|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_curr_iter_when_opt, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_max_minutes, > glob_start, > glob_last_good_h, > glob_hmax, > glob_reached_optimal_h, > years_in_century, > glob_html_log, > days_in_year, > glob_optimal_expect_sec, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_max_opt_iter, > glob_log10normmin, > glob_max_sec, > glob_warned2, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_not_yet_start_msg, > glob_not_yet_finished, > hours_in_day, > djd_debug, > glob_log10relerr, > glob_log10abserr, > glob_subiter_method, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_relerr, > glob_h, > glob_disp_incr, > glob_clock_sec, > glob_warned, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > min_in_hour, > glob_percent_done, > glob_normmax, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_almost_1, > sec_in_min, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_type_pole, > array_last_rel_error, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_norms, > array_y_init, > array_y, > array_x, > array_pole, > array_real_pole, > array_y_higher_work2, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher, > array_complex_pole, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt, glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start, glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century, glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug, glob_log10relerr, glob_log10abserr, glob_subiter_method, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr, glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour, glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2, array_const_1, array_const_0D0, array_type_pole, array_last_rel_error, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole, array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher, array_complex_pole, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_curr_iter_when_opt, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_max_minutes, > glob_start, > glob_last_good_h, > glob_hmax, > glob_reached_optimal_h, > years_in_century, > glob_html_log, > days_in_year, > glob_optimal_expect_sec, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_max_opt_iter, > glob_log10normmin, > glob_max_sec, > glob_warned2, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_not_yet_start_msg, > glob_not_yet_finished, > hours_in_day, > djd_debug, > glob_log10relerr, > glob_log10abserr, > glob_subiter_method, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_relerr, > glob_h, > glob_disp_incr, > glob_clock_sec, > glob_warned, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > min_in_hour, > glob_percent_done, > glob_normmax, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_almost_1, > sec_in_min, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_type_pole, > array_last_rel_error, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_norms, > array_y_init, > array_y, > array_x, > array_pole, > array_real_pole, > array_y_higher_work2, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher, > array_complex_pole, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt, glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start, glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century, glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug, glob_log10relerr, glob_log10abserr, glob_subiter_method, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr, glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour, glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2, array_const_1, array_const_0D0, array_type_pole, array_last_rel_error, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole, array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher, array_complex_pole, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_curr_iter_when_opt, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_max_minutes, > glob_start, > glob_last_good_h, > glob_hmax, > glob_reached_optimal_h, > years_in_century, > glob_html_log, > days_in_year, > glob_optimal_expect_sec, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_max_opt_iter, > glob_log10normmin, > glob_max_sec, > glob_warned2, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_not_yet_start_msg, > glob_not_yet_finished, > hours_in_day, > djd_debug, > glob_log10relerr, > glob_log10abserr, > glob_subiter_method, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_relerr, > glob_h, > glob_disp_incr, > glob_clock_sec, > glob_warned, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > min_in_hour, > glob_percent_done, > glob_normmax, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_almost_1, > sec_in_min, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_type_pole, > array_last_rel_error, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_norms, > array_y_init, > array_y, > array_x, > array_pole, > array_real_pole, > array_y_higher_work2, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher, > array_complex_pole, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt, glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start, glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century, glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug, glob_log10relerr, glob_log10abserr, glob_subiter_method, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr, glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour, glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2, array_const_1, array_const_0D0, array_type_pole, array_last_rel_error, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole, array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher, array_complex_pole, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_curr_iter_when_opt, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_max_minutes, > glob_start, > glob_last_good_h, > glob_hmax, > glob_reached_optimal_h, > years_in_century, > glob_html_log, > days_in_year, > glob_optimal_expect_sec, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_max_opt_iter, > glob_log10normmin, > glob_max_sec, > glob_warned2, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_not_yet_start_msg, > glob_not_yet_finished, > hours_in_day, > djd_debug, > glob_log10relerr, > glob_log10abserr, > glob_subiter_method, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_relerr, > glob_h, > glob_disp_incr, > glob_clock_sec, > glob_warned, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > min_in_hour, > glob_percent_done, > glob_normmax, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_almost_1, > sec_in_min, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_type_pole, > array_last_rel_error, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_norms, > array_y_init, > array_y, > array_x, > array_pole, > array_real_pole, > array_y_higher_work2, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher, > array_complex_pole, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt, glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start, glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century, glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug, glob_log10relerr, glob_log10abserr, glob_subiter_method, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr, glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour, glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2, array_const_1, array_const_0D0, array_type_pole, array_last_rel_error, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole, array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher, array_complex_pole, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_curr_iter_when_opt, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_max_minutes, > glob_start, > glob_last_good_h, > glob_hmax, > glob_reached_optimal_h, > years_in_century, > glob_html_log, > days_in_year, > glob_optimal_expect_sec, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_max_opt_iter, > glob_log10normmin, > glob_max_sec, > glob_warned2, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_not_yet_start_msg, > glob_not_yet_finished, > hours_in_day, > djd_debug, > glob_log10relerr, > glob_log10abserr, > glob_subiter_method, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_relerr, > glob_h, > glob_disp_incr, > glob_clock_sec, > glob_warned, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > min_in_hour, > glob_percent_done, > glob_normmax, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_almost_1, > sec_in_min, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_type_pole, > array_last_rel_error, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_norms, > array_y_init, > array_y, > array_x, > array_pole, > array_real_pole, > array_y_higher_work2, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher, > array_complex_pole, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt, glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start, glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century, glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug, glob_log10relerr, glob_log10abserr, glob_subiter_method, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr, glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour, glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2, array_const_1, array_const_0D0, array_type_pole, array_last_rel_error, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole, array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher, array_complex_pole, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_curr_iter_when_opt, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_max_minutes, > glob_start, > glob_last_good_h, > glob_hmax, > glob_reached_optimal_h, > years_in_century, > glob_html_log, > days_in_year, > glob_optimal_expect_sec, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_max_opt_iter, > glob_log10normmin, > glob_max_sec, > glob_warned2, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_not_yet_start_msg, > glob_not_yet_finished, > hours_in_day, > djd_debug, > glob_log10relerr, > glob_log10abserr, > glob_subiter_method, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_relerr, > glob_h, > glob_disp_incr, > glob_clock_sec, > glob_warned, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > min_in_hour, > glob_percent_done, > glob_normmax, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_almost_1, > sec_in_min, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_type_pole, > array_last_rel_error, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_norms, > array_y_init, > array_y, > array_x, > array_pole, > array_real_pole, > array_y_higher_work2, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher, > array_complex_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre exp $eq_no = 1 i = 1 > array_tmp1[1] := exp(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 exp $eq_no = 1 i = 2 > array_tmp1[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 exp $eq_no = 1 i = 3 > array_tmp1[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 exp $eq_no = 1 i = 4 > array_tmp1[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 exp $eq_no = 1 i = 5 > array_tmp1[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 exp $eq_no = 1 > array_tmp1[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 DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt, glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start, glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century, glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug, glob_log10relerr, glob_log10abserr, glob_subiter_method, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr, glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour, glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2, array_const_1, array_const_0D0, array_type_pole, array_last_rel_error, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole, array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher, array_complex_pole, glob_last; array_tmp1[1] := exp(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, 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, 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, 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, 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, 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 + exp(x) > end; exact_soln_y := proc(x) 1.0 + exp(x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > INFO, > glob_max_terms, > DEBUGL, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_curr_iter_when_opt, > glob_max_hours, > glob_abserr, > glob_large_float, > glob_max_minutes, > glob_start, > glob_last_good_h, > glob_hmax, > glob_reached_optimal_h, > years_in_century, > glob_html_log, > days_in_year, > glob_optimal_expect_sec, > glob_initial_pass, > glob_clock_start_sec, > centuries_in_millinium, > glob_display_flag, > glob_max_opt_iter, > glob_log10normmin, > glob_max_sec, > glob_warned2, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_not_yet_start_msg, > glob_not_yet_finished, > hours_in_day, > djd_debug, > glob_log10relerr, > glob_log10abserr, > glob_subiter_method, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_small_float, > glob_relerr, > glob_h, > glob_disp_incr, > glob_clock_sec, > glob_warned, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > min_in_hour, > glob_percent_done, > glob_normmax, > glob_iter, > MAX_UNCHANGED, > glob_current_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmin, > glob_optimal_done, > glob_almost_1, > sec_in_min, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_type_pole, > array_last_rel_error, > array_m1, > array_tmp0, > array_tmp1, > array_tmp2, > array_1st_rel_error, > array_norms, > array_y_init, > array_y, > array_x, > array_pole, > array_real_pole, > array_y_higher_work2, > array_y_higher_work, > array_poles, > array_y_set_initial, > array_y_higher, > array_complex_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > INFO := 2; > glob_max_terms := 30; > DEBUGL := 3; > ALWAYS := 1; > glob_iolevel := 5; > glob_log10_abserr := 0.1e-10; > glob_hmin_init := 0.001; > glob_dump := false; > glob_curr_iter_when_opt := 0; > glob_max_hours := 0.0; > glob_abserr := 0.1e-10; > glob_large_float := 9.0e100; > glob_max_minutes := 0.0; > glob_start := 0; > glob_last_good_h := 0.1; > glob_hmax := 1.0; > glob_reached_optimal_h := false; > years_in_century := 100.0; > glob_html_log := true; > days_in_year := 365.0; > glob_optimal_expect_sec := 0.1; > glob_initial_pass := true; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > glob_display_flag := true; > glob_max_opt_iter := 10; > glob_log10normmin := 0.1; > glob_max_sec := 10000.0; > glob_warned2 := false; > glob_smallish_float := 0.1e-100; > glob_optimal_clock_start_sec := 0.0; > glob_max_iter := 1000; > glob_not_yet_start_msg := true; > glob_not_yet_finished := true; > hours_in_day := 24.0; > djd_debug := true; > glob_log10relerr := 0.0; > glob_log10abserr := 0.0; > glob_subiter_method := 3; > glob_orig_start_sec := 0.0; > glob_unchanged_h_cnt := 0; > glob_small_float := 0.1e-50; > glob_relerr := 0.1e-10; > glob_h := 0.1; > glob_disp_incr := 0.1; > glob_clock_sec := 0.0; > glob_warned := false; > glob_optimal_start := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_look_poles := false; > min_in_hour := 60.0; > glob_percent_done := 0.0; > glob_normmax := 0.0; > glob_iter := 0; > MAX_UNCHANGED := 10; > glob_current_iter := 0; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_dump_analytic := false; > glob_hmin := 0.00000000001; > glob_optimal_done := false; > glob_almost_1 := 0.9990; > sec_in_min := 60.0; > djd_debug2 := true; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/exppostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = exp ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 1.0;"); > 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 + exp(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 > max_terms := 30; > Digits := 32; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_type_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= 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_norms:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > 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_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_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_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 > ; > 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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 1.0; > 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 ) = exp ( 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,"2012-06-13T13:42:15-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"exp") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = exp ( 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,"exp diffeq.mxt") > ; > logitem_str(html_log_file,"exp maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel, glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt, glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start, glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century, glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass, glob_clock_start_sec, centuries_in_millinium, glob_display_flag, glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug, glob_log10relerr, glob_log10abserr, glob_subiter_method, glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr, glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour, glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED, glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic, glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2, array_const_1, array_const_0D0, array_type_pole, array_last_rel_error, array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error, array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole, array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial, array_y_higher, array_complex_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; INFO := 2; glob_max_terms := 30; DEBUGL := 3; ALWAYS := 1; glob_iolevel := 5; glob_log10_abserr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_dump := false; glob_curr_iter_when_opt := 0; glob_max_hours := 0.; glob_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_max_minutes := 0.; glob_start := 0; glob_last_good_h := 0.1; glob_hmax := 1.0; glob_reached_optimal_h := false; years_in_century := 100.0; glob_html_log := true; days_in_year := 365.0; glob_optimal_expect_sec := 0.1; glob_initial_pass := true; glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; glob_display_flag := true; glob_max_opt_iter := 10; glob_log10normmin := 0.1; glob_max_sec := 10000.0; glob_warned2 := false; glob_smallish_float := 0.1*10^(-100); glob_optimal_clock_start_sec := 0.; glob_max_iter := 1000; glob_not_yet_start_msg := true; glob_not_yet_finished := true; hours_in_day := 24.0; djd_debug := true; glob_log10relerr := 0.; glob_log10abserr := 0.; glob_subiter_method := 3; glob_orig_start_sec := 0.; glob_unchanged_h_cnt := 0; glob_small_float := 0.1*10^(-50); glob_relerr := 0.1*10^(-10); glob_h := 0.1; glob_disp_incr := 0.1; glob_clock_sec := 0.; glob_warned := false; glob_optimal_start := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_look_poles := false; min_in_hour := 60.0; glob_percent_done := 0.; glob_normmax := 0.; glob_iter := 0; MAX_UNCHANGED := 10; glob_current_iter := 0; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_dump_analytic := false; glob_hmin := 0.1*10^(-10); glob_optimal_done := false; glob_almost_1 := 0.9990; sec_in_min := 60.0; djd_debug2 := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/exppostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 1.0;"); 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 +\texp(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; max_terms := 30; Digits := 32; glob_max_terms := max_terms; glob_html_log := true; array_type_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := 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_norms := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); 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_last_rel_error[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_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; 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_pole[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[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; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 1.0; 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 ) = exp ( 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, "2012-06-13T13:42:15-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "exp"); logitem_str(html_log_file, "diff ( y , x , 1 ) = exp ( 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, "exp diffeq.mxt"); logitem_str(html_log_file, "exp 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/exppostode.ode################# diff ( y , x , 1 ) = exp ( x ) ; ! #BEGIN FIRST INPUT BLOCK max_terms := 30; Digits := 32; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 1.0; 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 + exp(x) end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 1 y[1] (analytic) = 3.7182818284590452353602874713527 y[1] (numeric) = 3.7182818284590452353602874713527 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0001 y[1] (analytic) = 3.718553670233753340476860330281 y[1] (numeric) = 3.7185536702337533404768604624223 absolute error = 1.321413e-25 relative error = 3.5535671048064614376381461241884e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0002 y[1] (analytic) = 3.718825539193998170585580520144 y[1] (numeric) = 3.7188255391939981705855807844399 absolute error = 2.642959e-25 relative error = 7.1069722742971784190449233196766e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0003 y[1] (analytic) = 3.7190974353424984152911619166985 y[1] (numeric) = 3.7190974353424984152911623131621 absolute error = 3.964636e-25 relative error = 1.0660210088405197950413569259573e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0004 y[1] (analytic) = 3.7193693586819730360808727682385 y[1] (numeric) = 3.719369358681973036080873296883 absolute error = 5.286445e-25 relative error = 1.4213283194528840904418162446224e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0005 y[1] (analytic) = 3.7196413092151412663517253104907 y[1] (numeric) = 3.7196413092151412663517259713294 absolute error = 6.608387e-25 relative error = 1.7766194239289151434980099269341e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0006 y[1] (analytic) = 3.7199132869447226114376681006077 y[1] (numeric) = 3.7199132869447226114376688936537 absolute error = 7.930460e-25 relative error = 2.1318937803825870527265940894989e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0007 y[1] (analytic) = 3.7201852918734368486367810705293 y[1] (numeric) = 3.7201852918734368486367819957959 absolute error = 9.252666e-25 relative error = 2.4871519223012889071992866085730e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0008 y[1] (analytic) = 3.7204573240040040272384732999867 y[1] (numeric) = 3.7204573240040040272384743574872 absolute error = 1.0575005e-24 relative error = 2.8423938454477536099861357601398e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0009 y[1] (analytic) = 3.7207293833391444685506835094191 y[1] (numeric) = 3.7207293833391444685506846991666 absolute error = 1.1897475e-24 relative error = 3.1976190080566107112888830564260e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.001 y[1] (analytic) = 3.7210014698815787659270832730755 y[1] (numeric) = 3.7210014698815787659270845950832 absolute error = 1.3220077e-24 relative error = 3.5528276747551863336654151816023e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0011 y[1] (analytic) = 3.7212735836340277847942829525741 y[1] (numeric) = 3.7212735836340277847942844068554 absolute error = 1.4542813e-24 relative error = 3.9080203788183037485333193709641e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0012 y[1] (analytic) = 3.7215457245992126626790403511916 y[1] (numeric) = 3.7215457245992126626790419377596 absolute error = 1.5865680e-24 relative error = 4.2631963098367238514840500710621e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0013 y[1] (analytic) = 3.7218178927798548092354720891528 y[1] (numeric) = 3.7218178927798548092354738080207 absolute error = 1.7188679e-24 relative error = 4.6183557323815329413065357578692e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0014 y[1] (analytic) = 3.7220900881786759062722677001948 y[1] (numeric) = 3.7220900881786759062722695513758 absolute error = 1.8511810e-24 relative error = 4.9734986422798683272350584717538e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0015 y[1] (analytic) = 3.7223623107983979077799064496764 y[1] (numeric) = 3.7223623107983979077799084331839 absolute error = 1.9835075e-24 relative error = 5.3286255726529845751235728651829e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0016 y[1] (analytic) = 3.7226345606417430399578768745059 y[1] (numeric) = 3.722634560641743039957878990353 absolute error = 2.1158471e-24 relative error = 5.6837357133310722191892415838760e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0017 y[1] (analytic) = 3.7229068377114338012418990451582 y[1] (numeric) = 3.7229068377114338012419012933582 absolute error = 2.2482000e-24 relative error = 6.0388295974175548525704732948227e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0018 y[1] (analytic) = 3.723179142010192962331149550055 y[1] (numeric) = 3.7231791420101929623311519306212 absolute error = 2.3805662e-24 relative error = 6.3939072206842598240336565106360e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=2.9MB, time=0.18 x[1] = 1.0019 y[1] (analytic) = 3.7234514735407435662154892025794 y[1] (numeric) = 3.7234514735407435662154917155249 absolute error = 2.5129455e-24 relative error = 6.7489680417678801726174852687932e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.002 y[1] (analytic) = 3.7237238323058089282026934709967 y[1] (numeric) = 3.7237238323058089282026961163348 absolute error = 2.6453381e-24 relative error = 7.1040125936566848824237437771029e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0021 y[1] (analytic) = 3.7239962183081126359456856315552 y[1] (numeric) = 3.7239962183081126359456884092991 absolute error = 2.7777439e-24 relative error = 7.4590406035964925187794556157825e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0022 y[1] (analytic) = 3.7242686315503785494697726450381 y[1] (numeric) = 3.7242686315503785494697755552011 absolute error = 2.9101630e-24 relative error = 7.8140523359307894162131731368020e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0023 y[1] (analytic) = 3.7245410720353308011998837570394 y[1] (numeric) = 3.7245410720353308011998867996347 absolute error = 3.0425953e-24 relative error = 8.1690475179464958807013602764940e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0024 y[1] (analytic) = 3.7248135397656937959878118222354 y[1] (numeric) = 3.7248135397656937959878149972763 absolute error = 3.1750409e-24 relative error = 8.5240264139496314953666548237691e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0025 y[1] (analytic) = 3.7250860347441922111394573529259 y[1] (numeric) = 3.7250860347441922111394606604256 absolute error = 3.3074997e-24 relative error = 8.8789887512682145285751910523650e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0026 y[1] (analytic) = 3.7253585569735509964420752921156 y[1] (numeric) = 3.7253585569735509964420787320874 absolute error = 3.4399718e-24 relative error = 9.2339347941708013085154069584456e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0027 y[1] (analytic) = 3.7256311064564953741915245114094 y[1] (numeric) = 3.7256311064564953741915280838665 absolute error = 3.5724571e-24 relative error = 9.5888642700265042872396801894202e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0028 y[1] (analytic) = 3.7259036831957508392195200339938 y[1] (numeric) = 3.7259036831957508392195237389494 absolute error = 3.7049556e-24 relative error = 9.9437771746751557863728680822559e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0029 y[1] (analytic) = 3.7261762871940431589208879829766 y[1] (numeric) = 3.726176287194043158920891820444 absolute error = 3.8374674e-24 relative error = 1.0298673772329122443508685006067e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.003 y[1] (analytic) = 3.726448918454098373280823255358 y[1] (numeric) = 3.7264489184540983732808272253505 absolute error = 3.9699925e-24 relative error = 1.0653554058771144124469845031648e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0031 y[1] (analytic) = 3.7267215769786427949021499219052 y[1] (numeric) = 3.7267215769786427949021540244361 absolute error = 4.1025309e-24 relative error = 1.1008418029784871434109011296561e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0032 y[1] (analytic) = 3.7269942627704030090325843532036 y[1] (numeric) = 3.726994262770403009032588588286 absolute error = 4.2350824e-24 relative error = 1.1363265144529408545738045228672e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0033 y[1] (analytic) = 3.7272669758321058735920010721561 y[1] (numeric) = 3.7272669758321058735920054398034 absolute error = 4.3676473e-24 relative error = 1.1718096203787308077525745412846e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0034 y[1] (analytic) = 3.7275397161664785191997013332053 y[1] (numeric) = 3.7275397161664785191997058334306 absolute error = 4.5002253e-24 relative error = 1.2072910398465656416478209120490e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0035 y[1] (analytic) = 3.7278124837762483492016844285486 y[1] (numeric) = 3.7278124837762483492016890613653 absolute error = 4.6328167e-24 relative error = 1.2427708529231032077593028924174e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0036 y[1] (analytic) = 3.7280852786641430396979217216215 y[1] (numeric) = 3.7280852786641430396979264870427 absolute error = 4.7654212e-24 relative error = 1.2782489787110121566774160994971e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0037 y[1] (analytic) = 3.7283581008328905395696334081194 y[1] (numeric) = 3.7283581008328905395696383061585 absolute error = 4.8980391e-24 relative error = 1.3137254972653540070993380015349e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0038 y[1] (analytic) = 3.7286309502852190705065680048332 y[1] (numeric) = 3.7286309502852190705065730355034 absolute error = 5.0306702e-24 relative error = 1.3492003545202515494210017822221e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0039 y[1] (analytic) = 3.728903827023857127034284566569 y[1] (numeric) = 3.7289038270238571270342897298836 absolute error = 5.1633146e-24 relative error = 1.3846735768782179606949136682991e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.004 y[1] (analytic) = 3.7291767310515334765414376314268 y[1] (numeric) = 3.729176731051533476541442927399 absolute error = 5.2959722e-24 relative error = 1.4201451371028666283640588053859e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0041 y[1] (analytic) = 3.7294496623709771593070648947095 y[1] (numeric) = 3.7294496623709771593070703233526 absolute error = 5.4286431e-24 relative error = 1.4556150615929670267274042623660e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0042 y[1] (analytic) = 3.729722620984917488527877611736 y[1] (numeric) = 3.7297226209849174885278831730634 absolute error = 5.5613274e-24 relative error = 1.4910833767395297362343892506607e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0043 y[1] (analytic) = 3.7299956068960840503455537298316 y[1] (numeric) = 3.7299956068960840503455594238564 absolute error = 5.6940248e-24 relative error = 1.5265500016870751486438168799525e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0044 y[1] (analytic) = 3.7302686201072067038740337497667 y[1] (numeric) = 3.7302686201072067038740395765022 absolute error = 5.8267355e-24 relative error = 1.5620149896423656271592068384080e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0045 y[1] (analytic) = 3.7305416606210155812268193169196 y[1] (numeric) = 3.7305416606210155812268252763791 absolute error = 5.9594595e-24 relative error = 1.5974783401850392578306532708378e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0046 y[1] (analytic) = 3.730814728440241087544274542434 y[1] (numeric) = 3.7308147284402410875442806346308 absolute error = 6.0921968e-24 relative error = 1.6329400528948251474842406005118e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0047 y[1] (analytic) = 3.7310878235676139010209300546455 y[1] (numeric) = 3.7310878235676139010209362795928 absolute error = 6.2249473e-24 relative error = 1.6684001005497084785353946949457e-22 % h = 0.0001 memory used=7.6MB, alloc=3.9MB, time=0.38 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0048 y[1] (analytic) = 3.7313609460058649729327897810493 y[1] (numeric) = 3.7313609460058649729327961387605 absolute error = 6.3577112e-24 relative error = 1.7038585363352320715968309998599e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0049 y[1] (analytic) = 3.7316340957577255276646404610838 y[1] (numeric) = 3.731634095757725527664646951572 absolute error = 6.4904882e-24 relative error = 1.7393152794317783753975975398153e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.005 y[1] (analytic) = 3.7319072728259270627373638900002 y[1] (numeric) = 3.7319072728259270627373705132788 absolute error = 6.6232786e-24 relative error = 1.7747704098190596972541702690524e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0051 y[1] (analytic) = 3.7321804772132013488352518940949 y[1] (numeric) = 3.7321804772132013488352586501772 absolute error = 6.7560823e-24 relative error = 1.8102239002773867794301338185971e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0052 y[1] (analytic) = 3.7324537089222804298333240375749 y[1] (numeric) = 3.7324537089222804298333309264741 absolute error = 6.8888992e-24 relative error = 1.8456757235950076518162311725540e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0053 y[1] (analytic) = 3.7327269679558966228246480613306 y[1] (numeric) = 3.73272696795589662282465508306 absolute error = 7.0217294e-24 relative error = 1.8811259061482377366726227218959e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0054 y[1] (analytic) = 3.7330002543167825181476630538896 y[1] (numeric) = 3.7330002543167825181476702084624 absolute error = 7.1545728e-24 relative error = 1.9165744207294293767770884093140e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0055 y[1] (analytic) = 3.7332735680076709794135053548233 y[1] (numeric) = 3.7332735680076709794135126422529 absolute error = 7.2874296e-24 relative error = 1.9520213204972998337301976351345e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0056 y[1] (analytic) = 3.7335469090312951435333371908818 y[1] (numeric) = 3.7335469090312951435333446111814 absolute error = 7.4202996e-24 relative error = 1.9874665514582401484979996774692e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0057 y[1] (analytic) = 3.7338202773903884207456780451276 y[1] (numeric) = 3.7338202773903884207456855983106 absolute error = 7.5531830e-24 relative error = 2.0229101667633048998750448393740e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0058 y[1] (analytic) = 3.7340936730876844946437387593441 y[1] (numeric) = 3.7340936730876844946437464454237 absolute error = 7.6860796e-24 relative error = 2.0583521124269113736352093192583e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0059 y[1] (analytic) = 3.73436709612591732220275836999 y[1] (numeric) = 3.7343670961259173222027661889796 absolute error = 7.8189896e-24 relative error = 2.0937924415924521798823987558885e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.006 y[1] (analytic) = 3.7346405465078211338073436779749 y[1] (numeric) = 3.7346405465078211338073516298878 absolute error = 7.9519129e-24 relative error = 2.1292311270587087539533070430260e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0061 y[1] (analytic) = 3.734914024236130433278811552528 y[1] (numeric) = 3.7349140242361304332788196373774 absolute error = 8.0848494e-24 relative error = 2.1646681416323965088979254105180e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0062 y[1] (analytic) = 3.735187529313579997902533969434 y[1] (numeric) = 3.7351875293135799979025421872332 absolute error = 8.2177992e-24 relative error = 2.2001035116729989342990825170014e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0063 y[1] (analytic) = 3.7354610617429048784552857839095 y[1] (numeric) = 3.7354610617429048784552941346719 absolute error = 8.3507624e-24 relative error = 2.2355372635322481978760246453028e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0064 y[1] (analytic) = 3.735734621526840399232595238394 y[1] (numeric) = 3.7357346215268403992326037221328 absolute error = 8.4837388e-24 relative error = 2.2709693432486358630338865470324e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0065 y[1] (analytic) = 3.7360082086681221580760972055273 y[1] (numeric) = 3.7360082086681221580761058222558 absolute error = 8.6167285e-24 relative error = 2.3063997771760364407333541943489e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0066 y[1] (analytic) = 3.7362818231694860264008891665893 y[1] (numeric) = 3.7362818231694860264008979163208 absolute error = 8.7497315e-24 relative error = 2.3418285648959978846926720478127e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0067 y[1] (analytic) = 3.7365554650336681492228899256734 y[1] (numeric) = 3.7365554650336681492228988084212 absolute error = 8.8827478e-24 relative error = 2.3772557059901590943330896824954e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0068 y[1] (analytic) = 3.7368291342634049451862010598685 y[1] (numeric) = 3.7368291342634049451862100756459 absolute error = 9.0157774e-24 relative error = 2.4126812000402499111835548480248e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0069 y[1] (analytic) = 3.7371028308614331065904711057229 y[1] (numeric) = 3.7371028308614331065904802545432 absolute error = 9.1488203e-24 relative error = 2.4481050466280911152833740327938e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.007 y[1] (analytic) = 3.7373765548304895994182624822638 y[1] (numeric) = 3.7373765548304895994182717641402 absolute error = 9.2818764e-24 relative error = 2.4835272185788578356608625385441e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0071 y[1] (analytic) = 3.7376503061733116633624211508451 y[1] (numeric) = 3.7376503061733116633624305657911 absolute error = 9.4149460e-24 relative error = 2.5189477957447624763418332834887e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0072 y[1] (analytic) = 3.7379240848926368118534490120995 y[1] (numeric) = 3.7379240848926368118534585601283 absolute error = 9.5480288e-24 relative error = 2.5543666974376888535263783104991e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0073 y[1] (analytic) = 3.7381978909912028320868790402657 y[1] (numeric) = 3.7381978909912028320868887213907 absolute error = 9.6811250e-24 relative error = 2.5897839767474157949820953349628e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0074 y[1] (analytic) = 3.7384717244717477850506531551669 y[1] (numeric) = 3.7384717244717477850506629694013 absolute error = 9.8142344e-24 relative error = 2.6251995797525437998834606064904e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0075 y[1] (analytic) = 3.7387455853370100055525028321126 y[1] (numeric) = 3.7387455853370100055525127794698 absolute error = 9.9473572e-24 relative error = 2.6606135595351954416358018807899e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0076 memory used=11.4MB, alloc=4.0MB, time=0.59 y[1] (analytic) = 3.7390194735897281022473324499995 y[1] (numeric) = 3.7390194735897281022473425304927 absolute error = 1.00804932e-23 relative error = 2.6960258621819907768866777225286e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0077 y[1] (analytic) = 3.7392933892326409576646053778824 y[1] (numeric) = 3.739293389232640957664615591525 absolute error = 1.02136426e-23 relative error = 2.7314365407673968391453693099351e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0078 y[1] (analytic) = 3.7395673322684877282357328002926 y[1] (numeric) = 3.7395673322684877282357431470979 absolute error = 1.03468053e-23 relative error = 2.7668455681271139949712358045975e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0079 y[1] (analytic) = 3.7398413027000078443214652815741 y[1] (numeric) = 3.7398413027000078443214757615554 absolute error = 1.04799813e-23 relative error = 2.8022529438438724846021208837401e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.008 y[1] (analytic) = 3.7401153005299410102392870695142 y[1] (numeric) = 3.7401153005299410102392976826849 absolute error = 1.06131707e-23 relative error = 2.8376586942376370816325930892346e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0081 y[1] (analytic) = 3.7403893257610272042908131385416 y[1] (numeric) = 3.7403893257610272042908238849149 absolute error = 1.07463733e-23 relative error = 2.8730627654150737572977471052409e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0082 y[1] (analytic) = 3.7406633783960066787891889727645 y[1] (numeric) = 3.7406633783960066787891998523538 absolute error = 1.08795893e-23 relative error = 2.9084652104315140948358054807711e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0083 y[1] (analytic) = 3.7409374584376199600864930891256 y[1] (numeric) = 3.7409374584376199600865041019442 absolute error = 1.10128186e-23 relative error = 2.9438660021329085469160528752466e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0084 y[1] (analytic) = 3.7412115658886078486011423009455 y[1] (numeric) = 3.7412115658886078486011534470067 absolute error = 1.11460612e-23 relative error = 2.9792651401024420850792457490399e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0085 y[1] (analytic) = 3.7414857007517114188452997221297 y[1] (numeric) = 3.7414857007517114188453110014469 absolute error = 1.12793172e-23 relative error = 3.0146626506507411378157610640158e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0086 y[1] (analytic) = 3.7417598630296720194522855123131 y[1] (numeric) = 3.7417598630296720194522969248996 absolute error = 1.14125865e-23 relative error = 3.0500585066299051817748007505478e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0087 y[1] (analytic) = 3.7420340527252312732039903632159 y[1] (numeric) = 3.742034052725231273204001909085 absolute error = 1.15458691e-23 relative error = 3.0854527076233920931833326697822e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0088 y[1] (analytic) = 3.7423082698411310770582917264857 y[1] (numeric) = 3.7423082698411310770583034056507 absolute error = 1.16791650e-23 relative error = 3.1208452532147506180846962296091e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0089 y[1] (analytic) = 3.7425825143801136021764727832987 y[1] (numeric) = 3.7425825143801136021764845957729 absolute error = 1.18124742e-23 relative error = 3.1562361429876203687006802499435e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.009 y[1] (analytic) = 3.7428567863449212939506441559956 y[1] (numeric) = 3.7428567863449212939506561017924 absolute error = 1.19457968e-23 relative error = 3.1916254032432916165837977174239e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0091 y[1] (analytic) = 3.7431310857382968720311683620257 y[1] (numeric) = 3.7431310857382968720311804411584 absolute error = 1.20791327e-23 relative error = 3.2270130068441101338141082459373e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0092 y[1] (analytic) = 3.7434054125629833303540870104731 y[1] (numeric) = 3.7434054125629833303540992229551 absolute error = 1.22124820e-23 relative error = 3.2623989800876325060050663457563e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0093 y[1] (analytic) = 3.7436797668217239371685507414401 y[1] (numeric) = 3.7436797668217239371685630872847 absolute error = 1.23458446e-23 relative error = 3.2977832958403025239454808291233e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0094 y[1] (analytic) = 3.7439541485172622350642519085617 y[1] (numeric) = 3.7439541485172622350642643877822 absolute error = 1.24792205e-23 relative error = 3.3331659536862146232022176627457e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0095 y[1] (analytic) = 3.744228557652342040998860004925 y[1] (numeric) = 3.7442285576523420409988726175348 absolute error = 1.26126098e-23 relative error = 3.3685469799173253802839862473522e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0096 y[1] (analytic) = 3.7445029942297074463254598326694 y[1] (numeric) = 3.7445029942297074463254725786818 absolute error = 1.27460124e-23 relative error = 3.4039263474062247661958648937348e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0097 y[1] (analytic) = 3.7447774582521028168199924165395 y[1] (numeric) = 3.7447774582521028168200052959679 absolute error = 1.28794284e-23 relative error = 3.4393040824411365469494048787607e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0098 y[1] (analytic) = 3.7450519497222727927086986616681 y[1] (numeric) = 3.7450519497222727927087116745258 absolute error = 1.30128577e-23 relative error = 3.4746801578987477640954265495812e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0099 y[1] (analytic) = 3.7453264686429622886955657558611 y[1] (numeric) = 3.7453264686429622886955789021615 absolute error = 1.31463004e-23 relative error = 3.5100546000635497233499756271357e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.01 y[1] (analytic) = 3.7456010150169164939897763166604 y[1] (numeric) = 3.7456010150169164939897895964168 absolute error = 1.32797564e-23 relative error = 3.5454273818163261574736399777247e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0101 y[1] (analytic) = 3.7458755888468808723331602834584 y[1] (numeric) = 3.7458755888468808723331736966841 absolute error = 1.34132257e-23 relative error = 3.5807985027418081564829438412732e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0102 y[1] (analytic) = 3.7461501901356011620276495549394 y[1] (numeric) = 3.7461501901356011620276631016478 absolute error = 1.35467084e-23 relative error = 3.6161679891188888554914798756537e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0103 y[1] (analytic) = 3.7464248188858233759627353721219 y[1] (numeric) = 3.7464248188858233759627490523262 absolute error = 1.36802043e-23 relative error = 3.6515357871423817376561034565408e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0104 y[1] (analytic) = 3.7466994751002938016429284472758 y[1] (numeric) = 3.7466994751002938016429422609895 absolute error = 1.38137137e-23 relative error = 3.6869019764736339266961443482778e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0105 y[1] (analytic) = 3.7469741587817590012152218389912 y[1] (numeric) = 3.7469741587817590012152357862276 absolute error = 1.39472364e-23 relative error = 3.7222665033095978603532745637155e-22 % h = 0.0001 memory used=15.2MB, alloc=4.1MB, time=0.81 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0106 y[1] (analytic) = 3.7472488699329658114965565736706 y[1] (numeric) = 3.7472488699329658114965706544431 absolute error = 1.40807725e-23 relative error = 3.7576293939217038544648963682021e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0107 y[1] (analytic) = 3.7475236085566613440012900137215 y[1] (numeric) = 3.7475236085566613440013042280435 absolute error = 1.42143220e-23 relative error = 3.7929906478893591344019054331635e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0108 y[1] (analytic) = 3.7477983746555929849686669727228 y[1] (numeric) = 3.7477983746555929849686813206076 absolute error = 1.43478848e-23 relative error = 3.8283502381097304035204042408414e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0109 y[1] (analytic) = 3.7480731682325083953902935778402 y[1] (numeric) = 3.7480731682325083953903080593012 absolute error = 1.44814610e-23 relative error = 3.8637081908486519194572579808177e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.011 y[1] (analytic) = 3.748347989290155511037613879765 y[1] (numeric) = 3.7483479892901555110376284948155 absolute error = 1.46150505e-23 relative error = 3.8990644790073851794460496762524e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0111 y[1] (analytic) = 3.7486228378312825424893892104515 y[1] (numeric) = 3.7486228378312825424894039591049 absolute error = 1.47486534e-23 relative error = 3.9344191288480340822701759647140e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0112 y[1] (analytic) = 3.7488977138586379751591802889277 y[1] (numeric) = 3.7488977138586379751591951711973 absolute error = 1.48822696e-23 relative error = 3.9697721132759545394439398261842e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0113 y[1] (analytic) = 3.7491726173749705693228320754534 y[1] (numeric) = 3.7491726173749705693228470913527 absolute error = 1.50158993e-23 relative error = 4.0051234852220720160397016570884e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0114 y[1] (analytic) = 3.7494475483830293601459613743022 y[1] (numeric) = 3.7494475483830293601459765238444 absolute error = 1.51495422e-23 relative error = 4.0404731642487775239604079529666e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0115 y[1] (analytic) = 3.7497225068855636577114471854399 y[1] (numeric) = 3.7497225068855636577114624686384 absolute error = 1.52831985e-23 relative error = 4.0758212032852227457710616540652e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0116 y[1] (analytic) = 3.7499974928853230470469238053765 y[1] (numeric) = 3.7499974928853230470469392222447 absolute error = 1.54168682e-23 relative error = 4.1111676019116357776366736727850e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0117 y[1] (analytic) = 3.7502725063850573881522766774655 y[1] (numeric) = 3.7502725063850573881522922280168 absolute error = 1.55505513e-23 relative error = 4.1465123597083360269365915145675e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0118 y[1] (analytic) = 3.7505475473875168160271409919258 y[1] (numeric) = 3.7505475473875168160271566761735 absolute error = 1.56842477e-23 relative error = 4.1818554495929606438043612116637e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0119 y[1] (analytic) = 3.7508226158954517406984030358606 y[1] (numeric) = 3.7508226158954517406984188538181 absolute error = 1.58179575e-23 relative error = 4.2171968978126958683130676853867e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.012 y[1] (analytic) = 3.7510977119116128472477042935493 y[1] (numeric) = 3.75109771191161284724772024523 absolute error = 1.59516807e-23 relative error = 4.2525367039481347456929716710585e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0121 y[1] (analytic) = 3.7513728354387510958389482972872 y[1] (numeric) = 3.7513728354387510958389643827044 absolute error = 1.60854172e-23 relative error = 4.2878748409230537637895845278254e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0122 y[1] (analytic) = 3.7516479864796177217458102290468 y[1] (numeric) = 3.7516479864796177217458264482139 absolute error = 1.62191671e-23 relative error = 4.3232113349790465199822419824904e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0123 y[1] (analytic) = 3.7519231650369642353792492732381 y[1] (numeric) = 3.7519231650369642353792656261685 absolute error = 1.63529304e-23 relative error = 4.3585461856969796642625456674563e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0124 y[1] (analytic) = 3.7521983711135424223150237208408 y[1] (numeric) = 3.7521983711135424223150402075479 absolute error = 1.64867071e-23 relative error = 4.3938793926578111321283250116412e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0125 y[1] (analytic) = 3.752473604712104343321208825185 y[1] (numeric) = 3.7524736047121043433212254456821 absolute error = 1.66204971e-23 relative error = 4.4292109287935019569348533297114e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0126 y[1] (analytic) = 3.7527488658354023343857174096545 y[1] (numeric) = 3.7527488658354023343857341639551 absolute error = 1.67543006e-23 relative error = 4.4645408469853236913757810419545e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0127 y[1] (analytic) = 3.7530241544861890067438232275895 y[1] (numeric) = 3.7530241544861890067438401157068 absolute error = 1.68881173e-23 relative error = 4.4998690668731073474193551053749e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0128 y[1] (analytic) = 3.7532994706672172469056870746615 y[1] (numeric) = 3.753299470667217246905704096609 absolute error = 1.70219475e-23 relative error = 4.5351956679795761760070982830601e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0129 y[1] (analytic) = 3.7535748143812402166838856539986 y[1] (numeric) = 3.7535748143812402166839028097897 absolute error = 1.71557911e-23 relative error = 4.5705206232390107163688442868285e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.013 y[1] (analytic) = 3.7538501856310113532209431943337 y[1] (numeric) = 3.7538501856310113532209604839818 absolute error = 1.72896481e-23 relative error = 4.6058439322329162658358027479376e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0131 y[1] (analytic) = 3.7541255844192843690168658214529 y[1] (numeric) = 3.7541255844192843690168832449714 absolute error = 1.74235185e-23 relative error = 4.6411655945428893814515763178610e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0132 y[1] (analytic) = 3.7544010107488132519566786832185 y[1] (numeric) = 3.7544010107488132519566962406207 absolute error = 1.75574022e-23 relative error = 4.6764855831152105999404081700276e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0133 y[1] (analytic) = 3.7546764646223522653379658284421 y[1] (numeric) = 3.7546764646223522653379835197414 absolute error = 1.76912993e-23 relative error = 4.7118039241709743633356839720057e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0134 y[1] (analytic) = 3.7549519460426559478984128398835 y[1] (numeric) = 3.7549519460426559478984306650933 absolute error = 1.78252098e-23 relative error = 4.7471206172920507117140371751295e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.1MB, time=1.03 NO POLE x[1] = 1.0135 y[1] (analytic) = 3.7552274550124791138433522216505 y[1] (numeric) = 3.7552274550124791138433701807842 absolute error = 1.79591337e-23 relative error = 4.7824356620604009300748576635737e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0136 y[1] (analytic) = 3.7555029915345768528733115412751 y[1] (numeric) = 3.7555029915345768528733296343461 absolute error = 1.80930710e-23 relative error = 4.8177490580580775446411971231058e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0137 y[1] (analytic) = 3.7557785556117045302115643267417 y[1] (numeric) = 3.7557785556117045302115825537635 absolute error = 1.82270218e-23 relative error = 4.8530608314928622579516046431799e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0138 y[1] (analytic) = 3.7560541472466177866316837187432 y[1] (numeric) = 3.756054147246617786631702079729 absolute error = 1.83609858e-23 relative error = 4.8883709020700762511922197451921e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0139 y[1] (analytic) = 3.756329766442072538485098878439 y[1] (numeric) = 3.7563297664420725384851173734023 absolute error = 1.84949633e-23 relative error = 4.9236793492489595684211429054855e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.014 y[1] (analytic) = 3.7566054132008249777286541509929 y[1] (numeric) = 3.7566054132008249777286727799471 absolute error = 1.86289542e-23 relative error = 4.9589861459862917249317178902857e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0141 y[1] (analytic) = 3.7568810875256315719521709851641 y[1] (numeric) = 3.7568810875256315719521897481226 absolute error = 1.87629585e-23 relative error = 4.9942912918645813975080924091009e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0142 y[1] (analytic) = 3.7571567894192490644060126092286 y[1] (numeric) = 3.7571567894192490644060315062048 absolute error = 1.88969762e-23 relative error = 5.0295947864664284819210378417125e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0143 y[1] (analytic) = 3.7574325188844344740286514635058 y[1] (numeric) = 3.757432518884434474028670494513 absolute error = 1.90310072e-23 relative error = 5.0648966027606063415475874375284e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0144 y[1] (analytic) = 3.7577082759239450954742393897659 y[1] (numeric) = 3.7577082759239450954742585548176 absolute error = 1.91650517e-23 relative error = 5.1001967935596858398054027926122e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0145 y[1] (analytic) = 3.757984060540538499140180577795 y[1] (numeric) = 3.7579840605405384991401998769045 absolute error = 1.92991095e-23 relative error = 5.1354953052206578745771960590844e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0146 y[1] (analytic) = 3.7582598727369725311947072693914 y[1] (numeric) = 3.7582598727369725311947267025722 absolute error = 1.94331808e-23 relative error = 5.1707921905484635393115449040615e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0147 y[1] (analytic) = 3.7585357125160053136044582200715 y[1] (numeric) = 3.758535712516005313604477787337 absolute error = 1.95672655e-23 relative error = 5.2060874225141940667805839665994e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0148 y[1] (analytic) = 3.7588115798803952441620599187588 y[1] (numeric) = 3.7588115798803952441620796201224 absolute error = 1.97013636e-23 relative error = 5.2413810007009965886192307481348e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0149 y[1] (analytic) = 3.7590874748329009965137105657334 y[1] (numeric) = 3.7590874748329009965137304012085 absolute error = 1.98354751e-23 relative error = 5.2766729246921094294138861078194e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.015 y[1] (analytic) = 3.7593633973762815201867668091167 y[1] (numeric) = 3.7593633973762815201867867787168 absolute error = 1.99696001e-23 relative error = 5.3119632206711104508180858682251e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0151 y[1] (analytic) = 3.7596393475132960406173332401683 y[1] (numeric) = 3.7596393475132960406173533439067 absolute error = 2.01037384e-23 relative error = 5.3472518350189712505157991237845e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0152 y[1] (analytic) = 3.7599153252467040591778546476696 y[1] (numeric) = 3.7599153252467040591778748855598 absolute error = 2.02378902e-23 relative error = 5.3825388205177481820806402060264e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0153 y[1] (analytic) = 3.7601913305792653532047110316718 y[1] (numeric) = 3.7601913305792653532047314037272 absolute error = 2.03720554e-23 relative error = 5.4178241501507962309093153637151e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0154 y[1] (analytic) = 3.7604673635137399760258153768822 y[1] (numeric) = 3.7604673635137399760258358831162 absolute error = 2.05062340e-23 relative error = 5.4531078235018099045493547898762e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0155 y[1] (analytic) = 3.7607434240528882569882141859666 y[1] (numeric) = 3.7607434240528882569882348263926 absolute error = 2.06404260e-23 relative error = 5.4883898401545748811186117933794e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0156 y[1] (analytic) = 3.7610195121994708014856907730425 y[1] (numeric) = 3.761019512199470801485711547674 absolute error = 2.07746315e-23 relative error = 5.5236702262815032885213549578947e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0157 y[1] (analytic) = 3.7612956279562484909863713176405 y[1] (numeric) = 3.7612956279562484909863922264908 absolute error = 2.09088503e-23 relative error = 5.5589489282875407112621336982590e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0158 y[1] (analytic) = 3.7615717713259824830603336794078 y[1] (numeric) = 3.7615717713259824830603547224904 absolute error = 2.10430826e-23 relative error = 5.5942259989318652078079716623286e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0159 y[1] (analytic) = 3.7618479423114342114072189738327 y[1] (numeric) = 3.761847942311434211407240151161 absolute error = 2.11773283e-23 relative error = 5.6295014112100920923889800929404e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.016 y[1] (analytic) = 3.7621241409153653858838459092636 y[1] (numeric) = 3.762124140915365385883867220851 absolute error = 2.13115874e-23 relative error = 5.6647751647064631140569544372848e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0161 y[1] (analytic) = 3.7624003671405379925318278855001 y[1] (numeric) = 3.7624003671405379925318493313601 absolute error = 2.14458600e-23 relative error = 5.7000472855840880788292559772407e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0162 y[1] (analytic) = 3.7626766209897142936051928542328 y[1] (numeric) = 3.7626766209897142936052144343788 absolute error = 2.15801460e-23 relative error = 5.7353177468447113181839847400411e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0163 y[1] (analytic) = 3.7629529024656568275980059416058 y[1] (numeric) = 3.7629529024656568275980276560512 absolute error = 2.17144454e-23 relative error = 5.7705865480728482885074040873082e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.1MB, time=1.26 NO POLE x[1] = 1.0164 y[1] (analytic) = 3.7632292115711284092719948331808 y[1] (numeric) = 3.7632292115711284092720166819391 absolute error = 2.18487583e-23 relative error = 5.8058537154260285643395085073017e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0165 y[1] (analytic) = 3.7635055483088921296841779215776 y[1] (numeric) = 3.7635055483088921296841999046621 absolute error = 2.19830845e-23 relative error = 5.8411191953411527831264245673832e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0166 y[1] (analytic) = 3.7637819126817113562144952170666 y[1] (numeric) = 3.7637819126817113562145173344908 absolute error = 2.21174242e-23 relative error = 5.8763830405469048196522897998197e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0167 y[1] (analytic) = 3.7640583046923497325934420213919 y[1] (numeric) = 3.7640583046923497325934642731693 absolute error = 2.22517774e-23 relative error = 5.9116452506223118247278751152012e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0168 y[1] (analytic) = 3.7643347243435711789297053650993 y[1] (numeric) = 3.7643347243435711789297277512432 absolute error = 2.23861439e-23 relative error = 5.9469057720162545707039270666122e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0169 y[1] (analytic) = 3.7646111716381398917378032086454 y[1] (numeric) = 3.7646111716381398917378257291694 absolute error = 2.25205240e-23 relative error = 5.9821646840091529006910789476706e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.017 y[1] (analytic) = 3.7648876465788203439657264075669 y[1] (numeric) = 3.7648876465788203439657490624844 absolute error = 2.26549175e-23 relative error = 6.0174219330520212201105144943047e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0171 y[1] (analytic) = 3.7651641491683772850225834419828 y[1] (numeric) = 3.7651641491683772850226062313072 absolute error = 2.27893244e-23 relative error = 6.0526775187301047979565785498957e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0172 y[1] (analytic) = 3.7654406794095757408062479107087 y[1] (numeric) = 3.7654406794095757408062708344534 absolute error = 2.29237447e-23 relative error = 6.0879314406287400100153949976981e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0173 y[1] (analytic) = 3.7657172373051810137310087902586 y[1] (numeric) = 3.7657172373051810137310318484371 absolute error = 2.30581785e-23 relative error = 6.1231837248887204707497919465270e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0174 y[1] (analytic) = 3.7659938228579586827552234590109 y[1] (numeric) = 3.7659938228579586827552466516367 absolute error = 2.31926258e-23 relative error = 6.1584343710897138479547341369552e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0175 y[1] (analytic) = 3.7662704360706746034089734868152 y[1] (numeric) = 3.7662704360706746034089968139016 absolute error = 2.33270864e-23 relative error = 6.1936833257085482130563542982370e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0176 y[1] (analytic) = 3.7665470769460949078217231903156 y[1] (numeric) = 3.7665470769460949078217466518761 absolute error = 2.34615605e-23 relative error = 6.2289306414358062410588821720491e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0177 y[1] (analytic) = 3.7668237454869860047499809542688 y[1] (numeric) = 3.7668237454869860047500045503169 absolute error = 2.35960481e-23 relative error = 6.2641763178514299723148010790524e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0178 y[1] (analytic) = 3.7671004416961145796049633191324 y[1] (numeric) = 3.7671004416961145796049870496815 absolute error = 2.37305491e-23 relative error = 6.2994203279898375469480597503126e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0179 y[1] (analytic) = 3.7673771655762475944802618351996 y[1] (numeric) = 3.7673771655762475944802857002632 absolute error = 2.38650636e-23 relative error = 6.3346626979806694927622925732693e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.018 y[1] (analytic) = 3.7676539171301522881795126835586 y[1] (numeric) = 3.7676539171301522881795366831502 absolute error = 2.39995916e-23 relative error = 6.3699034274041424631838950561117e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0181 y[1] (analytic) = 3.767930696360596176244069064152 y[1] (numeric) = 3.7679306963605961762440931982849 absolute error = 2.41341329e-23 relative error = 6.4051424627610321948527293884380e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0182 y[1] (analytic) = 3.768207503270347050980676351213 y[1] (numeric) = 3.7682075032703470509807006199008 absolute error = 2.42686878e-23 relative error = 6.4403798832568861034312919060640e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0183 y[1] (analytic) = 3.7684843378621729814891500163565 y[1] (numeric) = 3.7684843378621729814891744196126 absolute error = 2.44032561e-23 relative error = 6.4756156353946122718498300427641e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0184 y[1] (analytic) = 3.7687612001388423136900563195999 y[1] (numeric) = 3.7687612001388423136900808574377 absolute error = 2.45378378e-23 relative error = 6.5108497187606417092595360027921e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0185 y[1] (analytic) = 3.7690380901031236703523957685918 y[1] (numeric) = 3.7690380901031236703524204410248 absolute error = 2.46724330e-23 relative error = 6.5460821594734650137979261881930e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0186 y[1] (analytic) = 3.7693150077577859511212893463255 y[1] (numeric) = 3.7693150077577859511213141533672 absolute error = 2.48070417e-23 relative error = 6.5813129571138476888691138164907e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0187 y[1] (analytic) = 3.7695919531055983325456675076128 y[1] (numeric) = 3.7695919531055983325456924492767 absolute error = 2.49416639e-23 relative error = 6.6165421112626468368929251152959e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0188 y[1] (analytic) = 3.7698689261493302681059619445968 y[1] (numeric) = 3.7698689261493302681059870208963 absolute error = 2.50762995e-23 relative error = 6.6517695949746899669803914165902e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0189 y[1] (analytic) = 3.7701459268917514882418001215789 y[1] (numeric) = 3.7701459268917514882418253325274 absolute error = 2.52109485e-23 relative error = 6.6869954078368641620572097769828e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.019 y[1] (analytic) = 3.7704229553356320003797025794385 y[1] (numeric) = 3.7704229553356320003797279250495 absolute error = 2.53456110e-23 relative error = 6.7222195759583709612571823324760e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0191 y[1] (analytic) = 3.7707000114837420889607830099209 y[1] (numeric) = 3.7707000114837420889608084902079 absolute error = 2.54802870e-23 relative error = 6.7574420989204332762913850114541e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0192 y[1] (analytic) = 3.7709770953388523154684511000721 y[1] (numeric) = 3.7709770953388523154684767150485 absolute error = 2.56149764e-23 relative error = 6.7926629497860395864505353884159e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=1.47 NO POLE x[1] = 1.0193 y[1] (analytic) = 3.7712542069037335184561181470954 y[1] (numeric) = 3.7712542069037335184561438967747 absolute error = 2.57496793e-23 relative error = 6.8278821546588191028898369534761e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0194 y[1] (analytic) = 3.771531346181156813574905443909 y[1] (numeric) = 3.7715313461811568135749313283046 absolute error = 2.58843956e-23 relative error = 6.8630996866058402181784634243280e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0195 y[1] (analytic) = 3.7718085131738935936013554356799 y[1] (numeric) = 3.7718085131738935936013814548054 absolute error = 2.60191255e-23 relative error = 6.8983155982394981966110880353797e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0196 y[1] (analytic) = 3.772085707884715528465145647613 y[1] (numeric) = 3.7720857078847155284651718014818 absolute error = 2.61538688e-23 relative error = 6.9335298361145637900303013984910e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0197 y[1] (analytic) = 3.7723629303163945652768053842703 y[1] (numeric) = 3.772362930316394565276831672896 absolute error = 2.62886257e-23 relative error = 6.9687424528358218600957866197724e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0198 y[1] (analytic) = 3.7726401804717029283554352007001 y[1] (numeric) = 3.772640180471702928355461624096 absolute error = 2.64233959e-23 relative error = 7.0039533684593834459009537475374e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0199 y[1] (analytic) = 3.7729174583534131192564291456501 y[1] (numeric) = 3.7729174583534131192564557038298 absolute error = 2.65581797e-23 relative error = 7.0391626620929557496394979370520e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.02 y[1] (analytic) = 3.7731947639642979167991997771454 y[1] (numeric) = 3.7731947639642979167992264701224 absolute error = 2.66929770e-23 relative error = 7.0743703068100011169439334193009e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0201 y[1] (analytic) = 3.7734720973071303770949059507052 y[1] (numeric) = 3.7734720973071303770949327784929 absolute error = 2.68277877e-23 relative error = 7.1095762756918653206783631273453e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0202 y[1] (analytic) = 3.7737494583846838335741833804776 y[1] (numeric) = 3.7737494583846838335742103430895 absolute error = 2.69626119e-23 relative error = 7.1447805948254655995067136363308e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0203 y[1] (analytic) = 3.774026847199731897014877973569 y[1] (numeric) = 3.7740268471997318970149050710186 absolute error = 2.70974496e-23 relative error = 7.1799832637931227525757780005134e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0204 y[1] (analytic) = 3.774304263755048455569781937846 y[1] (numeric) = 3.7743042637550484555698091701467 absolute error = 2.72323007e-23 relative error = 7.2151842556822998430043828359935e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0205 y[1] (analytic) = 3.7745817080534076747943726634859 y[1] (numeric) = 3.7745817080534076747944000306512 absolute error = 2.73671653e-23 relative error = 7.2503835965743449395054672743627e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0206 y[1] (analytic) = 3.7748591800975839976745543785551 y[1] (numeric) = 3.7748591800975839976745818805985 absolute error = 2.75020434e-23 relative error = 7.2855812860518531588572104198802e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0207 y[1] (analytic) = 3.7751366798903521446544025788909 y[1] (numeric) = 3.775136679890352144654430215826 absolute error = 2.76369351e-23 relative error = 7.3207773501866182858074924899093e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0208 y[1] (analytic) = 3.7754142074344871136639112325658 y[1] (numeric) = 3.775414207434487113663939004406 absolute error = 2.77718402e-23 relative error = 7.3559717355812569978004503515992e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0209 y[1] (analytic) = 3.77569176273276418014674275921 y[1] (numeric) = 3.7756917627327641801467706659688 absolute error = 2.79067588e-23 relative error = 7.3911644683096933981257847348653e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.021 y[1] (analytic) = 3.7759693457879588970879807844716 y[1] (numeric) = 3.7759693457879588970880088261625 absolute error = 2.80416909e-23 relative error = 7.4263555479548886732421972902431e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0211 y[1] (analytic) = 3.7762469566028470950418856698903 y[1] (numeric) = 3.7762469566028470950419138465268 absolute error = 2.81766365e-23 relative error = 7.4615449740998955174899572796427e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0212 y[1] (analytic) = 3.7765245951802048821596528184635 y[1] (numeric) = 3.776524595180204882159681130059 absolute error = 2.83115955e-23 relative error = 7.4967327198484860294249692313198e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0213 y[1] (analytic) = 3.7768022615228086442171737561807 y[1] (numeric) = 3.7768022615228086442172022027489 absolute error = 2.84465682e-23 relative error = 7.5319188642220122072317130960313e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0214 y[1] (analytic) = 3.7770799556334350446427999898065 y[1] (numeric) = 3.7770799556334350446428285713607 absolute error = 2.85815542e-23 relative error = 7.5671033008902062235492002066819e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0215 y[1] (analytic) = 3.7773576775148610245451096411863 y[1] (numeric) = 3.7773576775148610245451383577401 absolute error = 2.87165538e-23 relative error = 7.6022861088687628627504140423687e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0216 y[1] (analytic) = 3.7776354271698638027406768583559 y[1] (numeric) = 3.7776354271698638027407057099228 absolute error = 2.88515669e-23 relative error = 7.6374672612637669356795541208786e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0217 y[1] (analytic) = 3.7779132046012208757818440037302 y[1] (numeric) = 3.7779132046012208757818729903236 absolute error = 2.89865934e-23 relative error = 7.6726467311891807593549304087736e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0218 y[1] (analytic) = 3.7781910098117100179844966196495 y[1] (numeric) = 3.778191009811710017984525741283 absolute error = 2.91216335e-23 relative error = 7.7078245711699224412384168346756e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0219 y[1] (analytic) = 3.7784688428041092814558411715618 y[1] (numeric) = 3.778468842804109281455870428249 absolute error = 2.92566872e-23 relative error = 7.7430007807839377720748744060787e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.022 y[1] (analytic) = 3.7787467035811969961221855691182 y[1] (numeric) = 3.7787467035811969961222149608724 absolute error = 2.93917542e-23 relative error = 7.7781752802178621952013753416413e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0221 y[1] (analytic) = 3.7790245921457517697567224654584 y[1] (numeric) = 3.7790245921457517697567519922932 absolute error = 2.95268348e-23 relative error = 7.8133481484529039232136276517839e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.1MB, time=1.70 x[1] = 1.0222 y[1] (analytic) = 3.7793025085005524880073153349667 y[1] (numeric) = 3.7793025085005524880073449968956 absolute error = 2.96619289e-23 relative error = 7.8485193586073751013623542489293e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0223 y[1] (analytic) = 3.7795804526483783144242873297729 y[1] (numeric) = 3.7795804526483783144243171268095 absolute error = 2.97970366e-23 relative error = 7.8836889367233892804994025951274e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0224 y[1] (analytic) = 3.7798584245920086904882129152796 y[1] (numeric) = 3.7798584245920086904882428474373 absolute error = 2.99321577e-23 relative error = 7.9188568294673165616489270779436e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0225 y[1] (analytic) = 3.7801364243342233356377122849904 y[1] (numeric) = 3.7801364243342233356377423522827 absolute error = 3.00672923e-23 relative error = 7.9540230628833992262771882891599e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0226 y[1] (analytic) = 3.7804144518778022472972485549194 y[1] (numeric) = 3.7804144518778022472972787573598 absolute error = 3.02024404e-23 relative error = 7.9891876365560621275256295551178e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0227 y[1] (analytic) = 3.7806925072255257009049277378592 y[1] (numeric) = 3.7806925072255257009049580754613 absolute error = 3.03376021e-23 relative error = 8.0243505765200022684424743959767e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0228 y[1] (analytic) = 3.7809705903801742499403014977852 y[1] (numeric) = 3.7809705903801742499403319705625 absolute error = 3.04727773e-23 relative error = 8.0595118559057559676220760925586e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0229 y[1] (analytic) = 3.7812487013445287259521726846739 y[1] (numeric) = 3.7812487013445287259522032926399 absolute error = 3.06079660e-23 relative error = 8.0946714742980226811478134789864e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.023 y[1] (analytic) = 3.7815268401213702385864036500145 y[1] (numeric) = 3.7815268401213702385864343931827 absolute error = 3.07431682e-23 relative error = 8.1298294312815933000910782174033e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0231 y[1] (analytic) = 3.7818050067134801756137273432902 y[1] (numeric) = 3.7818050067134801756137582216742 absolute error = 3.08783840e-23 relative error = 8.1649857528837499590397761270636e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0232 y[1] (analytic) = 3.7820832011236402029575611897096 y[1] (numeric) = 3.7820832011236402029575922033228 absolute error = 3.10136132e-23 relative error = 8.2001403858027217890437036322189e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0233 y[1] (analytic) = 3.7823614233546322647218237494628 y[1] (numeric) = 3.7823614233546322647218548983189 absolute error = 3.11488561e-23 relative error = 8.2352934089449386941193821955899e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0234 y[1] (analytic) = 3.782639673409238583218754158785 y[1] (numeric) = 3.7826396734092385832187854428974 absolute error = 3.12841124e-23 relative error = 8.2704447425741930854432571449702e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0235 y[1] (analytic) = 3.7829179512902416589967343531013 y[1] (numeric) = 3.7829179512902416589967657724836 absolute error = 3.14193823e-23 relative error = 8.3055944391508084524741038831706e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0236 y[1] (analytic) = 3.783196257000424270868114072534 y[1] (numeric) = 3.7831962570004242708681456271996 absolute error = 3.15546656e-23 relative error = 8.3407424453889390877460838380686e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0237 y[1] (analytic) = 3.7834745905425694759370386500491 y[1] (numeric) = 3.7834745905425694759370703400116 absolute error = 3.16899625e-23 relative error = 8.3758888137413124256826241257766e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0238 y[1] (analytic) = 3.7837529519194606096272795825212 y[1] (numeric) = 3.7837529519194606096273114077941 absolute error = 3.18252729e-23 relative error = 8.4110335173588308605547137667989e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0239 y[1] (analytic) = 3.7840313411338812857100678849942 y[1] (numeric) = 3.7840313411338812857100998455911 absolute error = 3.19605969e-23 relative error = 8.4461765822539510038993554153077e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.024 y[1] (analytic) = 3.784309758188615396331930228417 y[1] (numeric) = 3.7843097581886153963319623243514 absolute error = 3.20959344e-23 relative error = 8.4813179815816474840183658767412e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0241 y[1] (analytic) = 3.7845882030864471120425278611318 y[1] (numeric) = 3.7845882030864471120425600924172 absolute error = 3.22312854e-23 relative error = 8.5164577149277175468995649665622e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0242 y[1] (analytic) = 3.7848666758301608818224983143939 y[1] (numeric) = 3.7848666758301608818225306810439 absolute error = 3.23666500e-23 relative error = 8.5515958082990597503128356056306e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0243 y[1] (analytic) = 3.7851451764225414331112998922014 y[1] (numeric) = 3.7851451764225414331113323942295 absolute error = 3.25020281e-23 relative error = 8.5867322348567562196300370660140e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0244 y[1] (analytic) = 3.7854237048663737718350589457129 y[1] (numeric) = 3.7854237048663737718350915831327 absolute error = 3.26374198e-23 relative error = 8.6218670206040006741340493423300e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0245 y[1] (analytic) = 3.785702261164443182434419932532 y[1] (numeric) = 3.7857022611644431824344527053571 absolute error = 3.27728251e-23 relative error = 8.6570001651211247599252717358370e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0246 y[1] (analytic) = 3.7859808453195352278923982611372 y[1] (numeric) = 3.785980845319535227892431169381 absolute error = 3.29082438e-23 relative error = 8.6921316151620829828785000187519e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0247 y[1] (analytic) = 3.7862594573344357497622359207346 y[1] (numeric) = 3.7862594573344357497622689644107 absolute error = 3.30436761e-23 relative error = 8.7272614231416343696650658323168e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0248 y[1] (analytic) = 3.7865380972119308681952598968142 y[1] (numeric) = 3.7865380972119308681952930759362 absolute error = 3.31791220e-23 relative error = 8.7623895886403857742605294632752e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0249 y[1] (analytic) = 3.7868167649548069819687433726863 y[1] (numeric) = 3.7868167649548069819687766872676 absolute error = 3.33145813e-23 relative error = 8.7975160584242280605458964875743e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.025 y[1] (analytic) = 3.787095460565850768513769717277 y[1] (numeric) = 3.7870954605658507685138031673312 absolute error = 3.34500542e-23 relative error = 8.8326408848965331777707957988940e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=34.3MB, alloc=4.1MB, time=1.92 x[1] = 1.0251 y[1] (analytic) = 3.7873741840478491839430992594628 y[1] (numeric) = 3.7873741840478491839431328450034 absolute error = 3.35855406e-23 relative error = 8.8677640412346657974756267784534e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0252 y[1] (analytic) = 3.787652935403589463079038849221 y[1] (numeric) = 3.7876529354035894630790725702616 absolute error = 3.37210406e-23 relative error = 8.9028855534270035223378416559783e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0253 y[1] (analytic) = 3.7879317146358591194813142058764 y[1] (numeric) = 3.7879317146358591194813480624305 absolute error = 3.38565541e-23 relative error = 8.9380053946549807734563209836630e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0254 y[1] (analytic) = 3.7882105217474459454749450537212 y[1] (numeric) = 3.7882105217474459454749790458025 absolute error = 3.39920813e-23 relative error = 8.9731236173009602213717427029614e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0255 y[1] (analytic) = 3.7884893567411380121781230452893 y[1] (numeric) = 3.7884893567411380121781571729113 absolute error = 3.41276220e-23 relative error = 9.0082401681488717342340671766688e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0256 y[1] (analytic) = 3.7887682196197236695300924725606 y[1] (numeric) = 3.7887682196197236695301267357368 absolute error = 3.42631762e-23 relative error = 9.0433550467858849049172649619712e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0257 y[1] (analytic) = 3.7890471103859915463190337663771 y[1] (numeric) = 3.789047110385991546319068165121 absolute error = 3.43987439e-23 relative error = 9.0784682527992606565648524311671e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0258 y[1] (analytic) = 3.7893260290427305502099497843478 y[1] (numeric) = 3.7893260290427305502099843186731 absolute error = 3.45343253e-23 relative error = 9.1135798385561855593809578910224e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0259 y[1] (analytic) = 3.7896049755927298677725548875223 y[1] (numeric) = 3.7896049755927298677725895574425 absolute error = 3.46699202e-23 relative error = 9.1486897508564987921155817443517e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.026 y[1] (analytic) = 3.7898839500387789645091668061106 y[1] (numeric) = 3.7898839500387789645092016116393 absolute error = 3.48055287e-23 relative error = 9.1837980156737680114692774196776e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0261 y[1] (analytic) = 3.7901629523836675848826012945301 y[1] (numeric) = 3.7901629523836675848826362356808 absolute error = 3.49411507e-23 relative error = 9.2189046062057030877953580265215e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0262 y[1] (analytic) = 3.7904419826301857523440695760567 y[1] (numeric) = 3.7904419826301857523441046528429 absolute error = 3.50767862e-23 relative error = 9.2540095220400223625303928475481e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0263 y[1] (analytic) = 3.79072104078112376936107857736 y[1] (numeric) = 3.7907210407811237693611137897954 absolute error = 3.52124354e-23 relative error = 9.2891128155249464580798729702292e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0264 y[1] (analytic) = 3.7910001268392722174453339532022 y[1] (numeric) = 3.7910001268392722174453693013003 absolute error = 3.53480981e-23 relative error = 9.3242144334801971136830520560725e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0265 y[1] (analytic) = 3.7912792408074219571806459015777 y[1] (numeric) = 3.7912792408074219571806813853521 absolute error = 3.54837744e-23 relative error = 9.3593144018700885898800339546397e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0266 y[1] (analytic) = 3.7915583826883641282508377695751 y[1] (numeric) = 3.7915583826883641282508733890394 absolute error = 3.56194643e-23 relative error = 9.3944127202768793545054858900370e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0267 y[1] (analytic) = 3.7918375524848901494676574502383 y[1] (numeric) = 3.791837552484890149467693205406 absolute error = 3.57551677e-23 relative error = 9.4295093619104819172107168354011e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0268 y[1] (analytic) = 3.7921167501997917187986915707072 y[1] (numeric) = 3.7921167501997917187987274615919 absolute error = 3.58908847e-23 relative error = 9.4646043527296596099311983473011e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0269 y[1] (analytic) = 3.7923959758358608133952824719172 y[1] (numeric) = 3.7923959758358608133953184985324 absolute error = 3.60266152e-23 relative error = 9.4996976659483916317391173738892e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.027 y[1] (analytic) = 3.7926752293958896896204479801354 y[1] (numeric) = 3.7926752293958896896204841424948 absolute error = 3.61623594e-23 relative error = 9.5347893538883540407917136166769e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0271 y[1] (analytic) = 3.7929545108826708830768039706147 y[1] (numeric) = 3.7929545108826708830768402687318 absolute error = 3.62981171e-23 relative error = 9.5698793633970965107545680029270e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0272 y[1] (analytic) = 3.7932338202989972086344897236425 y[1] (numeric) = 3.7932338202989972086345261575309 absolute error = 3.64338884e-23 relative error = 9.6049677204259824569865965605505e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0273 y[1] (analytic) = 3.7935131576476617604590960732658 y[1] (numeric) = 3.7935131576476617604591326429391 absolute error = 3.65696733e-23 relative error = 9.6400544245579126063037202659930e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0274 y[1] (analytic) = 3.7937925229314579120395963489704 y[1] (numeric) = 3.7937925229314579120396330544421 absolute error = 3.67054717e-23 relative error = 9.6751394490170316198769356625747e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0275 y[1] (analytic) = 3.7940719161531793162162801105936 y[1] (numeric) = 3.7940719161531793162163169518773 absolute error = 3.68412837e-23 relative error = 9.7102228197491538292083088863409e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0276 y[1] (analytic) = 3.7943513373156199052086896767507 y[1] (numeric) = 3.79435133731561990520872665386 absolute error = 3.69771093e-23 relative error = 9.7453045363374551169064181244887e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0277 y[1] (analytic) = 3.7946307864215738906435594470537 y[1] (numeric) = 3.7946307864215738906435965600021 absolute error = 3.71129484e-23 relative error = 9.7803845720121781629340794678679e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0278 y[1] (analytic) = 3.7949102634738357635827580184015 y[1] (numeric) = 3.7949102634738357635827952672027 absolute error = 3.72488012e-23 relative error = 9.8154629790646732360945415523931e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0279 y[1] (analytic) = 3.7951897684752002945512330956226 y[1] (numeric) = 3.7951897684752002945512704802901 absolute error = 3.73846675e-23 relative error = 9.8505397043742821955755031746355e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.028 y[1] (analytic) = 3.795469301428462533564959196747 y[1] (numeric) = 3.7954693014284625335649967172945 absolute error = 3.75205475e-23 relative error = 9.8856148002247757969281055175121e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=2.14 NO POLE x[1] = 1.0281 y[1] (analytic) = 3.7957488623364178101588881531901 y[1] (numeric) = 3.7957488623364178101589258096311 absolute error = 3.76564410e-23 relative error = 9.9206882135034422084861524002852e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0282 y[1] (analytic) = 3.7960284512018617334149024051249 y[1] (numeric) = 3.796028451201861733414940197473 absolute error = 3.77923481e-23 relative error = 9.9557599701431513414555823769493e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0283 y[1] (analytic) = 3.7963080680275901919897710923242 y[1] (numeric) = 3.7963080680275901919898090205931 absolute error = 3.79282689e-23 relative error = 9.9908300960691030724623137406614e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0284 y[1] (analytic) = 3.7965877128163993541431089407521 y[1] (numeric) = 3.7965877128163993541431470049553 absolute error = 3.80642032e-23 relative error = 1.0025898538180503627127868864453e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0285 y[1] (analytic) = 3.7968673855710856677653379451827 y[1] (numeric) = 3.7968673855710856677653761453338 absolute error = 3.82001511e-23 relative error = 1.0060965322404676743928631210640e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0286 y[1] (analytic) = 3.7971470862944458604056518481281 y[1] (numeric) = 3.7971470862944458604056901842407 absolute error = 3.83361126e-23 relative error = 1.0096030448325715878776752662732e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0287 y[1] (analytic) = 3.7974268149892769392999834153536 y[1] (numeric) = 3.7974268149892769393000218874413 absolute error = 3.84720877e-23 relative error = 1.0131093915527806250826659673118e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0288 y[1] (analytic) = 3.7977065716583761913989745082602 y[1] (numeric) = 3.7977065716583761913990131163366 absolute error = 3.86080764e-23 relative error = 1.0166155723595224838535975997156e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0289 y[1] (analytic) = 3.7979863563045411833959489534145 y[1] (numeric) = 3.7979863563045411833959876974931 absolute error = 3.87440786e-23 relative error = 1.0201215845782598607694382439089e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.029 y[1] (analytic) = 3.7982661689305697617548882095049 y[1] (numeric) = 3.7982661689305697617549270895994 absolute error = 3.88800945e-23 relative error = 1.0236274334335811252561868177300e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0291 y[1] (analytic) = 3.7985460095392600527384098320052 y[1] (numeric) = 3.7985460095392600527384488481292 absolute error = 3.90161240e-23 relative error = 1.0271331162507733473029629237474e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0292 y[1] (analytic) = 3.7988258781334104624357487358239 y[1] (numeric) = 3.798825878133410462435787887991 absolute error = 3.91521671e-23 relative error = 1.0306386329883009245334204948382e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0293 y[1] (analytic) = 3.7991057747158196767907412562196 y[1] (numeric) = 3.7991057747158196767907805444435 absolute error = 3.92882239e-23 relative error = 1.0341439862368357912471376823149e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0294 y[1] (analytic) = 3.7993856992892866616298120082633 y[1] (numeric) = 3.7993856992892866616298514325574 absolute error = 3.94242941e-23 relative error = 1.0376491680582656044338268125472e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0295 y[1] (analytic) = 3.7996656518566106626899635451252 y[1] (numeric) = 3.7996656518566106626900031055032 absolute error = 3.95603780e-23 relative error = 1.0411541863076773705593999692990e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0296 y[1] (analytic) = 3.7999456324205912056467688154686 y[1] (numeric) = 3.7999456324205912056468085119442 absolute error = 3.96964756e-23 relative error = 1.0446590409429904165744628300804e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0297 y[1] (analytic) = 3.800225640984028096142366420229 y[1] (numeric) = 3.8002256409840280961424062528157 absolute error = 3.98325867e-23 relative error = 1.0481637266592879057597151425464e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0298 y[1] (analytic) = 3.8005056775497214198134586690583 y[1] (numeric) = 3.8005056775497214198134986377698 absolute error = 3.99687115e-23 relative error = 1.0516682486781285860881311414840e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0299 y[1] (analytic) = 3.8007857421204715423193124367158 y[1] (numeric) = 3.8007857421204715423193525415656 absolute error = 4.01048498e-23 relative error = 1.0551726016953895764379224691463e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.03 y[1] (analytic) = 3.8010658346990791093697628196836 y[1] (numeric) = 3.8010658346990791093698030606854 absolute error = 4.02410018e-23 relative error = 1.0586767909318723922646239683533e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0301 y[1] (analytic) = 3.8013459552883450467532195932887 y[1] (numeric) = 3.8013459552883450467532599704561 absolute error = 4.03771674e-23 relative error = 1.0621808137148952083760042065812e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0302 y[1] (analytic) = 3.8016261038910705603646764696105 y[1] (numeric) = 3.8016261038910705603647169829571 absolute error = 4.05133466e-23 relative error = 1.0656846700030141717301778630842e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0303 y[1] (analytic) = 3.8019062805100571362337231564535 y[1] (numeric) = 3.801906280510057136233763805993 absolute error = 4.06495395e-23 relative error = 1.0691883623850540697145893646532e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0304 y[1] (analytic) = 3.8021864851481065405525602176674 y[1] (numeric) = 3.8021864851481065405526010034133 absolute error = 4.07857459e-23 relative error = 1.0726918855588766093231410655892e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0305 y[1] (analytic) = 3.8024667178080208197040167350916 y[1] (numeric) = 3.8024667178080208197040576570575 absolute error = 4.09219659e-23 relative error = 1.0761952421135187646419238378171e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0306 y[1] (analytic) = 3.8027469784926023002895707724074 y[1] (numeric) = 3.802746978492602300289611830607 absolute error = 4.10581996e-23 relative error = 1.0796984346372513421214113745087e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0307 y[1] (analytic) = 3.803027267204653589157372641176 y[1] (numeric) = 3.8030272672046535891574138356229 absolute error = 4.11944469e-23 relative error = 1.0832014604586107305805539609019e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0308 y[1] (analytic) = 3.8033075839469775734302709693433 y[1] (numeric) = 3.8033075839469775734303123000512 absolute error = 4.13307079e-23 relative error = 1.0867043221654984873621589537411e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0309 y[1] (analytic) = 3.8035879287223774205338415724918 y[1] (numeric) = 3.8035879287223774205338830394742 absolute error = 4.14669824e-23 relative error = 1.0902070144577604383037421630654e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=2.36 NO POLE x[1] = 1.031 y[1] (analytic) = 3.8038683015336565782244191281195 y[1] (numeric) = 3.8038683015336565782244607313902 absolute error = 4.16032707e-23 relative error = 1.0937095451813158624250575085238e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0311 y[1] (analytic) = 3.8041487023836187746171316532272 y[1] (numeric) = 3.8041487023836187746171733927996 absolute error = 4.17395724e-23 relative error = 1.0972119037788047313764142034962e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0312 y[1] (analytic) = 3.8044291312750680182139377854922 y[1] (numeric) = 3.8044291312750680182139796613801 absolute error = 4.18758879e-23 relative error = 1.1007141007240985595569727297457e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0313 y[1] (analytic) = 3.8047095882108085979316668683123 y[1] (numeric) = 3.8047095882108085979317088805293 absolute error = 4.20122170e-23 relative error = 1.1042161307180488398605728057070e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0314 y[1] (analytic) = 3.8049900731936450831300618399967 y[1] (numeric) = 3.8049900731936450831301039885564 absolute error = 4.21485597e-23 relative error = 1.1077179937193218156975613764853e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0315 y[1] (analytic) = 3.805270586226382323639824927387 y[1] (numeric) = 3.8052705862263823236398672123031 absolute error = 4.22849161e-23 relative error = 1.1112196923145269081212996538658e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0316 y[1] (analytic) = 3.8055511273118254497906661441879 y[1] (numeric) = 3.8055511273118254497907085654739 absolute error = 4.24212860e-23 relative error = 1.1147212212062869373206949229174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0317 y[1] (analytic) = 3.8058316964527798724393545942871 y[1] (numeric) = 3.8058316964527798724393971519568 absolute error = 4.25576697e-23 relative error = 1.1182225882365165207083464030435e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0318 y[1] (analytic) = 3.8061122936520512829977725803471 y[1] (numeric) = 3.806112293652051282997815274414 absolute error = 4.26940669e-23 relative error = 1.1217237854806977358164332066465e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0319 y[1] (analytic) = 3.8063929189124456534609725179466 y[1] (numeric) = 3.8063929189124456534610153484244 absolute error = 4.28304778e-23 relative error = 1.1252248181524421135733079315424e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.032 y[1] (analytic) = 3.8066735722367692364352366555551 y[1] (numeric) = 3.8066735722367692364352796224574 absolute error = 4.29669023e-23 relative error = 1.1287256835829243731522221685157e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0321 y[1] (analytic) = 3.8069542536278285651661396006186 y[1] (numeric) = 3.8069542536278285651661827039592 absolute error = 4.31033406e-23 relative error = 1.1322263869844185206751761309021e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0322 y[1] (analytic) = 3.8072349630884304535666136520393 y[1] (numeric) = 3.8072349630884304535666568918317 absolute error = 4.32397924e-23 relative error = 1.1357269204347678063961244799652e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0323 y[1] (analytic) = 3.8075157006213819962450169393275 y[1] (numeric) = 3.8075157006213819962450603155854 absolute error = 4.33762579e-23 relative error = 1.1392272891460709335731997964326e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0324 y[1] (analytic) = 3.8077964662294905685332043687095 y[1] (numeric) = 3.8077964662294905685332478814464 absolute error = 4.35127369e-23 relative error = 1.1427274878241233230717331008033e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0325 y[1] (analytic) = 3.8080772599155638265146013764686 y[1] (numeric) = 3.8080772599155638265146450256983 absolute error = 4.36492297e-23 relative error = 1.1462275243062644863712830016760e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0326 y[1] (analytic) = 3.8083580816824097070522804898037 y[1] (numeric) = 3.8083580816824097070523242755398 absolute error = 4.37857361e-23 relative error = 1.1497273932985018764440042841902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0327 y[1] (analytic) = 3.8086389315328364278170406954826 y[1] (numeric) = 3.8086389315328364278170846177388 absolute error = 4.39222562e-23 relative error = 1.1532270973852308692287111086543e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0328 y[1] (analytic) = 3.8089198094696524873154896165741 y[1] (numeric) = 3.808919809469652487315533675364 absolute error = 4.40587899e-23 relative error = 1.1567266338992490086433174244463e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0329 y[1] (analytic) = 3.8092007154956666649181284975368 y[1] (numeric) = 3.8092007154956666649181726928741 absolute error = 4.41953373e-23 relative error = 1.1602260054245827908125640959622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.033 y[1] (analytic) = 3.8094816496136880208874399979479 y[1] (numeric) = 3.8094816496136880208874843298463 absolute error = 4.43318984e-23 relative error = 1.1637252119194644210347598344126e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0331 y[1] (analytic) = 3.8097626118265258964059787951517 y[1] (numeric) = 3.8097626118265258964060232636248 absolute error = 4.44684731e-23 relative error = 1.1672242507172998579960831048197e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0332 y[1] (analytic) = 3.8100436021369899136044649961078 y[1] (numeric) = 3.8100436021369899136045096011693 absolute error = 4.46050615e-23 relative error = 1.1707231244015623578508014792790e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0333 y[1] (analytic) = 3.8103246205478899755898803587226 y[1] (numeric) = 3.8103246205478899755899251003861 absolute error = 4.47416635e-23 relative error = 1.1742218303060634319541273807368e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0334 y[1] (analytic) = 3.8106056670620362664735673229417 y[1] (numeric) = 3.8106056670620362664736122012209 absolute error = 4.48782792e-23 relative error = 1.1777203710139075445909771326096e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0335 y[1] (analytic) = 3.8108867416822392513993308518873 y[1] (numeric) = 3.8108867416822392513993758667959 absolute error = 4.50149086e-23 relative error = 1.1812187464833729118323140667642e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0336 y[1] (analytic) = 3.8111678444113096765715430833196 y[1] (numeric) = 3.8111678444113096765715882348712 absolute error = 4.51515516e-23 relative error = 1.1847169540488793158492370454774e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0337 y[1] (analytic) = 3.8114489752520585692832507917036 y[1] (numeric) = 3.811448975252058569283296079912 absolute error = 4.52882084e-23 relative error = 1.1882149989166522234164683396130e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0338 y[1] (analytic) = 3.8117301342072972379442856611636 y[1] (numeric) = 3.8117301342072972379443310860423 absolute error = 4.54248787e-23 relative error = 1.1917128731739751261646861796636e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=2.57 NO POLE x[1] = 1.0339 y[1] (analytic) = 3.8120113212798372721093773696043 y[1] (numeric) = 3.812011321279837272109422931167 absolute error = 4.55615627e-23 relative error = 1.1952105820268983223015280109344e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.034 y[1] (analytic) = 3.8122925364724905425062694842819 y[1] (numeric) = 3.8122925364724905425063151825423 absolute error = 4.56982604e-23 relative error = 1.1987081254337460286408451025987e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0341 y[1] (analytic) = 3.8125737797880692010638381691049 y[1] (numeric) = 3.8125737797880692010638840040766 absolute error = 4.58349717e-23 relative error = 1.2022055007299516108656517933845e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0342 y[1] (analytic) = 3.8128550512293856809402137039462 y[1] (numeric) = 3.8128550512293856809402596756429 absolute error = 4.59716967e-23 relative error = 1.2057027104971447451809127541035e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0343 y[1] (analytic) = 3.813136350799252696550904816248 y[1] (numeric) = 3.8131363507992526965509509246834 absolute error = 4.61084354e-23 relative error = 1.2091997546936772495408893090025e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0344 y[1] (analytic) = 3.8134176785004832435969258252002 y[1] (numeric) = 3.813417678500483243596972070388 absolute error = 4.62451878e-23 relative error = 1.2126966332779101506745571521921e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0345 y[1] (analytic) = 3.8136990343358905990929265987741 y[1] (numeric) = 3.8136990343358905990929729807279 absolute error = 4.63819538e-23 relative error = 1.2161933435860875248107057475668e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0346 y[1] (analytic) = 3.8139804183082883213953253238921 y[1] (numeric) = 3.8139804183082883213953718426257 absolute error = 4.65187336e-23 relative error = 1.2196898908210345853264775821065e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0347 y[1] (analytic) = 3.8142618304204902502304440900158 y[1] (numeric) = 3.8142618304204902502304907455428 absolute error = 4.66555270e-23 relative error = 1.2231862696970810992743596989658e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0348 y[1] (analytic) = 3.8145432706753105067226472864321 y[1] (numeric) = 3.8145432706753105067226940787661 absolute error = 4.67923340e-23 relative error = 1.2266824801732052269330894350943e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0349 y[1] (analytic) = 3.8148247390755634934224828135206 y[1] (numeric) = 3.8148247390755634934225297426754 absolute error = 4.69291548e-23 relative error = 1.2301785274510990878138135301700e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.035 y[1] (analytic) = 3.8151062356240638943348261082825 y[1] (numeric) = 3.8151062356240638943348731742718 absolute error = 4.70659893e-23 relative error = 1.2336744088674396622826863622939e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0351 y[1] (analytic) = 3.8153877603236266749470269844131 y[1] (numeric) = 3.8153877603236266749470741872504 absolute error = 4.72028373e-23 relative error = 1.2371701191387212365537699409265e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0352 y[1] (analytic) = 3.8156693131770670822570592871979 y[1] (numeric) = 3.8156693131770670822571066268971 absolute error = 4.73396992e-23 relative error = 1.2406656687076275862759590874710e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0353 y[1] (analytic) = 3.8159508941872006448016733635169 y[1] (numeric) = 3.8159508941872006448017208400916 absolute error = 4.74765747e-23 relative error = 1.2441610496697057992237109520963e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0354 y[1] (analytic) = 3.8162325033568431726845513472347 y[1] (numeric) = 3.8162325033568431726845989606986 absolute error = 4.76134639e-23 relative error = 1.2476562646043744940345472718312e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0355 y[1] (analytic) = 3.8165141406888107576044652602612 y[1] (numeric) = 3.816514140688810757604513010628 absolute error = 4.77503668e-23 relative error = 1.2511513134700959121537124538372e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0356 y[1] (analytic) = 3.8167958061859197728834379295628 y[1] (numeric) = 3.8167958061859197728834858168462 absolute error = 4.78872834e-23 relative error = 1.2546461962253414989601136681725e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0357 y[1] (analytic) = 3.8170774998509868734949067204059 y[1] (numeric) = 3.8170774998509868734949547446195 absolute error = 4.80242136e-23 relative error = 1.2581409102087865678949864438638e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0358 y[1] (analytic) = 3.8173592216868289960918900861148 y[1] (numeric) = 3.8173592216868289960919382472724 absolute error = 4.81611576e-23 relative error = 1.2616354606187249840560162963188e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0359 y[1] (analytic) = 3.8176409716962633590351569346256 y[1] (numeric) = 3.8176409716962633590352052327408 absolute error = 4.82981152e-23 relative error = 1.2651298421742384549843900925882e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.036 y[1] (analytic) = 3.8179227498821074624213988121168 y[1] (numeric) = 3.8179227498821074624214472472034 absolute error = 4.84350866e-23 relative error = 1.2686240600728658822851399892412e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0361 y[1] (analytic) = 3.8182045562471790881114049040005 y[1] (numeric) = 3.8182045562471790881114534760722 absolute error = 4.85720717e-23 relative error = 1.2721181116535127315979983223563e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0362 y[1] (analytic) = 3.8184863907942962997582398535532 y[1] (numeric) = 3.8184863907942962997582885626235 absolute error = 4.87090703e-23 relative error = 1.2756119916370282296895838028820e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0363 y[1] (analytic) = 3.8187682535262774428354243984698 y[1] (numeric) = 3.8187682535262774428354732445525 absolute error = 4.88460827e-23 relative error = 1.2791057078390442770244409260863e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0364 y[1] (analytic) = 3.8190501444459411446651188256228 y[1] (numeric) = 3.8190501444459411446651678087317 absolute error = 4.89831089e-23 relative error = 1.2825992602175260199338094483319e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0365 y[1] (analytic) = 3.8193320635561063144463092443073 y[1] (numeric) = 3.819332063556106314446358364456 absolute error = 4.91201487e-23 relative error = 1.2860926434939301479610780279559e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0366 y[1] (analytic) = 3.8196140108595921432829966782539 y[1] (numeric) = 3.8196140108595921432830459354561 absolute error = 4.92572022e-23 relative error = 1.2895858602454655166698776653928e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0367 y[1] (analytic) = 3.8198959863592181042123889766926 y[1] (numeric) = 3.8198959863592181042124383709621 absolute error = 4.93942695e-23 relative error = 1.2930789130485770887316703945359e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=49.5MB, alloc=4.1MB, time=2.80 x[1] = 1.0368 y[1] (analytic) = 3.8201779900578039522330955447485 y[1] (numeric) = 3.8201779900578039522331450760989 absolute error = 4.95313504e-23 relative error = 1.2965717966259087906532483574329e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0369 y[1] (analytic) = 3.8204600219581697243333248934508 y[1] (numeric) = 3.8204600219581697243333745618959 absolute error = 4.96684451e-23 relative error = 1.3000645161716030795560359233222e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.037 y[1] (analytic) = 3.820742082063135739519085009639 y[1] (numeric) = 3.8207420820631357395191348151925 absolute error = 4.98055535e-23 relative error = 1.3035570690263878849390724345269e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0371 y[1] (analytic) = 3.8210241703755225988423865460463 y[1] (numeric) = 3.8210241703755225988424364887219 absolute error = 4.99426756e-23 relative error = 1.3070494551488726625319854977416e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0372 y[1] (analytic) = 3.821306286898151185429448831843 y[1] (numeric) = 3.8213062868981511854294989116544 absolute error = 5.00798114e-23 relative error = 1.3105416744976760655021771711571e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0373 y[1] (analytic) = 3.8215884316338426645089087039224 y[1] (numeric) = 3.8215884316338426645089589208833 absolute error = 5.02169609e-23 relative error = 1.3140337270314259440471466528188e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0374 y[1] (analytic) = 3.8218706045854184834400321592107 y[1] (numeric) = 3.8218706045854184834400825133348 absolute error = 5.03541241e-23 relative error = 1.3175256127087593449866150788370e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0375 y[1] (analytic) = 3.822152805755700371740928828283 y[1] (numeric) = 3.822152805755700371740979319584 absolute error = 5.04913010e-23 relative error = 1.3210173314883225113544524739221e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0376 y[1] (analytic) = 3.822435035147510341116769270568 y[1] (numeric) = 3.8224350351475103411168198990597 absolute error = 5.06284917e-23 relative error = 1.3245088859449042912045397585990e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0377 y[1] (analytic) = 3.8227172927636706854880050914234 y[1] (numeric) = 3.8227172927636706854880558571195 absolute error = 5.07656961e-23 relative error = 1.3280002734206495751683732805176e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0378 y[1] (analytic) = 3.8229995786070039810185918813637 y[1] (numeric) = 3.8229995786070039810186427842779 absolute error = 5.09029142e-23 relative error = 1.3314914938742322201025231180887e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0379 y[1] (analytic) = 3.8232818926803330861442149777232 y[1] (numeric) = 3.8232818926803330861442660178693 absolute error = 5.10401461e-23 relative error = 1.3349825498798892127024835039007e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.038 y[1] (analytic) = 3.8235642349864811416005180490368 y[1] (numeric) = 3.8235642349864811416005692264285 absolute error = 5.11773917e-23 relative error = 1.3384734387803725841918122060238e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0381 y[1] (analytic) = 3.8238466055282715704513345024195 y[1] (numeric) = 3.8238466055282715704513858170705 absolute error = 5.13146510e-23 relative error = 1.3419641605343838015764479923480e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0382 y[1] (analytic) = 3.8241290043085280781169217142285 y[1] (numeric) = 3.8241290043085280781169731661525 absolute error = 5.14519240e-23 relative error = 1.3454547151006335252168838941648e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0383 y[1] (analytic) = 3.8244114313300746524021980842892 y[1] (numeric) = 3.8244114313300746524022496735 absolute error = 5.15892108e-23 relative error = 1.3489451050526230406877237657473e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0384 y[1] (analytic) = 3.8246938865957355635249829139682 y[1] (numeric) = 3.8246938865957355635250346404794 absolute error = 5.17265112e-23 relative error = 1.3524353251193254265732222803270e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0385 y[1] (analytic) = 3.8249763701083353641442391083744 y[1] (numeric) = 3.8249763701083353641442909721999 absolute error = 5.18638255e-23 relative error = 1.3559253831032439371302817094813e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0386 y[1] (analytic) = 3.825258881870698889388318702973 y[1] (numeric) = 3.8252588818706988893883707041264 absolute error = 5.20011534e-23 relative error = 1.3594152711193610410230564942275e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0387 y[1] (analytic) = 3.8255414218856512568832112148919 y[1] (numeric) = 3.8255414218856512568832633533869 absolute error = 5.21384950e-23 relative error = 1.3629049917410217164270410121865e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0388 y[1] (analytic) = 3.8258239901560178667807948192054 y[1] (numeric) = 3.8258239901560178667808470950558 absolute error = 5.22758504e-23 relative error = 1.3663945475408078136683370614980e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0389 y[1] (analytic) = 3.8261065866846244017870903504765 y[1] (numeric) = 3.826106586684624401787142763696 absolute error = 5.24132195e-23 relative error = 1.3698839358632922386370364189442e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.039 y[1] (analytic) = 3.8263892114742968271905181298406 y[1] (numeric) = 3.826389211474296827190570680443 absolute error = 5.25506024e-23 relative error = 1.3733731592806891457661887730820e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0391 y[1] (analytic) = 3.8266718645278613908901576179135 y[1] (numeric) = 3.8266718645278613908902103059125 absolute error = 5.26879990e-23 relative error = 1.3768622151379759892715913733475e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0392 y[1] (analytic) = 3.8269545458481446234240098938054 y[1] (numeric) = 3.8269545458481446234240627192147 absolute error = 5.28254093e-23 relative error = 1.3803511033939554234290015932637e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0393 y[1] (analytic) = 3.8272372554379733379972629605245 y[1] (numeric) = 3.8272372554379733379973159233579 absolute error = 5.29628334e-23 relative error = 1.3838398266202901110403091291430e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0394 y[1] (analytic) = 3.8275199933001746305105598770528 y[1] (numeric) = 3.8275199933001746305106129773241 absolute error = 5.31002713e-23 relative error = 1.3873283847752220519108561787301e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0395 y[1] (analytic) = 3.8278027594375758795882697173758 y[1] (numeric) = 3.8278027594375758795883229550986 absolute error = 5.32377228e-23 relative error = 1.3908167725920728736762230893556e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0396 y[1] (analytic) = 3.8280855538530047466067613567495 y[1] (numeric) = 3.8280855538530047466068147319377 absolute error = 5.33751882e-23 relative error = 1.3943049978670764620191479582965e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0397 y[1] (analytic) = 3.8283683765492891757226800854884 y[1] (numeric) = 3.8283683765492891757227335981557 absolute error = 5.35126673e-23 relative error = 1.3977930553337658760361751529590e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=3.03 NO POLE x[1] = 1.0398 y[1] (analytic) = 3.8286512275292573939012270505547 y[1] (numeric) = 3.8286512275292573939012807007149 absolute error = 5.36501602e-23 relative error = 1.4012809475628848387577157524433e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0399 y[1] (analytic) = 3.8289341067957379109444415252345 y[1] (numeric) = 3.8289341067957379109444953129013 absolute error = 5.37876668e-23 relative error = 1.4047686719010286127032340989013e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.04 y[1] (analytic) = 3.8292170143515595195194860071813 y[1] (numeric) = 3.8292170143515595195195399323685 absolute error = 5.39251872e-23 relative error = 1.4082562309185734010994718724644e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0401 y[1] (analytic) = 3.8294999501995512951869341451116 y[1] (numeric) = 3.8294999501995512951869882078329 absolute error = 5.40627213e-23 relative error = 1.4117436219625188222722096759566e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0402 y[1] (analytic) = 3.8297829143425425964290614944339 y[1] (numeric) = 3.829782914342542596429115694703 absolute error = 5.42002691e-23 relative error = 1.4152308449917595386217308785329e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0403 y[1] (analytic) = 3.8300659067833630646781391020952 y[1] (numeric) = 3.8300659067833630646781934399258 absolute error = 5.43378306e-23 relative error = 1.4187178999651993972684207445009e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0404 y[1] (analytic) = 3.8303489275248426243447299209271 y[1] (numeric) = 3.8303489275248426243447843963331 absolute error = 5.44754060e-23 relative error = 1.4222047920632078500397922292518e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0405 y[1] (analytic) = 3.8306319765698114828459880537755 y[1] (numeric) = 3.8306319765698114828460426667706 absolute error = 5.46129951e-23 relative error = 1.4256915160224790550785833239198e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0406 y[1] (analytic) = 3.830915053921100130633960827695 y[1] (numeric) = 3.830915053921100130634015578293 absolute error = 5.47505980e-23 relative error = 1.4291780744122868675260208067439e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0407 y[1] (analytic) = 3.8311981595815393412238936984937 y[1] (numeric) = 3.8311981595815393412239485867083 absolute error = 5.48882146e-23 relative error = 1.4326644645808437420145392545772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0408 y[1] (analytic) = 3.8314812935539601712225379859085 y[1] (numeric) = 3.8314812935539601712225930117535 absolute error = 5.50258450e-23 relative error = 1.4361506890970561547686065800387e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0409 y[1] (analytic) = 3.831764455841193960356461439697 y[1] (numeric) = 3.8317644558411939603565166031861 absolute error = 5.51634891e-23 relative error = 1.4396367453095407621391438043498e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.041 y[1] (analytic) = 3.832047646446072331500361636926 y[1] (numeric) = 3.832047646446072331500416938073 absolute error = 5.53011470e-23 relative error = 1.4431226357868366966577164868785e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0411 y[1] (analytic) = 3.8323308653714271907053822107427 y[1] (numeric) = 3.8323308653714271907054376495614 absolute error = 5.54388187e-23 relative error = 1.4466083604873428173100256111108e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0412 y[1] (analytic) = 3.8326141126200907272274319109094 y[1] (numeric) = 3.8326141126200907272274874874135 absolute error = 5.55765041e-23 relative error = 1.4500939167602820246068231364248e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0413 y[1] (analytic) = 3.8328973881948954135555064963862 y[1] (numeric) = 3.8328973881948954135555622105895 absolute error = 5.57142033e-23 relative error = 1.4535793071736425154183298817536e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0414 y[1] (analytic) = 3.8331806920986740054400134602447 y[1] (numeric) = 3.833180692098674005440069312161 absolute error = 5.58519163e-23 relative error = 1.4570645316858508287805963128087e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0415 y[1] (analytic) = 3.8334640243342595419210995871955 y[1] (numeric) = 3.8334640243342595419211555768386 absolute error = 5.59896431e-23 relative error = 1.4605495902553427388075050939009e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0416 y[1] (analytic) = 3.8337473849044853453569813440136 y[1] (numeric) = 3.8337473849044853453570374713972 absolute error = 5.61273836e-23 relative error = 1.4640344802321493458977201410589e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0417 y[1] (analytic) = 3.8340307738121850214522781031437 y[1] (numeric) = 3.8340307738121850214523343682816 absolute error = 5.62651379e-23 relative error = 1.4675192041835243985582309113375e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0418 y[1] (analytic) = 3.8343141910601924592863481997704 y[1] (numeric) = 3.8343141910601924592864046026764 absolute error = 5.64029060e-23 relative error = 1.4710037620679313459896017707742e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0419 y[1] (analytic) = 3.8345976366513418313416278226354 y[1] (numeric) = 3.8345976366513418313416843633232 absolute error = 5.65406878e-23 relative error = 1.4744881512360073304135338740063e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.042 y[1] (analytic) = 3.834881110588467593531972738885 y[1] (numeric) = 3.8348811105884675935320294173684 absolute error = 5.66784834e-23 relative error = 1.4779723742544553496251007580654e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0421 y[1] (analytic) = 3.8351646128744044852310028532329 y[1] (numeric) = 3.8351646128744044852310596695257 absolute error = 5.68162928e-23 relative error = 1.4814564310817665241816716280789e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0422 y[1] (analytic) = 3.8354481435119875293004496017196 y[1] (numeric) = 3.8354481435119875293005065558357 absolute error = 5.69541161e-23 relative error = 1.4849403242836984622506942340174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0423 y[1] (analytic) = 3.8357317025040520321185061803537 y[1] (numeric) = 3.8357317025040520321185632723067 absolute error = 5.70919530e-23 relative error = 1.4884240459969889820414683397172e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0424 y[1] (analytic) = 3.8360152898534335836081806089169 y[1] (numeric) = 3.8360152898534335836082378387207 absolute error = 5.72298038e-23 relative error = 1.4919076040019286656978544709010e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0425 y[1] (analytic) = 3.8362989055629680572656516302184 y[1] (numeric) = 3.8362989055629680572657089978867 absolute error = 5.73676683e-23 relative error = 1.4953909930431092511009559127544e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0426 y[1] (analytic) = 3.8365825496354916101886274450798 y[1] (numeric) = 3.8365825496354916101886849506264 absolute error = 5.75055466e-23 relative error = 1.4988742156861325001046924141223e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=3.25 NO POLE x[1] = 1.0427 y[1] (analytic) = 3.8368662220738406831047072833359 y[1] (numeric) = 3.8368662220738406831047649267746 absolute error = 5.76434387e-23 relative error = 1.5023572718895448924453930455653e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0428 y[1] (analytic) = 3.8371499228808520003997458111346 y[1] (numeric) = 3.8371499228808520003998035924792 absolute error = 5.77813446e-23 relative error = 1.5058401616119021375474626246554e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0429 y[1] (analytic) = 3.8374336520593625701462203748188 y[1] (numeric) = 3.8374336520593625701462782940832 absolute error = 5.79192644e-23 relative error = 1.5093228874176774207905894099222e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.043 y[1] (analytic) = 3.8377174096122096841316010816751 y[1] (numeric) = 3.8377174096122096841316591388729 absolute error = 5.80571978e-23 relative error = 1.5128054414477201696793105122404e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0431 y[1] (analytic) = 3.8380011955422309178867237178316 y[1] (numeric) = 3.8380011955422309178867819129767 absolute error = 5.81951451e-23 relative error = 1.5162878314783385202559924307928e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0432 y[1] (analytic) = 3.8382850098522641307141655035906 y[1] (numeric) = 3.8382850098522641307142238366968 absolute error = 5.83331062e-23 relative error = 1.5197700548622168498554644825267e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0433 y[1] (analytic) = 3.8385688525451474657166236864776 y[1] (numeric) = 3.8385688525451474657166821575587 absolute error = 5.84710811e-23 relative error = 1.5232521115579570101030674417987e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0434 y[1] (analytic) = 3.838852723623719349825296972292 y[1] (numeric) = 3.8388527236237193498253555813618 absolute error = 5.86090698e-23 relative error = 1.5267340015241700798150600686900e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0435 y[1] (analytic) = 3.8391366230908184938282697944428 y[1] (numeric) = 3.839136623090818493828328541515 absolute error = 5.87470722e-23 relative error = 1.5302157221147240513001150693722e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0436 y[1] (analytic) = 3.8394205509492838923988994218528 y[1] (numeric) = 3.8394205509492838923989583069414 absolute error = 5.88850886e-23 relative error = 1.5336972811025053963503437172759e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0437 y[1] (analytic) = 3.8397045072019548241242059057165 y[1] (numeric) = 3.8397045072019548241242649288352 absolute error = 5.90231187e-23 relative error = 1.5371786706318959330078091394727e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0438 y[1] (analytic) = 3.8399884918516708515332648653933 y[1] (numeric) = 3.8399884918516708515333240265559 absolute error = 5.91611626e-23 relative error = 1.5406598932662959579632617084487e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0439 y[1] (analytic) = 3.8402725049012718211256031137222 y[1] (numeric) = 3.8402725049012718211256624129425 absolute error = 5.92992203e-23 relative error = 1.5441409489643626797303631847473e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.044 y[1] (analytic) = 3.8405565463535978633995971220407 y[1] (numeric) = 3.8405565463535978633996565593325 absolute error = 5.94372918e-23 relative error = 1.5476218376847625315094396917258e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0441 y[1] (analytic) = 3.8408406162114893928808743251923 y[1] (numeric) = 3.8408406162114893928809339005694 absolute error = 5.95753771e-23 relative error = 1.5511025593861711707694168857911e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0442 y[1] (analytic) = 3.8411247144777871081507172668062 y[1] (numeric) = 3.8411247144777871081507769802825 absolute error = 5.97134763e-23 relative error = 1.5545831166306776230138044187592e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0443 y[1] (analytic) = 3.8414088411553319918744705851342 y[1] (numeric) = 3.8414088411553319918745304367234 absolute error = 5.98515892e-23 relative error = 1.5580635041699751459572277935490e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0444 y[1] (analytic) = 3.8416929962469653108299508397275 y[1] (numeric) = 3.8416929962469653108300108294434 absolute error = 5.99897159e-23 relative error = 1.5615437245663637794465523262654e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0445 y[1] (analytic) = 3.8419771797555286159358591792386 y[1] (numeric) = 3.8419771797555286159359193070951 absolute error = 6.01278565e-23 relative error = 1.5650237803813825697119654819073e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0446 y[1] (analytic) = 3.842261391683863742280196850632 y[1] (numeric) = 3.8422613916838637422802571166429 absolute error = 6.02660109e-23 relative error = 1.5685036689705417314637837599175e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0447 y[1] (analytic) = 3.8425456320348128091486835500882 y[1] (numeric) = 3.8425456320348128091487439542672 absolute error = 6.04041790e-23 relative error = 1.5719833876901308435364450742839e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0448 y[1] (analytic) = 3.8428299008112182200531786158839 y[1] (numeric) = 3.8428299008112182200532391582449 absolute error = 6.05423610e-23 relative error = 1.5754629417039655480642441036856e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0449 y[1] (analytic) = 3.843114198015922662760105063535 y[1] (numeric) = 3.8431141980159226627601657440918 absolute error = 6.06805568e-23 relative error = 1.5789423283681613443920197285091e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.045 y[1] (analytic) = 3.843398523651769109318876463484 y[1] (numeric) = 3.8433985236517691093189372822505 absolute error = 6.08187665e-23 relative error = 1.5824215502433408505607894809935e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0451 y[1] (analytic) = 3.8436828777216008160903266616181 y[1] (numeric) = 3.8436828777216008160903876186082 absolute error = 6.09569901e-23 relative error = 1.5859006072876945169332331945937e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0452 y[1] (analytic) = 3.8439672602282613237751423429014 y[1] (numeric) = 3.8439672602282613237752034381287 absolute error = 6.10952273e-23 relative error = 1.5893794916549851502256994475919e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0453 y[1] (analytic) = 3.8442516711745944574422984384048 y[1] (numeric) = 3.8442516711745944574423596718832 absolute error = 6.12334784e-23 relative error = 1.5928582111090134673050420393500e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0454 y[1] (analytic) = 3.8445361105634443265574963760202 y[1] (numeric) = 3.8445361105634443265575577477635 absolute error = 6.13717433e-23 relative error = 1.5963367630069036099152679052038e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0455 y[1] (analytic) = 3.8448205783976553250116051751407 y[1] (numeric) = 3.8448205783976553250116666851628 absolute error = 6.15100221e-23 relative error = 1.5998151499083619882260993398030e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=61.0MB, alloc=4.2MB, time=3.47 x[1] = 1.0456 y[1] (analytic) = 3.8451050746800721311491053855934 y[1] (numeric) = 3.8451050746800721311491670339081 absolute error = 6.16483147e-23 relative error = 1.6032933691709161499940601297133e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0457 y[1] (analytic) = 3.8453895994135397077965358711075 y[1] (numeric) = 3.8453895994135397077965976577286 absolute error = 6.17866211e-23 relative error = 1.6067714207533893670797902859206e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0458 y[1] (analytic) = 3.8456741526009033022909434376036 y[1] (numeric) = 3.845674152600903302291005362545 absolute error = 6.19249414e-23 relative error = 1.6102493072149384417691661978787e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0459 y[1] (analytic) = 3.845958734245008446508335306588 y[1] (numeric) = 3.8459587342450084465083973698635 absolute error = 6.20632755e-23 relative error = 1.6137270259136959445837801347647e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.046 y[1] (analytic) = 3.8462433443487009568921344339362 y[1] (numeric) = 3.8462433443487009568921966355597 absolute error = 6.22016235e-23 relative error = 1.6172045794084523258572926288263e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0461 y[1] (analytic) = 3.8465279829148269344816376743512 y[1] (numeric) = 3.8465279829148269344817000143365 absolute error = 6.23399853e-23 relative error = 1.6206819650577434655814101185213e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0462 y[1] (analytic) = 3.8468126499462327649404767917798 y[1] (numeric) = 3.8468126499462327649405392701407 absolute error = 6.24783609e-23 relative error = 1.6241591828204387724878646376254e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0463 y[1] (analytic) = 3.847097345445765118585082316073 y[1] (numeric) = 3.8470973454457651185851449328233 absolute error = 6.26167503e-23 relative error = 1.6276362326554168703357781732267e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0464 y[1] (analytic) = 3.8473820694162709504131502461736 y[1] (numeric) = 3.8473820694162709504132130013272 absolute error = 6.27551536e-23 relative error = 1.6311131171207355836186893005018e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0465 y[1] (analytic) = 3.8476668218605975001321116001174 y[1] (numeric) = 3.8476668218605975001321744936881 absolute error = 6.28935707e-23 relative error = 1.6345898335757372676846325536679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0466 y[1] (analytic) = 3.8479516027815922921876048121308 y[1] (numeric) = 3.8479516027815922921876678441324 absolute error = 6.30320016e-23 relative error = 1.6380663819793282165489461441408e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0467 y[1] (analytic) = 3.8482364121821031357919509771111 y[1] (numeric) = 3.8482364121821031357920141475576 absolute error = 6.31704465e-23 relative error = 1.6415427674876098320395781279893e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0468 y[1] (analytic) = 3.8485212500649781249526319427736 y[1] (numeric) = 3.8485212500649781249526952516787 absolute error = 6.33089051e-23 relative error = 1.6450189822631510092405111558415e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0469 y[1] (analytic) = 3.8488061164330656385007712497498 y[1] (numeric) = 3.8488061164330656385008346971274 absolute error = 6.34473776e-23 relative error = 1.6484950314618792937489221797584e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.047 y[1] (analytic) = 3.8490910112892143401196179199226 y[1] (numeric) = 3.8490910112892143401196815057865 absolute error = 6.35858639e-23 relative error = 1.6519709124441449385777237238742e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0471 y[1] (analytic) = 3.8493759346362731783730330932825 y[1] (numeric) = 3.8493759346362731783730968176466 absolute error = 6.37243641e-23 relative error = 1.6554466277667240469955998513418e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0472 y[1] (analytic) = 3.8496608864770913867339795135899 y[1] (numeric) = 3.8496608864770913867340433764681 absolute error = 6.38628782e-23 relative error = 1.6589221773880013695071752546074e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0473 y[1] (analytic) = 3.8499458668145184836130138631286 y[1] (numeric) = 3.8499458668145184836130778645347 absolute error = 6.40014061e-23 relative error = 1.6623975586689318039753978759712e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0474 y[1] (analytic) = 3.850230875651404272386781946835 y[1] (numeric) = 3.8502308756514042723868460867828 absolute error = 6.41399478e-23 relative error = 1.6658727715684954501195911815062e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0475 y[1] (analytic) = 3.8505159129905988414265167260882 y[1] (numeric) = 3.8505159129905988414265810045916 absolute error = 6.42785034e-23 relative error = 1.6693478186427362009339548886861e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0476 y[1] (analytic) = 3.8508009788349525641265392024463 y[1] (numeric) = 3.8508009788349525641266036195192 absolute error = 6.44170729e-23 relative error = 1.6728226998500758138716508691352e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0477 y[1] (analytic) = 3.8510860731873160989327621516133 y[1] (numeric) = 3.8510860731873160989328267072695 absolute error = 6.45556562e-23 relative error = 1.6762974125522752261864661788183e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0478 y[1] (analytic) = 3.8513711960505403893711967079219 y[1] (numeric) = 3.8513711960505403893712614021753 absolute error = 6.46942534e-23 relative error = 1.6797719593048292795930013330445e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0479 y[1] (analytic) = 3.8516563474274766640764617996174 y[1] (numeric) = 3.8516563474274766640765266324819 absolute error = 6.48328645e-23 relative error = 1.6832463400661874961737318735867e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.048 y[1] (analytic) = 3.8519415273209764368202964352279 y[1] (numeric) = 3.8519415273209764368203614067172 absolute error = 6.49714893e-23 relative error = 1.6867205496026218489575162153289e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0481 y[1] (analytic) = 3.8522267357338915065400748413048 y[1] (numeric) = 3.8522267357338915065401399514329 absolute error = 6.51101281e-23 relative error = 1.6901945956614572277620934248921e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0482 y[1] (analytic) = 3.852511972669073957367324451821 y[1] (numeric) = 3.8525119726690739573673897006018 absolute error = 6.52487808e-23 relative error = 1.6936684756048852923743115585396e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0483 y[1] (analytic) = 3.8527972381293761586562467495098 y[1] (numeric) = 3.8527972381293761586563121369571 absolute error = 6.53874473e-23 relative error = 1.6971421867958757769382742736989e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0484 y[1] (analytic) = 3.8530825321176507650122409594303 y[1] (numeric) = 3.8530825321176507650123064855579 absolute error = 6.55261276e-23 relative error = 1.7006157291935010278852066392471e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=64.8MB, alloc=4.2MB, time=3.70 x[1] = 1.0485 y[1] (analytic) = 3.8533678546367507163204305950455 y[1] (numeric) = 3.8533678546367507163204962598673 absolute error = 6.56648218e-23 relative error = 1.7040891053519750573736135611009e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0486 y[1] (analytic) = 3.8536532056895292377741928570973 y[1] (numeric) = 3.8536532056895292377742586606272 absolute error = 6.58035299e-23 relative error = 1.7075623152298121383051777771793e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0487 y[1] (analytic) = 3.8539385852788398399036908855639 y[1] (numeric) = 3.8539385852788398399037568278158 absolute error = 6.59422519e-23 relative error = 1.7110353587855358038837785222009e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0488 y[1] (analytic) = 3.8542239934075363186044088649854 y[1] (numeric) = 3.8542239934075363186044749459731 absolute error = 6.60809877e-23 relative error = 1.7145082333831228439322554592107e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0489 y[1] (analytic) = 3.8545094300784727551656899834421 y[1] (numeric) = 3.8545094300784727551657562031796 absolute error = 6.62197375e-23 relative error = 1.7179809441704194512734124409600e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.049 y[1] (analytic) = 3.8547948952945035162992772454722 y[1] (numeric) = 3.8547948952945035162993436039733 absolute error = 6.63585011e-23 relative error = 1.7214534859170570462353427906668e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0491 y[1] (analytic) = 3.8550803890584832541678571392126 y[1] (numeric) = 3.8550803890584832541679236364912 absolute error = 6.64972786e-23 relative error = 1.7249258611761521745117946574744e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0492 y[1] (analytic) = 3.8553659113732669064136061580498 y[1] (numeric) = 3.8553659113732669064136727941197 absolute error = 6.66360699e-23 relative error = 1.7283980673124871130715903961670e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0493 y[1] (analytic) = 3.8556514622417096961867401770651 y[1] (numeric) = 3.8556514622417096961868069519402 absolute error = 6.67748751e-23 relative error = 1.7318701068788126375079037053621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0494 y[1] (analytic) = 3.8559370416666671321740666845611 y[1] (numeric) = 3.8559370416666671321741335982553 absolute error = 6.69136942e-23 relative error = 1.7353419798337170357764118902921e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0495 y[1] (analytic) = 3.8562226496509950086275398689531 y[1] (numeric) = 3.8562226496509950086276069214803 absolute error = 6.70525272e-23 relative error = 1.7388136861357978527324244951922e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0496 y[1] (analytic) = 3.8565082861975494053928185613128 y[1] (numeric) = 3.8565082861975494053928857526869 absolute error = 6.71913741e-23 relative error = 1.7422852257436618897049731207020e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0497 y[1] (analytic) = 3.8567939513091866879378270338483 y[1] (numeric) = 3.8567939513091866879378943640832 absolute error = 6.73302349e-23 relative error = 1.7457565986159252040707049864413e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0498 y[1] (analytic) = 3.8570796449887635073813186546075 y[1] (numeric) = 3.8570796449887635073813861237171 absolute error = 6.74691096e-23 relative error = 1.7492278047112131088275802819271e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0499 y[1] (analytic) = 3.8573653672391368005214423986893 y[1] (numeric) = 3.8573653672391368005215100066874 absolute error = 6.76079981e-23 relative error = 1.7526988413957171319184992266071e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.05 y[1] (analytic) = 3.8576511180631637898643122162488 y[1] (numeric) = 3.8576511180631637898643799631493 absolute error = 6.77469005e-23 relative error = 1.7561697112209082006970576147390e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0501 y[1] (analytic) = 3.8579368974637019836525792575823 y[1] (numeric) = 3.8579368974637019836526471433992 absolute error = 6.78858169e-23 relative error = 1.7596404167374983500782674382461e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0502 y[1] (analytic) = 3.8582227054436091758940069555778 y[1] (numeric) = 3.858222705443609175894074980325 absolute error = 6.80247472e-23 relative error = 1.7631109553117068710279331554546e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0503 y[1] (analytic) = 3.8585085420057434463900489658164 y[1] (numeric) = 3.8585085420057434463901171295076 absolute error = 6.81636912e-23 relative error = 1.7665813217188554133528845532836e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0504 y[1] (analytic) = 3.8587944071529631607644299646103 y[1] (numeric) = 3.8587944071529631607644982672595 absolute error = 6.83026492e-23 relative error = 1.7700515236932257024026491241755e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0505 y[1] (analytic) = 3.8590803008881269704917293052642 y[1] (numeric) = 3.8590803008881269704917977468853 absolute error = 6.84416211e-23 relative error = 1.7735215586016408290486608349628e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0506 y[1] (analytic) = 3.8593662232140938129259675328451 y[1] (numeric) = 3.859366223214093812926036113452 absolute error = 6.85806069e-23 relative error = 1.7769914264028001081421784289634e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0507 y[1] (analytic) = 3.8596521741337229113291957577457 y[1] (numeric) = 3.8596521741337229113292644773524 absolute error = 6.87196067e-23 relative error = 1.7804611296463191489221550647067e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0508 y[1] (analytic) = 3.8599381536498737749000878883295 y[1] (numeric) = 3.8599381536498737749001567469498 absolute error = 6.88586203e-23 relative error = 1.7839306631089097260479851734619e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0509 y[1] (analytic) = 3.8602241617654061988025357229408 y[1] (numeric) = 3.8602241617654061988026047205885 absolute error = 6.89976477e-23 relative error = 1.7874000267498747826696035419609e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.051 y[1] (analytic) = 3.8605101984831802641942469015675 y[1] (numeric) = 3.8605101984831802641943160382566 absolute error = 6.91366891e-23 relative error = 1.7908692257091888491326523226668e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0511 y[1] (analytic) = 3.8607962638060563382553457174423 y[1] (numeric) = 3.8607962638060563382554149931868 absolute error = 6.92757445e-23 relative error = 1.7943382599450216761146008071809e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0512 y[1] (analytic) = 3.8610823577368950742169767888678 y[1] (numeric) = 3.8610823577368950742170462036815 absolute error = 6.94148137e-23 relative error = 1.7978071242356576300707370434445e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0513 y[1] (analytic) = 3.8613684802785574113899115915512 y[1] (numeric) = 3.8613684802785574113899811454481 absolute error = 6.95538969e-23 relative error = 1.8012758237199474082166177359125e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0514 y[1] (analytic) = 3.8616546314339045751931578517367 y[1] (numeric) = 3.8616546314339045751932275447306 absolute error = 6.96929939e-23 relative error = 1.8047443531769615593317671946446e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.2MB, time=3.92 NO POLE x[1] = 1.0515 y[1] (analytic) = 3.8619408112057980771825718004187 y[1] (numeric) = 3.8619408112057980771826416325235 absolute error = 6.98321048e-23 relative error = 1.8082127151554299934826046976118e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0516 y[1] (analytic) = 3.8622270195970997150794732889245 y[1] (numeric) = 3.8622270195970997150795432601542 absolute error = 6.99712297e-23 relative error = 1.8116809122033242768085132107276e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0517 y[1] (analytic) = 3.8625132566106715727992637661515 y[1] (numeric) = 3.86251325661067157279933387652 absolute error = 7.01103685e-23 relative error = 1.8151489416898819675955878876323e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0518 y[1] (analytic) = 3.8627995222493760204800471177449 y[1] (numeric) = 3.862799522249376020480117367266 absolute error = 7.02495211e-23 relative error = 1.8186168009851173890127082791691e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0519 y[1] (analytic) = 3.8630858165160757145112533675024 y[1] (numeric) = 3.8630858165160757145113237561901 absolute error = 7.03886877e-23 relative error = 1.8220844952256340044573719886499e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.052 y[1] (analytic) = 3.8633721394136335975622652412928 y[1] (numeric) = 3.863372139413633597562335769161 absolute error = 7.05278682e-23 relative error = 1.8255520217812727643355677653062e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0521 y[1] (analytic) = 3.8636584909449128986110475937732 y[1] (numeric) = 3.8636584909449128986111182608359 absolute error = 7.06670627e-23 relative error = 1.8290193831990922140236973615153e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0522 y[1] (analytic) = 3.863944871112777132972779698193 y[1] (numeric) = 3.863944871112777132972850504464 absolute error = 7.08062710e-23 relative error = 1.8324865742613069020527697514249e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0523 y[1] (analytic) = 3.8642312799200901023284903995691 y[1] (numeric) = 3.8642312799200901023285613450624 absolute error = 7.09454933e-23 relative error = 1.8359536001030225251719074609297e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0524 y[1] (analytic) = 3.8645177173697158947536961315204 y[1] (numeric) = 3.8645177173697158947537672162499 absolute error = 7.10847295e-23 relative error = 1.8394204580948844488134083448102e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0525 y[1] (analytic) = 3.8648041834645188847470417970467 y[1] (numeric) = 3.8648041834645188847471130210263 absolute error = 7.12239796e-23 relative error = 1.8428871481957677536506241207948e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0526 y[1] (analytic) = 3.8650906782073637332589445135388 y[1] (numeric) = 3.8650906782073637332590158767824 absolute error = 7.13632436e-23 relative error = 1.8463536703645567639634173895935e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0527 y[1] (analytic) = 3.865377201601115387720240222307 y[1] (numeric) = 3.8653772016011153877203117248285 absolute error = 7.15025215e-23 relative error = 1.8498200245601450472061870371278e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0528 y[1] (analytic) = 3.8656637536486390820708331629129 y[1] (numeric) = 3.8656637536486390820709048047263 absolute error = 7.16418134e-23 relative error = 1.8532862133283132791327887088844e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0529 y[1] (analytic) = 3.8659503343528003367883482125926 y[1] (numeric) = 3.8659503343528003367884199937119 absolute error = 7.17811193e-23 relative error = 1.8567522366273982208860252507044e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.053 y[1] (analytic) = 3.8662369437164649589167860910568 y[1] (numeric) = 3.8662369437164649589168580114959 absolute error = 7.19204391e-23 relative error = 1.8602180918292515837825341083687e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0531 y[1] (analytic) = 3.8665235817424990420951814309545 y[1] (numeric) = 3.8665235817424990420952534907273 absolute error = 7.20597728e-23 relative error = 1.8636837788928039591862417121228e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0532 y[1] (analytic) = 3.8668102484337689665862637142874 y[1] (numeric) = 3.8668102484337689665863359134078 absolute error = 7.21991204e-23 relative error = 1.8671492977769951794751229851319e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0533 y[1] (analytic) = 3.8670969437931413993051210750611 y[1] (numeric) = 3.867096943793141399305193413543 absolute error = 7.23384819e-23 relative error = 1.8706146484407743176080566999460e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0534 y[1] (analytic) = 3.8673836678234832938478669684596 y[1] (numeric) = 3.867383667823483293847939446317 absolute error = 7.24778574e-23 relative error = 1.8740798334288271083589306539470e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0535 y[1] (analytic) = 3.8676704205276618905203097068308 y[1] (numeric) = 3.8676704205276618905203823240776 absolute error = 7.26172468e-23 relative error = 1.8775448501140102663794630714264e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0536 y[1] (analytic) = 3.8679572019085447163666248627681 y[1] (numeric) = 3.8679572019085447163666976194182 absolute error = 7.27566501e-23 relative error = 1.8810096984553006115421229927487e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0537 y[1] (analytic) = 3.8682440119689995851980305395759 y[1] (numeric) = 3.8682440119689995851981034356434 absolute error = 7.28960675e-23 relative error = 1.8844743835819888519418271284428e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0538 y[1] (analytic) = 3.8685308507118945976214655094065 y[1] (numeric) = 3.8685308507118945976215385449052 absolute error = 7.30354987e-23 relative error = 1.8879388976970382692153156293061e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0539 y[1] (analytic) = 3.8688177181400981410682702193523 y[1] (numeric) = 3.8688177181400981410683433942962 absolute error = 7.31749439e-23 relative error = 1.8914032459295664136623909594147e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.054 y[1] (analytic) = 3.8691046142564788898228706657838 y[1] (numeric) = 3.8691046142564788898229439801869 absolute error = 7.33144031e-23 relative error = 1.8948674282380120998310118597430e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0541 y[1] (analytic) = 3.8693915390639058050514651372178 y[1] (numeric) = 3.869391539063905805051538591094 absolute error = 7.34538762e-23 relative error = 1.8983314419964377766074163498103e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0542 y[1] (analytic) = 3.8696784925652481348307138260029 y[1] (numeric) = 3.8696784925652481348307874193661 absolute error = 7.35933632e-23 relative error = 1.9017952871638757737656458068861e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0543 y[1] (analytic) = 3.8699654747633754141764313091102 y[1] (numeric) = 3.8699654747633754141765050419744 absolute error = 7.37328642e-23 relative error = 1.9052589662833700380191229122828e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.2MB, time=4.14 NO POLE x[1] = 1.0544 y[1] (analytic) = 3.8702524856611574650722818983154 y[1] (numeric) = 3.8702524856611574650723557706945 absolute error = 7.38723791e-23 relative error = 1.9087224767295857406468352199090e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0545 y[1] (analytic) = 3.8705395252614643964984778600593 y[1] (numeric) = 3.8705395252614643964985518719673 absolute error = 7.40119080e-23 relative error = 1.9121858210452020867316862890282e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0546 y[1] (analytic) = 3.8708265935671666044604805052739 y[1] (numeric) = 3.8708265935671666044605546567248 absolute error = 7.41514509e-23 relative error = 1.9156489991887135569733385774765e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0547 y[1] (analytic) = 3.8711136905811347720177041494609 y[1] (numeric) = 3.8711136905811347720177784404686 absolute error = 7.42910077e-23 relative error = 1.9191120085353879855807978099544e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0548 y[1] (analytic) = 3.8714008163062398693122229433097 y[1] (numeric) = 3.8714008163062398693122973738882 absolute error = 7.44305785e-23 relative error = 1.9225748516273575452732641077201e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0549 y[1] (analytic) = 3.8716879707453531535974805741421 y[1] (numeric) = 3.8716879707453531535975551443054 absolute error = 7.45701633e-23 relative error = 1.9260375284231445578613382104038e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.055 y[1] (analytic) = 3.8719751539013461692670028384709 y[1] (numeric) = 3.8719751539013461692670775482329 absolute error = 7.47097620e-23 relative error = 1.9295000362986194332331492746397e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0551 y[1] (analytic) = 3.8722623657770907478831130859587 y[1] (numeric) = 3.8722623657770907478831879353333 absolute error = 7.48493746e-23 relative error = 1.9329623752128977505933771186345e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0552 y[1] (analytic) = 3.8725496063754590082056505350652 y[1] (numeric) = 3.8725496063754590082057255240664 absolute error = 7.49890012e-23 relative error = 1.9364245477073824112177714428632e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0553 y[1] (analytic) = 3.8728368756993233562206914606696 y[1] (numeric) = 3.8728368756993233562207665893114 absolute error = 7.51286418e-23 relative error = 1.9398865537406328337933701109034e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0554 y[1] (analytic) = 3.8731241737515564851692732539554 y[1] (numeric) = 3.8731241737515564851693485222518 absolute error = 7.52682964e-23 relative error = 1.9433483932712177240318313568200e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0555 y[1] (analytic) = 3.8734115005350313755761213548445 y[1] (numeric) = 3.8734115005350313755761967628094 absolute error = 7.54079649e-23 relative error = 1.9468100636760115814304746907375e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0556 y[1] (analytic) = 3.8736988560526212952783790572685 y[1] (numeric) = 3.8736988560526212952784546049158 absolute error = 7.55476473e-23 relative error = 1.9502715649141762258118148158601e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0557 y[1] (analytic) = 3.8739862403071997994543401875639 y[1] (numeric) = 3.8739862403071997994544158749076 absolute error = 7.56873437e-23 relative error = 1.9537328995262031816298355812822e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0558 y[1] (analytic) = 3.8742736533016407306521846562793 y[1] (numeric) = 3.8742736533016407306522604833334 absolute error = 7.58270541e-23 relative error = 1.9571940674706982427655626906944e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0559 y[1] (analytic) = 3.874561095038818218818716883681 y[1] (numeric) = 3.8745610950388182188187928504595 absolute error = 7.59667785e-23 relative error = 1.9606550687062764879475809049020e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.056 y[1] (analytic) = 3.8748485655216066813281070992449 y[1] (numeric) = 3.8748485655216066813281832057618 absolute error = 7.61065169e-23 relative error = 1.9641159031915622803164932253765e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0561 y[1] (analytic) = 3.8751360647528808230106355154223 y[1] (numeric) = 3.8751360647528808230107117616915 absolute error = 7.62462692e-23 relative error = 1.9675765683046347179613161340314e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0562 y[1] (analytic) = 3.8754235927355156361814393759666 y[1] (numeric) = 3.8754235927355156361815157620021 absolute error = 7.63860355e-23 relative error = 1.9710370665850741969765768687449e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0563 y[1] (analytic) = 3.8757111494723864006692628791085 y[1] (numeric) = 3.8757111494723864006693394049243 absolute error = 7.65258158e-23 relative error = 1.9744973979915329033288478248106e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0564 y[1] (analytic) = 3.8759987349663686838452099758676 y[1] (numeric) = 3.8759987349663686838452866414777 absolute error = 7.66656101e-23 relative error = 1.9779575624826723056514652334285e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0565 y[1] (analytic) = 3.8762863492203383406515000437875 y[1] (numeric) = 3.8762863492203383406515768492058 absolute error = 7.68054183e-23 relative error = 1.9814175574373743830080755081641e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0566 y[1] (analytic) = 3.8765739922371715136302264363816 y[1] (numeric) = 3.8765739922371715136303033816221 absolute error = 7.69452405e-23 relative error = 1.9848773853944907821420430966156e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0567 y[1] (analytic) = 3.8768616640197446329521179085782 y[1] (numeric) = 3.8768616640197446329521949936549 absolute error = 7.70850767e-23 relative error = 1.9883370463127107892688164945727e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0568 y[1] (analytic) = 3.8771493645709344164453029184518 y[1] (numeric) = 3.8771493645709344164453801433787 absolute error = 7.72249269e-23 relative error = 1.9917965401507329715222361257065e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0569 y[1] (analytic) = 3.8774370938936178696240768055282 y[1] (numeric) = 3.8774370938936178696241541703193 absolute error = 7.73647911e-23 relative error = 1.9952558668672651765172386974678e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.057 y[1] (analytic) = 3.8777248519906722857176718459518 y[1] (numeric) = 3.8777248519906722857177493506211 absolute error = 7.75046693e-23 relative error = 1.9987150264210245319123666601754e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0571 y[1] (analytic) = 3.8780126388649752456990301848014 y[1] (numeric) = 3.8780126388649752456991078293628 absolute error = 7.76445614e-23 relative error = 2.0021740161920970610338755695992e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0572 y[1] (analytic) = 3.8783004545194046183135796458439 y[1] (numeric) = 3.8783004545194046183136574303114 absolute error = 7.77844675e-23 relative error = 2.0056328387182415653370548518277e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=76.2MB, alloc=4.2MB, time=4.35 x[1] = 1.0573 y[1] (analytic) = 3.8785882989568385601080124190126 y[1] (numeric) = 3.8785882989568385601080903434002 absolute error = 7.79243876e-23 relative error = 2.0090914939582029821809609157085e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0574 y[1] (analytic) = 3.8788761721801555154590666258977 y[1] (numeric) = 3.8788761721801555154591446902195 absolute error = 7.80643218e-23 relative error = 2.0125499844488018423302453343052e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0575 y[1] (analytic) = 3.8791640741922342166023107635384 y[1] (numeric) = 3.8791640741922342166023889678083 absolute error = 7.82042699e-23 relative error = 2.0160083049924776713185291959571e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0576 y[1] (analytic) = 3.8794520049959536836609310268018 y[1] (numeric) = 3.8794520049959536836610093710338 absolute error = 7.83442320e-23 relative error = 2.0194664581262609021826828961823e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0577 y[1] (analytic) = 3.8797399645941932246745215096392 y[1] (numeric) = 3.8797399645941932246745999938474 absolute error = 7.84842082e-23 relative error = 2.0229244463864259125199269117151e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0578 y[1] (analytic) = 3.8800279529898324356278772855061 y[1] (numeric) = 3.8800279529898324356279559097044 absolute error = 7.86241983e-23 relative error = 2.0263822645765880574102168745051e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0579 y[1] (analytic) = 3.8803159701857512004797903672338 y[1] (numeric) = 3.8803159701857512004798691314362 absolute error = 7.87642024e-23 relative error = 2.0298399152332315862833281885069e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.058 y[1] (analytic) = 3.8806040161848296911918485466416 y[1] (numeric) = 3.880604016184829691191927450862 absolute error = 7.89042204e-23 relative error = 2.0332973957382479475959264596870e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0581 y[1] (analytic) = 3.8808920909899483677572371141764 y[1] (numeric) = 3.8808920909899483677573161584289 absolute error = 7.90442525e-23 relative error = 2.0367547112044844303107788228503e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0582 y[1] (analytic) = 3.8811801946039879782295434588689 y[1] (numeric) = 3.8811801946039879782296226431676 absolute error = 7.91842987e-23 relative error = 2.0402118615901956142359425321746e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0583 y[1] (analytic) = 3.8814683270298295587515645488934 y[1] (numeric) = 3.8814683270298295587516438732522 absolute error = 7.93243588e-23 relative error = 2.0436688417009561908033416905299e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0584 y[1] (analytic) = 3.8817564882703544335841172930196 y[1] (numeric) = 3.8817564882703544335841967574525 absolute error = 7.94644329e-23 relative error = 2.0471256540723402800216448835324e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0585 y[1] (analytic) = 3.8820446783284442151348517832447 y[1] (numeric) = 3.8820446783284442151349313877658 absolute error = 7.96045211e-23 relative error = 2.0505823012391662395751757077475e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0586 y[1] (analytic) = 3.8823328972069808039870674188944 y[1] (numeric) = 3.8823328972069808039871471635177 absolute error = 7.97446233e-23 relative error = 2.0540387805839550089911100752943e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0587 y[1] (analytic) = 3.8826211449088463889285319124795 y[1] (numeric) = 3.8826211449088463889286117972189 absolute error = 7.98847394e-23 relative error = 2.0574950894900017619846417047548e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0588 y[1] (analytic) = 3.8829094214369234469803031775975 y[1] (numeric) = 3.8829094214369234469803832024671 absolute error = 8.00248696e-23 relative error = 2.0609512330675411042996420562944e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0589 y[1] (analytic) = 3.8831977267940947434255540991677 y[1] (numeric) = 3.8831977267940947434256342641814 absolute error = 8.01650137e-23 relative error = 2.0644072061244983046033802564821e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.059 y[1] (analytic) = 3.8834860609832433318384001862864 y[1] (numeric) = 3.8834860609832433318384804914583 absolute error = 8.03051719e-23 relative error = 2.0678630137703616426925024196957e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0591 y[1] (analytic) = 3.8837744240072525541127301079925 y[1] (numeric) = 3.8837744240072525541128105533366 absolute error = 8.04453441e-23 relative error = 2.0713186533886545953992284501630e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0592 y[1] (analytic) = 3.8840628158690060404910391122302 y[1] (numeric) = 3.8840628158690060404911196977605 absolute error = 8.05855303e-23 relative error = 2.0747741249382983402584617753165e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0593 y[1] (analytic) = 3.8843512365713877095932653282979 y[1] (numeric) = 3.8843512365713877095933460540285 absolute error = 8.07257306e-23 relative error = 2.0782294309526558080389429656476e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0594 y[1] (analytic) = 3.8846396861172817684456289530719 y[1] (numeric) = 3.8846396861172817684457098190168 absolute error = 8.08659449e-23 relative error = 2.0816845688158519092118702889229e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0595 y[1] (analytic) = 3.8849281645095727125094743212924 y[1] (numeric) = 3.8849281645095727125095553274656 absolute error = 8.10061732e-23 relative error = 2.0851395384868356575904268706300e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0596 y[1] (analytic) = 3.8852166717511453257101148602012 y[1] (numeric) = 3.8852166717511453257101960066167 absolute error = 8.11464155e-23 relative error = 2.0885943399245653355895064359983e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0597 y[1] (analytic) = 3.8855052078448846804656809288185 y[1] (numeric) = 3.8855052078448846804657622154903 absolute error = 8.12866718e-23 relative error = 2.0920489730880084937829764238871e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0598 y[1] (analytic) = 3.8857937727936761377159705421485 y[1] (numeric) = 3.8857937727936761377160519690907 absolute error = 8.14269422e-23 relative error = 2.0955034405096187185833488874397e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0599 y[1] (analytic) = 3.8860823666004053469513029806017 y[1] (numeric) = 3.8860823666004053469513845478283 absolute error = 8.15672266e-23 relative error = 2.0989577395745230970059773080329e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.06 y[1] (analytic) = 3.8863709892679582462413752849215 y[1] (numeric) = 3.8863709892679582462414569924465 absolute error = 8.17075250e-23 relative error = 2.1024118702417170092695387938853e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0601 y[1] (analytic) = 3.8866596407992210622641216369058 y[1] (numeric) = 3.8866596407992210622642034847432 absolute error = 8.18478374e-23 relative error = 2.1058658324702051019799212117945e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0602 memory used=80.1MB, alloc=4.2MB, time=4.58 y[1] (analytic) = 3.8869483211970803103345756262099 y[1] (numeric) = 3.8869483211970803103346576143738 absolute error = 8.19881639e-23 relative error = 2.1093196287917136506129835968627e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0603 y[1] (analytic) = 3.8872370304644227944337354035214 y[1] (numeric) = 3.8872370304644227944338175320258 absolute error = 8.21285044e-23 relative error = 2.1127732565921713140730706403037e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0604 y[1] (analytic) = 3.8875257686041356072374317203939 y[1] (numeric) = 3.8875257686041356072375139892529 absolute error = 8.22688590e-23 relative error = 2.1162267184029407792791154950439e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0605 y[1] (analytic) = 3.8878145356191061301451988560295 y[1] (numeric) = 3.887814535619106130145281265257 absolute error = 8.24092275e-23 relative error = 2.1196800090382122902522180766533e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0606 y[1] (analytic) = 3.8881033315122220333091484312979 y[1] (numeric) = 3.8881033315122220333092309809081 absolute error = 8.25496102e-23 relative error = 2.1231331361734543438252063514637e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0607 y[1] (analytic) = 3.8883921562863712756628461102822 y[1] (numeric) = 3.888392156286371275662928800289 absolute error = 8.26900068e-23 relative error = 2.1265860920513097619808077142786e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0608 y[1] (analytic) = 3.888681009944442104950191189638 y[1] (numeric) = 3.8886810099444421049502740200555 absolute error = 8.28304175e-23 relative error = 2.1300388817745532891229982240264e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0609 y[1] (analytic) = 3.8889698924893230577542990760569 y[1] (numeric) = 3.8889698924893230577543820468991 absolute error = 8.29708422e-23 relative error = 2.1334915027303156643186445690477e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.061 y[1] (analytic) = 3.8892588039239029595263866521213 y[1] (numeric) = 3.8892588039239029595264697634024 absolute error = 8.31112811e-23 relative error = 2.1369439600200529908000150550992e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0611 y[1] (analytic) = 3.8895477442510709246146605308412 y[1] (numeric) = 3.8895477442510709246147437825751 absolute error = 8.32517339e-23 relative error = 2.1403962458887376330154044635830e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0612 y[1] (analytic) = 3.8898367134737163562932081991599 y[1] (numeric) = 3.8898367134737163562932915913606 absolute error = 8.33922007e-23 relative error = 2.1438483628668512608327463204176e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0613 y[1] (analytic) = 3.8901257115947289467908920507189 y[1] (numeric) = 3.8901257115947289467909755834005 absolute error = 8.35326816e-23 relative error = 2.1473003134841208081765860690911e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0614 y[1] (analytic) = 3.890414738616998677320246308171 y[1] (numeric) = 3.8904147386169986773203299813476 absolute error = 8.36731766e-23 relative error = 2.1507520976990985274423744601279e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0615 y[1] (analytic) = 3.8907037945434158181063768353295 y[1] (numeric) = 3.8907037945434158181064606490151 absolute error = 8.38136856e-23 relative error = 2.1542037129001169157074588753239e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0616 y[1] (analytic) = 3.8909928793768709284158638394433 y[1] (numeric) = 3.890992879376870928415947793652 absolute error = 8.39542087e-23 relative error = 2.1576551616163578427459677908395e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0617 y[1] (analytic) = 3.8912819931202548565856674638869 y[1] (numeric) = 3.8912819931202548565857515586327 absolute error = 8.40947458e-23 relative error = 2.1611064412365543138478825660434e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0618 y[1] (analytic) = 3.8915711357764587400520362715539 y[1] (numeric) = 3.8915711357764587400521205068509 absolute error = 8.42352970e-23 relative error = 2.1645575542895248575807514897695e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0619 y[1] (analytic) = 3.8918603073483740053794186192439 y[1] (numeric) = 3.8918603073483740053795029951062 absolute error = 8.43758623e-23 relative error = 2.1680085007338682454161153653002e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.062 y[1] (analytic) = 3.8921495078388923682893769233309 y[1] (numeric) = 3.8921495078388923682894614397724 absolute error = 8.45164415e-23 relative error = 2.1714592753896438094417854996777e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0621 y[1] (analytic) = 3.8924387372509058336895048170028 y[1] (numeric) = 3.8924387372509058336895894740377 absolute error = 8.46570349e-23 relative error = 2.1749098859238648106878931418371e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0622 y[1] (analytic) = 3.8927279955873066957023471993618 y[1] (numeric) = 3.8927279955873066957024319970042 absolute error = 8.47976424e-23 relative error = 2.1783603297256926354289822207104e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0623 y[1] (analytic) = 3.8930172828509875376943231766739 y[1] (numeric) = 3.8930172828509875376944081149378 absolute error = 8.49382639e-23 relative error = 2.1818106041850616080129671667882e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0624 y[1] (analytic) = 3.893306599044841232304651896057 y[1] (numeric) = 3.8933065990448412323047369749564 absolute error = 8.50788994e-23 relative error = 2.1852607092611896854337082806933e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0625 y[1] (analytic) = 3.8935959441717609414742812718972 y[1] (numeric) = 3.8935959441717609414743664914462 absolute error = 8.52195490e-23 relative error = 2.1887106474816239942574206957402e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0626 y[1] (analytic) = 3.8938853182346401164748196052827 y[1] (numeric) = 3.8938853182346401164749049654953 absolute error = 8.53602126e-23 relative error = 2.1921604162368993591923461232570e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0627 y[1] (analytic) = 3.8941747212363724979374700967436 y[1] (numeric) = 3.8941747212363724979375555976339 absolute error = 8.55008903e-23 relative error = 2.1956100180541997246291494771675e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0628 y[1] (analytic) = 3.8944641531798521158819682525883 y[1] (numeric) = 3.8944641531798521158820538941705 absolute error = 8.56415822e-23 relative error = 2.1990594554599549048629484681987e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0629 y[1] (analytic) = 3.894753614067973289745522185125 y[1] (numeric) = 3.8947536140679732897456079674131 absolute error = 8.57822881e-23 relative error = 2.2025087232771711438960463861063e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.063 y[1] (analytic) = 3.8950431039036306284117558070577 y[1] (numeric) = 3.8950431039036306284118417300657 absolute error = 8.59230080e-23 relative error = 2.2059578214651220375826593131208e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0631 y[1] (analytic) = 3.8953326226897190302396549203467 y[1] (numeric) = 3.8953326226897190302397409840887 absolute error = 8.60637420e-23 relative error = 2.2094067525502652998412123255786e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.2MB, time=4.82 NO POLE x[1] = 1.0632 y[1] (analytic) = 3.8956221704291336830925161998224 y[1] (numeric) = 3.8956221704291336830926024043125 absolute error = 8.62044901e-23 relative error = 2.2128555164913206051644601273101e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0633 y[1] (analytic) = 3.8959117471247700643668990718429 y[1] (numeric) = 3.8959117471247700643669854170951 absolute error = 8.63452522e-23 relative error = 2.2163041106802236794748948112780e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0634 y[1] (analytic) = 3.8962013527795239410215804882829 y[1] (numeric) = 3.8962013527795239410216669743114 absolute error = 8.64860285e-23 relative error = 2.2197525402094901156338477539175e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0635 y[1] (analytic) = 3.8964909873962913696065125961464 y[1] (numeric) = 3.8964909873962913696065992229653 absolute error = 8.66268189e-23 relative error = 2.2232008024708834541642725793500e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0636 y[1] (analytic) = 3.89678065097796869629178330309 y[1] (numeric) = 3.8967806509779686962918700707133 absolute error = 8.67676233e-23 relative error = 2.2266488948569396851211572866511e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0637 y[1] (analytic) = 3.8970703435274525568965797391478 y[1] (numeric) = 3.8970703435274525568966666475895 absolute error = 8.69084417e-23 relative error = 2.2300968173269973052610999690086e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0638 y[1] (analytic) = 3.8973600650476398769181546149475 y[1] (numeric) = 3.8973600650476398769182416642218 absolute error = 8.70492743e-23 relative error = 2.2335445749720828556180933747252e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0639 y[1] (analytic) = 3.8976498155414278715607954767074 y[1] (numeric) = 3.8976498155414278715608826668283 absolute error = 8.71901209e-23 relative error = 2.2369921626191115618977056708476e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.064 y[1] (analytic) = 3.8979395950117140457647968583027 y[1] (numeric) = 3.8979395950117140457648841892844 absolute error = 8.73309817e-23 relative error = 2.2404395853583655618870229333512e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0641 y[1] (analytic) = 3.8982294034613961942354353306936 y[1] (numeric) = 3.89822940346139619423552280255 absolute error = 8.74718564e-23 relative error = 2.2438868354522744729877884127119e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0642 y[1] (analytic) = 3.898519240893372401471947449001 y[1] (numeric) = 3.8985192408933724014720350617463 absolute error = 8.76127453e-23 relative error = 2.2473339205560247276049091457669e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0643 y[1] (analytic) = 3.8988091073105410417965105975241 y[1] (numeric) = 3.8988091073105410417965983511724 absolute error = 8.77536483e-23 relative error = 2.2507808380629803873319768709399e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0644 y[1] (analytic) = 3.8990990027158007793832267329858 y[1] (numeric) = 3.8990990027158007793833146275511 absolute error = 8.78945653e-23 relative error = 2.2542275853672776625452131505262e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0645 y[1] (analytic) = 3.8993889271120505682871090262977 y[1] (numeric) = 3.8993889271120505682871970617943 absolute error = 8.80354966e-23 relative error = 2.2576741701218423566166936243273e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0646 y[1] (analytic) = 3.8996788805021896524730714031351 y[1] (numeric) = 3.8996788805021896524731595795769 absolute error = 8.81764418e-23 relative error = 2.2611205820271254336490621344489e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0647 y[1] (analytic) = 3.8999688628891175658449209836094 y[1] (numeric) = 3.8999688628891175658450093010106 absolute error = 8.83174012e-23 relative error = 2.2645668287354992357735241984722e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0648 y[1] (analytic) = 3.900258874275734132274353421331 y[1] (numeric) = 3.9002588742757341322744418797057 absolute error = 8.84583747e-23 relative error = 2.2680129076413278686702079642446e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0649 y[1] (analytic) = 3.9005489146649394656299511421502 y[1] (numeric) = 3.9005489146649394656300397415125 absolute error = 8.85993623e-23 relative error = 2.2714588187034891230416350245267e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.065 y[1] (analytic) = 3.9008389840596339698061844828672 y[1] (numeric) = 3.9008389840596339698062732232311 absolute error = 8.87403639e-23 relative error = 2.2749045593173190073404269437612e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0651 y[1] (analytic) = 3.9011290824627183387524157302009 y[1] (numeric) = 3.9011290824627183387525046115805 absolute error = 8.88813796e-23 relative error = 2.2783501320056462596748292570036e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0652 y[1] (analytic) = 3.9014192098770935565019060603067 y[1] (numeric) = 3.9014192098770935565019950827162 absolute error = 8.90224095e-23 relative error = 2.2817955392905463687723053804957e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0653 y[1] (analytic) = 3.9017093663056608972008253791335 y[1] (numeric) = 3.901709366305660897200914542587 absolute error = 8.91634535e-23 relative error = 2.2852407785673832409441387690134e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0654 y[1] (analytic) = 3.9019995517513219251372650639094 y[1] (numeric) = 3.901999551751321925137354368421 absolute error = 8.93045116e-23 relative error = 2.2886858497950811633236761885521e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0655 y[1] (analytic) = 3.9022897662169784947702536060468 y[1] (numeric) = 3.9022897662169784947703430516305 absolute error = 8.94455837e-23 relative error = 2.2921307503699757082488555392440e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0656 y[1] (analytic) = 3.9025800097055327507587751557567 y[1] (numeric) = 3.9025800097055327507588647424267 absolute error = 8.95866700e-23 relative error = 2.2955754853763963697964970121026e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0657 y[1] (analytic) = 3.9028702822198871279907909686632 y[1] (numeric) = 3.9028702822198871279908806964336 absolute error = 8.97277704e-23 relative error = 2.2990200522105067194560153136391e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0658 y[1] (analytic) = 3.9031605837629443516122637547069 y[1] (numeric) = 3.9031605837629443516123536235918 absolute error = 8.98688849e-23 relative error = 2.3024644508312682333854802400344e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0659 y[1] (analytic) = 3.9034509143376074370561849296288 y[1] (numeric) = 3.9034509143376074370562749396423 absolute error = 9.00100135e-23 relative error = 2.3059086811976516838698111543888e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.066 y[1] (analytic) = 3.9037412739467796900716047693244 y[1] (numeric) = 3.9037412739467796900716949204806 absolute error = 9.01511562e-23 relative error = 2.3093527432686371388686315412146e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=87.7MB, alloc=4.2MB, time=5.04 x[1] = 1.0661 y[1] (analytic) = 3.9040316625933647067526654673584 y[1] (numeric) = 3.9040316625933647067527557596715 absolute error = 9.02923131e-23 relative error = 2.3127966395646685972461665671257e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0662 y[1] (analytic) = 3.9043220802802663735676370959306 y[1] (numeric) = 3.9043220802802663735677275294147 absolute error = 9.04334841e-23 relative error = 2.3162403674829090206345358663706e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0663 y[1] (analytic) = 3.9046125270103888673879564705823 y[1] (numeric) = 3.9046125270103888673880470452515 absolute error = 9.05746692e-23 relative error = 2.3196839269823663891811834304088e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0664 y[1] (analytic) = 3.9049030027866366555172689189352 y[1] (numeric) = 3.9049030027866366555173596348036 absolute error = 9.07158684e-23 relative error = 2.3231273180220579768988396348633e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0665 y[1] (analytic) = 3.9051935076119144957204729537519 y[1] (numeric) = 3.9051935076119144957205638108336 absolute error = 9.08570817e-23 relative error = 2.3265705405610103512124120677480e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0666 y[1] (analytic) = 3.9054840414891274362527678506092 y[1] (numeric) = 3.9054840414891274362528588489184 absolute error = 9.09983092e-23 relative error = 2.3300135971187614495253318834043e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0667 y[1] (analytic) = 3.9057746044211808158887041304744 y[1] (numeric) = 3.9057746044211808158887952700252 absolute error = 9.11395508e-23 relative error = 2.3334564850934733800034568287762e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0668 y[1] (analytic) = 3.9060651964109802639512369474748 y[1] (numeric) = 3.9060651964109802639513282282813 absolute error = 9.12808065e-23 relative error = 2.3368992044442006154702408086579e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0669 y[1] (analytic) = 3.9063558174614317003407823821514 y[1] (numeric) = 3.9063558174614317003408738042278 absolute error = 9.14220764e-23 relative error = 2.3403417576899375736950684421593e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.067 y[1] (analytic) = 3.9066464675754413355642766404877 y[1] (numeric) = 3.906646467575441335564368203848 absolute error = 9.15633603e-23 relative error = 2.3437841396697055475826590940615e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0671 y[1] (analytic) = 3.9069371467559156707642381590028 y[1] (numeric) = 3.9069371467559156707643298636611 absolute error = 9.17046583e-23 relative error = 2.3472263529027080020012313474642e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0672 y[1] (analytic) = 3.907227855005761497747832616201 y[1] (numeric) = 3.9072278550057614977479244621715 absolute error = 9.18459705e-23 relative error = 2.3506683999073958867720122350010e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0673 y[1] (analytic) = 3.9075185923278858990159408506679 y[1] (numeric) = 3.9075185923278858990160328379647 absolute error = 9.19872968e-23 relative error = 2.3541102780831299586784017063395e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0674 y[1] (analytic) = 3.907809358725196247792229686103 y[1] (numeric) = 3.9078093587251962477923218147403 absolute error = 9.21286373e-23 relative error = 2.3575519899479989276679056408379e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0675 y[1] (analytic) = 3.9081001542006002080522256635809 y[1] (numeric) = 3.9081001542006002080523179335729 absolute error = 9.22699920e-23 relative error = 2.3609935354605510976310188031893e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0676 y[1] (analytic) = 3.9083909787570057345523916813308 y[1] (numeric) = 3.9083909787570057345524840926916 absolute error = 9.24113608e-23 relative error = 2.3644349120207464598810194128080e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0677 y[1] (analytic) = 3.9086818323973210728592065423253 y[1] (numeric) = 3.9086818323973210728592990950689 absolute error = 9.25527436e-23 relative error = 2.3678761170293159130646323977457e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0678 y[1] (analytic) = 3.9089727151244547593782474099691 y[1] (numeric) = 3.9089727151244547593783401041098 absolute error = 9.26941407e-23 relative error = 2.3713171581206287068382844130667e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0679 y[1] (analytic) = 3.9092636269413156213832751721797 y[1] (numeric) = 3.9092636269413156213833680077315 absolute error = 9.28355518e-23 relative error = 2.3747580275786197826595260171020e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.068 y[1] (analytic) = 3.9095545678508127770453227141486 y[1] (numeric) = 3.9095545678508127770454156911257 absolute error = 9.29769771e-23 relative error = 2.3781987304786985810488004629152e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0681 y[1] (analytic) = 3.9098455378558556354617861000763 y[1] (numeric) = 3.9098455378558556354618792184928 absolute error = 9.31184165e-23 relative error = 2.3816392642218235574452286887801e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0682 y[1] (analytic) = 3.9101365369593538966855186641702 y[1] (numeric) = 3.9101365369593538966856119240403 absolute error = 9.32598701e-23 relative error = 2.3850796313246347880941238243399e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0683 y[1] (analytic) = 3.9104275651642175517539280111976 y[1] (numeric) = 3.9104275651642175517540214125355 absolute error = 9.34013379e-23 relative error = 2.3885198317457551782870086288178e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0684 y[1] (analytic) = 3.910718622473356882718075926884 y[1] (numeric) = 3.9107186224733568827181694697038 absolute error = 9.35428198e-23 relative error = 2.3919598628867421839579169306577e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0685 y[1] (analytic) = 3.9110097088896824626717811984478 y[1] (numeric) = 3.9110097088896824626718748827636 absolute error = 9.36843158e-23 relative error = 2.3953997247068083406147198521694e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0686 y[1] (analytic) = 3.9113008244161051557807253455628 y[1] (numeric) = 3.9113008244161051557808191713889 absolute error = 9.38258261e-23 relative error = 2.3988394222785638000059473359273e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0687 y[1] (analytic) = 3.9115919690555361173115612620397 y[1] (numeric) = 3.9115919690555361173116552293901 absolute error = 9.39673504e-23 relative error = 2.4022789478905862725823728259094e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0688 y[1] (analytic) = 3.911883142810886793661024768516 y[1] (numeric) = 3.9118831428108867936611188774049 absolute error = 9.41088889e-23 relative error = 2.4057183066153142250221844118265e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0689 y[1] (analytic) = 3.9121743456850689223850490764485 y[1] (numeric) = 3.9121743456850689223851433268901 absolute error = 9.42504416e-23 relative error = 2.4091574984114265154784208510975e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=91.5MB, alloc=4.2MB, time=5.25 x[1] = 1.069 y[1] (analytic) = 3.9124655776809945322278821636965 y[1] (numeric) = 3.9124655776809945322279765557049 absolute error = 9.43920084e-23 relative error = 2.4125965206816783096118124500273e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0691 y[1] (analytic) = 3.9127568388015759431512070619884 y[1] (numeric) = 3.9127568388015759431513015955778 absolute error = 9.45335894e-23 relative error = 2.4160353759410806925394087371045e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0692 y[1] (analytic) = 3.9130481290497257663632650565632 y[1] (numeric) = 3.9130481290497257663633597317477 absolute error = 9.46751845e-23 relative error = 2.4194740615927879884482905769445e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0693 y[1] (analytic) = 3.9133394484283569043479817982768 y[1] (numeric) = 3.9133394484283569043480766150706 absolute error = 9.48167938e-23 relative error = 2.4229125801514493786025749883685e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0694 y[1] (analytic) = 3.9136307969403825508940963284658 y[1] (numeric) = 3.9136307969403825508941912868831 absolute error = 9.49584173e-23 relative error = 2.4263509315757903499491195471873e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0695 y[1] (analytic) = 3.913922174588716191124293016859 y[1] (numeric) = 3.913922174588716191124388116914 absolute error = 9.51000550e-23 relative error = 2.4297891158245457249852075870491e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0696 y[1] (analytic) = 3.9142135813762716015243364128288 y[1] (numeric) = 3.9142135813762716015244316545355 absolute error = 9.52417067e-23 relative error = 2.4332271277468764502174521711586e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0697 y[1] (analytic) = 3.9145050173059628499722090102725 y[1] (numeric) = 3.9145050173059628499723043936451 absolute error = 9.53833726e-23 relative error = 2.4366649724118800485914429312615e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0698 y[1] (analytic) = 3.9147964823807042957672519264171 y[1] (numeric) = 3.9147964823807042957673474514699 absolute error = 9.55250528e-23 relative error = 2.4401026523327304957315184055435e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0699 y[1] (analytic) = 3.9150879766034105896593084948368 y[1] (numeric) = 3.9150879766034105896594041615839 absolute error = 9.56667471e-23 relative error = 2.4435401623591872995945775843970e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.07 y[1] (analytic) = 3.9153794999769966738778707729755 y[1] (numeric) = 3.915379499976996673877966581431 absolute error = 9.58084555e-23 relative error = 2.4469775024506024566717950273091e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0701 y[1] (analytic) = 3.9156710525043777821612289644662 y[1] (numeric) = 3.9156710525043777821613249146443 absolute error = 9.59501781e-23 relative error = 2.4504146751201779144719524972679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0702 y[1] (analytic) = 3.915962634188469439785623756538 y[1] (numeric) = 3.9159626341884694397857198484529 absolute error = 9.60919149e-23 relative error = 2.4538516803267137478237267440047e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0703 y[1] (analytic) = 3.9162542450321874635944015728032 y[1] (numeric) = 3.9162542450321874635944978064691 absolute error = 9.62336659e-23 relative error = 2.4572885180290193634466140097003e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0704 y[1] (analytic) = 3.9165458850384479620271727417147 y[1] (numeric) = 3.9165458850384479620272691171457 absolute error = 9.63754310e-23 relative error = 2.4607251856326432727350744508360e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0705 y[1] (analytic) = 3.9168375542101673351489725809865 y[1] (numeric) = 3.9168375542101673351490690981968 absolute error = 9.65172103e-23 relative error = 2.4641616856500640325383087800691e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0706 y[1] (analytic) = 3.9171292525502622746794253982685 y[1] (numeric) = 3.9171292525502622746795220572722 absolute error = 9.66590037e-23 relative error = 2.4675980154872290394883199954040e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0707 y[1] (analytic) = 3.9174209800616497640219114083666 y[1] (numeric) = 3.917420980061649764022008209178 absolute error = 9.68008114e-23 relative error = 2.4710341802089550574419092969201e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0708 y[1] (analytic) = 3.9177127367472470782927365673016 y[1] (numeric) = 3.9177127367472470782928335099348 absolute error = 9.69426332e-23 relative error = 2.4744701746685082608508128449563e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0709 y[1] (analytic) = 3.9180045226099717843503053234958 y[1] (numeric) = 3.918004522609971784350402407965 absolute error = 9.70844692e-23 relative error = 2.4779060013776439574225045762133e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.071 y[1] (analytic) = 3.9182963376527417408242962863816 y[1] (numeric) = 3.9182963376527417408243935127011 absolute error = 9.72263195e-23 relative error = 2.4813416628473663918832783241365e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0711 y[1] (analytic) = 3.918588181878475098144840812723 y[1] (numeric) = 3.9185881818784750981449381809069 absolute error = 9.73681839e-23 relative error = 2.4847771539321103122143651373708e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0712 y[1] (analytic) = 3.9188800552900902985717045109407 y[1] (numeric) = 3.9188800552900902985718020210031 absolute error = 9.75100624e-23 relative error = 2.4882124745913392596385445305622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0713 y[1] (analytic) = 3.9191719578905060762234716637341 y[1] (numeric) = 3.9191719578905060762235693156893 absolute error = 9.76519552e-23 relative error = 2.4916476298876448216475234510112e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0714 y[1] (analytic) = 3.9194638896826414571067325692919 y[1] (numeric) = 3.9194638896826414571068303631541 absolute error = 9.77938622e-23 relative error = 2.4950826172279994608655006716678e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0715 y[1] (analytic) = 3.919755850669415759145273801382 y[1] (numeric) = 3.9197558506694157591453717371654 absolute error = 9.79357834e-23 relative error = 2.4985174365713244750843099942172e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0716 y[1] (analytic) = 3.9200478408537485922092713886138 y[1] (numeric) = 3.9200478408537485922093694663325 absolute error = 9.80777187e-23 relative error = 2.5019520853255612128902618866365e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0717 y[1] (analytic) = 3.9203398602385598581444869131641 y[1] (numeric) = 3.9203398602385598581445851328323 absolute error = 9.82196682e-23 relative error = 2.5053865660010189362046008234397e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0718 y[1] (analytic) = 3.9206319088267697508014665292593 y[1] (numeric) = 3.9206319088267697508015648908913 absolute error = 9.83616320e-23 relative error = 2.5088208811072561380892169577812e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0719 y[1] (analytic) = 3.9209239866212987560647429017051 y[1] (numeric) = 3.9209239866212987560648414053151 absolute error = 9.85036100e-23 relative error = 2.5122550280522421421290328921325e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.2MB, time=5.48 NO POLE x[1] = 1.072 y[1] (analytic) = 3.9212160936250676518820400647562 y[1] (numeric) = 3.9212160936250676518821387103583 absolute error = 9.86456021e-23 relative error = 2.5156890042447156153837829536110e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0721 y[1] (analytic) = 3.9215082298409975082934812016178 y[1] (numeric) = 3.9215082298409975082935799892262 absolute error = 9.87876084e-23 relative error = 2.5191228121942630231464847949173e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0722 y[1] (analytic) = 3.9218003952720096874607993448711 y[1] (numeric) = 3.9218003952720096874608982745 absolute error = 9.89296289e-23 relative error = 2.5225564518598709070524670560891e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0723 y[1] (analytic) = 3.9220925899210258436965509981152 y[1] (numeric) = 3.9220925899210258436966500697789 absolute error = 9.90716637e-23 relative error = 2.5259899257501944703495980947435e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0724 y[1] (analytic) = 3.922384813790967923493332679117 y[1] (numeric) = 3.9223848137909679234934318928297 absolute error = 9.92137127e-23 relative error = 2.5294232312741996533737982626077e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0725 y[1] (analytic) = 3.9226770668847581655530003847613 y[1] (numeric) = 3.9226770668847581655530997405371 absolute error = 9.93557758e-23 relative error = 2.5328563658416215514562390159939e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0726 y[1] (analytic) = 3.9229693492053191008158919780937 y[1] (numeric) = 3.9229693492053191008159914759469 absolute error = 9.94978532e-23 relative error = 2.5362893345102328390456720671526e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0727 y[1] (analytic) = 3.9232616607555735524900524977488 y[1] (numeric) = 3.9232616607555735524901521376935 absolute error = 9.96399447e-23 relative error = 2.5397221321406977291136993596832e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0728 y[1] (analytic) = 3.9235540015384446360804623900544 y[1] (numeric) = 3.9235540015384446360805621721048 absolute error = 9.97820504e-23 relative error = 2.5431547612413381334488513059246e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0729 y[1] (analytic) = 3.9238463715568557594182686641059 y[1] (numeric) = 3.9238463715568557594183685882763 absolute error = 9.99241704e-23 relative error = 2.5465872243197255994904950131338e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.073 y[1] (analytic) = 3.9241387708137306226900189701024 y[1] (numeric) = 3.924138770813730622690119036407 absolute error = 1.000663046e-22 relative error = 2.5500195187860216852388602065343e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0731 y[1] (analytic) = 3.9244311993119932184668986012361 y[1] (numeric) = 3.9244311993119932184669988096891 absolute error = 1.002084530e-22 relative error = 2.5534516445992968478594214882837e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0732 y[1] (analytic) = 3.9247236570545678317339704194288 y[1] (numeric) = 3.9247236570545678317340707700444 absolute error = 1.003506156e-22 relative error = 2.5568836017186308630488298126641e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0733 y[1] (analytic) = 3.9250161440443790399194177052068 y[1] (numeric) = 3.9250161440443790399195181979993 absolute error = 1.004927925e-22 relative error = 2.5603153926508730459334506341826e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0734 y[1] (analytic) = 3.9253086602843517129237899320072 y[1] (numeric) = 3.9253086602843517129238905669908 absolute error = 1.006349836e-22 relative error = 2.5637470148069818654302669988046e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0735 y[1] (analytic) = 3.9256012057774110131492514652077 y[1] (numeric) = 3.9256012057774110131493522423965 absolute error = 1.007771888e-22 relative error = 2.5671784655986845683995009449190e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0736 y[1] (analytic) = 3.9258937805264823955288331861724 y[1] (numeric) = 3.9258937805264823955289341055807 absolute error = 1.009194083e-22 relative error = 2.5706097500800490890530615857205e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0737 y[1] (analytic) = 3.926186384534491607555687041607 y[1] (numeric) = 3.926186384534491607555788103249 absolute error = 1.010616420e-22 relative error = 2.5740408656626314559084742217544e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0738 y[1] (analytic) = 3.9264790178043646893123435185141 y[1] (numeric) = 3.9264790178043646893124447224041 absolute error = 1.012038900e-22 relative error = 2.5774718148523783858119480339666e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0739 y[1] (analytic) = 3.9267716803390279734999720450435 y[1] (numeric) = 3.9267716803390279735000733911957 absolute error = 1.013461522e-22 relative error = 2.5809025950612442594053666495234e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.074 y[1] (analytic) = 3.9270643721414080854676443175278 y[1] (numeric) = 3.9270643721414080854677458059564 absolute error = 1.014884286e-22 relative error = 2.5843332062483834398154238671923e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0741 y[1] (analytic) = 3.9273570932144319432416005539977 y[1] (numeric) = 3.9273570932144319432417021847169 absolute error = 1.016307192e-22 relative error = 2.5877636483729596045238996942617e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0742 y[1] (analytic) = 3.9276498435610267575545186744687 y[1] (numeric) = 3.9276498435610267575546204474928 absolute error = 1.017730241e-22 relative error = 2.5911939239401975566223765540685e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0743 y[1] (analytic) = 3.9279426231841200318747864082925 y[1] (numeric) = 3.9279426231841200318748883236357 absolute error = 1.019153432e-22 relative error = 2.5946240303628482357356739844612e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0744 y[1] (analytic) = 3.9282354320866395624357763288649 y[1] (numeric) = 3.9282354320866395624358783865415 absolute error = 1.020576766e-22 relative error = 2.5980539701457755551455039440337e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0745 y[1] (analytic) = 3.9285282702715134382651238159845 y[1] (numeric) = 3.9285282702715134382652260160086 absolute error = 1.022000241e-22 relative error = 2.6014837381566461797823035437380e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0746 y[1] (analytic) = 3.9288211377416700412140079461527 y[1] (numeric) = 3.9288211377416700412141102885386 absolute error = 1.023423859e-22 relative error = 2.6049133394458251755669822367579e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0747 y[1] (analytic) = 3.9291140345000380459864353111105 y[1] (numeric) = 3.9291140345000380459865377958725 absolute error = 1.024847620e-22 relative error = 2.6083427739719629058850118800097e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0748 y[1] (analytic) = 3.9294069605495464201685267649028 y[1] (numeric) = 3.929406960549546420168629392055 absolute error = 1.026271522e-22 relative error = 2.6117720366038925189332052326194e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.2MB, time=5.71 NO POLE x[1] = 1.0749 y[1] (analytic) = 3.9296999158931244242578070997638 y[1] (numeric) = 3.9296999158931244242579098693205 absolute error = 1.027695567e-22 relative error = 2.6152011323908685771277373325725e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.075 y[1] (analytic) = 3.9299929005337016116924976511169 y[1] (numeric) = 3.9299929005337016116926005630924 absolute error = 1.029119755e-22 relative error = 2.6186300612915694875332384079362e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0751 y[1] (analytic) = 3.9302859144742078288808118319814 y[1] (numeric) = 3.9302859144742078288809148863899 absolute error = 1.030544085e-22 relative error = 2.6220588207203388662752707505335e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0752 y[1] (analytic) = 3.9305789577175732152302535970788 y[1] (numeric) = 3.9305789577175732152303567939345 absolute error = 1.031968557e-22 relative error = 2.6254874106364429297999354577818e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0753 y[1] (analytic) = 3.9308720302667282031769188369323 y[1] (numeric) = 3.9308720302667282031770221762495 absolute error = 1.033393172e-22 relative error = 2.6289158335431219833975849930417e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0754 y[1] (analytic) = 3.9311651321246035182147997022524 y[1] (numeric) = 3.9311651321246035182149031840453 absolute error = 1.034817929e-22 relative error = 2.6323440868553167319927030865075e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0755 y[1] (analytic) = 3.931458263294130178925091858901 y[1] (numeric) = 3.9314582632941301789251954831839 absolute error = 1.036242829e-22 relative error = 2.6357721730759067857685165893265e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0756 y[1] (analytic) = 3.9317514237782394970055046737278 y[1] (numeric) = 3.931751423778239497005608440515 absolute error = 1.037667872e-22 relative error = 2.6392000921636266545271108852792e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0757 y[1] (analytic) = 3.9320446135798630772995743315722 y[1] (numeric) = 3.9320446135798630772996782408778 absolute error = 1.039093056e-22 relative error = 2.6426278389908079329122469620478e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0758 y[1] (analytic) = 3.9323378327019328178259798837223 y[1] (numeric) = 3.9323378327019328178260839355607 absolute error = 1.040518384e-22 relative error = 2.6460554211463911837448160832202e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0759 y[1] (analytic) = 3.9326310811473809098078622281271 y[1] (numeric) = 3.9326310811473809098079664225125 absolute error = 1.041943854e-22 relative error = 2.6494828335029163162630325134991e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.076 y[1] (analytic) = 3.9329243589191398377021460216515 y[1] (numeric) = 3.9329243589191398377022503585982 absolute error = 1.043369467e-22 relative error = 2.6529100785623613717494751057130e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0761 y[1] (analytic) = 3.9332176660201423792288645246706 y[1] (numeric) = 3.9332176660201423792289690041928 absolute error = 1.044795222e-22 relative error = 2.6563371537410599664711322290287e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0762 y[1] (analytic) = 3.933511002453321605400487378294 y[1] (numeric) = 3.933511002453321605400592000406 absolute error = 1.046221120e-22 relative error = 2.6597640615406295705171847627886e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0763 y[1] (analytic) = 3.9338043682216108805512513145152 y[1] (numeric) = 3.9338043682216108805513560792313 absolute error = 1.047647161e-22 relative error = 2.6631908019198701396404937995903e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0764 y[1] (analytic) = 3.9340977633279438623664937995785 y[1] (numeric) = 3.9340977633279438623665987069129 absolute error = 1.049073344e-22 relative error = 2.6666173722957121133127655909565e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0765 y[1] (analytic) = 3.9343911877752545019119896108566 y[1] (numeric) = 3.9343911877752545019120946608235 absolute error = 1.050499669e-22 relative error = 2.6700437726275428811264324854913e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0766 y[1] (analytic) = 3.9346846415664770436632903475328 y[1] (numeric) = 3.9346846415664770436633955401465 absolute error = 1.051926137e-22 relative error = 2.6734700054162588769993668313973e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0767 y[1] (analytic) = 3.934978124704546025535066875381 y[1] (numeric) = 3.9349781247045460255351722106559 absolute error = 1.053352749e-22 relative error = 2.6768960731620076246409343264377e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0768 y[1] (analytic) = 3.9352716371923962789104547059373 y[1] (numeric) = 3.9352716371923962789105601838875 absolute error = 1.054779502e-22 relative error = 2.6803219681997052512582197129754e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0769 y[1] (analytic) = 3.9355651790329629286704023103549 y[1] (numeric) = 3.9355651790329629286705079309947 absolute error = 1.056206398e-22 relative error = 2.6837476955712072622089661294420e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.077 y[1] (analytic) = 3.9358587502291813932230223682388 y[1] (numeric) = 3.9358587502291813932231281315826 absolute error = 1.057633438e-22 relative error = 2.6871732577761206214402945354746e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0771 y[1] (analytic) = 3.9361523507839873845329459517514 y[1] (numeric) = 3.9361523507839873845330518578133 absolute error = 1.059060619e-22 relative error = 2.6905986471510953085421427042920e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0772 y[1] (analytic) = 3.9364459807003169081506796452826 y[1] (numeric) = 3.9364459807003169081507856940769 absolute error = 1.060487943e-22 relative error = 2.6940238687368776069834590865588e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0773 y[1] (analytic) = 3.9367396399811062632419656009801 y[1] (numeric) = 3.9367396399811062632420717925211 absolute error = 1.061915410e-22 relative error = 2.6974489224923609349638916436877e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0774 y[1] (analytic) = 3.9370333286292920426171445304307 y[1] (numeric) = 3.9370333286292920426172508647327 absolute error = 1.063343020e-22 relative error = 2.7008738083764480655358167681503e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0775 y[1] (analytic) = 3.9373270466478111327605216327886 y[1] (numeric) = 3.9373270466478111327606281098659 absolute error = 1.064770773e-22 relative error = 2.7042985263480511261354487043996e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0776 y[1] (analytic) = 3.9376207940396007138597354596427 y[1] (numeric) = 3.9376207940396007138598420795096 absolute error = 1.066198669e-22 relative error = 2.7077230763660915981137577718833e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0777 y[1] (analytic) = 3.9379145708075982598351297169176 y[1] (numeric) = 3.9379145708075982598352364795883 absolute error = 1.067626707e-22 relative error = 2.7111474558500851460825449201393e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=103.0MB, alloc=4.2MB, time=5.92 x[1] = 1.0778 y[1] (analytic) = 3.9382083769547415383691280041013 y[1] (numeric) = 3.9382083769547415383692349095901 absolute error = 1.069054888e-22 relative error = 2.7145716672987660291213415961499e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0779 y[1] (analytic) = 3.9385022124839686109356114910941 y[1] (numeric) = 3.9385022124839686109357185394153 absolute error = 1.070483212e-22 relative error = 2.7179957106710837595379685941521e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.078 y[1] (analytic) = 3.938796077398217832829299532972 y[1] (numeric) = 3.9387960773982178328294067241398 absolute error = 1.071911678e-22 relative error = 2.7214195833871503552034115066397e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0781 y[1] (analytic) = 3.939089971700427853195133222958 y[1] (numeric) = 3.9390899717004278531952405569868 absolute error = 1.073340288e-22 relative error = 2.7248432904838171475604656024654e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0782 y[1] (analytic) = 3.9393838953935376150576618838964 y[1] (numeric) = 3.9393838953935376150577693608004 absolute error = 1.074769040e-22 relative error = 2.7282668268425574146089778258451e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0783 y[1] (analytic) = 3.9396778484804863553504324985225 y[1] (numeric) = 3.939677848480486355350540118316 absolute error = 1.076197935e-22 relative error = 2.7316901949612048924759134962135e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0784 y[1] (analytic) = 3.9399718309642136049453820788228 y[1] (numeric) = 3.9399718309642136049454898415201 absolute error = 1.077626973e-22 relative error = 2.7351133947987558209690777429128e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0785 y[1] (analytic) = 3.9402658428476591886822329747785 y[1] (numeric) = 3.940265842847659188682340880394 absolute error = 1.079056155e-22 relative error = 2.7385364288521156163509629638250e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0786 y[1] (analytic) = 3.9405598841337632253978911227879 y[1] (numeric) = 3.9405598841337632253979991713357 absolute error = 1.080485478e-22 relative error = 2.7419592894665997370061126646412e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0787 y[1] (analytic) = 3.940853954825466127955847234059 y[1] (numeric) = 3.9408539548254661279559554255535 absolute error = 1.081914945e-22 relative error = 2.7453819842149319506932327213680e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0788 y[1] (analytic) = 3.9411480549257086032755809232699 y[1] (numeric) = 3.9411480549257086032756892577254 absolute error = 1.083344555e-22 relative error = 2.7488045105182460663505278056249e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0789 y[1] (analytic) = 3.9414421844374316523619677777874 y[1] (numeric) = 3.9414421844374316523620762552181 absolute error = 1.084774307e-22 relative error = 2.7522268657984426886163319840064e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.079 y[1] (analytic) = 3.9417363433635765703346893677405 y[1] (numeric) = 3.9417363433635765703347979881607 absolute error = 1.086204202e-22 relative error = 2.7556490525520952045135488251798e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0791 y[1] (analytic) = 3.9420305317070849464576461972417 y[1] (numeric) = 3.9420305317070849464577549606658 absolute error = 1.087634241e-22 relative error = 2.7590710732750289746247745917636e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0792 y[1] (analytic) = 3.9423247494708986641683735970508 y[1] (numeric) = 3.942324749470898664168482503493 absolute error = 1.089064422e-22 relative error = 2.7624929228525982532785316066701e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0793 y[1] (analytic) = 3.9426189966579599011074605589742 y[1] (numeric) = 3.9426189966579599011075696084489 absolute error = 1.090494747e-22 relative error = 2.7659146063172215028702307393100e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0794 y[1] (analytic) = 3.9429132732712111291479715122958 y[1] (numeric) = 3.9429132732712111291480807048173 absolute error = 1.091925215e-22 relative error = 2.7693361210912247279369934484608e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0795 y[1] (analytic) = 3.943207579313595114424871042532 y[1] (numeric) = 3.9432075793135951144249803781146 absolute error = 1.093355826e-22 relative error = 2.7727574671337069888558838022658e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0796 y[1] (analytic) = 3.9435019147880549173644515528058 y[1] (numeric) = 3.9435019147880549173645610314638 absolute error = 1.094786580e-22 relative error = 2.7761786444037766904949514442828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0797 y[1] (analytic) = 3.9437962796975338927137638681343 y[1] (numeric) = 3.943796279697533892713873489882 absolute error = 1.096217477e-22 relative error = 2.7795996528605515817401461476027e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0798 y[1] (analytic) = 3.9440906740449756895700507829238 y[1] (numeric) = 3.9440906740449756895701605477755 absolute error = 1.097648517e-22 relative error = 2.7830204924631587550220421522832e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0799 y[1] (analytic) = 3.9443850978333242514101835519665 y[1] (numeric) = 3.9443850978333242514102934599366 absolute error = 1.099079701e-22 relative error = 2.7864411657059840578465560544841e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.08 y[1] (analytic) = 3.9446795510655238161201013252344 y[1] (numeric) = 3.9446795510655238161202113763371 absolute error = 1.100511027e-22 relative error = 2.7898616674774851989237505473099e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0801 y[1] (analytic) = 3.9449740337445189160242535267623 y[1] (numeric) = 3.9449740337445189160243637210119 absolute error = 1.101942496e-22 relative error = 2.7932820002722559651908465031393e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0802 y[1] (analytic) = 3.9452685458732543779150451779175 y[1] (numeric) = 3.9452685458732543779151555153284 absolute error = 1.103374109e-22 relative error = 2.7967021665841425223706553977921e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0803 y[1] (analytic) = 3.9455630874546753230822851653482 y[1] (numeric) = 3.9455630874546753230823956459347 absolute error = 1.104805865e-22 relative error = 2.8001221638372585348772620045991e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0804 y[1] (analytic) = 3.9458576584917271673426374539063 y[1] (numeric) = 3.9458576584917271673427480776826 absolute error = 1.106237763e-22 relative error = 2.8035419894564838960540174697872e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0805 y[1] (analytic) = 3.946152258987355621069075244838 y[1] (numeric) = 3.9461522589873556210691860118186 absolute error = 1.107669806e-22 relative error = 2.8069616510039209530561268045898e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0806 y[1] (analytic) = 3.9464468889445066892203380795389 y[1] (numeric) = 3.946446888944506689220448989738 absolute error = 1.109101991e-22 relative error = 2.8103811408358617224147078319317e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0807 y[1] (analytic) = 3.9467415483661266713703918891653 y[1] (numeric) = 3.9467415483661266713705029425972 absolute error = 1.110534319e-22 relative error = 2.8138004614458206735229496616866e-21 % memory used=106.8MB, alloc=4.2MB, time=6.15 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0808 y[1] (analytic) = 3.9470362372551621617378919903987 y[1] (numeric) = 3.9470362372551621617380031870778 absolute error = 1.111966791e-22 relative error = 2.8172196153265648756350349150044e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0809 y[1] (analytic) = 3.9473309556145600492156490276569 y[1] (numeric) = 3.9473309556145600492157603675975 absolute error = 1.113399406e-22 relative error = 2.8206385999033993346078090729071e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.081 y[1] (analytic) = 3.9476257034472675174000978620467 y[1] (numeric) = 3.9476257034472675174002093452631 absolute error = 1.114832164e-22 relative error = 2.8240574151355632844142972329033e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0811 y[1] (analytic) = 3.9479204807562320446207694073525 y[1] (numeric) = 3.9479204807562320446208810338591 absolute error = 1.116265066e-22 relative error = 2.8274760635152843796315654331767e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0812 y[1] (analytic) = 3.9482152875444014039697654133566 y[1] (numeric) = 3.9482152875444014039698771831677 absolute error = 1.117698111e-22 relative error = 2.8308945424684631784593518155453e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0813 y[1] (analytic) = 3.9485101238147236633312361967845 y[1] (numeric) = 3.9485101238147236633313481099145 absolute error = 1.119131300e-22 relative error = 2.8343128544869677793062516645504e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0814 y[1] (analytic) = 3.9488049895701471854108613201711 y[1] (numeric) = 3.9488049895701471854109733766343 absolute error = 1.120564632e-22 relative error = 2.8377309969970957355648105187996e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0815 y[1] (analytic) = 3.9490998848136206277653332189421 y[1] (numeric) = 3.9490998848136206277654454187527 absolute error = 1.121998106e-22 relative error = 2.8411489674259104137534401518779e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0816 y[1] (analytic) = 3.9493948095480929428318437770051 y[1] (numeric) = 3.9493948095480929428319561201776 absolute error = 1.123431725e-22 relative error = 2.8445667733293749376891482582367e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0817 y[1] (analytic) = 3.9496897637765133779575738511468 y[1] (numeric) = 3.9496897637765133779576863376954 absolute error = 1.124865486e-22 relative error = 2.8479844070701261322573092140201e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0818 y[1] (analytic) = 3.9499847475018314754291857445287 y[1] (numeric) = 3.9499847475018314754292983744679 absolute error = 1.126299392e-22 relative error = 2.8514018762030112693555407337042e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0819 y[1] (analytic) = 3.9502797607269970725023186295789 y[1] (numeric) = 3.9502797607269970725024314029229 absolute error = 1.127733440e-22 relative error = 2.8548191730918204179642093283710e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.082 y[1] (analytic) = 3.9505748034549603014310869205724 y[1] (numeric) = 3.9505748034549603014311998373356 absolute error = 1.129167632e-22 relative error = 2.8582363027590078896515167071596e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0821 y[1] (analytic) = 3.9508698756886715894975815961975 y[1] (numeric) = 3.9508698756886715894976946563942 absolute error = 1.130601967e-22 relative error = 2.8616532626322603700108196881930e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0822 y[1] (analytic) = 3.9511649774310816590413744724009 y[1] (numeric) = 3.9511649774310816590414876760454 absolute error = 1.132036445e-22 relative error = 2.8650700526709292221044248459491e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0823 y[1] (analytic) = 3.951460108685141527489025425808 y[1] (numeric) = 3.9514601086851415274891387729148 absolute error = 1.133471068e-22 relative error = 2.8684866778957953372117289047172e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0824 y[1] (analytic) = 3.9517552694538025073835925680134 y[1] (numeric) = 3.9517552694538025073837060585968 absolute error = 1.134905834e-22 relative error = 2.8719031332040524590464474316043e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0825 y[1] (analytic) = 3.9520504597400162064141453710358 y[1] (numeric) = 3.9520504597400162064142590051101 absolute error = 1.136340743e-22 relative error = 2.8753194185550800002201954346977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0826 y[1] (analytic) = 3.9523456795467345274452807442332 y[1] (numeric) = 3.9523456795467345274453945218128 absolute error = 1.137775796e-22 relative error = 2.8787355364384097656366482184001e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0827 y[1] (analytic) = 3.9526409288769096685466420629738 y[1] (numeric) = 3.952640928876909668546755984073 absolute error = 1.139210992e-22 relative error = 2.8821514842829187790103895929339e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0828 y[1] (analytic) = 3.9529362077334941230224411493569 y[1] (numeric) = 3.95293620773349412302255521399 absolute error = 1.140646331e-22 relative error = 2.8855672620480144701970458579638e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0829 y[1] (analytic) = 3.9532315161194406794409832052794 y[1] (numeric) = 3.9532315161194406794410974134609 absolute error = 1.142081815e-22 relative error = 2.8889828747522658176001004252471e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.083 y[1] (analytic) = 3.9535268540377024216641946981439 y[1] (numeric) = 3.953526854037702421664309049888 absolute error = 1.143517441e-22 relative error = 2.8923983147658036823634266700687e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0831 y[1] (analytic) = 3.9538222214912327288771541995021 y[1] (numeric) = 3.9538222214912327288772686948232 absolute error = 1.144953211e-22 relative error = 2.8958135871070267803236858174930e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0832 y[1] (analytic) = 3.9541176184829852756176261769304 y[1] (numeric) = 3.954117618482985275617740815843 absolute error = 1.146389126e-22 relative error = 2.8992286942638222832000890008711e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0833 y[1] (analytic) = 3.9544130450159140318055977394325 y[1] (numeric) = 3.9544130450159140318057125219508 absolute error = 1.147825183e-22 relative error = 2.9026436286080497787185546428894e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0834 y[1] (analytic) = 3.9547085010929732627728183366632 y[1] (numeric) = 3.9547085010929732627729332628016 absolute error = 1.149261384e-22 relative error = 2.9060583951570023110519804346532e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0835 y[1] (analytic) = 3.9550039867171175292923424122711 y[1] (numeric) = 3.9550039867171175292924574820439 absolute error = 1.150697728e-22 relative error = 2.9094729913411434718353374738461e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0836 y[1] (analytic) = 3.9552995018913016876080750116533 y[1] (numeric) = 3.955299501891301687608190225075 absolute error = 1.152134217e-22 relative error = 2.9128874221764625163341792898313e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.2MB, time=6.38 NO POLE x[1] = 1.0837 y[1] (analytic) = 3.9555950466184808894643203444197 y[1] (numeric) = 3.9555950466184808894644357015046 absolute error = 1.153570849e-22 relative error = 2.9163016825651882317128345347608e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0838 y[1] (analytic) = 3.9558906209016105821353333018599 y[1] (numeric) = 3.9558906209016105821354488026224 absolute error = 1.155007625e-22 relative error = 2.9197157749946972397425172484773e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0839 y[1] (analytic) = 3.956186224743646508454873929711 y[1] (numeric) = 3.9561862247436465084549895741655 absolute error = 1.156444545e-22 relative error = 2.9231296994239330846177697666859e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.084 y[1] (analytic) = 3.9564818581475447068457648565196 y[1] (numeric) = 3.9564818581475447068458806446804 absolute error = 1.157881608e-22 relative error = 2.9265434532843506859102519710786e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0841 y[1] (analytic) = 3.9567775211162615113494516778944 y[1] (numeric) = 3.9567775211162615113495676097759 absolute error = 1.159318815e-22 relative error = 2.9299570390627880759357952870254e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0842 y[1] (analytic) = 3.9570732136527535516555662969459 y[1] (numeric) = 3.9570732136527535516556823725624 absolute error = 1.160756165e-22 relative error = 2.9333704541910966199010430193299e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0843 y[1] (analytic) = 3.9573689357599777531314932212068 y[1] (numeric) = 3.9573689357599777531316094405727 absolute error = 1.162193659e-22 relative error = 2.9367837011557553254413613109086e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0844 y[1] (analytic) = 3.9576646874408913368519388163306 y[1] (numeric) = 3.9576646874408913368520551794604 absolute error = 1.163631298e-22 relative error = 2.9401967824424971831832094539234e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0845 y[1] (analytic) = 3.9579604686984518196285035168637 y[1] (numeric) = 3.9579604686984518196286200237716 absolute error = 1.165069079e-22 relative error = 2.9436096904300941227700520895907e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0846 y[1] (analytic) = 3.9582562795356170140392569943854 y[1] (numeric) = 3.9582562795356170140393736450859 absolute error = 1.166507005e-22 relative error = 2.9470224326577831077099722286315e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0847 y[1] (analytic) = 3.9585521199553450284583162833139 y[1] (numeric) = 3.9585521199553450284584330778214 absolute error = 1.167945075e-22 relative error = 2.9504350065578400395681610368648e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0848 y[1] (analytic) = 3.9588479899605942670854268646717 y[1] (numeric) = 3.9588479899605942670855438030005 absolute error = 1.169383288e-22 relative error = 2.9538474095633054408061915349976e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0849 y[1] (analytic) = 3.9591438895543234299755467081077 y[1] (numeric) = 3.9591438895543234299756637902722 absolute error = 1.170821645e-22 relative error = 2.9572596441595815136895106772531e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.085 y[1] (analytic) = 3.9594398187394915130684332724717 y[1] (numeric) = 3.9594398187394915130685504984863 absolute error = 1.172260146e-22 relative error = 2.9606717103057148669729119662616e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0851 y[1] (analytic) = 3.9597357775190578082182334652364 y[1] (numeric) = 3.9597357775190578082183508351155 absolute error = 1.173698791e-22 relative error = 2.9640836079607614836762108426045e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0852 y[1] (analytic) = 3.9600317658959819032230765610638 y[1] (numeric) = 3.9600317658959819032231940748218 absolute error = 1.175137580e-22 relative error = 2.9674953370837867206032534561900e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0853 y[1] (analytic) = 3.9603277838732236818546700798108 y[1] (numeric) = 3.960327783873223681854787737462 absolute error = 1.176576512e-22 relative error = 2.9709068951088217898163932124126e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0854 y[1] (analytic) = 3.9606238314537433238878986242712 y[1] (numeric) = 3.96062383145374332388801642583 absolute error = 1.178015588e-22 relative error = 2.9743182845203717947535558136884e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0855 y[1] (analytic) = 3.960919908640501305130425677949 y[1] (numeric) = 3.9609199086405013051305436234299 absolute error = 1.179454809e-22 relative error = 2.9777295078021962275757566882283e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0856 y[1] (analytic) = 3.96121601543645839745229836316 y[1] (numeric) = 3.9612160154364583974524164525774 absolute error = 1.180894174e-22 relative error = 2.9811405623883544173644201887362e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0857 y[1] (analytic) = 3.9615121518445756688155551597568 y[1] (numeric) = 3.961512151844575668815673393125 absolute error = 1.182333682e-22 relative error = 2.9845514457136699734489707777073e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0858 y[1] (analytic) = 3.9618083178678144833038365847737 y[1] (numeric) = 3.9618083178678144833039549621071 absolute error = 1.183773334e-22 relative error = 2.9879621602619305021164347811926e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0859 y[1] (analytic) = 3.962104513509136501151998833288 y[1] (numeric) = 3.962104513509136501152117354601 absolute error = 1.185213130e-22 relative error = 2.9913727059922669351426849447025e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.086 y[1] (analytic) = 3.9624007387715036787757303807931 y[1] (numeric) = 3.9624007387715036787758490461001 absolute error = 1.186653070e-22 relative error = 2.9947830828638195742318782608931e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0861 y[1] (analytic) = 3.9626969936578782688011715473803 y[1] (numeric) = 3.9626969936578782688012903566957 absolute error = 1.188093154e-22 relative error = 2.9981932908357380905337611803452e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0862 y[1] (analytic) = 3.9629932781712228200945370240246 y[1] (numeric) = 3.9629932781712228200946559773628 absolute error = 1.189533382e-22 relative error = 3.0016033298671815241607856968647e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0863 y[1] (analytic) = 3.9632895923145001777917413612716 y[1] (numeric) = 3.9632895923145001777918604586471 absolute error = 1.190973755e-22 relative error = 3.0050132024404748098876597551408e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0864 y[1] (analytic) = 3.9635859360906734833280274206216 y[1] (numeric) = 3.9635859360906734833281466620487 absolute error = 1.192414271e-22 relative error = 3.0084229034682940241461972418299e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0865 y[1] (analytic) = 3.9638823095027061744675977889063 y[1] (numeric) = 3.9638823095027061744677171743994 absolute error = 1.193854931e-22 relative error = 3.0118324354331714943572917613637e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=114.4MB, alloc=4.2MB, time=6.60 x[1] = 1.0866 y[1] (analytic) = 3.9641787125535619853332491559559 y[1] (numeric) = 3.9641787125535619853333686855294 absolute error = 1.195295735e-22 relative error = 3.0152417982943037316518460805027e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0867 y[1] (analytic) = 3.9644751452462049464360096558515 y[1] (numeric) = 3.9644751452462049464361293295198 absolute error = 1.196736683e-22 relative error = 3.0186509920108966137062135087868e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0868 y[1] (analytic) = 3.9647716075835993847047791720602 y[1] (numeric) = 3.9647716075835993847048989898378 absolute error = 1.198177776e-22 relative error = 3.0220600190643787649413307903274e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0869 y[1] (analytic) = 3.9650680995687099235159726067489 y[1] (numeric) = 3.9650680995687099235160925686501 absolute error = 1.199619012e-22 relative error = 3.0254688743693594322445067952874e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.087 y[1] (analytic) = 3.9653646212045014827231661145728 y[1] (numeric) = 3.9653646212045014827232862206121 absolute error = 1.201060393e-22 relative error = 3.0288775629293107690219708720693e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0871 y[1] (analytic) = 3.9656611724939392786867463012363 y[1] (numeric) = 3.9656611724939392786868665514281 absolute error = 1.202501918e-22 relative error = 3.0322860821812627616476375947822e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0872 y[1] (analytic) = 3.9659577534399888243035623871215 y[1] (numeric) = 3.9659577534399888243036827814801 absolute error = 1.203943586e-22 relative error = 3.0356944295630091087840436056998e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0873 y[1] (analytic) = 3.9662543640456159290365813362809 y[1] (numeric) = 3.9662543640456159290367018748209 absolute error = 1.205385400e-22 relative error = 3.0391026125981890028092086507076e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0874 y[1] (analytic) = 3.9665510043137866989445459510925 y[1] (numeric) = 3.9665510043137866989446666338283 absolute error = 1.206827358e-22 relative error = 3.0425106262027787186623875048275e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0875 y[1] (analytic) = 3.9668476742474675367116359328716 y[1] (numeric) = 3.9668476742474675367117567598175 absolute error = 1.208269459e-22 relative error = 3.0459184678151657354880576142114e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0876 y[1] (analytic) = 3.9671443738496251416771319087371 y[1] (numeric) = 3.9671443738496251416772528799077 absolute error = 1.209711706e-22 relative error = 3.0493261449573203727896832471515e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0877 y[1] (analytic) = 3.9674411031232265098650824250296 y[1] (numeric) = 3.9674411031232265098652035404392 absolute error = 1.211154096e-22 relative error = 3.0527336500258620945077250779908e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0878 y[1] (analytic) = 3.9677378620712389340139739075761 y[1] (numeric) = 3.9677378620712389340140951672391 absolute error = 1.212596630e-22 relative error = 3.0561409855009932039700090339630e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0879 y[1] (analytic) = 3.9680346506966300036064035890996 y[1] (numeric) = 3.9680346506966300036065249930305 absolute error = 1.214039309e-22 relative error = 3.0595481538621712788070109667346e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.088 y[1] (analytic) = 3.9683314690023676048987554040703 y[1] (numeric) = 3.9683314690023676048988769522835 absolute error = 1.215482132e-22 relative error = 3.0629551525482076941834615573775e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0881 y[1] (analytic) = 3.9686283169914199209508788512937 y[1] (numeric) = 3.9686283169914199209510005438036 absolute error = 1.216925099e-22 relative error = 3.0663619815184394926532113371717e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0882 y[1] (analytic) = 3.9689251946667554316557708245339 y[1] (numeric) = 3.9689251946667554316558926613549 absolute error = 1.218368210e-22 relative error = 3.0697686407322130760384506259961e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0883 y[1] (analytic) = 3.9692221020313429137692604114684 y[1] (numeric) = 3.969222102031342913769382392615 absolute error = 1.219811466e-22 relative error = 3.0731751326682695512257688729671e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0884 y[1] (analytic) = 3.9695190390881514409396966612712 y[1] (numeric) = 3.9695190390881514409398187867578 absolute error = 1.221254866e-22 relative error = 3.0765814547662117691618937334012e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0885 y[1] (analytic) = 3.9698160058401503837376393211209 y[1] (numeric) = 3.969816005840150383737761590962 absolute error = 1.222698411e-22 relative error = 3.0799876095044226685684101083352e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0886 y[1] (analytic) = 3.9701130022903094096855525419311 y[1] (numeric) = 3.9701130022903094096856749561411 absolute error = 1.224142100e-22 relative error = 3.0833935943229007932918037881008e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0887 y[1] (analytic) = 3.9704100284415984832875015535997 y[1] (numeric) = 3.970410028441598483287624112193 absolute error = 1.225585933e-22 relative error = 3.0867994091810393902956606946924e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0888 y[1] (analytic) = 3.9707070842969878660588523100744 y[1] (numeric) = 3.9707070842969878660589750130655 absolute error = 1.227029911e-22 relative error = 3.0902050565566841985085987636320e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0889 y[1] (analytic) = 3.9710041698594481165559741045312 y[1] (numeric) = 3.9710041698594481165560969519345 absolute error = 1.228474033e-22 relative error = 3.0936105338904272133213544442209e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.089 y[1] (analytic) = 3.9713012851319500904059451549626 y[1] (numeric) = 3.9713012851319500904060681467925 absolute error = 1.229918299e-22 relative error = 3.0970158411416897773276624504644e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0891 y[1] (analytic) = 3.9715984301174649403362611604733 y[1] (numeric) = 3.9715984301174649403363842967443 absolute error = 1.231362710e-22 relative error = 3.1004209807877805094394880835850e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0892 y[1] (analytic) = 3.97189560481896411620454682858 y[1] (numeric) = 3.9718956048189641162046701093065 absolute error = 1.232807265e-22 relative error = 3.1038259502698847680449977166429e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0893 y[1] (analytic) = 3.972192809239419365028270373812 y[1] (numeric) = 3.9721928092394193650283937990085 absolute error = 1.234251965e-22 relative error = 3.1072307520649531457183336097763e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0894 y[1] (analytic) = 3.9724900433818027310144609879114 y[1] (numeric) = 3.9724900433818027310145845575923 absolute error = 1.235696809e-22 relative error = 3.1106353836145665363334789822071e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=118.2MB, alloc=4.2MB, time=6.82 x[1] = 1.0895 y[1] (analytic) = 3.9727873072490865555894292819273 y[1] (numeric) = 3.9727873072490865555895529961071 absolute error = 1.237141798e-22 relative error = 3.1140398473953175415851851842650e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0896 y[1] (analytic) = 3.9730846008442434774284907005043 y[1] (numeric) = 3.9730846008442434774286145591974 absolute error = 1.238586931e-22 relative error = 3.1174441408491825514715726331230e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0897 y[1] (analytic) = 3.9733819241702464324856919086601 y[1] (numeric) = 3.973381924170246432485815911881 absolute error = 1.240032209e-22 relative error = 3.1208482664523962122668889193445e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0898 y[1] (analytic) = 3.973679277230068654023540151351 y[1] (numeric) = 3.9736792772300686540236642991141 absolute error = 1.241477631e-22 relative error = 3.1242522216473303707282422603924e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0899 y[1] (analytic) = 3.9739766600266836726427355861214 y[1] (numeric) = 3.9739766600266836726428598784412 absolute error = 1.242923198e-22 relative error = 3.1276560089098617531687174914964e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.09 y[1] (analytic) = 3.9742740725630653163119065891359 y[1] (numeric) = 3.9742740725630653163120310260268 absolute error = 1.244368909e-22 relative error = 3.1310596256827576237357940911056e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0901 y[1] (analytic) = 3.9745715148421877103973480348902 y[1] (numeric) = 3.9745715148421877103974726163667 absolute error = 1.245814765e-22 relative error = 3.1344630744415368242411878338759e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0902 y[1] (analytic) = 3.9748689868670252776927625498989 y[1] (numeric) = 3.9748689868670252776928872759755 absolute error = 1.247260766e-22 relative error = 3.1378663551451681864483681074214e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0903 y[1] (analytic) = 3.9751664886405527384490047406574 y[1] (numeric) = 3.9751664886405527384491296113484 absolute error = 1.248706910e-22 relative error = 3.1412694627213941343348276827268e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0904 y[1] (analytic) = 3.9754640201657451104038283961748 y[1] (numeric) = 3.9754640201657451104039534114948 absolute error = 1.250153200e-22 relative error = 3.1446724046766208501876973217032e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0905 y[1] (analytic) = 3.9757615814455777088116366653769 y[1] (numeric) = 3.9757615814455777088117618253403 absolute error = 1.251599634e-22 relative error = 3.1480751759387977938052318265022e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0906 y[1] (analytic) = 3.9760591724830261464732352096745 y[1] (numeric) = 3.9760591724830261464733605142958 absolute error = 1.253046213e-22 relative error = 3.1514777789825492649187438148594e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0907 y[1] (analytic) = 3.9763567932810663337655883309965 y[1] (numeric) = 3.9763567932810663337657137802902 absolute error = 1.254492937e-22 relative error = 3.1548802137668910599811319133828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0908 y[1] (analytic) = 3.9766544438426744786715780755843 y[1] (numeric) = 3.9766544438426744786717036695648 absolute error = 1.255939805e-22 relative error = 3.1582824777361717470144517615600e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0909 y[1] (analytic) = 3.9769521241708270868097663138453 y[1] (numeric) = 3.9769521241708270868098920525271 absolute error = 1.257386818e-22 relative error = 3.1616845733644790125013753300771e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.091 y[1] (analytic) = 3.9772498342685009614641597965635 y[1] (numeric) = 3.9772498342685009614642856799611 absolute error = 1.258833976e-22 relative error = 3.1650865006108568314465990238555e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0911 y[1] (analytic) = 3.9775475741386732036139781877642 y[1] (numeric) = 3.9775475741386732036141042158921 absolute error = 1.260281279e-22 relative error = 3.1684882594343585800819286059832e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0912 y[1] (analytic) = 3.9778453437843212119634250745314 y[1] (numeric) = 3.977845343784321211963551247404 absolute error = 1.261728726e-22 relative error = 3.1718898472801232561058798456711e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0913 y[1] (analytic) = 3.9781431432084226829714619540739 y[1] (numeric) = 3.9781431432084226829715882717057 absolute error = 1.263176318e-22 relative error = 3.1752912666215231951483577870129e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0914 y[1] (analytic) = 3.9784409724139556108815851983405 y[1] (numeric) = 3.978440972413955610881711660746 absolute error = 1.264624055e-22 relative error = 3.1786925174176399461099399108834e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0915 y[1] (analytic) = 3.9787388314038982877516059964794 y[1] (numeric) = 3.978738831403898287751732603673 absolute error = 1.266071936e-22 relative error = 3.1820935971142052185280074091700e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0916 y[1] (analytic) = 3.979036720181229303483433275441 y[1] (numeric) = 3.9790367201812293034835600274373 absolute error = 1.267519963e-22 relative error = 3.1854945106972259980993695486995e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0917 y[1] (analytic) = 3.9793346387489275458528595990224 y[1] (numeric) = 3.9793346387489275458529864958358 absolute error = 1.268968134e-22 relative error = 3.1888952530992816955733797705274e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0918 y[1] (analytic) = 3.9796325871099722005393500456494 y[1] (numeric) = 3.9796325871099722005394770872944 absolute error = 1.270416450e-22 relative error = 3.1922958267928506645216608706607e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0919 y[1] (analytic) = 3.9799305652673427511558340651964 y[1] (numeric) = 3.9799305652673427511559612516875 absolute error = 1.271864911e-22 relative error = 3.1956962317370614171880865859147e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.092 y[1] (analytic) = 3.9802285732240189792785003151405 y[1] (numeric) = 3.9802285732240189792786276464922 absolute error = 1.273313517e-22 relative error = 3.1990964678910518626261796106216e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0921 y[1] (analytic) = 3.9805266109829809644765944763481 y[1] (numeric) = 3.9805266109829809644767219525749 absolute error = 1.274762268e-22 relative error = 3.2024965352139693062075573829441e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0922 y[1] (analytic) = 3.9808246785472090843422200487925 y[1] (numeric) = 3.9808246785472090843423476699088 absolute error = 1.276211163e-22 relative error = 3.2058964311529281444564073045222e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0923 y[1] (analytic) = 3.9811227759196840145201421274992 y[1] (numeric) = 3.9811227759196840145202698935196 absolute error = 1.277660204e-22 relative error = 3.2092961606913671792378430943149e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0924 y[1] (analytic) = 3.981420903103386728737594159019 y[1] (numeric) = 3.9814209031033867287377220699579 absolute error = 1.279109389e-22 relative error = 3.2126957187645653698442085532004e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.2MB, time=7.04 NO POLE x[1] = 1.0925 y[1] (analytic) = 3.9817190601012984988340876787246 y[1] (numeric) = 3.9817190601012984988342157345965 absolute error = 1.280558719e-22 relative error = 3.2160951078437498785933367221423e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0926 y[1] (analytic) = 3.9820172469164008947912250292311 y[1] (numeric) = 3.9820172469164008947913532300506 absolute error = 1.282008195e-22 relative error = 3.2194943303994049338797638763026e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0927 y[1] (analytic) = 3.9823154635516757847625150602366 y[1] (numeric) = 3.9823154635516757847626434060181 absolute error = 1.283457815e-22 relative error = 3.2228933813679661682362082450681e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0928 y[1] (analytic) = 3.9826137100101053351031918100821 y[1] (numeric) = 3.9826137100101053351033203008401 absolute error = 1.284907580e-22 relative error = 3.2262922632201246641968009302692e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0929 y[1] (analytic) = 3.9829119862946720104000361693288 y[1] (numeric) = 3.9829119862946720104001648050778 absolute error = 1.286357490e-22 relative error = 3.2296909759151028518751310029979e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.093 y[1] (analytic) = 3.9832102924083585735012005266506 y[1] (numeric) = 3.9832102924083585735013293074051 absolute error = 1.287807545e-22 relative error = 3.2330895194121325532694670949153e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0931 y[1] (analytic) = 3.9835086283541480855460363973408 y[1] (numeric) = 3.9835086283541480855461653231153 absolute error = 1.289257745e-22 relative error = 3.2364878936704549817693239241632e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0932 y[1] (analytic) = 3.9838069941350239059949250347301 y[1] (numeric) = 3.9838069941350239059950541055391 absolute error = 1.290708090e-22 relative error = 3.2398860986493207416618410853272e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0933 y[1] (analytic) = 3.9841053897539696926591110248156 y[1] (numeric) = 3.9841053897539696926592402406736 absolute error = 1.292158580e-22 relative error = 3.2432841343079898276379741487267e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0934 y[1] (analytic) = 3.9844038152139694017305388643977 y[1] (numeric) = 3.9844038152139694017306682253193 absolute error = 1.293609216e-22 relative error = 3.2466820031155173949616513017967e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0935 y[1] (analytic) = 3.984702270518007287811692523025 y[1] (numeric) = 3.9847022705180072878118220290246 absolute error = 1.295059996e-22 relative error = 3.2500797000114226926734086133425e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0936 y[1] (analytic) = 3.9850007556690679039454379890435 y[1] (numeric) = 3.9850007556690679039455676401356 absolute error = 1.296510921e-22 relative error = 3.2534772274649676473865057330126e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0937 y[1] (analytic) = 3.9852992706701361016448688000502 y[1] (numeric) = 3.9852992706701361016449985962494 absolute error = 1.297961992e-22 relative error = 3.2568745879446716582688454721145e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0938 y[1] (analytic) = 3.9855978155241970309231545580492 y[1] (numeric) = 3.98559781552419703092328449937 absolute error = 1.299413208e-22 relative error = 3.2602717789002439056932142374704e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0939 y[1] (analytic) = 3.9858963902342361403233924296082 y[1] (numeric) = 3.985896390234236140323522516065 absolute error = 1.300864568e-22 relative error = 3.2636687977821547984376035718230e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.094 y[1] (analytic) = 3.9861949948032391769484616313138 y[1] (numeric) = 3.9861949948032391769485918629212 absolute error = 1.302316074e-22 relative error = 3.2670656495676099071948013806214e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0941 y[1] (analytic) = 3.986493629234192186490880900826 y[1] (numeric) = 3.9864936292341921864910112775985 absolute error = 1.303767725e-22 relative error = 3.2704623317069104679363063471490e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0942 y[1] (analytic) = 3.9867922935300815132626689538278 y[1] (numeric) = 3.9867922935300815132627994757799 absolute error = 1.305219521e-22 relative error = 3.2738588441594009948287046189271e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0943 y[1] (analytic) = 3.9870909876938938002252079271702 y[1] (numeric) = 3.9870909876938938002253385943165 absolute error = 1.306671463e-22 relative error = 3.2772551893925296423953000866932e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0944 y[1] (analytic) = 3.9873897117286159890191098085113 y[1] (numeric) = 3.9873897117286159890192406208663 absolute error = 1.308123550e-22 relative error = 3.2806513648571896415689191976683e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0945 y[1] (analytic) = 3.987688465637235319994085852747 y[1] (numeric) = 3.9876884656372353199942168103251 absolute error = 1.309575781e-22 relative error = 3.2840473680050352239774517985466e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0946 y[1] (analytic) = 3.9879872494227393322388189855329 y[1] (numeric) = 3.9879872494227393322389500883487 absolute error = 1.311028158e-22 relative error = 3.2874432038110732824080459278972e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0947 y[1] (analytic) = 3.9882860630881158636108391941965 y[1] (numeric) = 3.9882860630881158636109704422645 absolute error = 1.312480680e-22 relative error = 3.2908388697267889259201079669794e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0948 y[1] (analytic) = 3.9885849066363530507664019063369 y[1] (numeric) = 3.9885849066363530507665332996717 absolute error = 1.313933348e-22 relative error = 3.2942343682187378537516020976216e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0949 y[1] (analytic) = 3.9888837800704393291903693564126 y[1] (numeric) = 3.9888837800704393291905008950286 absolute error = 1.315386160e-22 relative error = 3.2976296942318327400403896673002e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.095 y[1] (analytic) = 3.9891826833933634332260949406148 y[1] (numeric) = 3.9891826833933634332262266245266 absolute error = 1.316839118e-22 relative error = 3.3010248527396150663480859556200e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0951 y[1] (analytic) = 3.9894816166081143961053105603258 y[1] (numeric) = 3.989481616608114396105442389548 absolute error = 1.318292222e-22 relative error = 3.3044198437009503247374763396715e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0952 y[1] (analytic) = 3.9897805797176815499780169544617 y[1] (numeric) = 3.9897805797176815499781489290088 absolute error = 1.319745471e-22 relative error = 3.3078146645683099467742937942959e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0953 y[1] (analytic) = 3.9900795727250545259423770209968 y[1] (numeric) = 3.9900795727250545259425091408832 absolute error = 1.321198864e-22 relative error = 3.3112093127949260610423462738683e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.3MB, time=7.26 NO POLE x[1] = 1.0954 y[1] (analytic) = 3.9903785956332232540746121279702 y[1] (numeric) = 3.9903785956332232540747443932105 absolute error = 1.322652403e-22 relative error = 3.3146037933528750296449099865605e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0955 y[1] (analytic) = 3.9906776484451779634589014142731 y[1] (numeric) = 3.9906776484451779634590338248819 absolute error = 1.324106088e-22 relative error = 3.3179981062010600061177681005581e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0956 y[1] (analytic) = 3.9909767311639091822172840805157 y[1] (numeric) = 3.9909767311639091822174166365075 absolute error = 1.325559918e-22 relative error = 3.3213922487927412856363144823163e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0957 y[1] (analytic) = 3.991275843792407737539564670272 y[1] (numeric) = 3.9912758437924077375396973716613 absolute error = 1.327013893e-22 relative error = 3.3247862210874042244805607032982e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0958 y[1] (analytic) = 3.991574986333664755713221342003 y[1] (numeric) = 3.9915749863336647557133541888045 absolute error = 1.328468015e-22 relative error = 3.3281800280550970523516989214565e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0959 y[1] (analytic) = 3.9918741587906716621533171319568 y[1] (numeric) = 3.9918741587906716621534501241849 absolute error = 1.329922281e-22 relative error = 3.3315736621389303612837982999261e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.096 y[1] (analytic) = 3.9921733611664201814324142083434 y[1] (numeric) = 3.9921733611664201814325473460127 absolute error = 1.331376693e-22 relative error = 3.3349671283087834234550704593362e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0961 y[1] (analytic) = 3.9924725934639023373104911170859 y[1] (numeric) = 3.9924725934639023373106244002109 absolute error = 1.332831250e-22 relative error = 3.3383604240189024126665530202927e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0962 y[1] (analytic) = 3.9927718556861104527648630194449 y[1] (numeric) = 3.9927718556861104527649964480402 absolute error = 1.334285953e-22 relative error = 3.3417535517333453948601942586677e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0963 y[1] (analytic) = 3.9930711478360371500201049218168 y[1] (numeric) = 3.9930711478360371500202384958969 absolute error = 1.335740801e-22 relative error = 3.3451465089067528318432676395495e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0964 y[1] (analytic) = 3.9933704699166753505779778980041 y[1] (numeric) = 3.9933704699166753505781116175836 absolute error = 1.337195795e-22 relative error = 3.3485392980028261347567758925822e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0965 y[1] (analytic) = 3.9936698219310182752473583042583 y[1] (numeric) = 3.9936698219310182752474921693518 absolute error = 1.338650935e-22 relative error = 3.3519319189805626462789520153132e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0966 y[1] (analytic) = 3.9939692038820594441741699873938 y[1] (numeric) = 3.9939692038820594441743039980157 absolute error = 1.340106219e-22 relative error = 3.3553243667914192612275663207723e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0967 y[1] (analytic) = 3.9942686157727926768713194862713 y[1] (numeric) = 3.9942686157727926768714536424363 absolute error = 1.341561650e-22 relative error = 3.3587166489063000511395082138623e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0968 y[1] (analytic) = 3.9945680576062120922486342269527 y[1] (numeric) = 3.9945680576062120922487685286753 absolute error = 1.343017226e-22 relative error = 3.3621087602768684068674256139534e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0969 y[1] (analytic) = 3.9948675293853121086428037118238 y[1] (numeric) = 3.9948675293853121086429381591185 absolute error = 1.344472947e-22 relative error = 3.3655007008627223564468164089550e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.097 y[1] (analytic) = 3.9951670311130874438473237029863 y[1] (numeric) = 3.9951670311130874438474582958677 absolute error = 1.345928814e-22 relative error = 3.3688924731264935595173708226634e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0971 y[1] (analytic) = 3.9954665627925331151424434002177 y[1] (numeric) = 3.9954665627925331151425781387003 absolute error = 1.347384826e-22 relative error = 3.3722840745243992351729575357086e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0972 y[1] (analytic) = 3.9957661244266444393251156137987 y[1] (numeric) = 3.9957661244266444393252504978971 absolute error = 1.348840984e-22 relative error = 3.3756755075187145301878416302062e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0973 y[1] (analytic) = 3.9960657160184170327389499325077 y[1] (numeric) = 3.9960657160184170327390849622366 absolute error = 1.350297289e-22 relative error = 3.3790667745709734510746540562328e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0974 y[1] (analytic) = 3.9963653375708468113041688870822 y[1] (numeric) = 3.996365337570846811304304062456 absolute error = 1.351753738e-22 relative error = 3.3824578681328740369878880986722e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0975 y[1] (analytic) = 3.9966649890869299905475671094453 y[1] (numeric) = 3.9966649890869299905477024304786 absolute error = 1.353210333e-22 relative error = 3.3858487931688057220885931536787e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0976 y[1] (analytic) = 3.9969646705696630856324734879992 y[1] (numeric) = 3.9969646705696630856326089547066 absolute error = 1.354667074e-22 relative error = 3.3892395496378694135932095985730e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0977 y[1] (analytic) = 3.9972643820220429113887163192833 y[1] (numeric) = 3.9972643820220429113888519316793 absolute error = 1.356123960e-22 relative error = 3.3926301349974645121083117303218e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0978 y[1] (analytic) = 3.9975641234470665823425914562973 y[1] (numeric) = 3.9975641234470665823427272143965 absolute error = 1.357580992e-22 relative error = 3.3960205517087968668419896910765e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0979 y[1] (analytic) = 3.9978638948477315127468334537894 y[1] (numeric) = 3.9978638948477315127469693576063 absolute error = 1.359038169e-22 relative error = 3.3994107972296598505503252475416e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.098 y[1] (analytic) = 3.9981636962270354166105897108083 y[1] (numeric) = 3.9981636962270354166107257603575 absolute error = 1.360495492e-22 relative error = 3.4028008740209029415197274870083e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0981 y[1] (analytic) = 3.9984635275879763077293976108199 y[1] (numeric) = 3.9984635275879763077295338061161 absolute error = 1.361952962e-22 relative error = 3.4061907845426347736903394546016e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0982 y[1] (analytic) = 3.9987633889335524997151646596877 y[1] (numeric) = 3.9987633889335524997153010007454 absolute error = 1.363410577e-22 relative error = 3.4095805237519038671040442650743e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.3MB, time=7.47 x[1] = 1.0983 y[1] (analytic) = 3.9990632802667626060261516218167 y[1] (numeric) = 3.9990632802667626060262881086504 absolute error = 1.364868337e-22 relative error = 3.4129700916084396654191526572072e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0984 y[1] (analytic) = 3.9993632015906055399969586547609 y[1] (numeric) = 3.9993632015906055399970952873853 absolute error = 1.366326244e-22 relative error = 3.4163594930727771020389544632983e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0985 y[1] (analytic) = 3.9996631529080805148685144425947 y[1] (numeric) = 3.9996631529080805148686512210243 absolute error = 1.367784296e-22 relative error = 3.4197487231031181644877617499248e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0986 y[1] (analytic) = 3.9999631342221870438180683283467 y[1] (numeric) = 3.9999631342221870438182052525961 absolute error = 1.369242494e-22 relative error = 3.4231377841592434874565333540440e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0987 y[1] (analytic) = 4.0002631455359249399891854457975 y[1] (numeric) = 4.0002631455359249399893225158813 absolute error = 1.370700838e-22 relative error = 3.4265266762003575384003844868861e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0988 y[1] (analytic) = 4.0005631868522943165217448509402 y[1] (numeric) = 4.000563186852294316521882066873 absolute error = 1.372159328e-22 relative error = 3.4299153991856742040028456504961e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0989 y[1] (analytic) = 4.0008632581742955865819406534044 y[1] (numeric) = 4.0008632581742955865820780152008 absolute error = 1.373617964e-22 relative error = 3.4333039530744167896739446320381e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.099 y[1] (analytic) = 4.0011633595049294633922861481429 y[1] (numeric) = 4.0011633595049294633924236558174 absolute error = 1.375076745e-22 relative error = 3.4366923353265449073305844375845e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0991 y[1] (analytic) = 4.0014634908471969602616209476819 y[1] (numeric) = 4.0014634908471969602617586012491 absolute error = 1.376535672e-22 relative error = 3.4400805484009487279714218368070e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0992 y[1] (analytic) = 4.0017636522040993906151211152345 y[1] (numeric) = 4.001763652204099390615258914709 absolute error = 1.377994745e-22 relative error = 3.4434685922568797820441750247667e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0993 y[1] (analytic) = 4.0020638435786383680243122989773 y[1] (numeric) = 4.0020638435786383680244502443738 absolute error = 1.379453965e-22 relative error = 3.4468564693523097796718322984148e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0994 y[1] (analytic) = 4.002364064973815806237085867791 y[1] (numeric) = 4.002364064973815806237223959124 absolute error = 1.380913330e-22 relative error = 3.4502441746489001274796256068692e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0995 y[1] (analytic) = 4.0026643163926339192077180487639 y[1] (numeric) = 4.002664316392633919207856286048 absolute error = 1.382372841e-22 relative error = 3.4536317106048288077238727317805e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0996 y[1] (analytic) = 4.00296459783809522112689206676 y[1] (numeric) = 4.0029645978380952211270304500098 absolute error = 1.383832498e-22 relative error = 3.4570190771793850146987595163910e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0997 y[1] (analytic) = 4.0032649093132025264517232863507 y[1] (numeric) = 4.0032649093132025264518618155808 absolute error = 1.385292301e-22 relative error = 3.4604062743318673574019690454152e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0998 y[1] (analytic) = 4.0035652508209589499357873564111 y[1] (numeric) = 4.0035652508209589499359260316361 absolute error = 1.386752250e-22 relative error = 3.4637933020215838590310840974857e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.0999 y[1] (analytic) = 4.0038656223643679066591513576805 y[1] (numeric) = 4.0038656223643679066592901789151 absolute error = 1.388212346e-22 relative error = 3.4671801627054382750972564106999e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.1 y[1] (analytic) = 4.0041660239464331120584079535887 y[1] (numeric) = 4.0041660239464331120585469208473 absolute error = 1.389672586e-22 relative error = 3.4705668488499984998339699440511e-21 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = exp ( x ) ; Iterations = 1000 Total Elapsed Time = 7 Seconds Elapsed Time(since restart) = 7 Seconds Expected Time Remaining = 11 Minutes 12 Seconds Optimized Time Remaining = 11 Minutes 11 Seconds Time to Timeout = 14 Minutes 52 Seconds Percent Done = 1.112 % > quit memory used=132.0MB, alloc=4.3MB, time=7.60