|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_hmax, > glob_not_yet_start_msg, > glob_html_log, > glob_optimal_clock_start_sec, > glob_look_poles, > glob_last_good_h, > glob_hmin, > glob_display_flag, > glob_iter, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned2, > glob_warned, > glob_optimal_done, > glob_reached_optimal_h, > days_in_year, > min_in_hour, > glob_dump, > glob_optimal_expect_sec, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_log10_relerr, > glob_disp_incr, > glob_log10normmin, > glob_start, > glob_smallish_float, > glob_relerr, > glob_abserr, > centuries_in_millinium, > glob_subiter_method, > glob_log10abserr, > glob_max_hours, > glob_h, > glob_clock_sec, > hours_in_day, > glob_log10relerr, > glob_log10_abserr, > sec_in_min, > djd_debug, > glob_max_trunc_err, > glob_max_rel_trunc_err, > years_in_century, > glob_percent_done, > glob_normmax, > glob_current_iter, > glob_optimal_start, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_initial_pass, > djd_debug2, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_pole, > array_fact_1, > array_last_rel_error, > array_tmp1_g, > array_type_pole, > array_1st_rel_error, > array_m1, > array_y_init, > array_y, > array_x, > array_poles, > array_fact_2, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_real_pole, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax, glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec, glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter, MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned, glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour, glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs, glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start, glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium, glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h, glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr, sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err, years_in_century, glob_percent_done, glob_normmax, glob_current_iter, glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float, glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g, array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y, array_x, array_poles, array_fact_2, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_real_pole, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_hmax, > glob_not_yet_start_msg, > glob_html_log, > glob_optimal_clock_start_sec, > glob_look_poles, > glob_last_good_h, > glob_hmin, > glob_display_flag, > glob_iter, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned2, > glob_warned, > glob_optimal_done, > glob_reached_optimal_h, > days_in_year, > min_in_hour, > glob_dump, > glob_optimal_expect_sec, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_log10_relerr, > glob_disp_incr, > glob_log10normmin, > glob_start, > glob_smallish_float, > glob_relerr, > glob_abserr, > centuries_in_millinium, > glob_subiter_method, > glob_log10abserr, > glob_max_hours, > glob_h, > glob_clock_sec, > hours_in_day, > glob_log10relerr, > glob_log10_abserr, > sec_in_min, > djd_debug, > glob_max_trunc_err, > glob_max_rel_trunc_err, > years_in_century, > glob_percent_done, > glob_normmax, > glob_current_iter, > glob_optimal_start, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_initial_pass, > djd_debug2, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_pole, > array_fact_1, > array_last_rel_error, > array_tmp1_g, > array_type_pole, > array_1st_rel_error, > array_m1, > array_y_init, > array_y, > array_x, > array_poles, > array_fact_2, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_real_pole, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax, glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec, glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter, MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned, glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour, glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs, glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start, glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium, glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h, glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr, sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err, years_in_century, glob_percent_done, glob_normmax, glob_current_iter, glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float, glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g, array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y, array_x, array_poles, array_fact_2, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_real_pole, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_hmax, > glob_not_yet_start_msg, > glob_html_log, > glob_optimal_clock_start_sec, > glob_look_poles, > glob_last_good_h, > glob_hmin, > glob_display_flag, > glob_iter, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned2, > glob_warned, > glob_optimal_done, > glob_reached_optimal_h, > days_in_year, > min_in_hour, > glob_dump, > glob_optimal_expect_sec, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_log10_relerr, > glob_disp_incr, > glob_log10normmin, > glob_start, > glob_smallish_float, > glob_relerr, > glob_abserr, > centuries_in_millinium, > glob_subiter_method, > glob_log10abserr, > glob_max_hours, > glob_h, > glob_clock_sec, > hours_in_day, > glob_log10relerr, > glob_log10_abserr, > sec_in_min, > djd_debug, > glob_max_trunc_err, > glob_max_rel_trunc_err, > years_in_century, > glob_percent_done, > glob_normmax, > glob_current_iter, > glob_optimal_start, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_initial_pass, > djd_debug2, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_pole, > array_fact_1, > array_last_rel_error, > array_tmp1_g, > array_type_pole, > array_1st_rel_error, > array_m1, > array_y_init, > array_y, > array_x, > array_poles, > array_fact_2, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_real_pole, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax, glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec, glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter, MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned, glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour, glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs, glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start, glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium, glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h, glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr, sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err, years_in_century, glob_percent_done, glob_normmax, glob_current_iter, glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float, glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g, array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y, array_x, array_poles, array_fact_2, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_real_pole, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_hmax, > glob_not_yet_start_msg, > glob_html_log, > glob_optimal_clock_start_sec, > glob_look_poles, > glob_last_good_h, > glob_hmin, > glob_display_flag, > glob_iter, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned2, > glob_warned, > glob_optimal_done, > glob_reached_optimal_h, > days_in_year, > min_in_hour, > glob_dump, > glob_optimal_expect_sec, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_log10_relerr, > glob_disp_incr, > glob_log10normmin, > glob_start, > glob_smallish_float, > glob_relerr, > glob_abserr, > centuries_in_millinium, > glob_subiter_method, > glob_log10abserr, > glob_max_hours, > glob_h, > glob_clock_sec, > hours_in_day, > glob_log10relerr, > glob_log10_abserr, > sec_in_min, > djd_debug, > glob_max_trunc_err, > glob_max_rel_trunc_err, > years_in_century, > glob_percent_done, > glob_normmax, > glob_current_iter, > glob_optimal_start, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_initial_pass, > djd_debug2, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_pole, > array_fact_1, > array_last_rel_error, > array_tmp1_g, > array_type_pole, > array_1st_rel_error, > array_m1, > array_y_init, > array_y, > array_x, > array_poles, > array_fact_2, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_real_pole, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax, glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec, glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter, MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned, glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour, glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs, glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start, glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium, glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h, glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr, sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err, years_in_century, glob_percent_done, glob_normmax, glob_current_iter, glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float, glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g, array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y, array_x, array_poles, array_fact_2, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_real_pole, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_hmax, > glob_not_yet_start_msg, > glob_html_log, > glob_optimal_clock_start_sec, > glob_look_poles, > glob_last_good_h, > glob_hmin, > glob_display_flag, > glob_iter, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned2, > glob_warned, > glob_optimal_done, > glob_reached_optimal_h, > days_in_year, > min_in_hour, > glob_dump, > glob_optimal_expect_sec, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_log10_relerr, > glob_disp_incr, > glob_log10normmin, > glob_start, > glob_smallish_float, > glob_relerr, > glob_abserr, > centuries_in_millinium, > glob_subiter_method, > glob_log10abserr, > glob_max_hours, > glob_h, > glob_clock_sec, > hours_in_day, > glob_log10relerr, > glob_log10_abserr, > sec_in_min, > djd_debug, > glob_max_trunc_err, > glob_max_rel_trunc_err, > years_in_century, > glob_percent_done, > glob_normmax, > glob_current_iter, > glob_optimal_start, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_initial_pass, > djd_debug2, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_pole, > array_fact_1, > array_last_rel_error, > array_tmp1_g, > array_type_pole, > array_1st_rel_error, > array_m1, > array_y_init, > array_y, > array_x, > array_poles, > array_fact_2, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_real_pole, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax, glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec, glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter, MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned, glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour, glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs, glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start, glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium, glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h, glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr, sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err, years_in_century, glob_percent_done, glob_normmax, glob_current_iter, glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float, glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g, array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y, array_x, array_poles, array_fact_2, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_real_pole, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_hmax, > glob_not_yet_start_msg, > glob_html_log, > glob_optimal_clock_start_sec, > glob_look_poles, > glob_last_good_h, > glob_hmin, > glob_display_flag, > glob_iter, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned2, > glob_warned, > glob_optimal_done, > glob_reached_optimal_h, > days_in_year, > min_in_hour, > glob_dump, > glob_optimal_expect_sec, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_log10_relerr, > glob_disp_incr, > glob_log10normmin, > glob_start, > glob_smallish_float, > glob_relerr, > glob_abserr, > centuries_in_millinium, > glob_subiter_method, > glob_log10abserr, > glob_max_hours, > glob_h, > glob_clock_sec, > hours_in_day, > glob_log10relerr, > glob_log10_abserr, > sec_in_min, > djd_debug, > glob_max_trunc_err, > glob_max_rel_trunc_err, > years_in_century, > glob_percent_done, > glob_normmax, > glob_current_iter, > glob_optimal_start, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_initial_pass, > djd_debug2, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_pole, > array_fact_1, > array_last_rel_error, > array_tmp1_g, > array_type_pole, > array_1st_rel_error, > array_m1, > array_y_init, > array_y, > array_x, > array_poles, > array_fact_2, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_real_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sinh $eq_no = 1 > array_tmp1[1] := sinh(array_x[1]); > array_tmp1_g[1] := cosh(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sinh $eq_no = 1 > array_tmp1[2] := att(1,array_tmp1_g,array_x,1); > array_tmp1_g[2] := att(1,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sinh $eq_no = 1 > array_tmp1[3] := att(2,array_tmp1_g,array_x,1); > array_tmp1_g[3] := att(2,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sinh $eq_no = 1 > array_tmp1[4] := att(3,array_tmp1_g,array_x,1); > array_tmp1_g[4] := att(3,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sinh $eq_no = 1 > array_tmp1[5] := att(4,array_tmp1_g,array_x,1); > array_tmp1_g[5] := att(4,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sinh $eq_no = 1 > array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1); > array_tmp1_g[kkk] := att(kkk-1,array_tmp1,array_x,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax, glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec, glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter, MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned, glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour, glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs, glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start, glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium, glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h, glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr, sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err, years_in_century, glob_percent_done, glob_normmax, glob_current_iter, glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float, glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g, array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y, array_x, array_poles, array_fact_2, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_real_pole, glob_last; array_tmp1[1] := sinh(array_x[1]); array_tmp1_g[1] := cosh(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := att(1, array_tmp1_g, array_x, 1); array_tmp1_g[2] := att(1, array_tmp1, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := att(2, array_tmp1_g, array_x, 1); array_tmp1_g[3] := att(2, array_tmp1, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := att(3, array_tmp1_g, array_x, 1); array_tmp1_g[4] := att(3, array_tmp1, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := att(4, array_tmp1_g, array_x, 1); array_tmp1_g[5] := att(4, array_tmp1, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 13 > if array_fact_1[nnn] = 0 then # if number 14 > ret := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > if array_fact_2[mmm,nnn] = 0 then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0 + cosh(x); > end; exact_soln_y := proc(x) 1.0 + cosh(x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > glob_max_terms, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_max_sec, > glob_small_float, > glob_hmax, > glob_not_yet_start_msg, > glob_html_log, > glob_optimal_clock_start_sec, > glob_look_poles, > glob_last_good_h, > glob_hmin, > glob_display_flag, > glob_iter, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_warned2, > glob_warned, > glob_optimal_done, > glob_reached_optimal_h, > days_in_year, > min_in_hour, > glob_dump, > glob_optimal_expect_sec, > glob_unchanged_h_cnt, > glob_no_eqs, > glob_log10_relerr, > glob_disp_incr, > glob_log10normmin, > glob_start, > glob_smallish_float, > glob_relerr, > glob_abserr, > centuries_in_millinium, > glob_subiter_method, > glob_log10abserr, > glob_max_hours, > glob_h, > glob_clock_sec, > hours_in_day, > glob_log10relerr, > glob_log10_abserr, > sec_in_min, > djd_debug, > glob_max_trunc_err, > glob_max_rel_trunc_err, > years_in_century, > glob_percent_done, > glob_normmax, > glob_current_iter, > glob_optimal_start, > glob_max_iter, > glob_dump_analytic, > glob_large_float, > glob_initial_pass, > djd_debug2, > glob_max_opt_iter, > glob_max_minutes, > glob_hmin_init, > glob_not_yet_finished, > glob_clock_start_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_pole, > array_fact_1, > array_last_rel_error, > array_tmp1_g, > array_type_pole, > array_1st_rel_error, > array_m1, > array_y_init, > array_y, > array_x, > array_poles, > array_fact_2, > array_y_set_initial, > array_y_higher_work, > array_y_higher, > array_y_higher_work2, > array_complex_pole, > array_real_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > ALWAYS := 1; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGL := 3; > INFO := 2; > glob_curr_iter_when_opt := 0; > glob_max_sec := 10000.0; > glob_small_float := 0.1e-50; > glob_hmax := 1.0; > glob_not_yet_start_msg := true; > glob_html_log := true; > glob_optimal_clock_start_sec := 0.0; > glob_look_poles := false; > glob_last_good_h := 0.1; > glob_hmin := 0.00000000001; > glob_display_flag := true; > glob_iter := 0; > MAX_UNCHANGED := 10; > glob_orig_start_sec := 0.0; > glob_warned2 := false; > glob_warned := false; > glob_optimal_done := false; > glob_reached_optimal_h := false; > days_in_year := 365.0; > min_in_hour := 60.0; > glob_dump := false; > glob_optimal_expect_sec := 0.1; > glob_unchanged_h_cnt := 0; > glob_no_eqs := 0; > glob_log10_relerr := 0.1e-10; > glob_disp_incr := 0.1; > glob_log10normmin := 0.1; > glob_start := 0; > glob_smallish_float := 0.1e-100; > glob_relerr := 0.1e-10; > glob_abserr := 0.1e-10; > centuries_in_millinium := 10.0; > glob_subiter_method := 3; > glob_log10abserr := 0.0; > glob_max_hours := 0.0; > glob_h := 0.1; > glob_clock_sec := 0.0; > hours_in_day := 24.0; > glob_log10relerr := 0.0; > glob_log10_abserr := 0.1e-10; > sec_in_min := 60.0; > djd_debug := true; > glob_max_trunc_err := 0.1e-10; > glob_max_rel_trunc_err := 0.1e-10; > years_in_century := 100.0; > glob_percent_done := 0.0; > glob_normmax := 0.0; > glob_current_iter := 0; > glob_optimal_start := 0.0; > glob_max_iter := 1000; > glob_dump_analytic := false; > glob_large_float := 9.0e100; > glob_initial_pass := true; > djd_debug2 := true; > glob_max_opt_iter := 10; > glob_max_minutes := 0.0; > glob_hmin_init := 0.001; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > glob_almost_1 := 0.9990; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sinhpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"1.0 + cosh(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 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_norms[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_fact_1[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_tmp1_g[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_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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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 <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > #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 > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > 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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sinh ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-18T01:21:32-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sinh") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 092 ") > ; > logitem_str(html_log_file,"sinh diffeq.mxt") > ; > logitem_str(html_log_file,"sinh maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > 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, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO, glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax, glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec, glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter, MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned, glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour, glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs, glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start, glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium, glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h, glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr, sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err, years_in_century, glob_percent_done, glob_normmax, glob_current_iter, glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float, glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes, glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1, array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2, array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g, array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y, array_x, array_poles, array_fact_2, array_y_set_initial, array_y_higher_work, array_y_higher, array_y_higher_work2, array_complex_pole, array_real_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; ALWAYS := 1; glob_iolevel := 5; glob_max_terms := 30; DEBUGL := 3; INFO := 2; glob_curr_iter_when_opt := 0; glob_max_sec := 10000.0; glob_small_float := 0.1*10^(-50); glob_hmax := 1.0; glob_not_yet_start_msg := true; glob_html_log := true; glob_optimal_clock_start_sec := 0.; glob_look_poles := false; glob_last_good_h := 0.1; glob_hmin := 0.1*10^(-10); glob_display_flag := true; glob_iter := 0; MAX_UNCHANGED := 10; glob_orig_start_sec := 0.; glob_warned2 := false; glob_warned := false; glob_optimal_done := false; glob_reached_optimal_h := false; days_in_year := 365.0; min_in_hour := 60.0; glob_dump := false; glob_optimal_expect_sec := 0.1; glob_unchanged_h_cnt := 0; glob_no_eqs := 0; glob_log10_relerr := 0.1*10^(-10); glob_disp_incr := 0.1; glob_log10normmin := 0.1; glob_start := 0; glob_smallish_float := 0.1*10^(-100); glob_relerr := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); centuries_in_millinium := 10.0; glob_subiter_method := 3; glob_log10abserr := 0.; glob_max_hours := 0.; glob_h := 0.1; glob_clock_sec := 0.; hours_in_day := 24.0; glob_log10relerr := 0.; glob_log10_abserr := 0.1*10^(-10); sec_in_min := 60.0; djd_debug := true; glob_max_trunc_err := 0.1*10^(-10); glob_max_rel_trunc_err := 0.1*10^(-10); years_in_century := 100.0; glob_percent_done := 0.; glob_normmax := 0.; glob_current_iter := 0; glob_optimal_start := 0.; glob_max_iter := 1000; glob_dump_analytic := false; glob_large_float := 0.90*10^101; glob_initial_pass := true; djd_debug2 := true; glob_max_opt_iter := 10; glob_max_minutes := 0.; glob_hmin_init := 0.001; glob_not_yet_finished := true; glob_clock_start_sec := 0.; glob_almost_1 := 0.9990; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sinhpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "1.0 + \t cosh(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); 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_norms[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_fact_1[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_tmp1_g[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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; 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 <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_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; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.001; 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)/factorial_1(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)/factorial_1(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)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sinh ( x ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-18T01:21:32-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sinh"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 092 "); logitem_str(html_log_file, "sinh diffeq.mxt"); logitem_str(html_log_file, "sinh maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/sinhpostode.ode################# diff ( y , x , 1 ) = sinh ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0 + cosh(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 2.0000005000000416666680555555804 y[1] (numeric) = 2.000000500000041666716666668254 absolute error = 4.86111126736e-20 relative error = 2.4305550260411928531370563054199e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 2.0000020000006666667555555619048 y[1] (numeric) = 2.0000020000006666668527778210814 absolute error = 9.72222591766e-20 relative error = 4.8611080977202819101361338390097e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 2.0000045000033750010125001627232 y[1] (numeric) = 2.0000045000033750011583336508434 absolute error = 1.458334881202e-19 relative error = 7.2916579997671958472433341038629e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 2.0000080000106666723555571809527 y[1] (numeric) = 2.0000080000106666725500020290681 absolute error = 1.944448481154e-19 relative error = 9.7222035169040806039331534881948e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 2.0000125000260416883680652436783 y[1] (numeric) = 2.0000125000260416886111216314521 absolute error = 2.430563877738e-19 relative error = 1.2152743433885299238218615101705e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 2.0000180000540000648000416571595 y[1] (numeric) = 2.0000180000540000650917098128664 absolute error = 2.916681557069e-19 relative error = 1.4583276535462431899156958428176e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 2.0000245001000418300681985318487 y[1] (numeric) = 2.000024500100041830408478732375 absolute error = 3.402802005263e-19 relative error = 1.7013801606394275745561647200906e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 2.0000320001706670307559716574388 y[1] (numeric) = 2.000032000170667031144864228283 absolute error = 3.888925708442e-19 relative error = 1.9444317431471844489935220484395e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 2.0000405002733757381135676279698 y[1] (numeric) = 2.0000405002733757385510729432428 absolute error = 4.375053152730e-19 relative error = 2.1874822795498368244131625717739e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 2.0000500004166680555580357170414 y[1] (numeric) = 2.0000500004166680560441541994669 absolute error = 4.861184824255e-19 relative error = 2.4305316483299293038264547823902e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 2.0000605006100441271733720032042 y[1] (numeric) = 2.0000605006100441277081041241188 absolute error = 5.347321209146e-19 relative error = 2.6735797279707280796864274025255e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 2.0000720008640041472106642456342 y[1] (numeric) = 2.0000720008640041477940105249884 absolute error = 5.833462793542e-19 relative error = 2.9166263969607207626334652778816e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 2.0000845011900483705882870102372 y[1] (numeric) = 2.0000845011900483712202480165955 absolute error = 6.319610063583e-19 relative error = 3.1596715337891164296408818473526e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=3.0MB, time=0.18 x[1] = 0.014 y[1] (analytic) = 2.0000980016006771243921575463776 y[1] (numeric) = 2.0000980016006771250727338969194 absolute error = 6.805763505418e-19 relative error = 3.4027150169498454133461009507791e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.015 y[1] (analytic) = 2.00011250210939082037606391449 y[1] (numeric) = 2.00011250210939082110525627501 absolute error = 7.291923605200e-19 relative error = 3.6457567249390592934593657715165e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 2.0001280027306899684620778649013 y[1] (numeric) = 2.0001280027306899692398869498101 absolute error = 7.778090849088e-19 relative error = 3.8887965362561307621588761563099e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 2.0001445034800751912410659682783 y[1] (numeric) = 2.0001445034800751920674925406034 absolute error = 8.264265723251e-19 relative error = 4.1318343294056533695026630777249e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 2.0001620043740472394733134982132 y[1] (numeric) = 2.0001620043740472403483583695994 absolute error = 8.750448713862e-19 relative error = 4.3748699828944415643662391501815e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 2.000180505430107008589276566571 y[1] (numeric) = 2.0001805054301070095129405972816 absolute error = 9.236640307106e-19 relative error = 4.6179033752355302519674955747643e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 2.0002000066667555561904790123542 y[1] (numeric) = 2.0002000066667555571627631112715 absolute error = 9.722840989173e-19 relative error = 4.8609343849446748729590741212497e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 2.0002205081034941205505715449809 y[1] (numeric) = 2.0002205081034941215714766696073 absolute error = 1.0209051246264e-18 relative error = 5.1039628905433509580437032678271e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 2.0002420097608241401165716430391 y[1] (numeric) = 2.000242009760824141186098799498 absolute error = 1.0695271564589e-18 relative error = 5.3469887705577539774725490446703e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 2.0002645116602472740103037097573 y[1] (numeric) = 2.0002645116602472751284539527943 absolute error = 1.1181502430370e-18 relative error = 5.5900119035202989106152140197659e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 2.000288013824265423530059986634 y[1] (numeric) = 2.0002880138242654246968344196177 absolute error = 1.1667744329837e-18 relative error = 5.8330321679676202057037000940392e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 2.0003125162763807546525037268886 y[1] (numeric) = 2.0003125162763807558679035018117 absolute error = 1.2153997749231e-18 relative error = 6.0760494424420713217153793086748e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 2.0003380190410957215348371306378 y[1] (numeric) = 2.0003380190410957227988634481186 absolute error = 1.2640263174808e-18 relative error = 6.3190636054937240692957633583413e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 2.0003645221439130910172575439702 y[1] (numeric) = 2.0003645221439130923299116532532 absolute error = 1.3126541092830e-18 relative error = 6.5620745356758689654891063066106e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 2.0003920256113359681257264243733 y[1] (numeric) = 2.000392025611335969487009623331 absolute error = 1.3612831989577e-18 relative error = 6.8050821115510138764724870911207e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 2.0004205294708678225750765752876 y[1] (numeric) = 2.0004205294708678239849902104216 absolute error = 1.4099136351340e-18 relative error = 7.0480862116873841541051997459931e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 2.0004500337510125162724841528952 y[1] (numeric) = 2.0004500337510125177310296193375 absolute error = 1.4585454664423e-18 relative error = 7.2910867146599220356844435516512e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 2.0004805384812743318213329486178 y[1] (numeric) = 2.0004805384812743333285116901322 absolute error = 1.5071787415144e-18 relative error = 7.5340834990507860657368728601849e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 2.0005120436921580020254994511908 y[1] (numeric) = 2.0005120436921580035813129601745 absolute error = 1.5558135089837e-18 relative error = 7.7770764434503503297839573907328e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 2.0005445494151687403940881926011 y[1] (numeric) = 2.000544549415168741998538010086 absolute error = 1.6044498174849e-18 relative error = 8.0200654264557042558616921406166e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 2.000578055682812272646647882626 y[1] (numeric) = 2.0005780556828122742997355982802 absolute error = 1.6530877156542e-18 relative error = 8.2630503266716518228786145627560e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 2.0006125625285948692188998371924 y[1] (numeric) = 2.0006125625285948709206270893221 absolute error = 1.7017272521297e-18 relative error = 8.5060310227127103503498195277735e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 2.0006480699870233787690112062878 y[1] (numeric) = 2.0006480699870233805193796818386 absolute error = 1.7503684755508e-18 relative error = 8.7490073932001106796802490491907e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=7.6MB, alloc=4.1MB, time=0.42 x[1] = 0.037 y[1] (analytic) = 2.0006845780936052626844465076978 y[1] (numeric) = 2.0006845780936052644834579422566 absolute error = 1.7990114345588e-18 relative error = 8.9919793167647956018787892484365e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 2.000722086884848630589431973426 y[1] (numeric) = 2.0007220868848486324370881512227 absolute error = 1.8476561777967e-18 relative error = 9.2349466720464193864421076161965e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 2.0007605963982622768530682162631 y[1] (numeric) = 2.0007605963982622787493709701722 absolute error = 1.8963027539091e-18 relative error = 9.4779093376928472092737530447173e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 2.00080010667235571809812772462 y[1] (numeric) = 2.0008001066723557200430789361627 absolute error = 1.9449512115427e-18 relative error = 9.7208671923626534225815747046723e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.041 y[1] (analytic) = 2.0008406177466392317105746944272 y[1] (numeric) = 2.000840617746639233704176293773 absolute error = 1.9936015993458e-18 relative error = 9.9638201147226216093158866486414e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 2.0008821296616238953498457076217 y[1] (numeric) = 2.0008821296616238973920996735907 absolute error = 2.0422539659690e-18 relative error = 1.0206767983451242273480718152154e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 2.0009246424588216274599307675074 y[1] (numeric) = 2.000924642458821629550839127572 absolute error = 2.0909083600646e-18 relative error = 1.0449710677235713078186627085854e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 2.0009681561807452287812952020716 y[1] (numeric) = 2.0009681561807452309208600323586 absolute error = 2.1395648302870e-18 relative error = 1.0692648074773937020838381131364e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 2.0010126708709084248636839471835 y[1] (numeric) = 2.0010126708709084270519073724762 absolute error = 2.1882234252927e-18 relative error = 1.0935580054774521342498847344031e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 2.0010581865738259095798507224835 y[1] (numeric) = 2.0010581865738259118167349162237 absolute error = 2.2368841937402e-18 relative error = 1.1178506495956276676811045835179e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 2.0011047033350133896402556136946 y[1] (numeric) = 2.001104703335013391925802797985 absolute error = 2.2855471842904e-18 relative error = 1.1421427277050214864936896140203e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 2.0011522212009876301087755760583 y[1] (numeric) = 2.0011522212009876324429880216645 absolute error = 2.3342124456062e-18 relative error = 1.1664342276797548770283608091576e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 2.0012007402192665009194733746086 y[1] (numeric) = 2.0012007402192665033023534009615 absolute error = 2.3828800263529e-18 relative error = 1.1907251373951689951736186731611e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 2.0012502604383690243944714780576 y[1] (numeric) = 2.0012502604383690268260214532557 absolute error = 2.4315499751981e-18 relative error = 1.2150154447277747586003913848516e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 2.00130078190781542376297842417 y[1] (numeric) = 2.0013007819078154262432007649816 absolute error = 2.4802223408116e-18 relative error = 1.2393051375552027435993327354580e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 2.0013523046781271726815161756566 y[1] (numeric) = 2.0013523046781271752104133475226 absolute error = 2.5288971718660e-18 relative error = 1.2635942037565028506794329280333e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 2.0014048288008270457553979868197 y[1] (numeric) = 2.0014048288008270483329725038558 absolute error = 2.5775745170361e-18 relative error = 1.2878826312118443421517168337705e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 2.001458354328439170061507302431 y[1] (numeric) = 2.0014583543284391726877617274301 absolute error = 2.6262544249991e-18 relative error = 1.3121704078026156322821190891442e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 2.0015128813144890776724292116254 y[1] (numeric) = 2.0015128813144890803473661560605 absolute error = 2.6749369444351e-18 relative error = 1.3364575214116739460258621469225e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 2.0015684098135037591819869809478 y[1] (numeric) = 2.0015684098135037619056091049742 absolute error = 2.7236221240264e-18 relative error = 1.3607439599229954040099261994242e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 2.0016249398810117182322371920918 y[1] (numeric) = 2.0016249398810117210045472045501 absolute error = 2.7723100124583e-18 relative error = 1.3850297112220745538550370782956e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 2.0016824715735430270419780113322 y[1] (numeric) = 2.0016824715735430298629786697509 absolute error = 2.8210006584187e-18 relative error = 1.4093147631957243355715911847133e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 2.0017410049486293829368261191625 y[1] (numeric) = 2.0017410049486293858065202297607 absolute error = 2.8696941105982e-18 relative error = 1.4335991037321258603981749013121e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 2.0018005400648041658809188302198 y[1] (numeric) = 2.0018005400648041687993092479102 absolute error = 2.9183904176904e-18 relative error = 1.4578827207209780882222523908772e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=0.66 NO POLE x[1] = 0.061 y[1] (analytic) = 2.001861076981602497010298935204 y[1] (numeric) = 2.0018610769816024999773885635955 absolute error = 2.9670896283915e-18 relative error = 1.4821656020532978003922734868907e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 2.0019226157595612981680407981811 y[1] (numeric) = 2.0019226157595613011838325895817 absolute error = 3.0157917914006e-18 relative error = 1.5064477356215692694539920210575e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 2.0019851564602193524411772444006 y[1] (numeric) = 2.0019851564602193555056741998207 absolute error = 3.0644969554201e-18 relative error = 1.5307291093199438490471581851936e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 2.002048699146117365699487775561 y[1] (numeric) = 2.0020486991461173688126929447161 absolute error = 3.1132051691551e-18 relative error = 1.5550097110439400342404646967206e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 2.0021132438807980291362096513148 y[1] (numeric) = 2.0021132438807980322981261326285 absolute error = 3.1619164813137e-18 relative error = 1.5792895286905931003293764089851e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 2.00217879072880608281073437773 y[1] (numeric) = 2.0021787907288060860213653183374 absolute error = 3.2106309406074e-18 relative error = 1.6035685501586546556316193277513e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 2.0022453397556883801933531454105 y[1] (numeric) = 2.002245339755688383452701741161 absolute error = 3.2593485957505e-18 relative error = 1.6278467633482927119963374342339e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 2.0023128910279939537121157620248 y[1] (numeric) = 2.0023128910279939570201852574856 absolute error = 3.3080694954608e-18 relative error = 1.6521241561614410606347878255316e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 2.0023814446132740813018686261092 y[1] (numeric) = 2.0023814446132740846586623145682 absolute error = 3.3567936884590e-18 relative error = 1.6764007165014993470413665458050e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 2.002451000580082353955538291187 y[1] (numeric) = 2.0024510005800823573610595146565 absolute error = 3.4055212234695e-18 relative error = 1.7006764322737323469338059948241e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 2.0025215589979747442777281714951 y[1] (numeric) = 2.0025215589979747477319803207148 absolute error = 3.4542521492197e-18 relative error = 1.7249512913849200998657101047806e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 2.0025931199375096760406969429182 y[1] (numeric) = 2.0025931199375096795436834573587 absolute error = 3.5029865144405e-18 relative error = 1.7492252817436073357397538576868e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 2.0026656834702480947427881951162 y[1] (numeric) = 2.0026656834702480982945125629828 absolute error = 3.5517243678666e-18 relative error = 1.7734983912602529777709613403106e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 2.0027392496687535391693818932809 y[1] (numeric) = 2.0027392496687535427698476515164 absolute error = 3.6004657582355e-18 relative error = 1.7977706078467304973598228118959e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 2.0028138186065922139564392104767 y[1] (numeric) = 2.0028138186065922176056499447655 absolute error = 3.6492107342888e-18 relative error = 1.8220419194169767597336479244727e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 2.0028893903583330631567132941199 y[1] (numeric) = 2.0028893903583330668546726388912 absolute error = 3.6979593447713e-18 relative error = 1.8463123138865423082704912504005e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 2.0029659649995478448086995328102 y[1] (numeric) = 2.0029659649995478485554111712419 absolute error = 3.7467116384317e-18 relative error = 1.8705817791729405613051468446754e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 2.003043542606811206508399892473 y[1] (numeric) = 2.0030435426068112103038675564953 absolute error = 3.7954676640223e-18 relative error = 1.8948503031954976849750042556055e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 2.003122123257700761983976893582 y[1] (numeric) = 2.0031221232577007658282043638812 absolute error = 3.8442274702992e-18 relative error = 1.9191178738754521067037440577105e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 2.0032017070307971686733738041236 y[1] (numeric) = 2.0032017070307971725663649101457 absolute error = 3.8929911060221e-18 relative error = 1.9433844791358543208344202953833e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 2.0032822940056842063049786259279 y[1] (numeric) = 2.0032822940056842102467372458826 absolute error = 3.9417586199547e-18 relative error = 1.9676501069017662224974255740702e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 2.003363884262948856481410455039 y[1] (numeric) = 2.0033638842629488604719405159034 absolute error = 3.9905300608644e-18 relative error = 1.9919147451001109769269782989192e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 2.0034464778841813832665077999156 y[1] (numeric) = 2.0034464778841813873058132774385 absolute error = 4.0393054775229e-18 relative error = 2.0161783816599721468834910765093e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.1MB, time=0.90 x[1] = 0.084 y[1] (analytic) = 2.0035300749519754147755994444593 y[1] (numeric) = 2.0035300749519754188636843631646 absolute error = 4.0880849187053e-18 relative error = 2.0404410045121440629817123863466e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 2.0036146755499280257691394461449 y[1] (numeric) = 2.0036146755499280299060078793362 absolute error = 4.1368684331913e-18 relative error = 2.0647026015897304078726382262475e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.086 y[1] (analytic) = 2.0037002797626398212497888628985 y[1] (numeric) = 2.0037002797626398254354449326628 absolute error = 4.1856560697643e-18 relative error = 2.0889631608276945837711155293052e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 2.0037868876757150210630278058084 y[1] (numeric) = 2.0037868876757150252974756830205 absolute error = 4.2344478772121e-18 relative error = 2.1132226701632086780493037464416e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 2.0038744993757615455013824182913 y[1] (numeric) = 2.0038744993757615497846263226175 absolute error = 4.2832439043262e-18 relative error = 2.1374811175353036875963120096289e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 2.0039631149503911019123523859445 y[1] (numeric) = 2.0039631149503911062443965858474 absolute error = 4.3320441999029e-18 relative error = 2.1617384908854180504647062102692e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 2.0040527344882192723101255850222 y[1] (numeric) = 2.0040527344882192766909743977646 absolute error = 4.3808488127424e-18 relative error = 2.1859947781569480497185761240518e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 2.0041433580788656019911674812549 y[1] (numeric) = 2.0041433580788656064208252729042 absolute error = 4.4296577916493e-18 relative error = 2.2102499672954968851975121035864e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 2.0042349858129536891537738946108 y[1] (numeric) = 2.0042349858129536936322450800435 absolute error = 4.4784711854327e-18 relative error = 2.2345040462489240961797212386323e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 2.0043276177821112755216767495584 y[1] (numeric) = 2.0043276177821112800489657924643 absolute error = 4.5272890429059e-18 relative error = 2.2587570029671953970366347616410e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 2.0044212540789703379717934344438 y[1] (numeric) = 2.0044212540789703425479048473306 absolute error = 4.5761114128868e-18 relative error = 2.2830088254025817775854471003581e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 2.0045158947971671811662113977398 y[1] (numeric) = 2.0045158947971671857911497419375 absolute error = 4.6249383441977e-18 relative error = 2.3072595015095592187719847564973e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 2.0046115400313425311885006131587 y[1] (numeric) = 2.0046115400313425358622704988243 absolute error = 4.6737698856656e-18 relative error = 2.3315090192449578564473615831214e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 2.0047081898771416301844475499503 y[1] (numeric) = 2.0047081898771416349070536360722 absolute error = 4.7226060861219e-18 relative error = 2.3557573665678118019448507255876e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 2.0048058444312143320073052891247 y[1] (numeric) = 2.0048058444312143367787522835277 absolute error = 4.7714469944030e-18 relative error = 2.3800045314396579222066993782900e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 2.0049045037912151988676554308609 y[1] (numeric) = 2.0049045037912152036879480902107 absolute error = 4.8202926593498e-18 relative error = 2.4042505018242858727677950089933e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 2.0050041680558035989879784429683 y[1] (numeric) = 2.0050041680558036038571215727763 absolute error = 4.8691431298080e-18 relative error = 2.4284952656878872004665822609131e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 2.0051048373246438052620301049819 y[1] (numeric) = 2.0051048373246438101800285596098 absolute error = 4.9179984546279e-18 relative error = 2.4527388109989550332342208492950e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 2.0052065116984050949191227072741 y[1] (numeric) = 2.0052065116984050998859813899389 absolute error = 4.9668586826648e-18 relative error = 2.4769811257284830159683854141489e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 2.0053091912787618501934106694736 y[1] (numeric) = 2.0053091912787618552091345322528 absolute error = 5.0157238627792e-18 relative error = 2.5012221978500644454396693346535e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 2.0054128761683936599982812474859 y[1] (numeric) = 2.0054128761683936650628752913219 absolute error = 5.0645940438360e-18 relative error = 2.5254620153394927180323675765884e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 2.0055175664709854226059520035125 y[1] (numeric) = 2.0055175664709854277194212782181 absolute error = 5.1134692747056e-18 relative error = 2.5497005661753092823926364279080e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 2.0056232622912274493323777186775 y[1] (numeric) = 2.0056232622912274544947273229407 absolute error = 5.1623496042632e-18 relative error = 2.5739378383384539387141382657635e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 2.0057299637348155692275704331751 y[1] (numeric) = 2.0057299637348155744388055145641 absolute error = 5.2112350813890e-18 relative error = 2.5981738198123639566142367911301e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=1.15 NO POLE x[1] = 0.108 y[1] (analytic) = 2.0058376709084512347714373042674 y[1] (numeric) = 2.0058376709084512400315630592361 absolute error = 5.2601257549687e-18 relative error = 2.6224084985832227198061148815000e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 2.0059463839198416285752419779802 y[1] (numeric) = 2.0059463839198416338842636518729 absolute error = 5.3090216738927e-18 relative error = 2.6466418626395602114227671547146e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 2.0060561028776997710887961759647 y[1] (numeric) = 2.0060561028776997764467190630219 absolute error = 5.3579228870572e-18 relative error = 2.6708738999728007553932469641177e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 2.0061668278917446293134892047287 y[1] (numeric) = 2.0061668278917446347203186480919 absolute error = 5.4068294433632e-18 relative error = 2.6951045985767638001029929500415e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 2.0062785590727012265212641002729 y[1] (numeric) = 2.0062785590727012319770054919902 absolute error = 5.4557413917173e-18 relative error = 2.7193339464480620443954594348589e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 2.0063912965323007529796501271196 y[1] (numeric) = 2.0063912965323007584843089081511 absolute error = 5.5046587810315e-18 relative error = 2.7435619315860010180040515438943e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 2.006505040383280677682962356775 y[1] (numeric) = 2.0065050403832806832365440169983 absolute error = 5.5535816602233e-18 relative error = 2.7677885419926282028885046546873e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 2.0066197907393848610897800568335 y[1] (numeric) = 2.006619790739384866692290135049 absolute error = 5.6025100782155e-18 relative error = 2.7920137656726326264864490344727e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 2.0067355477153636688668166282126 y[1] (numeric) = 2.0067355477153636745182607121489 absolute error = 5.6514440839363e-18 relative error = 2.8162375906333939799212871902528e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 2.0068523114269740866392948343964 y[1] (numeric) = 2.0068523114269740923396785607165 absolute error = 5.7003837263201e-18 relative error = 2.8404600048853805185560651403084e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 2.0069700819909798357479420730751 y[1] (numeric) = 2.0069700819909798414972711273814 absolute error = 5.7493290543063e-18 relative error = 2.8646809964415502896956745732354e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 2.0070888595251514900127214471822 y[1] (numeric) = 2.0070888595251514958110015640224 absolute error = 5.7982801168402e-18 relative error = 2.8889005533177988558236436763263e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 2.0072086441482665935034153990723 y[1] (numeric) = 2.0072086441482665993506523619454 absolute error = 5.8472369628731e-18 relative error = 2.9131186635330082901370460236187e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 2.0073294359801097793171796784333 y[1] (numeric) = 2.0073294359801097852133793197949 absolute error = 5.8961996413616e-18 relative error = 2.9373353151086976077388393181233e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 2.0074512351414728893631864214943 y[1] (numeric) = 2.0074512351414728953083546227629 absolute error = 5.9451682012686e-18 relative error = 2.9615504960695201616322535033574e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 2.0075740417541550951544761261857 y[1] (numeric) = 2.0075740417541551011486188177482 absolute error = 5.9941426915625e-18 relative error = 2.9857641944428642469337019860978e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 2.0076978559409630196071393151105 y[1] (numeric) = 2.0076978559409630256502624763282 absolute error = 6.0431231612177e-18 relative error = 3.0099763982591013523535864107025e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 2.0078226778257108598469496855204 y[1] (numeric) = 2.0078226778257108659390593447354 absolute error = 6.0921096592150e-18 relative error = 3.0341870955517845087051066950105e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 2.0079485075332205110235715529401 y[1] (numeric) = 2.0079485075332205171646737874807 absolute error = 6.1411022345406e-18 relative error = 3.0583962743571493268749911671553e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 2.008075345189321691132465402656 y[1] (numeric) = 2.0080753451893216973225663388432 absolute error = 6.1901009361872e-18 relative error = 3.0826039227146609940873950126888e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 2.008203190920852066844616370987 y[1] (numeric) = 2.0082031909208520730837221841406 absolute error = 6.2391058131536e-18 relative error = 3.1068100286668141204419570610255e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 2.0083320448556573803442114860759 y[1] (numeric) = 2.0083320448556573866323284005204 absolute error = 6.2881169144445e-18 relative error = 3.1310145802590322392107515321132e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 2.0084619071225915771743925058882 y[1] (numeric) = 2.0084619071225915835115267949593 absolute error = 6.3371342890711e-18 relative error = 3.1552175655399656540820360483258e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 2.0085927778515169350912121991831 y[1] (numeric) = 2.0085927778515169414773701852339 absolute error = 6.3861579860508e-18 relative error = 3.1794189725613410891568271031674e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.2MB, time=1.40 NO POLE x[1] = 0.132 y[1] (analytic) = 2.0087246571733041939259229234232 y[1] (numeric) = 2.0087246571733042003611109778305 absolute error = 6.4351880544073e-18 relative error = 3.2036187893780105214593892644384e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 2.0088575452198326864557273619225 y[1] (numeric) = 2.008857545219832692939951905093 absolute error = 6.4842245431705e-18 relative error = 3.2278170040479004282071542550238e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 2.008991442123990470283122290993 y[1] (numeric) = 2.0089914421239904768163897923702 absolute error = 6.5332675013772e-18 relative error = 3.2520136046323592571055472203543e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 2.0091263480196744607239672564477 y[1] (numeric) = 2.0091263480196744673062842345178 absolute error = 6.5823169780701e-18 relative error = 3.2762085791956586112050183744091e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 2.0092622630417905647044110475359 y[1] (numeric) = 2.0092622630417905713357840698347 absolute error = 6.6313730222988e-18 relative error = 3.3004019158054900174009630952166e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 2.0093991873262538156668098652518 y[1] (numeric) = 2.0093991873262538223472455483712 absolute error = 6.6804356831194e-18 relative error = 3.3245936025327647610082466018742e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 2.0095371210099885094847720909438 y[1] (numeric) = 2.0095371210099885162142771005382 absolute error = 6.7295050095944e-18 relative error = 3.3487836274515630821107636428141e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 2.0096760642309283413874655702809 y[1] (numeric) = 2.0096760642309283481660466210742 absolute error = 6.7785810507933e-18 relative error = 3.3729719786394317006834779562431e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 2.0098160171280165438933243368962 y[1] (numeric) = 2.0098160171280165507209881926882 absolute error = 6.8276638557920e-18 relative error = 3.3971586441770841411873961174051e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 2.0099569798412060257532927094232 y[1] (numeric) = 2.0099569798412060326300461830966 absolute error = 6.8767534736734e-18 relative error = 3.4213436121486982022056396844575e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 2.0100989525114595119037457051836 y[1] (numeric) = 2.0100989525114595188295956587107 absolute error = 6.9258499535271e-18 relative error = 3.4455268706417655544801867156497e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.143 y[1] (analytic) = 2.0102419352807496844292257234561 y[1] (numeric) = 2.0102419352807496914041790679057 absolute error = 6.9749533444496e-18 relative error = 3.4697084077471901209062903765216e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 2.0103859282920593245351364610762 y[1] (numeric) = 2.0103859282920593315592001566204 absolute error = 7.0240636955442e-18 relative error = 3.4938882115592371819122349277434e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 2.0105309316893814555305360330718 y[1] (numeric) = 2.0105309316893814626037170889932 absolute error = 7.0731810559214e-18 relative error = 3.5180662701757311855120971558831e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 2.0106769456177194868211722811407 y[1] (numeric) = 2.0106769456177194939434777558392 absolute error = 7.1223054746985e-18 relative error = 3.5422425716978555878426760824180e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 2.0108239702230873589129042630159 y[1] (numeric) = 2.0108239702230873660843412640159 absolute error = 7.1714370010000e-18 relative error = 3.5664171042303506196195995608261e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.148 y[1] (analytic) = 2.0109720056525096894256549261538 y[1] (numeric) = 2.0109720056525096966462306101111 absolute error = 7.2205756839573e-18 relative error = 3.5905898558813628677461100878513e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 2.0111210520540219201180409797089 y[1] (numeric) = 2.011121052054021927387762552418 absolute error = 7.2697215727091e-18 relative error = 3.6147608147626429798911317715965e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 2.0112711095766704649228269894375 y[1] (numeric) = 2.0112711095766704722417017058388 absolute error = 7.3188747164013e-18 relative error = 3.6389299689894946743160420483026e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 2.0114221783705128589933517309974 y[1] (numeric) = 2.0114221783705128663613868951846 absolute error = 7.3680351641872e-18 relative error = 3.6630973066808729122657725975110e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 2.0115742585866179087610758480819 y[1] (numeric) = 2.0115742585866179161782788133089 absolute error = 7.4172029652270e-18 relative error = 3.6872628159591340315558845783162e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.153 y[1] (analytic) = 2.0117273503770658430044008729476 y[1] (numeric) = 2.0117273503770658504707790416362 absolute error = 7.4663781686886e-18 relative error = 3.7114264849504321963427623302219e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.154 y[1] (analytic) = 2.0118814538949484649289106781689 y[1] (numeric) = 2.0118814538949484724444715019163 absolute error = 7.5155608237474e-18 relative error = 3.7355883017846186107822622552324e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 2.0120365692943693052591874398729 y[1] (numeric) = 2.0120365692943693128239384194587 absolute error = 7.5647509795858e-18 relative error = 3.7597482545949916670453069294169e-16 % memory used=26.7MB, alloc=4.2MB, time=1.65 h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.156 y[1] (analytic) = 2.0121926967304437763423552042824 y[1] (numeric) = 2.0121926967304437839563038896766 absolute error = 7.6139486853942e-18 relative error = 3.7839063315187926563667763417872e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 2.0123498363592993272635051611252 y[1] (numeric) = 2.0123498363592993349266591514953 absolute error = 7.6631539903701e-18 relative error = 3.8080625206967570712870262012996e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 2.0125079883380755999731577393461 y[1] (numeric) = 2.012507988338075607685524683065 absolute error = 7.7123669437189e-18 relative error = 3.8322168102735108262534568512786e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.159 y[1] (analytic) = 2.0126671528249245864269176525981 y[1] (numeric) = 2.0126671528249245941885052472516 absolute error = 7.7615875946535e-18 relative error = 3.8563691883973700596032738445720e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 2.0128273299790107867374790341803 y[1] (numeric) = 2.0128273299790107945482950265749 absolute error = 7.8108159923946e-18 relative error = 3.8805196432204887909391396279470e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 2.0129885199605113683391388134405 y[1] (numeric) = 2.0129885199605113761991909996112 absolute error = 7.8600521861707e-18 relative error = 3.9046681628988574673255486365631e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.162 y[1] (analytic) = 2.0131507229306163261649774981705 y[1] (numeric) = 2.0131507229306163340742737233882 absolute error = 7.9092962252177e-18 relative error = 3.9288147355921028075812645610452e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 2.0133139390515286438368675401857 y[1] (numeric) = 2.0133139390515286517954156989656 absolute error = 7.9585481587799e-18 relative error = 3.9529593494639831059053998860422e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 2.0134781684864644558684704741142 y[1] (numeric) = 2.0134781684864644638762785102234 absolute error = 8.0078080361092e-18 relative error = 3.9771019926819893103487310465044e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.165 y[1] (analytic) = 2.0136434113996532108813850324027 y[1] (numeric) = 2.0136434113996532189384609388682 absolute error = 8.0570759064655e-18 relative error = 4.0012426534175422214544849197988e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 2.0138096679563378358346094527036 y[1] (numeric) = 2.0138096679563378439409612718202 absolute error = 8.1063518191166e-18 relative error = 4.0253813198459412997591239905252e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 2.0139769383227749012674822071171 y[1] (numeric) = 2.0139769383227749094231180304555 absolute error = 8.1556358233384e-18 relative error = 4.0495179801464624486069123054480e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 2.0141452226662347875562663962447 y[1] (numeric) = 2.0141452226662347957611943646597 absolute error = 8.2049279684150e-18 relative error = 4.0736526225024060903931593506058e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.169 y[1] (analytic) = 2.0143145211550018521845440646509 y[1] (numeric) = 2.0143145211550018604387723682894 absolute error = 8.2542283036385e-18 relative error = 4.0977852351009962752012887995989e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.17 y[1] (analytic) = 2.0144848339583745980275877081423 y[1] (numeric) = 2.0144848339583746063311245864516 absolute error = 8.3035368783093e-18 relative error = 4.1219158061335280334638389041476e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 2.0146561612466658426508772572493 y[1] (numeric) = 2.0146561612466658510037309989852 absolute error = 8.3528537417359e-18 relative error = 4.1460443237952664634385490082025e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 2.0148285031912028886229318354409 y[1] (numeric) = 2.014828503191202897025110778676 absolute error = 8.4021789432351e-18 relative error = 4.1701707762855443888482998418384e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 2.0150018599643276948426266049198 y[1] (numeric) = 2.0150018599643277032941391370521 absolute error = 8.4515125321323e-18 relative error = 4.1942951518079095850439480587569e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 2.0151762317393970488811660273279 y[1] (numeric) = 2.0151762317393970573820205850888 absolute error = 8.5008545577609e-18 relative error = 4.2184174385698253082326196260409e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.175 y[1] (analytic) = 2.0153516186907827403388858813502 y[1] (numeric) = 2.0153516186907827488890909508132 absolute error = 8.5502050694630e-18 relative error = 4.2425376247830160193721392524459e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.176 y[1] (analytic) = 2.0155280209938717352170573940335 y[1] (numeric) = 2.0155280209938717438166215106227 absolute error = 8.5995641165892e-18 relative error = 4.2666556986633663853483384976524e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.177 y[1] (analytic) = 2.0157054388250663513048678576385 y[1] (numeric) = 2.015705438825066359953799606137 absolute error = 8.6489317484985e-18 relative error = 4.2907716484308699333611506128471e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 2.0158838723617844345817531190212 y[1] (numeric) = 2.0158838723617844432800611335796 absolute error = 8.6983080145584e-18 relative error = 4.3148854623096769349684380635998e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.3MB, time=1.90 x[1] = 0.179 y[1] (analytic) = 2.016063321782459536635258343889 y[1] (numeric) = 2.0160633217824595453829513080344 absolute error = 8.7476929641454e-18 relative error = 4.3389971285283406618506691600439e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.18 y[1] (analytic) = 2.0162437872665410930946044738096 y[1] (numeric) = 2.016243787266541101891691120454 absolute error = 8.7970866466444e-18 relative error = 4.3631066353195179309602077791991e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 2.016425268994494603080138809552 y[1] (numeric) = 2.016425268994494611926627921001 absolute error = 8.8464891114490e-18 relative error = 4.3872139709201161346298698807507e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 2.0166077671478018096688491702255 y[1] (numeric) = 2.0166077671478018185647495781872 absolute error = 8.8959004079617e-18 relative error = 4.4113191235713905938305090313508e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 2.0167912819089608813761220937471 y[1] (numeric) = 2.0167912819089608903214426793408 absolute error = 8.9453205855937e-18 relative error = 4.4354220815188435136375016596425e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 2.0169758134614865946539265604088 y[1] (numeric) = 2.0169758134614866036486762541742 absolute error = 8.9947496937654e-18 relative error = 4.4595228330124700379893172350029e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 2.0171613619899105174056057377456 y[1] (numeric) = 2.0171613619899105264497935196513 absolute error = 9.0441877819057e-18 relative error = 4.4836213663064092637201736848481e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.186 y[1] (analytic) = 2.0173479276797811935174602615094 y[1] (numeric) = 2.0173479276797812026110951609623 absolute error = 9.0936348994529e-18 relative error = 4.5077176696593885574598734939027e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 2.0175355107176643284073075843492 y[1] (numeric) = 2.0175355107176643375503986802032 absolute error = 9.1430910958540e-18 relative error = 4.5318117313343745693792315171449e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.188 y[1] (analytic) = 2.0177241112911429755902029407709 y[1] (numeric) = 2.017724111291142984782759361336 absolute error = 9.1925564205651e-18 relative error = 4.5559035395987695995665664350595e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.189 y[1] (analytic) = 2.0179137295888177242615084941142 y[1] (numeric) = 2.0179137295888177335035394171659 absolute error = 9.2420309230517e-18 relative error = 4.5799930827245582885355723626787e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 2.0181043658003068878974982486313 y[1] (numeric) = 2.0181043658003068971890129014195 absolute error = 9.2915146527882e-18 relative error = 4.6040803489880578025861114522002e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 2.0182960201162466938736873272872 y[1] (numeric) = 2.0182960201162467032146949865457 absolute error = 9.3410076592585e-18 relative error = 4.6281653266702131643076587068444e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 2.018488692728291474101075233628 y[1] (numeric) = 2.0184886927282914834915852255834 absolute error = 9.3905099919554e-18 relative error = 4.6522480040562979003511077233544e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.193 y[1] (analytic) = 2.018682383829113856680493733975 y[1] (numeric) = 2.0186823838291138661205154343563 absolute error = 9.4400217003813e-18 relative error = 4.6763283694362588344400778070061e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 2.0188770936124049585752510143094 y[1] (numeric) = 2.0188770936124049680647938483574 absolute error = 9.4895428340480e-18 relative error = 4.7004064111046148793569148865205e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.195 y[1] (analytic) = 2.0190728222728745793022647845074 y[1] (numeric) = 2.019072822272874588841338226984 absolute error = 9.5390734424766e-18 relative error = 4.7244821173604054038444217219242e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 2.0192695700062513956418780210754 y[1] (numeric) = 2.019269570006251405230491596273 absolute error = 9.5886135751976e-18 relative error = 4.7485554765072376646516525501705e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 2.0194673370092831573665520582161 y[1] (numeric) = 2.0194673370092831670047153399674 absolute error = 9.6381632817513e-18 relative error = 4.7726264768534827544792303790582e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 2.0196661234797368839886327559364 y[1] (numeric) = 2.0196661234797368936763553676237 absolute error = 9.6877226116873e-18 relative error = 4.7966951067120258054961941146152e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 2.0198659296163990625273864929789 y[1] (numeric) = 2.0198659296163990722646781075439 absolute error = 9.7372916145650e-18 relative error = 4.8207613544005114116063050684688e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2 y[1] (analytic) = 2.0200667556190758462955037516294 y[1] (numeric) = 2.0200667556190758560823740915827 absolute error = 9.7868703399533e-18 relative error = 4.8448252082411928679328685492927e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 2.0202686016885932547052690809203 y[1] (numeric) = 2.0202686016885932645417279183514 absolute error = 9.8364588374311e-18 relative error = 4.8688866565611774760080445037546e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.202 y[1] (analytic) = 2.0204714680267973740945972444179 y[1] (numeric) = 2.0204714680267973839806544010047 absolute error = 9.8860571565868e-18 relative error = 4.8929456876921767568273160902815e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=2.15 NO POLE x[1] = 0.203 y[1] (analytic) = 2.0206753548365545595731363786447 y[1] (numeric) = 2.0206753548365545695088017256634 absolute error = 9.9356653470187e-18 relative error = 4.9170022899707021986538547215949e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.204 y[1] (analytic) = 2.0208802623217516378886400082574 y[1] (numeric) = 2.0208802623217516478739234665925 absolute error = 9.9852834583351e-18 relative error = 4.9410564517381124254619645474793e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.205 y[1] (analytic) = 2.0210861906872961113138107843703 y[1] (numeric) = 2.0210861906872961213487223245244 absolute error = 1.00349115401541e-17 relative error = 4.9651081613405118900239485306877e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.206 y[1] (analytic) = 2.0212931401391163625538198328837 y[1] (numeric) = 2.0212931401391163726383694749873 absolute error = 1.00845496421036e-17 relative error = 4.9891574071287485640562760296655e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.207 y[1] (analytic) = 2.0215011108841618606747066203537 y[1] (numeric) = 2.0215011108841618708089044341756 absolute error = 1.01341978138219e-17 relative error = 5.0132041774587084280729859383164e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.208 y[1] (analytic) = 2.0217101031304033680528652658218 y[1] (numeric) = 2.0217101031304033782367213707789 absolute error = 1.01838561049571e-17 relative error = 5.0372484606910162109462339664952e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.209 y[1] (analytic) = 2.0219201170868331483458242481064 y[1] (numeric) = 2.0219201170868331585793488132738 absolute error = 1.02335245651674e-17 relative error = 5.0612902451911814245617107936291e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.21 y[1] (analytic) = 2.0221311529634651754845274793535 y[1] (numeric) = 2.022131152963465185767730723475 absolute error = 1.02832032441215e-17 relative error = 5.0853295193297937493335607783078e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.211 y[1] (analytic) = 2.0223432109713353436873257371461 y[1] (numeric) = 2.022343210971335354020217928644 absolute error = 1.03328921914979e-17 relative error = 5.1093662714821743618213211737579e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.212 y[1] (analytic) = 2.0225562913225016784958884691798 y[1] (numeric) = 2.0225562913225016888784799261654 absolute error = 1.03825914569856e-17 relative error = 5.1334004900287196632462584596239e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.213 y[1] (analytic) = 2.0227703942300445488332470064351 y[1] (numeric) = 2.022770394230044559265548096719 absolute error = 1.04323010902839e-17 relative error = 5.1574321633547998452873183563873e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.214 y[1] (analytic) = 2.0229855199080668800841812429068 y[1] (numeric) = 2.0229855199080668905662023840092 absolute error = 1.04820211411024e-17 relative error = 5.1814612798507563717903879593796e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.215 y[1] (analytic) = 2.0232016685716943681981628622947 y[1] (numeric) = 2.0232016685716943787299145214558 absolute error = 1.05317516591611e-17 relative error = 5.2054878279119488769908681488400e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.216 y[1] (analytic) = 2.0234188404370756948150692146173 y[1] (numeric) = 2.023418840437075705396561908808 absolute error = 1.05814926941907e-17 relative error = 5.2295117959389008645616863242593e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.217 y[1] (analytic) = 2.0236370357213827434138829684801 y[1] (numeric) = 2.0236370357213827540451272644122 absolute error = 1.06312442959321e-17 relative error = 5.2535331723370499727603864819298e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.218 y[1] (analytic) = 2.0238562546428108164845936877157 y[1] (numeric) = 2.0238562546428108271656002018526 absolute error = 1.06810065141369e-17 relative error = 5.2775519455169924952893251048293e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.219 y[1] (analytic) = 2.0240764974205788537235185043155 y[1] (numeric) = 2.0240764974205788644542979028829 absolute error = 1.07307793985674e-17 relative error = 5.3015681038944807054527504089751e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.22 y[1] (analytic) = 2.0242977642749296512522600829931 y[1] (numeric) = 2.0242977642749296620328230819895 absolute error = 1.07805629989964e-17 relative error = 5.3255816358903213698008279803972e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.221 y[1] (analytic) = 2.0245200554271300818605210963532 y[1] (numeric) = 2.0245200554271300926908784615608 absolute error = 1.08303573652076e-17 relative error = 5.3495925299305706827242682913373e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.222 y[1] (analytic) = 2.0247433710994713162729954535016 y[1] (numeric) = 2.0247433710994713271531580004969 absolute error = 1.08801625469953e-17 relative error = 5.3736007744463833376542169687175e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.223 y[1] (analytic) = 2.0249677115152690454405575490035 y[1] (numeric) = 2.0249677115152690563705361431682 absolute error = 1.09299785941647e-17 relative error = 5.3976063578741579866674220547707e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.224 y[1] (analytic) = 2.0251930768988637038559718233995 y[1] (numeric) = 2.0251930768988637148357773799314 absolute error = 1.09798055565319e-17 relative error = 5.4216092686555344572570618915424e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.225 y[1] (analytic) = 2.0254194674756206938943459510072 y[1] (numeric) = 2.0254194674756207049239894349309 absolute error = 1.10296434839237e-17 relative error = 5.4456094952372922133060549255756e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.226 y[1] (analytic) = 2.0256468834719306111785519954791 y[1] (numeric) = 2.0256468834719306222580444216574 absolute error = 1.10794924261783e-17 relative error = 5.4696070260716931744117237937190e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=2.40 NO POLE x[1] = 0.227 y[1] (analytic) = 2.025875325115209470969840898559 y[1] (numeric) = 2.0258753251152094820991933317034 absolute error = 1.11293524331444e-17 relative error = 5.4936018496160345095208646200868e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.228 y[1] (analytic) = 2.0261047926338989355838766926674 y[1] (numeric) = 2.0261047926338989467631002473496 absolute error = 1.11792235546822e-17 relative error = 5.5175939543331394802624748635003e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.229 y[1] (analytic) = 2.026335286257466542832417853372 y[1] (numeric) = 2.0263352862574665540615236940347 absolute error = 1.12291058406627e-17 relative error = 5.5415833286910089856393901987381e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.23 y[1] (analytic) = 2.0265668062164059354908742334413 y[1] (numeric) = 2.0265668062164059467698735744096 absolute error = 1.12789993409683e-17 relative error = 5.5655699611631148102475076085038e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.231 y[1] (analytic) = 2.0267993527422370917919690460588 y[1] (numeric) = 2.0267993527422371031208731515512 absolute error = 1.13289041054924e-17 relative error = 5.5895538402281992703214506330119e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.232 y[1] (analytic) = 2.0270329260675065569457363908782 y[1] (numeric) = 2.027032926067506568324556575018 absolute error = 1.13788201841398e-17 relative error = 5.6135349543704696501490909467353e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.233 y[1] (analytic) = 2.0272675264257876756860858429371 y[1] (numeric) = 2.0272675264257876871148334697636 absolute error = 1.14287476268265e-17 relative error = 5.6375132920794965265556457198051e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.234 y[1] (analytic) = 2.0275031540516808258441666510125 y[1] (numeric) = 2.0275031540516808373228531344926 absolute error = 1.14786864834801e-17 relative error = 5.6614888418504080813605660651905e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.235 y[1] (analytic) = 2.0277398091808136529487651188023 y[1] (numeric) = 2.0277398091808136644774019228416 absolute error = 1.15286368040393e-17 relative error = 5.6854615921836404213028761807060e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.236 y[1] (analytic) = 2.0279774920498413058539697693492 y[1] (numeric) = 2.0279774920498413174325684078038 absolute error = 1.15785986384546e-17 relative error = 5.7094315315852797821791401858040e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.237 y[1] (analytic) = 2.0282162028964466733943399203925 y[1] (numeric) = 2.0282162028964466850229119570802 absolute error = 1.16285720366877e-17 relative error = 5.7333986485667635221112983967630e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.238 y[1] (analytic) = 2.0284559419593406220678143258353 y[1] (numeric) = 2.0284559419593406337463713745474 absolute error = 1.16785570487121e-17 relative error = 5.7573629316451728954192476914204e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.239 y[1] (analytic) = 2.0286967094782622347465975662562 y[1] (numeric) = 2.0286967094782622464751512907691 absolute error = 1.17285537245129e-17 relative error = 5.7813243693431312641435305967001e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.24 y[1] (analytic) = 2.0289385056939790504162628993717 y[1] (numeric) = 2.0289385056939790621948250134582 absolute error = 1.17785621140865e-17 relative error = 5.8052829501886530813462763383798e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.241 y[1] (analytic) = 2.0291813308482873049433113095711 y[1] (numeric) = 2.0291813308482873167718935770126 absolute error = 1.18285822674415e-17 relative error = 5.8292386627155843410670671229776e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.242 y[1] (analytic) = 2.0294251851840121728714275241051 y[1] (numeric) = 2.0294251851840121847500417587031 absolute error = 1.18786142345980e-17 relative error = 5.8531914954632542981313431652362e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.243 y[1] (analytic) = 2.0296700689450080102466747922021 y[1] (numeric) = 2.02967006894500802217533285779 absolute error = 1.19286580655879e-17 relative error = 5.8771414369766201157302779740255e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.244 y[1] (analytic) = 2.0299159823761585984718712523284 y[1] (numeric) = 2.0299159823761586104505850627836 absolute error = 1.19787138104552e-17 relative error = 5.9010884758064113953471742068069e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.245 y[1] (analytic) = 2.030162925723377389190391741989 y[1] (numeric) = 2.0301629257233774012191732612446 absolute error = 1.20287815192556e-17 relative error = 5.9250326005089297877784331130862e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.246 y[1] (analytic) = 2.0304108992336077501996399338908 y[1] (numeric) = 2.0304108992336077622785011759475 absolute error = 1.20788612420567e-17 relative error = 5.9489737996461442431747214094801e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.247 y[1] (analytic) = 2.0306599031548232123944367119608 y[1] (numeric) = 2.030659903154823224523389740899 absolute error = 1.21289530289382e-17 relative error = 5.9729120617857861781224358638829e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.248 y[1] (analytic) = 2.0309099377360277177405717306283 y[1] (numeric) = 2.0309099377360277299196286606205 absolute error = 1.21790569299922e-17 relative error = 5.9968473755014937979355103970949e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.249 y[1] (analytic) = 2.0311610032272558682787661309445 y[1] (numeric) = 2.0311610032272558805079391262668 absolute error = 1.22291729953223e-17 relative error = 6.0207797293723655026702422919899e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.25 y[1] (analytic) = 2.0314130998795731761592954175204 y[1] (numeric) = 2.0314130998795731884385966925651 absolute error = 1.22793012750447e-17 relative error = 6.0447091119834981468796959911580e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=2.65 NO POLE x[1] = 0.251 y[1] (analytic) = 2.0316662279450763147075225309294 y[1] (numeric) = 2.0316662279450763270369643502171 absolute error = 1.23294418192877e-17 relative error = 6.0686355119257373544389901120549e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.252 y[1] (analytic) = 2.0319203876768933705205921811271 y[1] (numeric) = 2.0319203876768933829001868593188 absolute error = 1.23795946781917e-17 relative error = 6.0925589177956740777747778296260e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.253 y[1] (analytic) = 2.0321755793291840965955385386037 y[1] (numeric) = 2.0321755793291841090252984405134 absolute error = 1.24297599019097e-17 relative error = 6.1164793181958871878040570482648e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.254 y[1] (analytic) = 2.0324318031571401664890594113985 y[1] (numeric) = 2.0324318031571401789689969520053 absolute error = 1.24799375406068e-17 relative error = 6.1403967017346938454596397222690e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.255 y[1] (analytic) = 2.0326890594169854295092110677709 y[1] (numeric) = 2.0326890594169854420393387122318 absolute error = 1.25301276444609e-17 relative error = 6.1643110570264903985284991989445e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.256 y[1] (analytic) = 2.0329473483659761669392788962454 y[1] (numeric) = 2.0329473483659761795196091599072 absolute error = 1.25803302636618e-17 relative error = 6.1882223726913059707410317344592e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.257 y[1] (analytic) = 2.0332066702624013492940801269205 y[1] (numeric) = 2.0332066702624013619246255753328 absolute error = 1.26305454484123e-17 relative error = 6.2121306373553400445842845939843e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.258 y[1] (analytic) = 2.0334670253655828946089558703679 y[1] (numeric) = 2.0334670253655829072897291192955 absolute error = 1.26807732489276e-17 relative error = 6.2360358396506636083047964924219e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.259 y[1] (analytic) = 2.0337284139358759277617107631341 y[1] (numeric) = 2.0337284139358759404927244785696 absolute error = 1.27310137154355e-17 relative error = 6.2599379682153138833418729725393e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.26 y[1] (analytic) = 2.0339908362346690408277595418062 y[1] (numeric) = 2.0339908362346690536090264399825 absolute error = 1.27812668981763e-17 relative error = 6.2838370116932414712944027265318e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.261 y[1] (analytic) = 2.0342542925243845544687409008098 y[1] (numeric) = 2.0342542925243845673002737482132 absolute error = 1.28315328474034e-17 relative error = 6.3077329587346016339269756785552e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.262 y[1] (analytic) = 2.0345187830684787803548600225756 y[1] (numeric) = 2.0345187830684787932366716359582 absolute error = 1.28818116133826e-17 relative error = 6.3316257979954063602714388177892e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.263 y[1] (analytic) = 2.0347843081314422846212222024373 y[1] (numeric) = 2.0347843081314422975533254488301 absolute error = 1.29321032463928e-17 relative error = 6.3555155181378647236699292876775e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.264 y[1] (analytic) = 2.0350508679788001523584210246188 y[1] (numeric) = 2.0350508679788001653408288213444 absolute error = 1.29824077967256e-17 relative error = 6.3794021078301824309633756228077e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.265 y[1] (analytic) = 2.0353184628771122531376455799187 y[1] (numeric) = 2.0353184628771122661703708946042 absolute error = 1.30327253146855e-17 relative error = 6.4032855557466563081346968269428e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.266 y[1] (analytic) = 2.0355870930939735075705722502224 y[1] (numeric) = 2.0355870930939735206536281008124 absolute error = 1.30830558505900e-17 relative error = 6.4271658505677195710556369542693e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.267 y[1] (analytic) = 2.0358567588980141549043076197562 y[1] (numeric) = 2.0358567588980141680377070745259 absolute error = 1.31333994547697e-17 relative error = 6.4510429809799870454264501448758e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.268 y[1] (analytic) = 2.0361274605589000216516501080476 y[1] (numeric) = 2.0361274605589000348354062856159 absolute error = 1.31837561775683e-17 relative error = 6.4749169356762512227293998685537e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.269 y[1] (analytic) = 2.0363991983473327912569389548773 y[1] (numeric) = 2.0363991983473328044910650242197 absolute error = 1.32341260693424e-17 relative error = 6.4987877033553800914467380611797e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.27 y[1] (analytic) = 2.0366719725350502747977602230921 y[1] (numeric) = 2.0366719725350502880822694035539 absolute error = 1.32845091804618e-17 relative error = 6.5226552727224605337274155015254e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.271 y[1] (analytic) = 2.0369457833948266827227805210095 y[1] (numeric) = 2.0369457833948266960576860823194 absolute error = 1.33349055613099e-17 relative error = 6.5465196324889906851903753078282e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.272 y[1] (analytic) = 2.0372206312004728976259801822697 y[1] (numeric) = 2.0372206312004729110112954445525 absolute error = 1.33853152622828e-17 relative error = 6.5703807713724339993967719333167e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.273 y[1] (analytic) = 2.0374965162268367480575586773896 y[1] (numeric) = 2.03749651622683676149329701118 absolute error = 1.34357383337904e-17 relative error = 6.5942386780967552546947067034742e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=45.7MB, alloc=4.3MB, time=2.89 x[1] = 0.274 y[1] (analytic) = 2.0377734387498032833717860679493 y[1] (numeric) = 2.037773438749803296857960894205 absolute error = 1.34861748262557e-17 relative error = 6.6180933413920727937976337133500e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.275 y[1] (analytic) = 2.0380513990462950496120753512833 y[1] (numeric) = 2.0380513990462950631487001413986 absolute error = 1.35366247901153e-17 relative error = 6.6419447499948998284700879109838e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.276 y[1] (analytic) = 2.0383303973942723664335515807735 y[1] (numeric) = 2.0383303973942723800206398565924 absolute error = 1.35870882758189e-17 relative error = 6.6657928926478949340123908350523e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.277 y[1] (analytic) = 2.0386104340727336050633946843345 y[1] (numeric) = 2.0386104340727336187009600181647 absolute error = 1.36375653338302e-17 relative error = 6.6896377581002994755030081404852e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.278 y[1] (analytic) = 2.0388915093617154672992339414589 y[1] (numeric) = 2.0388915093617154809872899560852 absolute error = 1.36880560146263e-17 relative error = 6.7134793351076389641768771496013e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.279 y[1] (analytic) = 2.0391736235422932655458731172394 y[1] (numeric) = 2.0391736235422932792844334859371 absolute error = 1.37385603686977e-17 relative error = 6.7373176124317188811218151047378e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.28 y[1] (analytic) = 2.0394567768965812038906262901154 y[1] (numeric) = 2.0394567768965812176797047366643 absolute error = 1.37890784465489e-17 relative error = 6.7611525788409146853988535462580e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.281 y[1] (analytic) = 2.0397409697077326602175454487053 y[1] (numeric) = 2.0397409697077326740571557474034 absolute error = 1.38396102986981e-17 relative error = 6.7849842231100203323142005293920e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.282 y[1] (analytic) = 2.0400262022599404693608219719743 y[1] (numeric) = 2.0400262022599404832509779476512 absolute error = 1.38901559756769e-17 relative error = 6.8088125340200969017342887984187e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.283 y[1] (analytic) = 2.0403124748384372072976451461622 y[1] (numeric) = 2.0403124748384372212383606741933 absolute error = 1.39407155280311e-17 relative error = 6.8326375003588604711544561881627e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.284 y[1] (analytic) = 2.0405997877294954763808019113554 y[1] (numeric) = 2.0405997877294954903720909176756 absolute error = 1.39912890063202e-17 relative error = 6.8564591109204325789697877210990e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.285 y[1] (analytic) = 2.0408881412204281916113030703244 y[1] (numeric) = 2.0408881412204282056531795314421 absolute error = 1.40418764611177e-17 relative error = 6.8802773545054828680893178066210e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.286 y[1] (analytic) = 2.0411775355995888679513222322786 y[1] (numeric) = 2.0411775355995888820438001752897 absolute error = 1.40924779430111e-17 relative error = 6.9040922199212246188207738035075e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.287 y[1] (analytic) = 2.0414679711563719086777348045 y[1] (numeric) = 2.041467971156371922820828307102 absolute error = 1.41430935026020e-17 relative error = 6.9279036959814592535303831259131e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.288 y[1] (analytic) = 2.0417594481812128947765453854202 y[1] (numeric) = 2.0417594481812129089702685759259 absolute error = 1.41937231905057e-17 relative error = 6.9517117715063759000825954237287e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.289 y[1] (analytic) = 2.0420519669655888753784929535903 y[1] (numeric) = 2.0420519669655888896228600109424 absolute error = 1.42443670573521e-17 relative error = 6.9755164353229877255887043385785e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.29 y[1] (analytic) = 2.0423455278020186592361242881752 y[1] (numeric) = 2.0423455278020186735311494419601 absolute error = 1.42950251537849e-17 relative error = 6.9993176762647355026691581943761e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.291 y[1] (analytic) = 2.0426401309840631072426270980681 y[1] (numeric) = 2.0426401309840631215883246285305 absolute error = 1.43456975304624e-17 relative error = 7.0231154831718748006317101679561e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.292 y[1] (analytic) = 2.0429357768063254259927153784849 y[1] (numeric) = 2.0429357768063254403890996165417 absolute error = 1.43963842380568e-17 relative error = 7.0469098448911285879727532309626e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.293 y[1] (analytic) = 2.0432324655644514623858605559455 y[1] (numeric) = 2.0432324655644514768329458832004 absolute error = 1.44470853272549e-17 relative error = 7.0707007502760253084633206866469e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.294 y[1] (analytic) = 2.0435301975551299992721630249001 y[1] (numeric) = 2.0435301975551300137699638736579 absolute error = 1.44978008487578e-17 relative error = 7.0944881881867472973072596076825e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.295 y[1] (analytic) = 2.043828973076093052141159721896 y[1] (numeric) = 2.043828973076093066689690575177 absolute error = 1.45485308532810e-17 relative error = 7.1182721474901750237230173200559e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.296 y[1] (analytic) = 2.0441287924261161668538644261162 y[1] (numeric) = 2.0441287924261161814531398176708 absolute error = 1.45992753915546e-17 relative error = 7.1420526170599801988160589376831e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.297 y[1] (analytic) = 2.0444296559050187184183385183567 y[1] (numeric) = 2.0444296559050187330683730326797 absolute error = 1.46500345143230e-17 relative error = 7.1658295857764742176352170636487e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=49.5MB, alloc=4.3MB, time=3.14 x[1] = 0.298 y[1] (analytic) = 2.044731563813664210809090974036 y[1] (numeric) = 2.0447315638136642255098992463814 absolute error = 1.47008082723454e-17 relative error = 7.1896030425268479676575290954197e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.299 y[1] (analytic) = 2.045034516453960577830607409664 y[1] (numeric) = 2.0450345164539605925822041260596 absolute error = 1.47515967163956e-17 relative error = 7.2133729762050691156228184225136e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3 y[1] (analytic) = 2.0453385141288604850253090463229 y[1] (numeric) = 2.0453385141288604998277089435848 absolute error = 1.48023998972619e-17 relative error = 7.2371393757118283598946650850589e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.301 y[1] (analytic) = 2.0456435571423616326262434981446 y[1] (numeric) = 2.0456435571423616474794613638922 absolute error = 1.48532178657476e-17 relative error = 7.2609022299547790202846690560080e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.302 y[1] (analytic) = 2.0459496457995070595548103385009 y[1] (numeric) = 2.0459496457995070744588610111716 absolute error = 1.49040506726707e-17 relative error = 7.2846615278483853799920306830494e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.303 y[1] (analytic) = 2.0462567804063854484638254416571 y[1] (numeric) = 2.0462567804063854634187238105211 absolute error = 1.49548983688640e-17 relative error = 7.3084172583139666249117166447831e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304 y[1] (analytic) = 2.0465649612701314318262291429792 y[1] (numeric) = 2.0465649612701314468319901481543 absolute error = 1.50057610051751e-17 relative error = 7.3321694102796918640339551276505e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.305 y[1] (analytic) = 2.0468741886989258990697443064274 y[1] (numeric) = 2.0468741886989259141263829388941 absolute error = 1.50566386324667e-17 relative error = 7.3559179726807217022079305966479e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.306 y[1] (analytic) = 2.0471844630019963047577914340209 y[1] (numeric) = 2.0471844630019963198653227356374 absolute error = 1.51075313016165e-17 relative error = 7.3796629344591542768918728818946e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.307 y[1] (analytic) = 2.0474957844896169778169689982138 y[1] (numeric) = 2.0474957844896169929754080617308 absolute error = 1.51584390635170e-17 relative error = 7.4034042845639224860228638826830e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.308 y[1] (analytic) = 2.0478081534731094318114082246882 y[1] (numeric) = 2.0478081534731094470207701937644 absolute error = 1.52093619690762e-17 relative error = 7.4271420119511307867828189075650e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.309 y[1] (analytic) = 2.0481215702648426762643125999463 y[1] (numeric) = 2.0481215702648426915246126691631 absolute error = 1.52603000692168e-17 relative error = 7.4508761055836592901481940334139e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.31 y[1] (analytic) = 2.0484360351782335290269934252649 y[1] (numeric) = 2.048436035178233544338246840142 absolute error = 1.53112534148771e-17 relative error = 7.4746065544315981024593528241058e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.311 y[1] (analytic) = 2.0487515485277469296957137860763 y[1] (numeric) = 2.0487515485277469450579358430866 absolute error = 1.53622220570103e-17 relative error = 7.4983333474719002862892386342616e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.312 y[1] (analytic) = 2.0490681106288962540766543536436 y[1] (numeric) = 2.0490681106288962694898604002286 absolute error = 1.54132060465850e-17 relative error = 7.5220564736886207558733508702858e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.313 y[1] (analytic) = 2.0493857217982436296993154840235 y[1] (numeric) = 2.0493857217982436451635209186089 absolute error = 1.54642054345854e-17 relative error = 7.5457759220730085486268216816168e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.314 y[1] (analytic) = 2.049704382353400252378671127745 y[1] (numeric) = 2.0497043823534002678938913997558 absolute error = 1.55152202720108e-17 relative error = 7.5694916816232574797393827721556e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.315 y[1] (analytic) = 2.0500240926130267038263911123841 y[1] (numeric) = 2.05002409261302671939264172226 absolute error = 1.55662506098759e-17 relative error = 7.5932037413446472505949798481202e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.316 y[1] (analytic) = 2.0503448528968332703114494092822 y[1] (numeric) = 2.0503448528968332859287459084934 absolute error = 1.56172964992112e-17 relative error = 7.6169120902497331802145612450846e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.317 y[1] (analytic) = 2.0506666635255802623704370450457 y[1] (numeric) = 2.0506666635255802780387950361083 absolute error = 1.56683579910626e-17 relative error = 7.6406167173581456232113909370230e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.318 y[1] (analytic) = 2.0509895248210783355678993681634 y[1] (numeric) = 2.0509895248210783512873345046549 absolute error = 1.57194351364915e-17 relative error = 7.6643176116966333427865868712810e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.319 y[1] (analytic) = 2.0513134371061888123070184311073 y[1] (numeric) = 2.0513134371061888280775464176824 absolute error = 1.57705279865751e-17 relative error = 7.6880147622992043235919303704545e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.32 y[1] (analytic) = 2.0516384007048240046909622986259 y[1] (numeric) = 2.0516384007048240205125988910321 absolute error = 1.58216365924062e-17 relative error = 7.7117081582070227253128822245183e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.321 y[1] (analytic) = 2.0519644159419475384352241436057 y[1] (numeric) = 2.0519644159419475543079851486992 absolute error = 1.58727610050935e-17 relative error = 7.7353977884685495846353519977519e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=3.38 NO POLE x[1] = 0.322 y[1] (analytic) = 2.0522914831435746778312750428676 y[1] (numeric) = 2.0522914831435746937551763186291 absolute error = 1.59239012757615e-17 relative error = 7.7590836421394884606719906014837e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.323 y[1] (analytic) = 2.0526196026367726517618554365776 y[1] (numeric) = 2.0526196026367726677369128921278 absolute error = 1.59750574555502e-17 relative error = 7.7827657082826336771462013591727e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.324 y[1] (analytic) = 2.0529487747496609807682312665902 y[1] (numeric) = 2.0529487747496609967944608622062 absolute error = 1.60262295956160e-17 relative error = 7.8064439759683032172255024898220e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.325 y[1] (analytic) = 2.053278999811411805169741861009 y[1] (numeric) = 2.05327899981141182124715960814 absolute error = 1.60774177471310e-17 relative error = 7.8301184342739919420725870185423e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.326 y[1] (analytic) = 2.0536102781522502142359676845385 y[1] (numeric) = 2.0536102781522502303645896458218 absolute error = 1.61286219612833e-17 relative error = 7.8537890722845120719543755350832e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.327 y[1] (analytic) = 2.0539426101034545764118471268228 y[1] (numeric) = 2.0539426101034545925916894161001 absolute error = 1.61798422892773e-17 relative error = 7.8774558790921335133241665851444e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.328 y[1] (analytic) = 2.054275995997356870596072553916 y[1] (numeric) = 2.0542759959973568868271513362491 absolute error = 1.62310787823331e-17 relative error = 7.9011188437962859200638603914196e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.329 y[1] (analytic) = 2.0546104361673430184730969013066 y[1] (numeric) = 2.0546104361673430347554283929939 absolute error = 1.62823314916873e-17 relative error = 7.9247779555039424204486580687124e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.33 y[1] (analytic) = 2.0549459309478532178990831405318 y[1] (numeric) = 2.0549459309478532342326836091243 absolute error = 1.63336004685925e-17 relative error = 7.9484332033293703309110127946311e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.331 y[1] (analytic) = 2.0552824806743822773421300053576 y[1] (numeric) = 2.0552824806743822937270157696755 absolute error = 1.63848857643179e-17 relative error = 7.9720845763944173008311067156785e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.332 y[1] (analytic) = 2.0556200856834799513771084177797 y[1] (numeric) = 2.0556200856834799678132958479283 absolute error = 1.64361874301486e-17 relative error = 7.9957320638281647446494663046291e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.333 y[1] (analytic) = 2.0559587463127512772354441087076 y[1] (numeric) = 2.055958746312751293722949626094 absolute error = 1.64875055173864e-17 relative error = 8.0193756547673111828775466763527e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.334 y[1] (analytic) = 2.0562984629008569124101829831449 y[1] (numeric) = 2.0562984629008569289490230604942 absolute error = 1.65388400773493e-17 relative error = 8.0430153383559229816809248971982e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.335 y[1] (analytic) = 2.0566392357875134733166768349572 y[1] (numeric) = 2.0566392357875134899068679963291 absolute error = 1.65901911613719e-17 relative error = 8.0666511037456229270348815648964e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.336 y[1] (analytic) = 2.0569810653134938750092280719431 y[1] (numeric) = 2.0569810653134938916507868927485 absolute error = 1.66415588208054e-17 relative error = 8.0902829400955841327534946204395e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.337 y[1] (analytic) = 2.0573239518206276719540331678806 y[1] (numeric) = 2.0573239518206276886469762748979 absolute error = 1.66929431070173e-17 relative error = 8.1139108365723781143794245681970e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.338 y[1] (analytic) = 2.0576678956518013998587656145203 y[1] (numeric) = 2.0576678956518014166031096859122 absolute error = 1.67443440713919e-17 relative error = 8.1375347823502117854955094161210e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.339 y[1] (analytic) = 2.0580128971509589185591402031382 y[1] (numeric) = 2.0580128971509589353549019684685 absolute error = 1.67957617653303e-17 relative error = 8.1611547666109212445030868375075e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.34 y[1] (analytic) = 2.0583589566631017559628015222396 y[1] (numeric) = 2.0583589566631017728099977624897 absolute error = 1.68471962402501e-17 relative error = 8.1847707785438198003956735431474e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.341 y[1] (analytic) = 2.0587060745342894530508806153321 y[1] (numeric) = 2.0587060745342894699495281629179 absolute error = 1.68986475475858e-17 relative error = 8.2083828073458861517066250896412e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.342 y[1] (analytic) = 2.0590542511116399099375648003526 y[1] (numeric) = 2.0590542511116399268876805391412 absolute error = 1.69501157387886e-17 relative error = 8.2319908422216609599022729013640e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.343 y[1] (analytic) = 2.0594034867433297329880267103471 y[1] (numeric) = 2.059403486743329749989627575674 absolute error = 1.70016008653269e-17 relative error = 8.2555948723834834121737826514891e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.344 y[1] (analytic) = 2.0597537817785945829950596733617 y[1] (numeric) = 2.0597537817785946000481626520475 absolute error = 1.70531029786858e-17 relative error = 8.2791948870512420287099878565868e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.345 y[1] (analytic) = 2.0601051365677295244147676082088 y[1] (numeric) = 2.0601051365677295415193897385761 absolute error = 1.71046221303673e-17 relative error = 8.3027908754524654925010097972236e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=3.63 NO POLE x[1] = 0.346 y[1] (analytic) = 2.0604575514620893756616586718269 y[1] (numeric) = 2.0604575514620893928178170437175 absolute error = 1.71561583718906e-17 relative error = 8.3263828268224618998878137734573e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.347 y[1] (analytic) = 2.0608110268140890604634929533583 y[1] (numeric) = 2.0608110268140890776712047081503 absolute error = 1.72077117547920e-17 relative error = 8.3499707304042637498910232002848e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.348 y[1] (analytic) = 2.0611655629772039602762355698204 y[1] (numeric) = 2.0611655629772039775355179004452 absolute error = 1.72592823306248e-17 relative error = 8.3735545754485729697450000855608e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.349 y[1] (analytic) = 2.0615211603059702677594675783534 y[1] (numeric) = 2.061521160305970285070337729313 absolute error = 1.73108701509596e-17 relative error = 8.3971343512139000087425054368053e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.35 y[1] (analytic) = 2.0618778191559853413126081804854 y[1] (numeric) = 2.0618778191559853586750834478696 absolute error = 1.73624752673842e-17 relative error = 8.4207100469665087702412595126312e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.351 y[1] (analytic) = 2.0622355398839080606723027546654 y[1] (numeric) = 2.0622355398839080780864004861693 absolute error = 1.74140977315039e-17 relative error = 8.4442816519805555446919093052116e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.352 y[1] (analytic) = 2.0625943228474591835713323144834 y[1] (numeric) = 2.0625943228474592010370699094243 absolute error = 1.74657375949409e-17 relative error = 8.4678491555377914339292685636745e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.353 y[1] (analytic) = 2.0629541684054217034594010515152 y[1] (numeric) = 2.0629541684054217209767959608504 absolute error = 1.75173949093352e-17 relative error = 8.4914125469279921784708898776299e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.354 y[1] (analytic) = 2.0633150769176412082861596836105 y[1] (numeric) = 2.0633150769176412258552294099547 absolute error = 1.75690697263442e-17 relative error = 8.5149718154487574610001092730482e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.355 y[1] (analytic) = 2.063677048745026240346823391677 y[1] (numeric) = 2.0636770487450262579675854893196 absolute error = 1.76207620976426e-17 relative error = 8.5385269504054557707322991629163e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.356 y[1] (analytic) = 2.0640400842495486571907441906084 y[1] (numeric) = 2.0640400842495486748632162655313 absolute error = 1.76724720749229e-17 relative error = 8.5620779411114599977086217495470e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.357 y[1] (analytic) = 2.0644041837942439935932986429589 y[1] (numeric) = 2.0644041837942440113174983528539 absolute error = 1.77241997098950e-17 relative error = 8.5856247768879467968559834551603e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.358 y[1] (analytic) = 2.064769347743211824591452887282 y[1] (numeric) = 2.0647693477432118423673979415685 absolute error = 1.77759450542865e-17 relative error = 8.6091674470640351643375099160906e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.359 y[1] (analytic) = 2.0651355764616161295833680167288 y[1] (numeric) = 2.0651355764616161474110761765716 absolute error = 1.78277081598428e-17 relative error = 8.6327059409768280006110986854979e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.36 y[1] (analytic) = 2.0655028703156856574924099075419 y[1] (numeric) = 2.0655028703156856753718989858688 absolute error = 1.78794890783269e-17 relative error = 8.6562402479713083651667432161102e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.361 y[1] (analytic) = 2.0658712296727142929959286614845 y[1] (numeric) = 2.0658712296727143109272165230044 absolute error = 1.79312878615199e-17 relative error = 8.6797703574005746612071402163635e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.362 y[1] (analytic) = 2.0662406549010614238191738910155 y[1] (numeric) = 2.066240654901061441802278452236 absolute error = 1.79831045612205e-17 relative error = 8.7032962586255915770413136825907e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.363 y[1] (analytic) = 2.0666111463701523090947131411555 y[1] (numeric) = 2.0666111463701523271296523704009 absolute error = 1.80349392292454e-17 relative error = 8.7268179410153767689415085275000e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.364 y[1] (analytic) = 2.0669827044504784487877218074939 y[1] (numeric) = 2.0669827044504784668745137249232 absolute error = 1.80867919174293e-17 relative error = 8.7503353939469938038545191543491e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.365 y[1] (analytic) = 2.0673553295135979541875139756568 y[1] (numeric) = 2.0673553295135979723261766532817 absolute error = 1.81386626776249e-17 relative error = 8.7738486068055450883710675034543e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.366 y[1] (analytic) = 2.0677290219321359194656846737981 y[1] (numeric) = 2.067729021932135937656236235501 absolute error = 1.81905515617029e-17 relative error = 8.7973575689841647841177855542181e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.367 y[1] (analytic) = 2.0681037820797847943012350962868 y[1] (numeric) = 2.0681037820797848125436937178391 absolute error = 1.82424586215523e-17 relative error = 8.8208622698841567701546647299871e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.368 y[1] (analytic) = 2.0684796103313047575730534237467 y[1] (numeric) = 2.0684796103313047758674373328267 absolute error = 1.82943839090800e-17 relative error = 8.8443626989147940211737826497788e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.369 y[1] (analytic) = 2.0688565070625240921201249319604 y[1] (numeric) = 2.0688565070625241104664524081718 absolute error = 1.83463274762114e-17 relative error = 8.8678588454936015418086670287082e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=3.87 NO POLE x[1] = 0.37 y[1] (analytic) = 2.0692344726503395605698461498793 y[1] (numeric) = 2.0692344726503395789681355247694 absolute error = 1.83982893748901e-17 relative error = 8.8913506990462040270465285822390e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.371 y[1] (analytic) = 2.0696135074727167822348188950849 y[1] (numeric) = 2.0696135074727168006850885521628 absolute error = 1.84502696570779e-17 relative error = 8.9148382490063186221686394781388e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.372 y[1] (analytic) = 2.0699936119086906110785010835261 y[1] (numeric) = 2.0699936119086906295807694582813 absolute error = 1.85022683747552e-17 relative error = 8.9383214848159409067598844455727e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.373 y[1] (analytic) = 2.0703747863383655147500922792166 y[1] (numeric) = 2.0703747863383655333043778591373 absolute error = 1.85542855799207e-17 relative error = 8.9618003959251925491451533899697e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.374 y[1] (analytic) = 2.0707570311429159546890330188074 y[1] (numeric) = 2.0707570311429159732953543433989 absolute error = 1.86063213245915e-17 relative error = 8.9852749717923622731685030396924e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.375 y[1] (analytic) = 2.071140346704586767299498015567 y[1] (numeric) = 2.0711403467045867859578736763705 absolute error = 1.86583756608035e-17 relative error = 9.0087452018840916060159760297926e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.376 y[1] (analytic) = 2.0715247334066935461952644172937 y[1] (numeric) = 2.0715247334066935649057130579047 absolute error = 1.87104486406110e-17 relative error = 9.0322110756751742088176746013695e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.377 y[1] (analytic) = 2.0719101916336230255153373630596 y[1] (numeric) = 2.0719101916336230442778776791465 absolute error = 1.87625403160869e-17 relative error = 9.0556725826486449962665764096535e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.378 y[1] (analytic) = 2.072296721770833464310716154445 y[1] (numeric) = 2.0722967217708334831253668937679 absolute error = 1.88146507393229e-17 relative error = 9.0791297122958691353083598937122e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.379 y[1] (analytic) = 2.07268432420485503200268542806 y[1] (numeric) = 2.0726843242048550508694653904895 absolute error = 1.88667799624295e-17 relative error = 9.1025824541165344289325915109739e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.38 y[1] (analytic) = 2.0730729993232901949130167876779 y[1] (numeric) = 2.0730729993232902138319448252138 absolute error = 1.89189280375359e-17 relative error = 9.1260307976185954485318585813800e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.381 y[1] (analytic) = 2.0734627475148141038664674262136 y[1] (numeric) = 2.0734627475148141228375624430037 absolute error = 1.89710950167901e-17 relative error = 9.1494747323183141639692358363291e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.382 y[1] (analytic) = 2.0738535691691749828659633400772 y[1] (numeric) = 2.0738535691691750018892442924364 absolute error = 1.90232809523592e-17 relative error = 9.1729142477403969447312349495912e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.383 y[1] (analytic) = 2.0742454646771945188408558111204 y[1] (numeric) = 2.0742454646771945379163417075495 absolute error = 1.90754858964291e-17 relative error = 9.1963493334178421219214387702514e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.384 y[1] (analytic) = 2.0746384344307682524686409044622 y[1] (numeric) = 2.074638434430768271596350805667 absolute error = 1.91277099012048e-17 relative error = 9.2197799788920769074826158868238e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.385 y[1] (analytic) = 2.0750324788228659700705328039483 y[1] (numeric) = 2.0750324788228659892504858228584 absolute error = 1.91799530189101e-17 relative error = 9.2432061737128049835304192173238e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.386 y[1] (analytic) = 2.075427598247532096581282880848 y[1] (numeric) = 2.0754275982475321158134981826364 absolute error = 1.92322153017884e-17 relative error = 9.2666279074383842542664071237361e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.387 y[1] (analytic) = 2.0758237930998860895936374656428 y[1] (numeric) = 2.0758237930998861088781342677445 absolute error = 1.92844968021017e-17 relative error = 9.2900451696353370181535758892086e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.388 y[1] (analytic) = 2.0762210637761228344778283673944 y[1] (numeric) = 2.0762210637761228538146259395262 absolute error = 1.93367975721318e-17 relative error = 9.3134579498789202954685119753232e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.389 y[1] (analytic) = 2.0766194106735130405764912602189 y[1] (numeric) = 2.0766194106735130599656089243982 absolute error = 1.93891176641793e-17 relative error = 9.3368662377526360647641435327380e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.39 y[1] (analytic) = 2.0770188341904036384754081318156 y[1] (numeric) = 2.0770188341904036579168652623799 absolute error = 1.94414571305643e-17 relative error = 9.3602700228485605203411181340361e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.391 y[1] (analytic) = 2.0774193347262181783504710648275 y[1] (numeric) = 2.0774193347262181978442870884539 absolute error = 1.94938160236264e-17 relative error = 9.3836692947673359713281727680609e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.392 y[1] (analytic) = 2.0778209126814572293912656980308 y[1] (numeric) = 2.0778209126814572489374600937552 absolute error = 1.95461943957244e-17 relative error = 9.4070640431180183446294033735505e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.393 y[1] (analytic) = 2.0782235684576987803016737909688 y[1] (numeric) = 2.0782235684576987999002660902054 absolute error = 1.95985922992366e-17 relative error = 9.4304542575182135498923313836711e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=4.12 NO POLE x[1] = 0.394 y[1] (analytic) = 2.078627302457598640877895392667 y[1] (numeric) = 2.078627302457598660528905179228 absolute error = 1.96510097865610e-17 relative error = 9.4538399275941655547713617276232e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.395 y[1] (analytic) = 2.0790321150848908446642921924854 y[1] (numeric) = 2.0790321150848908643677391026005 absolute error = 1.97034469101151e-17 relative error = 9.4772210429806519369669132004198e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.396 y[1] (analytic) = 2.0794380067443880526874547089841 y[1] (numeric) = 2.07943800674438807244335843132 absolute error = 1.97559037223359e-17 relative error = 9.5005975933209757146954253193096e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.397 y[1] (analytic) = 2.079844977841981958268897050903 y[1] (numeric) = 2.0798449778419819780772773265834 absolute error = 1.98083802756804e-17 relative error = 9.5239695682671975664352617738601e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.398 y[1] (analytic) = 2.0802530287846436929167840629853 y[1] (numeric) = 2.0802530287846437127776606856104 absolute error = 1.98608766226251e-17 relative error = 9.5473369574798870438957428824695e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.399 y[1] (analytic) = 2.080662159980424233297096748404 y[1] (numeric) = 2.0806621599804242532104895640704 absolute error = 1.99133928156664e-17 relative error = 9.5706997506283066086528117846450e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4 y[1] (analytic) = 2.0810723718384548092846429389925 y[1] (numeric) = 2.0810723718384548292505718463128 absolute error = 1.99659289073203e-17 relative error = 9.5940579373902590636237107249481e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.401 y[1] (analytic) = 2.0814836647689473130943212643223 y[1] (numeric) = 2.0814836647689473331128062144454 absolute error = 2.00184849501231e-17 relative error = 9.6174115074524155681396974733254e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.402 y[1] (analytic) = 2.0818960391831947094930475509275 y[1] (numeric) = 2.0818960391831947295641085475582 absolute error = 2.00710609966307e-17 relative error = 9.6407604505099707766804409933194e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.403 y[1] (analytic) = 2.0823094954935714470927538636352 y[1] (numeric) = 2.0823094954935714672164109630545 absolute error = 2.01236570994193e-17 relative error = 9.6641047562669706938032983908734e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.404 y[1] (analytic) = 2.0827240341135338707248714820363 y[1] (numeric) = 2.0827240341135338909011447931212 absolute error = 2.01762733110849e-17 relative error = 9.6874444144360639467211514411922e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.405 y[1] (analytic) = 2.0831396554576206348967101866133 y[1] (numeric) = 2.083139655457620655125619870857 absolute error = 2.02289096842437e-17 relative error = 9.7107794147386853709937075894455e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.406 y[1] (analytic) = 2.0835563599414531183301473109388 y[1] (numeric) = 2.083556359941453138611713582471 absolute error = 2.02815662715322e-17 relative error = 9.7341097469050953685329694304100e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.407 y[1] (analytic) = 2.0839741479817358395830410986696 y[1] (numeric) = 2.0839741479817358599172842242765 absolute error = 2.03342431256069e-17 relative error = 9.7574354006742272531377043449270e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.408 y[1] (analytic) = 2.0843930199962568737537839867819 y[1] (numeric) = 2.0843930199962568941407242859265 absolute error = 2.03869402991446e-17 relative error = 9.7807563657938226092604393804252e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.409 y[1] (analytic) = 2.084812976403888270269412519638 y[1] (numeric) = 2.0848129764038882907090703644806 absolute error = 2.04396578448426e-17 relative error = 9.8040726320205184980859147668690e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.41 y[1] (analytic) = 2.0852340176245864717576916820286 y[1] (numeric) = 2.085234017624586492250087497447 absolute error = 2.04923958154184e-17 relative error = 9.8273841891196947525676232058616e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.411 y[1] (analytic) = 2.0856561440793927340035925233085 y[1] (numeric) = 2.0856561440793927545487467869185 absolute error = 2.05451542636100e-17 relative error = 9.8506910268656091123870718954301e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.412 y[1] (analytic) = 2.0860793561904335469905830291406 y[1] (numeric) = 2.0860793561904335675885162713164 absolute error = 2.05979332421758e-17 relative error = 9.8739931350413404236446557582968e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.413 y[1] (analytic) = 2.0865036543809210570271532821724 y[1] (numeric) = 2.0865036543809210776778860860672 absolute error = 2.06507328038948e-17 relative error = 9.8972905034388756645452092868407e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.414 y[1] (analytic) = 2.0869290390751534899589970382061 y[1] (numeric) = 2.0869290390751535106625500397727 absolute error = 2.07035530015666e-17 relative error = 9.9205831218591010060519679039511e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.415 y[1] (analytic) = 2.087355510698515575467272930079 y[1] (numeric) = 2.0873555106985155962236668180904 absolute error = 2.07563938880114e-17 relative error = 9.9438709801117928588766825435005e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.416 y[1] (analytic) = 2.0877830696774789724533695975508 y[1] (numeric) = 2.0877830696774789932626251136209 absolute error = 2.08092555160701e-17 relative error = 9.9671540680156568046755867812436e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=68.6MB, alloc=4.3MB, time=4.37 x[1] = 0.417 y[1] (analytic) = 2.0882117164396026955106001279986 y[1] (numeric) = 2.0882117164396027163727380666028 absolute error = 2.08621379386042e-17 relative error = 9.9904323753982706792066252641605e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.418 y[1] (analytic) = 2.0886414514135335424832522796486 y[1] (numeric) = 2.0886414514135335633982934881448 absolute error = 2.09150412084962e-17 relative error = 1.0013705892096267091204068354339e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.419 y[1] (analytic) = 2.0890722750290065231134220464317 y[1] (numeric) = 2.0890722750290065440813874250812 absolute error = 2.09679653786495e-17 relative error = 1.0036974607955276350621002374629e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.42 y[1] (analytic) = 2.0895041877168452887760592113318 y[1] (numeric) = 2.08950418771684530979696971332 absolute error = 2.10209105019882e-17 relative error = 1.0060238512829821583944246045003e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.421 y[1] (analytic) = 2.0899371899089625633026546233074 y[1] (numeric) = 2.0899371899089625843765312547647 absolute error = 2.10738766314573e-17 relative error = 1.0083497596583405348242449340270e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.422 y[1] (analytic) = 2.0903712820383605748940000215105 y[1] (numeric) = 2.0903712820383605960208638415336 absolute error = 2.11268638200231e-17 relative error = 1.0106751849088691789996548582292e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.423 y[1] (analytic) = 2.0908064645391314891224523195991 y[1] (numeric) = 2.0908064645391315103023244402718 absolute error = 2.11798721206727e-17 relative error = 1.0130001260227258095831752561748e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.424 y[1] (analytic) = 2.0912427378464578430241353524419 y[1] (numeric) = 2.0912427378464578642570369388564 absolute error = 2.12329015864145e-17 relative error = 1.0153245819889824412861662248799e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.425 y[1] (analytic) = 2.0916801023966129802815131774552 y[1] (numeric) = 2.091680102396613001567465447733 absolute error = 2.12859522702778e-17 relative error = 1.0176485517976053180393958352047e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.426 y[1] (analytic) = 2.0921185586269614874967701131797 y[1] (numeric) = 2.0921185586269615088357943384932 absolute error = 2.13390242253135e-17 relative error = 1.0199720344394874470984507731998e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.427 y[1] (analytic) = 2.0925581069759596315564337885153 y[1] (numeric) = 2.0925581069759596529485512931087 absolute error = 2.13921175045934e-17 relative error = 1.0222950289064141859707680593372e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.428 y[1] (analytic) = 2.0929987478831557980876785672719 y[1] (numeric) = 2.0929987478831558195329107284829 absolute error = 2.14452321612110e-17 relative error = 1.0246175341911005376520797901711e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.429 y[1] (analytic) = 2.0934404817891909310067478043776 y[1] (numeric) = 2.0934404817891909525051160526582 absolute error = 2.14983682482806e-17 relative error = 1.0269395492871471902192696422930e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.43 y[1] (analytic) = 2.0938833091357989731599344822012 y[1] (numeric) = 2.0938833091357989947114603011398 absolute error = 2.15515258189386e-17 relative error = 1.0292610731891016774647912438264e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.431 y[1] (analytic) = 2.0943272303658073080575608680088 y[1] (numeric) = 2.0943272303658073296622657943513 absolute error = 2.16047049263425e-17 relative error = 1.0315821048924096389507169989678e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.432 y[1] (analytic) = 2.0947722459231372027013989265695 y[1] (numeric) = 2.0947722459231372243593045502408 absolute error = 2.16579056236713e-17 relative error = 1.0339026433934329724290405119454e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.433 y[1] (analytic) = 2.0952183562528042515059743153667 y[1] (numeric) = 2.0952183562528042732171022794925 absolute error = 2.17111279641258e-17 relative error = 1.0362226876894631878860631140935e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.434 y[1] (analytic) = 2.0956655618009188213141978837586 y[1] (numeric) = 2.095665561800918843078569884687 absolute error = 2.17643720009284e-17 relative error = 1.0385422367787108831694850133400e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.435 y[1] (analytic) = 2.096113863014686497507769691754 y[1] (numeric) = 2.096113863014686519325407479077 absolute error = 2.18176377873230e-17 relative error = 1.0408612896603000012044050189099e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.436 y[1] (analytic) = 2.0965632603424085312128016588456 y[1] (numeric) = 2.096563260342408553083727035421 absolute error = 2.18709253765754e-17 relative error = 1.0431798453342859405865433059188e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.437 y[1] (analytic) = 2.0970137542334822876011060485606 y[1] (numeric) = 2.0970137542334823095253408705339 absolute error = 2.19242348219733e-17 relative error = 1.0454979028016545655769270035573e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.438 y[1] (analytic) = 2.0974653451384016952875980900551 y[1] (numeric) = 2.0974653451384017172651642668813 absolute error = 2.19775661768262e-17 relative error = 1.0478154610643164470687082433665e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.439 y[1] (analytic) = 2.0979180335087576968242621341911 y[1] (numeric) = 2.0979180335087577188551816286563 absolute error = 2.20309194944652e-17 relative error = 1.0501325191250963417452332743250e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.44 y[1] (analytic) = 2.0983718197972387002911318381003 y[1] (numeric) = 2.0983718197972387223754266663442 absolute error = 2.20842948282439e-17 relative error = 1.0524490759877751039015948232547e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=72.4MB, alloc=4.3MB, time=4.62 x[1] = 0.441 y[1] (analytic) = 2.0988267044576310319847359692537 y[1] (numeric) = 2.0988267044576310541224282007911 absolute error = 2.21376922315374e-17 relative error = 1.0547651306570410134994658664827e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.442 y[1] (analytic) = 2.0992826879448193902044625175181 y[1] (numeric) = 2.0992826879448194123955742752615 absolute error = 2.21911117577434e-17 relative error = 1.0570806821385411990038225049095e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.443 y[1] (analytic) = 2.0997397707147873001372949016042 y[1] (numeric) = 2.0997397707147873223818483618853 absolute error = 2.22445534602811e-17 relative error = 1.0593957294388282157352479122104e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.444 y[1] (analytic) = 2.1001979532246175698413751546778 y[1] (numeric) = 2.1001979532246175921393925472703 absolute error = 2.22980173925925e-17 relative error = 1.0617102715654209662613401633648e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.445 y[1] (analytic) = 2.1006572359324927473288500727377 y[1] (numeric) = 2.1006572359324927696803536808789 absolute error = 2.23515036081412e-17 relative error = 1.0640243075267465280930074644572e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.446 y[1] (analytic) = 2.101117619297695578748457408642 y[1] (numeric) = 2.1011176192976956011534695690558 absolute error = 2.24050121604138e-17 relative error = 1.0663378363322057986472513326912e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.447 y[1] (analytic) = 2.1015791037806094676683102944102 y[1] (numeric) = 2.1015791037806094901268533973288 absolute error = 2.24585431029186e-17 relative error = 1.0686508569921105764821192033090e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.448 y[1] (analytic) = 2.1020416898427189354593391746206 y[1] (numeric) = 2.1020416898427189579714356638073 absolute error = 2.25120964891867e-17 relative error = 1.0709633685177348973913649573266e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.449 y[1] (analytic) = 2.1025053779466100827798516343857 y[1] (numeric) = 2.1025053779466101053455240071571 absolute error = 2.25656723727714e-17 relative error = 1.0732753699212854442242104671290e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.45 y[1] (analytic) = 2.1029701685559710521616716065027 y[1] (numeric) = 2.1029701685559710747809424137513 absolute error = 2.26192708072486e-17 relative error = 1.0755868602159195449102948986029e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.451 y[1] (analytic) = 2.1034360621355924916983205439575 y[1] (numeric) = 2.1034360621355925143712123901742 absolute error = 2.26728918462167e-17 relative error = 1.0778978384157393733477676774317e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.452 y[1] (analytic) = 2.1039030591513680198357042460012 y[1] (numeric) = 2.103903059151368042562239789298 absolute error = 2.27265355432968e-17 relative error = 1.0802083035358004145017503536254e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.453 y[1] (analytic) = 2.1043711600702946912657701285254 y[1] (numeric) = 2.104371160070294714045972080658 absolute error = 2.27802019521326e-17 relative error = 1.0825182545921056594901669275741e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.454 y[1] (analytic) = 2.1048403653604734639236008324323 y[1] (numeric) = 2.1048403653604734867574919588228 absolute error = 2.28338911263905e-17 relative error = 1.0848276906016093076058989306911e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.455 y[1] (analytic) = 2.1053106754911096670884111671317 y[1] (numeric) = 2.1053106754911096899760142868914 absolute error = 2.28876031197597e-17 relative error = 1.0871366105822204606915518617489e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.456 y[1] (analytic) = 2.1057820909325134705889164902013 y[1] (numeric) = 2.1057820909325134935302544761535 absolute error = 2.29413379859522e-17 relative error = 1.0894450135528020610129167677615e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.457 y[1] (analytic) = 2.1062546121561003551135417286173 y[1] (numeric) = 2.1062546121561003781086375073202 absolute error = 2.29950957787029e-17 relative error = 1.0917528985331745755924464454778e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.458 y[1] (analytic) = 2.1067282396343915836259413518044 y[1] (numeric) = 2.1067282396343916066748179035739 absolute error = 2.30488765517695e-17 relative error = 1.0940602645441101794590059648326e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.459 y[1] (analytic) = 2.1072029738410146738863017120632 y[1] (numeric) = 2.107202973841014696988982070996 absolute error = 2.31026803589328e-17 relative error = 1.0963671106073459265249888611583e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.46 y[1] (analytic) = 2.1076788152507038720788982737177 y[1] (numeric) = 2.1076788152507038952354055277143 absolute error = 2.31565072539966e-17 relative error = 1.0986734357455779217045254453018e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.461 y[1] (analytic) = 2.1081557643393006275463813585793 y[1] (numeric) = 2.1081557643393006507567386493672 absolute error = 2.32103572907879e-17 relative error = 1.1009792389824697285972037153112e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.462 y[1] (analytic) = 2.1086338215837540686312651420527 y[1] (numeric) = 2.1086338215837540918954956652094 absolute error = 2.32642305231567e-17 relative error = 1.1032845193426417933641988702739e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.463 y[1] (analytic) = 2.1091129874621214796250957414119 y[1] (numeric) = 2.1091129874621215029432227463881 absolute error = 2.33181270049762e-17 relative error = 1.1055892758516798455358350022151e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.464 y[1] (analytic) = 2.1095932624535687788257753454548 y[1] (numeric) = 2.1095932624535688021978221355977 absolute error = 2.33720467901429e-17 relative error = 1.1078935075361385443777686400646e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=4.87 NO POLE x[1] = 0.465 y[1] (analytic) = 2.1100746470383709977035204428998 y[1] (numeric) = 2.1100746470383710211295103754763 absolute error = 2.34259899325765e-17 relative error = 1.1101972134235356391509075929705e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.466 y[1] (analytic) = 2.1105571416979127611759333155229 y[1] (numeric) = 2.1105571416979127846558898017433 absolute error = 2.34799564862204e-17 relative error = 1.1125003925423745630924103355492e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.467 y[1] (analytic) = 2.1110407469146887689926670711471 y[1] (numeric) = 2.111040746914688792526613576188 absolute error = 2.35339465050409e-17 relative error = 1.1148030439221054125904641537769e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.468 y[1] (analytic) = 2.1115254631723042782301656011879 y[1] (numeric) = 2.111525463172304301818125644216 absolute error = 2.35879600430281e-17 relative error = 1.1171051665931664876934404017391e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.469 y[1] (analytic) = 2.1120112909554755868969609575369 y[1] (numeric) = 2.1120112909554756105389581117325 absolute error = 2.36419971541956e-17 relative error = 1.1194067595869689547953200387488e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.47 y[1] (analytic) = 2.1124982307500305186500117541203 y[1] (numeric) = 2.1124982307500305423460696467008 absolute error = 2.36960578925805e-17 relative error = 1.1217078219358957287929396725660e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.471 y[1] (analytic) = 2.1129862830429089086225673095104 y[1] (numeric) = 2.1129862830429089323727096217539 absolute error = 2.37501423122435e-17 relative error = 1.1240083526733050866209237677248e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.472 y[1] (analytic) = 2.113475448322163090364043358496 y[1] (numeric) = 2.1134754483221631141682938257651 absolute error = 2.38042504672691e-17 relative error = 1.1263083508335390045149168555330e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.473 y[1] (analytic) = 2.1139657270769583838923962725276 y[1] (numeric) = 2.1139657270769584077507786842929 absolute error = 2.38583824117653e-17 relative error = 1.1286078154519078286241739772488e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.474 y[1] (analytic) = 2.1144571197975735848594838414512 y[1] (numeric) = 2.1144571197975736087720220413154 absolute error = 2.39125381998642e-17 relative error = 1.1309067455647175282338634473191e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.475 y[1] (analytic) = 2.1149496269754014548299017819344 y[1] (numeric) = 2.1149496269754014787966196676559 absolute error = 2.39667178857215e-17 relative error = 1.1332051402092448974570421743092e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.476 y[1] (analytic) = 2.1154432491029492126737862514597 y[1] (numeric) = 2.1154432491029492366947077749767 absolute error = 2.40209215235170e-17 relative error = 1.1355029984237600600948810189079e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.477 y[1] (analytic) = 2.1159379866738390270740737607307 y[1] (numeric) = 2.1159379866738390511492229281849 absolute error = 2.40751491674542e-17 relative error = 1.1378003192475064058298397421521e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.478 y[1] (analytic) = 2.1164338401828085101487109917904 y[1] (numeric) = 2.1164338401828085342781118635514 absolute error = 2.41294008717610e-17 relative error = 1.1400971017207325259028978104493e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.479 y[1] (analytic) = 2.1169308101257112121883081441041 y[1] (numeric) = 2.1169308101257112363719848347928 absolute error = 2.41836766906887e-17 relative error = 1.1423933448846437960901969477184e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.48 y[1] (analytic) = 2.1174288969995171175097305462993 y[1] (numeric) = 2.1174288969995171417477072248128 absolute error = 2.42379766785135e-17 relative error = 1.1446890477814720927075252279038e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.481 y[1] (analytic) = 2.1179281013023131414261243871986 y[1] (numeric) = 2.1179281013023131657184252767338 absolute error = 2.42923008895352e-17 relative error = 1.1469842094544132027046920536602e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.482 y[1] (analytic) = 2.1184284235333036283338735362098 y[1] (numeric) = 2.1184284235333036526805229142879 absolute error = 2.43466493780781e-17 relative error = 1.1492788289476681698369109146786e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.483 y[1] (analytic) = 2.1189298641928108509169855400733 y[1] (numeric) = 2.118929864192810875318007738564 absolute error = 2.44010221984907e-17 relative error = 1.1515729053064279470813680572833e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.484 y[1] (analytic) = 2.1194324237822755104694060003938 y[1] (numeric) = 2.1194324237822755349248254055395 absolute error = 2.44554194051457e-17 relative error = 1.1538664375768722226115709886921e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.485 y[1] (analytic) = 2.1199361028042572383357616543121 y[1] (numeric) = 2.1199361028042572628456027067526 absolute error = 2.45098410524405e-17 relative error = 1.1561594248061918301769217533908e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.486 y[1] (analytic) = 2.1204409017624350984710335991031 y[1] (numeric) = 2.1204409017624351230353207938997 absolute error = 2.45642871947966e-17 relative error = 1.1584518660425592485965204060529e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.487 y[1] (analytic) = 2.120946821161608091119663220413 y[1] (numeric) = 2.1209468211616081157384211070732 absolute error = 2.46187578866602e-17 relative error = 1.1607437603351557189340654513465e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.488 y[1] (analytic) = 2.1214538615076956576145945032859 y[1] (numeric) = 2.1214538615076956822878476857879 absolute error = 2.46732531825020e-17 relative error = 1.1630351067341606099901600551661e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=5.12 NO POLE x[1] = 0.489 y[1] (analytic) = 2.1219620233077381862967575250624 y[1] (numeric) = 2.1219620233077382110245306618796 absolute error = 2.47277731368172e-17 relative error = 1.1653259042907502212959895555449e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.49 y[1] (analytic) = 2.1224713070698975195554990496768 y[1] (numeric) = 2.1224713070698975443378168538027 absolute error = 2.47823178041259e-17 relative error = 1.1676161520571154308557497131958e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.491 y[1] (analytic) = 2.1229817133034574619904672638255 y[1] (numeric) = 2.1229817133034574868273545027982 absolute error = 2.48368872389727e-17 relative error = 1.1699058490864416316658238721493e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.492 y[1] (analytic) = 2.1234932425188242896954588169337 y[1] (numeric) = 2.1234932425188243145869403128608 absolute error = 2.48914814959271e-17 relative error = 1.1721949944329263679515701867792e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.493 y[1] (analytic) = 2.1240058952275272606647374488098 y[1] (numeric) = 2.1240058952275272856108380783931 absolute error = 2.49461006295833e-17 relative error = 1.1744835871517686944647880280023e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.494 y[1] (analytic) = 2.1245196719422191263223346113487 y[1] (numeric) = 2.1245196719422191513230793059092 absolute error = 2.50007446945605e-17 relative error = 1.1767716262991820829262031429320e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.495 y[1] (analytic) = 2.1250345731766766441748436136273 y[1] (numeric) = 2.12503457317667666923025735913 absolute error = 2.50554137455027e-17 relative error = 1.1790591109323837777375736689220e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.496 y[1] (analytic) = 2.1255505994458010915882199432289 y[1] (numeric) = 2.1255505994458011166983277803079 absolute error = 2.51101078370790e-17 relative error = 1.1813460401096076874788694845335e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.497 y[1] (analytic) = 2.1260677512656187806891015406401 y[1] (numeric) = 2.1260677512656188058539285646236 absolute error = 2.51648270239835e-17 relative error = 1.1836324128900984405665973806790e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.498 y[1] (analytic) = 2.1265860291532815743911639280829 y[1] (numeric) = 2.1265860291532815996107352890182 absolute error = 2.52195713609353e-17 relative error = 1.1859182283341101489300566480409e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.499 y[1] (analytic) = 2.1271054336270674035470262191799 y[1] (numeric) = 2.1271054336270674288213671218587 absolute error = 2.52743409026788e-17 relative error = 1.1882034855029192741759866500857e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5 y[1] (analytic) = 2.1276259652063807852262251614027 y[1] (numeric) = 2.1276259652063808105553608653863 absolute error = 2.53291357039836e-17 relative error = 1.1904881834588186715869612946438e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.501 y[1] (analytic) = 2.1281476244117533421197754893198 y[1] (numeric) = 2.1281476244117533675037313089643 absolute error = 2.53839558196445e-17 relative error = 1.1927723212651163387202718748455e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.502 y[1] (analytic) = 2.128670411764844323071835993248 y[1] (numeric) = 2.1286704117648443485106372977296 absolute error = 2.54388013044816e-17 relative error = 1.1950558979861388605884025379872e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.503 y[1] (analytic) = 2.1291943277884411247390018350168 y[1] (numeric) = 2.1291943277884411502326740483571 absolute error = 2.54936722133403e-17 relative error = 1.1973389126872301501238720642039e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.504 y[1] (analytic) = 2.1297193730064598143777447701809 y[1] (numeric) = 2.1297193730064598399263133712726 absolute error = 2.55485686010917e-17 relative error = 1.1996213644347689692834354851469e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.505 y[1] (analytic) = 2.1302455479439456537605240641665 y[1] (numeric) = 2.1302455479439456793640145867985 absolute error = 2.56034905226320e-17 relative error = 1.2019032522961394782131285096815e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.506 y[1] (analytic) = 2.1307728531270736242210920185032 y[1] (numeric) = 2.1307728531270736498795300513865 absolute error = 2.56584380328833e-17 relative error = 1.2041845753397675288387199620384e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.507 y[1] (analytic) = 2.1313012890831489528295191524932 y[1] (numeric) = 2.1313012890831489785429303392861 absolute error = 2.57134111867929e-17 relative error = 1.2064653326350865220005387314465e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.508 y[1] (analytic) = 2.1318308563406076396974652153853 y[1] (numeric) = 2.1318308563406076654658752547194 absolute error = 2.57684100393341e-17 relative error = 1.2087455232525736743206531969789e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.509 y[1] (analytic) = 2.1323615554290169864142233343697 y[1] (numeric) = 2.1323615554290170122376579798755 absolute error = 2.58234346455058e-17 relative error = 1.2110251462637299523429508372641e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.51 y[1] (analytic) = 2.1328933868790761256140657344809 y[1] (numeric) = 2.1328933868790761514925507948134 absolute error = 2.58784850603325e-17 relative error = 1.2133042007410787873394726707306e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.511 y[1] (analytic) = 2.1334263512226165516754205977991 y[1] (numeric) = 2.1334263512226165776089819366638 absolute error = 2.59335613388647e-17 relative error = 1.2155826857581835381671287777298e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.512 y[1] (analytic) = 2.1339604489926026525524107611713 y[1] (numeric) = 2.13396044899260267854107429735 absolute error = 2.59886635361787e-17 relative error = 1.2178606003896368081205294062137e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.3MB, time=5.36 NO POLE x[1] = 0.513 y[1] (analytic) = 2.1344956807231322427392860840343 y[1] (numeric) = 2.1344956807231322687830777914109 absolute error = 2.60437917073766e-17 relative error = 1.2201379437110591445717617934947e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.514 y[1] (analytic) = 2.1350320469494370973682824508175 y[1] (numeric) = 2.1350320469494371234672283584041 absolute error = 2.60989459075866e-17 relative error = 1.2224147147991117887889793659763e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.515 y[1] (analytic) = 2.1355695482078834874414415058279 y[1] (numeric) = 2.1355695482078835135955676977909 absolute error = 2.61541261919630e-17 relative error = 1.2246909127314953556471740109556e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.516 y[1] (analytic) = 2.136108185035972716196926352483 y[1] (numeric) = 2.1361081850359727424062589681689 absolute error = 2.62093326156859e-17 relative error = 1.2269665365869344679264138264635e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.517 y[1] (analytic) = 2.1366479579723416566103695832499 y[1] (numeric) = 2.1366479579723416828749348172119 absolute error = 2.62645652339620e-17 relative error = 1.2292415854452138932468244470582e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.518 y[1] (analytic) = 2.1371888675567632900317911416864 y[1] (numeric) = 2.1371888675567633163516152437101 absolute error = 2.63198241020237e-17 relative error = 1.2315160583871350793469182328691e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.519 y[1] (analytic) = 2.1377309143301472459586246535433 y[1] (numeric) = 2.1377309143301472723337339286733 absolute error = 2.63751092751300e-17 relative error = 1.2337899544945569535943031165814e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.52 y[1] (analytic) = 2.1382740988345403429453920000028 y[1] (numeric) = 2.1382740988345403693758128085688 absolute error = 2.64304208085660e-17 relative error = 1.2360632728503711839721530348215e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.521 y[1] (analytic) = 2.1388184216131271306505670427694 y[1] (numeric) = 2.1388184216131271571363258004127 absolute error = 2.64857587576433e-17 relative error = 1.2383360125385195538536989689901e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.522 y[1] (analytic) = 2.1393638832102304330211705479249 y[1] (numeric) = 2.1393638832102304595622937256247 absolute error = 2.65411231776998e-17 relative error = 1.2406081726439832613811833194064e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.523 y[1] (analytic) = 2.1399104841713118926156394931857 y[1] (numeric) = 2.1399104841713119192121536172857 absolute error = 2.65965141241000e-17 relative error = 1.2428797522527955974759907121140e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.524 y[1] (analytic) = 2.1404582250429725160655150814786 y[1] (numeric) = 2.1404582250429725427174467337133 absolute error = 2.66519316522347e-17 relative error = 1.2451507504520265698585227600624e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.525 y[1] (analytic) = 2.1410071063729532206764949225669 y[1] (numeric) = 2.1410071063729532473838707400884 absolute error = 2.67073758175215e-17 relative error = 1.2474211663298049130703210241349e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.526 y[1] (analytic) = 2.141557128710135382169395983826 y[1] (numeric) = 2.1415571287101354089322426592307 absolute error = 2.67628466754047e-17 relative error = 1.2496909989753120444653450012866e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.527 y[1] (analytic) = 2.1421082926045413835615760511772 y[1] (numeric) = 2.1421082926045414103799203325322 absolute error = 2.68183442813550e-17 relative error = 1.2519602474787666896464696707765e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.528 y[1] (analytic) = 2.1426605986073351651893625816447 y[1] (numeric) = 2.1426605986073351920632312725148 absolute error = 2.68738686908701e-17 relative error = 1.2542289109314515322945106751793e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.529 y[1] (analytic) = 2.1432140472708227758720389700136 y[1] (numeric) = 2.1432140472708228028014589294879 absolute error = 2.69294199594743e-17 relative error = 1.2564969884256931606979601684690e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.53 y[1] (analytic) = 2.1437686391484529252179393936186 y[1] (numeric) = 2.1437686391484529522029375363376 absolute error = 2.69849981427190e-17 relative error = 1.2587644790548840242288229797141e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.531 y[1] (analytic) = 2.1443243747948175370732045414055 y[1] (numeric) = 2.1443243747948175641138078375879 absolute error = 2.70406032961824e-17 relative error = 1.2610313819134670447277761309297e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.532 y[1] (analytic) = 2.1448812547656523041137516760674 y[1] (numeric) = 2.1448812547656523312099871515369 absolute error = 2.70962354754695e-17 relative error = 1.2632976960969342353167809750880e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.533 y[1] (analytic) = 2.1454392796178372435810136212707 y[1] (numeric) = 2.1454392796178372707329083574834 absolute error = 2.71518947362127e-17 relative error = 1.2655634207018532844604493025732e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.534 y[1] (analytic) = 2.1459984499093972541620024097582 y[1] (numeric) = 2.1459984499093972813695835438293 absolute error = 2.72075811340711e-17 relative error = 1.2678285548258335174095958864155e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.535 y[1] (analytic) = 2.146558766199502674014254472437 y[1] (numeric) = 2.1465587661995027012775491971681 absolute error = 2.72632947247311e-17 relative error = 1.2700930975675524696015827034793e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.536 y[1] (analytic) = 2.147120229048469839936215393445 y[1] (numeric) = 2.1471202290484698672552509573514 absolute error = 2.73190355639064e-17 relative error = 1.2723570480267544708323958922495e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=5.61 NO POLE x[1] = 0.537 y[1] (analytic) = 2.1476828390177616476836234016259 y[1] (numeric) = 2.1476828390177616750584271089637 absolute error = 2.73748037073378e-17 relative error = 1.2746204053042399159527990369874e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.538 y[1] (analytic) = 2.148246596669988113432451914844 y[1] (numeric) = 2.1482465966699881408630511256374 absolute error = 2.74305992107934e-17 relative error = 1.2768831685018731689691821521715e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.539 y[1] (analytic) = 2.1488115025689069363889726001267 y[1] (numeric) = 2.1488115025689069638753947301955 absolute error = 2.74864221300688e-17 relative error = 1.2791453367225904514396583385022e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.54 y[1] (analytic) = 2.1493775572794240625475015597464 y[1] (numeric) = 2.1493775572794240900897740807332 absolute error = 2.75422725209868e-17 relative error = 1.2814069090703844525585675178698e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.541 y[1] (analytic) = 2.1499447613675942495963924010334 y[1] (numeric) = 2.1499447613675942771945428404313 absolute error = 2.75981504393979e-17 relative error = 1.2836678846503261705015382727284e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.542 y[1] (analytic) = 2.1505131154006216329728410959611 y[1] (numeric) = 2.1505131154006216606268970371411 absolute error = 2.76540559411800e-17 relative error = 1.2859282625685495154787090526307e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.543 y[1] (analytic) = 2.1510826199468602930670686853548 y[1] (numeric) = 2.1510826199468603207770577675934 absolute error = 2.77099890822386e-17 relative error = 1.2881880419322591779495605278528e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.544 y[1] (analytic) = 2.151653275575814823576449031954 y[1] (numeric) = 2.1516532755758148513423989504609 absolute error = 2.77659499185069e-17 relative error = 1.2904472218497338334476202855096e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.545 y[1] (analytic) = 2.1522250828581409010101499765046 y[1] (numeric) = 2.1522250828581409288320884824503 absolute error = 2.78219385059457e-17 relative error = 1.2927058014303200462466950904551e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.546 y[1] (analytic) = 2.1527980423656458553448574015677 y[1] (numeric) = 2.1527980423656458832228123021111 absolute error = 2.78779549005434e-17 relative error = 1.2949637797844308245148953137431e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.547 y[1] (analytic) = 2.1533721546712892418321528588176 y[1] (numeric) = 2.1533721546712892697661520171343 absolute error = 2.79339991583167e-17 relative error = 1.2972211560235766816200337741464e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.548 y[1] (analytic) = 2.1539474203491834139581165672551 y[1] (numeric) = 2.1539474203491834419481879025649 absolute error = 2.79900713353098e-17 relative error = 1.2994779292603270047778859514449e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.549 y[1] (analytic) = 2.1545238399745940975557287419852 y[1] (numeric) = 2.15452383997459412560190022958 absolute error = 2.80461714875948e-17 relative error = 1.3017340986083271789267481683012e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.55 y[1] (analytic) = 2.1551014141239409660706433660095 y[1] (numeric) = 2.1551014141239409941729430372813 absolute error = 2.81022996712718e-17 relative error = 1.3039896631823017593728202466815e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.551 y[1] (analytic) = 2.1556801433747982169809096708541 y[1] (numeric) = 2.1556801433747982451393656133232 absolute error = 2.81584559424691e-17 relative error = 1.3062446220980622748616857765469e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.552 y[1] (analytic) = 2.1562600283058951493712177458042 y[1] (numeric) = 2.1562600283058951775858581031472 absolute error = 2.82146403573430e-17 relative error = 1.3084989744724964640264854262947e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.553 y[1] (analytic) = 2.1568410694971167426622458500373 y[1] (numeric) = 2.156841069497116770933098822115 absolute error = 2.82708529720777e-17 relative error = 1.3107527194235621621893727539340e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.554 y[1] (analytic) = 2.1574232675295042364956881570507 y[1] (numeric) = 2.1574232675295042648227819999368 absolute error = 2.83270938428861e-17 relative error = 1.3130058560703229111263294128915e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.555 y[1] (analytic) = 2.1580066229852557117755428164614 y[1] (numeric) = 2.1580066229852557401589058424704 absolute error = 2.83833630260090e-17 relative error = 1.3152583835329093652630754069528e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.556 y[1] (analytic) = 2.1585911364477266728662413745122 y[1] (numeric) = 2.1585911364477267013059019522277 absolute error = 2.84396605777155e-17 relative error = 1.3175103009325363487902671856535e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.557 y[1] (analytic) = 2.1591768085014306309482017514636 y[1] (numeric) = 2.1591768085014306594441883057668 absolute error = 2.84959865543032e-17 relative error = 1.3197616073915106189416155983690e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.558 y[1] (analytic) = 2.1597636397320396885313881314727 y[1] (numeric) = 2.1597636397320397170837291435707 absolute error = 2.85523410120980e-17 relative error = 1.3220123020332200926478039251690e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.559 y[1] (analytic) = 2.1603516307263851251274622785674 y[1] (numeric) = 2.1603516307263851537361862860219 absolute error = 2.86087240074545e-17 relative error = 1.3242623839821508605566834730984e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.56 y[1] (analytic) = 2.1609407820724579840811119509166 y[1] (numeric) = 2.1609407820724580127462475476723 absolute error = 2.86651355967557e-17 relative error = 1.3265118523638717765279383081119e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=5.85 NO POLE x[1] = 0.561 y[1] (analytic) = 2.1615310943594096605611432447731 y[1] (numeric) = 2.1615310943594096892827190811862 absolute error = 2.87215758364131e-17 relative error = 1.3287607063050375742500984327217e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.562 y[1] (analytic) = 2.1621225681775524907119248592309 y[1] (numeric) = 2.1621225681775525194899696420979 absolute error = 2.87780447828670e-17 relative error = 1.3310089449334012255068526589125e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.563 y[1] (analytic) = 2.1627152041183603419657734332904 y[1] (numeric) = 2.1627152041183603708003159258767 absolute error = 2.88345424925863e-17 relative error = 1.3332565673778031556100578327176e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.564 y[1] (analytic) = 2.1633090027744692045168702676655 y[1] (numeric) = 2.1633090027744692334079392897342 absolute error = 2.88910690220687e-17 relative error = 1.3355035727681789632606494708559e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.565 y[1] (analytic) = 2.1639039647396777839573009052987 y[1] (numeric) = 2.1639039647396778129049253331396 absolute error = 2.89476244278409e-17 relative error = 1.3377499602355671242367520815725e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.566 y[1] (analytic) = 2.1645000906089480950758102066747 y[1] (numeric) = 2.1645000906089481240800189731328 absolute error = 2.90042087664581e-17 relative error = 1.3399957289120843388226721978296e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.567 y[1] (analytic) = 2.1650973809784060568198667187338 y[1] (numeric) = 2.1650973809784060858806888132386 absolute error = 2.90608220945048e-17 relative error = 1.3422408779309609599736028605432e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.568 y[1] (analytic) = 2.1656958364453420884216312995027 y[1] (numeric) = 2.1656958364453421175390957680969 absolute error = 2.91174644685942e-17 relative error = 1.3444854064265117150318109237927e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.569 y[1] (analytic) = 2.1662954576082117066884261244582 y[1] (numeric) = 2.166295457608211735862562069827 absolute error = 2.91741359453688e-17 relative error = 1.3467293135341618665306811285376e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.57 y[1] (analytic) = 2.1668962450666361244583013651443 y[1] (numeric) = 2.1668962450666361536891379466444 absolute error = 2.92308365815001e-17 relative error = 1.3489725983904317920135659302457e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.571 y[1] (analytic) = 2.1674981994214028502212979956586 y[1] (numeric) = 2.1674981994214028795088644293472 absolute error = 2.92875664336886e-17 relative error = 1.3512152601329354267747045096947e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.572 y[1] (analytic) = 2.1681013212744662889070063483202 y[1] (numeric) = 2.1681013212744663182513319069845 absolute error = 2.93443255586643e-17 relative error = 1.3534572979004017673633307895702e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.573 y[1] (analytic) = 2.1687056112289483438390212061293 y[1] (numeric) = 2.1687056112289483732401352193155 absolute error = 2.94011140131862e-17 relative error = 1.3556987108326502252085373578762e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.574 y[1] (analytic) = 2.1693110698891390198568953865219 y[1] (numeric) = 2.1693110698891390493148272405647 absolute error = 2.94579318540428e-17 relative error = 1.3579394980706121154543057650635e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.575 y[1] (analytic) = 2.1699176978604970276061949384248 y[1] (numeric) = 2.1699176978604970571209740764767 absolute error = 2.95147791380519e-17 relative error = 1.3601796587563198470148143271704e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.576 y[1] (analytic) = 2.1705254957496503889972602427159 y[1] (numeric) = 2.1705254957496504185689161647768 absolute error = 2.95716559220609e-17 relative error = 1.3624191920329191630689365141528e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.577 y[1] (analytic) = 2.1711344641643970438332784749014 y[1] (numeric) = 2.171134464164397073461840737848 absolute error = 2.96285622629466e-17 relative error = 1.3646580970446583279895422055564e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.578 y[1] (analytic) = 2.1717446037137054576082740581332 y[1] (numeric) = 2.1717446037137054872937722757484 absolute error = 2.96854982176152e-17 relative error = 1.3668963729368865380576195484551e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.579 y[1] (analytic) = 2.1723559150077152304756249046068 y[1] (numeric) = 2.1723559150077152602180887476095 absolute error = 2.97424638430027e-17 relative error = 1.3691340188560707445089663588563e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.58 y[1] (analytic) = 2.1729683986577377073877134139076 y[1] (numeric) = 2.1729683986577377371871726099825 absolute error = 2.97994591960749e-17 relative error = 1.3713710339497940366051951998680e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.581 y[1] (analytic) = 2.1735820552762565894073223680074 y[1] (numeric) = 2.1735820552762566192638067018344 absolute error = 2.98564843338270e-17 relative error = 1.3736074173667356209810377871051e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.582 y[1] (analytic) = 2.1741968854769285461913870343572 y[1] (numeric) = 2.1741968854769285761049263476413 absolute error = 2.99135393132841e-17 relative error = 1.3758431682566922259094230457488e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.583 y[1] (analytic) = 2.1748128898745838296477159608796 y[1] (numeric) = 2.174812889874583859618340152381 absolute error = 2.99706241915014e-17 relative error = 1.3780782857705856714169959413388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.584 y[1] (analytic) = 2.175430069085226888765294119634 y[1] (numeric) = 2.1754300690852269187930331451975 absolute error = 3.00277390255635e-17 relative error = 1.3803127690604290517278731714353e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=6.10 NO POLE x[1] = 0.585 y[1] (analytic) = 2.1760484237260369856187832295067 y[1] (numeric) = 2.1760484237260370157036671020922 absolute error = 3.00848838725855e-17 relative error = 1.3825466172793756903970498225802e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.586 y[1] (analytic) = 2.1766679544153688125478352624802 y[1] (numeric) = 2.1766679544153688426898940521922 absolute error = 3.01420587897120e-17 relative error = 1.3847798295816715306621670499948e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.587 y[1] (analytic) = 2.1772886617727531105118363128439 y[1] (numeric) = 2.1772886617727531407111001469621 absolute error = 3.01992638341182e-17 relative error = 1.3870124051227040536279756043072e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.588 y[1] (analytic) = 2.1779105464188972886206991841443 y[1] (numeric) = 2.1779105464188973188771982471532 absolute error = 3.02564990630089e-17 relative error = 1.3892443430589546864983863425386e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.589 y[1] (analytic) = 2.1785336089756860448423242247164 y[1] (numeric) = 2.1785336089756860751560887583358 absolute error = 3.03137645336194e-17 relative error = 1.3914756425480385032590567181989e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.59 y[1] (analytic) = 2.1791578500661819878873491193109 y[1] (numeric) = 2.1791578500661820182584094225262 absolute error = 3.03710603032153e-17 relative error = 1.3937063027486933754491276758299e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.591 y[1] (analytic) = 2.1797832703146262602718095216178 y[1] (numeric) = 2.17978327031462629070019595071 absolute error = 3.04283864290922e-17 relative error = 1.3959363228207645502175642512889e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.592 y[1] (analytic) = 2.1804098703464391625583335903986 y[1] (numeric) = 2.180409870346439193044076558975 absolute error = 3.04857429685764e-17 relative error = 1.3981657019252351142160427314750e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.593 y[1] (analytic) = 2.1810376507882207787764946704749 y[1] (numeric) = 2.1810376507882208093196246494993 absolute error = 3.05431299790244e-17 relative error = 1.4003944392242013816315493003623e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.594 y[1] (analytic) = 2.1816666122677516030229475389772 y[1] (numeric) = 2.1816666122677516336234950568003 absolute error = 3.06005475178231e-17 relative error = 1.4026225338808804065418248811843e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.595 y[1] (analytic) = 2.1822967554139931672419748170421 y[1] (numeric) = 2.1822967554139931978999704594323 absolute error = 3.06579956423902e-17 relative error = 1.4048499850596266433000878306288e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.596 y[1] (analytic) = 2.1829280808570886701870713275584 y[1] (numeric) = 2.1829280808570887009025457377321 absolute error = 3.07154744101737e-17 relative error = 1.4070767919259073453107688327607e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.597 y[1] (analytic) = 2.1835605892283636075641953605963 y[1] (numeric) = 2.1835605892283636383371792392487 absolute error = 3.07729838786524e-17 relative error = 1.4093029536463237995153472275510e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.598 y[1] (analytic) = 2.1841942811603264033573169898256 y[1] (numeric) = 2.1841942811603264341878410951614 absolute error = 3.08305241053358e-17 relative error = 1.4115284693886050502237654377298e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.599 y[1] (analytic) = 2.184829157286669042336894765523 y[1] (numeric) = 2.1848291572866690732249899132872 absolute error = 3.08880951477642e-17 relative error = 1.4137533383216107841436848094899e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6 y[1] (analytic) = 2.1854652182422677037519132926977 y[1] (numeric) = 2.1854652182422677346976103562062 absolute error = 3.09456970635085e-17 relative error = 1.4159775596153204795903360812784e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.601 y[1] (analytic) = 2.1861024646631833962061153864261 y[1] (numeric) = 2.1861024646631834272094452965968 absolute error = 3.10033299101707e-17 relative error = 1.4182011324408545913813650083798e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.602 y[1] (analytic) = 2.1867408971866625937190636806802 y[1] (numeric) = 2.1867408971866626247800574260639 absolute error = 3.10609937453837e-17 relative error = 1.4204240559704636838516130644933e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.603 y[1] (analytic) = 2.1873805164511378729726677517652 y[1] (numeric) = 2.1873805164511379040913563785764 absolute error = 3.11186886268112e-17 relative error = 1.4226463293775221507789325876541e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.604 y[1] (analytic) = 2.1880213230962285517438140029452 y[1] (numeric) = 2.1880213230962285829202286150935 absolute error = 3.11764146121483e-17 relative error = 1.4248679518365539349767085844254e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.605 y[1] (analytic) = 2.1886633177627413285237367429417 y[1] (numeric) = 2.1886633177627413597579085020625 absolute error = 3.12341717591208e-17 relative error = 1.4270889225231988019439845762384e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.606 y[1] (analytic) = 2.1893065010926709233247700777273 y[1] (numeric) = 2.1893065010926709546167302032132 absolute error = 3.12919601254859e-17 relative error = 1.4293092406142426162537815332761e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.607 y[1] (analytic) = 2.1899508737292007196751214224219 y[1] (numeric) = 2.1899508737292007510249011914539 absolute error = 3.13497797690320e-17 relative error = 1.4315289052876064640508210312941e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.608 y[1] (analytic) = 2.1905964363167034078023086281173 y[1] (numeric) = 2.190596436316703439209939375696 absolute error = 3.14076307475787e-17 relative error = 1.4337479157223449208429535554173e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.3MB, time=6.34 NO POLE x[1] = 0.609 y[1] (analytic) = 2.1912431895007416290059039071208 y[1] (numeric) = 2.1912431895007416604714170260978 absolute error = 3.14655131189770e-17 relative error = 1.4359662710986534458145562054925e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.61 y[1] (analytic) = 2.1918911339280686212202289294161 y[1] (numeric) = 2.1918911339280686527436558705254 absolute error = 3.15234269411093e-17 relative error = 1.4381839705978666347140169076230e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.611 y[1] (analytic) = 2.1925402702466288657676466530899 y[1] (numeric) = 2.1925402702466288973490189249794 absolute error = 3.15813722718895e-17 relative error = 1.4404010134024610329341783219311e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.612 y[1] (analytic) = 2.1931905991055587353030966420702 y[1] (numeric) = 2.1931905991055587669424458113329 absolute error = 3.16393491692627e-17 relative error = 1.4426173986960397015031172446963e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.613 y[1] (analytic) = 2.193842121155187142950521815765 y[1] (numeric) = 2.1938421211551871746478795069711 absolute error = 3.16973576912061e-17 relative error = 1.4448331256633715052953115927188e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.614 y[1] (analytic) = 2.1944948370470361926318357670838 y[1] (numeric) = 2.1944948370470362243872336628118 absolute error = 3.17553978957280e-17 relative error = 1.4470481934903437471260900651747e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.615 y[1] (analytic) = 2.195148747433821830589080977861 y[1] (numeric) = 2.1951487474338218624025508187298 absolute error = 3.18134698408688e-17 relative error = 1.4492626013640059924704379925223e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.616 y[1] (analytic) = 2.1958038529694544981004294538961 y[1] (numeric) = 2.1958038529694545299720030385964 absolute error = 3.18715735847003e-17 relative error = 1.4514763484725363916917444175180e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.617 y[1] (analytic) = 2.1964601543090397853906784956642 y[1] (numeric) = 2.1964601543090398173203876809905 absolute error = 3.19297091853263e-17 relative error = 1.4536894340052672447844074664530e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.618 y[1] (analytic) = 2.1971176521088790867368955152475 y[1] (numeric) = 2.1971176521088791187247722161299 absolute error = 3.19878767008824e-17 relative error = 1.4559018571526741051437634764403e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.619 y[1] (analytic) = 2.1977763470264702567698670051877 y[1] (numeric) = 2.1977763470264702888159431947238 absolute error = 3.20460761895361e-17 relative error = 1.4581136171063785491525060156387e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.62 y[1] (analytic) = 2.198436239720508267972007960762 y[1] (numeric) = 2.1984362397205083000763156702488 absolute error = 3.21043077094868e-17 relative error = 1.4603247130591463882419356902338e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.621 y[1] (analytic) = 2.1990973308508858693723892536474 y[1] (numeric) = 2.1990973308508859015349605726137 absolute error = 3.21625713189663e-17 relative error = 1.4625351442049086169076171115416e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.622 y[1] (analytic) = 2.1997596210786942464395416520563 y[1] (numeric) = 2.1997596210786942786604087282943 absolute error = 3.22208670762380e-17 relative error = 1.4647449097387232216596618406613e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.623 y[1] (analytic) = 2.2004231110662236821726963802011 y[1] (numeric) = 2.2004231110662237144518914197988 absolute error = 3.22791950395977e-17 relative error = 1.4669540088568097683261897893767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.624 y[1] (analytic) = 2.2010878014769642193921233083838 y[1] (numeric) = 2.2010878014769642517296785757572 absolute error = 3.23375552673734e-17 relative error = 1.4691624407565384908897284887213e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.625 y[1] (analytic) = 2.2017536929756063242292290641051 y[1] (numeric) = 2.2017536929756063566251768820304 absolute error = 3.23959478179253e-17 relative error = 1.4713702046364284797912106507239e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.626 y[1] (analytic) = 2.2024207862280415508170785543448 y[1] (numeric) = 2.2024207862280415832714513039908 absolute error = 3.24543727496460e-17 relative error = 1.4735772996961549505319851654767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.627 y[1] (analytic) = 2.2030890819013632071820045895915 y[1] (numeric) = 2.2030890819013632396948347105519 absolute error = 3.25128301209604e-17 relative error = 1.4757837251365428779064062673088e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.628 y[1] (analytic) = 2.2037585806638670223369715012861 y[1] (numeric) = 2.203758580663867054908291491612 absolute error = 3.25713199903259e-17 relative error = 1.4779894801595742509876444919817e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.629 y[1] (analytic) = 2.2044292831850518145773598460989 y[1] (numeric) = 2.2044292831850518472072022623313 absolute error = 3.26298424162324e-17 relative error = 1.4801945639683862383214885747354e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.63 y[1] (analytic) = 2.2051011901356201609798404928803 y[1] (numeric) = 2.2051011901356201936682379500825 absolute error = 3.26883974572022e-17 relative error = 1.4823989757672648175706135642771e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.631 y[1] (analytic) = 2.2057743021874790681050075912146 y[1] (numeric) = 2.2057743021874791008519927630051 absolute error = 3.27469851717905e-17 relative error = 1.4846027147616656142049471267861e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.632 memory used=102.9MB, alloc=4.3MB, time=6.60 y[1] (analytic) = 2.206448620013740643904441124267 y[1] (numeric) = 2.2064486200137406767100467428519 absolute error = 3.28056056185849e-17 relative error = 1.4868057801581893763833855079208e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.633 y[1] (analytic) = 2.2071241442887227708328709530407 y[1] (numeric) = 2.2071241442887228036971298092466 absolute error = 3.28642588562059e-17 relative error = 1.4890081711646027986310543025922e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.634 y[1] (analytic) = 2.2078008756879497801661154642659 y[1] (numeric) = 2.2078008756879498130890604075726 absolute error = 3.29229449433067e-17 relative error = 1.4912098869898275975924731977032e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.635 y[1] (analytic) = 2.2084788148881531275254691399139 y[1] (numeric) = 2.2084788148881531605071330784874 absolute error = 3.29816639385735e-17 relative error = 1.4934109268439522438827589397424e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.636 y[1] (analytic) = 2.2091579625672720696092145727818 y[1] (numeric) = 2.2091579625672721026496304735071 absolute error = 3.30404159007253e-17 relative error = 1.4956112899382210352895707862852e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.637 y[1] (analytic) = 2.209838319404454342131935659715 y[1] (numeric) = 2.209838319404454375231136548229 absolute error = 3.30992008885140e-17 relative error = 1.4978109754850367617651066021249e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.638 y[1] (analytic) = 2.2105198860800568389723099118374 y[1] (numeric) = 2.210519886080056872130328872562 absolute error = 3.31580189607246e-17 relative error = 1.5000099826979678853512432993516e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.639 y[1] (analytic) = 2.2112026632756462925300590296388 y[1] (numeric) = 2.2112026632756463257469292058139 absolute error = 3.32168701761751e-17 relative error = 1.5022083107917421355431922327527e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.64 y[1] (analytic) = 2.2118866516739999552927380999261 y[1] (numeric) = 2.2118866516739999885684926936429 absolute error = 3.32757545937168e-17 relative error = 1.5044059589822581966040488517513e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.641 y[1] (analytic) = 2.2125718519591062826130449814848 y[1] (numeric) = 2.2125718519591063159477172537189 absolute error = 3.33346722722341e-17 relative error = 1.5066029264865747710371312073891e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.642 y[1] (analytic) = 2.2132582648161656166973326568164 y[1] (numeric) = 2.2132582648161656500909559274612 absolute error = 3.33936232706448e-17 relative error = 1.5087992125229222504503791085223e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.643 y[1] (analytic) = 2.2139458909315908718060085385224 y[1] (numeric) = 2.2139458909315909052586161864221 absolute error = 3.34526076478997e-17 relative error = 1.5109948163106827429186949701423e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.644 y[1] (analytic) = 2.214634730993008220666505930789 y[1] (numeric) = 2.2146347309930082541781313937724 absolute error = 3.35116254629834e-17 relative error = 1.5131897370704243185335037162728e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.645 y[1] (analytic) = 2.2153247856892577820995140590041 y[1] (numeric) = 2.2153247856892578156701908339176 absolute error = 3.35706767749135e-17 relative error = 1.5153839740238629628454974329880e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.646 y[1] (analytic) = 2.2160160557103943098591542937911 y[1] (numeric) = 2.2160160557103943434889159365326 absolute error = 3.36297616427415e-17 relative error = 1.5175775263939013115496773636892e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.647 y[1] (analytic) = 2.2167085417476878826877914096955 y[1] (numeric) = 2.2167085417476879163766715352477 absolute error = 3.36888801255522e-17 relative error = 1.5197703934045996407715032592733e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.648 y[1] (analytic) = 2.2174022444936245955861699333913 y[1] (numeric) = 2.2174022444936246293342022158553 absolute error = 3.37480322824640e-17 relative error = 1.5219625742811874956202861611089e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.649 y[1] (analytic) = 2.2180971646419072522995668516017 y[1] (numeric) = 2.2180971646419072861067850242309 absolute error = 3.38072181726292e-17 relative error = 1.5241540682500752929001931154174e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.65 y[1] (analytic) = 2.2187933028874560590206531649455 y[1] (numeric) = 2.2187933028874560928870910201792 absolute error = 3.38664378552337e-17 relative error = 1.5263448745388388561736287293905e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.651 y[1] (analytic) = 2.2194906599264093193097579906269 y[1] (numeric) = 2.2194906599264093532354493801241 absolute error = 3.39256913894972e-17 relative error = 1.5285349923762265034932926407363e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.652 y[1] (analytic) = 2.2201892364561241302332301342922 y[1] (numeric) = 2.2201892364561241642182089689652 absolute error = 3.39849788346730e-17 relative error = 1.5307244209921481012207698354174e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.653 y[1] (analytic) = 2.2208890331751770797205932694713 y[1] (numeric) = 2.2208890331751771137648935195201 absolute error = 3.40443002500488e-17 relative error = 1.5329131596177091614432327411661e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.654 y[1] (analytic) = 2.2215900507833649451411920818197 y[1] (numeric) = 2.2215900507833649792448477767656 absolute error = 3.41036556949459e-17 relative error = 1.5351012074851728503250182663093e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.655 y[1] (analytic) = 2.2222922899817053931010279548629 y[1] (numeric) = 2.2222922899817054272640731835827 absolute error = 3.41630452287198e-17 relative error = 1.5372885638279850622014794834559e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=106.8MB, alloc=4.3MB, time=6.85 x[1] = 0.656 y[1] (analytic) = 2.2229957514724376804604839941385 y[1] (numeric) = 2.2229957514724377146829529048985 absolute error = 3.42224689107600e-17 relative error = 1.5394752278807634546007897857956e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.657 y[1] (analytic) = 2.2237004359590233565736404075195 y[1] (numeric) = 2.2237004359590233908555672080098 absolute error = 3.42819268004903e-17 relative error = 1.5416611988793089849584089773774e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.658 y[1] (analytic) = 2.2244063441461469667498824810923 y[1] (numeric) = 2.2244063441461470010913014384608 absolute error = 3.43414189573685e-17 relative error = 1.5438464760605904477658914858753e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.659 y[1] (analytic) = 2.225113476739716756938504612256 y[1] (numeric) = 2.2251134767397167913394500531427 absolute error = 3.44009454408867e-17 relative error = 1.5460310586627560019144763621926e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.66 y[1] (analytic) = 2.2258218344468653796370150847057 y[1] (numeric) = 2.2258218344468654140975213952772 absolute error = 3.44605063105715e-17 relative error = 1.5482149459251401792249026223100e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.661 y[1] (analytic) = 2.2265314179759506010238474936642 y[1] (numeric) = 2.2265314179759506355439491196479 absolute error = 3.45201016259837e-17 relative error = 1.5503981370882484189453817420542e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.662 y[1] (analytic) = 2.2272422280365560093161859541311 y[1] (numeric) = 2.2272422280365560438959174008498 absolute error = 3.45797314467187e-17 relative error = 1.5525806313937730566298509320896e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.663 y[1] (analytic) = 2.2279542653394917243536124500346 y[1] (numeric) = 2.2279542653394917589930082824408 absolute error = 3.46393958324062e-17 relative error = 1.5547624280845778592898347908056e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.664 y[1] (analytic) = 2.2286675305967951084082859079922 y[1] (numeric) = 2.2286675305967951431073807507029 absolute error = 3.46990948427107e-17 relative error = 1.5569435264047184818875685241942e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.665 y[1] (analytic) = 2.2293820245217314782223638059184 y[1] (numeric) = 2.2293820245217315129811923432497 absolute error = 3.47588285373313e-17 relative error = 1.5591239255994314815400852299963e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.666 y[1] (analytic) = 2.2300977478287948182733783539607 y[1] (numeric) = 2.2300977478287948530919753299622 absolute error = 3.48185969760015e-17 relative error = 1.5613036249151233485905599920976e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.667 y[1] (analytic) = 2.230814701233708495268280513199 y[1] (numeric) = 2.2308147012337085301466807316888 absolute error = 3.48784002184898e-17 relative error = 1.5634826235993954159711635743728e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.668 y[1] (analytic) = 2.2315328854534259738668663462125 y[1] (numeric) = 2.231532885453426008805104670812 absolute error = 3.49382383245995e-17 relative error = 1.5656609209010328665603125870429e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.669 y[1] (analytic) = 2.2322523012061315336353014229997 y[1] (numeric) = 2.2322523012061315686334127771684 absolute error = 3.49981113541687e-17 relative error = 1.5678385160700027170405390319404e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.67 y[1] (analytic) = 2.2329729492112409872304602358361 y[1] (numeric) = 2.2329729492112410222884796029066 absolute error = 3.50580193670705e-17 relative error = 1.5700154083574607581023301592035e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.671 y[1] (analytic) = 2.2336948301894023998157988074685 y[1] (numeric) = 2.2336948301894024349337612306812 absolute error = 3.51179624232127e-17 relative error = 1.5721915970157360925417848208765e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.672 y[1] (analytic) = 2.234417944862496809709479908578 y[1] (numeric) = 2.2344179448624968448874204911166 absolute error = 3.51779405825386e-17 relative error = 1.5743670812983649289331588266953e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.673 y[1] (analytic) = 2.2351422939536389502654715326986 y[1] (numeric) = 2.2351422939536389855034254377248 absolute error = 3.52379539050262e-17 relative error = 1.5765418604600527216373073307209e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.674 y[1] (analytic) = 2.2358678781871779729883405097476 y[1] (numeric) = 2.2358678781871780082863429604366 absolute error = 3.52980024506890e-17 relative error = 1.5787159337567079406804842318824e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.675 y[1] (analytic) = 2.2365946982886981718824643730246 y[1] (numeric) = 2.2365946982886982072405506525999 absolute error = 3.53580862795753e-17 relative error = 1.5808893004454087054322716346059e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.676 y[1] (analytic) = 2.2373227549850197090363858289479 y[1] (numeric) = 2.2373227549850197444545912807171 absolute error = 3.54182054517692e-17 relative error = 1.5830619597844454627070559914018e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.677 y[1] (analytic) = 2.2380520490041993414430354139469 y[1] (numeric) = 2.2380520490041993769213954413366 absolute error = 3.54783600273897e-17 relative error = 1.5852339110332786820457421982364e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.678 y[1] (analytic) = 2.2387825810755311490565491587907 y[1] (numeric) = 2.2387825810755311845950992253821 absolute error = 3.55385500665914e-17 relative error = 1.5874051534525680967594770599849e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.679 y[1] (analytic) = 2.2395143519295472640864093172327 y[1] (numeric) = 2.2395143519295472996851849467971 absolute error = 3.55987756295644e-17 relative error = 1.5895756863041661614865382584215e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=110.6MB, alloc=4.3MB, time=7.09 x[1] = 0.68 y[1] (analytic) = 2.2402473622980186015296374531729 y[1] (numeric) = 2.2402473622980186371886742297071 absolute error = 3.56590367765342e-17 relative error = 1.5917455088511115182204198888987e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.681 y[1] (analytic) = 2.2409816129139555909417704185907 y[1] (numeric) = 2.2409816129139556266611039863529 absolute error = 3.57193335677622e-17 relative error = 1.5939146203576492448436462379165e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.682 y[1] (analytic) = 2.2417171045116089094473509932868 y[1] (numeric) = 2.2417171045116089452270170568317 absolute error = 3.57796660635449e-17 relative error = 1.5960830200891930682725136254506e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.683 y[1] (analytic) = 2.2424538378264702159906661969838 y[1] (numeric) = 2.2424538378264702518307005211987 absolute error = 3.58400343242149e-17 relative error = 1.5982507073123679168608509757042e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.684 y[1] (analytic) = 2.2431918135952728868274675245872 y[1] (numeric) = 2.2431918135952729227279059347277 absolute error = 3.59004384101405e-17 relative error = 1.6004176812949899736130186402475e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.685 y[1] (analytic) = 2.2439310325559927522584085963871 y[1] (numeric) = 2.2439310325559927882192869781127 absolute error = 3.59608783817256e-17 relative error = 1.6025839413060601337359265528003e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.686 y[1] (analytic) = 2.2446714954478488346049369566992 y[1] (numeric) = 2.2446714954478488706262912561097 absolute error = 3.60213542994105e-17 relative error = 1.6047494866157975657753181311235e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.687 y[1] (analytic) = 2.2454132030113040874283779969003 y[1] (numeric) = 2.2454132030113041235102442205712 absolute error = 3.60818662236709e-17 relative error = 1.6069143164955930385506072688238e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.688 y[1] (analytic) = 2.2461561559880661359929502220013 y[1] (numeric) = 2.24615615598806617213536443702 absolute error = 3.61424142150187e-17 relative error = 1.6090784302180424730732297558636e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.689 y[1] (analytic) = 2.2469003551210880189734523238367 y[1] (numeric) = 2.2469003551210880551764506578388 absolute error = 3.62029983340021e-17 relative error = 1.6112418270569492695970080698156e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.69 y[1] (analytic) = 2.2476458011545689314083637686188 y[1] (numeric) = 2.2476458011545689676719824098238 absolute error = 3.62636186412050e-17 relative error = 1.6134045062872954818977431996136e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.691 y[1] (analytic) = 2.2483924948339549688991018520184 y[1] (numeric) = 2.2483924948339550052233770492663 absolute error = 3.63242751972479e-17 relative error = 1.6155664671852797588569374426698e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.692 y[1] (analytic) = 2.2491404369059398730561794210927 y[1] (numeric) = 2.2491404369059399094411474838799 absolute error = 3.63849680627872e-17 relative error = 1.6177277090282840678266354249150e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.693 y[1] (analytic) = 2.249889628118465778193008709278 y[1] (numeric) = 2.2498896281184658146387060077939 absolute error = 3.64456972985159e-17 relative error = 1.6198882310949027052084556845359e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.694 y[1] (analytic) = 2.2506400692207239592680979783159 y[1] (numeric) = 2.2506400692207239957745609434791 absolute error = 3.65064629651632e-17 relative error = 1.6220480326649223697381747875719e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.695 y[1] (analytic) = 2.2513917609631555810763889093694 y[1] (numeric) = 2.2513917609631556176436540328641 absolute error = 3.65672651234947e-17 relative error = 1.6242071130193289213563898708447e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.696 y[1] (analytic) = 2.2521447040974524486904839347305 y[1] (numeric) = 2.2521447040974524853185877690432 absolute error = 3.66281038343127e-17 relative error = 1.6263654714403185623824319061898e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.697 y[1] (analytic) = 2.2528988993765577591525139514087 y[1] (numeric) = 2.2528988993765577958414931098645 absolute error = 3.66889791584558e-17 relative error = 1.6285231072112779207410105590355e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.698 y[1] (analytic) = 2.25365434755466685441739810853 y[1] (numeric) = 2.2536543475546668911672892653294 absolute error = 3.67498911567994e-17 relative error = 1.6306800196168041038805522852261e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.699 y[1] (analytic) = 2.2544110493872279755482486118705 y[1] (numeric) = 2.2544110493872280123590885021259 absolute error = 3.68108398902554e-17 relative error = 1.6328362079426892219762507702753e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7 y[1] (analytic) = 2.2551690056309430181646747409903 y[1] (numeric) = 2.255169005630943055036500160763 absolute error = 3.68718254197727e-17 relative error = 1.6349916714759404118915973714845e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.701 y[1] (analytic) = 2.2559282170437682891447415273365 y[1] (numeric) = 2.2559282170437683260775893336732 absolute error = 3.69328478063367e-17 relative error = 1.6371464095047554886701080006538e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.702 y[1] (analytic) = 2.2566886843849152645813397953357 y[1] (numeric) = 2.2566886843849153015752469063056 absolute error = 3.69939071109699e-17 relative error = 1.6393004213185473856879895328612e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.703 y[1] (analytic) = 2.2574504084148513489937255229102 y[1] (numeric) = 2.2574504084148513860487289176417 absolute error = 3.70550033947315e-17 relative error = 1.6414537062079242432106141827980e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=114.4MB, alloc=4.3MB, time=7.33 x[1] = 0.704 y[1] (analytic) = 2.2582133898953006357949877330194 y[1] (numeric) = 2.2582133898953006729111244517373 absolute error = 3.71161367187179e-17 relative error = 1.6436062634647093872683710175805e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.705 y[1] (analytic) = 2.2589776295892446690162053837593 y[1] (numeric) = 2.2589776295892447061935125278216 absolute error = 3.71773071440623e-17 relative error = 1.6457580923819214225488344348381e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.706 y[1] (analytic) = 2.2597431282609232062880549812383 y[1] (numeric) = 2.2597431282609232435265697131735 absolute error = 3.72385147319352e-17 relative error = 1.6479091922537941887196575216924e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.707 y[1] (analytic) = 2.2605098866758349830806318969027 y[1] (numeric) = 2.2605098866758350203803914404468 absolute error = 3.72997595435441e-17 relative error = 1.6500595623757612814880396865456e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.708 y[1] (analytic) = 2.2612779056007384782022496291953 y[1] (numeric) = 2.2612779056007385155632912693293 absolute error = 3.73610416401340e-17 relative error = 1.6522092020444759788567643187083e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.709 y[1] (analytic) = 2.2620471858036526805579825084111 y[1] (numeric) = 2.2620471858036527179803435913979 absolute error = 3.74223610829868e-17 relative error = 1.6543581105577824937579270326738e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.71 y[1] (analytic) = 2.2628177280538578571687186033559 y[1] (numeric) = 2.262817728053857894652436536778 absolute error = 3.74837179334221e-17 relative error = 1.6565062872147491505706038399610e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.711 y[1] (analytic) = 2.2635895331218963224514908489257 y[1] (numeric) = 2.2635895331218963599966031017225 absolute error = 3.75451122527968e-17 relative error = 1.6586537313156484762434971236791e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.712 y[1] (analytic) = 2.2643626017795732087618556750013 y[1] (numeric) = 2.2643626017795732463683997775064 absolute error = 3.76065441025051e-17 relative error = 1.6608004421619549925567314424105e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.713 y[1] (analytic) = 2.265136934799957238199089679101 y[1] (numeric) = 2.2651369347999572758671032230798 absolute error = 3.76680135439788e-17 relative error = 1.6629464190563562526496736805468e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.714 y[1] (analytic) = 2.2659125329573814956749761480529 y[1] (numeric) = 2.2659125329573815334044967867404 absolute error = 3.77295206386875e-17 relative error = 1.6650916613027594371705577233266e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.715 y[1] (analytic) = 2.2666893970274442032469544975378 y[1] (numeric) = 2.266689397027444241038019945676 absolute error = 3.77910654481382e-17 relative error = 1.6672361682062714619646996433753e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.716 y[1] (analytic) = 2.2674675277870094957164069627153 y[1] (numeric) = 2.2674675277870095335690549965911 absolute error = 3.78526480338758e-17 relative error = 1.6693799390732188139472746157840e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.717 y[1] (analytic) = 2.2682469260142081974928581382867 y[1] (numeric) = 2.2682469260142082354071265957695 absolute error = 3.79142684574828e-17 relative error = 1.6715229732111320720832167512641e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.718 y[1] (analytic) = 2.2690275924884386007248642322568 y[1] (numeric) = 2.2690275924884386387007910128365 absolute error = 3.79759267805797e-17 relative error = 1.6736652699287613059022658359410e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.719 y[1] (analytic) = 2.2698095279903672446983701643499 y[1] (numeric) = 2.2698095279903672827359932291747 absolute error = 3.80376230648248e-17 relative error = 1.6758068285360650037380970325708e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.72 y[1] (analytic) = 2.2705927333019296965033139075021 y[1] (numeric) = 2.2705927333019297346026712794165 absolute error = 3.80993573719144e-17 relative error = 1.6779476483442166357831734416670e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.721 y[1] (analytic) = 2.2713772092063313329692587390984 y[1] (numeric) = 2.2713772092063313711303885026812 absolute error = 3.81611297635828e-17 relative error = 1.6800877286656023937586017937597e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.722 y[1] (analytic) = 2.2721629564880481238708353376532 y[1] (numeric) = 2.2721629564880481620937756392556 absolute error = 3.82229403016024e-17 relative error = 1.6822270688138233317543263868808e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.723 y[1] (analytic) = 2.2729499759328274164037769304403 y[1] (numeric) = 2.2729499759328274546885659782241 absolute error = 3.82847890477838e-17 relative error = 1.6843656681036974980250527703170e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.724 y[1] (analytic) = 2.2737382683276887209323319681743 y[1] (numeric) = 2.2737382683276887592790080321499 absolute error = 3.83466760639756e-17 relative error = 1.6865035258512488636031243495325e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.725 y[1] (analytic) = 2.2745278344609244980088400742199 y[1] (numeric) = 2.2745278344609245364174414862849 absolute error = 3.84086014120650e-17 relative error = 1.6886406413737314414669357246277e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.726 y[1] (analytic) = 2.2753186751221009466662582879727 y[1] (numeric) = 2.2753186751221009851368234419499 absolute error = 3.84705651539772e-17 relative error = 1.6907770139896006109958730649239e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.727 y[1] (analytic) = 2.2761107911020587939844258950013 y[1] (numeric) = 2.2761107911020588325169932466773 absolute error = 3.85325673516760e-17 relative error = 1.6929126430185372190577787964254e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=118.2MB, alloc=4.3MB, time=7.58 x[1] = 0.728 y[1] (analytic) = 2.2769041831929140859308574102828 y[1] (numeric) = 2.2769041831929141245254654774464 absolute error = 3.85946080671636e-17 relative error = 1.6950475277814364907636890872987e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.729 y[1] (analytic) = 2.2776988521880589794768545553899 y[1] (numeric) = 2.2776988521880590181335419178707 absolute error = 3.86566873624808e-17 relative error = 1.6971816676004145202968385461594e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.73 y[1] (analytic) = 2.2784947988821625359897293458082 y[1] (numeric) = 2.278494798882162574708534645515 absolute error = 3.87188052997068e-17 relative error = 1.6993150617987971880539836230073e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.731 y[1] (analytic) = 2.2792920240711715159019316806719 y[1] (numeric) = 2.2792920240711715546828936216315 absolute error = 3.87809619409596e-17 relative error = 1.7014477097011354203171205422205e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.732 y[1] (analytic) = 2.2800905285523111746578761041129 y[1] (numeric) = 2.2800905285523112135010334525087 absolute error = 3.88431573483958e-17 relative error = 1.7035796106331940975143480651056e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.733 y[1] (analytic) = 2.2808903131240860599392636851151 y[1] (numeric) = 2.2808903131240860988446552693259 absolute error = 3.89053915842108e-17 relative error = 1.7057107639219585180942160483744e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.734 y[1] (analytic) = 2.2816913785862808101696962412638 y[1] (numeric) = 2.2816913785862808491373609519027 absolute error = 3.89676647106389e-17 relative error = 1.7078411688956364614262504448541e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.735 y[1] (analytic) = 2.2824937257399609542993814110692 y[1] (numeric) = 2.2824937257399609933293582010224 absolute error = 3.90299767899532e-17 relative error = 1.7099708248836514793025303208362e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.736 y[1] (analytic) = 2.2832973553874737128707283596373 y[1] (numeric) = 2.2832973553874737519630562441031 absolute error = 3.90923278844658e-17 relative error = 1.7120997312166493357762895561041e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.737 y[1] (analytic) = 2.2841022683324488003656351833496 y[1] (numeric) = 2.2841022683324488395203532398774 absolute error = 3.91547180565278e-17 relative error = 1.7142278872264956725388769490991e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.738 y[1] (analytic) = 2.2849084653797992288352703609061 y[1] (numeric) = 2.2849084653797992680524177294355 absolute error = 3.92171473685294e-17 relative error = 1.7163552922462780510542370921360e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.739 y[1] (analytic) = 2.2857159473357221128131518805808 y[1] (numeric) = 2.2857159473357221520927677634806 absolute error = 3.92796158828998e-17 relative error = 1.7184819456102992356593355761521e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.74 y[1] (analytic) = 2.2865247150076994755123289568342 y[1] (numeric) = 2.2865247150076995148544526189419 absolute error = 3.93421236621077e-17 relative error = 1.7206078466540967268829043579381e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.741 y[1] (analytic) = 2.287334769204499056307472533534 y[1] (numeric) = 2.2873347692044990957121433021947 absolute error = 3.94046707686607e-17 relative error = 1.7227329947144141576729366966902e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.742 y[1] (analytic) = 2.2881461107361751195026820559393 y[1] (numeric) = 2.2881461107361751589699393210454 absolute error = 3.94672572651061e-17 relative error = 1.7248573891292339305345767653973e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.743 y[1] (analytic) = 2.2889587404140692643858172793247 y[1] (numeric) = 2.2889587404140693039157004933551 absolute error = 3.95298832140304e-17 relative error = 1.7269810292377529861526739524646e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.744 y[1] (analytic) = 2.2897726590508112365701651686424 y[1] (numeric) = 2.2897726590508112761627138467017 absolute error = 3.95925486780593e-17 relative error = 1.7291039143803804550327718233038e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.745 y[1] (analytic) = 2.2905878674603197406242532309562 y[1] (numeric) = 2.2905878674603197802795069508147 absolute error = 3.96552537198585e-17 relative error = 1.7312260438987702349994880365294e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.746 y[1] (analytic) = 2.2914043664578032539906219105309 y[1] (numeric) = 2.2914043664578032937086203126638 absolute error = 3.97179984021329e-17 relative error = 1.7333474171357836681973915572168e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.747 y[1] (analytic) = 2.292222156859760842194369965414 y[1] (numeric) = 2.2922221568597608819751527530413 absolute error = 3.97807827876273e-17 relative error = 1.7354680334355177317167822806077e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.748 y[1] (analytic) = 2.2930412394839829753422880341259 y[1] (numeric) = 2.293041239483983015185894973252 absolute error = 3.98436069391261e-17 relative error = 1.7375878921432895529541569017338e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.749 y[1] (analytic) = 2.2938616151495523459133968916587 y[1] (numeric) = 2.2938616151495523858198678111121 absolute error = 3.99064709194534e-17 relative error = 1.7397069926056383911607004936682e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.75 y[1] (analytic) = 2.2946832846768446878417081853902 y[1] (numeric) = 2.2946832846768447278110829768634 absolute error = 3.99693747914732e-17 relative error = 1.7418253341703319678772291144754e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.751 y[1] (analytic) = 2.2955062488875295968920267337422 y[1] (numeric) = 2.2955062488875296369243453518315 absolute error = 4.00323186180893e-17 relative error = 1.7439429161863597099625122007282e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=122.0MB, alloc=4.3MB, time=7.83 x[1] = 0.752 y[1] (analytic) = 2.296330508604571352329614763454 y[1] (numeric) = 2.2963305086045713924249172256997 absolute error = 4.00953024622457e-17 relative error = 1.7460597380039477762086416717508e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.753 y[1] (analytic) = 2.2971560646522297398845397552037 y[1] (numeric) = 2.2971560646522297800428661421299 absolute error = 4.01583263869262e-17 relative error = 1.7481757989745392211029110222860e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.754 y[1] (analytic) = 2.2979829178560608760115288619932 y[1] (numeric) = 2.2979829178560609162329193171478 absolute error = 4.02213904551546e-17 relative error = 1.7502910984508003063562490279024e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.755 y[1] (analytic) = 2.2988110690429180334461541602208 y[1] (numeric) = 2.2988110690429180737306488902159 absolute error = 4.02844947299951e-17 relative error = 1.7524056357866354941899229788774e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.756 y[1] (analytic) = 2.2996405190409524680581742896949 y[1] (numeric) = 2.2996405190409525084058135642468 absolute error = 4.03476392745519e-17 relative error = 1.7545194103371676153227148601875e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.757 y[1] (analytic) = 2.3004712686796142470028593359996 y[1] (numeric) = 2.3004712686796142874136834879692 absolute error = 4.04108241519696e-17 relative error = 1.7566324214587528504744186344887e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.758 y[1] (analytic) = 2.3013033187896530781711271066062 y[1] (numeric) = 2.3013033187896531186451765320393 absolute error = 4.04740494254331e-17 relative error = 1.7587446685089739477770266549170e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.759 y[1] (analytic) = 2.3021366702031191409393202509354 y[1] (numeric) = 2.302136670203119181476635409103 absolute error = 4.05373151581676e-17 relative error = 1.7608561508466377938032292487469e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.76 y[1] (analytic) = 2.3029713237533639182194549742173 y[1] (numeric) = 2.3029713237533639588200763876562 absolute error = 4.06006214134389e-17 relative error = 1.7629668678317860116746081066079e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.761 y[1] (analytic) = 2.3038072802750410298107733954668 y[1] (numeric) = 2.3038072802750410704747416500201 absolute error = 4.06639682545533e-17 relative error = 1.7650768188256881686974523445335e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.762 y[1] (analytic) = 2.3046445406041070670534329011966 y[1] (numeric) = 2.3046445406041071077807886460541 absolute error = 4.07273557448575e-17 relative error = 1.7671860031908349938748064616788e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.763 y[1] (analytic) = 2.3054831055778224287851671486257 y[1] (numeric) = 2.3054831055778224695759510963648 absolute error = 4.07907839477391e-17 relative error = 1.7692944202909576302583377814776e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.764 y[1] (analytic) = 2.3063229760347521586017546751156 y[1] (numeric) = 2.3063229760347521994560076017421 absolute error = 4.08542529266265e-17 relative error = 1.7714020694910208249746767418422e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.765 y[1] (analytic) = 2.3071641528147667834221323743718 y[1] (numeric) = 2.3071641528147668243398951193601 absolute error = 4.09177627449883e-17 relative error = 1.7735089501571944575316285442320e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.766 y[1] (analytic) = 2.3080066367590431533589924045926 y[1] (numeric) = 2.3080066367590431943403058709272 absolute error = 4.09813134663346e-17 relative error = 1.7756150616569074476648165261516e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.767 y[1] (analytic) = 2.3088504287100652828957023992357 y[1] (numeric) = 2.3088504287100653239406075534516 absolute error = 4.10449051542159e-17 relative error = 1.7777204033587975924439455330026e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.768 y[1] (analytic) = 2.3096955295116251933703901573883 y[1] (numeric) = 2.3096955295116252344789280296124 absolute error = 4.11085378722241e-17 relative error = 1.7798249746327524294168853983613e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.769 y[1] (analytic) = 2.3105419400088237567680352978996 y[1] (numeric) = 2.3105419400088237979402469818915 absolute error = 4.11722116839919e-17 relative error = 1.7819287748498807573745064840243e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.77 y[1] (analytic) = 2.3113896610480715408214116694355 y[1] (numeric) = 2.3113896610480715820573383226285 absolute error = 4.12359266531930e-17 relative error = 1.7840318033825188259060057156746e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.771 y[1] (analytic) = 2.3122386934770896554217256174682 y[1] (numeric) = 2.3122386934770896967214084610108 absolute error = 4.12996828435426e-17 relative error = 1.7861340596042494809018407380553e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.772 y[1] (analytic) = 2.3130890381449106003397965189116 y[1] (numeric) = 2.3130890381449106417032768377081 absolute error = 4.13634803187965e-17 relative error = 1.7882355428898607377909627766358e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.773 y[1] (analytic) = 2.3139406959018791142586273056503 y[1] (numeric) = 2.3139406959018791556859464484029 absolute error = 4.14273191427526e-17 relative error = 1.7903362526154081603487705912767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.774 y[1] (analytic) = 2.3147936675996530251182140096074 y[1] (numeric) = 2.3147936675996530666094133888569 absolute error = 4.14911993792495e-17 relative error = 1.7924361881581518157141234379099e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.775 y[1] (analytic) = 2.3156479540912041017734446742281 y[1] (numeric) = 2.3156479540912041433285657663955 absolute error = 4.15551210921674e-17 relative error = 1.7945353488965926879415415291641e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=125.8MB, alloc=4.3MB, time=8.08 x[1] = 0.776 y[1] (analytic) = 2.3165035562308189069659392903508 y[1] (numeric) = 2.316503556230818948585023635779 absolute error = 4.16190843454282e-17 relative error = 1.7966337342104744713162893994479e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.777 y[1] (analytic) = 2.3173604748740996516106837283765 y[1] (numeric) = 2.3173604748740996932937729313716 absolute error = 4.16830892029951e-17 relative error = 1.7987313434807637783685816386847e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.778 y[1] (analytic) = 2.3182187108779650503983119534413 y[1] (numeric) = 2.3182187108779650921454476823142 absolute error = 4.17471357288729e-17 relative error = 1.8008281760896605823791064794219e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.779 y[1] (analytic) = 2.3190782651006511787138921259457 y[1] (numeric) = 2.3190782651006512205251161130538 absolute error = 4.18112239871081e-17 relative error = 1.8029242314206000076395345731363e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.78 y[1] (analytic) = 2.3199391384017123308730735062978 y[1] (numeric) = 2.3199391384017123727484275480869 absolute error = 4.18753540417891e-17 relative error = 1.8050195088582584211850038017458e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.781 y[1] (analytic) = 2.3208013316420218796764524000898 y[1] (numeric) = 2.3208013316420219216159783571356 absolute error = 4.19395259570458e-17 relative error = 1.8071140077885336527885498622103e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.782 y[1] (analytic) = 2.3216648456837731372830166981443 y[1] (numeric) = 2.3216648456837731792867564951945 absolute error = 4.20037397970502e-17 relative error = 1.8092077275985683265593184537872e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.783 y[1] (analytic) = 2.3225296813904802174035298849471 y[1] (numeric) = 2.3225296813904802594715255109633 absolute error = 4.20679956260162e-17 relative error = 1.8113006676767386902998327022574e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.784 y[1] (analytic) = 2.3233958396269788988147167089229 y[1] (numeric) = 2.3233958396269789409470102171225 absolute error = 4.21322935081996e-17 relative error = 1.8133928274126520728224088791571e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.785 y[1] (analytic) = 2.3242633212594274901951140288106 y[1] (numeric) = 2.3242633212594275323917475367088 absolute error = 4.21966335078982e-17 relative error = 1.8154842061971486443714373119949e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.786 y[1] (analytic) = 2.3251321271553076962834516720611 y[1] (numeric) = 2.3251321271553077385444673615133 absolute error = 4.22610156894522e-17 relative error = 1.8175748034223160705815805705256e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.787 y[1] (analytic) = 2.3260022581834254853604294637126 y[1] (numeric) = 2.3260022581834255276858695809561 absolute error = 4.23254401172435e-17 relative error = 1.8196646184814568370732158049252e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.788 y[1] (analytic) = 2.3268737152139119580547579075891 y[1] (numeric) = 2.3268737152139120004446647632859 absolute error = 4.23899068556968e-17 relative error = 1.8217536507691329993259093289869e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.789 y[1] (analytic) = 2.3277464991182242174743313259392 y[1] (numeric) = 2.327746499118224259928747295218 absolute error = 4.24544159692788e-17 relative error = 1.8238418996811292029842724741317e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.79 y[1] (analytic) = 2.3286206107691462406634035887577 y[1] (numeric) = 2.3286206107691462831823711112562 absolute error = 4.25189675224985e-17 relative error = 1.8259293646144630204444804879155e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.791 y[1] (analytic) = 2.3294960510407897513866378900402 y[1] (numeric) = 2.3294960510407897939701994699477 absolute error = 4.25835615799075e-17 relative error = 1.8280160449673952591710123820571e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.792 y[1] (analytic) = 2.330372820808595094240903355092 y[1] (numeric) = 2.3303728208085951368891015611919 absolute error = 4.26481982060999e-17 relative error = 1.8301019401394230770518955530753e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.793 y[1] (analytic) = 2.3312509209493321100956925907621 y[1] (numeric) = 2.3312509209493321528085700564744 absolute error = 4.27128774657123e-17 relative error = 1.8321870495312773977064944993178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.794 y[1] (analytic) = 2.3321303523411010128630356190915 y[1] (numeric) = 2.3321303523411010556406350425155 absolute error = 4.27775994234240e-17 relative error = 1.8342713725449289023957843529402e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.795 y[1] (analytic) = 2.3330111158633332675977869643636 y[1] (numeric) = 2.3330111158633333104401511083205 absolute error = 4.28423641439569e-17 relative error = 1.8363549085835811443630012546173e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.796 y[1] (analytic) = 2.3338932123967924699291639939162 y[1] (numeric) = 2.333893212396792512836335685992 absolute error = 4.29071716920758e-17 relative error = 1.8384376570516808123985744013794e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.797 y[1] (analytic) = 2.3347766428235752268244159443281 y[1] (numeric) = 2.3347766428235752697964380769163 absolute error = 4.29720221325882e-17 relative error = 1.8405196173549065506978571172908e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.798 y[1] (analytic) = 2.3356614080271120386855043967211 y[1] (numeric) = 2.3356614080271120817224199270657 absolute error = 4.30369155303446e-17 relative error = 1.8426007889001792061674537977222e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.799 y[1] (analytic) = 2.3365475088921681827796772979326 y[1] (numeric) = 2.3365475088921682258815292481709 absolute error = 4.31018519502383e-17 relative error = 1.8446811710956506482365546585876e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.3MB, time=8.33 x[1] = 0.8 y[1] (analytic) = 2.3374349463048445980048199582053 y[1] (numeric) = 2.3374349463048446411716514154112 absolute error = 4.31668314572059e-17 relative error = 1.8467607633507225563167714099948e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.801 y[1] (analytic) = 2.3383237211525787709904677908206 y[1] (numeric) = 2.3383237211525788142223219070473 absolute error = 4.32318541162267e-17 relative error = 1.8488395650760181170835200023167e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.802 y[1] (analytic) = 2.3392138343241456235353668947597 y[1] (numeric) = 2.3392138343241456668322868870833 absolute error = 4.32969199923236e-17 relative error = 1.8509175756834179052300905883707e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.803 y[1] (analytic) = 2.3401052867096584013824699180295 y[1] (numeric) = 2.3401052867096584447444990685917 absolute error = 4.33620291505622e-17 relative error = 1.8529947945860187575782638116508e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.804 y[1] (analytic) = 2.340998079200569564332255976721 y[1] (numeric) = 2.340998079200569607759437632773 absolute error = 4.34271816560520e-17 relative error = 1.8550712211981824412932269175395e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.805 y[1] (analytic) = 2.3418922126896716776952647431966 y[1] (numeric) = 2.3418922126896717211876423171418 absolute error = 4.34923775739452e-17 relative error = 1.8571468549354817243955042714657e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.806 y[1] (analytic) = 2.3427876880710983050847361560118 y[1] (numeric) = 2.3427876880710983486423531254497 absolute error = 4.35576169694379e-17 relative error = 1.8592216952147490066088572662003e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.807 y[1] (analytic) = 2.3436845062403249025502485442888 y[1] (numeric) = 2.3436845062403249461731484520582 absolute error = 4.36228999077694e-17 relative error = 1.8612957414540437646763468950135e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.808 y[1] (analytic) = 2.3445826680941697140532493002512 y[1] (numeric) = 2.344582668094169757741475754474 absolute error = 4.36882264542228e-17 relative error = 1.8633689930726755140999170222611e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.809 y[1] (analytic) = 2.3454821745307946682853735755283 y[1] (numeric) = 2.3454821745307947120389702496528 absolute error = 4.37535966741245e-17 relative error = 1.8654414494911798142753835080622e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.81 y[1] (analytic) = 2.3463830264497062768304478196196 y[1] (numeric) = 2.3463830264497063206494584524643 absolute error = 4.38190106328447e-17 relative error = 1.8675131101313369423900641541365e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.811 y[1] (analytic) = 2.3472852247517565336710763225998 y[1] (numeric) = 2.3472852247517565775555447183973 absolute error = 4.38844683957975e-17 relative error = 1.8695839744161734781941877842126e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.812 y[1] (analytic) = 2.3481887703391438160407102687252 y[1] (numeric) = 2.3481887703391438599906802971658 absolute error = 4.39499700284406e-17 relative error = 1.8716540417699468454429757338965e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.813 y[1] (analytic) = 2.3490936641154137866221001530857 y[1] (numeric) = 2.3490936641154138306376157493613 absolute error = 4.40155155962756e-17 relative error = 1.8737233116181554255488585477718e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.814 y[1] (analytic) = 2.3499999069854602970930337598291 y[1] (numeric) = 2.3499999069854603411741389246772 absolute error = 4.40811051648481e-17 relative error = 1.8757917833875401320370278657868e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.815 y[1] (analytic) = 2.3509074998555262930202632477729 y[1] (numeric) = 2.3509074998555263371670020475207 absolute error = 4.41467387997478e-17 relative error = 1.8778594565060859761042865266195e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.816 y[1] (analytic) = 2.3518164436332047201025262374043 y[1] (numeric) = 2.3518164436332047643149428040125 absolute error = 4.42124165666082e-17 relative error = 1.8799263304030066151484063485831e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.817 y[1] (analytic) = 2.3527267392274394317635671423658 y[1] (numeric) = 2.3527267392274394760417056734729 absolute error = 4.42781385311071e-17 relative error = 1.8819924045087629349781354107736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.818 y[1] (analytic) = 2.3536383875485260980960663385231 y[1] (numeric) = 2.3536383875485261424399710974896 absolute error = 4.43439047589665e-17 relative error = 1.8840576782550560912307299612333e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.819 y[1] (analytic) = 2.3545513895081131161573861146209 y[1] (numeric) = 2.3545513895081131605671014305734 absolute error = 4.44097153159525e-17 relative error = 1.8861221510748205616521800782917e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.82 y[1] (analytic) = 2.3554657460192025216180437003469 y[1] (numeric) = 2.3554657460192025660936139682228 absolute error = 4.44755702678759e-17 relative error = 1.8881858224022469274008441599767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.821 y[1] (analytic) = 2.3563814579961509017638230203552 y[1] (numeric) = 2.3563814579961509463052927009466 absolute error = 4.45414696805914e-17 relative error = 1.8902486916727451828833111650273e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.822 y[1] (analytic) = 2.3572985263546703098524381764344 y[1] (numeric) = 2.3572985263546703544598517964331 absolute error = 4.46074136199987e-17 relative error = 1.8923107583229887265489612131032e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.823 y[1] (analytic) = 2.3582169520118291808256630145627 y[1] (numeric) = 2.3582169520118292254990651666041 absolute error = 4.46734021520414e-17 relative error = 1.8943720217908649529558462023560e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=133.5MB, alloc=4.3MB, time=8.58 x[1] = 0.824 y[1] (analytic) = 2.359136735886053248377842489053 y[1] (numeric) = 2.3591367358860532931172778317614 absolute error = 4.47394353427084e-17 relative error = 1.8964324815155319258864027673597e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.825 y[1] (analytic) = 2.3600578788971264633817028923793 y[1] (numeric) = 2.3600578788971265081872161504119 absolute error = 4.48055132580326e-17 relative error = 1.8984921369373605096948449386940e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.826 y[1] (analytic) = 2.360980381966191913672379376567 y[1] (numeric) = 2.3609803819661919585440153406591 absolute error = 4.48716359640921e-17 relative error = 1.9005509874979825189650290017607e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.827 y[1] (analytic) = 2.3619042460157527451905805502554 y[1] (numeric) = 2.3619042460157527901283840772649 absolute error = 4.49378035270095e-17 relative error = 1.9026090326402583065221861910323e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.828 y[1] (analytic) = 2.3628294719696730844858112946707 y[1] (numeric) = 2.3628294719696731294898273076232 absolute error = 4.50040160129525e-17 relative error = 1.9046662718082994408780825795555e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.829 y[1] (analytic) = 2.3637560607531789625805763018108 y[1] (numeric) = 2.3637560607531790076508497899442 absolute error = 4.50702734881334e-17 relative error = 1.9067227044474447890089989801803e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.83 y[1] (analytic) = 2.3646840132928592401964881991215 y[1] (numeric) = 2.3646840132928592853330642179314 absolute error = 4.51365760188099e-17 relative error = 1.9087783300042916256529965135719e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.831 y[1] (analytic) = 2.3656133305166665343432054868507 y[1] (numeric) = 2.3656133305166665795461291581351 absolute error = 4.52029236712844e-17 relative error = 1.9108331479266632555509877807227e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.832 y[1] (analytic) = 2.3665440133539181462711268770934 y[1] (numeric) = 2.3665440133539181915404433889981 absolute error = 4.52693165119047e-17 relative error = 1.9128871576636358645799845438579e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.833 y[1] (analytic) = 2.3674760627352969907887699873024 y[1] (numeric) = 2.3674760627352970361245245943658 absolute error = 4.53357546070634e-17 relative error = 1.9149403586655103914344382122733e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.834 y[1] (analytic) = 2.3684094795928525269457637057171 y[1] (numeric) = 2.3684094795928525723480017289159 absolute error = 4.54022380231988e-17 relative error = 1.9169927503838477939980522254500e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.835 y[1] (analytic) = 2.3693442648600016900823849117839 y[1] (numeric) = 2.3693442648600017355511517385782 absolute error = 4.54687668267943e-17 relative error = 1.9190443322714409183483430559257e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.836 y[1] (analytic) = 2.3702804194715298252465716011802 y[1] (numeric) = 2.3702804194715298707819126855588 absolute error = 4.55353410843786e-17 relative error = 1.9210951037823201801640830378029e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.837 y[1] (analytic) = 2.3712179443635916219793458325333 y[1] (numeric) = 2.3712179443635916675813066950594 absolute error = 4.56019608625261e-17 relative error = 1.9231450643717676618355986703213e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.838 y[1] (analytic) = 2.3721568404737120504695812813365 y[1] (numeric) = 2.3721568404737120961382075091929 absolute error = 4.56686262278564e-17 relative error = 1.9251942134962932305827207027105e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.839 y[1] (analytic) = 2.3730971087407872990790515559056 y[1] (numeric) = 2.3730971087407873448143888029407 absolute error = 4.57353372470351e-17 relative error = 1.9272425506136654885935162616117e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.84 y[1] (analytic) = 2.3740387501050857132386968005047 y[1] (numeric) = 2.3740387501050857590407907872778 absolute error = 4.58020939867731e-17 relative error = 1.9292900751828794607523015950275e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.841 y[1] (analytic) = 2.374981765508248735717047481984 y[1] (numeric) = 2.3749817655082487815859439958112 absolute error = 4.58688965138272e-17 relative error = 1.9313367866641790910483499764558e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.842 y[1] (analytic) = 2.3759261558932918482617456284335 y[1] (numeric) = 2.3759261558932918941974905234332 absolute error = 4.59357448949997e-17 relative error = 1.9333826845190375911951411020255e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.843 y[1] (analytic) = 2.3768719222046055146151051614505 y[1] (numeric) = 2.3768719222046055606177443585898 absolute error = 4.60026391971393e-17 relative error = 1.9354277682101925244102358026271e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.844 y[1] (analytic) = 2.3778190653879561249046543376622 y[1] (numeric) = 2.3778190653879561709742338248024 absolute error = 4.60695794871402e-17 relative error = 1.9374720372016051004015896373999e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.845 y[1] (analytic) = 2.378767586390486941409604690122 y[1] (numeric) = 2.3787675863904869875461705220646 absolute error = 4.61365658319426e-17 relative error = 1.9395154909584784161083133085951e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.846 y[1] (analytic) = 2.3797174861607190457041922361288 y[1] (numeric) = 2.3797174861607190919077905346618 absolute error = 4.62035982985330e-17 relative error = 1.9415581289472672431068475970053e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.847 y[1] (analytic) = 2.3806687656485522871788380948894 y[1] (numeric) = 2.3806687656485523334495150488332 absolute error = 4.62706769539438e-17 relative error = 1.9435999506356583825950969452982e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=8.83 NO POLE x[1] = 0.848 y[1] (analytic) = 2.381621425805266232940077036263 y[1] (numeric) = 2.3816214258052662792778789015166 absolute error = 4.63378018652536e-17 relative error = 1.9456409554925804537203294814181e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.849 y[1] (analytic) = 2.3825754675835211190902038605954 y[1] (numeric) = 2.3825754675835211654951769601828 absolute error = 4.64049730995874e-17 relative error = 1.9476811429882094558697278218042e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.85 y[1] (analytic) = 2.3835308919373588033875888893701 y[1] (numeric) = 2.3835308919373588498597796134866 absolute error = 4.64721907241165e-17 relative error = 1.9497205125939617257407248780958e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.851 y[1] (analytic) = 2.3844876998222037192886152270691 y[1] (numeric) = 2.3844876998222037658280700331275 absolute error = 4.65394548060584e-17 relative error = 1.9517590637824869058394642083546e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.852 y[1] (analytic) = 2.3854458921948638313721918362615 y[1] (numeric) = 2.3854458921948638779789572489387 absolute error = 4.66067654126772e-17 relative error = 1.9537967960276818848940519622840e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.853 y[1] (analytic) = 2.386405470013531592147797850512 y[1] (numeric) = 2.3864054700135316388219204617956 absolute error = 4.66741226112836e-17 relative error = 1.9558337088046879376049788123477e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.854 y[1] (analytic) = 2.3873664342377849002480149332341 y[1] (numeric) = 2.3873664342377849469895414024688 absolute error = 4.67415264692347e-17 relative error = 1.9578698015898794883242250178736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.855 y[1] (analytic) = 2.3883287858285880600065058750989 y[1] (numeric) = 2.3883287858285881068154829290334 absolute error = 4.68089770539345e-17 relative error = 1.9599050738608822055681517089715e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.856 y[1] (analytic) = 2.3892925257482927424223990080597 y[1] (numeric) = 2.3892925257482927892988734408931 absolute error = 4.68764744328334e-17 relative error = 1.9619395250965491939077673545557e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.857 y[1] (analytic) = 2.3902576549606389475120394004551 y[1] (numeric) = 2.3902576549606389944560580738841 absolute error = 4.69440186734290e-17 relative error = 1.9639731547769916253777765785945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.858 y[1] (analytic) = 2.3912241744307559680490691850239 y[1] (numeric) = 2.3912241744307560150606790282892 absolute error = 4.70116098432653e-17 relative error = 1.9660059623835423798635599209054e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.859 y[1] (analytic) = 2.3921920851251633546938007599905 y[1] (numeric) = 2.3921920851251634017730487699242 absolute error = 4.70792480099337e-17 relative error = 1.9680379473987950128757595220597e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.86 y[1] (analytic) = 2.3931613880117718825128479926762 y[1] (numeric) = 2.3931613880117719296597812337485 absolute error = 4.71469332410723e-17 relative error = 1.9700691093065715875167930585490e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.861 y[1] (analytic) = 2.3941320840598845188899819453471 y[1] (numeric) = 2.3941320840598845661046475497134 absolute error = 4.72146656043663e-17 relative error = 1.9720994475919365246590788003275e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.862 y[1] (analytic) = 2.3951041742401973928291790342347 y[1] (numeric) = 2.3951041742401974401116242017828 absolute error = 4.72824451675481e-17 relative error = 1.9741289617411978884059972175130e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.863 y[1] (analytic) = 2.3960776595248007656508309248595 y[1] (numeric) = 2.3960776595248008130011029232568 absolute error = 4.73502719983973e-17 relative error = 1.9761576512419044893659270215239e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.864 y[1] (analytic) = 2.3970525408871800030820868599469 y[1] (numeric) = 2.3970525408871800505002330246876 absolute error = 4.74181461647407e-17 relative error = 1.9781855155828429894107676807699e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.865 y[1] (analytic) = 2.3980288193022165487423005103599 y[1] (numeric) = 2.3980288193022165962283682448123 absolute error = 4.74860677344524e-17 relative error = 1.9802125542540391780325675789614e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.866 y[1] (analytic) = 2.3990064957461888990245548345755 y[1] (numeric) = 2.3990064957461889465785916100295 absolute error = 4.75540367754540e-17 relative error = 1.9822387667467634084239697964836e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.867 y[1] (analytic) = 2.3999855711967735793742398283117 y[1] (numeric) = 2.3999855711967736269962931840264 absolute error = 4.76220533557147e-17 relative error = 1.9842641525535318479954514999052e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.868 y[1] (analytic) = 2.4009660466330461219656594429643 y[1] (numeric) = 2.4009660466330461696557769862153 absolute error = 4.76901175432510e-17 relative error = 1.9862887111680910602477016973786e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.869 y[1] (analytic) = 2.4019479230354820447776453495411 y[1] (numeric) = 2.4019479230354820925358747556681 absolute error = 4.77582294061270e-17 relative error = 1.9883124420854275985474708737751e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.87 y[1] (analytic) = 2.4029312013859578320691566237894 y[1] (numeric) = 2.4029312013859578798955456362441 absolute error = 4.78263890124547e-17 relative error = 1.9903353448017775708384455682790e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.871 y[1] (analytic) = 2.4039158826677519162558458281983 y[1] (numeric) = 2.4039158826677519641504422585918 absolute error = 4.78945964303935e-17 relative error = 1.9923574188146028962089939440708e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=9.08 NO POLE x[1] = 0.872 y[1] (analytic) = 2.404901967865545661188573367523 y[1] (numeric) = 2.4049019678655457091514250956741 absolute error = 4.79628517281511e-17 relative error = 1.9943786636226258286121527264329e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.873 y[1] (analytic) = 2.4058894579654243468348533964289 y[1] (numeric) = 2.4058894579654243948660083704115 absolute error = 4.80311549739826e-17 relative error = 1.9963990787257885736682258969766e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.874 y[1] (analytic) = 2.4068783539548781553642159607811 y[1] (numeric) = 2.4068783539548782034637221969725 absolute error = 4.80995062361914e-17 relative error = 1.9984186636252877848837687456700e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.875 y[1] (analytic) = 2.4078686568228031586384714580263 y[1] (numeric) = 2.407868656822803206806377041155 absolute error = 4.81679055831287e-17 relative error = 2.0004374178235508265847016774591e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.876 y[1] (analytic) = 2.4088603675595023071078649070117 y[1] (numeric) = 2.4088603675595023553442179902055 absolute error = 4.82363530831938e-17 relative error = 2.0024553408242453004451664066645e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.877 y[1] (analytic) = 2.4098534871566864201141089234785 y[1] (numeric) = 2.4098534871566864684189577283127 absolute error = 4.83048488048342e-17 relative error = 2.0044724321322802436378041312910e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.878 y[1] (analytic) = 2.4108480166074751776012857043457 y[1] (numeric) = 2.4108480166074752259746785208914 absolute error = 4.83733928165457e-17 relative error = 2.0064886912538073183646190002590e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.879 y[1] (analytic) = 2.4118439569063981132356097317683 y[1] (numeric) = 2.4118439569063981616775949186407 absolute error = 4.84419851868724e-17 relative error = 2.0085041176962178465637828852190e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.88 y[1] (analytic) = 2.4128413090493956089350443168161 y[1] (numeric) = 2.4128413090493956574456703012226 absolute error = 4.85106259844065e-17 relative error = 2.0105187109681315572985445677149e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.881 y[1] (analytic) = 2.4138400740338198908097665124707 y[1] (numeric) = 2.4138400740338199393890817902597 absolute error = 4.85793152777890e-17 relative error = 2.0125324705794226413998520309880e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.882 y[1] (analytic) = 2.414840252858436026514476336492 y[1] (numeric) = 2.4148402528584360751625294722009 absolute error = 4.86480531357089e-17 relative error = 2.0145453960411836198717521899121e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.883 y[1] (analytic) = 2.415841846523422924013547656542 y[1] (numeric) = 2.4158418465234229727303872834464 absolute error = 4.87168396269044e-17 relative error = 2.0165574868657720832373173291101e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.884 y[1] (analytic) = 2.4168448560303743317600195028051 y[1] (numeric) = 2.4168448560303743805456943229669 absolute error = 4.87856748201618e-17 relative error = 2.0185687425667621435990394266948e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.885 y[1] (analytic) = 2.4178492823822998402894279871747 y[1] (numeric) = 2.4178492823822998891439867714909 absolute error = 4.88545587843162e-17 relative error = 2.0205791626589704481105573987333e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.886 y[1] (analytic) = 2.4188551265836258852294804229247 y[1] (numeric) = 2.4188551265836259341529720111766 absolute error = 4.89234915882519e-17 relative error = 2.0225887466584697194784642493871e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.887 y[1] (analytic) = 2.4198623896401967517265746546231 y[1] (numeric) = 2.4198623896401968007190479555246 absolute error = 4.89924733009015e-17 relative error = 2.0245974940825485348433957899660e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.888 y[1] (analytic) = 2.4208710725592755802901680248894 y[1] (numeric) = 2.4208710725592756293516720161361 absolute error = 4.90615039912467e-17 relative error = 2.0266054044497414220029889298953e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.889 y[1] (analytic) = 2.4218811763495453740560018224496 y[1] (numeric) = 2.4218811763495454231865855507679 absolute error = 4.91305837283183e-17 relative error = 2.0286124772798258426261250966562e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.89 y[1] (analytic) = 2.4228927020211100074691884747977 y[1] (numeric) = 2.4228927020211100566689010559936 absolute error = 4.91997125811959e-17 relative error = 2.0306187120938067953372480204329e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.891 y[1] (analytic) = 2.4239056505854952363881701686333 y[1] (numeric) = 2.4239056505854952856570607876417 absolute error = 4.92688906190084e-17 relative error = 2.0326241084139344562177532846368e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.892 y[1] (analytic) = 2.4249200230556497096105590021199 y[1] (numeric) = 2.4249200230556497589486769130538 absolute error = 4.93381179109339e-17 relative error = 2.0346286657636970263018571931966e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.893 y[1] (analytic) = 2.4259358204459459818218701948871 y[1] (numeric) = 2.4259358204459460312292647210868 absolute error = 4.94073945261997e-17 relative error = 2.0366323836678177133536200465563e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.894 y[1] (analytic) = 2.426953043772181527968161304595 y[1] (numeric) = 2.4269530437721815774448818386774 absolute error = 4.94767205340824e-17 relative error = 2.0386352616522558358734544214855e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.895 y[1] (analytic) = 2.4279716940515797590535918227839 y[1] (numeric) = 2.4279716940515798085996878266919 absolute error = 4.95460960039080e-17 relative error = 2.0406372992442079185908381520472e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=9.32 NO POLE x[1] = 0.896 y[1] (analytic) = 2.4289917723027910393639189476544 y[1] (numeric) = 2.4289917723027910889794399527064 absolute error = 4.96155210050520e-17 relative error = 2.0426384959721087794445822502187e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.897 y[1] (analytic) = 2.4300132795458937051169467573578 y[1] (numeric) = 2.4300132795458937548019423642971 absolute error = 4.96849956069393e-17 relative error = 2.0446388513656243776443828705573e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.898 y[1] (analytic) = 2.4310362168023950845409474343307 y[1] (numeric) = 2.4310362168023951342954673133754 absolute error = 4.97545198790447e-17 relative error = 2.0466383649556693548355798164814e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.899 y[1] (analytic) = 2.4320605850952325193820746191814 y[1] (numeric) = 2.4320605850952325692061685100737 absolute error = 4.98240938908923e-17 relative error = 2.0486370362743792970667974823100e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9 y[1] (analytic) = 2.433086385448774387841790401624 y[1] (numeric) = 2.4330863854487744377355081136803 absolute error = 4.98937177120563e-17 relative error = 2.0506348648551406011166355223612e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.901 y[1] (analytic) = 2.4341136188888211289453288859756 y[1] (numeric) = 2.434113618888821178908720298136 absolute error = 4.99633914121604e-17 relative error = 2.0526318502325627437359640701388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.902 y[1] (analytic) = 2.4351422864426062683422206997627 y[1] (numeric) = 2.4351422864426063183753357606409 absolute error = 5.00331150608782e-17 relative error = 2.0546279919424916806092797887006e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.903 y[1] (analytic) = 2.4361723891387974455399042460485 y[1] (numeric) = 2.4361723891387974956427929739821 absolute error = 5.01028887279336e-17 relative error = 2.0566232895220232056313927221398e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.904 y[1] (analytic) = 2.437203928007497442571450933178 y[1] (numeric) = 2.437203928007497492744163416278 absolute error = 5.01727124831000e-17 relative error = 2.0586177425094670336913084551906e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.905 y[1] (analytic) = 2.4382369040802452140984330497498 y[1] (numeric) = 2.4382369040802452643410194459513 absolute error = 5.02425863962015e-17 relative error = 2.0606113504443929952960503748569e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.906 y[1] (analytic) = 2.4392713183900169189499643877719 y[1] (numeric) = 2.4392713183900169692624749248837 absolute error = 5.03125105371118e-17 relative error = 2.0626041128675828175690707457767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.907 y[1] (analytic) = 2.4403071719712269530989451531242 y[1] (numeric) = 2.4403071719712270034814301288792 absolute error = 5.03824849757550e-17 relative error = 2.0645960293210598810563945118736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.908 y[1] (analytic) = 2.4413444658597289840765441396612 y[1] (numeric) = 2.4413444658597290345290539217669 absolute error = 5.04525097821057e-17 relative error = 2.0665870993480902223159951331462e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.909 y[1] (analytic) = 2.4423832010928169868259525815233 y[1] (numeric) = 2.4423832010928170373485376077119 absolute error = 5.05225850261886e-17 relative error = 2.0685773224931630562380730278859e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.91 y[1] (analytic) = 2.4434233787092262809964455374948 y[1] (numeric) = 2.4434233787092263315891563155738 absolute error = 5.05927107780790e-17 relative error = 2.0705666983020081757637081420955e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.911 y[1] (analytic) = 2.4444649997491345696787881015588 y[1] (numeric) = 2.4444649997491346203416752094615 absolute error = 5.06628871079027e-17 relative error = 2.0725552263215887561145862511661e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.912 y[1] (analytic) = 2.4455080652541629795830251751404 y[1] (numeric) = 2.4455080652541630303161392609764 absolute error = 5.07331140858360e-17 relative error = 2.0745429061000982606502960000318e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.913 y[1] (analytic) = 2.4465525762673771026596949789151 y[1] (numeric) = 2.446552576267377153463086761021 absolute error = 5.08033917821059e-17 relative error = 2.0765297371869655235580971569307e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.914 y[1] (analytic) = 2.4475985338332880391655079254826 y[1] (numeric) = 2.4475985338332880900392281924725 absolute error = 5.08737202669899e-17 relative error = 2.0785157191328434711188426989880e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.915 y[1] (analytic) = 2.4486459389978534421745339186714 y[1] (numeric) = 2.4486459389978534931186335294882 absolute error = 5.09440996108168e-17 relative error = 2.0805008514896387049216648424031e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.916 y[1] (analytic) = 2.4496947928084785635359425907501 y[1] (numeric) = 2.4496947928084786145504724747159 absolute error = 5.10145298839658e-17 relative error = 2.0824851338104716068776108673322e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.917 y[1] (analytic) = 2.4507450963140173012793424353703 y[1] (numeric) = 2.4507450963140173523643535922374 absolute error = 5.10850111568671e-17 relative error = 2.0844685656496977466207526286769e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.918 y[1] (analytic) = 2.4517968505647732484687662416698 y[1] (numeric) = 2.4517968505647732996243097416719 absolute error = 5.11555435000021e-17 relative error = 2.0864511465629129135165834702374e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.919 y[1] (analytic) = 2.4528500566125007435063516836075 y[1] (numeric) = 2.4528500566125007947324786675107 absolute error = 5.12261269839032e-17 relative error = 2.0884328761069418222201307210743e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=9.57 NO POLE x[1] = 0.92 y[1] (analytic) = 2.4539047155104059218867673682993 y[1] (numeric) = 2.4539047155104059731835290474531 absolute error = 5.12967616791538e-17 relative error = 2.0904137538398349916559824660700e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.921 y[1] (analytic) = 2.4549608283131477694034360978672 y[1] (numeric) = 2.4549608283131478207708837542557 absolute error = 5.13674476563885e-17 relative error = 2.0923937793208737729366502386178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.922 y[1] (analytic) = 2.4560183960768391768076085511139 y[1] (numeric) = 2.4560183960768392282457935374073 absolute error = 5.14381849862934e-17 relative error = 2.0943729521105794300539522955454e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.923 y[1] (analytic) = 2.4570774198590479959213420441841 y[1] (numeric) = 2.45707741985904804743031578379 absolute error = 5.15089737396059e-17 relative error = 2.0963512717707018417876811381857e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.924 y[1] (analytic) = 2.458137900718798097205440483279 y[1] (numeric) = 2.4581379007187981487852544703936 absolute error = 5.15798139871146e-17 relative error = 2.0983287378642122949699895550964e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.925 y[1] (analytic) = 2.4591998397165704287834130774524 y[1] (numeric) = 2.4591998397165704804341188771122 absolute error = 5.16507057996598e-17 relative error = 2.1003053499553206886845519980671e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.926 y[1] (analytic) = 2.4602632379143040769225108355351 y[1] (numeric) = 2.4602632379143041286441600836685 absolute error = 5.17216492481334e-17 relative error = 2.1022811076094683003530534060831e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.927 y[1] (analytic) = 2.4613280963753973279729013283127 y[1] (numeric) = 2.4613280963753973797655457317916 absolute error = 5.17926444034789e-17 relative error = 2.1042560103933246274240020086295e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.928 y[1] (analytic) = 2.4623944161647087317660436552204 y[1] (numeric) = 2.4623944161647087836297349919116 absolute error = 5.18636913366912e-17 relative error = 2.1062300578747761091251292448867e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.929 y[1] (analytic) = 2.4634621983485581664733270140167 y[1] (numeric) = 2.4634621983485582184081171328343 absolute error = 5.19347901188176e-17 relative error = 2.1082032496229635835306250040357e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.93 y[1] (analytic) = 2.4645314439947279049260377321664 y[1] (numeric) = 2.464531443994727956931978553123 absolute error = 5.20059408209566e-17 relative error = 2.1101755852082303748070871670027e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.931 y[1] (analytic) = 2.4656021541724636823977210799852 y[1] (numeric) = 2.4656021541724637344748645942442 absolute error = 5.20771435142590e-17 relative error = 2.1121470642021637930245574519505e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.932 y[1] (analytic) = 2.4666743299524757658500056479996 y[1] (numeric) = 2.4666743299524758179984039179271 absolute error = 5.21483982699275e-17 relative error = 2.1141176861775757093716329329765e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.933 y[1] (analytic) = 2.4677479724069400246429595344339 y[1] (numeric) = 2.4677479724069400768626646936508 absolute error = 5.22197051592169e-17 relative error = 2.1160874507085074896222111222304e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.934 y[1] (analytic) = 2.4688230826094990027110490532703 y[1] (numeric) = 2.4688230826094990550021133067044 absolute error = 5.22910642534341e-17 relative error = 2.1180563573702268077292099169114e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.935 y[1] (analytic) = 2.4698996616352629922057721389306 y[1] (numeric) = 2.4698996616352630445682477628687 absolute error = 5.23624756239381e-17 relative error = 2.1200244057392244617425518728875e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.936 y[1] (analytic) = 2.4709777105608111086060400903009 y[1] (numeric) = 2.4709777105608111610399794324413 absolute error = 5.24339393421404e-17 relative error = 2.1219915953932273799972175707072e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.937 y[1] (analytic) = 2.4720572304641923672973827645726 y[1] (numeric) = 2.4720572304641924198028382440773 absolute error = 5.25054554795047e-17 relative error = 2.1239579259111832707575498670526e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.938 y[1] (analytic) = 2.4731382224249267616210538001932 y[1] (numeric) = 2.4731382224249268141980779077402 absolute error = 5.25770241075470e-17 relative error = 2.1259233968732614798075021086838e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.939 y[1] (analytic) = 2.4742206875240063423941139181219 y[1] (numeric) = 2.474220687524006395042759215958 absolute error = 5.26486452978361e-17 relative error = 2.1278880078608700065308798312693e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.94 y[1] (analytic) = 2.4753046268438962989015718215649 y[1] (numeric) = 2.475304626843896351621890943558 absolute error = 5.27203191219931e-17 relative error = 2.1298517584566320702337037012618e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.941 y[1] (analytic) = 2.4763900414685360413616636864191 y[1] (numeric) = 2.4763900414685360941537093381109 absolute error = 5.27920456516918e-17 relative error = 2.1318146482443990751757193455967e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.942 y[1] (analytic) = 2.4774769324833402848653537077954 y[1] (numeric) = 2.4774769324833403377291786664544 absolute error = 5.28638249586590e-17 relative error = 2.1337766768092594991685536069233e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.943 y[1] (analytic) = 2.4785653009752001347911396422128 y[1] (numeric) = 2.4785653009752001877267967568865 absolute error = 5.29356571146737e-17 relative error = 2.1357378437375033721760926682358e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=9.82 NO POLE x[1] = 0.944 y[1] (analytic) = 2.479655148032484173696248760357 y[1] (numeric) = 2.4796551480324842267037909519253 absolute error = 5.30075421915683e-17 relative error = 2.1376981486166674988106800955426e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.945 y[1] (analytic) = 2.4807464747450395496853111016935 y[1] (numeric) = 2.4807464747450396027647913629212 absolute error = 5.30794802612277e-17 relative error = 2.1396575910354959036794166931755e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.946 y[1] (analytic) = 2.4818392822041930662575983996958 y[1] (numeric) = 2.4818392822041931194090697952858 absolute error = 5.31514713955900e-17 relative error = 2.1416161705839648432889959833860e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.947 y[1] (analytic) = 2.4829335715027522736339185250206 y[1] (numeric) = 2.4829335715027523268574341916669 absolute error = 5.32235156666463e-17 relative error = 2.1435738868532714984513058243397e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.948 y[1] (analytic) = 2.4840293437350065615642567736144 y[1] (numeric) = 2.4840293437350066148598699200554 absolute error = 5.32956131464410e-17 relative error = 2.1455307394358428190583752845398e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.949 y[1] (analytic) = 2.4851265999967282536172568074846 y[1] (numeric) = 2.4851265999967283069850207145562 absolute error = 5.33677639070716e-17 relative error = 2.1474867279253242196731863454944e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.95 y[1] (analytic) = 2.4862253413851737029526355377064 y[1] (numeric) = 2.4862253413851737563926035583952 absolute error = 5.34399680206888e-17 relative error = 2.1494418519165803654383716826151e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.951 y[1] (analytic) = 2.4873255689990843895776277221722 y[1] (numeric) = 2.4873255689990844430898532816689 absolute error = 5.35122255594967e-17 relative error = 2.1513961110056999702325208577732e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.952 y[1] (analytic) = 2.4884272839386880190885575346191 y[1] (numeric) = 2.488427283938688072673094130372 absolute error = 5.35845365957529e-17 relative error = 2.1533495047899965574133081055708e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.953 y[1] (analytic) = 2.4895304873056996228986358465988 y[1] (numeric) = 2.4895304873056996765555370483672 absolute error = 5.36569012017684e-17 relative error = 2.1553020328680011787779278546226e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.954 y[1] (analytic) = 2.4906351802033226599530834502771 y[1] (numeric) = 2.4906351802033227136824029001849 absolute error = 5.37293194499078e-17 relative error = 2.1572536948394671918878228315242e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.955 y[1] (analytic) = 2.4917413637362501199326819372795 y[1] (numeric) = 2.4917413637362501737344733498689 absolute error = 5.38017914125894e-17 relative error = 2.1592044903053710053347479884422e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.956 y[1] (analytic) = 2.4928490390106656279468554372248 y[1] (numeric) = 2.49284903901066568182117259951 absolute error = 5.38743171622852e-17 relative error = 2.1611544188679088044178403657577e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.957 y[1] (analytic) = 2.4939582071342445507173879091215 y[1] (numeric) = 2.4939582071342446046642846806423 absolute error = 5.39468967715208e-17 relative error = 2.1631034801304892697244241526625e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.958 y[1] (analytic) = 2.4950688692161551042538821694347 y[1] (numeric) = 2.4950688692161551582734124823107 absolute error = 5.40195303128760e-17 relative error = 2.1650516736977543643733466119992e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.959 y[1] (analytic) = 2.4961810263670594630220683323775 y[1] (numeric) = 2.4961810263670595171142861913617 absolute error = 5.40922178589842e-17 relative error = 2.1669989991755519861856615166205e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.96 y[1] (analytic) = 2.4972946796991148706060708308246 y[1] (numeric) = 2.4972946796991149247710303133577 absolute error = 5.41649594825331e-17 relative error = 2.1689454561709607430983572394337e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.961 y[1] (analytic) = 2.4984098303259747518657446802108 y[1] (numeric) = 2.498409830325974806103499936475 absolute error = 5.42377552562642e-17 relative error = 2.1708910442922666256517494740101e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.962 y[1] (analytic) = 2.4995264793627898265901931428407 y[1] (numeric) = 2.499526479362789880900798395814 absolute error = 5.43106052529733e-17 relative error = 2.1728357631489797433261004709331e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.963 y[1] (analytic) = 2.5006446279262092246485804462218 y[1] (numeric) = 2.5006446279262092790320899917323 absolute error = 5.43835095455105e-17 relative error = 2.1747796123518310150761259085272e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.964 y[1] (analytic) = 2.5017642771343816026393547063264 y[1] (numeric) = 2.5017642771343816570958229131064 absolute error = 5.44564682067800e-17 relative error = 2.1767225915127608681779997124168e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.965 y[1] (analytic) = 2.5028854281069562620389977050968 y[1] (numeric) = 2.5028854281069563165684790148374 absolute error = 5.45294813097406e-17 relative error = 2.1786647002449359289751269609942e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.966 y[1] (analytic) = 2.5040080819650842688514196710394 y[1] (numeric) = 2.5040080819650843234539685984446 absolute error = 5.46025489274052e-17 relative error = 2.1806059381627257266487878345930e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.967 y[1] (analytic) = 2.5051322398314195747591187123931 y[1] (numeric) = 2.5051322398314196294347898452346 absolute error = 5.46756711328415e-17 relative error = 2.1825463048817273551135471141598e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=10.06 NO POLE x[1] = 0.968 y[1] (analytic) = 2.5062579028301201397772260541264 y[1] (numeric) = 2.5062579028301201945260740532982 absolute error = 5.47488479991718e-17 relative error = 2.1844858000187541522800019971204e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.969 y[1] (analytic) = 2.5073850720868490564115597329022 y[1] (numeric) = 2.5073850720868491112336393324751 absolute error = 5.48220795995729e-17 relative error = 2.1864244231918283917782696863884e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.97 y[1] (analytic) = 2.5085137487287756753218109081564 y[1] (numeric) = 2.5085137487287757302171769154328 absolute error = 5.48953660072764e-17 relative error = 2.1883621740201899339081197647442e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.971 y[1] (analytic) = 2.5096439338845767324909884525713 y[1] (numeric) = 2.50964393388457678745969574814 absolute error = 5.49687072955687e-17 relative error = 2.1902990521242928931838171612314e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.972 y[1] (analytic) = 2.5107756286844374779022489914824 y[1] (numeric) = 2.5107756286844375329443525292736 absolute error = 5.50421035377912e-17 relative error = 2.1922350571258102743268773177987e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.973 y[1] (analytic) = 2.5119088342600528057242410681426 y[1] (numeric) = 2.5119088342600528608397958754826 absolute error = 5.51155548073400e-17 relative error = 2.1941701886476186843195358751063e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.974 y[1] (analytic) = 2.5130435517446283860060936202811 y[1] (numeric) = 2.5130435517446284411951547979476 absolute error = 5.51890611776665e-17 relative error = 2.1961044463138188927632059018749e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.975 y[1] (analytic) = 2.514179782272881797883180463042 y[1] (numeric) = 2.514179782272881853145803185319 absolute error = 5.52626227222770e-17 relative error = 2.1980378297497165559509909453680e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.976 y[1] (analytic) = 2.515317526981043664294793984159 y[1] (numeric) = 2.5153175269810437196310334988921 absolute error = 5.53362395147331e-17 relative error = 2.1999703385818347920571115245414e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.977 y[1] (analytic) = 2.5164567870068587882148627691366 y[1] (numeric) = 2.5164567870068588436247743977882 absolute error = 5.54099116286516e-17 relative error = 2.2019019724379068467990186865103e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.978 y[1] (analytic) = 2.5175975634895872903968493872484 y[1] (numeric) = 2.517597563489587345880488524953 absolute error = 5.54836391377046e-17 relative error = 2.2038327309468767168360298517519e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.979 y[1] (analytic) = 2.5187398575700057486339660833466 y[1] (numeric) = 2.5187398575700058041913881989662 absolute error = 5.55574221156196e-17 relative error = 2.2057626137388997652435785779488e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.98 y[1] (analytic) = 2.5198836703904083385358476357918 y[1] (numeric) = 2.5198836703904083941671082719714 absolute error = 5.56312606361796e-17 relative error = 2.2076916204453433290682106589810e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.981 y[1] (analytic) = 2.5210290030946079758228221572727 y[1] (numeric) = 2.5210290030946080315279769304958 absolute error = 5.57051547732231e-17 relative error = 2.2096197506987833523342687152932e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.982 y[1] (analytic) = 2.52217585682793746013892213288 y[1] (numeric) = 2.5221758568279375159180267335243 absolute error = 5.57791046006443e-17 relative error = 2.2115470041330089516249315169306e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.983 y[1] (analytic) = 2.5233242327372506203847795085422 y[1] (numeric) = 2.5233242327372506762378897009352 absolute error = 5.58531101923930e-17 relative error = 2.2134733803830150738660314580801e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.984 y[1] (analytic) = 2.5244741319709234615715501628133 y[1] (numeric) = 2.5244741319709235174987217852881 absolute error = 5.59271716224748e-17 relative error = 2.2153988790850070515367276901896e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.985 y[1] (analytic) = 2.5256255556788553131970146160318 y[1] (numeric) = 2.525625555678855369198303580983 absolute error = 5.60012889649512e-17 relative error = 2.2173234998764011797593270225896e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.986 y[1] (analytic) = 2.5267785050124699791450033530492 y[1] (numeric) = 2.5267785050124700352204656469886 absolute error = 5.60754622939394e-17 relative error = 2.2192472423958134126875984350133e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.987 y[1] (analytic) = 2.5279329811247168891092966590468 y[1] (numeric) = 2.5279329811247169452589883426596 absolute error = 5.61496916836128e-17 relative error = 2.2211701062830757751650256127493e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.988 y[1] (analytic) = 2.5290889851700722515431503924384 y[1] (numeric) = 2.5290889851700723077671276006393 absolute error = 5.62239772082009e-17 relative error = 2.2230920911792289991984516661485e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.989 y[1] (analytic) = 2.5302465183045402081356006444805 y[1] (numeric) = 2.5302465183045402644339195864696 absolute error = 5.62983189419891e-17 relative error = 2.2250131967265112220834010173939e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.99 y[1] (analytic) = 2.5314055816856539898157017619896 y[1] (numeric) = 2.5314055816856540461884187213088 absolute error = 5.63727169593192e-17 relative error = 2.2269334225683743618806764323511e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.991 y[1] (analytic) = 2.5325661764724770742858537375025 y[1] (numeric) = 2.5325661764724771307330250720917 absolute error = 5.64471713345892e-17 relative error = 2.2288527683494728016916843585921e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=10.31 NO POLE x[1] = 0.992 y[1] (analytic) = 2.5337283038256043450853765003026 y[1] (numeric) = 2.5337283038256044016070586425561 absolute error = 5.65216821422535e-17 relative error = 2.2307712337156678857026126285793e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.993 y[1] (analytic) = 2.5348919649071632521854901719835 y[1] (numeric) = 2.5348919649071633087817396288065 absolute error = 5.65962494568230e-17 relative error = 2.2326888183140284516125701677911e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.994 y[1] (analytic) = 2.5360571608808149741168618816266 y[1] (numeric) = 2.5360571608808150307877352344914 absolute error = 5.66708733528648e-17 relative error = 2.2346055217928155827373640518160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.995 y[1] (analytic) = 2.5372238929117555816308812682357 y[1] (numeric) = 2.5372238929117556383764351732387 absolute error = 5.67455539050030e-17 relative error = 2.2365213438015107502985682098291e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.996 y[1] (analytic) = 2.5383921621667172028958283318034 y[1] (numeric) = 2.5383921621667172597161195197214 absolute error = 5.68202911879180e-17 relative error = 2.2384362839907847792481973184110e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.997 y[1] (analytic) = 2.5395619698139691902290988292709 y[1] (numeric) = 2.5395619698139692471241841056181 absolute error = 5.68950852763472e-17 relative error = 2.2403503420125220209905351753224e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.998 y[1] (analytic) = 2.5407333170233192883666539477067 y[1] (numeric) = 2.5407333170233193453365901927914 absolute error = 5.69699362450847e-17 relative error = 2.2422635175198050943025941548688e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.999 y[1] (analytic) = 2.5419062049661148042708625242498 y[1] (numeric) = 2.5419062049661148613157066932312 absolute error = 5.70448441689814e-17 relative error = 2.2441758101669153982721803836911e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1 y[1] (analytic) = 2.5430806348152437784779056207571 y[1] (numeric) = 2.5430806348152438355977147437024 absolute error = 5.71198091229453e-17 relative error = 2.2460872196093414819715649878145e-15 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sinh ( x ) ; Iterations = 1000 Total Elapsed Time = 10 Seconds Elapsed Time(since restart) = 10 Seconds Expected Time Remaining = 1 Minutes 33 Seconds Optimized Time Remaining = 1 Minutes 33 Seconds Time to Timeout = 14 Minutes 49 Seconds Percent Done = 10.01 % > quit memory used=161.6MB, alloc=4.4MB, time=10.40