408959197314288930519331437440e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0594 y[1] (analytic) = 2.0017646987828571577226403668137 y[1] (numeric) = 2.0017646987828571577226692587706 absolute error = 2.88919569e-23 relative error = 1.4433243286569754555615917572488e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0595 y[1] (analytic) = 2.001770647285383254958216559414 y[1] (numeric) = 2.0017706472853832549582455000679 absolute error = 2.89406539e-23 relative error = 1.4457527359214026772358817605083e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0596 y[1] (analytic) = 2.0017766058056158333957140317574 y[1] (numeric) = 2.0017766058056158333957430211085 absolute error = 2.89893511e-23 relative error = 1.4481811314970994732157018472807e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0597 y[1] (analytic) = 2.0017825743436144782375082225541 y[1] (numeric) = 2.0017825743436144782375372606027 absolute error = 2.90380486e-23 relative error = 1.4506095203432166387421571914638e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0598 y[1] (analytic) = 2.0017885528994388748636353180387 y[1] (numeric) = 2.0017885528994388748636644047852 absolute error = 2.90867465e-23 relative error = 1.4530379074188457140387234611827e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0599 y[1] (analytic) = 2.0017945414731488088323891057711 y[1] (numeric) = 2.0017945414731488088324182412157 absolute error = 2.91354446e-23 relative error = 1.4554662826964657318677651122739e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 2.0018005400648041658809188302198 y[1] (numeric) = 2.0018005400648041658809480143627 absolute error = 2.91841429e-23 relative error = 1.4578946461396810061379345280673e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0601 y[1] (analytic) = 2.0018065486744649319258280501337 y[1] (numeric) = 2.0018065486744649319258572829754 absolute error = 2.92328417e-23 relative error = 1.4603230126985593907901164529907e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0602 y[1] (analytic) = 2.0018125673021911930637744977093 y[1] (numeric) = 2.00181256730219119306380377925 absolute error = 2.92815407e-23 relative error = 1.4627513673501528273424960642915e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.3MB, time=6.41 NO POLE x[1] = 0.0603 y[1] (analytic) = 2.001818595948043135572070939557 y[1] (numeric) = 2.001818595948043135572100269797 absolute error = 2.93302400e-23 relative error = 1.4651797150535243323404453453779e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0604 y[1] (analytic) = 2.0018246346120810459092870394753 y[1] (numeric) = 2.0018246346120810459093164184149 absolute error = 2.93789396e-23 relative error = 1.4676080557722345054517075334256e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0605 y[1] (analytic) = 2.0018306832943653107158522230367 y[1] (numeric) = 2.0018306832943653107158816506761 absolute error = 2.94276394e-23 relative error = 1.4700363844744167521187806231275e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0606 y[1] (analytic) = 2.0018367419949564168146595439925 y[1] (numeric) = 2.001836741994956416814689020332 absolute error = 2.94763395e-23 relative error = 1.4724647061190899543559229557574e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0607 y[1] (analytic) = 2.0018428107139149512116705525024 y[1] (numeric) = 2.0018428107139149512117000775423 absolute error = 2.95250399e-23 relative error = 1.4748930206698156390741164938341e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0608 y[1] (analytic) = 2.0018488894513016010965211651945 y[1] (numeric) = 2.0018488894513016010965507389352 absolute error = 2.95737407e-23 relative error = 1.4773213330855376651980896872352e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0609 y[1] (analytic) = 2.0018549782071771538431285370622 y[1] (numeric) = 2.001854978207177153843158159504 absolute error = 2.96224418e-23 relative error = 1.4797496383344057011553806057476e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.061 y[1] (analytic) = 2.001861076981602497010298935204 y[1] (numeric) = 2.0018610769816024970103286063471 absolute error = 2.96711431e-23 relative error = 1.4821779313846304295390012610776e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0611 y[1] (analytic) = 2.0018671857746386183423366144118 y[1] (numeric) = 2.0018671857746386183423663342565 absolute error = 2.97198447e-23 relative error = 1.4846062171951565763487456373257e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0612 y[1] (analytic) = 2.0018733045863466057696536946145 y[1] (numeric) = 2.0018733045863466057696834631612 absolute error = 2.97685467e-23 relative error = 1.4870345007248682346370916358681e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0613 y[1] (analytic) = 2.001879433416787647409381040183 y[1] (numeric) = 2.0018794334167876474094108574319 absolute error = 2.98172489e-23 relative error = 1.4894627719466711337038305592140e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0614 y[1] (analytic) = 2.0018855722660230315659801411015 y[1] (numeric) = 2.0018855722660230315660100070529 absolute error = 2.98659514e-23 relative error = 1.4918910358194652216041824762143e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0615 y[1] (analytic) = 2.001891721134114146731855996013 y[1] (numeric) = 2.0018917211341141467318859106672 absolute error = 2.99146542e-23 relative error = 1.4943192923068143520072635782519e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0616 y[1] (analytic) = 2.0018978800211224815879709971437 y[1] (numeric) = 2.0018978800211224815880009605011 absolute error = 2.99633574e-23 relative error = 1.4967475463675424730006761472704e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0617 y[1] (analytic) = 2.0019040489271096250044598171132 y[1] (numeric) = 2.001904048927109625004489829174 absolute error = 3.00120608e-23 relative error = 1.4991757879746790428564185376217e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0618 y[1] (analytic) = 2.0019102278521372660412452976363 y[1] (numeric) = 2.0019102278521372660412753584008 absolute error = 3.00607645e-23 relative error = 1.5016040220870639739941703122188e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0619 y[1] (analytic) = 2.0019164167962671939486553401227 y[1] (numeric) = 2.0019164167962671939486854495913 absolute error = 3.01094686e-23 relative error = 1.5040322536634758570095625228946e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 2.0019226157595612981680407981811 y[1] (numeric) = 2.0019226157595612981680709563539 absolute error = 3.01581728e-23 relative error = 1.5064604676818394059296583701299e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0621 y[1] (analytic) = 2.0019288247420815683323943720326 y[1] (numeric) = 2.00192882474208156833242457891 absolute error = 3.02068774e-23 relative error = 1.5088886790913609037385476899183e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0622 y[1] (analytic) = 2.0019350437438900942669705048419 y[1] (numeric) = 2.0019350437438900942670007604242 absolute error = 3.02555823e-23 relative error = 1.5113168828603927592778135959882e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0623 y[1] (analytic) = 2.0019412727650490659899062809697 y[1] (numeric) = 2.0019412727650490659899365852573 absolute error = 3.03042876e-23 relative error = 1.5137450839476527548102000389755e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0624 y[1] (analytic) = 2.0019475118056207737128433261553 y[1] (numeric) = 2.0019475118056207737128736791484 absolute error = 3.03529931e-23 relative error = 1.5161732723263888387060119664597e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0625 y[1] (analytic) = 2.0019537608656676078415507096326 y[1] (numeric) = 2.0019537608656676078415811113316 absolute error = 3.04016990e-23 relative error = 1.5186014579504553135289888461708e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.3MB, time=6.64 NO POLE x[1] = 0.0626 y[1] (analytic) = 2.0019600199452520589765488481892 y[1] (numeric) = 2.0019600199452520589765792985943 absolute error = 3.04504051e-23 relative error = 1.5210296307931630125768374578212e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0627 y[1] (analytic) = 2.0019662890444367179137344121716 y[1] (numeric) = 2.0019662890444367179137649112832 absolute error = 3.04991116e-23 relative error = 1.5234578008083044876146779033721e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0628 y[1] (analytic) = 2.0019725681632842756450062334449 y[1] (numeric) = 2.0019725681632842756450367812633 absolute error = 3.05478184e-23 relative error = 1.5258859629643270995212193342370e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0629 y[1] (analytic) = 2.0019788573018575233588922153122 y[1] (numeric) = 2.0019788573018575233589228118377 absolute error = 3.05965255e-23 relative error = 1.5283141172247988859055620560451e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 2.0019851564602193524411772444006 y[1] (numeric) = 2.0019851564602193524412078896334 absolute error = 3.06452328e-23 relative error = 1.5307422585582461676414042517273e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0631 y[1] (analytic) = 2.0019914656384327544755321045191 y[1] (numeric) = 2.0019914656384327544755627984596 absolute error = 3.06939405e-23 relative error = 1.5331703969183374118006447083679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0632 y[1] (analytic) = 2.0019977848365608212441433924966 y[1] (numeric) = 2.001997784836560821244174135145 absolute error = 3.07426484e-23 relative error = 1.5355985222785733308790434060087e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0633 y[1] (analytic) = 2.0020041140546667447283444360035 y[1] (numeric) = 2.0020041140546667447283752273602 absolute error = 3.07913567e-23 relative error = 1.5380266445925600580632305264020e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0634 y[1] (analytic) = 2.002010453292813817109247213366 y[1] (numeric) = 2.0020104532928138171092780534314 absolute error = 3.08400654e-23 relative error = 1.5404547638238198352307121586551e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0635 y[1] (analytic) = 2.0020168025510654307683752753779 y[1] (numeric) = 2.0020168025510654307684061641522 absolute error = 3.08887743e-23 relative error = 1.5428828699459489284786174970870e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0636 y[1] (analytic) = 2.0020231618294850782882976691158 y[1] (numeric) = 2.0020231618294850782883286065993 absolute error = 3.09374835e-23 relative error = 1.5453109679175123243227940068689e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0637 y[1] (analytic) = 2.0020295311281363524532638637657 y[1] (numeric) = 2.0020295311281363524532948499588 absolute error = 3.09861931e-23 relative error = 1.5477390626970119163325026018717e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0638 y[1] (analytic) = 2.0020359104470829462498396784662 y[1] (numeric) = 2.0020359104470829462498707133691 absolute error = 3.10349029e-23 relative error = 1.5501671442581400580199235774395e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0639 y[1] (analytic) = 2.0020422997863886528675442121742 y[1] (numeric) = 2.0020422997863886528675752957872 absolute error = 3.10836130e-23 relative error = 1.5525952175594151811748807465753e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 2.002048699146117365699487775561 y[1] (numeric) = 2.0020486991461173656995189078844 absolute error = 3.11323234e-23 relative error = 1.5550232825644088362659345886349e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0641 y[1] (analytic) = 2.0020551085263330783430108249438 y[1] (numeric) = 2.0020551085263330783430420059779 absolute error = 3.11810341e-23 relative error = 1.5574513392366929003884875013722e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0642 y[1] (analytic) = 2.0020615279270998846003238982596 y[1] (numeric) = 2.0020615279270998846003551280048 absolute error = 3.12297452e-23 relative error = 1.5598793925346910655611757177536e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0643 y[1] (analytic) = 2.002067957348481978479148553088 y[1] (numeric) = 2.0020679573484819784791798315446 absolute error = 3.12784566e-23 relative error = 1.5623074374270922978528636913466e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0644 y[1] (analytic) = 2.0020743967905436541933593067287 y[1] (numeric) = 2.0020743967905436541933906338971 absolute error = 3.13271684e-23 relative error = 1.5647354788722887681773763967827e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0645 y[1] (analytic) = 2.0020808462533493061636265783412 y[1] (numeric) = 2.0020808462533493061636579542215 absolute error = 3.13758803e-23 relative error = 1.5671635018493954535148159265810e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0646 y[1] (analytic) = 2.0020873057369634290180606331513 y[1] (numeric) = 2.002087305736963429018092057744 absolute error = 3.14245927e-23 relative error = 1.5695915263012311276901849215122e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0647 y[1] (analytic) = 2.0020937752414506175928565287337 y[1] (numeric) = 2.002093775241450617592888002039 absolute error = 3.14733053e-23 relative error = 1.5720195372069597049085990373381e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=110.6MB, alloc=4.3MB, time=6.87 x[1] = 0.0648 y[1] (analytic) = 2.0021002547668755669329400633736 y[1] (numeric) = 2.0021002547668755669329715853919 absolute error = 3.15220183e-23 relative error = 1.5744475445197134701978162490267e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0649 y[1] (analytic) = 2.0021067443133030722926147265172 y[1] (numeric) = 2.0021067443133030722926462972488 absolute error = 3.15707316e-23 relative error = 1.5768755432082796319124532401352e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 2.0021132438807980291362096513148 y[1] (numeric) = 2.0021132438807980291362412707599 absolute error = 3.16194451e-23 relative error = 1.5793035282415104453294979682969e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0651 y[1] (analytic) = 2.0021197534694254331387285692647 y[1] (numeric) = 2.0021197534694254331387602374238 absolute error = 3.16681591e-23 relative error = 1.5817315145671483711020252934608e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0652 y[1] (analytic) = 2.0021262730792503801864997669642 y[1] (numeric) = 2.0021262730792503801865314838375 absolute error = 3.17168733e-23 relative error = 1.5841594871646014099162439993241e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0653 y[1] (analytic) = 2.0021328027103380663778270449727 y[1] (numeric) = 2.0021328027103380663778588105606 absolute error = 3.17655879e-23 relative error = 1.5865874559868414434853214484719e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0654 y[1] (analytic) = 2.002139342362753788023641678796 y[1] (numeric) = 2.0021393423627537880236734930988 absolute error = 3.18143028e-23 relative error = 1.5890154160027382542773308571354e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0655 y[1] (analytic) = 2.0021458920365629416481553819958 y[1] (numeric) = 2.0021458920365629416481872450137 absolute error = 3.18630179e-23 relative error = 1.5914433621812271756329251450625e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0656 y[1] (analytic) = 2.0021524517318310239895142714322 y[1] (numeric) = 2.0021524517318310239895461831656 absolute error = 3.19117334e-23 relative error = 1.5938713044751833091747036590321e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0657 y[1] (analytic) = 2.0021590214486236320004538346461 y[1] (numeric) = 2.0021590214486236320004857950953 absolute error = 3.19604492e-23 relative error = 1.5962992378535263399313149130089e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0658 y[1] (analytic) = 2.0021656011870064628489548993869 y[1] (numeric) = 2.0021656011870064628489869085522 absolute error = 3.20091653e-23 relative error = 1.5987271622798336591347226908312e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0659 y[1] (analytic) = 2.0021721909470453139189006052927 y[1] (numeric) = 2.0021721909470453139189326631745 absolute error = 3.20578818e-23 relative error = 1.6011550827122584207205105372781e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 2.00217879072880608281073437773 y[1] (numeric) = 2.0021787907288060828107664843286 absolute error = 3.21065986e-23 relative error = 1.6035829941197703725518245326956e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0661 y[1] (analytic) = 2.0021854005323547673421189037986 y[1] (numeric) = 2.0021854005323547673421510591142 absolute error = 3.21553156e-23 relative error = 1.6060108914714054180606006795510e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0662 y[1] (analytic) = 2.0021920203577574655485961105084 y[1] (numeric) = 2.0021920203577574655486283145415 absolute error = 3.22040331e-23 relative error = 1.6084387897143696612584320318523e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0663 y[1] (analytic) = 2.0021986502050803756842481451361 y[1] (numeric) = 2.0021986502050803756842803978869 absolute error = 3.22527508e-23 relative error = 1.6108666738286147867265780346914e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0664 y[1] (analytic) = 2.0022052900743897962223593577659 y[1] (numeric) = 2.0022052900743897962223916592347 absolute error = 3.23014688e-23 relative error = 1.6132945487722626820500450225419e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0665 y[1] (analytic) = 2.002211939965752125856079286023 y[1] (numeric) = 2.0022119399657521258561116362102 absolute error = 3.23501872e-23 relative error = 1.6157224195033693875957319790858e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0666 y[1] (analytic) = 2.0022185998792338634990866420061 y[1] (numeric) = 2.002218599879233863499119040912 absolute error = 3.23989059e-23 relative error = 1.6181502809910055563928689318889e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0667 y[1] (analytic) = 2.0022252698149016082862543014243 y[1] (numeric) = 2.0022252698149016082862867490492 absolute error = 3.24476249e-23 relative error = 1.6205781331987516100531251800682e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0668 y[1] (analytic) = 2.0022319497728220595743152949466 y[1] (numeric) = 2.0022319497728220595743477912908 absolute error = 3.24963442e-23 relative error = 1.6230059760901883295523014000209e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0669 y[1] (analytic) = 2.0022386397530620169425298017694 y[1] (numeric) = 2.0022386397530620169425623468333 absolute error = 3.25450639e-23 relative error = 1.6254338146233065144405010678466e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 2.0022453397556883801933531454105 y[1] (numeric) = 2.0022453397556883801933857391943 absolute error = 3.25937838e-23 relative error = 1.6278616387728516395446813865113e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.3MB, time=7.12 NO POLE x[1] = 0.0671 y[1] (analytic) = 2.0022520497807681493531047917331 y[1] (numeric) = 2.0022520497807681493531374342373 absolute error = 3.26425042e-23 relative error = 1.6302894634855843329864881615022e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0672 y[1] (analytic) = 2.0022587698283684246726383492106 y[1] (numeric) = 2.0022587698283684246726710404354 absolute error = 3.26912248e-23 relative error = 1.6327172737419079142085709634949e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0673 y[1] (analytic) = 2.0022654998985564066280125714348 y[1] (numeric) = 2.0022654998985564066280453113807 absolute error = 3.27399459e-23 relative error = 1.6351450844884831672198585626695e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0674 y[1] (analytic) = 2.002272239991399395921163361878 y[1] (numeric) = 2.0022722399913993959211961505451 absolute error = 3.27886671e-23 relative error = 1.6375728757114887214109488292882e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0675 y[1] (analytic) = 2.0022789901069647934805767809118 y[1] (numeric) = 2.0022789901069647934806096183006 absolute error = 3.28373888e-23 relative error = 1.6400006673518447433285517456549e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0676 y[1] (analytic) = 2.0022857502453201004619630550936 y[1] (numeric) = 2.0022857502453201004619959412043 absolute error = 3.28861107e-23 relative error = 1.6424284443901572435505875842413e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0677 y[1] (analytic) = 2.0022925204065329182489315887234 y[1] (numeric) = 2.0022925204065329182489645235564 absolute error = 3.29348330e-23 relative error = 1.6448562167786112501149901599986e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0678 y[1] (analytic) = 2.0022993005906709484536669776812 y[1] (numeric) = 2.0022993005906709484536999612368 absolute error = 3.29835556e-23 relative error = 1.6472839794864819707344395499739e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0679 y[1] (analytic) = 2.0023060907978019929176060255487 y[1] (numeric) = 2.0023060907978019929176390578273 absolute error = 3.30322786e-23 relative error = 1.6497117374715954083252050185283e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 2.0023128910279939537121157620248 y[1] (numeric) = 2.0023128910279939537121488430267 absolute error = 3.30810019e-23 relative error = 1.6521394857032611911158415278046e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0681 y[1] (analytic) = 2.0023197012813148331391724636396 y[1] (numeric) = 2.0023197012813148331392055933651 absolute error = 3.31297255e-23 relative error = 1.6545672241450645834813605482685e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0682 y[1] (analytic) = 2.0023265215578327337320416767745 y[1] (numeric) = 2.002326521557832733732074855224 absolute error = 3.31784495e-23 relative error = 1.6569949577547816802529587152207e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0683 y[1] (analytic) = 2.0023333518576158582559592429961 y[1] (numeric) = 2.0023333518576158582559924701699 absolute error = 3.32271738e-23 relative error = 1.6594226815017739734958101948084e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0684 y[1] (analytic) = 2.0023401921807325097088133267084 y[1] (numeric) = 2.0023401921807325097088466026067 absolute error = 3.32758983e-23 relative error = 1.6618503903554714283987585977539e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0685 y[1] (analytic) = 2.0023470425272510913218274451324 y[1] (numeric) = 2.0023470425272510913218607697557 absolute error = 3.33246233e-23 relative error = 1.6642780992619298188076684259376e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0686 y[1] (analytic) = 2.0023539028972401065602445006195 y[1] (numeric) = 2.002353902897240106560277873968 absolute error = 3.33733485e-23 relative error = 1.6667057932022671567189429743838e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0687 y[1] (analytic) = 2.0023607732907681591240118153037 y[1] (numeric) = 2.0023607732907681591240452373778 absolute error = 3.34220741e-23 relative error = 1.6691334821283322903316250418261e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0688 y[1] (analytic) = 2.0023676537079039529484671681021 y[1] (numeric) = 2.0023676537079039529485006389021 absolute error = 3.34708000e-23 relative error = 1.6715611610095737231359447908863e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0689 y[1] (analytic) = 2.0023745441487162922050258340687 y[1] (numeric) = 2.002374544148716292205059353595 absolute error = 3.35195263e-23 relative error = 1.6739888348036502941556520422441e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 2.0023814446132740813018686261092 y[1] (numeric) = 2.0023814446132740813019021943621 absolute error = 3.35682529e-23 relative error = 1.6764164984800454493301600357024e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0691 y[1] (analytic) = 2.0023883551016463248846309390634 y[1] (numeric) = 2.0023883551016463248846645560433 absolute error = 3.36169799e-23 relative error = 1.6788441569963842810039120375327e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0692 y[1] (analytic) = 2.0023952756139021278370927961621 y[1] (numeric) = 2.0023952756139021278371264618692 absolute error = 3.36657071e-23 relative error = 1.6812718003281663078764700406815e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0693 y[1] (analytic) = 2.0024022061501106952818698978653 y[1] (numeric) = 2.0024022061501106952819036123 absolute error = 3.37144347e-23 relative error = 1.6836994384270363247152873351167e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.3MB, time=7.36 NO POLE x[1] = 0.0694 y[1] (analytic) = 2.0024091467103413325811056730892 y[1] (numeric) = 2.0024091467103413325811394362519 absolute error = 3.37631627e-23 relative error = 1.6861270712565324296129427654897e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0695 y[1] (analytic) = 2.0024160972946634453371643328282 y[1] (numeric) = 2.0024160972946634453371981447192 absolute error = 3.38118910e-23 relative error = 1.6885546937862259186027259350891e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0696 y[1] (analytic) = 2.0024230579031465393933249261788 y[1] (numeric) = 2.0024230579031465393933587867985 absolute error = 3.38606197e-23 relative error = 1.6909823109736571404595119685480e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0697 y[1] (analytic) = 2.0024300285358602208344763987735 y[1] (numeric) = 2.0024300285358602208345103081221 absolute error = 3.39093486e-23 relative error = 1.6934099127945003979767764430838e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0698 y[1] (analytic) = 2.0024370091928741959878136536295 y[1] (numeric) = 2.0024370091928741959878476117075 absolute error = 3.39580780e-23 relative error = 1.6958375141941439731569763234461e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0699 y[1] (analytic) = 2.0024439998742582714235346144223 y[1] (numeric) = 2.0024439998742582714235686212299 absolute error = 3.40068076e-23 relative error = 1.6982651001543827389302753026502e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 2.002451000580082353955538291187 y[1] (numeric) = 2.0024510005800823539555723467247 absolute error = 3.40555377e-23 relative error = 1.7006926856205011676042477119314e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0701 y[1] (analytic) = 2.0024580113104164506421238484591 y[1] (numeric) = 2.0024580113104164506421579527271 absolute error = 3.41042680e-23 relative error = 1.7031202555743993851204344174838e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0702 y[1] (analytic) = 2.0024650320653306687866906758572 y[1] (numeric) = 2.0024650320653306687867248288559 absolute error = 3.41529987e-23 relative error = 1.7055478199674127544384738196636e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0703 y[1] (analytic) = 2.0024720628448952159384394611179 y[1] (numeric) = 2.0024720628448952159384736628476 absolute error = 3.42017297e-23 relative error = 1.7079753737692545034676687871515e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0704 y[1] (analytic) = 2.0024791036491803998930742655885 y[1] (numeric) = 2.0024791036491803998931085160495 absolute error = 3.42504610e-23 relative error = 1.7104029169435182617235662236425e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0705 y[1] (analytic) = 2.0024861544782566286935056021843 y[1] (numeric) = 2.002486154478256628693539901377 absolute error = 3.42991927e-23 relative error = 1.7128304544475903933427797873320e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0706 y[1] (analytic) = 2.0024932153321944106305545158186 y[1] (numeric) = 2.0024932153321944106305888637434 absolute error = 3.43479248e-23 relative error = 1.7152579862450125126541246652342e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0707 y[1] (analytic) = 2.0025002862110643542436576663115 y[1] (numeric) = 2.0025002862110643542436920629686 absolute error = 3.43966571e-23 relative error = 1.7176855023118123133495845036615e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0708 y[1] (analytic) = 2.0025073671149371683215734137845 y[1] (numeric) = 2.0025073671149371683216078591744 absolute error = 3.44453899e-23 relative error = 1.7201130175928561667882245149291e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0709 y[1] (analytic) = 2.0025144580438836619030889065491 y[1] (numeric) = 2.0025144580438836619031234006721 absolute error = 3.44941230e-23 relative error = 1.7225405220641900674433806391441e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 2.0025215589979747442777281714951 y[1] (numeric) = 2.0025215589979747442777627143515 absolute error = 3.45428564e-23 relative error = 1.7249680156894098643481874536859e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0711 y[1] (analytic) = 2.0025286699772814249864612069863 y[1] (numeric) = 2.0025286699772814249864957985764 absolute error = 3.45915901e-23 relative error = 1.7273954984321118180091669623147e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0712 y[1] (analytic) = 2.0025357909818748138224140782709 y[1] (numeric) = 2.0025357909818748138224487185951 absolute error = 3.46403242e-23 relative error = 1.7298229752495611517790165178537e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0713 y[1] (analytic) = 2.0025429220118261208315800154135 y[1] (numeric) = 2.0025429220118261208316147044721 absolute error = 3.46890586e-23 relative error = 1.7322504411116508378005471960987e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0714 y[1] (analytic) = 2.0025500630672066563135315137552 y[1] (numeric) = 2.0025500630672066563135662515486 absolute error = 3.47377934e-23 relative error = 1.7346779009756112641536761626567e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0715 y[1] (analytic) = 2.0025572141480878308221334369105 y[1] (numeric) = 2.002557214148087830822168223439 absolute error = 3.47865285e-23 relative error = 1.7371053498113716499472312562450e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0716 y[1] (analytic) = 2.0025643752545411551662571223061 y[1] (numeric) = 2.0025643752545411551662919575701 absolute error = 3.48352640e-23 relative error = 1.7395327925761274533449579499024e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.3MB, time=7.60 NO POLE x[1] = 0.0717 y[1] (analytic) = 2.0025715463866382404104954892703 y[1] (numeric) = 2.0025715463866382404105303732702 absolute error = 3.48839999e-23 relative error = 1.7419602292334236342455880077167e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0718 y[1] (analytic) = 2.0025787275444507978758791496797 y[1] (numeric) = 2.0025787275444507978759140824158 absolute error = 3.49327361e-23 relative error = 1.7443876547532439405388543920557e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0719 y[1] (analytic) = 2.0025859187280506391405935211699 y[1] (numeric) = 2.0025859187280506391406285026426 absolute error = 3.49814727e-23 relative error = 1.7468150740927312207567235112124e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 2.0025931199375096760406969429182 y[1] (numeric) = 2.0025931199375096760407319731277 absolute error = 3.50302095e-23 relative error = 1.7492424772283801359935638226139e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0721 y[1] (analytic) = 2.0026003311728999206708397940042 y[1] (numeric) = 2.002600331172899920670874872951 absolute error = 3.50789468e-23 relative error = 1.7516698791043675388573354430446e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0722 y[1] (analytic) = 2.0026075524342934853849846143579 y[1] (numeric) = 2.0026075524342934853850197420422 absolute error = 3.51276843e-23 relative error = 1.7540972647037171390870470123012e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0723 y[1] (analytic) = 2.0026147837217625827971272282989 y[1] (numeric) = 2.0026147837217625827971624047211 absolute error = 3.51764222e-23 relative error = 1.7565246439770270267780883566846e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0724 y[1] (analytic) = 2.0026220250353795257820188706775 y[1] (numeric) = 2.002622025035379525782054095838 absolute error = 3.52251605e-23 relative error = 1.7589520168878443808033033181640e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0725 y[1] (analytic) = 2.0026292763752167274758893156229 y[1] (numeric) = 2.002629276375216727475924589522 absolute error = 3.52738991e-23 relative error = 1.7613793784062812201647246154541e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0726 y[1] (analytic) = 2.0026365377413467012771710079057 y[1] (numeric) = 2.0026365377413467012772063305438 absolute error = 3.53226381e-23 relative error = 1.7638067334893569338874011207452e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0727 y[1] (analytic) = 2.0026438091338420608472241969232 y[1] (numeric) = 2.0026438091338420608472595683007 absolute error = 3.53713775e-23 relative error = 1.7662340821006196167323770412105e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0728 y[1] (analytic) = 2.0026510905527755201110630733135 y[1] (numeric) = 2.0026510905527755201110984934306 absolute error = 3.54201171e-23 relative error = 1.7686614142168555516357616280356e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0729 y[1] (analytic) = 2.0026583819982198932580829082059 y[1] (numeric) = 2.0026583819982198932581183770631 absolute error = 3.54688572e-23 relative error = 1.7710887447818110832520009802840e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 2.0026656834702480947427881951162 y[1] (numeric) = 2.0026656834702480947428237127138 absolute error = 3.55175976e-23 relative error = 1.7735160637722913685216179628924e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0731 y[1] (analytic) = 2.0026729949689331392855217944917 y[1] (numeric) = 2.00267299496893313928555736083 absolute error = 3.55663383e-23 relative error = 1.7759433711519004056617725359310e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0732 y[1] (analytic) = 2.0026803164943481418731950809153 y[1] (numeric) = 2.0026803164943481418732306959947 absolute error = 3.56150794e-23 relative error = 1.7783706718775508066638166609739e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0733 y[1] (analytic) = 2.0026876480465663177600190929757 y[1] (numeric) = 2.0026876480465663177600547567965 absolute error = 3.56638208e-23 relative error = 1.7807979609195027083351883610211e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0734 y[1] (analytic) = 2.0026949896256609824682366858095 y[1] (numeric) = 2.0026949896256609824682723983722 absolute error = 3.57125627e-23 relative error = 1.7832252482279045335103517400770e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0735 y[1] (analytic) = 2.0027023412317055517888556863248 y[1] (numeric) = 2.0027023412317055517888914476297 absolute error = 3.57613049e-23 relative error = 1.7856525237797454577771681592507e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0736 y[1] (analytic) = 2.0027097028647735417823830511116 y[1] (numeric) = 2.002709702864773541782418861159 absolute error = 3.58100474e-23 relative error = 1.7880797875386314522087069237027e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0737 y[1] (analytic) = 2.0027170745249385687795600270472 y[1] (numeric) = 2.0027170745249385687795958858375 absolute error = 3.58587903e-23 relative error = 1.7905070444613854601265162356411e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0738 y[1] (analytic) = 2.0027244562122743493820983146049 y[1] (numeric) = 2.0027244562122743493821342221385 absolute error = 3.59075336e-23 relative error = 1.7929342945115591274068444995933e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=125.8MB, alloc=4.3MB, time=7.84 x[1] = 0.0739 y[1] (analytic) = 2.0027318479268547004634172338712 y[1] (numeric) = 2.0027318479268547004634531901484 absolute error = 3.59562772e-23 relative error = 1.7953615326595246999251990008647e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 2.0027392496687535391693818932809 y[1] (numeric) = 2.002739249668753539169417898302 absolute error = 3.60050211e-23 relative error = 1.7977887588688897786850630897118e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0741 y[1] (analytic) = 2.002746661438044882919042361076 y[1] (numeric) = 2.0027466614380448829190784148415 absolute error = 3.60537655e-23 relative error = 1.8002159830895479398123186933258e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0742 y[1] (analytic) = 2.0027540832348028494053738394974 y[1] (numeric) = 2.0027540832348028494054099420075 absolute error = 3.61025101e-23 relative error = 1.8026431903056238794621126437528e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0743 y[1] (analytic) = 2.0027615150591016565960178417146 y[1] (numeric) = 2.0027615150591016565960539929698 absolute error = 3.61512552e-23 relative error = 1.8050703954600991767888445247474e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0744 y[1] (analytic) = 2.0027689569110156227340243715032 y[1] (numeric) = 2.0027689569110156227340605715039 absolute error = 3.62000007e-23 relative error = 1.8074975935233846585776833204724e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0745 y[1] (analytic) = 2.0027764087906191663385951056761 y[1] (numeric) = 2.0027764087906191663386313544225 absolute error = 3.62487464e-23 relative error = 1.8099247744728970183029379880268e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0746 y[1] (analytic) = 2.0027838706979868062058275792756 y[1] (numeric) = 2.0027838706979868062058638767681 absolute error = 3.62974925e-23 relative error = 1.8123519482584020670758690822852e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0747 y[1] (analytic) = 2.0027913426331931614094603735353 y[1] (numeric) = 2.0027913426331931614094967197744 absolute error = 3.63462391e-23 relative error = 1.8147791198364858279134989386226e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0748 y[1] (analytic) = 2.0027988245963129513016193066186 y[1] (numeric) = 2.0027988245963129513016557016045 absolute error = 3.63949859e-23 relative error = 1.8172062741916091536076226045203e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0749 y[1] (analytic) = 2.0028063165874209955135646271394 y[1] (numeric) = 2.0028063165874209955136010708726 absolute error = 3.64437332e-23 relative error = 1.8196334262664214212877588266638e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 2.0028138186065922139564392104767 y[1] (numeric) = 2.0028138186065922139564757029575 absolute error = 3.64924808e-23 relative error = 1.8220605660384715037371490504606e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0751 y[1] (analytic) = 2.0028213306539016268220177578856 y[1] (numeric) = 2.0028213306539016268220542991143 absolute error = 3.65412287e-23 relative error = 1.8244876934713714723231549200251e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0752 y[1] (analytic) = 2.0028288527294243545834569984161 y[1] (numeric) = 2.0028288527294243545834935883931 absolute error = 3.65899770e-23 relative error = 1.8269148135216717165945829452549e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0753 y[1] (analytic) = 2.0028363848332356179960468936454 y[1] (numeric) = 2.0028363848332356179960835323711 absolute error = 3.66387257e-23 relative error = 1.8293419261529289002750039458352e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0754 y[1] (analytic) = 2.0028439269654107380979628452311 y[1] (numeric) = 2.0028439269654107380979995327058 absolute error = 3.66874747e-23 relative error = 1.8317690263357997233480732275673e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0755 y[1] (analytic) = 2.0028514791260251362110189052938 y[1] (numeric) = 2.002851479126025136211055641518 absolute error = 3.67362242e-23 relative error = 1.8341961240196608625480108877004e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0756 y[1] (analytic) = 2.002859041315154333941421989636 y[1] (numeric) = 2.00285904131515433394145877461 absolute error = 3.67849740e-23 relative error = 1.8366232091822882486160936953294e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0757 y[1] (analytic) = 2.0028666135328739531805270938044 y[1] (numeric) = 2.0028666135328739531805639275286 absolute error = 3.68337242e-23 relative error = 1.8390502867801401628265519776319e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0758 y[1] (analytic) = 2.0028741957792597161055935120044 y[1] (numeric) = 2.0028741957792597161056303944792 absolute error = 3.68824748e-23 relative error = 1.8414773567767749275651592451472e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0759 y[1] (analytic) = 2.0028817880543874451805420588733 y[1] (numeric) = 2.002881788054387445180578990099 absolute error = 3.69312257e-23 relative error = 1.8439044141429452898683209962935e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 2.0028893903583330631567132941199 y[1] (numeric) = 2.0028893903583330631567502740969 absolute error = 3.69799770e-23 relative error = 1.8463314638350540121246369393020e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0761 y[1] (analytic) = 2.002897002691172593073626750039 y[1] (numeric) = 2.0028970026911725930736637787676 absolute error = 3.70287286e-23 relative error = 1.8487585008238924874174031606523e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.3MB, time=8.08 NO POLE x[1] = 0.0762 y[1] (analytic) = 2.0029046250529821582597411619065 y[1] (numeric) = 2.0029046250529821582597782393872 absolute error = 3.70774807e-23 relative error = 1.8511855350585753403077707408481e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0763 y[1] (analytic) = 2.0029122574438379823332157012655 y[1] (numeric) = 2.0029122574438379823332528274986 absolute error = 3.71262331e-23 relative error = 1.8536125565171456948590216243803e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0764 y[1] (analytic) = 2.0029198998638163892026722121079 y[1] (numeric) = 2.0029198998638163892027093870937 absolute error = 3.71749858e-23 relative error = 1.8560395651632210403254915991555e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0765 y[1] (analytic) = 2.0029275523129938030679584499613 y[1] (numeric) = 2.0029275523129938030679956737002 absolute error = 3.72237389e-23 relative error = 1.8584665659531111595831135240948e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0766 y[1] (analytic) = 2.0029352147914467484209123238885 y[1] (numeric) = 2.0029352147914467484209495963809 absolute error = 3.72724924e-23 relative error = 1.8608935588503771963192661293112e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0767 y[1] (analytic) = 2.0029428872992518500461271414062 y[1] (numeric) = 2.0029428872992518500461644626524 absolute error = 3.73212462e-23 relative error = 1.8633205388259270327998098617228e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0768 y[1] (analytic) = 2.0029505698364858330217178563315 y[1] (numeric) = 2.0029505698364858330217552263319 absolute error = 3.73700004e-23 relative error = 1.8657475108360143655597822996667e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0769 y[1] (analytic) = 2.002958262403225522720088319564 y[1] (numeric) = 2.002958262403225522720125738319 absolute error = 3.74187550e-23 relative error = 1.8681744748442014069530423399134e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 2.0029659649995478448086995328102 y[1] (numeric) = 2.0029659649995478448087370003202 absolute error = 3.74675100e-23 relative error = 1.8706014308140507031270482195819e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0771 y[1] (analytic) = 2.0029736776255298252508389052591 y[1] (numeric) = 2.0029736776255298252508764215244 absolute error = 3.75162653e-23 relative error = 1.8730283737165482922615685280198e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0772 y[1] (analytic) = 2.0029814002812485903063905132151 y[1] (numeric) = 2.0029814002812485903064280782362 absolute error = 3.75650211e-23 relative error = 1.8754553135004303269592889330545e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0773 y[1] (analytic) = 2.0029891329667813665326063626981 y[1] (numeric) = 2.0029891329667813665326439764754 absolute error = 3.76137773e-23 relative error = 1.8778822451366642946215730163057e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0774 y[1] (analytic) = 2.0029968756822054807848786550165 y[1] (numeric) = 2.0029968756822054807849163175503 absolute error = 3.76625338e-23 relative error = 1.8803091635962950681211504483711e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0775 y[1] (analytic) = 2.0030046284275983602175130553215 y[1] (numeric) = 2.0030046284275983602175507666121 absolute error = 3.77112906e-23 relative error = 1.8827360688429448522674057490505e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0776 y[1] (analytic) = 2.003012391203037532284502964151 y[1] (numeric) = 2.0030123912030375322845407241989 absolute error = 3.77600479e-23 relative error = 1.8851629708251970381592759387233e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0777 y[1] (analytic) = 2.0030201640086006247403047919704 y[1] (numeric) = 2.0030201640086006247403426007759 absolute error = 3.78088055e-23 relative error = 1.8875898595216366219040467758725e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0778 y[1] (analytic) = 2.0030279468443653656406142367173 y[1] (numeric) = 2.0030279468443653656406520942808 absolute error = 3.78575635e-23 relative error = 1.8900167398883287094973509864144e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0779 y[1] (analytic) = 2.0030357397104095833431435643596 y[1] (numeric) = 2.0030357397104095833431814706815 absolute error = 3.79063219e-23 relative error = 1.8924436118888390548969911107130e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 2.003043542606811206508399892473 y[1] (numeric) = 2.0030435426068112065084378475536 absolute error = 3.79550806e-23 relative error = 1.8948704704943310531500146560594e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0781 y[1] (analytic) = 2.0030513555336482641004644768467 y[1] (numeric) = 2.0030513555336482641005024806864 absolute error = 3.80038397e-23 relative error = 1.8972973206608128019498006992775e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0782 y[1] (analytic) = 2.003059178490998885387773001125 y[1] (numeric) = 2.0030591784909988853878110537242 absolute error = 3.80525992e-23 relative error = 1.8997241623518511711894217223747e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0783 y[1] (analytic) = 2.0030670114789412999438968694923 y[1] (numeric) = 2.0030670114789412999439349708514 absolute error = 3.81013591e-23 relative error = 1.9021509955310133803161110953275e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0784 y[1] (analytic) = 2.0030748544975538376483255024094 y[1] (numeric) = 2.0030748544975538376483636525288 absolute error = 3.81501194e-23 relative error = 1.9045778201618669995437827712649e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.3MB, time=8.32 NO POLE x[1] = 0.0785 y[1] (analytic) = 2.003082707546914928687249635409 y[1] (numeric) = 2.0030827075469149286872878342891 absolute error = 3.81988801e-23 relative error = 1.9070046362079799510655244307295e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0786 y[1] (analytic) = 2.0030905706271031035543456209584 y[1] (numeric) = 2.0030905706271031035543838685995 absolute error = 3.82476411e-23 relative error = 1.9094314386406350157218396386438e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0787 y[1] (analytic) = 2.0030984437381969930515607333968 y[1] (numeric) = 2.0030984437381969930515990297993 absolute error = 3.82964025e-23 relative error = 1.9118582324157255618663767548557e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0788 y[1] (analytic) = 2.0031063268802753282898994769555 y[1] (numeric) = 2.0031063268802753282899378221198 absolute error = 3.83451643e-23 relative error = 1.9142850174968206494409274999914e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0789 y[1] (analytic) = 2.0031142200534169406902108968686 y[1] (numeric) = 2.0031142200534169406902492907951 absolute error = 3.83939265e-23 relative error = 1.9167117938474896952145948559688e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 2.003122123257700761983976893582 y[1] (numeric) = 2.0031221232577007619840153362711 absolute error = 3.84426891e-23 relative error = 1.9191385614313024739961499108257e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0791 y[1] (analytic) = 2.0031300364932058242141015400692 y[1] (numeric) = 2.0031300364932058242141400315212 absolute error = 3.84914520e-23 relative error = 1.9215653152196419838047232202056e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0792 y[1] (analytic) = 2.0031379597600112597357014022605 y[1] (numeric) = 2.0031379597600112597357399424759 absolute error = 3.85402154e-23 relative error = 1.9239920651604727374825287395366e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0793 y[1] (analytic) = 2.0031458930581963012168968625955 y[1] (numeric) = 2.0031458930581963012169354515746 absolute error = 3.85889791e-23 relative error = 1.9264188012330111150688664891862e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0794 y[1] (analytic) = 2.0031538363878402816396044467042 y[1] (numeric) = 2.0031538363878402816396430844475 absolute error = 3.86377433e-23 relative error = 1.9288455333851433690350943842186e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0795 y[1] (analytic) = 2.0031617897490226343003301532276 y[1] (numeric) = 2.0031617897490226343003688397353 absolute error = 3.86865077e-23 relative error = 1.9312722466040576886710531523606e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0796 y[1] (analytic) = 2.0031697531418228928109637867826 y[1] (numeric) = 2.0031697531418228928110025220552 absolute error = 3.87352726e-23 relative error = 1.9336989558297095654372585278310e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0797 y[1] (analytic) = 2.0031777265663206910995742940824 y[1] (numeric) = 2.0031777265663206910996130781203 absolute error = 3.87840379e-23 relative error = 1.9361256560335435660787029652831e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0798 y[1] (analytic) = 2.0031857100225957634112061032172 y[1] (numeric) = 2.0031857100225957634112449360208 absolute error = 3.88328036e-23 relative error = 1.9385523471791324478861732934865e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0799 y[1] (analytic) = 2.0031937035107279443086764661057 y[1] (numeric) = 2.0031937035107279443087153476753 absolute error = 3.88815696e-23 relative error = 1.9409790242380208665245863595967e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 2.0032017070307971686733738041236 y[1] (numeric) = 2.0032017070307971686734127344597 absolute error = 3.89303361e-23 relative error = 1.9434056971578592045118668622958e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0801 y[1] (analytic) = 2.0032097205828834717060570569186 y[1] (numeric) = 2.0032097205828834717060960360215 absolute error = 3.89791029e-23 relative error = 1.9458323559181843831231173480282e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0802 y[1] (analytic) = 2.0032177441670669889276560344183 y[1] (numeric) = 2.0032177441670669889276950622883 absolute error = 3.90278700e-23 relative error = 1.9482590004826306266674932849829e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0803 y[1] (analytic) = 2.0032257777834279561800727720401 y[1] (numeric) = 2.0032257777834279561801118486777 absolute error = 3.90766376e-23 relative error = 1.9506856407987297655860962703821e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0804 y[1] (analytic) = 2.0032338214320467096269838891112 y[1] (numeric) = 2.0032338214320467096270230145169 absolute error = 3.91254057e-23 relative error = 1.9531122768299968050826618889667e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0805 y[1] (analytic) = 2.003241875113003685754643950506 y[1] (numeric) = 2.0032418751130036857546831246801 absolute error = 3.91741741e-23 relative error = 1.9555388985561301212448848780107e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0806 y[1] (analytic) = 2.0032499388263794213726898315091 y[1] (numeric) = 2.0032499388263794213727290544519 absolute error = 3.92229428e-23 relative error = 1.9579655059407657389045101340109e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0807 y[1] (analytic) = 2.0032580125722545536149460859124 y[1] (numeric) = 2.0032580125722545536149853576243 absolute error = 3.92717119e-23 memory used=137.3MB, alloc=4.3MB, time=8.57 relative error = 1.9603921039394084258627634237074e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0808 y[1] (analytic) = 2.003266096350709819940231317354 y[1] (numeric) = 2.0032660963507098199402706378355 absolute error = 3.93204815e-23 relative error = 1.9628186975074829040693909441992e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0809 y[1] (analytic) = 2.0032741901618260581331655539074 y[1] (numeric) = 2.0032741901618260581332049231589 absolute error = 3.93692515e-23 relative error = 1.9652452816166777962687025826871e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 2.0032822940056842063049786259279 y[1] (numeric) = 2.0032822940056842063050180439497 absolute error = 3.94180218e-23 relative error = 1.9676718512387627318873810502411e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0811 y[1] (analytic) = 2.0032904078823653028943195471658 y[1] (numeric) = 2.0032904078823653028943590139583 absolute error = 3.94667925e-23 relative error = 1.9700984113291635797045599477553e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0812 y[1] (analytic) = 2.0032985317919504866680668991535 y[1] (numeric) = 2.0032985317919504866681064147171 absolute error = 3.95155636e-23 relative error = 1.9725249618514585215840840294889e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0813 y[1] (analytic) = 2.0033066657345209967221402188751 y[1] (numeric) = 2.0033066657345209967221797832102 absolute error = 3.95643351e-23 relative error = 1.9749515027692261253012200994285e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0814 y[1] (analytic) = 2.003314809710158172482312389726 y[1] (numeric) = 2.0033148097101581724823520028331 absolute error = 3.96131071e-23 relative error = 1.9773780390377720337064993194438e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0815 y[1] (analytic) = 2.0033229637189434537050230357717 y[1] (numeric) = 2.0033229637189434537050626976511 absolute error = 3.96618794e-23 relative error = 1.9798045606372018965943108228772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0816 y[1] (analytic) = 2.0033311277609583804781929193126 y[1] (numeric) = 2.0033311277609583804782326299646 absolute error = 3.97106520e-23 relative error = 1.9822310675311563993474213940525e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0817 y[1] (analytic) = 2.0033393018362845932220393417636 y[1] (numeric) = 2.0033393018362845932220791011888 absolute error = 3.97594252e-23 relative error = 1.9846575746582737496506920280737e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0818 y[1] (analytic) = 2.0033474859450038326898925478579 y[1] (numeric) = 2.0033474859450038326899323560566 absolute error = 3.98081987e-23 relative error = 1.9870840670070763788645950061234e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0819 y[1] (analytic) = 2.0033556800871979399690131331798 y[1] (numeric) = 2.0033556800871979399690529901525 absolute error = 3.98569727e-23 relative error = 1.9895105545244560756674313815167e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 2.003363884262948856481410455039 y[1] (numeric) = 2.003363884262948856481450360786 absolute error = 3.99057470e-23 relative error = 1.9919370271907239975567109306847e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0821 y[1] (analytic) = 2.0033720984723386239846620466906 y[1] (numeric) = 2.0033720984723386239847020012123 absolute error = 3.99545217e-23 relative error = 1.9943634899611071120281332316324e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0822 y[1] (analytic) = 2.0033803227154493845727340349121 y[1] (numeric) = 2.0033803227154493845727740382089 absolute error = 4.00032968e-23 relative error = 1.9967899427991875145828134455341e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0823 y[1] (analytic) = 2.0033885569923633806768025609436 y[1] (numeric) = 2.0033885569923633806768426130159 absolute error = 4.00520723e-23 relative error = 1.9992163856685476987488101016573e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0824 y[1] (analytic) = 2.0033968013031629550660762047999 y[1] (numeric) = 2.0033968013031629550661163056482 absolute error = 4.01008483e-23 relative error = 2.0016428235242929524042755387828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0825 y[1] (analytic) = 2.003405055647930550848619412964 y[1] (numeric) = 2.0034050556479305508486595625885 absolute error = 4.01496245e-23 relative error = 2.0040692413554393834300250139202e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0826 y[1] (analytic) = 2.0034133200267487114721769294675 y[1] (numeric) = 2.0034133200267487114722171278688 absolute error = 4.01984013e-23 relative error = 2.0064956590916191106010929380208e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0827 y[1] (analytic) = 2.0034215944397000807249992303697 y[1] (numeric) = 2.0034215944397000807250394775481 absolute error = 4.02471784e-23 relative error = 2.0089220617219107439103723464851e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0828 y[1] (analytic) = 2.0034298788868674027366689616399 y[1] (numeric) = 2.0034298788868674027367092575959 absolute error = 4.02959560e-23 relative error = 2.0113484591928405971378073167014e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0829 y[1] (analytic) = 2.0034381733683335219789283804548 y[1] (numeric) = 2.0034381733683335219789687251886 absolute error = 4.03447338e-23 relative error = 2.0137748364936736293292862991659e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=141.1MB, alloc=4.3MB, time=8.81 x[1] = 0.083 y[1] (analytic) = 2.0034464778841813832665077999156 y[1] (numeric) = 2.0034464778841813832665481934278 absolute error = 4.03935122e-23 relative error = 2.0162012135537137297112158889316e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0831 y[1] (analytic) = 2.0034547924344940317579550371971 y[1] (numeric) = 2.003454792434494031757995479488 absolute error = 4.04422909e-23 relative error = 2.0186275753622886670871553026193e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0832 y[1] (analytic) = 2.003463117019354612956465865133 y[1] (numeric) = 2.003463117019354612956506356203 absolute error = 4.04910700e-23 relative error = 2.0210539268744038892537298690604e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0833 y[1] (analytic) = 2.0034714516388463727107154672489 y[1] (numeric) = 2.0034714516388463727107560070984 absolute error = 4.05398495e-23 relative error = 2.0234802680536459366309293457619e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0834 y[1] (analytic) = 2.0034797962930526572156908962497 y[1] (numeric) = 2.0034797962930526572157314848792 absolute error = 4.05886295e-23 relative error = 2.0259066038549173801947840596616e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0835 y[1] (analytic) = 2.0034881509820569130135245359703 y[1] (numeric) = 2.0034881509820569130135651733802 absolute error = 4.06374099e-23 relative error = 2.0283329292504483367853336396570e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0836 y[1] (analytic) = 2.0034965157059426869943285667975 y[1] (numeric) = 2.0034965157059426869943692529881 absolute error = 4.06861906e-23 relative error = 2.0307592392125525439367845410902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0837 y[1] (analytic) = 2.0035048904647936263970304345716 y[1] (numeric) = 2.0035048904647936263970711695434 absolute error = 4.07349718e-23 relative error = 2.0331855436873869162413282079688e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0838 y[1] (analytic) = 2.0035132752586934788102093229768 y[1] (numeric) = 2.0035132752586934788102501067302 absolute error = 4.07837534e-23 relative error = 2.0356118376472451834449617597628e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0839 y[1] (analytic) = 2.0035216700877260921729336294274 y[1] (numeric) = 2.0035216700877260921729744619628 absolute error = 4.08325354e-23 relative error = 2.0380381210557162977629853964849e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 2.0035300749519754147755994444593 y[1] (numeric) = 2.0035300749519754147756403257771 absolute error = 4.08813178e-23 relative error = 2.0404643938763896300289235722241e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0841 y[1] (analytic) = 2.0035384898515254952607700346346 y[1] (numeric) = 2.0035384898515254952608109647352 absolute error = 4.09301006e-23 relative error = 2.0428906560728549709054093183921e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0842 y[1] (analytic) = 2.0035469147864604826240163289678 y[1] (numeric) = 2.0035469147864604826240573078517 absolute error = 4.09788839e-23 relative error = 2.0453169125998509430449294699313e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0843 y[1] (analytic) = 2.0035553497568646262147584088828 y[1] (numeric) = 2.0035553497568646262147994365502 absolute error = 4.10276674e-23 relative error = 2.0477431484475229475511899139024e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0844 y[1] (analytic) = 2.0035637947628222757371080017068 y[1] (numeric) = 2.0035637947628222757371490781583 absolute error = 4.10764515e-23 relative error = 2.0501693835440136353344443089884e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0845 y[1] (analytic) = 2.0035722498044178812507119777131 y[1] (numeric) = 2.003572249804417881250753102949 absolute error = 4.11252359e-23 relative error = 2.0525956028795322938549638650256e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0846 y[1] (analytic) = 2.0035807148817359931715968507177 y[1] (numeric) = 2.0035807148817359931716380247385 absolute error = 4.11740208e-23 relative error = 2.0550218163998624403445761727616e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0847 y[1] (analytic) = 2.0035891899948612622730142822405 y[1] (numeric) = 2.0035891899948612622730555050465 absolute error = 4.12228060e-23 relative error = 2.0574480140864468757346898378067e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0848 y[1] (analytic) = 2.0035976751438784396862875892383 y[1] (numeric) = 2.00359767514387843968632886083 absolute error = 4.12715917e-23 relative error = 2.0598742058849856238265187406027e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0849 y[1] (analytic) = 2.0036061703288723769016592554191 y[1] (numeric) = 2.0036061703288723769017005757969 absolute error = 4.13203778e-23 relative error = 2.0623003867680075919901934376916e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 2.0036146755499280257691394461449 y[1] (numeric) = 2.0036146755499280257691808153092 absolute error = 4.13691643e-23 relative error = 2.0647265566991063293751066665358e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0851 y[1] (analytic) = 2.0036231908071304384993555269327 y[1] (numeric) = 2.0036231908071304384993969448838 absolute error = 4.14179511e-23 relative error = 2.0671527106509174143703106326894e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0852 y[1] (analytic) = 2.0036317161005647676644025855612 y[1] (numeric) = 2.0036317161005647676644440522997 absolute error = 4.14667385e-23 relative error = 2.0695788635599104693064956779419e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.3MB, time=9.05 NO POLE x[1] = 0.0853 y[1] (analytic) = 2.003640251430316266198694957793 y[1] (numeric) = 2.0036402514303162661987364733193 absolute error = 4.15155263e-23 relative error = 2.0720050054077210403016318358397e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0854 y[1] (analytic) = 2.003648796796470287399818756719 y[1] (numeric) = 2.0036487967964702873998603210334 absolute error = 4.15643144e-23 relative error = 2.0744311311670497172141383559241e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0855 y[1] (analytic) = 2.003657352199112284929385405735 y[1] (numeric) = 2.003657352199112284929427018838 absolute error = 4.16131030e-23 relative error = 2.0768572507833026968197778919935e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0856 y[1] (analytic) = 2.0036659176383278128138861751587 y[1] (numeric) = 2.0036659176383278128139278370507 absolute error = 4.16618920e-23 relative error = 2.0792833592291601579820355897403e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0857 y[1] (analytic) = 2.0036744931142025254455477224953 y[1] (numeric) = 2.0036744931142025254455894331767 absolute error = 4.17106814e-23 relative error = 2.0817094564682186243848396105808e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0858 y[1] (analytic) = 2.0036830786268221775831886363604 y[1] (numeric) = 2.0036830786268221775832303958316 absolute error = 4.17594712e-23 relative error = 2.0841355424640750601249267832172e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0859 y[1] (analytic) = 2.0036916741762726243530769840689 y[1] (numeric) = 2.0036916741762726243531187923303 absolute error = 4.18082614e-23 relative error = 2.0865616171803268709221693449113e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.086 y[1] (analytic) = 2.0037002797626398212497888628985 y[1] (numeric) = 2.0037002797626398212498307199505 absolute error = 4.18570520e-23 relative error = 2.0889876805805719053298697517926e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0861 y[1] (analytic) = 2.003708895386009824137067955036 y[1] (numeric) = 2.0037088953860098241371098608791 absolute error = 4.19058431e-23 relative error = 2.0914137376191533805332448855559e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0862 y[1] (analytic) = 2.0037175210464687892486860862157 y[1] (numeric) = 2.0037175210464687892487280408503 absolute error = 4.19546346e-23 relative error = 2.0938397832688821411921784381358e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0863 y[1] (analytic) = 2.0037261567441029731893047880576 y[1] (numeric) = 2.0037261567441029731893467914841 absolute error = 4.20034265e-23 relative error = 2.0962658174933572971775312150619e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0864 y[1] (analytic) = 2.0037348024789987329353378641148 y[1] (numeric) = 2.0037348024789987329353799163337 absolute error = 4.20522189e-23 relative error = 2.0986918452468588032764170446740e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0865 y[1] (analytic) = 2.0037434582512425258358149596386 y[1] (numeric) = 2.0037434582512425258358570606502 absolute error = 4.21010116e-23 relative error = 2.1011178565116043126970454239861e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0866 y[1] (analytic) = 2.0037521240609209096132461350691 y[1] (numeric) = 2.0037521240609209096132882848738 absolute error = 4.21498047e-23 relative error = 2.1035438562418962131397786700603e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0867 y[1] (analytic) = 2.0037607999081205423644874432612 y[1] (numeric) = 2.0037607999081205423645296418595 absolute error = 4.21985983e-23 relative error = 2.1059698493919510590080784726770e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0868 y[1] (analytic) = 2.0037694857929281825616075104541 y[1] (numeric) = 2.0037694857929281825616497578464 absolute error = 4.22473923e-23 relative error = 2.1083958309347112977201911408192e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0869 y[1] (analytic) = 2.0037781817154306890527551209924 y[1] (numeric) = 2.0037781817154306890527974171791 absolute error = 4.22961867e-23 relative error = 2.1108218008337786689183997522158e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 2.0037868876757150210630278058084 y[1] (numeric) = 2.00378688767571502106307015079 absolute error = 4.23449816e-23 relative error = 2.1132477640433060397645376170854e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0871 y[1] (analytic) = 2.003795603673868238195341434674 y[1] (numeric) = 2.0037956036738682381953838284509 absolute error = 4.23937769e-23 relative error = 2.1156737155363019731685478827803e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0872 y[1] (analytic) = 2.0038043297099775004313008122302 y[1] (numeric) = 2.0038043297099775004313432548028 absolute error = 4.24425726e-23 relative error = 2.1180996552763695027841629488923e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0873 y[1] (analytic) = 2.0038130657841300681320712778042 y[1] (numeric) = 2.003813065784130068132113769173 absolute error = 4.24913688e-23 relative error = 2.1205255882175975961286262369482e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0874 y[1] (analytic) = 2.0038218118964133020392513090218 y[1] (numeric) = 2.0038218118964133020392938491871 absolute error = 4.25401653e-23 relative error = 2.1229515043425974725669139025177e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0875 y[1] (analytic) = 2.0038305680469146632757461292237 y[1] (numeric) = 2.003830568046914663275788718186 absolute error = 4.25889623e-23 relative error = 2.1253774135959226640100197708459e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.3MB, time=9.30 NO POLE x[1] = 0.0876 y[1] (analytic) = 2.0038393342357217133466423186957 y[1] (numeric) = 2.0038393342357217133466849564555 absolute error = 4.26377598e-23 relative error = 2.1278033159411125506440897458050e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0877 y[1] (analytic) = 2.0038481104629221141400834297204 y[1] (numeric) = 2.0038481104629221141401261162779 absolute error = 4.26865575e-23 relative error = 2.1302291963705122324931262071322e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0878 y[1] (analytic) = 2.0038568967286036279281466054586 y[1] (numeric) = 2.0038568967286036279281893408144 absolute error = 4.27353558e-23 relative error = 2.1326550748093639194555161220572e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0879 y[1] (analytic) = 2.0038656930328541173677202026719 y[1] (numeric) = 2.0038656930328541173677629868263 absolute error = 4.27841544e-23 relative error = 2.1350809362500792114368804465227e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 2.0038744993757615455013824182913 y[1] (numeric) = 2.0038744993757615455014252512448 absolute error = 4.28329535e-23 relative error = 2.1375067906369954483015469185751e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0881 y[1] (analytic) = 2.0038833157574139757582809198444 y[1] (numeric) = 2.0038833157574139757583238015975 absolute error = 4.28817531e-23 relative error = 2.1399326379336538928404448188402e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0882 y[1] (analytic) = 2.0038921421778995719550134797474 y[1] (numeric) = 2.0038921421778995719550564103004 absolute error = 4.29305530e-23 relative error = 2.1423584681230190409852490563214e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0883 y[1] (analytic) = 2.0039009786373065982965096134715 y[1] (numeric) = 2.003900978637306598296552592825 absolute error = 4.29793535e-23 relative error = 2.1447842961395644451586871213284e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0884 y[1] (analytic) = 2.0039098251357234193769132215936 y[1] (numeric) = 2.0039098251357234193769562497479 absolute error = 4.30281543e-23 relative error = 2.1472101069760328672277182878450e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0885 y[1] (analytic) = 2.0039186816732385001804662357379 y[1] (numeric) = 2.0039186816732385001805093126934 absolute error = 4.30769555e-23 relative error = 2.1496359055863217171081337140190e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0886 y[1] (analytic) = 2.0039275482499404060823932684191 y[1] (numeric) = 2.0039275482499404060824363941763 absolute error = 4.31257572e-23 relative error = 2.1520616969242407089043076166772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0887 y[1] (analytic) = 2.0039364248659178028497872667958 y[1] (numeric) = 2.0039364248659178028498304413551 absolute error = 4.31745593e-23 relative error = 2.1544874759631550758950628765812e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0888 y[1] (analytic) = 2.0039453115212594566424961703417 y[1] (numeric) = 2.0039453115212594566425393937036 absolute error = 4.32233619e-23 relative error = 2.1569132476568311761185574615084e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0889 y[1] (analytic) = 2.0039542082160542340140105724451 y[1] (numeric) = 2.00395420821605423401405384461 absolute error = 4.32721649e-23 relative error = 2.1593390069786792577600891083047e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 2.0039631149503911019123523859445 y[1] (numeric) = 2.0039631149503911019123957069128 absolute error = 4.33209683e-23 relative error = 2.1617647538923104217740615717501e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0891 y[1] (analytic) = 2.0039720317243591276809645126095 y[1] (numeric) = 2.0039720317243591276810078823816 absolute error = 4.33697721e-23 relative error = 2.1641904883613362494654207540099e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0892 y[1] (analytic) = 2.003980958538047479059601516576 y[1] (numeric) = 2.0039809585380474790596449351523 absolute error = 4.34185763e-23 relative error = 2.1666162103493688036989095951048e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0893 y[1] (analytic) = 2.0039898953915454241852213017443 y[1] (numeric) = 2.0039898953915454241852647691254 absolute error = 4.34673811e-23 relative error = 2.1690419298001108720764705171182e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0894 y[1] (analytic) = 2.0039988422849423315928777931499 y[1] (numeric) = 2.0039988422849423315929213093362 absolute error = 4.35161863e-23 relative error = 2.1714676366969961296120758146571e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0895 y[1] (analytic) = 2.0040077992183276702166146223144 y[1] (numeric) = 2.0040077992183276702166581873063 absolute error = 4.35649919e-23 relative error = 2.1738933310036379423005129151630e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0896 y[1] (analytic) = 2.0040167661917910093903598165867 y[1] (numeric) = 2.0040167661917910093904034303846 absolute error = 4.36137979e-23 relative error = 2.1763190126836501625365999791734e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0897 y[1] (analytic) = 2.0040257432054220188488214924831 y[1] (numeric) = 2.0040257432054220188488651550875 absolute error = 4.36626044e-23 relative error = 2.1787446866906029898758008496733e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=152.5MB, alloc=4.3MB, time=9.54 x[1] = 0.0898 y[1] (analytic) = 2.0040347302593104687283845530352 y[1] (numeric) = 2.0040347302593104687284282644465 absolute error = 4.37114113e-23 relative error = 2.1811703479981106388730879320129e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0899 y[1] (analytic) = 2.0040437273535462295680083891544 y[1] (numeric) = 2.004043727353546229568052149373 absolute error = 4.37602186e-23 relative error = 2.1835959965697883539808378380490e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 2.0040527344882192723101255850222 y[1] (numeric) = 2.0040527344882192723101693940486 absolute error = 4.38090264e-23 relative error = 2.1860216373591405239710279857755e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0901 y[1] (analytic) = 2.0040617516634196683015416275155 y[1] (numeric) = 2.0040617516634196683015854853501 absolute error = 4.38578346e-23 relative error = 2.1884472653398498203924959669883e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0902 y[1] (analytic) = 2.0040707788792375892943356196751 y[1] (numeric) = 2.0040707788792375892943795263183 absolute error = 4.39066432e-23 relative error = 2.1908728804755328906454197900762e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0903 y[1] (analytic) = 2.0040798161357633074467619982274 y[1] (numeric) = 2.0040798161357633074468059536797 absolute error = 4.39554523e-23 relative error = 2.1932984877196281004255181746680e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0904 y[1] (analytic) = 2.0040888634330871953241532551678 y[1] (numeric) = 2.0040888634330871953241972594297 absolute error = 4.40042619e-23 relative error = 2.1957240870356855096400123987241e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0905 y[1] (analytic) = 2.0040979207712997258998236634147 y[1] (numeric) = 2.0040979207712997258998677164865 absolute error = 4.40530718e-23 relative error = 2.1981496684077032340168040393759e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0906 y[1] (analytic) = 2.004106988150491472555974006543 y[1] (numeric) = 2.0041069881504914725560181084253 absolute error = 4.41018823e-23 relative error = 2.2005752467686281979291034049464e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0907 y[1] (analytic) = 2.0041160655707531090845973126078 y[1] (numeric) = 2.0041160655707531090846414633009 absolute error = 4.41506931e-23 relative error = 2.2030008071127509473981089689410e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0908 y[1] (analytic) = 2.004125153032175409688385592064 y[1] (numeric) = 2.0041251530321754096884297915684 absolute error = 4.41995044e-23 relative error = 2.2054263593831754594765477761134e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0909 y[1] (analytic) = 2.0041342505348492489816375797947 y[1] (numeric) = 2.0041342505348492489816818281109 absolute error = 4.42483162e-23 relative error = 2.2078519035434537718853439162795e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 2.0041433580788656019911674812549 y[1] (numeric) = 2.0041433580788656019912117783832 absolute error = 4.42971283e-23 relative error = 2.2102774295778122374960641657230e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0911 y[1] (analytic) = 2.0041524756643155441572147227398 y[1] (numeric) = 2.0041524756643155441572590686808 absolute error = 4.43459410e-23 relative error = 2.2127029524188607626301431558709e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0912 y[1] (analytic) = 2.0041616032912902513343547057889 y[1] (numeric) = 2.0041616032912902513343991005429 absolute error = 4.43947540e-23 relative error = 2.2151284570612316411117035502581e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0913 y[1] (analytic) = 2.0041707409598809997924105657316 y[1] (numeric) = 2.0041707409598809997924550092991 absolute error = 4.44435675e-23 relative error = 2.2175539534478045987593395583623e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0914 y[1] (analytic) = 2.0041798886701791662173659343868 y[1] (numeric) = 2.0041798886701791662174104267682 absolute error = 4.44923814e-23 relative error = 2.2199794365525616092758168826541e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0915 y[1] (analytic) = 2.0041890464222762277122787069232 y[1] (numeric) = 2.004189046422276227712323248119 absolute error = 4.45411958e-23 relative error = 2.2224049113286747489761931238453e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0916 y[1] (analytic) = 2.0041982142162637617981958128908 y[1] (numeric) = 2.0041982142162637617982404029014 absolute error = 4.45900106e-23 relative error = 2.2248303727501724109540422497788e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0917 y[1] (analytic) = 2.0042073920522334464150689914319 y[1] (numeric) = 2.0042073920522334464151136302578 absolute error = 4.46388259e-23 relative error = 2.2272558257701819474039655490787e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0918 y[1] (analytic) = 2.0042165799302770599226715706818 y[1] (numeric) = 2.0042165799302770599227162583234 absolute error = 4.46876416e-23 relative error = 2.2296812653627782748191968444943e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0919 y[1] (analytic) = 2.0042257778504864811015162513669 y[1] (numeric) = 2.0042257778504864811015609878247 absolute error = 4.47364578e-23 relative error = 2.2321066964810439269521014462446e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 2.0042349858129536891537738946108 y[1] (numeric) = 2.0042349858129536891538186798852 absolute error = 4.47852744e-23 relative error = 2.2345321140991004477005248332407e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.3MB, time=9.77 NO POLE x[1] = 0.0921 y[1] (analytic) = 2.0042442038177707637041933139565 y[1] (numeric) = 2.004244203817770763704238148048 absolute error = 4.48340915e-23 relative error = 2.2369575231699854580562008899299e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0922 y[1] (analytic) = 2.0042534318650298848010220716152 y[1] (numeric) = 2.0042534318650298848010669545242 absolute error = 4.48829090e-23 relative error = 2.2393829186678672333226297607772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0923 y[1] (analytic) = 2.0042626699548233329169282789489 y[1] (numeric) = 2.0042626699548233329169732106759 absolute error = 4.49317270e-23 relative error = 2.2418083055457383874159093880673e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0924 y[1] (analytic) = 2.0042719180872434889499234011983 y[1] (numeric) = 2.0042719180872434889499683817438 absolute error = 4.49805455e-23 relative error = 2.2442336837671569988085888801104e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0925 y[1] (analytic) = 2.0042811762623828342242860664637 y[1] (numeric) = 2.004281176262382834224331095828 absolute error = 4.50293643e-23 relative error = 2.2466590433170416767307161122849e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0926 y[1] (analytic) = 2.0042904444803339504914868789482 y[1] (numeric) = 2.0042904444803339504915319571318 absolute error = 4.50781836e-23 relative error = 2.2490843941376833745833566581986e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0927 y[1] (analytic) = 2.0042997227411895199311142364733 y[1] (numeric) = 2.0042997227411895199311593634767 absolute error = 4.51270034e-23 relative error = 2.2515097361926414414336512240244e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0928 y[1] (analytic) = 2.0043090110450423251518011522759 y[1] (numeric) = 2.0043090110450423251518463280995 absolute error = 4.51758236e-23 relative error = 2.2539350644562249707690990501933e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0929 y[1] (analytic) = 2.0043183093919852491921530810949 y[1] (numeric) = 2.0043183093919852491921983057392 absolute error = 4.52246443e-23 relative error = 2.2563603838812909894228731336936e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 2.0043276177821112755216767495584 y[1] (numeric) = 2.0043276177821112755217220230238 absolute error = 4.52734654e-23 relative error = 2.2587856894421957382530314533595e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0931 y[1] (analytic) = 2.0043369362155134880417099908794 y[1] (numeric) = 2.0043369362155134880417553131664 absolute error = 4.53222870e-23 relative error = 2.2612109860917508597911365310354e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0932 y[1] (analytic) = 2.00434626469228507108635258387 y[1] (numeric) = 2.004346264692285071086397954979 absolute error = 4.53711090e-23 relative error = 2.2636362688043598462471691058956e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0933 y[1] (analytic) = 2.0043556032125193094233980962829 y[1] (numeric) = 2.0043556032125193094234435162145 absolute error = 4.54199316e-23 relative error = 2.2660615475219235160886388914539e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0934 y[1] (analytic) = 2.0043649517763095882552667324908 y[1] (numeric) = 2.0043649517763095882553122012453 absolute error = 4.54687545e-23 relative error = 2.2684868072406001379479046154276e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0935 y[1] (analytic) = 2.0043743103837493932199391855104 y[1] (numeric) = 2.0043743103837493932199847030883 absolute error = 4.55175779e-23 relative error = 2.2709120579022682024517472365754e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0936 y[1] (analytic) = 2.0043836790349323103918914933839 y[1] (numeric) = 2.0043836790349323103919370597857 absolute error = 4.55664018e-23 relative error = 2.2733372994704907871231136834243e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0937 y[1] (analytic) = 2.0043930577299520262830308999241 y[1] (numeric) = 2.0043930577299520262830765151502 absolute error = 4.56152261e-23 relative error = 2.2757625269197899302720986649755e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0938 y[1] (analytic) = 2.0044024464689023278436327198342 y[1] (numeric) = 2.004402446468902327843678383885 absolute error = 4.56640508e-23 relative error = 2.2781877402137995920949520604334e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0939 y[1] (analytic) = 2.0044118452518771024632782082115 y[1] (numeric) = 2.0044118452518771024633239210875 absolute error = 4.57128760e-23 relative error = 2.2806129443051489349725796517228e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 2.0044212540789703379717934344438 y[1] (numeric) = 2.0044212540789703379718391961455 absolute error = 4.57617017e-23 relative error = 2.2830381391574027415238361542734e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0941 y[1] (analytic) = 2.004430672950276122640189160509 y[1] (numeric) = 2.0044306729502761226402349710367 absolute error = 4.58105277e-23 relative error = 2.2854633147562305825746489005060e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0942 y[1] (analytic) = 2.004440101865888645181601723685 y[1] (numeric) = 2.0044401018658886451816475830394 absolute error = 4.58593544e-23 relative error = 2.2878884910210361702313676823081e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0943 y[1] (analytic) = 2.004449540825902194752234923683 y[1] (numeric) = 2.0044495408259021947522808318644 absolute error = 4.59081814e-23 relative error = 2.2903136479596412945766321057766e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.3MB, time=10.03 NO POLE x[1] = 0.0944 y[1] (analytic) = 2.0044589898304111609523029142092 y[1] (numeric) = 2.0044589898304111609523488712182 absolute error = 4.59570090e-23 relative error = 2.2927388005023853899933413525627e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0945 y[1] (analytic) = 2.0044684488795100338269740989688 y[1] (numeric) = 2.0044684488795100338270201048057 absolute error = 4.60058369e-23 relative error = 2.2951639336462033904164385828025e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0946 y[1] (analytic) = 2.0044779179732934038673160321176 y[1] (numeric) = 2.0044779179732934038673620867829 absolute error = 4.60546653e-23 relative error = 2.2975890573324643544579333180207e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0947 y[1] (analytic) = 2.0044873971118559620112413231738 y[1] (numeric) = 2.004487397111855962011287426668 absolute error = 4.61034942e-23 relative error = 2.3000141715247360580958606240711e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0948 y[1] (analytic) = 2.0044968862952924996444545463981 y[1] (numeric) = 2.0044968862952924996445006987217 absolute error = 4.61523236e-23 relative error = 2.3024392761865866779177895765778e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0949 y[1] (analytic) = 2.0045063855236979086014001546514 y[1] (numeric) = 2.0045063855236979086014463558048 absolute error = 4.62011534e-23 relative error = 2.3048643662928254288212485894267e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 2.0045158947971671811662113977398 y[1] (numeric) = 2.0045158947971671811662576477234 absolute error = 4.62499836e-23 relative error = 2.3072894418070922911525085115349e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0951 y[1] (analytic) = 2.004525414115795410073660245257 y[1] (numeric) = 2.0045254141157954100737065440713 absolute error = 4.62988143e-23 relative error = 2.3097145076817398042876151096479e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0952 y[1] (analytic) = 2.0045349434796777885101083139328 y[1] (numeric) = 2.0045349434796777885101546615783 absolute error = 4.63476455e-23 relative error = 2.3121395638803379080187744081050e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0953 y[1] (analytic) = 2.0045444828889096101144587994974 y[1] (numeric) = 2.0045444828889096101145051959745 absolute error = 4.63964771e-23 relative error = 2.3145646053777923991456231350040e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0954 y[1] (analytic) = 2.0045540323435862689791094130712 y[1] (numeric) = 2.0045540323435862689791558583804 absolute error = 4.64453092e-23 relative error = 2.3169896371263861124579975340843e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0955 y[1] (analytic) = 2.0045635918438032596509063220897 y[1] (numeric) = 2.0045635918438032596509528162315 absolute error = 4.64941418e-23 relative error = 2.3194146590896902856987108165419e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0956 y[1] (analytic) = 2.0045731613896561771320990957728 y[1] (numeric) = 2.0045731613896561771321456387476 absolute error = 4.65429748e-23 relative error = 2.3218396662426833877669616850972e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0957 y[1] (analytic) = 2.0045827409812407168812966551478 y[1] (numeric) = 2.0045827409812407168813432469561 absolute error = 4.65918083e-23 relative error = 2.3242646635375783367906883535511e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0958 y[1] (analytic) = 2.0045923306186526748144242276367 y[1] (numeric) = 2.0045923306186526748144708682789 absolute error = 4.66406422e-23 relative error = 2.3266896459494022044224705976401e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0959 y[1] (analytic) = 2.0046019303019879473056813062157 y[1] (numeric) = 2.0046019303019879473057279956924 absolute error = 4.66894767e-23 relative error = 2.3291146234188427903160298484916e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 2.0046115400313425311885006131587 y[1] (numeric) = 2.0046115400313425311885473514703 absolute error = 4.67383116e-23 relative error = 2.3315395859324064590642283467550e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0961 y[1] (analytic) = 2.0046211598068125237565080683719 y[1] (numeric) = 2.0046211598068125237565548555188 absolute error = 4.67871469e-23 relative error = 2.3339645334537388190892621815013e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0962 y[1] (analytic) = 2.0046307896284941227644837623308 y[1] (numeric) = 2.0046307896284941227645305983136 absolute error = 4.68359828e-23 relative error = 2.3363894759233855835451601564613e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0963 y[1] (analytic) = 2.0046404294964836264293239336293 y[1] (numeric) = 2.0046404294964836264293708184484 absolute error = 4.68848191e-23 relative error = 2.3388144033279980025238631385103e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0964 y[1] (analytic) = 2.0046500794108774334310039511491 y[1] (numeric) = 2.004650079410877433431050884805 absolute error = 4.69336559e-23 relative error = 2.3412393206196250058342781281019e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0965 y[1] (analytic) = 2.0046597393717720429135423008602 y[1] (numeric) = 2.0046597393717720429135892833534 absolute error = 4.69824932e-23 relative error = 2.3436642277618422116380870859722e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0966 y[1] (analytic) = 2.0046694093792640544859655772623 y[1] (numeric) = 2.0046694093792640544860126085932 absolute error = 4.70313309e-23 relative error = 2.3460891197298719932059574864183e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.3MB, time=10.28 NO POLE x[1] = 0.0967 y[1] (analytic) = 2.0046790894334501682232744794753 y[1] (numeric) = 2.0046790894334501682233215596444 absolute error = 4.70801691e-23 relative error = 2.3485140014756926568537900924602e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0968 y[1] (analytic) = 2.0046887795344271846674108119906 y[1] (numeric) = 2.0046887795344271846674579409983 absolute error = 4.71290077e-23 relative error = 2.3509388679745756981977688354199e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0969 y[1] (analytic) = 2.004698479682292004828225490091 y[1] (numeric) = 2.0046984796822920048282726679378 absolute error = 4.71778468e-23 relative error = 2.3533637241784522481997976006532e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 2.0047081898771416301844475499503 y[1] (numeric) = 2.0047081898771416301844947766367 absolute error = 4.72266864e-23 relative error = 2.3557885700509001977722079268725e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0971 y[1] (analytic) = 2.0047179101190731626846541634211 y[1] (numeric) = 2.0047179101190731626847014389476 absolute error = 4.72755265e-23 relative error = 2.3582134055554978662884085652868e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0972 y[1] (analytic) = 2.0047276404081838047482416575215 y[1] (numeric) = 2.0047276404081838047482889818886 absolute error = 4.73243671e-23 relative error = 2.3606382306558240027940895159556e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0973 y[1] (analytic) = 2.0047373807445708592663975386302 y[1] (numeric) = 2.0047373807445708592664449118383 absolute error = 4.73732081e-23 relative error = 2.3630630403272732519023795207191e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0974 y[1] (analytic) = 2.0047471311283317296030735213985 y[1] (numeric) = 2.0047471311283317296031209434481 absolute error = 4.74220496e-23 relative error = 2.3654878395216582824974487909389e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0975 y[1] (analytic) = 2.0047568915595639195959595623914 y[1] (numeric) = 2.0047568915595639195960070332829 absolute error = 4.74708915e-23 relative error = 2.3679126232144232251916408512174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0976 y[1] (analytic) = 2.0047666620383650335574588984644 y[1] (numeric) = 2.0047666620383650335575064181984 absolute error = 4.75197340e-23 relative error = 2.3703374013454449224350090895556e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0977 y[1] (analytic) = 2.0047764425648327762756640898895 y[1] (numeric) = 2.0047764425648327762757116584664 absolute error = 4.75685769e-23 relative error = 2.3727621639020567458969317705446e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0978 y[1] (analytic) = 2.0047862331390649530153340682359 y[1] (numeric) = 2.0047862331390649530153816856562 absolute error = 4.76174203e-23 relative error = 2.3751869158359761856697834465777e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0979 y[1] (analytic) = 2.0047960337611594695188721890189 y[1] (numeric) = 2.0047960337611594695189198552831 absolute error = 4.76662642e-23 relative error = 2.3776116571107851809838792275320e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 2.0048058444312143320073052891247 y[1] (numeric) = 2.0048058444312143320073530042333 absolute error = 4.77151086e-23 relative error = 2.3800363876900661104263761639440e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0981 y[1] (analytic) = 2.0048156651493276471812637490215 y[1] (numeric) = 2.0048156651493276471813115129749 absolute error = 4.77639534e-23 relative error = 2.3824611025494120373682419165855e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0982 y[1] (analytic) = 2.0048254959155976222219625597664 y[1] (numeric) = 2.0048254959155976222220103725652 absolute error = 4.78127988e-23 relative error = 2.3848858116284101931785002165416e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0983 y[1] (analytic) = 2.0048353367301225647921833948188 y[1] (numeric) = 2.0048353367301225647922312564634 absolute error = 4.78616446e-23 relative error = 2.3873105049146892785993695805329e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0984 y[1] (analytic) = 2.0048451875930008830372576866687 y[1] (numeric) = 2.0048451875930008830373055971595 absolute error = 4.79104908e-23 relative error = 2.3897351823719069669134792548850e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0985 y[1] (analytic) = 2.0048550485043310855860507082906 y[1] (numeric) = 2.0048550485043310855860986676282 absolute error = 4.79593376e-23 relative error = 2.3921598539395050688808305843679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0986 y[1] (analytic) = 2.0048649194642117815519466594338 y[1] (numeric) = 2.0048649194642117815519946676186 absolute error = 4.80081848e-23 relative error = 2.3945845096052606717886550120094e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0987 y[1] (analytic) = 2.0048748004727416805338347577562 y[1] (numeric) = 2.0048748004727416805338828147887 absolute error = 4.80570325e-23 relative error = 2.3970091543206757170729352783224e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0988 y[1] (analytic) = 2.0048846915300195926170963348144 y[1] (numeric) = 2.0048846915300195926171444406951 absolute error = 4.81058807e-23 relative error = 2.3994337880493362903065802836767e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=167.8MB, alloc=4.3MB, time=10.54 x[1] = 0.0989 y[1] (analytic) = 2.0048945926361444283745929369184 y[1] (numeric) = 2.0048945926361444283746410916478 absolute error = 4.81547294e-23 relative error = 2.4018584107548289273123347861523e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 2.0049045037912151988676554308609 y[1] (numeric) = 2.0049045037912151988677036344395 absolute error = 4.82035786e-23 relative error = 2.4042830224007406153733748968232e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0991 y[1] (analytic) = 2.0049144249953310156470741145315 y[1] (numeric) = 2.0049144249953310156471223669597 absolute error = 4.82524282e-23 relative error = 2.4067076179629147414660036568167e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0992 y[1] (analytic) = 2.0049243562485910907540898324253 y[1] (numeric) = 2.0049243562485910907541381337037 absolute error = 4.83012784e-23 relative error = 2.4091322073804520118246721958292e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0993 y[1] (analytic) = 2.0049342975510947367213860960565 y[1] (numeric) = 2.0049342975510947367214344461854 absolute error = 4.83501289e-23 relative error = 2.4115567756537828100370931043501e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0994 y[1] (analytic) = 2.0049442489029413665740822092854 y[1] (numeric) = 2.0049442489029413665741306082654 absolute error = 4.83989800e-23 relative error = 2.4139813377096540552004984811347e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0995 y[1] (analytic) = 2.0049542103042304938307273985712 y[1] (numeric) = 2.0049542103042304938307758464027 absolute error = 4.84478315e-23 relative error = 2.4164058835362906591050172342175e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0996 y[1] (analytic) = 2.0049641817550617325042959481577 y[1] (numeric) = 2.0049641817550617325043444448413 absolute error = 4.84966836e-23 relative error = 2.4188304230725973802924040759518e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0997 y[1] (analytic) = 2.0049741632555347971031833402043 y[1] (numeric) = 2.0049741632555347971032318857404 absolute error = 4.85455361e-23 relative error = 2.4212549463068991720270798559565e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0998 y[1] (analytic) = 2.0049841548057495026322033998704 y[1] (numeric) = 2.0049841548057495026322519942595 absolute error = 4.85943891e-23 relative error = 2.4236794581904319040434527436610e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0999 y[1] (analytic) = 2.0049941564058057645935864453648 y[1] (numeric) = 2.0049941564058057645936350886073 absolute error = 4.86432425e-23 relative error = 2.4261039536992411214217805473441e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 2.0050041680558035989879784429683 y[1] (numeric) = 2.0050041680558035989880271350649 absolute error = 4.86920966e-23 relative error = 2.4285284477595556661058911077677e-21 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sinh ( x ) ; Iterations = 1000 Total Elapsed Time = 10 Seconds Elapsed Time(since restart) = 10 Seconds Expected Time Remaining = 17 Minutes 30 Seconds Optimized Time Remaining = 17 Minutes 30 Seconds Time to Timeout = 14 Minutes 49 Seconds Percent Done = 1.001 % > quit memory used=169.8MB, alloc=4.3MB, time=10.66