|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > INFO, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_normmax, > glob_max_sec, > glob_optimal_start, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin_init, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_last_good_h, > glob_log10normmin, > glob_relerr, > glob_clock_sec, > sec_in_min, > glob_display_flag, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_max_rel_trunc_err, > glob_disp_incr, > glob_abserr, > glob_look_poles, > glob_large_float, > glob_not_yet_start_msg, > centuries_in_millinium, > djd_debug, > glob_max_minutes, > glob_warned2, > glob_hmin, > years_in_century, > glob_warned, > glob_reached_optimal_h, > glob_log10abserr, > glob_small_float, > glob_max_trunc_err, > glob_max_iter, > glob_log10_abserr, > glob_h, > glob_clock_start_sec, > djd_debug2, > glob_start, > glob_smallish_float, > glob_hmax, > glob_log10relerr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_hours, > glob_optimal_done, > glob_almost_1, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_not_yet_finished, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_m1, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_pole, > array_y, > array_x, > array_y_init, > array_norms, > array_y_higher, > array_complex_pole, > array_poles, > array_y_set_initial, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_normmax, glob_max_sec, glob_optimal_start, glob_log10_relerr, glob_dump_analytic, glob_hmin_init, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_optimal_clock_start_sec, glob_no_eqs, glob_last_good_h, glob_log10normmin, glob_relerr, glob_clock_sec, sec_in_min, glob_display_flag, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_max_rel_trunc_err, glob_disp_incr, glob_abserr, glob_look_poles, glob_large_float, glob_not_yet_start_msg, centuries_in_millinium, djd_debug, glob_max_minutes, glob_warned2, glob_hmin, years_in_century, glob_warned, glob_reached_optimal_h, glob_log10abserr, glob_small_float, glob_max_trunc_err, glob_max_iter, glob_log10_abserr, glob_h, glob_clock_start_sec, djd_debug2, glob_start, glob_smallish_float, glob_hmax, glob_log10relerr, glob_current_iter, glob_curr_iter_when_opt, glob_max_hours, glob_optimal_done, glob_almost_1, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_orig_start_sec, glob_unchanged_h_cnt, glob_not_yet_finished, days_in_year, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_m1, array_1st_rel_error, array_last_rel_error, array_type_pole, array_pole, array_y, array_x, array_y_init, array_norms, array_y_higher, array_complex_pole, array_poles, array_y_set_initial, array_y_higher_work, array_real_pole, array_y_higher_work2, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > INFO, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_normmax, > glob_max_sec, > glob_optimal_start, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin_init, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_last_good_h, > glob_log10normmin, > glob_relerr, > glob_clock_sec, > sec_in_min, > glob_display_flag, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_max_rel_trunc_err, > glob_disp_incr, > glob_abserr, > glob_look_poles, > glob_large_float, > glob_not_yet_start_msg, > centuries_in_millinium, > djd_debug, > glob_max_minutes, > glob_warned2, > glob_hmin, > years_in_century, > glob_warned, > glob_reached_optimal_h, > glob_log10abserr, > glob_small_float, > glob_max_trunc_err, > glob_max_iter, > glob_log10_abserr, > glob_h, > glob_clock_start_sec, > djd_debug2, > glob_start, > glob_smallish_float, > glob_hmax, > glob_log10relerr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_hours, > glob_optimal_done, > glob_almost_1, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_not_yet_finished, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_m1, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_pole, > array_y, > array_x, > array_y_init, > array_norms, > array_y_higher, > array_complex_pole, > array_poles, > array_y_set_initial, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_normmax, glob_max_sec, glob_optimal_start, glob_log10_relerr, glob_dump_analytic, glob_hmin_init, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_optimal_clock_start_sec, glob_no_eqs, glob_last_good_h, glob_log10normmin, glob_relerr, glob_clock_sec, sec_in_min, glob_display_flag, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_max_rel_trunc_err, glob_disp_incr, glob_abserr, glob_look_poles, glob_large_float, glob_not_yet_start_msg, centuries_in_millinium, djd_debug, glob_max_minutes, glob_warned2, glob_hmin, years_in_century, glob_warned, glob_reached_optimal_h, glob_log10abserr, glob_small_float, glob_max_trunc_err, glob_max_iter, glob_log10_abserr, glob_h, glob_clock_start_sec, djd_debug2, glob_start, glob_smallish_float, glob_hmax, glob_log10relerr, glob_current_iter, glob_curr_iter_when_opt, glob_max_hours, glob_optimal_done, glob_almost_1, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_orig_start_sec, glob_unchanged_h_cnt, glob_not_yet_finished, days_in_year, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_m1, array_1st_rel_error, array_last_rel_error, array_type_pole, array_pole, array_y, array_x, array_y_init, array_norms, array_y_higher, array_complex_pole, array_poles, array_y_set_initial, array_y_higher_work, array_real_pole, array_y_higher_work2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > INFO, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_normmax, > glob_max_sec, > glob_optimal_start, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin_init, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_last_good_h, > glob_log10normmin, > glob_relerr, > glob_clock_sec, > sec_in_min, > glob_display_flag, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_max_rel_trunc_err, > glob_disp_incr, > glob_abserr, > glob_look_poles, > glob_large_float, > glob_not_yet_start_msg, > centuries_in_millinium, > djd_debug, > glob_max_minutes, > glob_warned2, > glob_hmin, > years_in_century, > glob_warned, > glob_reached_optimal_h, > glob_log10abserr, > glob_small_float, > glob_max_trunc_err, > glob_max_iter, > glob_log10_abserr, > glob_h, > glob_clock_start_sec, > djd_debug2, > glob_start, > glob_smallish_float, > glob_hmax, > glob_log10relerr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_hours, > glob_optimal_done, > glob_almost_1, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_not_yet_finished, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_m1, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_pole, > array_y, > array_x, > array_y_init, > array_norms, > array_y_higher, > array_complex_pole, > array_poles, > array_y_set_initial, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_normmax, glob_max_sec, glob_optimal_start, glob_log10_relerr, glob_dump_analytic, glob_hmin_init, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_optimal_clock_start_sec, glob_no_eqs, glob_last_good_h, glob_log10normmin, glob_relerr, glob_clock_sec, sec_in_min, glob_display_flag, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_max_rel_trunc_err, glob_disp_incr, glob_abserr, glob_look_poles, glob_large_float, glob_not_yet_start_msg, centuries_in_millinium, djd_debug, glob_max_minutes, glob_warned2, glob_hmin, years_in_century, glob_warned, glob_reached_optimal_h, glob_log10abserr, glob_small_float, glob_max_trunc_err, glob_max_iter, glob_log10_abserr, glob_h, glob_clock_start_sec, djd_debug2, glob_start, glob_smallish_float, glob_hmax, glob_log10relerr, glob_current_iter, glob_curr_iter_when_opt, glob_max_hours, glob_optimal_done, glob_almost_1, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_orig_start_sec, glob_unchanged_h_cnt, glob_not_yet_finished, days_in_year, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_m1, array_1st_rel_error, array_last_rel_error, array_type_pole, array_pole, array_y, array_x, array_y_init, array_norms, array_y_higher, array_complex_pole, array_poles, array_y_set_initial, array_y_higher_work, array_real_pole, array_y_higher_work2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_normmax, > glob_max_sec, > glob_optimal_start, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin_init, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_last_good_h, > glob_log10normmin, > glob_relerr, > glob_clock_sec, > sec_in_min, > glob_display_flag, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_max_rel_trunc_err, > glob_disp_incr, > glob_abserr, > glob_look_poles, > glob_large_float, > glob_not_yet_start_msg, > centuries_in_millinium, > djd_debug, > glob_max_minutes, > glob_warned2, > glob_hmin, > years_in_century, > glob_warned, > glob_reached_optimal_h, > glob_log10abserr, > glob_small_float, > glob_max_trunc_err, > glob_max_iter, > glob_log10_abserr, > glob_h, > glob_clock_start_sec, > djd_debug2, > glob_start, > glob_smallish_float, > glob_hmax, > glob_log10relerr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_hours, > glob_optimal_done, > glob_almost_1, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_not_yet_finished, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_m1, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_pole, > array_y, > array_x, > array_y_init, > array_norms, > array_y_higher, > array_complex_pole, > array_poles, > array_y_set_initial, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_normmax, glob_max_sec, glob_optimal_start, glob_log10_relerr, glob_dump_analytic, glob_hmin_init, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_optimal_clock_start_sec, glob_no_eqs, glob_last_good_h, glob_log10normmin, glob_relerr, glob_clock_sec, sec_in_min, glob_display_flag, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_max_rel_trunc_err, glob_disp_incr, glob_abserr, glob_look_poles, glob_large_float, glob_not_yet_start_msg, centuries_in_millinium, djd_debug, glob_max_minutes, glob_warned2, glob_hmin, years_in_century, glob_warned, glob_reached_optimal_h, glob_log10abserr, glob_small_float, glob_max_trunc_err, glob_max_iter, glob_log10_abserr, glob_h, glob_clock_start_sec, djd_debug2, glob_start, glob_smallish_float, glob_hmax, glob_log10relerr, glob_current_iter, glob_curr_iter_when_opt, glob_max_hours, glob_optimal_done, glob_almost_1, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_orig_start_sec, glob_unchanged_h_cnt, glob_not_yet_finished, days_in_year, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_m1, array_1st_rel_error, array_last_rel_error, array_type_pole, array_pole, array_y, array_x, array_y_init, array_norms, array_y_higher, array_complex_pole, array_poles, array_y_set_initial, array_y_higher_work, array_real_pole, array_y_higher_work2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > INFO, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_normmax, > glob_max_sec, > glob_optimal_start, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin_init, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_last_good_h, > glob_log10normmin, > glob_relerr, > glob_clock_sec, > sec_in_min, > glob_display_flag, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_max_rel_trunc_err, > glob_disp_incr, > glob_abserr, > glob_look_poles, > glob_large_float, > glob_not_yet_start_msg, > centuries_in_millinium, > djd_debug, > glob_max_minutes, > glob_warned2, > glob_hmin, > years_in_century, > glob_warned, > glob_reached_optimal_h, > glob_log10abserr, > glob_small_float, > glob_max_trunc_err, > glob_max_iter, > glob_log10_abserr, > glob_h, > glob_clock_start_sec, > djd_debug2, > glob_start, > glob_smallish_float, > glob_hmax, > glob_log10relerr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_hours, > glob_optimal_done, > glob_almost_1, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_not_yet_finished, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_m1, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_pole, > array_y, > array_x, > array_y_init, > array_norms, > array_y_higher, > array_complex_pole, > array_poles, > array_y_set_initial, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_normmax, glob_max_sec, glob_optimal_start, glob_log10_relerr, glob_dump_analytic, glob_hmin_init, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_optimal_clock_start_sec, glob_no_eqs, glob_last_good_h, glob_log10normmin, glob_relerr, glob_clock_sec, sec_in_min, glob_display_flag, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_max_rel_trunc_err, glob_disp_incr, glob_abserr, glob_look_poles, glob_large_float, glob_not_yet_start_msg, centuries_in_millinium, djd_debug, glob_max_minutes, glob_warned2, glob_hmin, years_in_century, glob_warned, glob_reached_optimal_h, glob_log10abserr, glob_small_float, glob_max_trunc_err, glob_max_iter, glob_log10_abserr, glob_h, glob_clock_start_sec, djd_debug2, glob_start, glob_smallish_float, glob_hmax, glob_log10relerr, glob_current_iter, glob_curr_iter_when_opt, glob_max_hours, glob_optimal_done, glob_almost_1, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_orig_start_sec, glob_unchanged_h_cnt, glob_not_yet_finished, days_in_year, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_m1, array_1st_rel_error, array_last_rel_error, array_type_pole, array_pole, array_y, array_x, array_y_init, array_norms, array_y_higher, array_complex_pole, array_poles, array_y_set_initial, array_y_higher_work, array_real_pole, array_y_higher_work2, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > INFO, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_normmax, > glob_max_sec, > glob_optimal_start, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin_init, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_last_good_h, > glob_log10normmin, > glob_relerr, > glob_clock_sec, > sec_in_min, > glob_display_flag, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_max_rel_trunc_err, > glob_disp_incr, > glob_abserr, > glob_look_poles, > glob_large_float, > glob_not_yet_start_msg, > centuries_in_millinium, > djd_debug, > glob_max_minutes, > glob_warned2, > glob_hmin, > years_in_century, > glob_warned, > glob_reached_optimal_h, > glob_log10abserr, > glob_small_float, > glob_max_trunc_err, > glob_max_iter, > glob_log10_abserr, > glob_h, > glob_clock_start_sec, > djd_debug2, > glob_start, > glob_smallish_float, > glob_hmax, > glob_log10relerr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_hours, > glob_optimal_done, > glob_almost_1, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_not_yet_finished, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_m1, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_pole, > array_y, > array_x, > array_y_init, > array_norms, > array_y_higher, > array_complex_pole, > array_poles, > array_y_set_initial, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre cos $eq_no = 1 > array_tmp1_g[1] := sin(array_x[1]); > array_tmp1[1] := cos(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre 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 cos $eq_no = 1 > array_tmp1_g[2] := (att(1,array_tmp1,array_x,1)); > array_tmp1[2] := (-att(1,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre 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 cos $eq_no = 1 > array_tmp1_g[3] := (att(2,array_tmp1,array_x,1)); > array_tmp1[3] := (-att(2,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre 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 cos $eq_no = 1 > array_tmp1_g[4] := (att(3,array_tmp1,array_x,1)); > array_tmp1[4] := (-att(3,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre 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 cos $eq_no = 1 > array_tmp1_g[5] := (att(4,array_tmp1,array_x,1)); > array_tmp1[5] := (-att(4,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre 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 cos $eq_no = 1 > array_tmp1_g[kkk] := (att(kkk-1,array_tmp1,array_x,1)); > array_tmp1[kkk] := (-att(kkk-1,array_tmp1_g,array_x,1)); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit 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 INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_normmax, glob_max_sec, glob_optimal_start, glob_log10_relerr, glob_dump_analytic, glob_hmin_init, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_optimal_clock_start_sec, glob_no_eqs, glob_last_good_h, glob_log10normmin, glob_relerr, glob_clock_sec, sec_in_min, glob_display_flag, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_max_rel_trunc_err, glob_disp_incr, glob_abserr, glob_look_poles, glob_large_float, glob_not_yet_start_msg, centuries_in_millinium, djd_debug, glob_max_minutes, glob_warned2, glob_hmin, years_in_century, glob_warned, glob_reached_optimal_h, glob_log10abserr, glob_small_float, glob_max_trunc_err, glob_max_iter, glob_log10_abserr, glob_h, glob_clock_start_sec, djd_debug2, glob_start, glob_smallish_float, glob_hmax, glob_log10relerr, glob_current_iter, glob_curr_iter_when_opt, glob_max_hours, glob_optimal_done, glob_almost_1, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_orig_start_sec, glob_unchanged_h_cnt, glob_not_yet_finished, days_in_year, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_m1, array_1st_rel_error, array_last_rel_error, array_type_pole, array_pole, array_y, array_x, array_y_init, array_norms, array_y_higher, array_complex_pole, array_poles, array_y_set_initial, array_y_higher_work, array_real_pole, array_y_higher_work2, glob_last; array_tmp1_g[1] := sin(array_x[1]); array_tmp1[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; 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_g[2] := att(1, array_tmp1, array_x, 1); array_tmp1[2] := -att(1, array_tmp1_g, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; 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_g[3] := att(2, array_tmp1, array_x, 1); array_tmp1[3] := -att(2, array_tmp1_g, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; 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_g[4] := att(3, array_tmp1, array_x, 1); array_tmp1[4] := -att(3, array_tmp1_g, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; 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_g[5] := att(4, array_tmp1, array_x, 1); array_tmp1[5] := -att(4, array_tmp1_g, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; 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_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1); array_tmp1[kkk] := -att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; 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 + sin(x); > end; exact_soln_y := proc(x) 1.0 + sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > INFO, > ALWAYS, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_normmax, > glob_max_sec, > glob_optimal_start, > glob_log10_relerr, > glob_dump_analytic, > glob_hmin_init, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_optimal_clock_start_sec, > glob_no_eqs, > glob_last_good_h, > glob_log10normmin, > glob_relerr, > glob_clock_sec, > sec_in_min, > glob_display_flag, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_max_rel_trunc_err, > glob_disp_incr, > glob_abserr, > glob_look_poles, > glob_large_float, > glob_not_yet_start_msg, > centuries_in_millinium, > djd_debug, > glob_max_minutes, > glob_warned2, > glob_hmin, > years_in_century, > glob_warned, > glob_reached_optimal_h, > glob_log10abserr, > glob_small_float, > glob_max_trunc_err, > glob_max_iter, > glob_log10_abserr, > glob_h, > glob_clock_start_sec, > djd_debug2, > glob_start, > glob_smallish_float, > glob_hmax, > glob_log10relerr, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_hours, > glob_optimal_done, > glob_almost_1, > hours_in_day, > glob_dump, > glob_html_log, > glob_subiter_method, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_unchanged_h_cnt, > glob_not_yet_finished, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_m1, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_pole, > array_y, > array_x, > array_y_init, > array_norms, > array_y_higher, > array_complex_pole, > array_poles, > array_y_set_initial, > array_y_higher_work, > array_real_pole, > array_y_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > ALWAYS := 1; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_iolevel := 5; > glob_normmax := 0.0; > glob_max_sec := 10000.0; > glob_optimal_start := 0.0; > glob_log10_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_hmin_init := 0.001; > glob_initial_pass := true; > min_in_hour := 60.0; > glob_max_opt_iter := 10; > glob_optimal_clock_start_sec := 0.0; > glob_no_eqs := 0; > glob_last_good_h := 0.1; > glob_log10normmin := 0.1; > glob_relerr := 0.1e-10; > glob_clock_sec := 0.0; > sec_in_min := 60.0; > glob_display_flag := true; > glob_optimal_expect_sec := 0.1; > glob_percent_done := 0.0; > glob_iter := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_disp_incr := 0.1; > glob_abserr := 0.1e-10; > glob_look_poles := false; > glob_large_float := 9.0e100; > glob_not_yet_start_msg := true; > centuries_in_millinium := 10.0; > djd_debug := true; > glob_max_minutes := 0.0; > glob_warned2 := false; > glob_hmin := 0.00000000001; > years_in_century := 100.0; > glob_warned := false; > glob_reached_optimal_h := false; > glob_log10abserr := 0.0; > glob_small_float := 0.1e-50; > glob_max_trunc_err := 0.1e-10; > glob_max_iter := 1000; > glob_log10_abserr := 0.1e-10; > glob_h := 0.1; > glob_clock_start_sec := 0.0; > djd_debug2 := true; > glob_start := 0; > glob_smallish_float := 0.1e-100; > glob_hmax := 1.0; > glob_log10relerr := 0.0; > glob_current_iter := 0; > glob_curr_iter_when_opt := 0; > glob_max_hours := 0.0; > glob_optimal_done := false; > glob_almost_1 := 0.9990; > hours_in_day := 24.0; > glob_dump := false; > glob_html_log := true; > glob_subiter_method := 3; > MAX_UNCHANGED := 10; > glob_orig_start_sec := 0.0; > glob_unchanged_h_cnt := 0; > glob_not_yet_finished := true; > days_in_year := 365.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/cospostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 1.6;"); > omniout_str(ALWAYS,"x_end := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"1.0 + sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp1_g:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_norms:= Array(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),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[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_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_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[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 > ; > 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 > ; > 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_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_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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 1.6; > x_end := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = cos ( x ) ;"); > 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,"2012-06-13T12:56:26-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"cos") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( 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,"cos diffeq.mxt") > ; > logitem_str(html_log_file,"cos maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel, glob_normmax, glob_max_sec, glob_optimal_start, glob_log10_relerr, glob_dump_analytic, glob_hmin_init, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_optimal_clock_start_sec, glob_no_eqs, glob_last_good_h, glob_log10normmin, glob_relerr, glob_clock_sec, sec_in_min, glob_display_flag, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_max_rel_trunc_err, glob_disp_incr, glob_abserr, glob_look_poles, glob_large_float, glob_not_yet_start_msg, centuries_in_millinium, djd_debug, glob_max_minutes, glob_warned2, glob_hmin, years_in_century, glob_warned, glob_reached_optimal_h, glob_log10abserr, glob_small_float, glob_max_trunc_err, glob_max_iter, glob_log10_abserr, glob_h, glob_clock_start_sec, djd_debug2, glob_start, glob_smallish_float, glob_hmax, glob_log10relerr, glob_current_iter, glob_curr_iter_when_opt, glob_max_hours, glob_optimal_done, glob_almost_1, hours_in_day, glob_dump, glob_html_log, glob_subiter_method, MAX_UNCHANGED, glob_orig_start_sec, glob_unchanged_h_cnt, glob_not_yet_finished, days_in_year, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_m1, array_1st_rel_error, array_last_rel_error, array_type_pole, array_pole, array_y, array_x, array_y_init, array_norms, array_y_higher, array_complex_pole, array_poles, array_y_set_initial, array_y_higher_work, array_real_pole, array_y_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; ALWAYS := 1; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; glob_iolevel := 5; glob_normmax := 0.; glob_max_sec := 10000.0; glob_optimal_start := 0.; glob_log10_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_hmin_init := 0.001; glob_initial_pass := true; min_in_hour := 60.0; glob_max_opt_iter := 10; glob_optimal_clock_start_sec := 0.; glob_no_eqs := 0; glob_last_good_h := 0.1; glob_log10normmin := 0.1; glob_relerr := 0.1*10^(-10); glob_clock_sec := 0.; sec_in_min := 60.0; glob_display_flag := true; glob_optimal_expect_sec := 0.1; glob_percent_done := 0.; glob_iter := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_disp_incr := 0.1; glob_abserr := 0.1*10^(-10); glob_look_poles := false; glob_large_float := 0.90*10^101; glob_not_yet_start_msg := true; centuries_in_millinium := 10.0; djd_debug := true; glob_max_minutes := 0.; glob_warned2 := false; glob_hmin := 0.1*10^(-10); years_in_century := 100.0; glob_warned := false; glob_reached_optimal_h := false; glob_log10abserr := 0.; glob_small_float := 0.1*10^(-50); glob_max_trunc_err := 0.1*10^(-10); glob_max_iter := 1000; glob_log10_abserr := 0.1*10^(-10); glob_h := 0.1; glob_clock_start_sec := 0.; djd_debug2 := true; glob_start := 0; glob_smallish_float := 0.1*10^(-100); glob_hmax := 1.0; glob_log10relerr := 0.; glob_current_iter := 0; glob_curr_iter_when_opt := 0; glob_max_hours := 0.; glob_optimal_done := false; glob_almost_1 := 0.9990; hours_in_day := 24.0; glob_dump := false; glob_html_log := true; glob_subiter_method := 3; MAX_UNCHANGED := 10; glob_orig_start_sec := 0.; glob_unchanged_h_cnt := 0; glob_not_yet_finished := true; days_in_year := 365.0; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/cospostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 1.6;"); omniout_str(ALWAYS, "x_end := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "1.0 + sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp1_g := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 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; 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_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_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; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 1.6; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_h := 0.0001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = cos ( x ) ;"); 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, "2012-06-13T12:56:26-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "cos"); logitem_str(html_log_file, "diff ( y , x , 1 ) = cos ( 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, "cos diffeq.mxt"); logitem_str(html_log_file, "cos 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/cospostode.ode################# diff ( y , x , 1 ) = cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 1.6; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0 + sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 1.6 y[1] (analytic) = 1.9995736030415051643421138255462 y[1] (numeric) = 1.9995736030415051643421138255462 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6001 y[1] (analytic) = 1.9995706780914118910139052195682 y[1] (numeric) = 1.9995706780914118910139051709778 absolute error = 4.85904e-26 relative error = 2.4300416350563554817725609753854e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6002 y[1] (analytic) = 1.9995677431456118451013333514363 y[1] (numeric) = 1.9995677431456118451013332542557 absolute error = 9.71806e-26 relative error = 4.8600804015332201352639637735824e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6003 y[1] (analytic) = 1.9995647982041343760623742223945 y[1] (numeric) = 1.9995647982041343760623740766239 absolute error = 1.457706e-25 relative error = 7.2901163358607179532658238865852e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6004 y[1] (analytic) = 1.9995618432670089333117779816536 y[1] (numeric) = 1.9995618432670089333117777872931 absolute error = 1.943605e-25 relative error = 9.7201544755645909381627432151729e-24 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6005 y[1] (analytic) = 1.9995588783342650662207744322434 y[1] (numeric) = 1.9995588783342650662207741892931 absolute error = 2.429503e-25 relative error = 1.2150194857097183367609291804004e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6006 y[1] (analytic) = 1.9995559034059324241167775373012 y[1] (numeric) = 1.9995559034059324241167772457612 absolute error = 2.915400e-25 relative error = 1.4580237516910978227629948581315e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6007 y[1] (analytic) = 1.9995529184820407562830889267973 y[1] (numeric) = 1.9995529184820407562830885866679 absolute error = 3.401294e-25 relative error = 1.7010272489222691021930569573418e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6008 y[1] (analytic) = 1.9995499235626199119586004047031 y[1] (numeric) = 1.9995499235626199119586000159843 absolute error = 3.887188e-25 relative error = 1.9440314813816474934296051408991e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6009 y[1] (analytic) = 1.9995469186476998403374954566015 y[1] (numeric) = 1.9995469186476998403374950192935 absolute error = 4.373080e-25 relative error = 2.1870354524901713192056611228445e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.601 y[1] (analytic) = 1.9995439037373105905689497577459 y[1] (numeric) = 1.9995439037373105905689492718489 absolute error = 4.858970e-25 relative error = 2.4300391658908758591490252714533e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6011 y[1] (analytic) = 1.9995408788314823117568306815686 y[1] (numeric) = 1.9995408788314823117568301470827 absolute error = 5.344859e-25 relative error = 2.6730431253416025049702737981781e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6012 y[1] (analytic) = 1.9995378439302452529593958086421 y[1] (numeric) = 1.9995378439302452529593952255675 absolute error = 5.830746e-25 relative error = 2.9160468343720970900964754433778e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6013 y[1] (analytic) = 1.9995347990336297631889904360972 y[1] (numeric) = 1.999534799033629763188989804434 absolute error = 6.316632e-25 relative error = 3.1590507967417284593122923248377e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=2.9MB, time=0.48 x[1] = 1.6014 y[1] (analytic) = 1.9995317441416662914117440874996 y[1] (numeric) = 1.9995317441416662914117434072479 absolute error = 6.802517e-25 relative error = 3.4020550160958302258846171101885e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6015 y[1] (analytic) = 1.9995286792543853865472660231885 y[1] (numeric) = 1.9995286792543853865472652943485 absolute error = 7.288400e-25 relative error = 3.6450589959618930068492628332811e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6016 y[1] (analytic) = 1.9995256043718176974683397510816 y[1] (numeric) = 1.9995256043718176974683389736534 absolute error = 7.774282e-25 relative error = 3.8880632401016002586052058254974e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6017 y[1] (analytic) = 1.9995225194939939730006165379466 y[1] (numeric) = 1.9995225194939939730006157119304 absolute error = 8.260162e-25 relative error = 4.1310672520409247141024893264359e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6018 y[1] (analytic) = 1.9995194246209450619223079211456 y[1] (numeric) = 1.9995194246209450619223070465415 absolute error = 8.746041e-25 relative error = 4.3740715355431035210136488732234e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6019 y[1] (analytic) = 1.9995163197527019129638772208529 y[1] (numeric) = 1.9995163197527019129638762976611 absolute error = 9.231918e-25 relative error = 4.6170755941325820046970947234502e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.602 y[1] (analytic) = 1.9995132048892955748077300527509 y[1] (numeric) = 1.9995132048892955748077290809715 absolute error = 9.717794e-25 relative error = 4.8600799315741614995802961980130e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6021 y[1] (analytic) = 1.999510080030757196087903841206 y[1] (numeric) = 1.9995100800307571960879028208391 absolute error = 1.0203669e-24 relative error = 5.1030845515132604021660915153449e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6022 y[1] (analytic) = 1.9995069451771180253897563329285 y[1] (numeric) = 1.9995069451771180253897552639744 absolute error = 1.0689541e-24 relative error = 5.3460884573487247221716578275214e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6023 y[1] (analytic) = 1.9995038003284094112496531111198 y[1] (numeric) = 1.9995038003284094112496519935785 absolute error = 1.1175413e-24 relative error = 5.5890931530935271081620787319773e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6024 y[1] (analytic) = 1.9995006454846628021546541101082 y[1] (numeric) = 1.99950064548466280215465294398 absolute error = 1.1661282e-24 relative error = 5.8320971420208766457837337625836e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6025 y[1] (analytic) = 1.9994974806459097465421991304792 y[1] (numeric) = 1.9994974806459097465421979157642 absolute error = 1.2147150e-24 relative error = 6.0751014280228214023093579662746e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6026 y[1] (analytic) = 1.9994943058121818927997923547011 y[1] (numeric) = 1.9994943058121818927997910913994 absolute error = 1.2633017e-24 relative error = 6.3181060147448375443283821002085e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6027 y[1] (analytic) = 1.9994911209835109892646858632502 y[1] (numeric) = 1.999491120983510989264684551362 absolute error = 1.3118882e-24 relative error = 6.5611104057051655294223503408883e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6028 y[1] (analytic) = 1.9994879261599288842235621512386 y[1] (numeric) = 1.9994879261599288842235607907641 absolute error = 1.3604745e-24 relative error = 6.8041146045469171506092744048889e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6029 y[1] (analytic) = 1.9994847213414675259122156455479 y[1] (numeric) = 1.9994847213414675259122142364871 absolute error = 1.4090608e-24 relative error = 7.0471196151709115761731012512618e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.603 y[1] (analytic) = 1.9994815065281589625152332224708 y[1] (numeric) = 1.999481506528158962515231764824 absolute error = 1.4576468e-24 relative error = 7.2901239408361177924296002787795e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6031 y[1] (analytic) = 1.9994782817200353421656737258664 y[1] (numeric) = 1.9994782817200353421656722196337 absolute error = 1.5062327e-24 relative error = 7.5331285854441752655385235267723e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6032 y[1] (analytic) = 1.9994750469171289129447464858293 y[1] (numeric) = 1.9994750469171289129447449310108 absolute error = 1.5548185e-24 relative error = 7.7761335526406380007172753163831e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6033 y[1] (analytic) = 1.9994718021194720228814888378778 y[1] (numeric) = 1.9994718021194720228814872344737 absolute error = 1.6034041e-24 relative error = 8.0191383459389928020821131339709e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6034 y[1] (analytic) = 1.9994685473270971199524426426639 y[1] (numeric) = 1.9994685473270971199524409906745 absolute error = 1.6519894e-24 relative error = 8.2621424688494872301697520402593e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6035 y[1] (analytic) = 1.9994652825400367520813298062086 y[1] (numeric) = 1.9994652825400367520813281056339 absolute error = 1.7005747e-24 relative error = 8.5051474254139651565135593134799e-23 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=1.06 NO POLE x[1] = 1.6036 y[1] (analytic) = 1.9994620077583235671387268006639 y[1] (numeric) = 1.9994620077583235671387250515041 absolute error = 1.7491598e-24 relative error = 8.7481522190114163061497444116898e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6037 y[1] (analytic) = 1.9994587229819903129417381856084 y[1] (numeric) = 1.9994587229819903129417363878636 absolute error = 1.7977448e-24 relative error = 8.9911573534203576205692395086593e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6038 y[1] (analytic) = 1.9994554282110698372536691298758 y[1] (numeric) = 1.9994554282110698372536672835462 absolute error = 1.8463296e-24 relative error = 9.2341623321502452913789513806107e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6039 y[1] (analytic) = 1.9994521234455950877836969339224 y[1] (numeric) = 1.9994521234455950877836950390083 absolute error = 1.8949141e-24 relative error = 9.4771666587072468205194521643366e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604 y[1] (analytic) = 1.9994488086855991121865415527359 y[1] (numeric) = 1.9994488086855991121865396092373 absolute error = 1.9434986e-24 relative error = 9.7201718371455593766581594467404e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6041 y[1] (analytic) = 1.9994454839311150580621351192876 y[1] (numeric) = 1.9994454839311150580621331272048 absolute error = 1.9920828e-24 relative error = 9.9631763706973432168917258835215e-23 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6042 y[1] (analytic) = 1.9994421491821761729552904685344 y[1] (numeric) = 1.9994421491821761729552884278675 absolute error = 2.0406669e-24 relative error = 1.0206181263282290122897294463842e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6043 y[1] (analytic) = 1.9994388044388158043553686619702 y[1] (numeric) = 1.9994388044388158043553665727193 absolute error = 2.0892509e-24 relative error = 1.0449186518546096904201585228486e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6044 y[1] (analytic) = 1.9994354497010673996959455127329 y[1] (numeric) = 1.9994354497010673996959433748982 absolute error = 2.1378347e-24 relative error = 1.0692191639993301434108548204015e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6045 y[1] (analytic) = 1.9994320849689645063544771112688 y[1] (numeric) = 1.9994320849689645063544749248505 absolute error = 2.1864183e-24 relative error = 1.0935196631267112643919702715909e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6046 y[1] (analytic) = 1.9994287102425407716519643515585 y[1] (numeric) = 1.9994287102425407716519621165567 absolute error = 2.2350018e-24 relative error = 1.1178201996153606427993812315775e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6047 y[1] (analytic) = 1.9994253255218299428526164579068 y[1] (numeric) = 1.9994253255218299428526141743217 absolute error = 2.2835851e-24 relative error = 1.1421207238154829353082129211926e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6048 y[1] (analytic) = 1.9994219308068658671635135123014 y[1] (numeric) = 1.9994219308068658671635111801331 absolute error = 2.3321683e-24 relative error = 1.1664212861058568450873283767556e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6049 y[1] (analytic) = 1.9994185260976824917342679823418 y[1] (numeric) = 1.9994185260976824917342656015906 absolute error = 2.3807512e-24 relative error = 1.1907217868219789261375230655461e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.605 y[1] (analytic) = 1.9994151113943138636566852497442 y[1] (numeric) = 1.9994151113943138636566828204101 absolute error = 2.4293341e-24 relative error = 1.2150223763717967780946263016945e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6051 y[1] (analytic) = 1.9994116866967941299644231394228 y[1] (numeric) = 1.999411686696794129964420661506 absolute error = 2.4779168e-24 relative error = 1.2393229550907241420227554978753e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6052 y[1] (analytic) = 1.9994082520051575376326504491543 y[1] (numeric) = 1.999408252005157537632647922655 absolute error = 2.5264993e-24 relative error = 1.2636235233430870195912623828649e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6053 y[1] (analytic) = 1.9994048073194384335777044798261 y[1] (numeric) = 1.9994048073194384335777019047445 absolute error = 2.5750816e-24 relative error = 1.2879240814932118690463889581217e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6054 y[1] (analytic) = 1.9994013526396712646567475662734 y[1] (numeric) = 1.9994013526396712646567449426097 absolute error = 2.6236637e-24 relative error = 1.3122246299054256173548210458519e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6055 y[1] (analytic) = 1.9993978879658905776674226087078 y[1] (numeric) = 1.9993978879658905776674199364621 absolute error = 2.6722457e-24 relative error = 1.3365252189591130063010333924066e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6056 y[1] (analytic) = 1.9993944132981310193475076047408 y[1] (numeric) = 1.9993944132981310193475048839134 absolute error = 2.7208274e-24 relative error = 1.3608257489885741879882410482045e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=4.1MB, time=1.66 x[1] = 1.6057 y[1] (analytic) = 1.9993909286364273363745691820072 y[1] (numeric) = 1.9993909286364273363745664125981 absolute error = 2.7694091e-24 relative error = 1.3851263704035710786929610205584e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6058 y[1] (analytic) = 1.9993874339808143753656151313886 y[1] (numeric) = 1.9993874339808143753656123133981 absolute error = 2.8179905e-24 relative error = 1.4094269335230005932387811559958e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6059 y[1] (analytic) = 1.9993839293313270828767459408447 y[1] (numeric) = 1.9993839293313270828767430742728 absolute error = 2.8665719e-24 relative error = 1.4337275887571502133331304622389e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.606 y[1] (analytic) = 1.9993804146880005054028053298515 y[1] (numeric) = 1.9993804146880005054028024146986 absolute error = 2.9151529e-24 relative error = 1.4580281364089004751344763759368e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6061 y[1] (analytic) = 1.9993768900508697893770297844543 y[1] (numeric) = 1.9993768900508697893770268207204 absolute error = 2.9637339e-24 relative error = 1.4823287769043855695117911129090e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6062 y[1] (analytic) = 1.9993733554199701811706970929347 y[1] (numeric) = 1.99937335541997018117069408062 absolute error = 3.0123147e-24 relative error = 1.5066294105771258382518676141576e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6063 y[1] (analytic) = 1.9993698107953370270927738820984 y[1] (numeric) = 1.9993698107953370270927708212031 absolute error = 3.0608953e-24 relative error = 1.5309300377914552261124299119197e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6064 y[1] (analytic) = 1.9993662561770057733895621541862 y[1] (numeric) = 1.9993662561770057733895590447105 absolute error = 3.1094757e-24 relative error = 1.5552306589117082680323953279345e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6065 y[1] (analytic) = 1.9993626915650119662443448244108 y[1] (numeric) = 1.9993626915650119662443416663548 absolute error = 3.1580560e-24 relative error = 1.5795313243181578907948441339259e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6066 y[1] (analytic) = 1.9993591169593912517770302591243 y[1] (numeric) = 1.9993591169593912517770270524882 absolute error = 3.2066361e-24 relative error = 1.6038319843593809011774426727026e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6067 y[1] (analytic) = 1.9993555323601793760437958146198 y[1] (numeric) = 1.9993555323601793760437925594038 absolute error = 3.2552160e-24 relative error = 1.6281326393997144284913867171655e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6068 y[1] (analytic) = 1.9993519377674121850367303765695 y[1] (numeric) = 1.9993519377674121850367270727737 absolute error = 3.3037958e-24 relative error = 1.6524333398197030481389528765835e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6069 y[1] (analytic) = 1.9993483331811256246834759001043 y[1] (numeric) = 1.999348333181125624683472547729 absolute error = 3.3523753e-24 relative error = 1.6767339859513617377080360420239e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.607 y[1] (analytic) = 1.9993447186013557408468679505378 y[1] (numeric) = 1.9993447186013557408468645495831 absolute error = 3.4009547e-24 relative error = 1.7010346781915338677929358140253e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6071 y[1] (analytic) = 1.999341094028138679324575244738 y[1] (numeric) = 1.999341094028138679324571795204 absolute error = 3.4495340e-24 relative error = 1.7253354169048312173472400080768e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6072 y[1] (analytic) = 1.9993374594615106858487381931509 y[1] (numeric) = 1.9993374594615106858487346950379 absolute error = 3.4981130e-24 relative error = 1.7496361024227297500882630385534e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6073 y[1] (analytic) = 1.9993338149015081060856064424798 y[1] (numeric) = 1.9993338149015081060856028957879 absolute error = 3.5466919e-24 relative error = 1.7739368351426189420888186588722e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6074 y[1] (analytic) = 1.9993301603481673856351754190226 y[1] (numeric) = 1.999330160348167385635171823752 absolute error = 3.5952706e-24 relative error = 1.7982375654123640730250447754532e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6075 y[1] (analytic) = 1.9993264958015250700308218726725 y[1] (numeric) = 1.9993264958015250700308182288233 absolute error = 3.6438492e-24 relative error = 1.8225383436131525013885287623502e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6076 y[1] (analytic) = 1.9993228212616178047389384215842 y[1] (numeric) = 1.9993228212616178047389347291567 absolute error = 3.6924275e-24 relative error = 1.8468390700757344162684790866831e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6077 y[1] (analytic) = 1.9993191367284823351585670975109 y[1] (numeric) = 1.9993191367284823351585633565052 absolute error = 3.7410057e-24 relative error = 1.8711398451982343634016767990270e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6078 y[1] (analytic) = 1.9993154422021555066210318918133 y[1] (numeric) = 1.9993154422021555066210281022297 absolute error = 3.7895836e-24 relative error = 1.8954405693110363379271445326750e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.1MB, time=2.28 x[1] = 1.6079 y[1] (analytic) = 1.9993117376826742643895703021475 y[1] (numeric) = 1.9993117376826742643895664639861 absolute error = 3.8381614e-24 relative error = 1.9197413428126351218319979348664e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.608 y[1] (analytic) = 1.9993080231700756536589638798324 y[1] (numeric) = 1.9993080231700756536589599930934 absolute error = 3.8867390e-24 relative error = 1.9440421160503519703887974006325e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6081 y[1] (analytic) = 1.9993042986643968195551677779025 y[1] (numeric) = 1.999304298664396819555163842586 absolute error = 3.9353165e-24 relative error = 1.9683429394059348994931368507645e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6082 y[1] (analytic) = 1.9993005641656750071349392998483 y[1] (numeric) = 1.9993005641656750071349353159546 absolute error = 3.9838937e-24 relative error = 1.9926437132090304049935244992418e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6083 y[1] (analytic) = 1.9992968196739475613854654490496 y[1] (numeric) = 1.9992968196739475613854614165788 absolute error = 4.0324708e-24 relative error = 2.0169445378588806464060466222202e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6084 y[1] (analytic) = 1.9992930651892519272239894789032 y[1] (numeric) = 1.9992930651892519272239853978556 absolute error = 4.0810476e-24 relative error = 2.0412453136847600631517331919470e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6085 y[1] (analytic) = 1.9992893007116256494974364436516 y[1] (numeric) = 1.9992893007116256494974323140273 absolute error = 4.1296243e-24 relative error = 2.0655461410862872050495880591598e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6086 y[1] (analytic) = 1.9992855262411063729820377499134 y[1] (numeric) = 1.9992855262411063729820335717125 absolute error = 4.1782009e-24 relative error = 2.0898470204280989551950882819783e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6087 y[1] (analytic) = 1.9992817417777318423829547089215 y[1] (numeric) = 1.9992817417777318423829504821443 absolute error = 4.2267772e-24 relative error = 2.1141478520389087552637300671493e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6088 y[1] (analytic) = 1.9992779473215399023339010894721 y[1] (numeric) = 1.9992779473215399023338968141187 absolute error = 4.2753534e-24 relative error = 2.1384487363189043380059677593058e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6089 y[1] (analytic) = 1.9992741428725684973967646715874 y[1] (numeric) = 1.999274142872568497396760347658 absolute error = 4.3239294e-24 relative error = 2.1627496236145752195084468557493e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.609 y[1] (analytic) = 1.9992703284308556720612278008973 y[1] (numeric) = 1.9992703284308556720612234283922 absolute error = 4.3725051e-24 relative error = 2.1870504642720316021137155309631e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6091 y[1] (analytic) = 1.999266503996439570744386943743 y[1] (numeric) = 1.9992665039964395707443825226623 absolute error = 4.4210807e-24 relative error = 2.2113513586920342662190306971320e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6092 y[1] (analytic) = 1.9992626695693584377903712430061 y[1] (numeric) = 1.99926266956935843779036677335 absolute error = 4.4696561e-24 relative error = 2.2356522572207906931043953752737e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6093 y[1] (analytic) = 1.9992588251496506174699600746678 y[1] (numeric) = 1.9992588251496506174699555564364 absolute error = 4.5182314e-24 relative error = 2.2599532102411985634897403225035e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6094 y[1] (analytic) = 1.9992549707373545539801996051012 y[1] (numeric) = 1.9992549707373545539801950382948 absolute error = 4.5668064e-24 relative error = 2.2842541180806442229753278425125e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6095 y[1] (analytic) = 1.9992511063325087914440183491016 y[1] (numeric) = 1.9992511063325087914440137337203 absolute error = 4.6153813e-24 relative error = 2.3085550811406604468763371427788e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6096 y[1] (analytic) = 1.9992472319351519739098417286569 y[1] (numeric) = 1.999247231935151973909837064701 absolute error = 4.6639559e-24 relative error = 2.3328559997482497986203322954632e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6097 y[1] (analytic) = 1.9992433475453228453512056324644 y[1] (numeric) = 1.999243347545322845351200919934 absolute error = 4.7125304e-24 relative error = 2.3571569743053337527662042500163e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6098 y[1] (analytic) = 1.9992394531630602496663689761952 y[1] (numeric) = 1.9992394531630602496663642150905 absolute error = 4.7611047e-24 relative error = 2.3814579551575500402362504581780e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6099 y[1] (analytic) = 1.9992355487884031306779252635122 y[1] (numeric) = 1.9992355487884031306779204538334 absolute error = 4.8096788e-24 relative error = 2.4057589426692667621289888972986e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.61 y[1] (analytic) = 1.9992316344213905321324131478443 y[1] (numeric) = 1.9992316344213905321324082895916 absolute error = 4.8582527e-24 relative error = 2.4300599372048530470319621282032e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=19.0MB, alloc=4.1MB, time=2.91 x[1] = 1.6101 y[1] (analytic) = 1.9992277100620615976999259949215 y[1] (numeric) = 1.9992277100620615976999210880951 absolute error = 4.9068264e-24 relative error = 2.4543609391286790631695392850588e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6102 y[1] (analytic) = 1.9992237757104555709737204460744 y[1] (numeric) = 1.9992237757104555709737154906744 absolute error = 4.9554000e-24 relative error = 2.4786619988245291722654988583123e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6103 y[1] (analytic) = 1.9992198313666117954698239823015 y[1] (numeric) = 1.9992198313666117954698189783282 absolute error = 5.0039733e-24 relative error = 2.5029630166180480602100882817970e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6104 y[1] (analytic) = 1.9992158770305697146266414891099 y[1] (numeric) = 1.9992158770305697146266364365635 absolute error = 5.0525464e-24 relative error = 2.5272640428929237937532601356931e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6105 y[1] (analytic) = 1.9992119127023688718045608221311 y[1] (numeric) = 1.9992119127023688718045557210117 absolute error = 5.1011194e-24 relative error = 2.5515651280332407701697572181399e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6106 y[1] (analytic) = 1.9992079383820489102855573735174 y[1] (numeric) = 1.9992079383820489102855522238253 absolute error = 5.1496921e-24 relative error = 2.5758661723640540766034530611893e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6107 y[1] (analytic) = 1.999203954069649573272797639123 y[1] (numeric) = 1.9992039540696495732727924408583 absolute error = 5.1982647e-24 relative error = 2.6001672762892602096006861477120e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6108 y[1] (analytic) = 1.9991999597652107038902417864722 y[1] (numeric) = 1.9991999597652107038902365396351 absolute error = 5.2468371e-24 relative error = 2.6244683901535277571666503414621e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6109 y[1] (analytic) = 1.9991959554687722451822452235201 y[1] (numeric) = 1.9991959554687722451822399281108 absolute error = 5.2954093e-24 relative error = 2.6487695143212363931585429666461e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.611 y[1] (analytic) = 1.9991919411803742401131591682098 y[1] (numeric) = 1.9991919411803742401131538242285 absolute error = 5.3439813e-24 relative error = 2.6730706491567669404133312635443e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6111 y[1] (analytic) = 1.9991879169000568315669302188288 y[1] (numeric) = 1.9991879169000568315669248262757 absolute error = 5.3925531e-24 relative error = 2.6973717950245013828966361839189e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6112 y[1] (analytic) = 1.9991838826278602623466989251701 y[1] (numeric) = 1.9991838826278602623466934840454 absolute error = 5.4411247e-24 relative error = 2.7216729522888228778517258379024e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6113 y[1] (analytic) = 1.9991798383638248751743973605012 y[1] (numeric) = 1.999179838363824875174391870805 absolute error = 5.4896962e-24 relative error = 2.7459741713346282206163684094625e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6114 y[1] (analytic) = 1.9991757841079911126903456943446 y[1] (numeric) = 1.9991757841079911126903401560772 absolute error = 5.5382674e-24 relative error = 2.7702753524853794858824001460796e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6115 y[1] (analytic) = 1.9991717198603995174528477660756 y[1] (numeric) = 1.9991717198603995174528421792372 absolute error = 5.5868384e-24 relative error = 2.7945765461258746869199040786007e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6116 y[1] (analytic) = 1.9991676456210907319377856593394 y[1] (numeric) = 1.9991676456210907319377800239302 absolute error = 5.6354092e-24 relative error = 2.8188777526205017955769248368162e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6117 y[1] (analytic) = 1.9991635613901054985382132772922 y[1] (numeric) = 1.9991635613901054985382075933125 absolute error = 5.6839797e-24 relative error = 2.8431789223127303034500699302846e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6118 y[1] (analytic) = 1.9991594671674846595639489186717 y[1] (numeric) = 1.9991594671674846595639431861216 absolute error = 5.7325501e-24 relative error = 2.8674801556086876496938799122248e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6119 y[1] (analytic) = 1.9991553629532691572411668546986 y[1] (numeric) = 1.9991553629532691572411610735783 absolute error = 5.7811203e-24 relative error = 2.8917814028519480214252824480614e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.612 y[1] (analytic) = 1.9991512487475000337119879068157 y[1] (numeric) = 1.9991512487475000337119820771254 absolute error = 5.8296903e-24 relative error = 2.9160826644069043994858839432962e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6121 y[1] (analytic) = 1.9991471245502184310340690252667 y[1] (numeric) = 1.9991471245502184310340631470065 absolute error = 5.8782602e-24 relative error = 2.9403839906592820299211531014056e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6122 y[1] (analytic) = 1.99914299036146559118019186852 y[1] (numeric) = 1.9991429903614655911801859416902 absolute error = 5.9268298e-24 relative error = 2.9646852819309179489475272310993e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=22.8MB, alloc=4.1MB, time=3.54 x[1] = 1.6123 y[1] (analytic) = 1.9991388461812828560378503835415 y[1] (numeric) = 1.9991388461812828560378444081423 absolute error = 5.9753992e-24 relative error = 2.9889865886074368115992342150579e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6124 y[1] (analytic) = 1.9991346920097116674088373869199 y[1] (numeric) = 1.9991346920097116674088313629514 absolute error = 6.0239685e-24 relative error = 3.0132879610748788653981234788911e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6125 y[1] (analytic) = 1.9991305278467935670088301468488 y[1] (numeric) = 1.9991305278467935670088240743113 absolute error = 6.0725375e-24 relative error = 3.0375892996544636936744363274780e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6126 y[1] (analytic) = 1.9991263536925701964669749659706 y[1] (numeric) = 1.9991263536925701964669688448643 absolute error = 6.1211063e-24 relative error = 3.0618906547321302745548739829727e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6127 y[1] (analytic) = 1.9991221695470832973254707650854 y[1] (numeric) = 1.9991221695470832973254645954105 absolute error = 6.1696749e-24 relative error = 3.0861920266722808224075831300763e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6128 y[1] (analytic) = 1.9991179754103747110391516677292 y[1] (numeric) = 1.9991179754103747110391454494859 absolute error = 6.2182433e-24 relative error = 3.1104934158393189192777658213862e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6129 y[1] (analytic) = 1.9991137712824863789750685856259 y[1] (numeric) = 1.9991137712824863789750623188144 absolute error = 6.2668115e-24 relative error = 3.1347948225976495270386477068072e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.613 y[1] (analytic) = 1.9991095571634603424120698050174 y[1] (numeric) = 1.9991095571634603424120634896379 absolute error = 6.3153795e-24 relative error = 3.1590962473116789995425689395970e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6131 y[1] (analytic) = 1.999105333053338742540380573875 y[1] (numeric) = 1.9991053330533387425403742099277 absolute error = 6.3639473e-24 relative error = 3.1833976903458150947721984827994e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6132 y[1] (analytic) = 1.999101098952163820461181689998 y[1] (numeric) = 1.9991010989521638204611752774831 absolute error = 6.4125149e-24 relative error = 3.2076991520644669869918725398287e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6133 y[1] (analytic) = 1.9990968548599779171861870900019 y[1] (numeric) = 1.9990968548599779171861806289197 absolute error = 6.4610822e-24 relative error = 3.2320005828094564499029424468858e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6134 y[1] (analytic) = 1.9990926007768234736372204392019 y[1] (numeric) = 1.9990926007768234736372139295525 absolute error = 6.5096494e-24 relative error = 3.2563020829902667363579778771473e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6135 y[1] (analytic) = 1.9990883367027430306457907223946 y[1] (numeric) = 1.9990883367027430306457841641782 absolute error = 6.5582164e-24 relative error = 3.2806036029488287113472707520205e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6136 y[1] (analytic) = 1.9990840626377792289526668355436 y[1] (numeric) = 1.9990840626377792289526602287605 absolute error = 6.6067831e-24 relative error = 3.3049050930266484101496090647146e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6137 y[1] (analytic) = 1.9990797785819748092074511783723 y[1] (numeric) = 1.9990797785819748092074445230226 absolute error = 6.6553497e-24 relative error = 3.3292066536338529221715039760379e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6138 y[1] (analytic) = 1.9990754845353726119681522478677 y[1] (numeric) = 1.9990754845353726119681455439516 absolute error = 6.7039161e-24 relative error = 3.3535082351120581982542831227828e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6139 y[1] (analytic) = 1.9990711804980155777007562327011 y[1] (numeric) = 1.9990711804980155777007494802189 absolute error = 6.7524822e-24 relative error = 3.3778097878024523904968170513320e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.614 y[1] (analytic) = 1.9990668664699467467787976085685 y[1] (numeric) = 1.9990668664699467467787908075204 absolute error = 6.8010481e-24 relative error = 3.4021113620924718148999919078293e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6141 y[1] (analytic) = 1.9990625424512092594829287344557 y[1] (numeric) = 1.9990625424512092594829218848419 absolute error = 6.8496138e-24 relative error = 3.4264129583465381876890509838890e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6142 y[1] (analytic) = 1.9990582084418463560004884498318 y[1] (numeric) = 1.9990582084418463560004815516525 absolute error = 6.8981793e-24 relative error = 3.4507145769290747628826029385004e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6143 y[1] (analytic) = 1.9990538644419013764250696727766 y[1] (numeric) = 1.999053864441901376425062726032 absolute error = 6.9467446e-24 relative error = 3.4750162182045063444453482671257e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6144 y[1] (analytic) = 1.9990495104514177607560859990448 y[1] (numeric) = 1.9990495104514177607560790037351 absolute error = 6.9953097e-24 relative error = 3.4993178825372592984409385807384e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=26.7MB, alloc=4.1MB, time=4.15 x[1] = 1.6145 y[1] (analytic) = 1.999045146470439048898337302072 y[1] (numeric) = 1.9990451464704390488983302581975 absolute error = 7.0438745e-24 relative error = 3.5236195202678788246864153248941e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6146 y[1] (analytic) = 1.9990407724990088806615743339278 y[1] (numeric) = 1.9990407724990088806615672414886 absolute error = 7.0924392e-24 relative error = 3.5479212318084504768869372151211e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6147 y[1] (analytic) = 1.9990363885371709957600623272178 y[1] (numeric) = 1.9990363885371709957600551862142 absolute error = 7.1410036e-24 relative error = 3.5722229174755299443517456509867e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6148 y[1] (analytic) = 1.9990319945849692338121435979418 y[1] (numeric) = 1.999031994584969233812136408374 absolute error = 7.1895678e-24 relative error = 3.5965246276574319521234871206492e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6149 y[1] (analytic) = 1.9990275906424475343397991493108 y[1] (numeric) = 1.9990275906424475343397919111789 absolute error = 7.2381319e-24 relative error = 3.6208264127429121670406240703531e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.615 y[1] (analytic) = 1.999023176709649936768209276527 y[1] (numeric) = 1.9990231767096499367682019898313 absolute error = 7.2866957e-24 relative error = 3.6451281730478721685838820479803e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6151 y[1] (analytic) = 1.9990187527866205804253131725332 y[1] (numeric) = 1.9990187527866205804253058372739 absolute error = 7.3352593e-24 relative error = 3.6694299589609607003086762436393e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6152 y[1] (analytic) = 1.999014318873403704541367534733 y[1] (numeric) = 1.9990143188734037045413601509104 absolute error = 7.3838226e-24 relative error = 3.6937317208219621323653460261898e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6153 y[1] (analytic) = 1.9990098749700436482485041726891 y[1] (numeric) = 1.9990098749700436482484967403034 absolute error = 7.4323857e-24 relative error = 3.7180335090197484490265681745575e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6154 y[1] (analytic) = 1.9990054210765848505802866168022 y[1] (numeric) = 1.9990054210765848505802791358536 absolute error = 7.4809486e-24 relative error = 3.7423353239187608027984198186302e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6155 y[1] (analytic) = 1.9990009571930718504712657279757 y[1] (numeric) = 1.9990009571930718504712581984643 absolute error = 7.5295114e-24 relative error = 3.7666372159084305944484962269869e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6156 y[1] (analytic) = 1.9989964833195492867565343082704 y[1] (numeric) = 1.9989964833195492867565267301965 absolute error = 7.5780739e-24 relative error = 3.7909390853033372341125074479818e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6157 y[1] (analytic) = 1.9989919994560618981712807125543 y[1] (numeric) = 1.9989919994560618981712730859182 absolute error = 7.6266361e-24 relative error = 3.8152409324675911213379815955108e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6158 y[1] (analytic) = 1.998987505602654523350341461151 y[1] (numeric) = 1.9989875056026545233503337859528 absolute error = 7.6751982e-24 relative error = 3.8395428578159532463609465230574e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6159 y[1] (analytic) = 1.9989830017593721008277528534914 y[1] (numeric) = 1.9989830017593721008277451297314 absolute error = 7.7237600e-24 relative error = 3.8638447616623349595278347661978e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.616 y[1] (analytic) = 1.9989784879262596690363015827741 y[1] (numeric) = 1.9989784879262596690362938104525 absolute error = 7.7723216e-24 relative error = 3.8881466943963997395854919690066e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6161 y[1] (analytic) = 1.9989739641033623663070743516376 y[1] (numeric) = 1.9989739641033623663070665307547 absolute error = 7.8208829e-24 relative error = 3.9124486063569360496143669784629e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6162 y[1] (analytic) = 1.9989694302907254308690064888502 y[1] (numeric) = 1.9989694302907254308689986194061 absolute error = 7.8694441e-24 relative error = 3.9367505979596128622058880677279e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6163 y[1] (analytic) = 1.9989648864883942008484295670206 y[1] (numeric) = 1.9989648864883942008484216490154 absolute error = 7.9180052e-24 relative error = 3.9610526695692266637079882140417e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6164 y[1] (analytic) = 1.998960332696414114268618021335 y[1] (numeric) = 1.9989603326964141142686100547691 absolute error = 7.9665659e-24 relative error = 3.9853546714725616458206619479562e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6165 y[1] (analytic) = 1.9989557689148307090493347693251 y[1] (numeric) = 1.9989557689148307090493267541987 absolute error = 8.0151264e-24 relative error = 4.0096567040856318309274979149167e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6166 y[1] (analytic) = 1.9989511951436896230063758316706 y[1] (numeric) = 1.9989511951436896230063677679839 absolute error = 8.0636867e-24 relative error = 4.0339587677728980198715896572141e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.1MB, time=4.78 x[1] = 1.6167 y[1] (analytic) = 1.9989466113830365938511139540415 y[1] (numeric) = 1.9989466113830365938511058417948 absolute error = 8.1122467e-24 relative error = 4.0582608128724742620341421956140e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6168 y[1] (analytic) = 1.9989420176329174591900412299851 y[1] (numeric) = 1.9989420176329174591900330691785 absolute error = 8.1608066e-24 relative error = 4.0825629398014072747150964812061e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6169 y[1] (analytic) = 1.9989374138933781565243107248611 y[1] (numeric) = 1.9989374138933781565243025154948 absolute error = 8.2093663e-24 relative error = 4.1068650988979295415551545620291e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.617 y[1] (analytic) = 1.9989328001644647232492771008306 y[1] (numeric) = 1.9989328001644647232492688429049 absolute error = 8.2579257e-24 relative error = 4.1311672404998150628649037833471e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6171 y[1] (analytic) = 1.9989281764462232966540362429031 y[1] (numeric) = 1.9989281764462232966540279364182 absolute error = 8.3064849e-24 relative error = 4.1554694149979967756953436638475e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6172 y[1] (analytic) = 1.9989235427387001139209638860456 y[1] (numeric) = 1.9989235427387001139209555310018 absolute error = 8.3550438e-24 relative error = 4.1797715727300200374851194830808e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6173 y[1] (analytic) = 1.9989188990419415121252532433596 y[1] (numeric) = 1.998918899041941512125244839757 absolute error = 8.4036026e-24 relative error = 4.2040738141140936739674469855834e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6174 y[1] (analytic) = 1.998914245355993928234451635329 y[1] (numeric) = 1.998914245355993928234443183168 absolute error = 8.4521610e-24 relative error = 4.2283759894335656312606391027911e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6175 y[1] (analytic) = 1.9989095816809038991079961201458 y[1] (numeric) = 1.9989095816809038991079876194265 absolute error = 8.5007193e-24 relative error = 4.2526782491340386438984540354844e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6176 y[1] (analytic) = 1.9989049080167180614967481251155 y[1] (numeric) = 1.9989049080167180614967395758381 absolute error = 8.5492774e-24 relative error = 4.2769805435529488310468876884399e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6177 y[1] (analytic) = 1.9989002243634831520425270791489 y[1] (numeric) = 1.9989002243634831520425184813137 absolute error = 8.5978352e-24 relative error = 4.3012828230272668985701558712246e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6178 y[1] (analytic) = 1.9988955307212460072776430463446 y[1] (numeric) = 1.9988955307212460072776343999519 absolute error = 8.6463927e-24 relative error = 4.3255850879211226342565175219797e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6179 y[1] (analytic) = 1.9988908270900535636244283606663 y[1] (numeric) = 1.9988908270900535636244196657162 absolute error = 8.6949501e-24 relative error = 4.3498874386541357292366313262865e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.618 y[1] (analytic) = 1.9988861134699528573947682617194 y[1] (numeric) = 1.9988861134699528573947595182122 absolute error = 8.7435072e-24 relative error = 4.3741897755354194189652412904852e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6181 y[1] (analytic) = 1.9988813898609910247896305316332 y[1] (numeric) = 1.998881389860991024789621739569 absolute error = 8.7920642e-24 relative error = 4.3984921989850682901458794655316e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6182 y[1] (analytic) = 1.9988766562632153018985941330508 y[1] (numeric) = 1.99887665626321530189858529243 absolute error = 8.8406208e-24 relative error = 4.4227945592836283515248077300173e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6183 y[1] (analytic) = 1.9988719126766730246993768482347 y[1] (numeric) = 1.9988719126766730246993679590574 absolute error = 8.8891773e-24 relative error = 4.4470970068795330679614256677439e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6184 y[1] (analytic) = 1.9988671591014116290573619192891 y[1] (numeric) = 1.9988671591014116290573529815556 absolute error = 8.9377335e-24 relative error = 4.4713994420809572660613165438791e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6185 y[1] (analytic) = 1.998862395537478650725123689507 y[1] (numeric) = 1.9988623955374786507251147032175 absolute error = 8.9862895e-24 relative error = 4.4957019152804944336914625484838e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6186 y[1] (analytic) = 1.9988576219849217253419522458447 y[1] (numeric) = 1.9988576219849217253419432109994 absolute error = 9.0348453e-24 relative error = 4.5200044268426407552321027965877e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6187 y[1] (analytic) = 1.9988528384437885884333770625292 y[1] (numeric) = 1.9988528384437885884333679791285 absolute error = 9.0834007e-24 relative error = 4.5443068770745035036016083910014e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6188 y[1] (analytic) = 1.9988480449141270754106896458037 y[1] (numeric) = 1.9988480449141270754106805138477 absolute error = 9.1319560e-24 relative error = 4.5686094164263096106911867180870e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=34.3MB, alloc=4.2MB, time=5.40 x[1] = 1.6189 y[1] (analytic) = 1.9988432413959851215704651798144 y[1] (numeric) = 1.9988432413959851215704559993033 absolute error = 9.1805111e-24 relative error = 4.5929119952339850272454770496138e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.619 y[1] (analytic) = 1.9988384278894107620940831736458 y[1] (numeric) = 1.9988384278894107620940739445798 absolute error = 9.2290660e-24 relative error = 4.6172146138620335977426307157373e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6191 y[1] (analytic) = 1.9988336043944521320472471095069 y[1] (numeric) = 1.9988336043944521320472378318863 absolute error = 9.2776206e-24 relative error = 4.6415172226457843939636675192160e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6192 y[1] (analytic) = 1.9988287709111574663795030920747 y[1] (numeric) = 1.9988287709111574663794937658998 absolute error = 9.3261749e-24 relative error = 4.6658198219493826039182617512835e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6193 y[1] (analytic) = 1.9988239274395750999237574989993 y[1] (numeric) = 1.9988239274395750999237481242703 absolute error = 9.3747290e-24 relative error = 4.6901224621663931832843964981882e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6194 y[1] (analytic) = 1.998819073979753467395793632575 y[1] (numeric) = 1.998819073979753467395784209292 absolute error = 9.4232830e-24 relative error = 4.7144251936908676724955817943209e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6195 y[1] (analytic) = 1.9988142105317411033937873725828 y[1] (numeric) = 1.9988142105317411033937779007462 absolute error = 9.4718366e-24 relative error = 4.7387278667986974214204592622538e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6196 y[1] (analytic) = 1.9988093370955866423978218303094 y[1] (numeric) = 1.9988093370955866423978123099194 absolute error = 9.5203900e-24 relative error = 4.7630305819132352287169500875783e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6197 y[1] (analytic) = 1.9988044536713388187694010037466 y[1] (numeric) = 1.9988044536713388187693914348034 absolute error = 9.5689432e-24 relative error = 4.7873333393989978722908642936812e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6198 y[1] (analytic) = 1.9987995602590464667509624339764 y[1] (numeric) = 1.9987995602590464667509528164803 absolute error = 9.6174961e-24 relative error = 4.8116360895904753309532297620722e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6199 y[1] (analytic) = 1.9987946568587585204653888627476 y[1] (numeric) = 1.9987946568587585204653791966988 absolute error = 9.6660488e-24 relative error = 4.8359388828819723839982249601409e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.62 y[1] (analytic) = 1.9987897434705240139155188912468 y[1] (numeric) = 1.9987897434705240139155091766455 absolute error = 9.7146013e-24 relative error = 4.8602417196380117493309843815870e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6201 y[1] (analytic) = 1.9987848200943920809836566400707 y[1] (numeric) = 1.9987848200943920809836468769172 absolute error = 9.7631535e-24 relative error = 4.8845445501927204326326282771084e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6202 y[1] (analytic) = 1.9987798867304119554310804104036 y[1] (numeric) = 1.9987798867304119554310705986981 absolute error = 9.8117055e-24 relative error = 4.9088474249407766721123506388696e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6203 y[1] (analytic) = 1.9987749433786329708975503464048 y[1] (numeric) = 1.9987749433786329708975404861475 absolute error = 9.8602573e-24 relative error = 4.9331503442467092350744939618005e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6204 y[1] (analytic) = 1.9987699900391045609008150988113 y[1] (numeric) = 1.9987699900391045609008051900025 absolute error = 9.9088088e-24 relative error = 4.9574532584442800079974291583758e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6205 y[1] (analytic) = 1.9987650267118762588361174897612 y[1] (numeric) = 1.9987650267118762588361075324011 absolute error = 9.9573601e-24 relative error = 4.9817562179285430528377990323197e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6206 y[1] (analytic) = 1.9987600533969976979756991788413 y[1] (numeric) = 1.9987600533969976979756891729301 absolute error = 1.00059112e-23 relative error = 5.0060592230640332957032344816929e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6207 y[1] (analytic) = 1.9987550700945186114683043303649 y[1] (numeric) = 1.998755070094518611468294275903 absolute error = 1.00544619e-23 relative error = 5.0303621741530027248993433154887e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6208 y[1] (analytic) = 1.9987500768044888323386822818856 y[1] (numeric) = 1.9987500768044888323386721788731 absolute error = 1.01030125e-23 relative error = 5.0546652216530438685868978435894e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6209 y[1] (analytic) = 1.9987450735269582934870892139491 y[1] (numeric) = 1.9987450735269582934870790623864 absolute error = 1.01515627e-23 relative error = 5.0789682158348943063578363055021e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.621 y[1] (analytic) = 1.9987400602619770276887888210922 y[1] (numeric) = 1.9987400602619770276887786209794 absolute error = 1.02001128e-23 relative error = 5.1032713071568997078397254741733e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=38.1MB, alloc=4.2MB, time=6.01 x[1] = 1.6211 y[1] (analytic) = 1.9987350370095951675935519840895 y[1] (numeric) = 1.9987350370095951675935417354269 absolute error = 1.02486626e-23 relative error = 5.1275743959206935462965694088657e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6212 y[1] (analytic) = 1.9987300037698629457251554434571 y[1] (numeric) = 1.9987300037698629457251451462449 absolute error = 1.02972122e-23 relative error = 5.1518775325222155014587039545178e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6213 y[1] (analytic) = 1.9987249605428306944808794742143 y[1] (numeric) = 1.9987249605428306944808691284528 absolute error = 1.03457615e-23 relative error = 5.1761806672941184732161605313315e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6214 y[1] (analytic) = 1.9987199073285488461310045619121 y[1] (numeric) = 1.9987199073285488461309941676015 absolute error = 1.03943106e-23 relative error = 5.2004838506325974325484799581628e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6215 y[1] (analytic) = 1.9987148441270679328183070799302 y[1] (numeric) = 1.9987148441270679328182966370708 absolute error = 1.04428594e-23 relative error = 5.2247870328700561310872546472036e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6216 y[1] (analytic) = 1.99870977093843858655755396805 y[1] (numeric) = 1.9987097709384385865575434766419 absolute error = 1.04914081e-23 relative error = 5.2490903144352224308226918508319e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6217 y[1] (analytic) = 1.998704687762711539234996412307 y[1] (numeric) = 1.9987046877627115392349858723505 absolute error = 1.05399565e-23 relative error = 5.2733935956282279202392354401159e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6218 y[1] (analytic) = 1.9986995945999376226078625261291 y[1] (numeric) = 1.9986995945999376226078519376245 absolute error = 1.05885046e-23 relative error = 5.2976968768132507713050348415529e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6219 y[1] (analytic) = 1.9986944914501677683038490327645 y[1] (numeric) = 1.9986944914501677683038383957121 absolute error = 1.06370524e-23 relative error = 5.3220001583544701258701958518211e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.622 y[1] (analytic) = 1.9986893783134530078206119490054 y[1] (numeric) = 1.9986893783134530078206012634054 absolute error = 1.06856000e-23 relative error = 5.3463034906488531356643253627623e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6221 y[1] (analytic) = 1.9986842551898444725252562702115 y[1] (numeric) = 1.9986842551898444725252455360641 absolute error = 1.07341474e-23 relative error = 5.3706068740609656580565700926056e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6222 y[1] (analytic) = 1.9986791220793933936538246566396 y[1] (numeric) = 1.9986791220793933936538138739451 absolute error = 1.07826945e-23 relative error = 5.3949102589223322892579463130255e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6223 y[1] (analytic) = 1.9986739789821511023107851210836 y[1] (numeric) = 1.9986739789821511023107742898423 absolute error = 1.08312413e-23 relative error = 5.4192136455971376760072686624226e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6224 y[1] (analytic) = 1.9986688258981690294685177178302 y[1] (numeric) = 1.9986688258981690294685068380424 absolute error = 1.08797878e-23 relative error = 5.4435170344495674956420497703110e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6225 y[1] (analytic) = 1.9986636628274987059668002329357 y[1] (numeric) = 1.9986636628274987059667893046015 absolute error = 1.09283342e-23 relative error = 5.4678205259106700016394311520034e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6226 y[1] (analytic) = 1.9986584897701917625122928758283 y[1] (numeric) = 1.998658489770191762512281898948 absolute error = 1.09768803e-23 relative error = 5.4921240202782894346117399755814e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6227 y[1] (analytic) = 1.9986533067262999296780219722422 y[1] (numeric) = 1.998653306726299929678010946816 absolute error = 1.10254262e-23 relative error = 5.5164275679503061574621040668642e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6228 y[1] (analytic) = 1.9986481136958750379028626584876 y[1] (numeric) = 1.9986481136958750379028515845158 absolute error = 1.10739718e-23 relative error = 5.5407311192574815806894014085076e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6229 y[1] (analytic) = 1.9986429106789690174910205770626 y[1] (numeric) = 1.9986429106789690174910094545455 absolute error = 1.11225171e-23 relative error = 5.5650346745640089728223704487891e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.623 y[1] (analytic) = 1.9986376976756338986115125736116 y[1] (numeric) = 1.9986376976756338986115014025493 absolute error = 1.11710623e-23 relative error = 5.5893383343022442503928199135553e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6231 y[1] (analytic) = 1.998632474685921811297646395235 y[1] (numeric) = 1.9986324746859218112976351756279 absolute error = 1.12196071e-23 relative error = 5.6136419487345328436545556616732e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6232 y[1] (analytic) = 1.9986272417098849854464993901573 y[1] (numeric) = 1.9986272417098849854464881220056 absolute error = 1.12681517e-23 relative error = 5.6379456182933649190712995182865e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=41.9MB, alloc=4.2MB, time=6.63 x[1] = 1.6233 y[1] (analytic) = 1.9986219987475757508183962087564 y[1] (numeric) = 1.9986219987475757508183848920604 absolute error = 1.13166960e-23 relative error = 5.6622492933088589637517321191075e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6234 y[1] (analytic) = 1.9986167457990465370363855059607 y[1] (numeric) = 1.9986167457990465370363741407206 absolute error = 1.13652401e-23 relative error = 5.6865530241798206781037096298936e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6235 y[1] (analytic) = 1.9986114828643498735857156450193 y[1] (numeric) = 1.9986114828643498735857042312353 absolute error = 1.14137840e-23 relative error = 5.7108568112708469054576963187079e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6236 y[1] (analytic) = 1.9986062099435383898133094026497 y[1] (numeric) = 1.9986062099435383898132979403221 absolute error = 1.14623276e-23 relative error = 5.7351606049116681181695053619234e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6237 y[1] (analytic) = 1.9986009270366648149272376755692 y[1] (numeric) = 1.9986009270366648149272261646984 absolute error = 1.15108708e-23 relative error = 5.7594643554314884520856035031286e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6238 y[1] (analytic) = 1.9985956341437819779961921884148 y[1] (numeric) = 1.9985956341437819779961806290008 absolute error = 1.15594140e-23 relative error = 5.7837682633346522955659285287924e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6239 y[1] (analytic) = 1.998590331264942807948957203056 y[1] (numeric) = 1.9985903312649428079489455950992 absolute error = 1.16079568e-23 relative error = 5.8080721288454952809503994985669e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.624 y[1] (analytic) = 1.9985850184002003335738802293083 y[1] (numeric) = 1.998585018400200333573868572809 absolute error = 1.16564993e-23 relative error = 5.8323760023632285520945208390671e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6241 y[1] (analytic) = 1.9985796955496076835183417370496 y[1] (numeric) = 1.998579695549607683518330032008 absolute error = 1.17050416e-23 relative error = 5.8566799342875960261408742281606e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6242 y[1] (analytic) = 1.9985743627132180862882238697471 y[1] (numeric) = 1.9985743627132180862882121161635 absolute error = 1.17535836e-23 relative error = 5.8809838749475442011189019966623e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6243 y[1] (analytic) = 1.9985690198910848702473781593986 y[1] (numeric) = 1.9985690198910848702473663572733 absolute error = 1.18021253e-23 relative error = 5.9052878247072874118976247253243e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6244 y[1] (analytic) = 1.998563667083261463617092242895 y[1] (numeric) = 1.9985636670832614636170803922282 absolute error = 1.18506668e-23 relative error = 5.9295918339669753964620389601684e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6245 y[1] (analytic) = 1.9985583042898013944755555798071 y[1] (numeric) = 1.9985583042898013944755436805991 absolute error = 1.18992080e-23 relative error = 5.9538958530551594451869377333821e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6246 y[1] (analytic) = 1.998552931510758290757324171605 y[1] (numeric) = 1.998552931510758290757312223856 absolute error = 1.19477490e-23 relative error = 5.9781999323722614083399489448751e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6247 y[1] (analytic) = 1.9985475487461858802527842823121 y[1] (numeric) = 1.9985475487461858802527722860224 absolute error = 1.19962897e-23 relative error = 6.0025040222465681624298619326110e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6248 y[1] (analytic) = 1.9985421559961379906076151606026 y[1] (numeric) = 1.9985421559961379906076031157724 absolute error = 1.20448302e-23 relative error = 6.0268081730787747215128205395513e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6249 y[1] (analytic) = 1.9985367532606685493222507633443 y[1] (numeric) = 1.9985367532606685493222386699739 absolute error = 1.20933704e-23 relative error = 6.0511123351969025939640781789704e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.625 y[1] (analytic) = 1.9985313405398315837513404805954 y[1] (numeric) = 1.998531340539831583751328338685 absolute error = 1.21419104e-23 relative error = 6.0754165590019210091570911689221e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6251 y[1] (analytic) = 1.998525917833681221103208862058 y[1] (numeric) = 1.9985259178336812211031966716079 absolute error = 1.21904501e-23 relative error = 6.0997207948215851530458312141810e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6252 y[1] (analytic) = 1.9985204851422716884393143449954 y[1] (numeric) = 1.998520485142271688439302106006 absolute error = 1.22389894e-23 relative error = 6.1240249929831090143685632006469e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6253 y[1] (analytic) = 1.9985150424656573126737069836184 y[1] (numeric) = 1.9985150424656573126736946960898 absolute error = 1.22875286e-23 relative error = 6.1483293039617689797123675171605e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6254 y[1] (analytic) = 1.9985095898038925205724851799444 y[1] (numeric) = 1.9985095898038925205724728438769 absolute error = 1.23360675e-23 relative error = 6.1726336280480393502770317167403e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=45.7MB, alloc=4.2MB, time=7.26 x[1] = 1.6255 y[1] (analytic) = 1.9985041271570318387532514161377 y[1] (numeric) = 1.9985041271570318387532390315316 absolute error = 1.23846061e-23 relative error = 6.1969379656061543057404116668845e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6256 y[1] (analytic) = 1.9984986545251298936845669883334 y[1] (numeric) = 1.998498654525129893684554555189 absolute error = 1.24331444e-23 relative error = 6.2212423170003494450628122856421e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6257 y[1] (analytic) = 1.9984931719082414116854057419527 y[1] (numeric) = 1.9984931719082414116853932602702 absolute error = 1.24816825e-23 relative error = 6.2455467326325609039604917158174e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6258 y[1] (analytic) = 1.9984876793064212189246068085129 y[1] (numeric) = 1.9984876793064212189245942782926 absolute error = 1.25302203e-23 relative error = 6.2698511628296030961969666560511e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6259 y[1] (analytic) = 1.9984821767197242414203263439404 y[1] (numeric) = 1.9984821767197242414203137651825 absolute error = 1.25787579e-23 relative error = 6.2941556579936911049383487975594e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.626 y[1] (analytic) = 1.9984766641482055050394882683887 y[1] (numeric) = 1.9984766641482055050394756410936 absolute error = 1.26272951e-23 relative error = 6.3184601184132563016401068679988e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6261 y[1] (analytic) = 1.9984711415919201354972340075703 y[1] (numeric) = 1.9984711415919201354972213317382 absolute error = 1.26758321e-23 relative error = 6.3427646445286296441863646838491e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6262 y[1] (analytic) = 1.9984656090509233583563712356054 y[1] (numeric) = 1.9984656090509233583563585112365 absolute error = 1.27243689e-23 relative error = 6.3670692367044718314086690443812e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6263 y[1] (analytic) = 1.9984600665252704990268216193943 y[1] (numeric) = 1.9984600665252704990268088464889 absolute error = 1.27729054e-23 relative error = 6.3913738452669185689045787009660e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6264 y[1] (analytic) = 1.9984545140150169827650675645187 y[1] (numeric) = 1.9984545140150169827650547430771 absolute error = 1.28214416e-23 relative error = 6.4156784705802195040507596020921e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6265 y[1] (analytic) = 1.9984489515202183346735979626774 y[1] (numeric) = 1.9984489515202183346735850926999 absolute error = 1.28699775e-23 relative error = 6.4399831130086258128414706988504e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6266 y[1] (analytic) = 1.9984433790409301797003529406619 y[1] (numeric) = 1.9984433790409301797003400221487 absolute error = 1.29185132e-23 relative error = 6.4642878229553360479629754876633e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6267 y[1] (analytic) = 1.9984377965772082426381676108771 y[1] (numeric) = 1.9984377965772082426381546438285 absolute error = 1.29670486e-23 relative error = 6.4885925507459382021159649923132e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6268 y[1] (analytic) = 1.9984322041291083481242148234139 y[1] (numeric) = 1.9984322041291083481242018078302 absolute error = 1.30155837e-23 relative error = 6.5128972967446888623671464091247e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6269 y[1] (analytic) = 1.9984266016966864206394469196777 y[1] (numeric) = 1.9984266016966864206394338555592 absolute error = 1.30641185e-23 relative error = 6.5372020613158461929946302316623e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.627 y[1] (analytic) = 1.9984209892799984845080364875794 y[1] (numeric) = 1.9984209892799984845080233749263 absolute error = 1.31126531e-23 relative error = 6.5615068948631764061948001801870e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6271 y[1] (analytic) = 1.998415366879100663896816118294 y[1] (numeric) = 1.9984153668791006638968029571066 absolute error = 1.31611874e-23 relative error = 6.5858117477117159638008806403249e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6272 y[1] (analytic) = 1.9984097344940491828147171645928 y[1] (numeric) = 1.9984097344940491828147039548714 absolute error = 1.32097214e-23 relative error = 6.6101166202257285869823023318947e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6273 y[1] (analytic) = 1.9984040921249003651122075007549 y[1] (numeric) = 1.9984040921249003651121942424997 absolute error = 1.32582552e-23 relative error = 6.6344215628094091815424497766059e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6274 y[1] (analytic) = 1.9983984397717106344807282840624 y[1] (numeric) = 1.9983984397717106344807149772737 absolute error = 1.33067887e-23 relative error = 6.6587265257873782436190978277863e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6275 y[1] (analytic) = 1.9983927774345365144521297178869 y[1] (numeric) = 1.998392777434536514452116362565 absolute error = 1.33553219e-23 relative error = 6.6830315095239051606508720386522e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6276 y[1] (analytic) = 1.9983871051134346283981058163712 y[1] (numeric) = 1.9983871051134346283980924125164 absolute error = 1.34038548e-23 relative error = 6.7073365143832609823359966398036e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=49.5MB, alloc=4.2MB, time=7.89 x[1] = 1.6277 y[1] (analytic) = 1.9983814228084616995296281707132 y[1] (numeric) = 1.9983814228084616995296147183257 absolute error = 1.34523875e-23 relative error = 6.7316415907702156364930326730729e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6278 y[1] (analytic) = 1.998375730519674550896378717056 y[1] (numeric) = 1.9983757305196745508963652161362 absolute error = 1.35009198e-23 relative error = 6.7559466389681916645946784750288e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6279 y[1] (analytic) = 1.9983700282471301053861815059925 y[1] (numeric) = 1.9983700282471301053861679565406 absolute error = 1.35494519e-23 relative error = 6.7802517594226026232960743939207e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.628 y[1] (analytic) = 1.9983643159908853857244334736866 y[1] (numeric) = 1.9983643159908853857244198757029 absolute error = 1.35979837e-23 relative error = 6.8045569024572298815418006145940e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6281 y[1] (analytic) = 1.9983585937509975144735342146206 y[1] (numeric) = 1.9983585937509975144735205681053 absolute error = 1.36465153e-23 relative error = 6.8288621184774225965664723442484e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6282 y[1] (analytic) = 1.9983528615275237140323147559709 y[1] (numeric) = 1.9983528615275237140323010609244 absolute error = 1.36950465e-23 relative error = 6.8531673077654686175679964284005e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6283 y[1] (analytic) = 1.998347119320521306635465333621 y[1] (numeric) = 1.9983471193205213066354515900435 absolute error = 1.37435775e-23 relative error = 6.8774725707679334889705361211281e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6284 y[1] (analytic) = 1.9983413671300477143529621698142 y[1] (numeric) = 1.998341367130047714352948377706 absolute error = 1.37921082e-23 relative error = 6.9017778578080346392690081143993e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6285 y[1] (analytic) = 1.998335604956160459089493252455 y[1] (numeric) = 1.9983356049561604590894794118164 absolute error = 1.38406386e-23 relative error = 6.9260831692500601301391065594999e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6286 y[1] (analytic) = 1.9983298327989171625838831160624 y[1] (numeric) = 1.9983298327989171625838692268937 absolute error = 1.38891687e-23 relative error = 6.9503885054582998070178532521757e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6287 y[1] (analytic) = 1.9983240506583755464085166243822 y[1] (numeric) = 1.9983240506583755464085026866836 absolute error = 1.39376986e-23 relative error = 6.9746939168389791843164676271783e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6288 y[1] (analytic) = 1.9983182585345934319687617546634 y[1] (numeric) = 1.9983182585345934319687477684353 absolute error = 1.39862281e-23 relative error = 6.9989993036726690118159617624492e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6289 y[1] (analytic) = 1.9983124564276287405023913836056 y[1] (numeric) = 1.9983124564276287405023773488481 absolute error = 1.40347575e-23 relative error = 7.0233048164499020703582849909980e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.629 y[1] (analytic) = 1.998306644337539493079004074981 y[1] (numeric) = 1.9983066443375394930789899916945 absolute error = 1.40832865e-23 relative error = 7.0476103054087394557519016052128e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6291 y[1] (analytic) = 1.9983008222643838105994438689394 y[1] (numeric) = 1.9983008222643838105994297371242 absolute error = 1.41318152e-23 relative error = 7.0719158209555597865921683949598e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6292 y[1] (analytic) = 1.9982949902082199137952190730002 y[1] (numeric) = 1.9982949902082199137952048926565 absolute error = 1.41803437e-23 relative error = 7.0962214134973262326048263233993e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6293 y[1] (analytic) = 1.9982891481691061232279200547376 y[1] (numeric) = 1.9982891481691061232279058258657 absolute error = 1.42288719e-23 relative error = 7.1205270333559732057602950967329e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6294 y[1] (analytic) = 1.9982832961471008592886360361653 y[1] (numeric) = 1.9982832961471008592886217587655 absolute error = 1.42773998e-23 relative error = 7.1448326808958067641109370267304e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6295 y[1] (analytic) = 1.9982774341422626421973708898262 y[1] (numeric) = 1.9982774341422626421973565638988 absolute error = 1.43259274e-23 relative error = 7.1691383564811348588388636705775e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6296 y[1] (analytic) = 1.9982715621546500920024579365925 y[1] (numeric) = 1.9982715621546500920024435621378 absolute error = 1.43744547e-23 relative error = 7.1934440604762673464062491931111e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6297 y[1] (analytic) = 1.9982656801843219285799737451834 y[1] (numeric) = 1.9982656801843219285799593222016 absolute error = 1.44229818e-23 relative error = 7.2177498432889116270451006992585e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6298 y[1] (analytic) = 1.9982597882313369716331509334042 y[1] (numeric) = 1.9982597882313369716331364618957 absolute error = 1.44715085e-23 relative error = 7.2420556051967377066063947505492e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6299 y[1] (analytic) = 1.9982538862957541406917899711151 y[1] (numeric) = 1.9982538862957541406917754510801 absolute error = 1.45200350e-23 relative error = 7.2663614466510005397731434612755e-22 % h = 0.0001 memory used=53.4MB, alloc=4.2MB, time=8.55 TOP MAIN SOLVE Loop NO POLE x[1] = 1.63 y[1] (analytic) = 1.9982479743776324551116699849331 y[1] (numeric) = 1.9982479743776324551116554163719 absolute error = 1.45685612e-23 relative error = 7.2906673179726228519181694414123e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6301 y[1] (analytic) = 1.9982420524770310340739585646751 y[1] (numeric) = 1.998242052477031034073943947588 absolute error = 1.46170871e-23 relative error = 7.3149732195259249607996109303131e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6302 y[1] (analytic) = 1.9982361205940090965846205715465 y[1] (numeric) = 1.9982361205940090965846059059338 absolute error = 1.46656127e-23 relative error = 7.3392791516752291623729915698222e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6303 y[1] (analytic) = 1.9982301787286259614738259480823 y[1] (numeric) = 1.9982301787286259614738112339443 absolute error = 1.47141380e-23 relative error = 7.3635851147848597429427514947932e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6304 y[1] (analytic) = 1.9982242268809410473953565298455 y[1] (numeric) = 1.9982242268809410473953417671825 absolute error = 1.47626630e-23 relative error = 7.3878911092191429913139516851058e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6305 y[1] (analytic) = 1.9982182650510138728260118588901 y[1] (numeric) = 1.9982182650510138728259970477024 absolute error = 1.48111877e-23 relative error = 7.4121971353424072109441523036749e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6306 y[1] (analytic) = 1.9982122932389040560650139989936 y[1] (numeric) = 1.9982122932389040560649991392814 absolute error = 1.48597122e-23 relative error = 7.4365032435637153855563812636238e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6307 y[1] (analytic) = 1.998206311444671315233411352665 y[1] (numeric) = 1.9982063114446713152333964444286 absolute error = 1.49082364e-23 relative error = 7.4608093842029668569196551248854e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6308 y[1] (analytic) = 1.998200319668375468273481479935 y[1] (numeric) = 1.9982003196683754682734665231748 absolute error = 1.49567602e-23 relative error = 7.4851155075794642676866060276104e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6309 y[1] (analytic) = 1.998194317910076432948132918934 y[1] (numeric) = 1.9981943179100764329481179136502 absolute error = 1.50052838e-23 relative error = 7.5094217141474596000892470338988e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.631 y[1] (analytic) = 1.9981883061698342268403060082628 y[1] (numeric) = 1.9981883061698342268402909544557 absolute error = 1.50538071e-23 relative error = 7.5337279542264096993813341911294e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6311 y[1] (analytic) = 1.9981822844477089673523727111644 y[1] (numeric) = 1.9981822844477089673523576088343 absolute error = 1.51023301e-23 relative error = 7.5580342281806559648625886908982e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6312 y[1] (analytic) = 1.9981762527437608717055354415005 y[1] (numeric) = 1.9981762527437608717055202906477 absolute error = 1.51508528e-23 relative error = 7.5823405363745418955654035866252e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6313 y[1] (analytic) = 1.9981702110580502569392248915398 y[1] (numeric) = 1.9981702110580502569392096921647 absolute error = 1.51993751e-23 relative error = 7.6066468291266264889399149554395e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6314 y[1] (analytic) = 1.9981641593906375399104968615646 y[1] (numeric) = 1.9981641593906375399104816136674 absolute error = 1.52478972e-23 relative error = 7.6309532068926791375239190440203e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6315 y[1] (analytic) = 1.9981580977415832372934280913005 y[1] (numeric) = 1.9981580977415832372934127948814 absolute error = 1.52964191e-23 relative error = 7.6552596700375044205382349818272e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6316 y[1] (analytic) = 1.9981520261109479655785110931759 y[1] (numeric) = 1.9981520261109479655784957482353 absolute error = 1.53449406e-23 relative error = 7.6795661188334264224747076246371e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6317 y[1] (analytic) = 1.9981459444987924410720479874181 y[1] (numeric) = 1.9981459444987924410720325939563 absolute error = 1.53934618e-23 relative error = 7.7038726036907375061573695108390e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6318 y[1] (analytic) = 1.9981398529051774798955433389905 y[1] (numeric) = 1.9981398529051774798955278970078 absolute error = 1.54419827e-23 relative error = 7.7281791249737940242407396047355e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6319 y[1] (analytic) = 1.998133751330163997985095996378 y[1] (numeric) = 1.9981337513301639979850805058747 absolute error = 1.54905033e-23 relative error = 7.7524856830469545141890752990793e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.632 y[1] (analytic) = 1.9981276397738130110907899322266 y[1] (numeric) = 1.998127639773813011090774393203 absolute error = 1.55390236e-23 relative error = 7.7767922782745797104309726960476e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6321 y[1] (analytic) = 1.9981215182361856347760840858432 y[1] (numeric) = 1.9981215182361856347760684982996 absolute error = 1.55875436e-23 relative error = 7.8010989110210325565141524697663e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.2MB, time=9.25 NO POLE x[1] = 1.6322 y[1] (analytic) = 1.9981153867173430844172012075613 y[1] (numeric) = 1.9981153867173430844171855714979 absolute error = 1.56360634e-23 relative error = 7.8254056316978379882923017850906e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6323 y[1] (analytic) = 1.9981092452173466752025157049793 y[1] (numeric) = 1.9981092452173466752025000203965 absolute error = 1.56845828e-23 relative error = 7.8497123405751976896938000835590e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6324 y[1] (analytic) = 1.9981030937362578221319404910776 y[1] (numeric) = 1.9981030937362578221319247579756 absolute error = 1.57331020e-23 relative error = 7.8740191381119551762529966405159e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6325 y[1] (analytic) = 1.9980969322741380400163128342194 y[1] (numeric) = 1.9980969322741380400162970525986 absolute error = 1.57816208e-23 relative error = 7.8983259245777013242650016990478e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6326 y[1] (analytic) = 1.9980907608310489434767792100434 y[1] (numeric) = 1.9980907608310489434767633799041 absolute error = 1.58301393e-23 relative error = 7.9226327503841239039805901516825e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6327 y[1] (analytic) = 1.9980845794070522469441791552526 y[1] (numeric) = 1.998084579407052246944163276595 absolute error = 1.58786576e-23 relative error = 7.9469396659435307881668313015255e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6328 y[1] (analytic) = 1.9980783880022097646584281233062 y[1] (numeric) = 1.9980783880022097646584121961307 absolute error = 1.59271755e-23 relative error = 7.9712465715245929685930963629658e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6329 y[1] (analytic) = 1.9980721866165834106678993420216 y[1] (numeric) = 1.9980721866165834106678833663284 absolute error = 1.59756932e-23 relative error = 7.9955535675877099222674827700881e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.633 y[1] (analytic) = 1.9980659752502351988288046730904 y[1] (numeric) = 1.9980659752502351988287886488799 absolute error = 1.60242105e-23 relative error = 8.0198605544009369358237501989682e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6331 y[1] (analytic) = 1.9980597539032272428045744735174 y[1] (numeric) = 1.9980597539032272428045584007899 absolute error = 1.60727275e-23 relative error = 8.0441675823767462143119960108803e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6332 y[1] (analytic) = 1.9980535225756217560652364589865 y[1] (numeric) = 1.9980535225756217560652203377423 absolute error = 1.61212442e-23 relative error = 8.0684746518795258038724650042766e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6333 y[1] (analytic) = 1.998047281267481051886793569161 y[1] (numeric) = 1.9980472812674810518867773994004 absolute error = 1.61697606e-23 relative error = 8.0927817632736661056367162940759e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6334 y[1] (analytic) = 1.9980410299788675433506008349243 y[1] (numeric) = 1.9980410299788675433505846166475 absolute error = 1.62182768e-23 relative error = 8.1170889669725821549890115838081e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6335 y[1] (analytic) = 1.9980347687098437433427412475664 y[1] (numeric) = 1.9980347687098437433427249807738 absolute error = 1.62667926e-23 relative error = 8.1413961632427814046164349589006e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6336 y[1] (analytic) = 1.9980284974604722645534006299242 y[1] (numeric) = 1.9980284974604722645533843146161 absolute error = 1.63153081e-23 relative error = 8.1657034024975270723481353068400e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6337 y[1] (analytic) = 1.9980222162308158194762415094796 y[1] (numeric) = 1.9980222162308158194762251456563 absolute error = 1.63638233e-23 relative error = 8.1900106851012191008586803241082e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6338 y[1] (analytic) = 1.9980159250209372204077759934238 y[1] (numeric) = 1.9980159250209372204077595810856 absolute error = 1.64123382e-23 relative error = 8.2143180114182598486022435952944e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6339 y[1] (analytic) = 1.9980096238308993794467376456924 y[1] (numeric) = 1.9980096238308993794467211848396 absolute error = 1.64608528e-23 relative error = 8.2386253818130541019708548950098e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.634 y[1] (analytic) = 1.9980033126607653084934523659789 y[1] (numeric) = 1.9980033126607653084934358566118 absolute error = 1.65093671e-23 relative error = 8.2629327966500090874528498472753e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6341 y[1] (analytic) = 1.9979969915105981192492082707316 y[1] (numeric) = 1.9979969915105981192491917128506 absolute error = 1.65578810e-23 relative error = 8.2872402062434090707425367045490e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6342 y[1] (analytic) = 1.9979906603804610232156245761418 y[1] (numeric) = 1.997990660380461023215607969747 absolute error = 1.66063948e-23 relative error = 8.3115477611080424341439617134681e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6343 y[1] (analytic) = 1.9979843192704173316940194831273 y[1] (numeric) = 1.9979843192704173316940028282192 absolute error = 1.66549081e-23 relative error = 8.3358552614075047016535815540917e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=9.88 NO POLE x[1] = 1.6344 y[1] (analytic) = 1.9979779681805304557847770643206 y[1] (numeric) = 1.9979779681805304557847603608994 absolute error = 1.67034212e-23 relative error = 8.3601628576570650096739233688911e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6345 y[1] (analytic) = 1.9979716071108639063867131530651 y[1] (numeric) = 1.9979716071108639063866964011311 absolute error = 1.67519340e-23 relative error = 8.3844705001708589582408915006228e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6346 y[1] (analytic) = 1.9979652360614812941964402344274 y[1] (numeric) = 1.997965236061481294196423433981 absolute error = 1.68004464e-23 relative error = 8.4087781392623877652831262003679e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6347 y[1] (analytic) = 1.9979588550324463297077313382323 y[1] (numeric) = 1.9979588550324463297077144892737 absolute error = 1.68489586e-23 relative error = 8.4330858753977580360298421585250e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6348 y[1] (analytic) = 1.9979524640238228232108829341248 y[1] (numeric) = 1.9979524640238228232108660366544 absolute error = 1.68974704e-23 relative error = 8.4573936088393947931444718712464e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6349 y[1] (analytic) = 1.9979460630356746847920768286682 y[1] (numeric) = 1.9979460630356746847920598826863 absolute error = 1.69459819e-23 relative error = 8.4817013900026479225386054065345e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.635 y[1] (analytic) = 1.9979396520680659243327410644828 y[1] (numeric) = 1.9979396520680659243327240699896 absolute error = 1.69944932e-23 relative error = 8.5060092693035107832686395491410e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6351 y[1] (analytic) = 1.9979332311210606515089098214317 y[1] (numeric) = 1.9979332311210606515088927784277 absolute error = 1.70430040e-23 relative error = 8.5303170969517320444756299528974e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6352 y[1] (analytic) = 1.9979268001947230757905823198617 y[1] (numeric) = 1.9979268001947230757905652283471 absolute error = 1.70915146e-23 relative error = 8.5546250234664338569338644156006e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6353 y[1] (analytic) = 1.9979203592891175064410807259033 y[1] (numeric) = 1.9979203592891175064410635858783 absolute error = 1.71400250e-23 relative error = 8.5789330492125388411874597096917e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6354 y[1] (analytic) = 1.9979139084043083525164070588379 y[1] (numeric) = 1.997913908404308352516389870303 absolute error = 1.71885349e-23 relative error = 8.6032410243983535025894296492237e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6355 y[1] (analytic) = 1.9979074475403601228645991005392 y[1] (numeric) = 1.9979074475403601228645818634946 absolute error = 1.72370446e-23 relative error = 8.6275490995444577811565639845310e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6356 y[1] (analytic) = 1.9979009766973374261250853069921 y[1] (numeric) = 1.9979009766973374261250680214382 absolute error = 1.72855539e-23 relative error = 8.6518571749107229959358628570186e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6357 y[1] (analytic) = 1.9978944958753049707280387219 y[1] (numeric) = 1.9978944958753049707280213878371 absolute error = 1.73340629e-23 relative error = 8.6761653009138049530748702955371e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6358 y[1] (analytic) = 1.9978880050743275648937298923831 y[1] (numeric) = 1.9978880050743275648937125098116 absolute error = 1.73825715e-23 relative error = 8.7004734278652996851463500197074e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6359 y[1] (analytic) = 1.9978815042944701166318787867765 y[1] (numeric) = 1.9978815042944701166318613556966 absolute error = 1.74310799e-23 relative error = 8.7247816562352100978761256460194e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.636 y[1] (analytic) = 1.9978749935357976337410057145331 y[1] (numeric) = 1.9978749935357976337409882349451 absolute error = 1.74795880e-23 relative error = 8.7490899363353001909886259953479e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6361 y[1] (analytic) = 1.9978684727983752238077812482394 y[1] (numeric) = 1.9978684727983752238077637201436 absolute error = 1.75280958e-23 relative error = 8.7733982685300297355148097171920e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6362 y[1] (analytic) = 1.9978619420822680942063751477491 y[1] (numeric) = 1.9978619420822680942063575711459 absolute error = 1.75766032e-23 relative error = 8.7977066031303525598535193786071e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6363 y[1] (analytic) = 1.9978554013875415520978042864422 y[1] (numeric) = 1.9978554013875415520977866613318 absolute error = 1.76251104e-23 relative error = 8.8220150406075872948188214301909e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6364 y[1] (analytic) = 1.9978488507142610044292795796149 y[1] (numeric) = 1.9978488507142610044292619059977 absolute error = 1.76736172e-23 relative error = 8.8463234812190202000507603279699e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6365 y[1] (analytic) = 1.9978422900624919579335519150085 y[1] (numeric) = 1.9978422900624919579335341928848 absolute error = 1.77221237e-23 relative error = 8.8706319753826298469987679403364e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=10.52 NO POLE x[1] = 1.6366 y[1] (analytic) = 1.9978357194323000191282570854822 y[1] (numeric) = 1.9978357194323000191282393148524 absolute error = 1.77706298e-23 relative error = 8.8949404734087232841193889920898e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6367 y[1] (analytic) = 1.9978291388237508943152597238375 y[1] (numeric) = 1.9978291388237508943152419047018 absolute error = 1.78191357e-23 relative error = 8.9192490757699423428941680878855e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6368 y[1] (analytic) = 1.9978225482369103895799962397996 y[1] (numeric) = 1.9978225482369103895799783721584 absolute error = 1.78676412e-23 relative error = 8.9435576827222686172000792417360e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6369 y[1] (analytic) = 1.9978159476718444107908167591644 y[1] (numeric) = 1.9978159476718444107907988430179 absolute error = 1.79161465e-23 relative error = 8.9678663947390090014011707929179e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.637 y[1] (analytic) = 1.9978093371286189635983260651146 y[1] (numeric) = 1.9978093371286189635983081004632 absolute error = 1.79646514e-23 relative error = 8.9921751120754901930815177294467e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6371 y[1] (analytic) = 1.997802716607300153434723541715 y[1] (numeric) = 1.9978027166073001534347055285591 absolute error = 1.80131559e-23 relative error = 9.0164838350957012031135291053924e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6372 y[1] (analytic) = 1.9977960861079541855131421195906 y[1] (numeric) = 1.9977960861079541855131240579305 absolute error = 1.80616601e-23 relative error = 9.0407926142187909947375777978366e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6373 y[1] (analytic) = 1.9977894456306473648269862237962 y[1] (numeric) = 1.9977894456306473648269681136321 absolute error = 1.81101641e-23 relative error = 9.0651014998645753818272100845788e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6374 y[1] (analytic) = 1.9977827951754460961492687238823 y[1] (numeric) = 1.9977827951754460961492505652146 absolute error = 1.81586677e-23 relative error = 9.0894103922870646357601859857127e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6375 y[1] (analytic) = 1.9977761347424168840319468861662 y[1] (numeric) = 1.9977761347424168840319286789952 absolute error = 1.82071710e-23 relative error = 9.1137193419059139106927211990033e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6376 y[1] (analytic) = 1.9977694643316263328052573282124 y[1] (numeric) = 1.9977694643316263328052390725385 absolute error = 1.82556739e-23 relative error = 9.1380282990297969566532953190410e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6377 y[1] (analytic) = 1.9977627839431411465770499755314 y[1] (numeric) = 1.9977627839431411465770316713549 absolute error = 1.83041765e-23 relative error = 9.1623373140787069514019071946827e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6378 y[1] (analytic) = 1.9977560935770281292321210205012 y[1] (numeric) = 1.9977560935770281292321026678224 absolute error = 1.83526788e-23 relative error = 9.1866463874171483361115495387290e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6379 y[1] (analytic) = 1.9977493932333541844315448835201 y[1] (numeric) = 1.9977493932333541844315264823393 absolute error = 1.84011808e-23 relative error = 9.2109555194096284663133066264272e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.638 y[1] (analytic) = 1.9977426829121863156120051763966 y[1] (numeric) = 1.9977426829121863156119867267142 absolute error = 1.84496824e-23 relative error = 9.2352646603641609313929949384694e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6381 y[1] (analytic) = 1.9977359626135916259851246679832 y[1] (numeric) = 1.9977359626135916259851061697994 absolute error = 1.84981838e-23 relative error = 9.2595739107580839495187040203198e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6382 y[1] (analytic) = 1.9977292323376373185367942520603 y[1] (numeric) = 1.9977292323376373185367757053755 absolute error = 1.85466848e-23 relative error = 9.2838831708427514167684674941944e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6383 y[1] (analytic) = 1.9977224920843906960265009174783 y[1] (numeric) = 1.9977224920843906960264823222928 absolute error = 1.85951855e-23 relative error = 9.3081924910391784070340007614456e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6384 y[1] (analytic) = 1.997715741853919160986654720563 y[1] (numeric) = 1.9977157418539191609866360768772 absolute error = 1.86436858e-23 relative error = 9.3325018216547145255467951910716e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6385 y[1] (analytic) = 1.9977089816462902157219147597925 y[1] (numeric) = 1.9977089816462902157218960676066 absolute error = 1.86921859e-23 relative error = 9.3568112631680582259232852257782e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6386 y[1] (analytic) = 1.9977022114615714623085141527505 y[1] (numeric) = 1.9977022114615714623084954120649 absolute error = 1.87406856e-23 relative error = 9.3811207158292234543169408738128e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6387 y[1] (analytic) = 1.997695431299830602593584015365 y[1] (numeric) = 1.9976954312998306025935652261801 absolute error = 1.87891849e-23 relative error = 9.4054301800022308813490246907519e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=11.12 NO POLE x[1] = 1.6388 y[1] (analytic) = 1.9976886411611354381944764434376 y[1] (numeric) = 1.9976886411611354381944576057537 absolute error = 1.88376839e-23 relative error = 9.4297397061089535225506046504250e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6389 y[1] (analytic) = 1.9976818410455538704980864964702 y[1] (numeric) = 1.9976818410455538704980676102876 absolute error = 1.88861826e-23 relative error = 9.4540492945139262857999751914580e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.639 y[1] (analytic) = 1.9976750309531539006601731837968 y[1] (numeric) = 1.9976750309531539006601542491159 absolute error = 1.89346809e-23 relative error = 9.4783588955234952538174988291093e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6391 y[1] (analytic) = 1.9976682108840036296046794530267 y[1] (numeric) = 1.9976682108840036296046604698478 absolute error = 1.89831789e-23 relative error = 9.5026685595600515174732862111461e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6392 y[1] (analytic) = 1.9976613808381712580230511808052 y[1] (numeric) = 1.9976613808381712580230321491286 absolute error = 1.90316766e-23 relative error = 9.5269782869881384121451348761588e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6393 y[1] (analytic) = 1.9976545408157250863735551659 y[1] (numeric) = 1.997654540815725086373536085726 absolute error = 1.90801740e-23 relative error = 9.5512880781723023578712418082594e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6394 y[1] (analytic) = 1.997647690816733514880596124619 y[1] (numeric) = 1.997647690816733514880576995948 absolute error = 1.91286710e-23 relative error = 9.5755978834182158935105538127369e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6395 y[1] (analytic) = 1.997640830841265043534032688567 y[1] (numeric) = 1.9976408308412650435340135113992 absolute error = 1.91771678e-23 relative error = 9.5999078032080136968423449000283e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6396 y[1] (analytic) = 1.9976339608893882720884924047472 y[1] (numeric) = 1.9976339608893882720884731790831 absolute error = 1.92256641e-23 relative error = 9.6242176877291041150036848192404e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6397 y[1] (analytic) = 1.9976270809611719000626857380162 y[1] (numeric) = 1.9976270809611719000626664638561 absolute error = 1.92741601e-23 relative error = 9.6485276374637984772871543975288e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6398 y[1] (analytic) = 1.997620191056684726738719075897 y[1] (numeric) = 1.9976201910566847267386997532412 absolute error = 1.93226558e-23 relative error = 9.6728376527766573024513258684087e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6399 y[1] (analytic) = 1.9976132911759956511614067357584 y[1] (numeric) = 1.9976132911759956511613873646073 absolute error = 1.93711511e-23 relative error = 9.6971476839725052564995832906902e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.64 y[1] (analytic) = 1.9976063813191736721375819743679 y[1] (numeric) = 1.9976063813191736721375625547218 absolute error = 1.94196461e-23 relative error = 9.7214577814753018759785674551396e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6401 y[1] (analytic) = 1.9975994614862878882354069998236 y[1] (numeric) = 1.9975994614862878882353875316828 absolute error = 1.94681408e-23 relative error = 9.7457679456496164355331327567334e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6402 y[1] (analytic) = 1.9975925316774074977836819858732 y[1] (numeric) = 1.997592531677407497783662469238 absolute error = 1.95166352e-23 relative error = 9.7700781768600214039658397749561e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6403 y[1] (analytic) = 1.9975855918926017988711530886266 y[1] (numeric) = 1.9975855918926017988711335234974 absolute error = 1.95651292e-23 relative error = 9.7943884254106592985710242308836e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6404 y[1] (analytic) = 1.997578642131940189345819465669 y[1] (numeric) = 1.9975786421319401893457998520462 absolute error = 1.96136228e-23 relative error = 9.8186986916655865183665157823880e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6405 y[1] (analytic) = 1.9975716823954921668142392975817 y[1] (numeric) = 1.9975716823954921668142196354656 absolute error = 1.96621161e-23 relative error = 9.8430090260496429245613983132034e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6406 y[1] (analytic) = 1.9975647126833273286408348118768 y[1] (numeric) = 1.9975647126833273286408151012677 absolute error = 1.97106091e-23 relative error = 9.8673194289274123770090025521533e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6407 y[1] (analytic) = 1.9975577329955153719471963093536 y[1] (numeric) = 1.9975577329955153719471765502518 absolute error = 1.97591018e-23 relative error = 9.8916299006634819905555476804713e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6408 y[1] (analytic) = 1.9975507433321260936113851928833 y[1] (numeric) = 1.9975507433321260936113653852892 absolute error = 1.98075941e-23 relative error = 9.9159403915611356528465673705607e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6409 y[1] (analytic) = 1.9975437436932293902672359986293 y[1] (numeric) = 1.9975437436932293902672161425432 absolute error = 1.98560861e-23 relative error = 9.9402509520459226776541698393169e-22 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=11.77 NO POLE x[1] = 1.641 y[1] (analytic) = 1.9975367340788952583036574297089 y[1] (numeric) = 1.9975367340788952583036375251311 absolute error = 1.99045778e-23 relative error = 9.9645615824824392641518984528836e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6411 y[1] (analytic) = 1.9975297144891937938639323923051 y[1] (numeric) = 1.997529714489193793863912439236 absolute error = 1.99530691e-23 relative error = 9.9888722331734514042036365902294e-22 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6412 y[1] (analytic) = 1.9975226849241951928450170342344 y[1] (numeric) = 1.9975226849241951928449970326743 absolute error = 2.00015601e-23 relative error = 1.0013182954545043078134979755884e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6413 y[1] (analytic) = 1.9975156453839697508968387859775 y[1] (numeric) = 1.9975156453839697508968187359268 absolute error = 2.00500507e-23 relative error = 1.0037493696899633567362051005445e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6414 y[1] (analytic) = 1.9975085958685878634215934041811 y[1] (numeric) = 1.9975085958685878634215733056401 absolute error = 2.00985410e-23 relative error = 1.0061804510663664362313743457977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6415 y[1] (analytic) = 1.9975015363781200255730410176362 y[1] (numeric) = 1.9975015363781200255730208706052 absolute error = 2.01470310e-23 relative error = 1.0086115396201746794779712633111e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6416 y[1] (analytic) = 1.997494466912636832255801175741 y[1] (numeric) = 1.9974944669126368322557809802204 absolute error = 2.01955206e-23 relative error = 1.0110426303815778664254802151969e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6417 y[1] (analytic) = 1.9974873874722089781246468994556 y[1] (numeric) = 1.9974873874722089781246266554458 absolute error = 2.02440098e-23 relative error = 1.0134737233869845750987217412607e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6418 y[1] (analytic) = 1.9974802980569072575837977347547 y[1] (numeric) = 1.997480298056907257583777442256 absolute error = 2.02924987e-23 relative error = 1.0159048236791107726451628925851e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6419 y[1] (analytic) = 1.997473198666802564786211808586 y[1] (numeric) = 1.9974731986668025647861914675987 absolute error = 2.03409873e-23 relative error = 1.0183359312944187945989781308598e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.642 y[1] (analytic) = 1.997466089301965893632876887341 y[1] (numeric) = 1.9974660893019658936328564978655 absolute error = 2.03894755e-23 relative error = 1.0207670412630285050080877151882e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6421 y[1] (analytic) = 1.9974589699624683377721004378463 y[1] (numeric) = 1.9974589699624683377720799998829 absolute error = 2.04379634e-23 relative error = 1.0231981586277100488736567188342e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6422 y[1] (analytic) = 1.9974518406483810905987986908804 y[1] (numeric) = 1.9974518406483810905987782044295 absolute error = 2.04864509e-23 relative error = 1.0256292784185481888308870464995e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6423 y[1] (analytic) = 1.9974447013597754452537847072256 y[1] (numeric) = 1.9974447013597754452537641722876 absolute error = 2.05349380e-23 relative error = 1.0280604006719528760563488797195e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6424 y[1] (analytic) = 1.9974375520967227946230554462605 y[1] (numeric) = 1.9974375520967227946230348628356 absolute error = 2.05834249e-23 relative error = 1.0304915354371629330703171971810e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6425 y[1] (analytic) = 1.9974303928592946313370778371002 y[1] (numeric) = 1.9974303928592946313370572051888 absolute error = 2.06319114e-23 relative error = 1.0329226727378318036176330094371e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6426 y[1] (analytic) = 1.9974232236475625477700738522925 y[1] (numeric) = 1.997423223647562547770053171895 absolute error = 2.06803975e-23 relative error = 1.0353538126103701795513614437206e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6427 y[1] (analytic) = 1.9974160444615982360393045840766 y[1] (numeric) = 1.9974160444615982360392838551933 absolute error = 2.07288833e-23 relative error = 1.0377849600976571974660684880828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6428 y[1] (analytic) = 1.9974088553014734880043533232103 y[1] (numeric) = 1.9974088553014734880043325458416 absolute error = 2.07773687e-23 relative error = 1.0402161102296717418781744521427e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6429 y[1] (analytic) = 1.9974016561672601952664076403755 y[1] (numeric) = 1.9974016561672601952663868145217 absolute error = 2.08258538e-23 relative error = 1.0426472680493294906690928874180e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.643 y[1] (analytic) = 1.9973944470590303491675404701666 y[1] (numeric) = 1.997394447059030349167519595828 absolute error = 2.08743386e-23 relative error = 1.0450784335930962239015042549517e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6431 y[1] (analytic) = 1.9973872279768560407899901976703 y[1] (numeric) = 1.9973872279768560407899692748473 absolute error = 2.09228230e-23 relative error = 1.0475096018908976019036888229282e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=12.39 NO POLE x[1] = 1.6432 y[1] (analytic) = 1.997379998920809460955439747644 y[1] (numeric) = 1.997379998920809460955418776337 absolute error = 2.09713070e-23 relative error = 1.0499407729791457553175793135225e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6433 y[1] (analytic) = 1.9973727598909629002242946762996 y[1] (numeric) = 1.9973727598909629002242736565089 absolute error = 2.10197907e-23 relative error = 1.0523719519008297607505994716818e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6434 y[1] (analytic) = 1.9973655108873887488949602656998 y[1] (numeric) = 1.9973655108873887488949391974258 absolute error = 2.10682740e-23 relative error = 1.0548031336858217637231830977967e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6435 y[1] (analytic) = 1.9973582519101594970031176207749 y[1] (numeric) = 1.9973582519101594970030965040179 absolute error = 2.11167570e-23 relative error = 1.0572343233771476982877138618741e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6436 y[1] (analytic) = 1.9973509829593477343209987689663 y[1] (numeric) = 1.9973509829593477343209776037267 absolute error = 2.11652396e-23 relative error = 1.0596655160046439389804013812074e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6437 y[1] (analytic) = 1.9973437040350261503566607625052 y[1] (numeric) = 1.9973437040350261503566395487833 absolute error = 2.12137219e-23 relative error = 1.0620967166113733826908011819036e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6438 y[1] (analytic) = 1.9973364151372675343532587833324 y[1] (numeric) = 1.9973364151372675343532375211285 absolute error = 2.12622039e-23 relative error = 1.0645279252338043796457621084709e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6439 y[1] (analytic) = 1.9973291162661447752883182506671 y[1] (numeric) = 1.9973291162661447752882969399817 absolute error = 2.13106854e-23 relative error = 1.0669591318950333679509517700477e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.644 y[1] (analytic) = 1.9973218074217308618730059312328 y[1] (numeric) = 1.9973218074217308618729845720662 absolute error = 2.13591666e-23 relative error = 1.0693903466448284201959869422932e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6441 y[1] (analytic) = 1.9973144886040988825514000521459 y[1] (numeric) = 1.9973144886040988825513786444984 absolute error = 2.14076475e-23 relative error = 1.0718215695196588327950317019694e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6442 y[1] (analytic) = 1.9973071598133220254997594164755 y[1] (numeric) = 1.9973071598133220254997379603475 absolute error = 2.14561280e-23 relative error = 1.0742527955492530933371087649712e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6443 y[1] (analytic) = 1.9972998210494735786257915214815 y[1] (numeric) = 1.9972998210494735786257700168734 absolute error = 2.15046081e-23 relative error = 1.0766840247700260462024076105525e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6444 y[1] (analytic) = 1.9972924723126269295679196795383 y[1] (numeric) = 1.9972924723126269295678981264504 absolute error = 2.15530879e-23 relative error = 1.0791152622251707505162340429918e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6445 y[1] (analytic) = 1.9972851136028555656945491417509 y[1] (numeric) = 1.9972851136028555656945275401835 absolute error = 2.16015674e-23 relative error = 1.0815465079511578315780199550202e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6446 y[1] (analytic) = 1.9972777449202330741033322242716 y[1] (numeric) = 1.9972777449202330741033105742251 absolute error = 2.16500465e-23 relative error = 1.0839777569776433739887648074594e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6447 y[1] (analytic) = 1.9972703662648331416204324373239 y[1] (numeric) = 1.9972703662648331416204107387988 absolute error = 2.16985251e-23 relative error = 1.0864090043342098484314292407606e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6448 y[1] (analytic) = 1.9972629776367295547997876169421 y[1] (numeric) = 1.9972629776367295547997658699386 absolute error = 2.17470035e-23 relative error = 1.0888402650777735929408090580235e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6449 y[1] (analytic) = 1.9972555790359961999223720594316 y[1] (numeric) = 1.9972555790359961999223502639501 absolute error = 2.17954815e-23 relative error = 1.0912715292311211873521590382955e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.645 y[1] (analytic) = 1.9972481704627070629954576585605 y[1] (numeric) = 1.9972481704627070629954358146014 absolute error = 2.18439591e-23 relative error = 1.0937027968306692658471997935099e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6451 y[1] (analytic) = 1.9972407519169362297518740454873 y[1] (numeric) = 1.9972407519169362297518521530509 absolute error = 2.18924364e-23 relative error = 1.0961340729197423410045400572668e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6452 y[1] (analytic) = 1.997233323398757885649267731433 y[1] (numeric) = 1.9972333233987578856492457905197 absolute error = 2.19409133e-23 relative error = 1.0985653525278870999382165336740e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6453 y[1] (analytic) = 1.9972258849082463158693602531056 y[1] (numeric) = 1.9972258849082463158693382637158 absolute error = 2.19893898e-23 relative error = 1.1009966356915209405771029528187e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=13.01 NO POLE x[1] = 1.6454 y[1] (analytic) = 1.9972184364454759053172053208832 y[1] (numeric) = 1.9972184364454759053171832830173 absolute error = 2.20378659e-23 relative error = 1.1034279224470614927247808855728e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6455 y[1] (analytic) = 1.9972109780105211386204449697644 y[1] (numeric) = 1.9972109780105211386204228834226 absolute error = 2.20863418e-23 relative error = 1.1058592228448912029872446229748e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6456 y[1] (analytic) = 1.9972035096034566001285647130921 y[1] (numeric) = 1.9972035096034566001285425782748 absolute error = 2.21348173e-23 relative error = 1.1082905269075384779316854595631e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6457 y[1] (analytic) = 1.9971960312243569739121476990596 y[1] (numeric) = 1.9971960312243569739121255157672 absolute error = 2.21832924e-23 relative error = 1.1107218346714218011156116649146e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6458 y[1] (analytic) = 1.9971885428732970437621278700053 y[1] (numeric) = 1.9971885428732970437621056382382 absolute error = 2.22317671e-23 relative error = 1.1131531461729598928335141243507e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6459 y[1] (analytic) = 1.9971810445503516931890421245039 y[1] (numeric) = 1.9971810445503516931890198442624 absolute error = 2.22802415e-23 relative error = 1.1155844664556290471134425542539e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.646 y[1] (analytic) = 1.9971735362555959054222814822617 y[1] (numeric) = 1.9971735362555959054222591535462 absolute error = 2.23287155e-23 relative error = 1.1180157905488287732540154676800e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6461 y[1] (analytic) = 1.9971660179891047634093412518234 y[1] (numeric) = 1.9971660179891047634093188746343 absolute error = 2.23771891e-23 relative error = 1.1204471184889785844750234867463e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6462 y[1] (analytic) = 1.9971584897509534498150702010977 y[1] (numeric) = 1.9971584897509534498150477754353 absolute error = 2.24256624e-23 relative error = 1.1228784553196121183023047070918e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6463 y[1] (analytic) = 1.9971509515412172470209187307093 y[1] (numeric) = 1.997150951541217247020896256574 absolute error = 2.24741353e-23 relative error = 1.1253097960700732881784474904698e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6464 y[1] (analytic) = 1.9971434033599715371241860501854 y[1] (numeric) = 1.9971434033599715371241635275775 absolute error = 2.25226079e-23 relative error = 1.1277411457839341175611947016848e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6465 y[1] (analytic) = 1.9971358452072918019372663569828 y[1] (numeric) = 1.9971358452072918019372437859028 absolute error = 2.25710800e-23 relative error = 1.1301724944833307055878390470196e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6466 y[1] (analytic) = 1.9971282770832536229868940183652 y[1] (numeric) = 1.9971282770832536229868713988134 absolute error = 2.26195518e-23 relative error = 1.1326038522190062736234819349803e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6467 y[1] (analytic) = 1.9971206989879326815133877561359 y[1] (numeric) = 1.9971206989879326815133650881127 absolute error = 2.26680232e-23 relative error = 1.1350352140202302471960420100705e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6468 y[1] (analytic) = 1.9971131109214047584698938342358 y[1] (numeric) = 1.9971131109214047584698711177415 absolute error = 2.27164943e-23 relative error = 1.1374665849306516625111924297635e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6469 y[1] (analytic) = 1.997105512883745734521628249212 y[1] (numeric) = 1.997105512883745734521605484247 absolute error = 2.27649650e-23 relative error = 1.1398979599795025952931268444786e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.647 y[1] (analytic) = 1.9970979048750315900451179235668 y[1] (numeric) = 1.9970979048750315900450951101314 absolute error = 2.28134354e-23 relative error = 1.1423293442104707840003395883527e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6471 y[1] (analytic) = 1.9970902868953384051274409019925 y[1] (numeric) = 1.9970902868953384051274180400872 absolute error = 2.28619053e-23 relative error = 1.1447607276454659776244987185398e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6472 y[1] (analytic) = 1.997082658944742359565465550502 y[1] (numeric) = 1.9970826589447423595654426401271 absolute error = 2.29103749e-23 relative error = 1.1471921203354613524260880876863e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6473 y[1] (analytic) = 1.9970750210233197328650887584601 y[1] (numeric) = 1.9970750210233197328650657996159 absolute error = 2.29588442e-23 relative error = 1.1496235223169370794329046002469e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6474 y[1] (analytic) = 1.9970673731311469042404731435252 y[1] (numeric) = 1.9970673731311469042404501362122 absolute error = 2.30073130e-23 relative error = 1.1520549236116890700679091266969e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6475 y[1] (analytic) = 1.9970597152683003526132832595089 y[1] (numeric) = 1.9970597152683003526132602037274 absolute error = 2.30557815e-23 relative error = 1.1544863342708061733787093583322e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=83.9MB, alloc=4.3MB, time=13.61 x[1] = 1.6476 y[1] (analytic) = 1.9970520474348566566119208071593 y[1] (numeric) = 1.9970520474348566566118977029097 absolute error = 2.31042496e-23 relative error = 1.1569177493233888738775784188338e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6477 y[1] (analytic) = 1.997044369630892494570758847878 y[1] (numeric) = 1.9970443696308924945707356951607 absolute error = 2.31527173e-23 relative error = 1.1593491688058610733918724014661e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6478 y[1] (analytic) = 1.997036681856484644529375020377 y[1] (numeric) = 1.9970366818564846445293518191924 absolute error = 2.32011846e-23 relative error = 1.1617805927546469347967923558344e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6479 y[1] (analytic) = 1.9970289841117099842317837602834 y[1] (numeric) = 1.9970289841117099842317605106318 absolute error = 2.32496516e-23 relative error = 1.1642120262136094730356826228126e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.648 y[1] (analytic) = 1.9970212763966454911256675227001 y[1] (numeric) = 1.9970212763966454911256442245818 absolute error = 2.32981183e-23 relative error = 1.1666434692192313569437331308289e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6481 y[1] (analytic) = 1.9970135587113682423616070077293 y[1] (numeric) = 1.9970135587113682423615836611447 absolute error = 2.33465846e-23 relative error = 1.1690749168005184025128052119315e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6482 y[1] (analytic) = 1.9970058310559554147923103889676 y[1] (numeric) = 1.9970058310559554147922869939172 absolute error = 2.33950504e-23 relative error = 1.1715063639863993343899803925744e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6483 y[1] (analytic) = 1.9969980934304842849718415449797 y[1] (numeric) = 1.9969980934304842849718181014638 absolute error = 2.34435159e-23 relative error = 1.1739378208282736785764866391478e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6484 y[1] (analytic) = 1.996990345835032229154847293758 y[1] (numeric) = 1.996990345835032229154823801777 absolute error = 2.34919810e-23 relative error = 1.1763692823550900722285370727010e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6485 y[1] (analytic) = 1.996982588269676723295783630177 y[1] (numeric) = 1.9969825882696767232957600897313 absolute error = 2.35404457e-23 relative error = 1.1788007486032746904942228217973e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6486 y[1] (analytic) = 1.9969748207344953430481409664494 y[1] (numeric) = 1.9969748207344953430481173775393 absolute error = 2.35889101e-23 relative error = 1.1812322246168283844262712993619e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6487 y[1] (analytic) = 1.9969670432295657637636683755918 y[1] (numeric) = 1.9969670432295657637636447382177 absolute error = 2.36373741e-23 relative error = 1.1836637054246424723919983954660e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6488 y[1] (analytic) = 1.9969592557549657604915968379079 y[1] (numeric) = 1.9969592557549657604915731520702 absolute error = 2.36858377e-23 relative error = 1.1860951910631440209648081281651e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6489 y[1] (analytic) = 1.9969514583107732079778614904967 y[1] (numeric) = 1.9969514583107732079778377561958 absolute error = 2.37343009e-23 relative error = 1.1885266815687603711404757020950e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.649 y[1] (analytic) = 1.9969436508970660806643228797941 y[1] (numeric) = 1.9969436508970660806642990970303 absolute error = 2.37827638e-23 relative error = 1.1909581819855717067685389135939e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6491 y[1] (analytic) = 1.9969358335139224526879872171545 y[1] (numeric) = 1.9969358335139224526879633859282 absolute error = 2.38312263e-23 relative error = 1.1933896873423925609273432280416e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6492 y[1] (analytic) = 1.9969280061614204978802256374817 y[1] (numeric) = 1.9969280061614204978802017577934 absolute error = 2.38796883e-23 relative error = 1.1958211926679593814579476477326e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6493 y[1] (analytic) = 1.996920168839638489765992460916 y[1] (numeric) = 1.996920168839638489765968532766 absolute error = 2.39281500e-23 relative error = 1.1982527080140646393056309874948e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6494 y[1] (analytic) = 1.9969123215486548015630424575848 y[1] (numeric) = 1.9969123215486548015630184809735 absolute error = 2.39766113e-23 relative error = 1.2006842284094649706566311737735e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6495 y[1] (analytic) = 1.996904464288547906181147115426 y[1] (numeric) = 1.9969044642885479061811230903538 absolute error = 2.40250722e-23 relative error = 1.2031157538905894640342283839506e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6496 y[1] (analytic) = 1.9968965970593963762213099110912 y[1] (numeric) = 1.9968965970593963762212858375584 absolute error = 2.40735328e-23 relative error = 1.2055472895016380558438000532901e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6497 y[1] (analytic) = 1.9968887198612788839749805839358 y[1] (numeric) = 1.9968887198612788839749564619428 absolute error = 2.41219930e-23 relative error = 1.2079788302713093454050026083212e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=87.7MB, alloc=4.3MB, time=14.23 x[1] = 1.6498 y[1] (analytic) = 1.9968808326942742014232684131054 y[1] (numeric) = 1.9968808326942742014232442426526 absolute error = 2.41704528e-23 relative error = 1.2104103762360333491569566430437e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6499 y[1] (analytic) = 1.9968729355584612002361544977255 y[1] (numeric) = 1.9968729355584612002361302788133 absolute error = 2.42189122e-23 relative error = 1.2128419274322403701212265907247e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.65 y[1] (analytic) = 1.9968650284539188517717030402022 y[1] (numeric) = 1.9968650284539188517716787728309 absolute error = 2.42673713e-23 relative error = 1.2152734889042107323279784382379e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6501 y[1] (analytic) = 1.9968571113807262270752716326421 y[1] (numeric) = 1.9968571113807262270752473168121 absolute error = 2.43158300e-23 relative error = 1.2177050556805652923156276911052e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6502 y[1] (analytic) = 1.9968491843389624968787205463996 y[1] (numeric) = 1.9968491843389624968786961821113 absolute error = 2.43642883e-23 relative error = 1.2201366277977352956208522239547e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6503 y[1] (analytic) = 1.9968412473287069315996210247588 y[1] (numeric) = 1.9968412473287069315995966120127 absolute error = 2.44127461e-23 relative error = 1.2225682002842429056721581180990e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6504 y[1] (analytic) = 1.9968333003500389013404625787588 y[1] (numeric) = 1.9968333003500389013404381175552 absolute error = 2.44612036e-23 relative error = 1.2249997831923187687971028334533e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6505 y[1] (analytic) = 1.9968253434030378758878592861688 y[1] (numeric) = 1.9968253434030378758878347765081 absolute error = 2.45096607e-23 relative error = 1.2274313715505055402395112983700e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6506 y[1] (analytic) = 1.9968173764877834247117550936232 y[1] (numeric) = 1.9968173764877834247117305355058 absolute error = 2.45581174e-23 relative error = 1.2298629653952356386212442578564e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6507 y[1] (analytic) = 1.9968093996043552169646281219227 y[1] (numeric) = 1.996809399604355216964603515349 absolute error = 2.46065737e-23 relative error = 1.2322945647629417788754911308235e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6508 y[1] (analytic) = 1.99680141275283302148069397451 y[1] (numeric) = 1.9968014127528330214806693194803 absolute error = 2.46550297e-23 relative error = 1.2347261746980662507668316839261e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6509 y[1] (analytic) = 1.9967934159332967067751080491283 y[1] (numeric) = 1.9967934159332967067750833456431 absolute error = 2.47034852e-23 relative error = 1.2371577852210438671203316841710e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.651 y[1] (analytic) = 1.9967854091458262410431668526709 y[1] (numeric) = 1.9967854091458262410431421007305 absolute error = 2.47519404e-23 relative error = 1.2395894063843469002582440830614e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6511 y[1] (analytic) = 1.9967773923905016921595083192281 y[1] (numeric) = 1.996777392390501692159483518833 absolute error = 2.48003951e-23 relative error = 1.2420210282083305392246520934578e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6512 y[1] (analytic) = 1.9967693656674032276773111313423 y[1] (numeric) = 1.9967693656674032276772862824928 absolute error = 2.48488495e-23 relative error = 1.2444526607455479854714234405642e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6513 y[1] (analytic) = 1.9967613289766111148274930444763 y[1] (numeric) = 1.9967613289766111148274681471728 absolute error = 2.48973035e-23 relative error = 1.2468842990243844179001941967502e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6514 y[1] (analytic) = 1.9967532823182057205179082147049 y[1] (numeric) = 1.9967532823182057205178832689479 absolute error = 2.49457570e-23 relative error = 1.2493159380731447430624173514091e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6515 y[1] (analytic) = 1.9967452256922675113325435296375 y[1] (numeric) = 1.9967452256922675113325185354272 absolute error = 2.49942103e-23 relative error = 1.2517475929526541419475108115180e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6516 y[1] (analytic) = 1.9967371590988770535307139425781 y[1] (numeric) = 1.996737159098877053530688899915 absolute error = 2.50426631e-23 relative error = 1.2541792486749581502087203704136e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6517 y[1] (analytic) = 1.9967290825381150130462568099335 y[1] (numeric) = 1.996729082538115013046231718818 absolute error = 2.50911155e-23 relative error = 1.2566109102846225803697297350362e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6518 y[1] (analytic) = 1.9967209960100621554867252318752 y[1] (numeric) = 1.9967209960100621554867000923077 absolute error = 2.51395675e-23 relative error = 1.2590425778180835625457544348682e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6519 y[1] (analytic) = 1.9967128995147993461325803962649 y[1] (numeric) = 1.9967128995147993461325552082458 absolute error = 2.51880191e-23 relative error = 1.2614742513117775377588776348899e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.652 memory used=91.5MB, alloc=4.3MB, time=14.84 y[1] (analytic) = 1.9967047930524075499363829258502 y[1] (numeric) = 1.9967047930524075499363576893798 absolute error = 2.52364704e-23 relative error = 1.2639059358103928719091956637992e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6521 y[1] (analytic) = 1.9966966766229678315219832287397 y[1] (numeric) = 1.9966966766229678315219579438185 absolute error = 2.52849212e-23 relative error = 1.2663376213338837641571373579922e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6522 y[1] (analytic) = 1.9966885502265613551837108521655 y[1] (numeric) = 1.9966885502265613551836855187939 absolute error = 2.53333716e-23 relative error = 1.2687693129269188752786565295637e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6523 y[1] (analytic) = 1.9966804138632693848855628395403 y[1] (numeric) = 1.9966804138632693848855374577186 absolute error = 2.53818217e-23 relative error = 1.2712010156342486648951363278193e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6524 y[1] (analytic) = 1.9966722675331732842603910908181 y[1] (numeric) = 1.9966722675331732842603656605468 absolute error = 2.54302713e-23 relative error = 1.2736327194757060548763781829885e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6525 y[1] (analytic) = 1.9966641112363545166090887261667 y[1] (numeric) = 1.9966641112363545166090632474461 absolute error = 2.54787206e-23 relative error = 1.2760644345043753868627872555760e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6526 y[1] (analytic) = 1.9966559449728946448997754529587 y[1] (numeric) = 1.9966559449728946448997499257893 absolute error = 2.55271694e-23 relative error = 1.2784961507400084856182260986921e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6527 y[1] (analytic) = 1.996647768742875331766981936092 y[1] (numeric) = 1.9966477687428753317669563604741 absolute error = 2.55756179e-23 relative error = 1.2809278782357721682465650147812e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6528 y[1] (analytic) = 1.9966395825463783395108331716443 y[1] (numeric) = 1.9966395825463783395108075475783 absolute error = 2.56240660e-23 relative error = 1.2833596120197521488329287888277e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6529 y[1] (analytic) = 1.996631386383485530096230863873 y[1] (numeric) = 1.9966313863834855300962051913593 absolute error = 2.56725137e-23 relative error = 1.2857913521283881198769734461279e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.653 y[1] (analytic) = 1.9966231802542788651520348055667 y[1] (numeric) = 1.9966231802542788651520090846057 absolute error = 2.57209610e-23 relative error = 1.2882230985981200981678636937303e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6531 y[1] (analytic) = 1.9966149641588404059702432617572 y[1] (numeric) = 1.9966149641588404059702174923494 absolute error = 2.57694078e-23 relative error = 1.2906548464569114890302516013820e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6532 y[1] (analytic) = 1.9966067380972523135051723568007 y[1] (numeric) = 1.9966067380972523135051465389464 absolute error = 2.58178543e-23 relative error = 1.2930866057581362003935451648087e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6533 y[1] (analytic) = 1.9965985020695968483726344648345 y[1] (numeric) = 1.9965985020695968483726085985341 absolute error = 2.58663004e-23 relative error = 1.2955183715297789021043148389672e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6534 y[1] (analytic) = 1.9965902560759563708491156036202 y[1] (numeric) = 1.9965902560759563708490896888742 absolute error = 2.59147460e-23 relative error = 1.2979501387997420027044676336246e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6535 y[1] (analytic) = 1.9965820001164133408709518317795 y[1] (numeric) = 1.9965820001164133408709258685882 absolute error = 2.59631913e-23 relative error = 1.3003819176215242832808787663751e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6536 y[1] (analytic) = 1.9965737341910503180335046494311 y[1] (numeric) = 1.9965737341910503180334786377949 absolute error = 2.60116362e-23 relative error = 1.3028137030230494997081026987793e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6537 y[1] (analytic) = 1.9965654582999499615903354022381 y[1] (numeric) = 1.9965654582999499615903093421574 absolute error = 2.60600807e-23 relative error = 1.3052454950407599728676492651180e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6538 y[1] (analytic) = 1.9965571724431950304523786888731 y[1] (numeric) = 1.9965571724431950304523525803483 absolute error = 2.61085248e-23 relative error = 1.3076772937110983576641729207862e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6539 y[1] (analytic) = 1.9965488766208683831871147719094 y[1] (numeric) = 1.9965488766208683831870886149409 absolute error = 2.61569685e-23 relative error = 1.3101090990705076442422972021854e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.654 y[1] (analytic) = 1.996540570833052978017740992147 y[1] (numeric) = 1.9965405708330529780177147867352 absolute error = 2.62054118e-23 relative error = 1.3125409111554311592034660602735e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6541 y[1] (analytic) = 1.996532255079831872822342186381 y[1] (numeric) = 1.9965322550798318728223159325264 absolute error = 2.62538546e-23 relative error = 1.3149727249936281468457718111160e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6542 y[1] (analytic) = 1.9965239293612882251330601086221 y[1] (numeric) = 1.996523929361288225133033806325 absolute error = 2.63022971e-23 relative error = 1.3174045506388905635387747059267e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=15.47 NO POLE x[1] = 1.6543 y[1] (analytic) = 1.9965155936775052921352618547752 y[1] (numeric) = 1.9965155936775052921352355040361 absolute error = 2.63507391e-23 relative error = 1.3198363781102729755027030149668e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6544 y[1] (analytic) = 1.9965072480285664306667072907868 y[1] (numeric) = 1.9965072480285664306666808916061 absolute error = 2.63991807e-23 relative error = 1.3222682124529044117881274629893e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6545 y[1] (analytic) = 1.996498892414555097216715484268 y[1] (numeric) = 1.996498892414555097216689036646 absolute error = 2.64476220e-23 relative error = 1.3247000587119979420342493149466e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6546 y[1] (analytic) = 1.9964905268355548479253301396019 y[1] (numeric) = 1.9964905268355548479253036435391 absolute error = 2.64960628e-23 relative error = 1.3271319069064836130095914558504e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6547 y[1] (analytic) = 1.9964821512916493385824840365442 y[1] (numeric) = 1.9964821512916493385824574920409 absolute error = 2.65445033e-23 relative error = 1.3295637670903643389120684327519e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6548 y[1] (analytic) = 1.9964737657829223246271624723239 y[1] (numeric) = 1.9964737657829223246271358793807 absolute error = 2.65929432e-23 relative error = 1.3319956242736557519705053363660e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6549 y[1] (analytic) = 1.9964653703094576611465657072551 y[1] (numeric) = 1.9964653703094576611465390658723 absolute error = 2.66413828e-23 relative error = 1.3344274935192345404347603140436e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.655 y[1] (analytic) = 1.9964569648713393028752704138649 y[1] (numeric) = 1.9964569648713393028752437240428 absolute error = 2.66898221e-23 relative error = 1.3368593748636105758120773383002e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6551 y[1] (analytic) = 1.9964485494686513041943901295484 y[1] (numeric) = 1.9964485494686513041943633912876 absolute error = 2.67382608e-23 relative error = 1.3392912533166109693904417990084e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6552 y[1] (analytic) = 1.996440124101477819130734712759 y[1] (numeric) = 1.9964401241014778191307079260597 absolute error = 2.67866993e-23 relative error = 1.3417231489502185846507810859727e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6553 y[1] (analytic) = 1.9964316887699031013559688027399 y[1] (numeric) = 1.9964316887699031013559419676027 absolute error = 2.68351372e-23 relative error = 1.3441550417652611736353403580265e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6554 y[1] (analytic) = 1.9964232434740115041857692828092 y[1] (numeric) = 1.9964232434740115041857423992344 absolute error = 2.68835748e-23 relative error = 1.3465869468249335022486465584328e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6555 y[1] (analytic) = 1.996414788213887480578981747203 y[1] (numeric) = 1.996414788213887480578954815191 absolute error = 2.69320120e-23 relative error = 1.3490188591567684555547514678165e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6556 y[1] (analytic) = 1.9964063229896155831367759714882 y[1] (numeric) = 1.9964063229896155831367489910395 absolute error = 2.69804487e-23 relative error = 1.3514507737882144687062000936295e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6557 y[1] (analytic) = 1.9963978478012804641018003865513 y[1] (numeric) = 1.9963978478012804641017733576663 absolute error = 2.70288850e-23 relative error = 1.3538826957646785346379316983808e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6558 y[1] (analytic) = 1.9963893626489668753573355561727 y[1] (numeric) = 1.9963893626489668753573084788517 absolute error = 2.70773210e-23 relative error = 1.3563146301316530119248455820832e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6559 y[1] (analytic) = 1.9963808675327596684264466581944 y[1] (numeric) = 1.9963808675327596684264195324378 absolute error = 2.71257566e-23 relative error = 1.3587465719165874108079937997112e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.656 y[1] (analytic) = 1.9963723624527437944711349692902 y[1] (numeric) = 1.9963723624527437944711077950985 absolute error = 2.71741917e-23 relative error = 1.3611785161468463936023412571276e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6561 y[1] (analytic) = 1.9963638474090043042914883533464 y[1] (numeric) = 1.9963638474090043042914611307201 absolute error = 2.72226263e-23 relative error = 1.3636104628588164626855393830376e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6562 y[1] (analytic) = 1.9963553224016263483248307534619 y[1] (numeric) = 1.9963553224016263483248034824012 absolute error = 2.72710607e-23 relative error = 1.3660424271162693192852890298503e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6563 y[1] (analytic) = 1.9963467874306951766448706875749 y[1] (numeric) = 1.9963467874306951766448433680804 absolute error = 2.73194945e-23 relative error = 1.3684743889191856531539927612923e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6564 y[1] (analytic) = 1.9963382424962961389608487477273 y[1] (numeric) = 1.9963382424962961389608213797994 absolute error = 2.73679279e-23 relative error = 1.3709063583222308814979856486278e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.3MB, time=16.09 NO POLE x[1] = 1.6565 y[1] (analytic) = 1.9963296875985146846166841029728 y[1] (numeric) = 1.9963296875985146846166566866119 absolute error = 2.74163609e-23 relative error = 1.3733383353618569112321657648624e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6566 y[1] (analytic) = 1.9963211227374363625901200059382 y[1] (numeric) = 1.9963211227374363625900925411447 absolute error = 2.74647935e-23 relative error = 1.3757703200745160173708785463561e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6567 y[1] (analytic) = 1.9963125479131468214918683030468 y[1] (numeric) = 1.9963125479131468214918407898211 absolute error = 2.75132257e-23 relative error = 1.3782023124966608442455135980564e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6568 y[1] (analytic) = 1.996303963125731809564752948412 y[1] (numeric) = 1.9963039631257318095647253867546 absolute error = 2.75616574e-23 relative error = 1.3806343076554872070608095811072e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6569 y[1] (analytic) = 1.99629536837527717468285252141 y[1] (numeric) = 1.9962953683752771746828249113212 absolute error = 2.76100888e-23 relative error = 1.3830663156059413251518298974475e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.657 y[1] (analytic) = 1.9962867636618688643506417479393 y[1] (numeric) = 1.9962867636618688643506140894195 absolute error = 2.76585198e-23 relative error = 1.3854983313752412998657748082516e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6571 y[1] (analytic) = 1.996278148985592925702132025377 y[1] (numeric) = 1.9962781489855929257021043184266 absolute error = 2.77069504e-23 relative error = 1.3879303549998412649783249152092e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6572 y[1] (analytic) = 1.9962695243465355055000109512391 y[1] (numeric) = 1.9962695243465355054999831958586 absolute error = 2.77553805e-23 relative error = 1.3903623815068521124687188909372e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6573 y[1] (analytic) = 1.9962608897447828501347808555549 y[1] (numeric) = 1.9962608897447828501347530517447 absolute error = 2.78038102e-23 relative error = 1.3927944159420290106394446200466e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6574 y[1] (analytic) = 1.9962522451804213056238963369619 y[1] (numeric) = 1.9962522451804213056238684847225 absolute error = 2.78522394e-23 relative error = 1.3952264533324401704799399597625e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6575 y[1] (analytic) = 1.9962435906535373176109008025329 y[1] (numeric) = 1.9962435906535373176108729018646 absolute error = 2.79006683e-23 relative error = 1.3976585037332933955891015530200e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6576 y[1] (analytic) = 1.9962349261642174313645620113402 y[1] (numeric) = 1.9962349261642174313645340622436 absolute error = 2.79490966e-23 relative error = 1.4000905521528184733542092145247e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6577 y[1] (analytic) = 1.9962262517125482917780066217698 y[1] (numeric) = 1.9962262517125482917779786242452 absolute error = 2.79975246e-23 relative error = 1.4025226136556977415780950128483e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6578 y[1] (analytic) = 1.99621756729861664336785374259 y[1] (numeric) = 1.9962175672986166433678256966378 absolute error = 2.80459522e-23 relative error = 1.4049546832689791414896767834733e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6579 y[1] (analytic) = 1.9962088729225093302733474877861 y[1] (numeric) = 1.9962088729225093302733193934068 absolute error = 2.80943793e-23 relative error = 1.4073867560196238754462151682636e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.658 y[1] (analytic) = 1.9962001685843132962554885351691 y[1] (numeric) = 1.996200168584313296255460392363 absolute error = 2.81428061e-23 relative error = 1.4098188419630591401340214959838e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6581 y[1] (analytic) = 1.9961914542841155846961646887659 y[1] (numeric) = 1.9961914542841155846961364975335 absolute error = 2.81912324e-23 relative error = 1.4122509311167291977436085556416e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6582 y[1] (analytic) = 1.9961827300220033385972804450015 y[1] (numeric) = 1.9961827300220033385972522053432 absolute error = 2.82396583e-23 relative error = 1.4146830285265879693867020551312e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6583 y[1] (analytic) = 1.9961739957980638005798855626805 y[1] (numeric) = 1.9961739957980638005798572745967 absolute error = 2.82880838e-23 relative error = 1.4171151342290939473529483620104e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6584 y[1] (analytic) = 1.9961652516123843128833026367774 y[1] (numeric) = 1.9961652516123843128832743002685 absolute error = 2.83365089e-23 relative error = 1.4195472482607060139473816156495e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6585 y[1] (analytic) = 1.9961564974650523173642536760439 y[1] (numeric) = 1.9961564974650523173642252911105 absolute error = 2.83849334e-23 relative error = 1.4219793606386289276450782246079e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6586 y[1] (analytic) = 1.996147733356155355495985684443 y[1] (numeric) = 1.9961477333561553554959572510853 absolute error = 2.84333577e-23 relative error = 1.4244114914377873949144262367281e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.3MB, time=16.71 NO POLE x[1] = 1.6587 y[1] (analytic) = 1.9961389592857810683673952464164 y[1] (numeric) = 1.9961389592857810683673667646349 absolute error = 2.84817815e-23 relative error = 1.4268436256657596272404758156152e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6588 y[1] (analytic) = 1.9961301752540171966821521159969 y[1] (numeric) = 1.9961301752540171966821235857921 absolute error = 2.85302048e-23 relative error = 1.4292757633589399435364074127541e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6589 y[1] (analytic) = 1.9961213812609515807578218097724 y[1] (numeric) = 1.9961213812609515807577932311447 absolute error = 2.85786277e-23 relative error = 1.4317079095634382956473848758536e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.659 y[1] (analytic) = 1.9961125773066721605249872037106 y[1] (numeric) = 1.9961125773066721605249585766604 absolute error = 2.86270502e-23 relative error = 1.4341400643157157803834905337552e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6591 y[1] (analytic) = 1.9961037633912669755263691338542 y[1] (numeric) = 1.996103763391266975526340458382 absolute error = 2.86754722e-23 relative error = 1.4365722226424742887083497282052e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6592 y[1] (analytic) = 1.9960949395148241649159460008944 y[1] (numeric) = 1.9960949395148241649159172770006 absolute error = 2.87238938e-23 relative error = 1.4390043895898910281336090961732e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6593 y[1] (analytic) = 1.9960861056774319674580723786318 y[1] (numeric) = 1.9960861056774319674580436063167 absolute error = 2.87723151e-23 relative error = 1.4414365702042321407174622613932e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6594 y[1] (analytic) = 1.9960772618791787215265966263334 y[1] (numeric) = 1.9960772618791787215265678055976 absolute error = 2.88207358e-23 relative error = 1.4438687494925484844591571207983e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6595 y[1] (analytic) = 1.9960684081201528651039775049953 y[1] (numeric) = 1.9960684081201528651039486358392 absolute error = 2.88691561e-23 relative error = 1.4463009375108665106208627781466e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6596 y[1] (analytic) = 1.9960595444004429357803997975186 y[1] (numeric) = 1.9960595444004429357803708799426 absolute error = 2.89175760e-23 relative error = 1.4487331342956495743397071134954e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6597 y[1] (analytic) = 1.996050670720137570752888932808 y[1] (numeric) = 1.9960506707201375707528599668126 absolute error = 2.89659954e-23 relative error = 1.4511653348734685783219209361229e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6598 y[1] (analytic) = 1.996041787079325506824424613803 y[1] (numeric) = 1.9960417870793255068243955993885 absolute error = 2.90144145e-23 relative error = 1.4535975493005511099968731460799e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6599 y[1] (analytic) = 1.9960328934780955804030534494479 y[1] (numeric) = 1.9960328934780955804030243866148 absolute error = 2.90628331e-23 relative error = 1.4560297675935536815716377716128e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.66 y[1] (analytic) = 1.996023989916536727501000590613 y[1] (numeric) = 1.9960239899165367275009714793617 absolute error = 2.91112513e-23 relative error = 1.4584619947988340615592146999099e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6601 y[1] (analytic) = 1.9960150763947379837337803699724 y[1] (numeric) = 1.9960150763947379837337512103034 absolute error = 2.91596690e-23 relative error = 1.4608942259428753727524388681203e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6602 y[1] (analytic) = 1.9960061529127884843193059458502 y[1] (numeric) = 1.9960061529127884843192767377639 absolute error = 2.92080863e-23 relative error = 1.4633264660720807502650117763281e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6603 y[1] (analytic) = 1.9959972194707774640769979500415 y[1] (numeric) = 1.9959972194707774640769686935383 absolute error = 2.92565032e-23 relative error = 1.4657587152229162645434511850220e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6604 y[1] (analytic) = 1.9959882760687942574268921396193 y[1] (numeric) = 1.9959882760687942574268628346996 absolute error = 2.93049197e-23 relative error = 1.4681909734318484004070823826519e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6605 y[1] (analytic) = 1.9959793227069282983887460527348 y[1] (numeric) = 1.9959793227069282983887166993991 absolute error = 2.93533357e-23 relative error = 1.4706232357252721170213513909234e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6606 y[1] (analytic) = 1.9959703593852691205811446684207 y[1] (numeric) = 1.9959703593852691205811152666694 absolute error = 2.94017513e-23 relative error = 1.4730555071496816753044928751908e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6607 y[1] (analytic) = 1.9959613861039063572206050704058 y[1] (numeric) = 1.9959613861039063572205756202393 absolute error = 2.94501665e-23 relative error = 1.4754877877415447349001403686205e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6608 y[1] (analytic) = 1.9959524028629297411206801149508 y[1] (numeric) = 1.9959524028629297411206506163696 absolute error = 2.94985812e-23 relative error = 1.4779200725271898615230882009266e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.3MB, time=17.35 NO POLE x[1] = 1.6609 y[1] (analytic) = 1.9959434096624291046910611027136 y[1] (numeric) = 1.9959434096624291046910315557181 absolute error = 2.95469955e-23 relative error = 1.4803523665531799189387155210229e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.661 y[1] (analytic) = 1.9959344065024943799366794546528 y[1] (numeric) = 1.9959344065024943799366498592435 absolute error = 2.95954093e-23 relative error = 1.4827846648457990654321598665911e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6611 y[1] (analytic) = 1.9959253933832155984568073919795 y[1] (numeric) = 1.9959253933832155984567777481568 absolute error = 2.96438227e-23 relative error = 1.4852169724516560068955097589251e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6612 y[1] (analytic) = 1.9959163703046828914441576201651 y[1] (numeric) = 1.9959163703046828914441279279295 absolute error = 2.96922356e-23 relative error = 1.4876492843969903982375238537513e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6613 y[1] (analytic) = 1.9959073372669864896839820170151 y[1] (numeric) = 1.995907337266986489683952276367 absolute error = 2.97406481e-23 relative error = 1.4900816057284568931588069935054e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6614 y[1] (analytic) = 1.9958982942702167235531693248171 y[1] (numeric) = 1.9958982942702167235531395357569 absolute error = 2.97890602e-23 relative error = 1.4925139364825258847714856467181e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6615 y[1] (analytic) = 1.9958892413144640230193418465728 y[1] (numeric) = 1.995889241314464023019312009101 absolute error = 2.98374718e-23 relative error = 1.4949462716853701308208276959175e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6616 y[1] (analytic) = 1.9958801783998189176399511463226 y[1] (numeric) = 1.9958801783998189176399212604396 absolute error = 2.98858830e-23 relative error = 1.4973786163837134426915762840303e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6617 y[1] (analytic) = 1.9958711055263720365613727535718 y[1] (numeric) = 1.995871105526372036561342819278 absolute error = 2.99342938e-23 relative error = 1.4998109706140274248525709278254e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6618 y[1] (analytic) = 1.9958620226942141085179998718273 y[1] (numeric) = 1.9958620226942141085179698891232 absolute error = 2.99827041e-23 relative error = 1.5022433294024177219910989197632e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6619 y[1] (analytic) = 1.995852929903435961831336091255 y[1] (numeric) = 1.995852929903435961831306060141 absolute error = 3.00311140e-23 relative error = 1.5046756977956775409866511591550e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.662 y[1] (analytic) = 1.995843827154128524409087105465 y[1] (numeric) = 1.9958438271541285244090570259416 absolute error = 3.00795234e-23 relative error = 1.5071080708198676393328383666963e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6621 y[1] (analytic) = 1.9958347144463828237442514324357 y[1] (numeric) = 1.9958347144463828237442213045033 absolute error = 3.01279324e-23 relative error = 1.5095404535218275944872400197165e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6622 y[1] (analytic) = 1.9958255917802899869142101395841 y[1] (numeric) = 1.9958255917802899869141799632432 absolute error = 3.01763409e-23 relative error = 1.5119728409275731807860072647995e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6623 y[1] (analytic) = 1.9958164591559412405798155729934 y[1] (numeric) = 1.9958164591559412405797853482444 absolute error = 3.02247490e-23 relative error = 1.5144052380839904519660099485673e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6624 y[1] (analytic) = 1.9958073165734279109844790908045 y[1] (numeric) = 1.9958073165734279109844488176479 absolute error = 3.02731566e-23 relative error = 1.5168376400170501032387214949925e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6625 y[1] (analytic) = 1.9957981640328414239532578007833 y[1] (numeric) = 1.9957981640328414239532274792195 absolute error = 3.03215638e-23 relative error = 1.5192700517736847703254087620452e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6626 y[1] (analytic) = 1.9957890015342733048919403020704 y[1] (numeric) = 1.9957890015342733048919099320998 absolute error = 3.03699706e-23 relative error = 1.5217024733903696819098199572088e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6627 y[1] (analytic) = 1.9957798290778151787861314311243 y[1] (numeric) = 1.9957798290778151787861010127474 absolute error = 3.04183769e-23 relative error = 1.5241348998930077723872231144575e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6628 y[1] (analytic) = 1.995770646663558770200336011866 y[1] (numeric) = 1.9957706466635587702003055450832 absolute error = 3.04667828e-23 relative error = 1.5265673363286017864789210206368e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6629 y[1] (analytic) = 1.9957614542915959032770416100346 y[1] (numeric) = 1.9957614542915959032770110948464 absolute error = 3.05151882e-23 relative error = 1.5289997777230093395242331639907e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.663 y[1] (analytic) = 1.9957522519620185017358002917634 y[1] (numeric) = 1.9957522519620185017357697281702 absolute error = 3.05635932e-23 relative error = 1.5314322291232800225106224006640e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.3MB, time=17.98 NO POLE x[1] = 1.6631 y[1] (analytic) = 1.995743039674918588872309386385 y[1] (numeric) = 1.9957430396749185888722787743873 absolute error = 3.06119977e-23 relative error = 1.5338646855552260357421686516436e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6632 y[1] (analytic) = 1.9957338174303882875574912534752 y[1] (numeric) = 1.9957338174303882875574605930735 absolute error = 3.06604017e-23 relative error = 1.5362971470552556667427704348116e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6633 y[1] (analytic) = 1.9957245852285198202365720541446 y[1] (numeric) = 1.9957245852285198202365413453392 absolute error = 3.07088054e-23 relative error = 1.5387296236812003711442397879539e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6634 y[1] (analytic) = 1.9957153430694055089281595265866 y[1] (numeric) = 1.995715343069405508928128769378 absolute error = 3.07572086e-23 relative error = 1.5411621054481389832811332232288e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6635 y[1] (analytic) = 1.9957060909531377752233197658928 y[1] (numeric) = 1.9957060909531377752232889602815 absolute error = 3.08056113e-23 relative error = 1.5435945923924808408838817050377e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6636 y[1] (analytic) = 1.9956968288798091402846530081429 y[1] (numeric) = 1.9956968288798091402846221541292 absolute error = 3.08540137e-23 relative error = 1.5460270945721978323792047907410e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6637 y[1] (analytic) = 1.995687556849512224845368418779 y[1] (numeric) = 1.9956875568495122248453375163634 absolute error = 3.09024156e-23 relative error = 1.5484596020022307732523192811678e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6638 y[1] (analytic) = 1.9956782748623397492083578852748 y[1] (numeric) = 1.9956782748623397492083269344579 absolute error = 3.09508169e-23 relative error = 1.5508921097081623523577238750600e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6639 y[1] (analytic) = 1.9956689829183845332452688141075 y[1] (numeric) = 1.9956689829183845332452378148896 absolute error = 3.09992179e-23 relative error = 1.5533246327588864044214280007658e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.664 y[1] (analytic) = 1.9956596810177394963955759320416 y[1] (numeric) = 1.9956596810177394963955448844232 absolute error = 3.10476184e-23 relative error = 1.5557571611692052075120554784803e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6641 y[1] (analytic) = 1.9956503691604976576656520917354 y[1] (numeric) = 1.995650369160497657665620995717 absolute error = 3.10960184e-23 relative error = 1.5581896949755301569849635859186e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6642 y[1] (analytic) = 1.9956410473467521356278380816778 y[1] (numeric) = 1.9956410473467521356278069372598 absolute error = 3.11444180e-23 relative error = 1.5606222392251941416598679094473e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6643 y[1] (analytic) = 1.9956317155765961484195114404658 y[1] (numeric) = 1.9956317155765961484194802476486 absolute error = 3.11928172e-23 relative error = 1.5630547939546794715261772445846e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6644 y[1] (analytic) = 1.9956223738501230137421542754313 y[1] (numeric) = 1.9956223738501230137421230342154 absolute error = 3.12412159e-23 relative error = 1.5654873541895008472533246317346e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6645 y[1] (analytic) = 1.9956130221674261488604200856273 y[1] (numeric) = 1.9956130221674261488603887960132 absolute error = 3.12896141e-23 relative error = 1.5679199199660710602832209018771e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6646 y[1] (analytic) = 1.9956036605285990706011995891821 y[1] (numeric) = 1.9956036605285990706011682511702 absolute error = 3.13380119e-23 relative error = 1.5703524963318182779453948141202e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6647 y[1] (analytic) = 1.9955942889337353953526855550309 y[1] (numeric) = 1.9955942889337353953526541686218 absolute error = 3.13864091e-23 relative error = 1.5727850733011493304977573675096e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6648 y[1] (analytic) = 1.9955849073829288390634366390352 y[1] (numeric) = 1.9955849073829288390634052042292 absolute error = 3.14348060e-23 relative error = 1.5752176659435938136748010927733e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6649 y[1] (analytic) = 1.9955755158762732172414402244974 y[1] (numeric) = 1.9955755158762732172414087412949 absolute error = 3.14832025e-23 relative error = 1.5776502692846215458061180682679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.665 y[1] (analytic) = 1.9955661144138624449531742670819 y[1] (numeric) = 1.9955661144138624449531427354835 absolute error = 3.15315984e-23 relative error = 1.5800828733384991918195559971602e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6651 y[1] (analytic) = 1.9955567029957905368226681441514 y[1] (numeric) = 1.9955567029957905368226365641575 absolute error = 3.15799939e-23 relative error = 1.5825154881638367259539520170985e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6652 y[1] (analytic) = 1.995547281622151607030562508527 y[1] (numeric) = 1.9955472816221516070305308801381 absolute error = 3.16283889e-23 relative error = 1.5849481087859636571842077549600e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=114.4MB, alloc=4.3MB, time=18.59 x[1] = 1.6653 y[1] (analytic) = 1.9955378502930398693131681466829 y[1] (numeric) = 1.9955378502930398693131364698994 absolute error = 3.16767835e-23 relative error = 1.5873807402524758702653394219242e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6654 y[1] (analytic) = 1.9955284090085496369615238413837 y[1] (numeric) = 1.9955284090085496369614921162061 absolute error = 3.17251776e-23 relative error = 1.5898133775886563551223504353189e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6655 y[1] (analytic) = 1.9955189577687753228204532387752 y[1] (numeric) = 1.9955189577687753228204214652039 absolute error = 3.17735713e-23 relative error = 1.5922460258421491645461817810357e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6656 y[1] (analytic) = 1.9955094965738114392876207199366 y[1] (numeric) = 1.9955094965738114392875888979721 absolute error = 3.18219645e-23 relative error = 1.5946786800381906733888088722612e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6657 y[1] (analytic) = 1.9955000254237525983125862769049 y[1] (numeric) = 1.9955000254237525983125544065477 absolute error = 3.18703572e-23 relative error = 1.5971113402131979025107556324301e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6658 y[1] (analytic) = 1.99549054431869351139585939318 y[1] (numeric) = 1.9954905443186935113958274744305 absolute error = 3.19187495e-23 relative error = 1.5995440114148873172360023779082e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6659 y[1] (analytic) = 1.9954810532587289895879519287204 y[1] (numeric) = 1.9954810532587289895879199615791 absolute error = 3.19671413e-23 relative error = 1.6019766886684251519161707221456e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.666 y[1] (analytic) = 1.9954715522439539434884300094387 y[1] (numeric) = 1.9954715522439539434883979939061 absolute error = 3.20155326e-23 relative error = 1.6044093720102294932282296921854e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6661 y[1] (analytic) = 1.9954620412744633832449649212072 y[1] (numeric) = 1.9954620412744633832449328572837 absolute error = 3.20639235e-23 relative error = 1.6068420664880894570178135992969e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6662 y[1] (analytic) = 1.9954525203503524185523830083814 y[1] (numeric) = 1.9954525203503524185523508960675 absolute error = 3.21123139e-23 relative error = 1.6092747671271009210590975333249e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6663 y[1] (analytic) = 1.9954429894717162586517145768529 y[1] (numeric) = 1.995442989471716258651682416149 absolute error = 3.21607039e-23 relative error = 1.6117074789751015923296208709802e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6664 y[1] (analytic) = 1.9954334486386502123292418016398 y[1] (numeric) = 1.9954334486386502123292095925464 absolute error = 3.22090934e-23 relative error = 1.6141401970571403493985599028430e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6665 y[1] (analytic) = 1.9954238978512496879155456390246 y[1] (numeric) = 1.9954238978512496879155133815421 absolute error = 3.22574825e-23 relative error = 1.6165729264211035961605080650308e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6666 y[1] (analytic) = 1.9954143371096101932845517432492 y[1] (numeric) = 1.9954143371096101932845194373782 absolute error = 3.23058710e-23 relative error = 1.6190056570805026129260608845709e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6667 y[1] (analytic) = 1.9954047664138273358525753877767 y[1] (numeric) = 1.9954047664138273358525430335176 absolute error = 3.23542591e-23 relative error = 1.6214383990947150354022804776897e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6668 y[1] (analytic) = 1.9953951857639968225773653911287 y[1] (numeric) = 1.9953951857639968225773329884819 absolute error = 3.24026468e-23 relative error = 1.6238711525002339820794831076677e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6669 y[1] (analytic) = 1.9953855951602144599571470473087 y[1] (numeric) = 1.9953855951602144599571145962747 absolute error = 3.24510340e-23 relative error = 1.6263039123219903754798514973161e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.667 y[1] (analytic) = 1.9953759946025761540296640608207 y[1] (numeric) = 1.9953759946025761540296315614 absolute error = 3.24994207e-23 relative error = 1.6287366785964059845677027924101e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6671 y[1] (analytic) = 1.9953663840911779103712194862926 y[1] (numeric) = 1.9953663840911779103711869384857 absolute error = 3.25478069e-23 relative error = 1.6311694513599029229529385054992e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6672 y[1] (analytic) = 1.9953567636261158340957156727139 y[1] (numeric) = 1.9953567636261158340956830765212 absolute error = 3.25961927e-23 relative error = 1.6336022356605387533090371471828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6673 y[1] (analytic) = 1.9953471332074861298536932122974 y[1] (numeric) = 1.9953471332074861298536605677194 absolute error = 3.26445780e-23 relative error = 1.6360350265231495556726406324918e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6674 y[1] (analytic) = 1.9953374928353851018313688939749 y[1] (numeric) = 1.995337492835385101831336201012 absolute error = 3.26929629e-23 relative error = 1.6384678289958420657125038176494e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=118.2MB, alloc=4.3MB, time=19.21 x[1] = 1.6675 y[1] (analytic) = 1.9953278425099091537496726615354 y[1] (numeric) = 1.9953278425099091537496399201881 absolute error = 3.27413473e-23 relative error = 1.6409006381034048359845394093313e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6676 y[1] (analytic) = 1.9953181822311547888632835764169 y[1] (numeric) = 1.9953181822311547888632507866858 absolute error = 3.27897311e-23 relative error = 1.6433334488705298649929112171161e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6677 y[1] (analytic) = 1.9953085119992186099596647851605 y[1] (numeric) = 1.9953085119992186099596319470459 absolute error = 3.28381146e-23 relative error = 1.6457662763688375351235278959681e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6678 y[1] (analytic) = 1.9952988318141973193580974915362 y[1] (numeric) = 1.9952988318141973193580646050386 absolute error = 3.28864976e-23 relative error = 1.6481991106113371458051282133078e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6679 y[1] (analytic) = 1.9952891416761877189087139333511 y[1] (numeric) = 1.9952891416761877189086809984711 absolute error = 3.29348800e-23 relative error = 1.6506319466226488871847075286262e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.668 y[1] (analytic) = 1.9952794415852867099915293639491 y[1] (numeric) = 1.9952794415852867099914963806871 absolute error = 3.29832620e-23 relative error = 1.6530647944627837946264157220093e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6681 y[1] (analytic) = 1.9952697315415912935154730384112 y[1] (numeric) = 1.9952697315415912935154400067677 absolute error = 3.30316435e-23 relative error = 1.6554976491563871104410431926482e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6682 y[1] (analytic) = 1.9952600115451985699174182044672 y[1] (numeric) = 1.9952600115451985699173851244426 absolute error = 3.30800246e-23 relative error = 1.6579305157517631689706084748260e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6683 y[1] (analytic) = 1.9952502815962057391612110981278 y[1] (numeric) = 1.9952502815962057391611779697225 absolute error = 3.31284053e-23 relative error = 1.6603633942854118636928279359073e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6684 y[1] (analytic) = 1.9952405416947101007366989440466 y[1] (numeric) = 1.9952405416947101007366657672613 absolute error = 3.31767853e-23 relative error = 1.6627962697580525133945622381572e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6685 y[1] (analytic) = 1.9952307918408090536587569606232 y[1] (numeric) = 1.9952307918408090536587237354582 absolute error = 3.32251650e-23 relative error = 1.6652291622537716961087343067418e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6686 y[1] (analytic) = 1.9952210320346000964663143698545 y[1] (numeric) = 1.9952210320346000964662810963102 absolute error = 3.32735443e-23 relative error = 1.6676620667971681303004652691305e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6687 y[1] (analytic) = 1.9952112622761808272213794119464 y[1] (numeric) = 1.9952112622761808272213460900234 absolute error = 3.33219230e-23 relative error = 1.6700949734007424566691902036773e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6688 y[1] (analytic) = 1.9952014825656489435080633646949 y[1] (numeric) = 1.9952014825656489435080299943937 absolute error = 3.33703012e-23 relative error = 1.6725278871128747325513609156232e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6689 y[1] (analytic) = 1.9951916929031022424316035676453 y[1] (numeric) = 1.9951916929031022424315701489664 absolute error = 3.34186789e-23 relative error = 1.6749608079699938617914253094755e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.669 y[1] (analytic) = 1.9951818932886386206173854510412 y[1] (numeric) = 1.995181893288638620617351983985 absolute error = 3.34670562e-23 relative error = 1.6773937410206034705426113905303e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6691 y[1] (analytic) = 1.9951720837223560742099635695708 y[1] (numeric) = 1.9951720837223560742099300541378 absolute error = 3.35154330e-23 relative error = 1.6798266812891081301035065584933e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6692 y[1] (analytic) = 1.9951622642043526988720816409227 y[1] (numeric) = 1.9951622642043526988720480771134 absolute error = 3.35638093e-23 relative error = 1.6822596288119379269939591301622e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6693 y[1] (analytic) = 1.9951524347347266897836915891591 y[1] (numeric) = 1.9951524347347266897836579769739 absolute error = 3.36121852e-23 relative error = 1.6846925886376716772945705941175e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6694 y[1] (analytic) = 1.995142595313576341640971592917 y[1] (numeric) = 1.9951425953135763416409379323564 absolute error = 3.36605606e-23 relative error = 1.6871255557906412901410587082614e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6695 y[1] (analytic) = 1.9951327459410000486553431384473 y[1] (numeric) = 1.9951327459410000486553094295118 absolute error = 3.37089355e-23 relative error = 1.6895585303072780456895369708419e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6696 y[1] (analytic) = 1.9951228866170963045524870775016 y[1] (numeric) = 1.9951228866170963045524533201917 absolute error = 3.37573099e-23 relative error = 1.6919915122240135991665362221515e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6697 memory used=122.0MB, alloc=4.3MB, time=19.83 y[1] (analytic) = 1.9951130173419637025713586900759 y[1] (numeric) = 1.9951130173419637025713248843921 absolute error = 3.38056838e-23 relative error = 1.6944245015772799820858490918170e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6698 y[1] (analytic) = 1.9951031381157009354632017520222 y[1] (numeric) = 1.9951031381157009354631678979649 absolute error = 3.38540573e-23 relative error = 1.6968575034157818058161166517081e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6699 y[1] (analytic) = 1.9950932489384067954905616075364 y[1] (numeric) = 1.9950932489384067954905277051062 absolute error = 3.39024302e-23 relative error = 1.6992905077514322979721943690556e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.67 y[1] (analytic) = 1.9950833498101801744262972465342 y[1] (numeric) = 1.9950833498101801744262632957316 absolute error = 3.39508026e-23 relative error = 1.7017235196329120092508350043056e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6701 y[1] (analytic) = 1.9950734407311200635525923869232 y[1] (numeric) = 1.9950734407311200635525583877485 absolute error = 3.39991747e-23 relative error = 1.7041565491213481121290619950539e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6702 y[1] (analytic) = 1.9950635217013255536599655617814 y[1] (numeric) = 1.9950635217013255536599315142352 absolute error = 3.40475462e-23 relative error = 1.7065895812162088632982496173295e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6703 y[1] (analytic) = 1.9950535927208958350462792114536 y[1] (numeric) = 1.9950535927208958350462451155364 absolute error = 3.40959172e-23 relative error = 1.7090226209662505700476210912893e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6704 y[1] (analytic) = 1.9950436537899301975157477805732 y[1] (numeric) = 1.9950436537899301975157136362854 absolute error = 3.41442878e-23 relative error = 1.7114556734203296562431818957913e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6705 y[1] (analytic) = 1.9950337049085280303779448200206 y[1] (numeric) = 1.9950337049085280303779106273628 absolute error = 3.41926578e-23 relative error = 1.7138887285900629822778723512096e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6706 y[1] (analytic) = 1.9950237460767888224468090938291 y[1] (numeric) = 1.9950237460767888224467748528016 absolute error = 3.42410275e-23 relative error = 1.7163218015492261062637241228201e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6707 y[1] (analytic) = 1.9950137772948121620396496910454 y[1] (numeric) = 1.9950137772948121620396154016488 absolute error = 3.42893966e-23 relative error = 1.7187548772969151072724164157123e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6708 y[1] (analytic) = 1.995003798562697736976150142558 y[1] (numeric) = 1.9950037985626977369761158047928 absolute error = 3.43377652e-23 relative error = 1.7211879608820130323887718384024e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6709 y[1] (analytic) = 1.9949938098805453345773715429011 y[1] (numeric) = 1.9949938098805453345773371567677 absolute error = 3.43861334e-23 relative error = 1.7236210573535035563451496934680e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.671 y[1] (analytic) = 1.9949838112484548416647546770444 y[1] (numeric) = 1.9949838112484548416647202425434 absolute error = 3.44345010e-23 relative error = 1.7260541567227552242962317432821e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6711 y[1] (analytic) = 1.9949738026665262445591211521802 y[1] (numeric) = 1.994973802666526244559086669312 absolute error = 3.44828682e-23 relative error = 1.7284872690513245505722031585262e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6712 y[1] (analytic) = 1.9949637841348596290796735345153 y[1] (numeric) = 1.9949637841348596290796390032804 absolute error = 3.45312349e-23 relative error = 1.7309203893631027029832276282573e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6713 y[1] (analytic) = 1.9949537556535551805429944910804 y[1] (numeric) = 1.9949537556535551805429599114793 absolute error = 3.45796011e-23 relative error = 1.7333535176945281264418673575244e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6714 y[1] (analytic) = 1.9949437172227131837620449365647 y[1] (numeric) = 1.9949437172227131837620103085979 absolute error = 3.46279668e-23 relative error = 1.7357866540820396628451456071107e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6715 y[1] (analytic) = 1.9949336688424340230451611851875 y[1] (numeric) = 1.9949336688424340230451265088554 absolute error = 3.46763321e-23 relative error = 1.7382198035747745463072373347656e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6716 y[1] (analytic) = 1.9949236105128181821950511076152 y[1] (numeric) = 1.9949236105128181821950163829184 absolute error = 3.47246968e-23 relative error = 1.7406529561838017021500792534996e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6717 y[1] (analytic) = 1.9949135422339662445077892929356 y[1] (numeric) = 1.9949135422339662445077545198745 absolute error = 3.47730611e-23 relative error = 1.7430861219709824829034134062156e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6718 y[1] (analytic) = 1.9949034640059788927718112156974 y[1] (numeric) = 1.9949034640059788927717763942726 absolute error = 3.48214248e-23 relative error = 1.7455192909472855210442896078941e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6719 y[1] (analytic) = 1.9948933758289569092669064080274 y[1] (numeric) = 1.9948933758289569092668715382393 absolute error = 3.48697881e-23 relative error = 1.7479524731746741703885186177507e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.3MB, time=20.44 NO POLE x[1] = 1.672 y[1] (analytic) = 1.9948832777030011757632106368326 y[1] (numeric) = 1.9948832777030011757631757186818 absolute error = 3.49181508e-23 relative error = 1.7503856586640165733968075493727e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6721 y[1] (analytic) = 1.9948731696282126735201970861006 y[1] (numeric) = 1.9948731696282126735201621195875 absolute error = 3.49665131e-23 relative error = 1.7528188574773782920870589362135e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6722 y[1] (analytic) = 1.9948630516046924832856665443048 y[1] (numeric) = 1.9948630516046924832856315294299 absolute error = 3.50148749e-23 relative error = 1.7552520646384022229511489763724e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6723 y[1] (analytic) = 1.994852923632541785294736596928 y[1] (numeric) = 1.9948529236325417852947015336917 absolute error = 3.50632363e-23 relative error = 1.7576852851964318031658521284205e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6724 y[1] (analytic) = 1.9948427857118618592688298241114 y[1] (numeric) = 1.9948427857118618592687947125144 absolute error = 3.51115970e-23 relative error = 1.7601185041492073116442976842763e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6725 y[1] (analytic) = 1.994832637842754084414661003442 y[1] (numeric) = 1.9948326378427540844146258434847 absolute error = 3.51599573e-23 relative error = 1.7625517365718747888181352681977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6726 y[1] (analytic) = 1.9948224800253199394232233178855 y[1] (numeric) = 1.9948224800253199394231881095684 absolute error = 3.52083171e-23 relative error = 1.7649849774879771192908881034445e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6727 y[1] (analytic) = 1.9948123122596610024687735688777 y[1] (numeric) = 1.9948123122596610024687383122013 absolute error = 3.52566764e-23 relative error = 1.7674182269339584923379728970280e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6728 y[1] (analytic) = 1.9948021345458789512078163945826 y[1] (numeric) = 1.9948021345458789512077810895474 absolute error = 3.53050352e-23 relative error = 1.7698514849462635112680991490012e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6729 y[1] (analytic) = 1.9947919468840755627780874933284 y[1] (numeric) = 1.9947919468840755627780521399348 absolute error = 3.53533936e-23 relative error = 1.7722847565743913207219602412700e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.673 y[1] (analytic) = 1.9947817492743527137975358522306 y[1] (numeric) = 1.9947817492743527137975004504792 absolute error = 3.54017514e-23 relative error = 1.7747180318287047310168533368640e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6731 y[1] (analytic) = 1.9947715417168123803633049810138 y[1] (numeric) = 1.994771541716812380363269530905 absolute error = 3.54501088e-23 relative error = 1.7771513207717835250045741893533e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6732 y[1] (analytic) = 1.9947613242115566380507131510407 y[1] (numeric) = 1.9947613242115566380506776525751 absolute error = 3.54984656e-23 relative error = 1.7795846134138888397955421915215e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6733 y[1] (analytic) = 1.9947510967586876619122326395603 y[1] (numeric) = 1.9947510967586876619121970927383 absolute error = 3.55468220e-23 relative error = 1.7820179198177039081209788014665e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6734 y[1] (analytic) = 1.9947408593583077264764679791834 y[1] (numeric) = 1.9947408593583077264764323840056 absolute error = 3.55951778e-23 relative error = 1.7844512299933879966575308819980e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6735 y[1] (analytic) = 1.994730612010519205747133212598 y[1] (numeric) = 1.9947306120105192057470975690647 absolute error = 3.56435333e-23 relative error = 1.7868845590169362647136862848924e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6736 y[1] (analytic) = 1.9947203547154245732020281525323 y[1] (numeric) = 1.9947203547154245732019924606442 absolute error = 3.56918881e-23 relative error = 1.7893178868720151508825650996754e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6737 y[1] (analytic) = 1.9947100874731264017920136469785 y[1] (numeric) = 1.994710087473126401791977906736 absolute error = 3.57402425e-23 relative error = 1.7917512286346979245458870545975e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6738 y[1] (analytic) = 1.9946998102837273639399858496841 y[1] (numeric) = 1.9946998102837273639399500610878 absolute error = 3.57885963e-23 relative error = 1.7941845743149395198006443721298e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6739 y[1] (analytic) = 1.9946895231473302315398494959246 y[1] (numeric) = 1.9946895231473302315398136589749 absolute error = 3.58369497e-23 relative error = 1.7966179339757347609022905382030e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.674 y[1] (analytic) = 1.9946792260640378759554901835647 y[1] (numeric) = 1.9946792260640378759554542982621 absolute error = 3.58853026e-23 relative error = 1.7990513026402735373171019999631e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6741 y[1] (analytic) = 1.9946689190339532680197456594205 y[1] (numeric) = 1.9946689190339532680197097257655 absolute error = 3.59336550e-23 relative error = 1.8014846803450060214302563036745e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.3MB, time=21.05 NO POLE x[1] = 1.6742 y[1] (analytic) = 1.9946586020571794780333761109321 y[1] (numeric) = 1.9946586020571794780333401289253 absolute error = 3.59820068e-23 relative error = 1.8039180621129935631929256241143e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6743 y[1] (analytic) = 1.9946482751338196757640334631569 y[1] (numeric) = 1.9946482751338196757639974327987 absolute error = 3.60303582e-23 relative error = 1.8063514580074397495335639086522e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6744 y[1] (analytic) = 1.9946379382639771304452296810936 y[1] (numeric) = 1.9946379382639771304451936023845 absolute error = 3.60787091e-23 relative error = 1.8087848630514327268645960340853e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6745 y[1] (analytic) = 1.9946275914477552107753040773482 y[1] (numeric) = 1.9946275914477552107752679502888 absolute error = 3.61270594e-23 relative error = 1.8112182722679572022126804798597e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6746 y[1] (analytic) = 1.9946172346852573849163896251516 y[1] (numeric) = 1.9946172346852573849163534497423 absolute error = 3.61754093e-23 relative error = 1.8136516957203738779294438821195e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6747 y[1] (analytic) = 1.9946068679765872204933782767388 y[1] (numeric) = 1.9946068679765872204933420529801 absolute error = 3.62237587e-23 relative error = 1.8160851284316943406199211250022e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6748 y[1] (analytic) = 1.9945964913218483845928852871009 y[1] (numeric) = 1.9945964913218483845928490149934 absolute error = 3.62721075e-23 relative error = 1.8185185654248264379233024709626e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6749 y[1] (analytic) = 1.9945861047211446437622125431201 y[1] (numeric) = 1.9945861047211446437621762226643 absolute error = 3.63204558e-23 relative error = 1.8209520117497169779633971022592e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.675 y[1] (analytic) = 1.9945757081745798640083108980974 y[1] (numeric) = 1.9945757081745798640082745292937 absolute error = 3.63688037e-23 relative error = 1.8233854724564175892308766153343e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6751 y[1] (analytic) = 1.9945653016822580107967415116836 y[1] (numeric) = 1.9945653016822580107967050945326 absolute error = 3.64171510e-23 relative error = 1.8258189375542136755487666885055e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6752 y[1] (analytic) = 1.9945548852442831490506361952253 y[1] (numeric) = 1.9945548852442831490505997297274 absolute error = 3.64654979e-23 relative error = 1.8282524171067815676025972998467e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6753 y[1] (analytic) = 1.9945444588607594431496567625336 y[1] (numeric) = 1.9945444588607594431496202486894 absolute error = 3.65138442e-23 relative error = 1.8306859011233029247258715027422e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6754 y[1] (analytic) = 1.9945340225317911569289533860891 y[1] (numeric) = 1.9945340225317911569289168238991 absolute error = 3.65621900e-23 relative error = 1.8331193946538573089971199964921e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6755 y[1] (analytic) = 1.9945235762574826536781219586906 y[1] (numeric) = 1.9945235762574826536780853481554 absolute error = 3.66105352e-23 relative error = 1.8355528927211723117859998868216e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6756 y[1] (analytic) = 1.9945131200379383961401604605608 y[1] (numeric) = 1.9945131200379383961401238016808 absolute error = 3.66588800e-23 relative error = 1.8379864053891356421120546034954e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6757 y[1] (analytic) = 1.9945026538732629465104243319163 y[1] (numeric) = 1.994502653873262946510387624692 absolute error = 3.67072243e-23 relative error = 1.8404199276805020480146850537982e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6758 y[1] (analytic) = 1.9944921777635609664355808510156 y[1] (numeric) = 1.9944921777635609664355440954475 absolute error = 3.67555681e-23 relative error = 1.8428534596317291202714219672930e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6759 y[1] (analytic) = 1.9944816917089372170125625176929 y[1] (numeric) = 1.9944816917089372170125257137816 absolute error = 3.68039113e-23 relative error = 1.8452869962654409607604201574301e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.676 y[1] (analytic) = 1.99447119570949655878751944239 y[1] (numeric) = 1.9944711957094965587874825901359 absolute error = 3.68522541e-23 relative error = 1.8477205476457375609500132899940e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6761 y[1] (analytic) = 1.9944606897653439517547707406953 y[1] (numeric) = 1.9944606897653439517547338400989 absolute error = 3.69005964e-23 relative error = 1.8501541087952702902430090457685e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6762 y[1] (analytic) = 1.9944501738765844553557549334016 y[1] (numeric) = 1.9944501738765844553557179844635 absolute error = 3.69489381e-23 relative error = 1.8525876747365853807881746617965e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6763 y[1] (analytic) = 1.994439648043323228477979352093 y[1] (numeric) = 1.9944396480433232284779423548136 absolute error = 3.69972794e-23 relative error = 1.8550212555339425795024081300506e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.3MB, time=21.66 NO POLE x[1] = 1.6764 y[1] (analytic) = 1.9944291122656655294539685502699 y[1] (numeric) = 1.9944291122656655294539315046498 absolute error = 3.70456201e-23 relative error = 1.8574548411959493480241783807007e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6765 y[1] (analytic) = 1.9944185665437167160602117200253 y[1] (numeric) = 1.994418566543716716060174626065 absolute error = 3.70939603e-23 relative error = 1.8598884367729795626659017136420e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6766 y[1] (analytic) = 1.9944080108775822455161091142807 y[1] (numeric) = 1.9944080108775822455160719719807 absolute error = 3.71423000e-23 relative error = 1.8623220423014943869198099587027e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6767 y[1] (analytic) = 1.9943974452673676744829174745926 y[1] (numeric) = 1.9943974452673676744828802839534 absolute error = 3.71906392e-23 relative error = 1.8647556578179554458315856115663e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6768 y[1] (analytic) = 1.9943868697131786590626944645411 y[1] (numeric) = 1.9943868697131786590626572255633 absolute error = 3.72389778e-23 relative error = 1.8671892783447525066180373230489e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6769 y[1] (analytic) = 1.9943762842151209547972421087104 y[1] (numeric) = 1.9943762842151209547972048213944 absolute error = 3.72873160e-23 relative error = 1.8696229139464661492339698232393e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.677 y[1] (analytic) = 1.994365688773300416667049237271 y[1] (numeric) = 1.9943656887733004166670119016174 absolute error = 3.73356536e-23 relative error = 1.8720565546313880858740821706521e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6771 y[1] (analytic) = 1.9943550833878229990902329361766 y[1] (numeric) = 1.9943550833878229990901955521858 absolute error = 3.73839908e-23 relative error = 1.8744902104642062803680229006986e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6772 y[1] (analytic) = 1.9943444680587947559214790029829 y[1] (numeric) = 1.9943444680587947559214415706555 absolute error = 3.74323274e-23 relative error = 1.8769238714531068256232238574631e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6773 y[1] (analytic) = 1.9943338427863218404509814083024 y[1] (numeric) = 1.9943338427863218404509439276388 absolute error = 3.74806636e-23 relative error = 1.8793575476628852764843555395763e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6774 y[1] (analytic) = 1.9943232075705105054033807629026 y[1] (numeric) = 1.9943232075705105054033432339035 absolute error = 3.75289991e-23 relative error = 1.8817912240873895309799986973491e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6775 y[1] (analytic) = 1.9943125624114671029367017904613 y[1] (numeric) = 1.9943125624114671029366642131271 absolute error = 3.75773342e-23 relative error = 1.8842249158057017907969618639937e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6776 y[1] (analytic) = 1.9943019073092980846412898059866 y[1] (numeric) = 1.9943019073092980846412521803178 absolute error = 3.76256688e-23 relative error = 1.8866586178400821752461371064598e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6777 y[1] (analytic) = 1.9942912422641100015387461999144 y[1] (numeric) = 1.9942912422641100015387085259117 absolute error = 3.76740027e-23 relative error = 1.8890923201983714194165700976513e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6778 y[1] (analytic) = 1.9942805672760095040808629278939 y[1] (numeric) = 1.9942805672760095040808252055576 absolute error = 3.77223363e-23 relative error = 1.8915260429742335421967960144174e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6779 y[1] (analytic) = 1.9942698823451033421485560062695 y[1] (numeric) = 1.9942698823451033421485182356003 absolute error = 3.77706692e-23 relative error = 1.8939597661468309507408140646515e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.678 y[1] (analytic) = 1.9942591874714983650507980132736 y[1] (numeric) = 1.9942591874714983650507601942719 absolute error = 3.78190017e-23 relative error = 1.8963935047956499964193963846824e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6781 y[1] (analytic) = 1.994248482655301521523549595937 y[1] (numeric) = 1.9942484826553015215235117286034 absolute error = 3.78673336e-23 relative error = 1.8988272489283988907992280712359e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6782 y[1] (analytic) = 1.9942377678966198597286899827307 y[1] (numeric) = 1.9942377678966198597286520670656 absolute error = 3.79156651e-23 relative error = 1.9012610086103597601519857257735e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6783 y[1] (analytic) = 1.9942270431955605272529465019475 y[1] (numeric) = 1.9942270431955605272529085379515 absolute error = 3.79639960e-23 relative error = 1.9036947738491341110037211449737e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6784 y[1] (analytic) = 1.9942163085522307711068231058361 y[1] (numeric) = 1.9942163085522307711067850935097 absolute error = 3.80123264e-23 relative error = 1.9061285496956116363144604266069e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6785 y[1] (analytic) = 1.9942055639667379377235279004967 y[1] (numeric) = 1.9942055639667379377234898398404 absolute error = 3.80606563e-23 relative error = 1.9085623361862622499857575036962e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.3MB, time=22.26 NO POLE x[1] = 1.6786 y[1] (analytic) = 1.9941948094391894729578996815498 y[1] (numeric) = 1.9941948094391894729578615725642 absolute error = 3.81089856e-23 relative error = 1.9109961283430011263099474438848e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6787 y[1] (analytic) = 1.9941840449696929220853334755888 y[1] (numeric) = 1.9941840449696929220852953182744 absolute error = 3.81573144e-23 relative error = 1.9134299312168002377181001733411e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6788 y[1] (analytic) = 1.994173270558355929800705087427 y[1] (numeric) = 1.9941732705583559298006668817843 absolute error = 3.82056427e-23 relative error = 1.9158637448441308800494023746286e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6789 y[1] (analytic) = 1.9941624862052862402172946531495 y[1] (numeric) = 1.994162486205286240217256399179 absolute error = 3.82539705e-23 relative error = 1.9182975692614648375189314947645e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.679 y[1] (analytic) = 1.9941516919105916968657091989816 y[1] (numeric) = 1.9941516919105916968656708966838 absolute error = 3.83022978e-23 relative error = 1.9207314045052743839376687177665e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6791 y[1] (analytic) = 1.9941408876743802426928042059833 y[1] (numeric) = 1.9941408876743802426927658553588 absolute error = 3.83506245e-23 relative error = 1.9231652455973414655409442276588e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6792 y[1] (analytic) = 1.9941300734967599200606041805819 y[1] (numeric) = 1.9941300734967599200605657816313 absolute error = 3.83989506e-23 relative error = 1.9255990925740577549096212443816e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6793 y[1] (analytic) = 1.9941192493778388707452222309527 y[1] (numeric) = 1.9941192493778388707451837836764 absolute error = 3.84472763e-23 relative error = 1.9280329555013057322600536905751e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6794 y[1] (analytic) = 1.9941084153177253359357786492585 y[1] (numeric) = 1.9941084153177253359357401536571 absolute error = 3.84956014e-23 relative error = 1.9304668243860962693490522961945e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6795 y[1] (analytic) = 1.9940975713165276562333184997595 y[1] (numeric) = 1.9940975713165276562332799558335 absolute error = 3.85439260e-23 relative error = 1.9329007042796219675765507451843e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6796 y[1] (analytic) = 1.9940867173743542716497282128036 y[1] (numeric) = 1.9940867173743542716496896205536 absolute error = 3.85922500e-23 relative error = 1.9353345902035308673518594909013e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6797 y[1] (analytic) = 1.9940758534913137216066511847088 y[1] (numeric) = 1.9940758534913137216066125441352 absolute error = 3.86405736e-23 relative error = 1.9377684922239253204944928110830e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6798 y[1] (analytic) = 1.994064979667514644934402383547 y[1] (numeric) = 1.9940649796675146449343636946504 absolute error = 3.86888966e-23 relative error = 1.9402024003475999483119635073836e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6799 y[1] (analytic) = 1.9940540959030657798708819608426 y[1] (numeric) = 1.9940540959030657798708432236234 absolute error = 3.87372192e-23 relative error = 1.9426363246407673872472258946769e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.68 y[1] (analytic) = 1.9940432021980759640604878691936 y[1] (numeric) = 1.9940432021980759640604490836524 absolute error = 3.87855412e-23 relative error = 1.9450702551101138750822737254214e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6801 y[1] (analytic) = 1.9940322985526541345530274858291 y[1] (numeric) = 1.9940322985526541345529886519665 absolute error = 3.88338626e-23 relative error = 1.9475041917920347328028985565692e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6802 y[1] (analytic) = 1.994021384966909327802628242112 y[1] (numeric) = 1.9940213849669093278025893599284 absolute error = 3.88821836e-23 relative error = 1.9499381447529083365137379056807e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6803 y[1] (analytic) = 1.9940104614409506796666472589982 y[1] (numeric) = 1.9940104614409506796666083284943 absolute error = 3.89305039e-23 relative error = 1.9523720989842390781673542382942e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6804 y[1] (analytic) = 1.9939995279748874254045799884649 y[1] (numeric) = 1.9939995279748874254045410096411 absolute error = 3.89788238e-23 relative error = 1.9548060695674799644393863372526e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6805 y[1] (analytic) = 1.9939885845688288996769678609153 y[1] (numeric) = 1.9939885845688288996769288337722 absolute error = 3.90271431e-23 relative error = 1.9572400465090452583757432307115e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6806 y[1] (analytic) = 1.9939776312228845365443049385752 y[1] (numeric) = 1.9939776312228845365442658631133 absolute error = 3.90754619e-23 relative error = 1.9596740348604336780356911434881e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6807 y[1] (analytic) = 1.9939666679371638694659435748884 y[1] (numeric) = 1.9939666679371638694659044511082 absolute error = 3.91237802e-23 relative error = 1.9621080346581256274980514820512e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=141.1MB, alloc=4.3MB, time=22.87 x[1] = 1.6808 y[1] (analytic) = 1.9939556947117765312989990799242 y[1] (numeric) = 1.9939556947117765312989599078262 absolute error = 3.91720980e-23 relative error = 1.9645420459386020223931730698242e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6809 y[1] (analytic) = 1.9939447115468322542972533918071 y[1] (numeric) = 1.9939447115468322542972141713919 absolute error = 3.92204152e-23 relative error = 1.9669760637231600976550479815442e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.681 y[1] (analytic) = 1.9939337184424408701100577541801 y[1] (numeric) = 1.9939337184424408701100184854483 absolute error = 3.92687318e-23 relative error = 1.9694100880481988454143937845539e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6811 y[1] (analytic) = 1.993922715398712309781234399712 y[1] (numeric) = 1.9939227153987123097811950826641 absolute error = 3.93170479e-23 relative error = 1.9718441239653571401363055127916e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6812 y[1] (analytic) = 1.9939117024157566037479772396599 y[1] (numeric) = 1.9939117024157566037479378742964 absolute error = 3.93653635e-23 relative error = 1.9742781715111178040314099866873e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6813 y[1] (analytic) = 1.9939006794936838818397515594984 y[1] (numeric) = 1.9939006794936838818397121458199 absolute error = 3.94136785e-23 relative error = 1.9767122257066692313078029660914e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6814 y[1] (analytic) = 1.993889646632604373277192720626 y[1] (numeric) = 1.993889646632604373277153258633 absolute error = 3.94619930e-23 relative error = 1.9791462916037347237301112328209e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6815 y[1] (analytic) = 1.9938786038326284066710038681592 y[1] (numeric) = 1.9938786038326284066709643578522 absolute error = 3.95103070e-23 relative error = 1.9815803692387985842035537449679e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6816 y[1] (analytic) = 1.9938675510938664100208526448269 y[1] (numeric) = 1.9938675510938664100208130862064 absolute error = 3.95586205e-23 relative error = 1.9840144586483456369450762949816e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6817 y[1] (analytic) = 1.9938564884164289107142669109741 y[1] (numeric) = 1.9938564884164289107142273040408 absolute error = 3.96069333e-23 relative error = 1.9864485498380490232158605084289e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6818 y[1] (analytic) = 1.9938454158004265355255294706882 y[1] (numeric) = 1.9938454158004265355254898154426 absolute error = 3.96552456e-23 relative error = 1.9888826528750954088345726372602e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6819 y[1] (analytic) = 1.9938343332459700106145718040566 y[1] (numeric) = 1.9938343332459700106145321004991 absolute error = 3.97035575e-23 relative error = 1.9913167728114328705636733496846e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.682 y[1] (analytic) = 1.9938232407531701615258668055684 y[1] (numeric) = 1.9938232407531701615258270536996 absolute error = 3.97518688e-23 relative error = 1.9937508996526524150988778321911e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6821 y[1] (analytic) = 1.9938121383221379131873205286706 y[1] (numeric) = 1.9938121383221379131872807284911 absolute error = 3.98001795e-23 relative error = 1.9961850334351576301786144830867e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6822 y[1] (analytic) = 1.9938010259529842899091629364901 y[1] (numeric) = 1.9938010259529842899091230880005 absolute error = 3.98484896e-23 relative error = 1.9986191741953524803111205101870e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6823 y[1] (analytic) = 1.9937899036458204153828376587324 y[1] (numeric) = 1.9937899036458204153827977619331 absolute error = 3.98967993e-23 relative error = 2.0010533320007885033030179889760e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6824 y[1] (analytic) = 1.9937787714007575126798907547676 y[1] (numeric) = 1.9937787714007575126798508096592 absolute error = 3.99451084e-23 relative error = 2.0034874968568352431687087420334e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6825 y[1] (analytic) = 1.9937676292179069042508584829163 y[1] (numeric) = 1.9937676292179069042508184894994 absolute error = 3.99934169e-23 relative error = 2.0059216687998979538964610076265e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6826 y[1] (analytic) = 1.9937564770973800119241540759452 y[1] (numeric) = 1.9937564770973800119241140342203 absolute error = 4.00417249e-23 relative error = 2.0083558528820399579313328143259e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6827 y[1] (analytic) = 1.9937453150392883569049535227837 y[1] (numeric) = 1.9937453150392883569049134327512 absolute error = 4.00900325e-23 relative error = 2.0107900541554372819636746620489e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6828 y[1] (analytic) = 1.9937341430437435597740803564729 y[1] (numeric) = 1.9937341430437435597740402181335 absolute error = 4.01383394e-23 relative error = 2.0132242576095234199681503183880e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6829 y[1] (analytic) = 1.9937229611108573404868894483589 y[1] (numeric) = 1.993722961110857340486849261713 absolute error = 4.01866459e-23 relative error = 2.0156584783278470061030331828452e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=144.9MB, alloc=4.3MB, time=23.49 x[1] = 1.683 y[1] (analytic) = 1.9937117692407415183721498085394 y[1] (numeric) = 1.9937117692407415183721095735876 absolute error = 4.02349518e-23 relative error = 2.0180927063154439841528863514177e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6831 y[1] (analytic) = 1.9937005674335080121309263925776 y[1] (numeric) = 1.9937005674335080121308861093205 absolute error = 4.02832571e-23 relative error = 2.0205269416087222199632460880936e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6832 y[1] (analytic) = 1.9936893556892688398354609144922 y[1] (numeric) = 1.9936893556892688398354205829303 absolute error = 4.03315619e-23 relative error = 2.0229611892599165169574038619264e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6833 y[1] (analytic) = 1.9936781340081361189280516660358 y[1] (numeric) = 1.9936781340081361189280112861697 absolute error = 4.03798661e-23 relative error = 2.0253954442896654359298526767001e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6834 y[1] (analytic) = 1.9936669023902220662199323422731 y[1] (numeric) = 1.9936669023902220662198919141034 absolute error = 4.04281697e-23 relative error = 2.0278297067343780891518013131428e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6835 y[1] (analytic) = 1.9936556608356389978901498734695 y[1] (numeric) = 1.9936556608356389978901093969966 absolute error = 4.04764729e-23 relative error = 2.0302639866622866241269900123329e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6836 y[1] (analytic) = 1.9936444093444993294844412633012 y[1] (numeric) = 1.9936444093444993294844007385257 absolute error = 4.05247755e-23 relative error = 2.0326982740780915296795620560538e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6837 y[1] (analytic) = 1.9936331479169155759141094333992 y[1] (numeric) = 1.9936331479169155759140688603216 absolute error = 4.05730776e-23 relative error = 2.0351325740341712144585916373227e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6838 y[1] (analytic) = 1.9936218765530003514548980742369 y[1] (numeric) = 1.9936218765530003514548574528579 absolute error = 4.06213790e-23 relative error = 2.0375668765350289530848176130689e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6839 y[1] (analytic) = 1.993610595252866369745865502374 y[1] (numeric) = 1.993610595252866369745824832694 absolute error = 4.06696800e-23 relative error = 2.0400011966650650264637480922974e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.684 y[1] (analytic) = 1.9935993040166264437882575240663 y[1] (numeric) = 1.9935993040166264437882168060859 absolute error = 4.07179804e-23 relative error = 2.0424355244287552984428334365621e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6841 y[1] (analytic) = 1.9935880028443934859443793052545 y[1] (numeric) = 1.9935880028443934859443385389743 absolute error = 4.07662802e-23 relative error = 2.0448698598625119588415837228874e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6842 y[1] (analytic) = 1.9935766917362805079364662479423 y[1] (numeric) = 1.9935766917362805079364254333628 absolute error = 4.08145795e-23 relative error = 2.0473042080188576090346206620948e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6843 y[1] (analytic) = 1.9935653706924006208455538729744 y[1] (numeric) = 1.9935653706924006208455130100962 absolute error = 4.08628782e-23 relative error = 2.0497385639181522027401576524488e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6844 y[1] (analytic) = 1.9935540397128670351103467092278 y[1] (numeric) = 1.9935540397128670351103057980514 absolute error = 4.09111764e-23 relative error = 2.0521729326129762193993289138379e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6845 y[1] (analytic) = 1.9935426987977930605260861892251 y[1] (numeric) = 1.993542698797793060526045229751 absolute error = 4.09594741e-23 relative error = 2.0546073141398291448448845345008e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6846 y[1] (analytic) = 1.9935313479472921062434175511833 y[1] (numeric) = 1.9935313479472921062433765434121 absolute error = 4.10077712e-23 relative error = 2.0570417035189869186656693272846e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6847 y[1] (analytic) = 1.9935199871614776807672557475083 y[1] (numeric) = 1.9935199871614776807672146914405 absolute error = 4.10560678e-23 relative error = 2.0594761058031170744611818326425e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6848 y[1] (analytic) = 1.9935086164404633919556503597466 y[1] (numeric) = 1.9935086164404633919556092553828 absolute error = 4.11043638e-23 relative error = 2.0619105160124393965539477853048e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6849 y[1] (analytic) = 1.9934972357843629470186495200058 y[1] (numeric) = 1.9934972357843629470186083673466 absolute error = 4.11526592e-23 relative error = 2.0643449341833696216593508959726e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.685 y[1] (analytic) = 1.9934858451932901525171628388552 y[1] (numeric) = 1.9934858451932901525171216379011 absolute error = 4.12009541e-23 relative error = 2.0667793653686625004596238832928e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6851 y[1] (analytic) = 1.9934744446673589143618233397174 y[1] (numeric) = 1.9934744446673589143617820904689 absolute error = 4.12492485e-23 relative error = 2.0692138096048206567526151171287e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6852 memory used=148.7MB, alloc=4.3MB, time=24.12 y[1] (analytic) = 1.993463034206683237811848399763 y[1] (numeric) = 1.9934630342066832378118071022207 absolute error = 4.12975423e-23 relative error = 2.0716482619119512750497031665456e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6853 y[1] (analytic) = 1.9934516138113772274738996973195 y[1] (numeric) = 1.993451613811377227473858351484 absolute error = 4.13458355e-23 relative error = 2.0740827223264718947593683433994e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6854 y[1] (analytic) = 1.9934401834815550873009421658055 y[1] (numeric) = 1.9934401834815550873009007716774 absolute error = 4.13941281e-23 relative error = 2.0765171908848004710164722918324e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6855 y[1] (analytic) = 1.9934287432173311205911019542023 y[1] (numeric) = 1.993428743217331120591060511782 absolute error = 4.14424203e-23 relative error = 2.0789516776563199692160757645186e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6856 y[1] (analytic) = 1.9934172930188197299865233940729 y[1] (numeric) = 1.993417293018819729986481903361 absolute error = 4.14907119e-23 relative error = 2.0813861726445998450727522941121e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6857 y[1] (analytic) = 1.9934058328861354174722249731422 y[1] (numeric) = 1.9934058328861354174721834341394 absolute error = 4.15390028e-23 relative error = 2.0838206708695195088010490064345e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6858 y[1] (analytic) = 1.9933943628193927843749543154477 y[1] (numeric) = 1.9933943628193927843749127281544 absolute error = 4.15872933e-23 relative error = 2.0862551874171185967594278959318e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6859 y[1] (analytic) = 1.9933828828187065313620421680725 y[1] (numeric) = 1.9933828828187065313620005324893 absolute error = 4.16355832e-23 relative error = 2.0886897122907951662438432007888e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.686 y[1] (analytic) = 1.9933713928841914584402553944733 y[1] (numeric) = 1.9933713928841914584402137106008 absolute error = 4.16838725e-23 relative error = 2.0911242455269699202985901777414e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6861 y[1] (analytic) = 1.9933598930159624649546489744138 y[1] (numeric) = 1.9933598930159624649546072422525 absolute error = 4.17321613e-23 relative error = 2.0935587921787195510456424908976e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6862 y[1] (analytic) = 1.9933483832141345495874170105148 y[1] (numeric) = 1.9933483832141345495873752300653 absolute error = 4.17804495e-23 relative error = 2.0959933472658679798096291083404e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6863 y[1] (analytic) = 1.9933368634788228103567427414335 y[1] (numeric) = 1.9933368634788228103567009126963 absolute error = 4.18287372e-23 relative error = 2.0984279158415507855912792652185e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6864 y[1] (analytic) = 1.9933253338101424446156475616824 y[1] (numeric) = 1.9933253338101424446156056846581 absolute error = 4.18770243e-23 relative error = 2.1008624929255349629271899309811e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6865 y[1] (analytic) = 1.9933137942082087490508390481 y[1] (numeric) = 1.9933137942082087490507971227892 absolute error = 4.19253108e-23 relative error = 2.1032970785542435003045670042732e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6866 y[1] (analytic) = 1.9933022446731371196815579929852 y[1] (numeric) = 1.9933022446731371196815160193884 absolute error = 4.19735968e-23 relative error = 2.1057316777809004681963073581624e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6867 y[1] (analytic) = 1.993290685205043051858424443905 y[1] (numeric) = 1.9932906852050430518583824220228 absolute error = 4.20218822e-23 relative error = 2.1081662856251872520893121476601e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6868 y[1] (analytic) = 1.9932791158040421402622827501902 y[1] (numeric) = 1.9932791158040421402622406800231 absolute error = 4.20701671e-23 relative error = 2.1106009071403870748845565892576e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6869 y[1] (analytic) = 1.9932675364702500789030456161271 y[1] (numeric) = 1.9932675364702500789030034976757 absolute error = 4.21184514e-23 relative error = 2.1130355373461241541226033015595e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.687 y[1] (analytic) = 1.9932559472037826611185371608599 y[1] (numeric) = 1.9932559472037826611184949941248 absolute error = 4.21667351e-23 relative error = 2.1154701762788237942033845494340e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6871 y[1] (analytic) = 1.9932443480047557795733349850132 y[1] (numeric) = 1.9932443480047557795732927699949 absolute error = 4.22150183e-23 relative error = 2.1179048289918581078429893516750e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6872 y[1] (analytic) = 1.993232738873285426257611244047 y[1] (numeric) = 1.9932327388732854262575689807461 absolute error = 4.22633009e-23 relative error = 2.1203394905047653417699884023937e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6873 y[1] (analytic) = 1.9932211198094876924859727283565 y[1] (numeric) = 1.9932211198094876924859304167735 absolute error = 4.23115830e-23 relative error = 2.1227741658709770267090308126478e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6874 y[1] (analytic) = 1.9932094908134787688962999501263 y[1] (numeric) = 1.9932094908134787688962575902619 absolute error = 4.23598644e-23 relative error = 2.1252088450929398921566783374915e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.3MB, time=24.75 NO POLE x[1] = 1.6875 y[1] (analytic) = 1.9931978518853749454485852369532 y[1] (numeric) = 1.9931978518853749454485428288079 absolute error = 4.24081453e-23 relative error = 2.1276435382411205090124959460639e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6876 y[1] (analytic) = 1.9931862030252926114237698322469 y[1] (numeric) = 1.9931862030252926114237273758212 absolute error = 4.24564257e-23 relative error = 2.1300782453520348588516120305249e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6877 y[1] (analytic) = 1.9931745442333482554225800024214 y[1] (numeric) = 1.993174544233348255422537497716 absolute error = 4.25047054e-23 relative error = 2.1325129564279553742642461973499e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6878 y[1] (analytic) = 1.9931628755096584653643621508892 y[1] (numeric) = 1.9931628755096584653643195979046 absolute error = 4.25529846e-23 relative error = 2.1349476815395258859581971046160e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6879 y[1] (analytic) = 1.9931511968543399284859169388685 y[1] (numeric) = 1.9931511968543399284858743376052 absolute error = 4.26012633e-23 relative error = 2.1373824207232640145039105156047e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.688 y[1] (analytic) = 1.993139508267509431340332413016 y[1] (numeric) = 1.9931395082675094313402897634746 absolute error = 4.26495414e-23 relative error = 2.1398171689984777151629956281075e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6881 y[1] (analytic) = 1.9931278097492838597958161398973 y[1] (numeric) = 1.9931278097492838597957734420784 absolute error = 4.26978189e-23 relative error = 2.1422519264015974642049602798450e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6882 y[1] (analytic) = 1.9931161012997801990345263473058 y[1] (numeric) = 1.99311610129978019903448360121 absolute error = 4.27460958e-23 relative error = 2.1446866929690541877344639629378e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6883 y[1] (analytic) = 1.9931043829191155335514020724419 y[1] (numeric) = 1.9931043829191155335513592780697 absolute error = 4.27943722e-23 relative error = 2.1471214737545779481660827273062e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6884 y[1] (analytic) = 1.9930926546074070471529923169647 y[1] (numeric) = 1.9930926546074070471529494743167 absolute error = 4.28426480e-23 relative error = 2.1495562637773609380478778955581e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6885 y[1] (analytic) = 1.9930809163647720229562842089273 y[1] (numeric) = 1.9930809163647720229562413180041 absolute error = 4.28909232e-23 relative error = 2.1519910630738355163392234357430e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6886 y[1] (analytic) = 1.9930691681913278433875301716084 y[1] (numeric) = 1.9930691681913278433874872324105 absolute error = 4.29391979e-23 relative error = 2.1544258766978218305733766469282e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6887 y[1] (analytic) = 1.9930574100871919901810740992499 y[1] (numeric) = 1.993057410087191990181031111778 absolute error = 4.29874719e-23 relative error = 2.1568606946510080828479720723443e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6888 y[1] (analytic) = 1.9930456420524820443781765397155 y[1] (numeric) = 1.9930456420524820443781335039701 absolute error = 4.30357454e-23 relative error = 2.1592955270046323185639041114481e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6889 y[1] (analytic) = 1.9930338640873156863258388840783 y[1] (numeric) = 1.9930338640873156863257958000599 absolute error = 4.30840184e-23 relative error = 2.1617303737952176756193131761350e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.689 y[1] (analytic) = 1.9930220761918106956756265631518 y[1] (numeric) = 1.9930220761918106956755834308611 absolute error = 4.31322907e-23 relative error = 2.1641652250242761298099613677302e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6891 y[1] (analytic) = 1.9930102783660849513824912509758 y[1] (numeric) = 1.9930102783660849513824480704133 absolute error = 4.31805625e-23 relative error = 2.1666000907632250108785658957902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6892 y[1] (analytic) = 1.9929984706102564317035920752672 y[1] (numeric) = 1.9929984706102564317035488464335 absolute error = 4.32288337e-23 relative error = 2.1690349660310238278254098963149e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6893 y[1] (analytic) = 1.9929866529244432141971158348498 y[1] (numeric) = 1.9929866529244432141970725577455 absolute error = 4.32771043e-23 relative error = 2.1714698508641087635016692148517e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6894 y[1] (analytic) = 1.9929748253087634757210962240734 y[1] (numeric) = 1.992974825308763475721052898699 absolute error = 4.33253744e-23 relative error = 2.1739047503165413107542203138276e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6895 y[1] (analytic) = 1.9929629877633354924322320642341 y[1] (numeric) = 1.9929629877633354924321886905902 absolute error = 4.33736439e-23 relative error = 2.1763396594071933431178237218471e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6896 y[1] (analytic) = 1.9929511402882776397847045420086 y[1] (numeric) = 1.9929511402882776397846611200959 absolute error = 4.34219127e-23 relative error = 2.1787745731548180395571574175744e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.3MB, time=25.36 NO POLE x[1] = 1.6897 y[1] (analytic) = 1.9929392828837083925289934549136 y[1] (numeric) = 1.9929392828837083925289499847325 absolute error = 4.34701811e-23 relative error = 2.1812095066489069550641410726983e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6898 y[1] (analytic) = 1.9929274155497463247106924638014 y[1] (numeric) = 1.9929274155497463247106489453525 absolute error = 4.35184489e-23 relative error = 2.1836444498905894619336884313721e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6899 y[1] (analytic) = 1.9929155382865101096693233524054 y[1] (numeric) = 1.9929155382865101096692797856893 absolute error = 4.35667161e-23 relative error = 2.1860794029163047001767119685585e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.69 y[1] (analytic) = 1.9929036510941185200371492939456 y[1] (numeric) = 1.9929036510941185200371056789629 absolute error = 4.36149827e-23 relative error = 2.1885143657624922815771357084380e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6901 y[1] (analytic) = 1.9928917539726904277379871248072 y[1] (numeric) = 1.9928917539726904277379434615585 absolute error = 4.36632487e-23 relative error = 2.1909493384655922909103649177749e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6902 y[1] (analytic) = 1.9928798469223448039860186253034 y[1] (numeric) = 1.9928798469223448039859749137892 absolute error = 4.37115142e-23 relative error = 2.1933843260799092669914132529772e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6903 y[1] (analytic) = 1.9928679299432007192846008075342 y[1] (numeric) = 1.9928679299432007192845570477552 absolute error = 4.37597790e-23 relative error = 2.1958193186061862904672309881448e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6904 y[1] (analytic) = 1.9928560030353773434250752103544 y[1] (numeric) = 1.9928560030353773434250314023111 absolute error = 4.38080433e-23 relative error = 2.1982543261166228886680454021642e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6905 y[1] (analytic) = 1.9928440661989939454855762014608 y[1] (numeric) = 1.9928440661989939454855323451537 absolute error = 4.38563071e-23 relative error = 2.2006893486477512203528829409033e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6906 y[1] (analytic) = 1.9928321194341698938298382866117 y[1] (numeric) = 1.9928321194341698938297943820415 absolute error = 4.39045702e-23 relative error = 2.2031243762001357644172225182000e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6907 y[1] (analytic) = 1.9928201627410246561060024259912 y[1] (numeric) = 1.9928201627410246561059584731584 absolute error = 4.39528328e-23 relative error = 2.2055594188461578251174735613977e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6908 y[1] (analytic) = 1.992808196119677799245421357728 y[1] (numeric) = 1.9928081961196777992453773566332 absolute error = 4.40010948e-23 relative error = 2.2079944716043069108756011704545e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6909 y[1] (analytic) = 1.9927962195702489894614639285834 y[1] (numeric) = 1.9927962195702489894614198792272 absolute error = 4.40493562e-23 relative error = 2.2104295345110270864425564718277e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.691 y[1] (analytic) = 1.9927842330928579922483184318185 y[1] (numeric) = 1.9927842330928579922482743342015 absolute error = 4.40976170e-23 relative error = 2.2128646076027629005335694234278e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6911 y[1] (analytic) = 1.9927722366876246723797949522532 y[1] (numeric) = 1.9927722366876246723797508063759 absolute error = 4.41458773e-23 relative error = 2.2152996959340943328760121327259e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6912 y[1] (analytic) = 1.9927602303546689939081267185291 y[1] (numeric) = 1.9927602303546689939080825243921 absolute error = 4.41941370e-23 relative error = 2.2177347945233924262284892506749e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6913 y[1] (analytic) = 1.9927482140941110201627704625883 y[1] (numeric) = 1.9927482140941110201627262201922 absolute error = 4.42423961e-23 relative error = 2.2201699034071032646052482947153e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6914 y[1] (analytic) = 1.9927361879060709137492057863797 y[1] (numeric) = 1.9927361879060709137491614957252 absolute error = 4.42906545e-23 relative error = 2.2226050176034476965096005122382e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6915 y[1] (analytic) = 1.9927241517906689365477335358054 y[1] (numeric) = 1.992724151790668936547689196893 absolute error = 4.43389124e-23 relative error = 2.2250401471852939233278711598595e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6916 y[1] (analytic) = 1.9927121057480254497122731819185 y[1] (numeric) = 1.9927121057480254497122287947487 absolute error = 4.43871698e-23 relative error = 2.2274752921891804299734563021158e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6917 y[1] (analytic) = 1.9927000497782609136691592093848 y[1] (numeric) = 1.9927000497782609136691147739583 absolute error = 4.44354265e-23 relative error = 2.2299104426150128837227929715517e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6918 y[1] (analytic) = 1.9926879838814958881159365122209 y[1] (numeric) = 1.9926879838814958881158920285382 absolute error = 4.44836827e-23 relative error = 2.2323456085358429770898991521425e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.3MB, time=25.98 NO POLE x[1] = 1.6919 y[1] (analytic) = 1.9926759080578510320201547968193 y[1] (numeric) = 1.992675908057851032020110264881 absolute error = 4.45319383e-23 relative error = 2.2347807849698334513364746784078e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.692 y[1] (analytic) = 1.9926638223074471036181619922741 y[1] (numeric) = 1.9926638223074471036181174120809 absolute error = 4.45801932e-23 relative error = 2.2372159669350259477925728125421e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6921 y[1] (analytic) = 1.9926517266304049604138966680186 y[1] (numeric) = 1.9926517266304049604138520395711 absolute error = 4.46284475e-23 relative error = 2.2396511594862176128530115316211e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6922 y[1] (analytic) = 1.9926396210268455591776794587869 y[1] (numeric) = 1.9926396210268455591776347820856 absolute error = 4.46767013e-23 relative error = 2.2420863676783278905478629260029e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6923 y[1] (analytic) = 1.9926275054968899559450034969114 y[1] (numeric) = 1.9926275054968899559449587719569 absolute error = 4.47249545e-23 relative error = 2.2445215865293999180001267323691e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6924 y[1] (analytic) = 1.9926153800406593060153238519693 y[1] (numeric) = 1.9926153800406593060152790787622 absolute error = 4.47732071e-23 relative error = 2.2469568160758852996567520354828e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6925 y[1] (analytic) = 1.9926032446582748639508459777889 y[1] (numeric) = 1.9926032446582748639508011563297 absolute error = 4.48214592e-23 relative error = 2.2493920613727966744330509998829e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6926 y[1] (analytic) = 1.9925910993498579835753131668284 y[1] (numeric) = 1.9925910993498579835752682971178 absolute error = 4.48697106e-23 relative error = 2.2518273124194961773826022271346e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6927 y[1] (analytic) = 1.9925789441155301179727930119397 y[1] (numeric) = 1.9925789441155301179727480939783 absolute error = 4.49179614e-23 relative error = 2.2542625742709668916650075400851e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6928 y[1] (analytic) = 1.9925667789554128194864628755287 y[1] (numeric) = 1.992566778955412819486417909317 absolute error = 4.49662117e-23 relative error = 2.2566978519823148142985510214357e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6929 y[1] (analytic) = 1.9925546038696277397173943661243 y[1] (numeric) = 1.992554603869627739717349351663 absolute error = 4.50144613e-23 relative error = 2.2591331355527199861677357603427e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.693 y[1] (analytic) = 1.9925424188582966295233368223692 y[1] (numeric) = 1.9925424188582966295232917596588 absolute error = 4.50627104e-23 relative error = 2.2615684350559725121771993955659e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6931 y[1] (analytic) = 1.9925302239215413390174998044428 y[1] (numeric) = 1.9925302239215413390174546934839 absolute error = 4.51109589e-23 relative error = 2.2640037455098752380742155059286e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6932 y[1] (analytic) = 1.9925180190594838175673345929305 y[1] (numeric) = 1.9925180190594838175672894337237 absolute error = 4.51592068e-23 relative error = 2.2664390669508838966309059957636e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6933 y[1] (analytic) = 1.9925058042722461137933146951502 y[1] (numeric) = 1.9925058042722461137932694876961 absolute error = 4.52074541e-23 relative error = 2.2688743994154547326347469823513e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6934 y[1] (analytic) = 1.9924935795599503755677153589486 y[1] (numeric) = 1.9924935795599503755676701032478 absolute error = 4.52557008e-23 relative error = 2.2713097429400445041083422489720e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6935 y[1] (analytic) = 1.9924813449227188500133920939791 y[1] (numeric) = 1.9924813449227188500133467900322 absolute error = 4.53039469e-23 relative error = 2.2737450975611104835292370606427e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6936 y[1] (analytic) = 1.9924691003606738835025582004748 y[1] (numeric) = 1.9924691003606738835025128482824 absolute error = 4.53521924e-23 relative error = 2.2761804633151104590497724158237e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6937 y[1] (analytic) = 1.992456845873937921655561305527 y[1] (numeric) = 1.9924568458739379216555159050897 absolute error = 4.54004373e-23 relative error = 2.2786158402385027357169798073962e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6938 y[1] (analytic) = 1.9924445814626335093396589068829 y[1] (numeric) = 1.9924445814626335093396134582013 absolute error = 4.54486816e-23 relative error = 2.2810512283677461366925165662058e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6939 y[1] (analytic) = 1.992432307126883290667792924274 y[1] (numeric) = 1.9924323071268832906677474273487 absolute error = 4.54969253e-23 relative error = 2.2834866277393000044726418604780e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.694 y[1] (analytic) = 1.9924200228668100089973632582879 y[1] (numeric) = 1.9924200228668100089973177131194 absolute error = 4.55451685e-23 relative error = 2.2859220434086462382406636694375e-21 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.3MB, time=26.61 NO POLE x[1] = 1.6941 y[1] (analytic) = 1.9924077286825365069290003567948 y[1] (numeric) = 1.9924077286825365069289547633838 absolute error = 4.55934110e-23 relative error = 2.2883574653742321205143261340655e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6942 y[1] (analytic) = 1.9923954245741857263053367889428 y[1] (numeric) = 1.9923954245741857263052911472899 absolute error = 4.56416529e-23 relative error = 2.2907928986915096506714862508005e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6943 y[1] (analytic) = 1.9923831105418807082097778267323 y[1] (numeric) = 1.9923831105418807082097321368381 absolute error = 4.56898942e-23 relative error = 2.2932283433969402607480096678763e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6944 y[1] (analytic) = 1.9923707865857445929652710341831 y[1] (numeric) = 1.9923707865857445929652252960482 absolute error = 4.57381349e-23 relative error = 2.2956637995269859082148567883573e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6945 y[1] (analytic) = 1.9923584527059006201330748641058 y[1] (numeric) = 1.9923584527059006201330290777308 absolute error = 4.57863750e-23 relative error = 2.2980992671181090771983042444537e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6946 y[1] (analytic) = 1.9923461089024721285115262624904 y[1] (numeric) = 1.9923461089024721285114804278759 absolute error = 4.58346145e-23 relative error = 2.3005347462067727797002075409656e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6947 y[1] (analytic) = 1.9923337551755825561348072805238 y[1] (numeric) = 1.9923337551755825561347613976704 absolute error = 4.58828534e-23 relative error = 2.3029702368294405568183049411967e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6948 y[1] (analytic) = 1.9923213915253554402717106942491 y[1] (numeric) = 1.9923213915253554402716647631574 absolute error = 4.59310917e-23 relative error = 2.3054057390225764799665626686823e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6949 y[1] (analytic) = 1.9923090179519144174244046318789 y[1] (numeric) = 1.9923090179519144174243586525494 absolute error = 4.59793295e-23 relative error = 2.3078412578419468316512558273154e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.695 y[1] (analytic) = 1.9922966344553832233271962087742 y[1] (numeric) = 1.9922966344553832233271501812075 absolute error = 4.60275667e-23 relative error = 2.3102767883047774648620763194046e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6951 y[1] (analytic) = 1.9922842410358856929452941701026 y[1] (numeric) = 1.9922842410358856929452480942994 absolute error = 4.60758032e-23 relative error = 2.3127123254281700236662603024903e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6952 y[1] (analytic) = 1.9922718376935457604735705411875 y[1] (numeric) = 1.9922718376935457604735244171484 absolute error = 4.61240391e-23 relative error = 2.3151478742678923925039172730606e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6953 y[1] (analytic) = 1.9922594244284874593353212855599 y[1] (numeric) = 1.9922594244284874593352751132855 absolute error = 4.61722744e-23 relative error = 2.3175834348604113126780397050169e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6954 y[1] (analytic) = 1.9922470012408349221810259707269 y[1] (numeric) = 1.9922470012408349221809797502178 absolute error = 4.62205091e-23 relative error = 2.3200190072421940631307920160880e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6955 y[1] (analytic) = 1.9922345681307123808871064416677 y[1] (numeric) = 1.9922345681307123808870601729245 absolute error = 4.62687432e-23 relative error = 2.3224545914497084616641470343737e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6956 y[1] (analytic) = 1.9922221250982441665546845020705 y[1] (numeric) = 1.9922221250982441665546381850938 absolute error = 4.63169767e-23 relative error = 2.3248901875194228661605643676304e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6957 y[1] (analytic) = 1.9922096721435547095083386033223 y[1] (numeric) = 1.9922096721435547095082922381127 absolute error = 4.63652096e-23 relative error = 2.3273257954878061758037107486896e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6958 y[1] (analytic) = 1.9921972092667685392948595412642 y[1] (numeric) = 1.9921972092667685392948131278223 absolute error = 4.64134419e-23 relative error = 2.3297614153913278322992224303985e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6959 y[1] (analytic) = 1.9921847364680102846820051607244 y[1] (numeric) = 1.9921847364680102846819586990509 absolute error = 4.64616735e-23 relative error = 2.3321970422468430148254707759640e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.696 y[1] (analytic) = 1.992172253747404673657254067842 y[1] (numeric) = 1.9921722537474046736572075579374 absolute error = 4.65099046e-23 relative error = 2.3346326861300204140095678900654e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6961 y[1] (analytic) = 1.9921597611050765334265583501927 y[1] (numeric) = 1.9921597611050765334265117920576 absolute error = 4.65581351e-23 relative error = 2.3370683420577477271089292756632e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6962 y[1] (analytic) = 1.9921472585411507904130953047308 y[1] (numeric) = 1.9921472585411507904130486983658 absolute error = 4.66063650e-23 relative error = 2.3395040100664965781249035066353e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=167.8MB, alloc=4.3MB, time=27.23 x[1] = 1.6963 y[1] (analytic) = 1.9921347460557524702560181735582 y[1] (numeric) = 1.992134746055752470255971518964 absolute error = 4.66545942e-23 relative error = 2.3419396851729983717481949098475e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6964 y[1] (analytic) = 1.9921222236490066978092058875341 y[1] (numeric) = 1.9921222236490066978091591847113 absolute error = 4.67028228e-23 relative error = 2.3443753724334034905807933422902e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6965 y[1] (analytic) = 1.9921096913210386971400118177371 y[1] (numeric) = 1.9921096913210386971399650666863 absolute error = 4.67510508e-23 relative error = 2.3468110718841851319765235689842e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6966 y[1] (analytic) = 1.9920971490719737915280115347928 y[1] (numeric) = 1.9920971490719737915279647355146 absolute error = 4.67992782e-23 relative error = 2.3492467835618170455762597673322e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6967 y[1] (analytic) = 1.992084596901937403463749576079 y[1] (numeric) = 1.992084596901937403463702728574 absolute error = 4.68475050e-23 relative error = 2.3516825075027735345290670863874e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6968 y[1] (analytic) = 1.9920720348110550546474852208214 y[1] (numeric) = 1.9920720348110550546474383250902 absolute error = 4.68957312e-23 relative error = 2.3541182437435294567133859896578e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6969 y[1] (analytic) = 1.9920594627994523659879372730919 y[1] (numeric) = 1.9920594627994523659878903291352 absolute error = 4.69439567e-23 relative error = 2.3565539873006297536284105445868e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.697 y[1] (analytic) = 1.9920468808672550576010278527229 y[1] (numeric) = 1.9920468808672550576009808605411 absolute error = 4.69921818e-23 relative error = 2.3589897532703418132646031042825e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6971 y[1] (analytic) = 1.9920342890145889488086251941483 y[1] (numeric) = 1.9920342890145889488085781537421 absolute error = 4.70404062e-23 relative error = 2.3614255266293507480265183385736e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6972 y[1] (analytic) = 1.9920216872415799581372854531867 y[1] (numeric) = 1.9920216872415799581372383645567 absolute error = 4.70886300e-23 relative error = 2.3638613124340641192526485484762e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6973 y[1] (analytic) = 1.9920090755483541033169935217765 y[1] (numeric) = 1.9920090755483541033169463849233 absolute error = 4.71368532e-23 relative error = 2.3662971107209595767875784769075e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6974 y[1] (analytic) = 1.991996453935037501279902850677 y[1] (numeric) = 1.9919964539350375012798556656013 absolute error = 4.71850757e-23 relative error = 2.3687329165064260747207136803217e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6975 y[1] (analytic) = 1.9919838224017563681590742801483 y[1] (numeric) = 1.9919838224017563681590270468507 absolute error = 4.72332976e-23 relative error = 2.3711687348469679794395113060121e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6976 y[1] (analytic) = 1.9919711809486370192872138786213 y[1] (numeric) = 1.9919711809486370192871665971024 absolute error = 4.72815189e-23 relative error = 2.3736045657790645544142996159418e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6977 y[1] (analytic) = 1.991958529575805869195409789372 y[1] (numeric) = 1.9919585295758058691953624596324 absolute error = 4.73297396e-23 relative error = 2.3760404093391956288348145571506e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6978 y[1] (analytic) = 1.9919458682833894316118680852115 y[1] (numeric) = 1.9919458682833894316118207072519 absolute error = 4.73779596e-23 relative error = 2.3784762605436248553829780510359e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6979 y[1] (analytic) = 1.9919331970715143194606476312052 y[1] (numeric) = 1.9919331970715143194606002050261 absolute error = 4.74261791e-23 relative error = 2.3809121294692347503285303763284e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.698 y[1] (analytic) = 1.991920515940307244860393955433 y[1] (numeric) = 1.9919205159403072448603464810351 absolute error = 4.74743979e-23 relative error = 2.3833480061120413747178425950259e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6981 y[1] (analytic) = 1.9919078248898950191230721278041 y[1] (numeric) = 1.991907824889895019123024605188 absolute error = 4.75226161e-23 relative error = 2.3857838955287435000631491507519e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6982 y[1] (analytic) = 1.9918951239204045527526986469383 y[1] (numeric) = 1.9918951239204045527526510761046 absolute error = 4.75708337e-23 relative error = 2.3882197977558237262531872003007e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6983 y[1] (analytic) = 1.991882413031962855444072335127 y[1] (numeric) = 1.9918824130319628554440247160762 absolute error = 4.76190508e-23 relative error = 2.3906557178501418983479979827822e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6984 y[1] (analytic) = 1.991869692224697036081504241386 y[1] (numeric) = 1.9918696922246970360814565741189 absolute error = 4.76672671e-23 relative error = 2.3930916407870517471801190730104e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=171.6MB, alloc=4.3MB, time=27.85 x[1] = 1.6985 y[1] (analytic) = 1.991856961498734302737546552614 y[1] (numeric) = 1.9918569614987343027374988371311 absolute error = 4.77154829e-23 relative error = 2.3955275816641676118178649968635e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6986 y[1] (analytic) = 1.9918442208542019626717205128675 y[1] (numeric) = 1.9918442208542019626716727491694 absolute error = 4.77636981e-23 relative error = 2.3979635354975977195459261797969e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6987 y[1] (analytic) = 1.9918314702912274223292433507669 y[1] (numeric) = 1.9918314702912274223291955388544 absolute error = 4.78119125e-23 relative error = 2.4003994922828174028709620803646e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6988 y[1] (analytic) = 1.9918187098099381873397542150458 y[1] (numeric) = 1.9918187098099381873397063549193 absolute error = 4.78601265e-23 relative error = 2.4028354721382686807671049803660e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6989 y[1] (analytic) = 1.9918059394104618625160391182549 y[1] (numeric) = 1.9918059394104618625159912099151 absolute error = 4.79083398e-23 relative error = 2.4052714600389228966224861487250e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.699 y[1] (analytic) = 1.9917931590929261518527548886357 y[1] (numeric) = 1.9917931590929261518527069320833 absolute error = 4.79565524e-23 relative error = 2.4077074560211706256416389949646e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6991 y[1] (analytic) = 1.9917803688574588585251521301751 y[1] (numeric) = 1.9917803688574588585251041254106 absolute error = 4.80047645e-23 relative error = 2.4101434701626706319622020635882e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6992 y[1] (analytic) = 1.9917675687041878848877971908535 y[1] (numeric) = 1.9917675687041878848877491378776 absolute error = 4.80529759e-23 relative error = 2.4125794924586756551113046022192e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6993 y[1] (analytic) = 1.9917547586332412324732931391006 y[1] (numeric) = 1.9917547586332412324732450379139 absolute error = 4.81011867e-23 relative error = 2.4150155279662761526730564257657e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6994 y[1] (analytic) = 1.9917419386447470019909997484702 y[1] (numeric) = 1.9917419386447470019909515990733 absolute error = 4.81493969e-23 relative error = 2.4174515767219615292601726543059e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6995 y[1] (analytic) = 1.9917291087388333933257524905479 y[1] (numeric) = 1.9917291087388333933257042929414 absolute error = 4.81976065e-23 relative error = 2.4198876387622217771927370652080e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6996 y[1] (analytic) = 1.9917162689156287055365805361035 y[1] (numeric) = 1.9917162689156287055365322902881 absolute error = 4.82458154e-23 relative error = 2.4223237091027520180116732888810e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6997 y[1] (analytic) = 1.9917034191752613368554237645021 y[1] (numeric) = 1.9917034191752613368553754704784 absolute error = 4.82940237e-23 relative error = 2.4247597928007740981642889873206e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6998 y[1] (analytic) = 1.9916905595178597846858487813856 y[1] (numeric) = 1.9916905595178597846858004391542 absolute error = 4.83422314e-23 relative error = 2.4271958898927797041737887637243e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6999 y[1] (analytic) = 1.9916776899435526456017639446381 y[1] (numeric) = 1.9916776899435526456017155541996 absolute error = 4.83904385e-23 relative error = 2.4296320004152611151580130693718e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.7 y[1] (analytic) = 1.9916648104524686153461333986479 y[1] (numeric) = 1.991664810452468615346084960003 absolute error = 4.84386449e-23 relative error = 2.4320681193837860225059374730002e-21 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = cos ( x ) ; Iterations = 1000 Total Elapsed Time = 28 Seconds Elapsed Time(since restart) = 28 Seconds Expected Time Remaining = 38 Minutes 56 Seconds Optimized Time Remaining = 38 Minutes 54 Seconds Time to Timeout = 14 Minutes 31 Seconds Percent Done = 1.192 % > quit memory used=174.3MB, alloc=4.3MB, time=28.27