|\^/| 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_max_terms, > glob_iolevel, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_orig_start_sec, > glob_max_trunc_err, > glob_initial_pass, > glob_dump, > glob_normmax, > glob_warned2, > glob_small_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > glob_hmax, > glob_clock_sec, > glob_almost_1, > glob_optimal_start, > glob_last_good_h, > glob_h, > centuries_in_millinium, > sec_in_min, > glob_max_minutes, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_max_hours, > glob_abserr, > days_in_year, > djd_debug, > glob_start, > glob_dump_analytic, > glob_display_flag, > glob_log10abserr, > MAX_UNCHANGED, > glob_current_iter, > glob_relerr, > glob_optimal_done, > years_in_century, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_no_eqs, > glob_not_yet_start_msg, > min_in_hour, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_hmin, > glob_reached_optimal_h, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_disp_incr, > glob_not_yet_finished, > hours_in_day, > djd_debug2, > glob_html_log, > glob_hmin_init, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_last_rel_error, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_fact_1, > array_y, > array_x, > array_1st_rel_error, > array_m1, > array_norms, > array_y_init, > array_type_pole, > array_tmp1_g, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_fact_2, > 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_max_terms, glob_iolevel, DEBUGL, INFO, glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump, glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec, glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h, centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr, days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag, glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr, glob_optimal_done, years_in_century, glob_log10relerr, glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour, glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr, glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log, glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error, array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y, array_x, array_1st_rel_error, array_m1, array_norms, array_y_init, array_type_pole, array_tmp1_g, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2, 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_max_terms, > glob_iolevel, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_orig_start_sec, > glob_max_trunc_err, > glob_initial_pass, > glob_dump, > glob_normmax, > glob_warned2, > glob_small_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > glob_hmax, > glob_clock_sec, > glob_almost_1, > glob_optimal_start, > glob_last_good_h, > glob_h, > centuries_in_millinium, > sec_in_min, > glob_max_minutes, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_max_hours, > glob_abserr, > days_in_year, > djd_debug, > glob_start, > glob_dump_analytic, > glob_display_flag, > glob_log10abserr, > MAX_UNCHANGED, > glob_current_iter, > glob_relerr, > glob_optimal_done, > years_in_century, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_no_eqs, > glob_not_yet_start_msg, > min_in_hour, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_hmin, > glob_reached_optimal_h, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_disp_incr, > glob_not_yet_finished, > hours_in_day, > djd_debug2, > glob_html_log, > glob_hmin_init, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_last_rel_error, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_fact_1, > array_y, > array_x, > array_1st_rel_error, > array_m1, > array_norms, > array_y_init, > array_type_pole, > array_tmp1_g, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_fact_2, > 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_max_terms, glob_iolevel, DEBUGL, INFO, glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump, glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec, glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h, centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr, days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag, glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr, glob_optimal_done, years_in_century, glob_log10relerr, glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour, glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr, glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log, glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error, array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y, array_x, array_1st_rel_error, array_m1, array_norms, array_y_init, array_type_pole, array_tmp1_g, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2, 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_max_terms, > glob_iolevel, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_orig_start_sec, > glob_max_trunc_err, > glob_initial_pass, > glob_dump, > glob_normmax, > glob_warned2, > glob_small_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > glob_hmax, > glob_clock_sec, > glob_almost_1, > glob_optimal_start, > glob_last_good_h, > glob_h, > centuries_in_millinium, > sec_in_min, > glob_max_minutes, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_max_hours, > glob_abserr, > days_in_year, > djd_debug, > glob_start, > glob_dump_analytic, > glob_display_flag, > glob_log10abserr, > MAX_UNCHANGED, > glob_current_iter, > glob_relerr, > glob_optimal_done, > years_in_century, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_no_eqs, > glob_not_yet_start_msg, > min_in_hour, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_hmin, > glob_reached_optimal_h, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_disp_incr, > glob_not_yet_finished, > hours_in_day, > djd_debug2, > glob_html_log, > glob_hmin_init, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_last_rel_error, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_fact_1, > array_y, > array_x, > array_1st_rel_error, > array_m1, > array_norms, > array_y_init, > array_type_pole, > array_tmp1_g, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_fact_2, > 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_max_terms, glob_iolevel, DEBUGL, INFO, glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump, glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec, glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h, centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr, days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag, glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr, glob_optimal_done, years_in_century, glob_log10relerr, glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour, glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr, glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log, glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error, array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y, array_x, array_1st_rel_error, array_m1, array_norms, array_y_init, array_type_pole, array_tmp1_g, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2, 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_max_terms, > glob_iolevel, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_orig_start_sec, > glob_max_trunc_err, > glob_initial_pass, > glob_dump, > glob_normmax, > glob_warned2, > glob_small_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > glob_hmax, > glob_clock_sec, > glob_almost_1, > glob_optimal_start, > glob_last_good_h, > glob_h, > centuries_in_millinium, > sec_in_min, > glob_max_minutes, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_max_hours, > glob_abserr, > days_in_year, > djd_debug, > glob_start, > glob_dump_analytic, > glob_display_flag, > glob_log10abserr, > MAX_UNCHANGED, > glob_current_iter, > glob_relerr, > glob_optimal_done, > years_in_century, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_no_eqs, > glob_not_yet_start_msg, > min_in_hour, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_hmin, > glob_reached_optimal_h, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_disp_incr, > glob_not_yet_finished, > hours_in_day, > djd_debug2, > glob_html_log, > glob_hmin_init, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_last_rel_error, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_fact_1, > array_y, > array_x, > array_1st_rel_error, > array_m1, > array_norms, > array_y_init, > array_type_pole, > array_tmp1_g, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_fact_2, > 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_max_terms, glob_iolevel, DEBUGL, INFO, glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump, glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec, glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h, centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr, days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag, glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr, glob_optimal_done, years_in_century, glob_log10relerr, glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour, glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr, glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log, glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error, array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y, array_x, array_1st_rel_error, array_m1, array_norms, array_y_init, array_type_pole, array_tmp1_g, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2, 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_max_terms, > glob_iolevel, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_orig_start_sec, > glob_max_trunc_err, > glob_initial_pass, > glob_dump, > glob_normmax, > glob_warned2, > glob_small_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > glob_hmax, > glob_clock_sec, > glob_almost_1, > glob_optimal_start, > glob_last_good_h, > glob_h, > centuries_in_millinium, > sec_in_min, > glob_max_minutes, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_max_hours, > glob_abserr, > days_in_year, > djd_debug, > glob_start, > glob_dump_analytic, > glob_display_flag, > glob_log10abserr, > MAX_UNCHANGED, > glob_current_iter, > glob_relerr, > glob_optimal_done, > years_in_century, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_no_eqs, > glob_not_yet_start_msg, > min_in_hour, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_hmin, > glob_reached_optimal_h, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_disp_incr, > glob_not_yet_finished, > hours_in_day, > djd_debug2, > glob_html_log, > glob_hmin_init, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_last_rel_error, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_fact_1, > array_y, > array_x, > array_1st_rel_error, > array_m1, > array_norms, > array_y_init, > array_type_pole, > array_tmp1_g, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_fact_2, > 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_max_terms, glob_iolevel, DEBUGL, INFO, glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump, glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec, glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h, centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr, days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag, glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr, glob_optimal_done, years_in_century, glob_log10relerr, glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour, glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr, glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log, glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error, array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y, array_x, array_1st_rel_error, array_m1, array_norms, array_y_init, array_type_pole, array_tmp1_g, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2, 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_max_terms, > glob_iolevel, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_orig_start_sec, > glob_max_trunc_err, > glob_initial_pass, > glob_dump, > glob_normmax, > glob_warned2, > glob_small_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > glob_hmax, > glob_clock_sec, > glob_almost_1, > glob_optimal_start, > glob_last_good_h, > glob_h, > centuries_in_millinium, > sec_in_min, > glob_max_minutes, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_max_hours, > glob_abserr, > days_in_year, > djd_debug, > glob_start, > glob_dump_analytic, > glob_display_flag, > glob_log10abserr, > MAX_UNCHANGED, > glob_current_iter, > glob_relerr, > glob_optimal_done, > years_in_century, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_no_eqs, > glob_not_yet_start_msg, > min_in_hour, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_hmin, > glob_reached_optimal_h, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_disp_incr, > glob_not_yet_finished, > hours_in_day, > djd_debug2, > glob_html_log, > glob_hmin_init, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_last_rel_error, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_fact_1, > array_y, > array_x, > array_1st_rel_error, > array_m1, > array_norms, > array_y_init, > array_type_pole, > array_tmp1_g, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_fact_2, > array_complex_pole, > array_real_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin $eq_no = 1 iii = 1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin $eq_no = 1 iii = 2 > #emit pre sin 2 $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 sin $eq_no = 1 iii = 3 > #emit pre sin 3 $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 sin $eq_no = 1 iii = 4 > #emit pre sin 4 $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 sin $eq_no = 1 iii = 5 > #emit pre sin 5 $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 sin $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_max_terms, glob_iolevel, DEBUGL, INFO, glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump, glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec, glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h, centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr, days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag, glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr, glob_optimal_done, years_in_century, glob_log10relerr, glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour, glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr, glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log, glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error, array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y, array_x, array_1st_rel_error, array_m1, array_norms, array_y_init, array_type_pole, array_tmp1_g, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2, array_complex_pole, array_real_pole, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[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) > 2.0 - cos(x); > end; exact_soln_y := proc(x) 2.0 - cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,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_max_terms, > glob_iolevel, > DEBUGL, > INFO, > #Top Generate Globals Decl > glob_orig_start_sec, > glob_max_trunc_err, > glob_initial_pass, > glob_dump, > glob_normmax, > glob_warned2, > glob_small_float, > glob_max_rel_trunc_err, > glob_log10_relerr, > glob_look_poles, > glob_hmax, > glob_clock_sec, > glob_almost_1, > glob_optimal_start, > glob_last_good_h, > glob_h, > centuries_in_millinium, > sec_in_min, > glob_max_minutes, > glob_smallish_float, > glob_optimal_clock_start_sec, > glob_max_iter, > glob_max_hours, > glob_abserr, > days_in_year, > djd_debug, > glob_start, > glob_dump_analytic, > glob_display_flag, > glob_log10abserr, > MAX_UNCHANGED, > glob_current_iter, > glob_relerr, > glob_optimal_done, > years_in_century, > glob_log10relerr, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_no_eqs, > glob_not_yet_start_msg, > min_in_hour, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_percent_done, > glob_iter, > glob_warned, > glob_unchanged_h_cnt, > glob_hmin, > glob_reached_optimal_h, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_disp_incr, > glob_not_yet_finished, > hours_in_day, > djd_debug2, > glob_html_log, > glob_hmin_init, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_last_rel_error, > array_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_fact_1, > array_y, > array_x, > array_1st_rel_error, > array_m1, > array_norms, > array_y_init, > array_type_pole, > array_tmp1_g, > array_poles, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_fact_2, > 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_max_terms := 30; > glob_iolevel := 5; > DEBUGL := 3; > INFO := 2; > glob_orig_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_initial_pass := true; > glob_dump := false; > glob_normmax := 0.0; > glob_warned2 := false; > glob_small_float := 0.1e-50; > glob_max_rel_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_look_poles := false; > glob_hmax := 1.0; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > glob_optimal_start := 0.0; > glob_last_good_h := 0.1; > glob_h := 0.1; > centuries_in_millinium := 10.0; > sec_in_min := 60.0; > glob_max_minutes := 0.0; > glob_smallish_float := 0.1e-100; > glob_optimal_clock_start_sec := 0.0; > glob_max_iter := 1000; > glob_max_hours := 0.0; > glob_abserr := 0.1e-10; > days_in_year := 365.0; > djd_debug := true; > glob_start := 0; > glob_dump_analytic := false; > glob_display_flag := true; > glob_log10abserr := 0.0; > MAX_UNCHANGED := 10; > glob_current_iter := 0; > glob_relerr := 0.1e-10; > glob_optimal_done := false; > years_in_century := 100.0; > glob_log10relerr := 0.0; > glob_curr_iter_when_opt := 0; > glob_log10_abserr := 0.1e-10; > glob_large_float := 9.0e100; > glob_clock_start_sec := 0.0; > glob_no_eqs := 0; > glob_not_yet_start_msg := true; > min_in_hour := 60.0; > glob_max_opt_iter := 10; > glob_optimal_expect_sec := 0.1; > glob_percent_done := 0.0; > glob_iter := 0; > glob_warned := false; > glob_unchanged_h_cnt := 0; > glob_hmin := 0.00000000001; > glob_reached_optimal_h := false; > glob_log10normmin := 0.1; > glob_subiter_method := 3; > glob_max_sec := 10000.0; > glob_disp_incr := 0.1; > glob_not_yet_finished := true; > hours_in_day := 24.0; > djd_debug2 := true; > glob_html_log := true; > glob_hmin_init := 0.001; > #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/sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.05;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > 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,"2.0 - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := 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_fact_2 := Array(0..(max_terms+ 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_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[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 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_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 <=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 <=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_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_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_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 := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.05; > glob_look_poles := true; > glob_max_iter := 1000000; > #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 ) = sin(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,"2012-06-18T01:33:12-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(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,"sin diffeq.mxt") > ; > logitem_str(html_log_file,"sin 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_max_terms, glob_iolevel, DEBUGL, INFO, glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump, glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec, glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h, centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr, days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag, glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr, glob_optimal_done, years_in_century, glob_log10relerr, glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour, glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter, glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr, glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log, glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error, array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y, array_x, array_1st_rel_error, array_m1, array_norms, array_y_init, array_type_pole, array_tmp1_g, array_poles, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2, 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_max_terms := 30; glob_iolevel := 5; DEBUGL := 3; INFO := 2; glob_orig_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_initial_pass := true; glob_dump := false; glob_normmax := 0.; glob_warned2 := false; glob_small_float := 0.1*10^(-50); glob_max_rel_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_look_poles := false; glob_hmax := 1.0; glob_clock_sec := 0.; glob_almost_1 := 0.9990; glob_optimal_start := 0.; glob_last_good_h := 0.1; glob_h := 0.1; centuries_in_millinium := 10.0; sec_in_min := 60.0; glob_max_minutes := 0.; glob_smallish_float := 0.1*10^(-100); glob_optimal_clock_start_sec := 0.; glob_max_iter := 1000; glob_max_hours := 0.; glob_abserr := 0.1*10^(-10); days_in_year := 365.0; djd_debug := true; glob_start := 0; glob_dump_analytic := false; glob_display_flag := true; glob_log10abserr := 0.; MAX_UNCHANGED := 10; glob_current_iter := 0; glob_relerr := 0.1*10^(-10); glob_optimal_done := false; years_in_century := 100.0; glob_log10relerr := 0.; glob_curr_iter_when_opt := 0; glob_log10_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_clock_start_sec := 0.; glob_no_eqs := 0; glob_not_yet_start_msg := true; min_in_hour := 60.0; glob_max_opt_iter := 10; glob_optimal_expect_sec := 0.1; glob_percent_done := 0.; glob_iter := 0; glob_warned := false; glob_unchanged_h_cnt := 0; glob_hmin := 0.1*10^(-10); glob_reached_optimal_h := false; glob_log10normmin := 0.1; glob_subiter_method := 3; glob_max_sec := 10000.0; glob_disp_incr := 0.1; glob_not_yet_finished := true; hours_in_day := 24.0; djd_debug2 := true; glob_html_log := true; glob_hmin_init := 0.001; 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/sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.05;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); 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, "2.0 - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_last_rel_error := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := 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_fact_2 := Array(0 .. max_terms + 1, 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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; 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_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_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_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[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 <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_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 <= 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 <= 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_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_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_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 := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 1000000; 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 ) = sin(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, "2012-06-18T01:33:12-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(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, "sin diffeq.mxt"); logitem_str(html_log_file, "sin 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/sinpostode.ode################# diff ( y , x , 1 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 1000000; #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) 2.0 - cos(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 1.0000004999999583333347222221974 y[1] (numeric) = 1.000000499999958333383333331746 absolute error = 4.86111095486e-20 relative error = 4.8611085243059403932115646022377e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 1.000001999999333333422222215873 y[1] (numeric) = 1.0000019999993333335194444011408 absolute error = 9.72221852678e-20 relative error = 9.7221990823883166885573530174913e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 1.0000044999966250010124998372768 y[1] (numeric) = 1.0000044999966250011583330158234 absolute error = 1.458331785466e-19 relative error = 1.4583252230074183127686885267156e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 1.0000079999893333390222205968257 y[1] (numeric) = 1.0000079999893333392166646375997 absolute error = 1.944440407740e-19 relative error = 1.9444248523619216253239107952973e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 1.0000124999739583550347125341049 y[1] (numeric) = 1.000012499973958355277767257444 absolute error = 2.430547233391e-19 relative error = 2.4305168519936447363825618573404e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 1.0000179999460000647999583428738 y[1] (numeric) = 1.0000179999460000650916235205051 absolute error = 2.916651776313e-19 relative error = 2.9165992776834978690377545086004e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 1.0000244998999584967345792460848 y[1] (numeric) = 1.0000244998999584970748546011248 absolute error = 3.402753550400e-19 relative error = 3.4026701853208678791928872200746e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 1.0000319998293336974218061209308 y[1] (numeric) = 1.000031999829333697810691327886 absolute error = 3.888852069552e-19 relative error = 3.8887276309314849589860483133446e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 1.0000404997266257381114323739519 y[1] (numeric) = 1.0000404997266257385489270587189 absolute error = 4.374946847670e-19 relative error = 4.3747696706942863110629445287519e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 1.0000499995833347222197420662478 y[1] (numeric) = 1.0000499995833347227058458061136 absolute error = 4.861037398658e-19 relative error = 4.8607943609652759688458657701332e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 1.0000604993899607938294057888689 y[1] (numeric) = 1.0000604993899607943641181125116 absolute error = 5.347123236427e-19 relative error = 5.3467997583033801256109195451551e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 1.0000719991360041471893357884913 y[1] (numeric) = 1.0000719991360041477726561759804 absolute error = 5.833203874891e-19 relative error = 5.8327839194882979593255491368521e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 1.0000844988099650372144908435208 y[1] (numeric) = 1.0000844988099650378464187263176 absolute error = 6.319278827968e-19 relative error = 6.3187449015433469409427529332133e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 1.0000979983993437909856203908218 y[1] (numeric) = 1.0000979983993437916661551517803 absolute error = 6.805347609585e-19 relative error = 6.8046807617623018060985291621422e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.20 NO POLE x[1] = 0.015 y[1] (analytic) = 1.0001124978906408202489364033288 y[1] (numeric) = 1.0001124978906408209780773766959 absolute error = 7.291409733671e-19 relative error = 7.2905895577242280337290526502902e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 1.0001279972693566349157005188684 y[1] (numeric) = 1.000127997269356635693446990285 absolute error = 7.777464714166e-19 relative error = 7.7764693473243069157673332951171e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 1.0001444965199918575617129206072 y[1] (numeric) = 1.0001444965199918583880641271087 absolute error = 8.263512065015e-19 relative error = 8.2623181887896544673334282992764e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 1.0001619956260472389266884696369 y[1] (numeric) = 1.0001619956260472398016435996539 absolute error = 8.749551300170e-19 relative error = 8.7481341407031315716535560447777e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 1.0001804945700236744135045903217 y[1] (numeric) = 1.0001804945700236753370627836809 absolute error = 9.235581933592e-19 relative error = 9.2339152620271453655407396532496e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 1.0001999933334222215873044091625 y[1] (numeric) = 1.0001999933334222225594647570875 absolute error = 9.721603479250e-19 relative error = 9.7196596121244418955450553667846e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 1.0002204918967441186744376480752 y[1] (numeric) = 1.0002204918967441196951991931874 absolute error = 1.0207615451122e-18 relative error = 1.0205365250780888803484591400136e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 1.0002419902394908040612207731441 y[1] (numeric) = 1.0002419902394908051305825094639 absolute error = 1.0693617363198e-18 relative error = 1.0691030238230247234475142776005e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 1.0002644883401639367924969000924 y[1] (numeric) = 1.0002644883401639379104577730398 absolute error = 1.1179608729474e-18 relative error = 1.1176652635169935013686460405559e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 1.0002879861762654180699749579101 y[1] (numeric) = 1.0002879861762654192365338643062 absolute error = 1.1665589063961e-18 relative error = 1.1662230502791775072660918184101e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 1.0003124837242974137503266123044 y[1] (numeric) = 1.000312483724297414965482400372 absolute error = 1.2151557880676e-18 relative error = 1.2147761902794736463316759263114e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 1.0003379809597623778430184508743 y[1] (numeric) = 1.0003379809597623791067699202396 absolute error = 1.2637514693653e-18 relative error = 1.2633244897417657617459700190888e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 1.0003644778571630770078559321828 y[1] (numeric) = 1.0003644778571630783202018338761 absolute error = 1.3123459016933e-18 relative error = 1.3118677549450962746889635576401e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 1.0003919743900026160522146011815 y[1] (numeric) = 1.0003919743900026174131536376388 absolute error = 1.3609390364573e-18 relative error = 1.3604057922267358995614927715761e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 1.0004204705307844644279330737607 y[1] (numeric) = 1.0004204705307844658374638988248 absolute error = 1.4095308250641e-18 relative error = 1.4089384079838524112829740814420e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 1.0004499662510124837278412935334 y[1] (numeric) = 1.0004499662510124851859625124553 absolute error = 1.4581212189219e-18 relative error = 1.4574654086759776928422921137229e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 1.000480461521190956181896564327 y[1] (numeric) = 1.0004804615211909576886067337674 absolute error = 1.5067101694404e-18 relative error = 1.5059866008272733309458496592849e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 1.00051195631082461415289886225 y[1] (numeric) = 1.0005119563108246157081964902805 absolute error = 1.5552976280305e-18 relative error = 1.5545017910283948476909644778028e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 1.0005444505884186706317559316192 y[1] (numeric) = 1.0005444505884186722356394777242 absolute error = 1.6038835461050e-18 relative error = 1.6030107859393538431293073870928e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 1.0005779443214788507322676694872 y[1] (numeric) = 1.000577944321478852384735544565 absolute error = 1.6524678750778e-18 relative error = 1.6515133922908792127816275573293e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 1.0006124374765114241853983039858 y[1] (numeric) = 1.0006124374765114258864488703503 absolute error = 1.7010505663645e-18 relative error = 1.7000094168871759602469375195198e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 1.0006479300190232388330038722177 y[1] (numeric) = 1.0006479300190232405826354436003 absolute error = 1.7496315713826e-18 relative error = 1.7484986666082823878583567664127e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 1.0006844219135217551209815039716 y[1] (numeric) = 1.0006844219135217569191923455226 absolute error = 1.7982108415510e-18 relative error = 1.7969809484117259082301174627635e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.1MB, time=0.44 NO POLE x[1] = 0.038 y[1] (analytic) = 1.0007219131235150815918060181131 y[1] (numeric) = 1.0007219131235150834385943464036 absolute error = 1.8467883282905e-18 relative error = 1.8454560693351763778375182492343e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 1.0007604036115120113764183391194 y[1] (numeric) = 1.0007604036115120132717823221429 absolute error = 1.8953639830235e-18 relative error = 1.8939238364982980100474488106273e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 1.0007998933390220596854292418709 y[1] (numeric) = 1.0007998933390220616293669990454 absolute error = 1.9439377571745e-18 relative error = 1.9423840571053987475396215943732e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.041 y[1] (analytic) = 1.0008403822665555022996009335004 y[1] (numeric) = 1.00084038226655550429211053567 absolute error = 1.9925096021696e-18 relative error = 1.9908365384470783339134294132678e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 1.0008818703536234150595679818205 y[1] (numeric) = 1.0008818703536234171006474512575 absolute error = 2.0410794694370e-18 relative error = 2.0392810879028735503315639117806e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 1.0009243575587377143547581006123 y[1] (numeric) = 1.0009243575587377164444054110191 absolute error = 2.0896473104068e-18 relative error = 2.0877175129432018493678391796163e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 1.0009678438394111986114723028572 y[1] (numeric) = 1.0009678438394112007496853793684 absolute error = 2.1382130765112e-18 relative error = 2.1361456211317024734401878570621e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 1.001012329152157590780082933836 y[1] (numeric) = 1.0010123291521575929668596530206 absolute error = 2.1867767191846e-18 relative error = 2.1845652201274753921671646118860e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 1.0010578134524915818213070969007 y[1] (numeric) = 1.0010578134524915840566452867638 absolute error = 2.2353381898631e-18 relative error = 2.2329761176867185635149081263174e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 1.0011042966949288751915119856476 y[1] (numeric) = 1.0011042966949288774754094256329 absolute error = 2.2838974399853e-18 relative error = 2.2813781216656615646211925042762e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 1.0011517788329862323270076371929 y[1] (numeric) = 1.0011517788329862346594620581849 absolute error = 2.3324544209920e-18 relative error = 2.3297710400223978817996652150347e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 1.0012002598191815191272816222591 y[1] (numeric) = 1.0012002598191815215082907065854 absolute error = 2.3810090843263e-18 relative error = 2.3781546808191143664565735427898e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 1.0012497396050337534371291888435 y[1] (numeric) = 1.0012497396050337558666905702769 absolute error = 2.4295613814334e-18 relative error = 2.4265288522240185479992550313008e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 1.0013002181410631535276313773408 y[1] (numeric) = 1.0013002181410631560057426411019 absolute error = 2.4781112637611e-18 relative error = 2.4748933625139625582695888730663e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 1.0013516953767911875759326261474 y[1] (numeric) = 1.0013516953767911901025913089069 absolute error = 2.5266586827595e-18 relative error = 2.5232480200762653944145401110923e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 1.0014041712607406241437683879725 y[1] (numeric) = 1.0014041712607406267189719778537 absolute error = 2.5752035898812e-18 relative error = 2.5715926334110319296052648044776e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 1.0014576457404355836546922783338 y[1] (numeric) = 1.001457645740435586278438214915 absolute error = 2.6237459365812e-18 relative error = 2.6199270111331696053694992648674e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 1.0015121187624015908699512790137 y[1] (numeric) = 1.001512118762401593542236953331 absolute error = 2.6722856743173e-18 relative error = 2.6682509619749016574056641611207e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 1.0015675902721656283629565206066 y[1] (numeric) = 1.0015675902721656310837792751562 absolute error = 2.7208227545496e-18 relative error = 2.7165642947873788245492460387047e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 1.0016240602142561909922961696895 y[1] (numeric) = 1.0016240602142561937616532984307 absolute error = 2.7693571287412e-18 relative error = 2.7648668185434864322826714984863e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 1.0016815285322033413732359476087 y[1] (numeric) = 1.0016815285322033441911246959663 absolute error = 2.8178887483576e-18 relative error = 2.8131583423393505269820689696233e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 1.0017399951685387663476518093861 y[1] (numeric) = 1.0017399951685387692140693742533 absolute error = 2.8664175648672e-18 relative error = 2.8614386753969393581706208580082e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 1.0017994600647958344523383128172 y[1] (numeric) = 1.0017994600647958373672818425585 absolute error = 2.9149435297413e-18 relative error = 2.9097076270661625893588670760757e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=4.1MB, time=0.69 x[1] = 0.061 y[1] (analytic) = 1.0018599231615096543856352094576 y[1] (numeric) = 1.0018599231615096573491018039114 absolute error = 2.9634665944538e-18 relative error = 2.9579650068266680172040595295802e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 1.0019213843982171344723137908757 y[1] (numeric) = 1.0019213843982171374843005013574 absolute error = 3.0119867104817e-18 relative error = 3.0062106242904337687784473365934e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 1.0019838437134570431266635252906 y[1] (numeric) = 1.0019838437134570461871673545955 absolute error = 3.0605038293049e-18 relative error = 3.0544442892036585554300542357018e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 1.0020473010447700703137185215135 y[1] (numeric) = 1.0020473010447700734227364239198 absolute error = 3.1090179024063e-18 relative error = 3.1026658114489481903823420976132e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 1.0021117563286988900085623589714 y[1] (numeric) = 1.0021117563286988931660912402431 absolute error = 3.1575288812717e-18 relative error = 3.1508750010472992441374223117299e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 1.0021772095007882236536488245129 y[1] (numeric) = 1.0021772095007882268596855419032 absolute error = 3.2060367173903e-18 relative error = 3.1990716681606781400684386151655e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 1.0022436604955849046140750986816 y[1] (numeric) = 1.0022436604955849078686164609358 absolute error = 3.2545413622542e-18 relative error = 3.2472556230935989475569641072760e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 1.0023111092466379436307429361887 y[1] (numeric) = 1.0023111092466379469337857035474 absolute error = 3.3030427673587e-18 relative error = 3.2954266762954961333992207360567e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 1.0023795556864985952713423874285 y[1] (numeric) = 1.002379555686498598622883271631 absolute error = 3.3515408842025e-18 relative error = 3.3435846383629939884328200295394e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 1.0024489997467204253790916100603 y[1] (numeric) = 1.0024489997467204287791272743477 absolute error = 3.4000356642874e-18 relative error = 3.3917293200416737005168521973011e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 1.0025194413578593795191653219204 y[1] (numeric) = 1.0025194413578593829676923810391 absolute error = 3.4485270591187e-18 relative error = 3.4398605322285352512223556853121e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 1.0025908804494738524227434488436 y[1] (numeric) = 1.0025908804494738559197584690486 absolute error = 3.4970150202050e-18 relative error = 3.4879780859738571056333799783596e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 1.0026633169501247584286105233492 y[1] (numeric) = 1.0026633169501247619741100224075 absolute error = 3.5454994990583e-18 relative error = 3.5360817924833515512129771791641e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 1.0027367507873756029222353925998 y[1] (numeric) = 1.002736750787375606516215839794 absolute error = 3.5939804471942e-18 relative error = 3.5841714631204160346660196205819e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 1.0028111818877925547722597965581 y[1] (numeric) = 1.0028111818877925584147176126897 absolute error = 3.6424578161316e-18 relative error = 3.6322469094078820773869407858923e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 1.0028866101769445197643233798592 y[1] (numeric) = 1.0028866101769445234552549372525 absolute error = 3.6909315573933e-18 relative error = 3.6803079430306579508880026034915e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 1.0029630355794032150321517035803 y[1] (numeric) = 1.0029630355794032187715533260857 absolute error = 3.7394016225054e-18 relative error = 3.7283543758371707964897748991073e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 1.0030404580187432444858328258248 y[1] (numeric) = 1.0030404580187432482737007888229 absolute error = 3.7878679629981e-18 relative error = 3.7763860198422008951080779791445e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 1.0031188774175421752372070228519 y[1] (numeric) = 1.0031188774175421790735375532566 absolute error = 3.8363305304047e-18 relative error = 3.8244026872279172381598353073707e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 1.0031982936973806150222932253665 y[1] (numeric) = 1.0031982936973806189070825016294 absolute error = 3.8847892762629e-18 relative error = 3.8724041903472022595644135983094e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 1.0032787067788422906206747475516 y[1] (numeric) = 1.0032787067788422945539188996655 absolute error = 3.9332441521139e-18 relative error = 3.9203903417247791224663978793350e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 1.0033601165815141272717658894624 y[1] (numeric) = 1.0033601165815141312534609989652 absolute error = 3.9816951095028e-18 relative error = 3.9683609540596310119832004780790e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 1.0034425230239863290878799965224 y[1] (numeric) = 1.0034425230239863331180220965011 absolute error = 4.0301420999787e-18 relative error = 4.0163158402271171505210838182049e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 1.0035259260238524604640185630608 y[1] (numeric) = 1.0035259260238524645426036381554 absolute error = 4.0785850750946e-18 relative error = 4.0642548132808853039542902015182e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.93 NO POLE x[1] = 0.085 y[1] (analytic) = 1.0036103254977095284842999701085 y[1] (numeric) = 1.003610325497709532611323956516 absolute error = 4.1270239864075e-18 relative error = 4.1121776864549794090956892800184e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.086 y[1] (analytic) = 1.00369572136115806632494545103 y[1] (numeric) = 1.0036957213611580705004042365085 absolute error = 4.1754587854785e-18 relative error = 4.1600842731659428965071496065134e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 1.0037821135288022176537388820139 y[1] (numeric) = 1.0037821135288022218776283058867 absolute error = 4.2238894238728e-18 relative error = 4.2079743870148180378229470785932e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 1.0038695019142498220258759979679 y[1] (numeric) = 1.0038695019142498262981918511276 absolute error = 4.2723158531597e-18 relative error = 4.2558478417891409453977120269454e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 1.0039578864301125012761176379763 y[1] (numeric) = 1.0039578864301125055968556628892 absolute error = 4.3207380249129e-18 relative error = 4.3037044514652309963797900521872e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 1.0040472669880057469071606281749 y[1] (numeric) = 1.0040472669880057512763165188851 absolute error = 4.3691558907102e-18 relative error = 4.3515440302098780778245687262037e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 1.0041376434985490084741389136785 y[1] (numeric) = 1.0041376434985490128917083158122 absolute error = 4.4175694021337e-18 relative error = 4.3993663923825234457057829645061e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 1.0042290158713657829651665550681 y[1] (numeric) = 1.0042290158713657874311450658381 absolute error = 4.4659785107700e-18 relative error = 4.4471713525374359477314628147883e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 1.0043213840150837051778332089018 y[1] (numeric) = 1.0043213840150837096922163771117 absolute error = 4.5143831682099e-18 relative error = 4.4949587254253857127860921344015e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 1.0044147478373346390915617157617 y[1] (numeric) = 1.0044147478373346436543450418104 absolute error = 4.5627833260487e-18 relative error = 4.5427283259959107476756310098774e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 1.0045091072447547702357364234864 y[1] (numeric) = 1.0045091072447547748469153593727 absolute error = 4.6111789358863e-18 relative error = 4.5904799693993796014612981278123e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 1.0046044621429846990535098774693 y[1] (numeric) = 1.0046044621429847037130798267964 absolute error = 4.6595699493271e-18 relative error = 4.6382134709888501796289292115453e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 1.0047008124366695352611945142231 y[1] (numeric) = 1.0047008124366695399691508322031 absolute error = 4.7079563179800e-18 relative error = 4.6859286463220233923165613292625e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 1.0047981580294589932031449988264 y[1] (numeric) = 1.0047981580294589979594829922852 absolute error = 4.7563379934588e-18 relative error = 4.7336253111635900950091079578346e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 1.0048964988240074882020358513791 y[1] (numeric) = 1.0048964988240074930067507787609 absolute error = 4.8047149273818e-18 relative error = 4.7813032814867768528037296644333e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 1.0049958347219742339044380121961 y[1] (numeric) = 1.0049958347219742387575250835681 absolute error = 4.8530870713720e-18 relative error = 4.8289623734754840683814025794168e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 1.005096165624023340621597000171 y[1] (numeric) = 1.0050961656240233455230513772282 absolute error = 4.9014543770572e-18 relative error = 4.8766024035263195708922010048718e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 1.0051974914298239146653143235401 y[1] (numeric) = 1.0051974914298239196151311196103 absolute error = 4.9498167960702e-18 relative error = 4.9242231882507266550074960705896e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 1.0052998120380501586788328071734 y[1] (numeric) = 1.0052998120380501636770070872219 absolute error = 4.9981742800485e-18 relative error = 4.9718245444766096177876827897370e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 1.0054031273463814729626255055154 y[1] (numeric) = 1.0054031273463814780091522861501 absolute error = 5.0465267806347e-18 relative error = 5.0194062892506506558055426978071e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 1.0055074372515025577949868753959 y[1] (numeric) = 1.0055074372515025628898611248723 absolute error = 5.0948742494764e-18 relative error = 5.0669682398401241535663015244907e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 1.0056127416491035167473238881278 y[1] (numeric) = 1.0056127416491035218905405263537 absolute error = 5.1432166382259e-18 relative error = 5.1145102137345070032528797831376e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 1.0057190404338799609940437656082 y[1] (numeric) = 1.0057190404338799661855976641492 absolute error = 5.1915538985410e-18 relative error = 5.1620320286481776707340889779728e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 1.0058263334995331146169340305467 y[1] (numeric) = 1.005826333499533119856820012631 absolute error = 5.2398859820843e-18 relative error = 5.2095335025216182163567502254740e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=1.18 NO POLE x[1] = 0.109 y[1] (analytic) = 1.0059346207387699209039295664461 y[1] (numeric) = 1.00593462073876992619214240697 absolute error = 5.2882128405239e-18 relative error = 5.2570144535240032279426446436829e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 1.0060439020433031496421603885802 y[1] (numeric) = 1.006043902043303154978694814113 absolute error = 5.3365344255328e-18 relative error = 5.3044747000544908012279632525564e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 1.006154177303851505405172832928 y[1] (numeric) = 1.0061541773038515107900235217175 absolute error = 5.3848506887895e-18 relative error = 5.3519140607447012127681212559792e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 1.0062654464101397368342158758533 y[1] (numeric) = 1.006265446410139742267377457831 absolute error = 5.4331615819777e-18 relative error = 5.3993323544602954090318502791544e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 1.0063777092508987469134833032516 y[1] (numeric) = 1.006377709250898752394950360038 absolute error = 5.4814670567864e-18 relative error = 5.4467294003029457190482768676650e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 1.0064909657138657042392014539315 y[1] (numeric) = 1.0064909657138657097689685188419 absolute error = 5.5297670649104e-18 relative error = 5.4941050176126984432868512815493e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 1.0066052156857841552824512681535 y[1] (numeric) = 1.006605215685784160860512826203 absolute error = 5.5780615580495e-18 relative error = 5.5414590259690391161380058261190e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 1.006720459052404137645612378511 y[1] (numeric) = 1.0067204590524041432719628664203 absolute error = 5.6263504879093e-18 relative error = 5.5887912451935420677829735266697e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 1.006836695698482294312315986721 y[1] (numeric) = 1.0068366956984822999869497929217 absolute error = 5.6746338062007e-18 relative error = 5.6361014953512226692830291157337e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 1.00695392550778198889079227638 y[1] (numeric) = 1.0069539255077819946137037410205 absolute error = 5.7229114646405e-18 relative error = 5.6833895967529766835354811276700e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 1.0070721483630734218504971183478 y[1] (numeric) = 1.007072148363073427621680533299 absolute error = 5.7711834149512e-18 relative error = 5.7306553699572191379715388033321e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 1.0071913641461337477519018321424 y[1] (numeric) = 1.007191364146133753571351441003 absolute error = 5.8194496088606e-18 relative error = 5.7778986357713190422313195519583e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 1.0073115727377471934693287735644 y[1] (numeric) = 1.0073115727377471993370387716671 absolute error = 5.8677099981027e-18 relative error = 5.8251192152543191942223286363424e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 1.007432774017705177406714525728 y[1] (numeric) = 1.007432774017705183322679060145 absolute error = 5.9159645344170e-18 relative error = 5.8723169297180613532143124109338e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 1.0075549678648064297061814777427 y[1] (numeric) = 1.0075549678648064356703946472916 absolute error = 5.9642131695489e-18 relative error = 5.9194916007293978265877382590281e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 1.007678154156857113449297582485 y[1] (numeric) = 1.007678154156857119461753437735 absolute error = 6.0124558552500e-18 relative error = 5.9666430501122976554844240138183e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 1.0078023327706709468509030922118 y[1] (numeric) = 1.0078023327706709529115956354892 absolute error = 6.0606925432774e-18 relative error = 6.0137710999489544069220732173360e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 1.0079275035820693264453820781963 y[1] (numeric) = 1.0079275035820693325543052635909 absolute error = 6.1089231853946e-18 relative error = 6.0608755725824759420198585362060e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 1.0080536664658814512652555481279 y[1] (numeric) = 1.0080536664658814574224032814988 absolute error = 6.1571477333709e-18 relative error = 6.1079562906180795131021349172827e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 1.0081808212959444480119719826911 y[1] (numeric) = 1.0081808212959444542173381216728 absolute error = 6.2053661389817e-18 relative error = 6.1550130769251739737696420045352e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 1.0083089679451034972187701205446 y[1] (numeric) = 1.0083089679451035034723484745532 absolute error = 6.2535783540086e-18 relative error = 6.2020457546392373473552878878999e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 1.0084381062852119604054878288482 y[1] (numeric) = 1.0084381062852119667072721590876 absolute error = 6.3017843302394e-18 relative error = 6.2490541471635890522441532244981e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 1.0085682361871315082251899045384 y[1] (numeric) = 1.0085682361871315145751739240066 absolute error = 6.3499840194682e-18 relative error = 6.2960380781712551361657070174903e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 1.008699357520732249602486659737 y[1] (numeric) = 1.0086993575207322560006640332321 absolute error = 6.3981773734951e-18 relative error = 6.3429973716064307052599056002448e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.2MB, time=1.42 NO POLE x[1] = 0.133 y[1] (analytic) = 1.0088314701548928618634141529829 y[1] (numeric) = 1.00883147015489286830977849711 absolute error = 6.4463643441271e-18 relative error = 6.3899318516871258669002423172483e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 1.0089645739575007218567459364203 y[1] (numeric) = 1.0089645739575007283512908195972 absolute error = 6.4945448831769e-18 relative error = 6.4368413429057233783474218834531e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 1.0090986687954520380666051976395 y[1] (numeric) = 1.0090986687954520446093241401037 absolute error = 6.5427189424642e-18 relative error = 6.4837256700320084076340030975263e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 1.009233754534651983716245183572 y[1] (numeric) = 1.0092337545346519903071316573868 absolute error = 6.5908864738148e-18 relative error = 6.5305846581140110754881342693607e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 1.0093698310400148308628648026684 y[1] (numeric) = 1.0093698310400148375019122317296 absolute error = 6.6390474290612e-18 relative error = 6.5774181324803294283465259827352e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 1.0095068981754640854833253105562 y[1] (numeric) = 1.0095068981754640921705270705986 absolute error = 6.6872017600424e-18 relative error = 6.6242259187416530730165010153160e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 1.0096449558039326235506329934705 y[1] (numeric) = 1.0096449558039326302859824120748 absolute error = 6.7353494186043e-18 relative error = 6.6710078427928748113406613211533e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 1.0097840037873628281010517729886 y[1] (numeric) = 1.0097840037873628348845421295876 absolute error = 6.7834903565990e-18 relative error = 6.7177637308141061434417799041824e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 1.0099240419867067272917086649643 y[1] (numeric) = 1.00992404198670673412333319085 absolute error = 6.8316245258857e-18 relative error = 6.7644934092732711235157514777423e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 1.0100650702619261334485540350706 y[1] (numeric) = 1.0100650702619261403283059134008 absolute error = 6.8797518783302e-18 relative error = 6.8111967049273068941200577240674e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.143 y[1] (analytic) = 1.0102070884719927831045376030009 y[1] (numeric) = 1.0102070884719927900324099688059 absolute error = 6.9278723658050e-18 relative error = 6.8578734448239520039863750163814e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 1.0103500964748884780278601571639 y[1] (numeric) = 1.0103500964748884850038460973538 absolute error = 6.9759859401899e-18 relative error = 6.9045234563040229219002538113355e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 1.010494094127605227240159951634 y[1] (numeric) = 1.0104940941276052342642525050051 absolute error = 7.0240925533711e-18 relative error = 6.9511465670021989883476020249364e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 1.0106390812861453900244917671803 y[1] (numeric) = 1.0106390812861453970966839244224 absolute error = 7.0721921572421e-18 relative error = 6.9977426048495825118841938372796e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 1.0107850578055218199229556284092 y[1] (numeric) = 1.0107850578055218270432403321124 absolute error = 7.1202847037032e-18 relative error = 7.0443113980748663387875091187441e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.148 y[1] (analytic) = 1.0109320235397580097238311794022 y[1] (numeric) = 1.0109320235397580168922013240642 absolute error = 7.1683701446620e-18 relative error = 7.0908527752064843026639815342552e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 1.0110799783418882374380727307282 y[1] (numeric) = 1.0110799783418882446545211627612 absolute error = 7.2164484320330e-18 relative error = 7.1373665650738643398568664809413e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 1.0112289220639577132650190013457 y[1] (numeric) = 1.0112289220639577205295385190836 absolute error = 7.2645195177379e-18 relative error = 7.1838525968093673802924559987601e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 1.0113788545570227275471705896988 y[1] (numeric) = 1.0113788545570227348597539434045 absolute error = 7.3125833537057e-18 relative error = 7.2303106998500213975761542081552e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 1.0115297756711507997138872192414 y[1] (numeric) = 1.0115297756711508070745271111139 absolute error = 7.3606398918725e-18 relative error = 7.2767407039389519277776848241306e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.153 y[1] (analytic) = 1.0116816852554208282138558147042 y[1] (numeric) = 1.0116816852554208356225448988859 absolute error = 7.4086890841817e-18 relative error = 7.3231424391272012530997771953301e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.154 y[1] (analytic) = 1.0118345831579232414361794766499 y[1] (numeric) = 1.0118345831579232488929103592341 absolute error = 7.4567308825842e-18 relative error = 7.3695157357755404839640626134360e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 1.0119884692257601496199364332395 y[1] (numeric) = 1.0119884692257601571247016722778 absolute error = 7.5047652390383e-18 relative error = 7.4158604245559780592635162461508e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=26.7MB, alloc=4.2MB, time=1.67 x[1] = 0.156 y[1] (analytic) = 1.0121433433050454977520570596639 y[1] (numeric) = 1.0121433433050455053048491651733 absolute error = 7.5527921055094e-18 relative error = 7.4621763364530637486325428090468e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 1.0122992052409052194533660673757 y[1] (numeric) = 1.0122992052409052270541775013464 absolute error = 7.6008114339707e-18 relative error = 7.5084633027661737621235898574411e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 1.0124560548774773918526359770927 y[1] (numeric) = 1.0124560548774773995014591534958 absolute error = 7.6488231764031e-18 relative error = 7.5547211551109980173413710365212e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.159 y[1] (analytic) = 1.0126138920579123914484970015328 y[1] (numeric) = 1.0126138920579123991453242863275 absolute error = 7.6968272847947e-18 relative error = 7.6009497254206254007436577234661e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 1.0127727166243730509590474759817 y[1] (numeric) = 1.012772716624373058703871187123 absolute error = 7.7448237111413e-18 relative error = 7.6471488459476097734032281596417e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 1.0129325284180348171590079870976 y[1] (numeric) = 1.0129325284180348249518203945443 absolute error = 7.7928124074467e-18 relative error = 7.6933183492658309325402740121549e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.162 y[1] (analytic) = 1.0130933272790859097042613628125 y[1] (numeric) = 1.0130933272790859175450546885345 absolute error = 7.8407933257220e-18 relative error = 7.7394580682713610494430804362193e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 1.0132551130467274809436196988004 y[1] (numeric) = 1.0132551130467274888323861167868 absolute error = 7.8887664179864e-18 relative error = 7.7855678361848049488198497488158e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 1.0134178855591737767176586097624 y[1] (numeric) = 1.0134178855591737846543902460292 absolute error = 7.9367316362668e-18 relative error = 7.8316474865524482992749915945101e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.165 y[1] (analytic) = 1.0135816446536522981444579067051 y[1] (numeric) = 1.013581644653652306129146839303 absolute error = 7.9846889325979e-18 relative error = 7.8776968532478922317471949817439e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 1.0137463901664039643920869144861 y[1] (numeric) = 1.0137463901664039724247251735087 absolute error = 8.0326382590226e-18 relative error = 7.9237157704739765170231884929469e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 1.0139121219326832764376716571557 y[1] (numeric) = 1.013912121932683284518251224747 absolute error = 8.0805795675913e-18 relative error = 7.9697040727636101444497674846524e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 1.014078839786758481812880152039 y[1] (numeric) = 1.0140788397867584899413929624019 absolute error = 8.1285128103629e-18 relative error = 8.0156615949822716424969582908310e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.169 y[1] (analytic) = 1.0142465435619117403356610670895 y[1] (numeric) = 1.0142465435619117485120990064937 absolute error = 8.1764379394042e-18 relative error = 8.0615881723289235408488579215938e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.17 y[1] (analytic) = 1.0144152330904392908280700097875 y[1] (numeric) = 1.0144152330904392990524249165774 absolute error = 8.2243549067899e-18 relative error = 8.1074836403375115022229718843012e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 1.0145849082036516188200167297711 y[1] (numeric) = 1.0145849082036516270922803943742 absolute error = 8.2722636646031e-18 relative error = 8.1533478348789488544454315926107e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 1.0147555687318736252387655314679 y[1] (numeric) = 1.014755568731873633558929696403 absolute error = 8.3201641649351e-18 relative error = 8.1991805921624033661146400805366e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 1.0149272145044447960840202072392 y[1] (numeric) = 1.0149272145044448044520765671246 absolute error = 8.3680563598854e-18 relative error = 8.2449817487367738107000940090576e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 1.0150998453497193730884238159675 y[1] (numeric) = 1.0150998453497193815043640175293 absolute error = 8.4159402015618e-18 relative error = 8.2907511414922575506502944563689e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.175 y[1] (analytic) = 1.0152734610950665253633026466005 y[1] (numeric) = 1.0152734610950665338271182886809 absolute error = 8.4638156420804e-18 relative error = 8.3364886076618120074536596034688e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.176 y[1] (analytic) = 1.0154480615668705220294827209227 y[1] (numeric) = 1.0154480615668705305411653544886 absolute error = 8.5116826335659e-18 relative error = 8.3821939848229040245033767730041e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.177 y[1] (analytic) = 1.0156236465905309058330062047525 y[1] (numeric) = 1.0156236465905309143925473329037 absolute error = 8.5595411281512e-18 relative error = 8.4278671108985621242230029265938e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 1.0158002159904626677455741118622 y[1] (numeric) = 1.01580021599046267635296518984 absolute error = 8.6073910779778e-18 relative error = 8.4735078241592091367299765884266e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.179 y[1] (analytic) = 1.0159777695900964225495407001936 y[1] (numeric) = 1.0159777695900964312047731353893 absolute error = 8.6552324351957e-18 relative error = 8.5191159632239946648053439959577e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.3MB, time=1.91 x[1] = 0.18 y[1] (analytic) = 1.0161563072118785854072839753885 y[1] (numeric) = 1.0161563072118785941103491273522 absolute error = 8.7030651519637e-18 relative error = 8.5646913670625136499761128317704e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 1.0163358286772715494147757322793 y[1] (numeric) = 1.0163358286772715581656649127284 absolute error = 8.7508891804491e-18 relative error = 8.6102338749959266049390126970759e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 1.016516333806753864139173580784 y[1] (numeric) = 1.0165163338067538729378780536117 absolute error = 8.7987044728277e-18 relative error = 8.6557433266983675944429972947291e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 1.0166978224198204151402564186277 y[1] (numeric) = 1.0166978224198204239867673999121 absolute error = 8.8465109812844e-18 relative error = 8.7012195621989346517662974283919e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 1.0168802943349826044755238294719 y[1] (numeric) = 1.0168802943349826133698324874844 absolute error = 8.8943086580125e-18 relative error = 8.7466624218823934073105785494897e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 1.0170637493697685321887789013652 y[1] (numeric) = 1.0170637493697685411308763565796 absolute error = 8.9420974552144e-18 relative error = 8.7920717464912502111030373707372e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.186 y[1] (analytic) = 1.0172481873407231787820129769491 y[1] (numeric) = 1.0172481873407231877718903020505 absolute error = 8.9898773251014e-18 relative error = 8.8374473771269319916188247680875e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 1.0174336080634085886704098635492 y[1] (numeric) = 1.0174336080634085977080580834427 absolute error = 9.0376482198935e-18 relative error = 8.8827891552509585236825737614701e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.188 y[1] (analytic) = 1.0176200113524040546202860481617 y[1] (numeric) = 1.0176200113524040637056961399817 absolute error = 9.0854100918200e-18 relative error = 8.9280969226868932360276082396935e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.189 y[1] (analytic) = 1.0178073970213063031697824794125 y[1] (numeric) = 1.0178073970213063123029453725313 absolute error = 9.1331628931188e-18 relative error = 8.9733705216210082694177488383870e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 1.0179957648827296810321224958101 y[1] (numeric) = 1.0179957648827296902130290718473 absolute error = 9.1809065760372e-18 relative error = 9.0186097946044159105711840336598e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 1.0181851147483063424812494970519 y[1] (numeric) = 1.0181851147483063517098905898835 absolute error = 9.2286410928316e-18 relative error = 9.0638145845541109131792977198331e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 1.0183754464286864377196569727608 y[1] (numeric) = 1.0183754464286864469960233685282 absolute error = 9.2763663957674e-18 relative error = 9.1089847347542016275355944259232e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.193 y[1] (analytic) = 1.0185667597335383022282225208382 y[1] (numeric) = 1.0185667597335383115523049579576 absolute error = 9.3240824371194e-18 relative error = 9.1541200888576241978323905457759e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 1.0187590544715486470978565056148 y[1] (numeric) = 1.0187590544715486564696456747862 absolute error = 9.3717891691714e-18 relative error = 9.1992204908870630985992945044625e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.195 y[1] (analytic) = 1.0189523304504227503427750241667 y[1] (numeric) = 1.0189523304504227597622615683834 absolute error = 9.4194865442167e-18 relative error = 9.2442857852367474066809823660632e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 1.0191465874768846491952058675394 y[1] (numeric) = 1.0191465874768846586623803820975 absolute error = 9.4671745145581e-18 relative error = 9.2893158166737479203294063748437e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 1.019341825356677333381335182191 y[1] (numeric) = 1.0193418253566773428961882146984 absolute error = 9.5148530325074e-18 relative error = 9.3343104303387757553784101898360e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 1.0195380438945629393783015557216 y[1] (numeric) = 1.0195380438945629489408236061079 absolute error = 9.5625220503863e-18 relative error = 9.3792694717483466501030107413054e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 1.0197352428943229456520432699139 y[1] (numeric) = 1.0197352428943229552622247904396 absolute error = 9.6101815205257e-18 relative error = 9.4241927867953671709233999763464e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2 y[1] (analytic) = 1.0199334221587583688758034832518 y[1] (numeric) = 1.0199334221587583785336348785179 absolute error = 9.6578313952661e-18 relative error = 9.4690802217507921504710850568479e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 1.020132581489689961129097124429 y[1] (numeric) = 1.0201325814896899708345687513867 absolute error = 9.7054716269577e-18 relative error = 9.5139316232649795087943419749428e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.202 y[1] (analytic) = 1.0203327206879584080769422978976 y[1] (numeric) = 1.0203327206879584178300444658577 absolute error = 9.7531021679601e-18 relative error = 9.5587468383686448297623953870986e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.203 y[1] (analytic) = 1.0205338395534245281291580222406 y[1] (numeric) = 1.0205338395534245379298809928836 absolute error = 9.8007229706430e-18 relative error = 9.6035257144747880457989940988477e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=2.16 NO POLE x[1] = 0.204 y[1] (analytic) = 1.020735937884969472579529142089 y[1] (numeric) = 1.0207359378849694824278631294744 absolute error = 9.8483339873854e-18 relative error = 9.6482680993791416484502053475560e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.205 y[1] (analytic) = 1.0209390154804949267246382744327 y[1] (numeric) = 1.0209390154804949366205734450091 absolute error = 9.8959351705764e-18 relative error = 9.6929738412621788622691569706754e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.206 y[1] (analytic) = 1.0211430721369233119621636705127 y[1] (numeric) = 1.0211430721369233219056901431275 absolute error = 9.9435264726148e-18 relative error = 9.7376427886899375630960499419323e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.207 y[1] (analytic) = 1.0213481076501979888684408950116 y[1] (numeric) = 1.021348107650197998859548740921 absolute error = 9.9911078459094e-18 relative error = 9.7822747906155218483048884118121e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.208 y[1] (analytic) = 1.0215541218152834612550852449989 y[1] (numeric) = 1.0215541218152834712937644878776 absolute error = 1.00386792428787e-17 relative error = 9.8268696963800077124182035157584e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.209 y[1] (analytic) = 1.0217611144261655812044708520248 y[1] (numeric) = 1.021761114426165591290711467976 absolute error = 1.00862406159512e-17 relative error = 9.8714273557139280832275449136885e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.21 y[1] (analytic) = 1.0219690852758517550838614319006 y[1] (numeric) = 1.0219690852758517652176533494665 absolute error = 1.01337919175659e-17 relative error = 9.9159476187389449711692850052267e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.211 y[1] (analytic) = 1.0221780341563711505379866680538 y[1] (numeric) = 1.0221780341563711607193197682249 absolute error = 1.01813331001711e-17 relative error = 9.9604303359678496559350269284352e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.212 y[1] (analytic) = 1.022387960858774904459857235895 y[1] (numeric) = 1.0223879608587749146887213521208 absolute error = 1.02288641162258e-17 relative error = 1.0004875358307099117283267914551e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.213 y[1] (analytic) = 1.0225988651731363319396104974034 y[1] (numeric) = 1.0225988651731363422159954156025 absolute error = 1.02763849181991e-17 relative error = 1.0049282537057386703542939260458e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.214 y[1] (analytic) = 1.0228107468885511361911779170994 y[1] (numeric) = 1.0228107468885511465150733756695 absolute error = 1.03238954585701e-17 relative error = 1.0093651723914694080069390369464e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.215 y[1] (analytic) = 1.0230236057931376194565642727558 y[1] (numeric) = 1.0230236057931376298279599625839 absolute error = 1.03713956898281e-17 relative error = 1.0137982770971628244042227869148e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.216 y[1] (analytic) = 1.0232374416740368948875277565849 y[1] (numeric) = 1.023237441674036905306413321058 absolute error = 1.04188855644731e-17 relative error = 1.0182275530719043165255797553963e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.217 y[1] (analytic) = 1.0234522543174130994044490852411 y[1] (numeric) = 1.0234522543174131098708141202562 absolute error = 1.04663650350151e-17 relative error = 1.0226529856046479977990406826224e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.218 y[1] (analytic) = 1.023668043508453607532176759785 y[1] (numeric) = 1.0236680435084536180460108137596 absolute error = 1.05138340539746e-17 relative error = 1.0270745600243771942689063667821e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.219 y[1] (analytic) = 1.0238848090313692462126346397834 y[1] (numeric) = 1.0238848090313692567739272136662 absolute error = 1.05612925738828e-17 relative error = 1.0314922617002347431802730970857e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.22 y[1] (analytic) = 1.0241025506693945105939770189553 y[1] (numeric) = 1.0241025506693945212027175662363 absolute error = 1.06087405472810e-17 relative error = 1.0359060760415743122666994830223e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.221 y[1] (analytic) = 1.0243212682047877807960754132258 y[1] (numeric) = 1.0243212682047877914522533399471 absolute error = 1.06561779267213e-17 relative error = 1.0403159884981378687812140900401e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.222 y[1] (analytic) = 1.0245409614188315396521202957203 y[1] (numeric) = 1.0245409614188315503557249604866 absolute error = 1.07036046647663e-17 relative error = 1.0447219845601346169099237905780e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.223 y[1] (analytic) = 1.024761630091832591426120037115 y[1] (numeric) = 1.0247616300918326021771407511042 absolute error = 1.07510207139892e-17 relative error = 1.0491240497583581654820782729116e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.224 y[1] (analytic) = 1.0249832740031222815060783338625 y[1] (numeric) = 1.0249832740031222923045043608366 absolute error = 1.07984260269741e-17 relative error = 1.0535221696643223538235157246340e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.225 y[1] (analytic) = 1.0252058929310567170726304311345 y[1] (numeric) = 1.0252058929310567279184509874502 absolute error = 1.08458205563157e-17 relative error = 1.0579163298903376717569394520885e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.226 y[1] (analytic) = 1.0254294866530169887429174718627 y[1] (numeric) = 1.025429486653016999636121726482 absolute error = 1.08932042546193e-17 relative error = 1.0623065160896161296274439934312e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.227 y[1] (analytic) = 1.0256540549454093931894773280223 y[1] (numeric) = 1.0256540549454094041300544025236 absolute error = 1.09405770745013e-17 relative error = 1.0666927139564240327946097519581e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=2.41 NO POLE x[1] = 0.228 y[1] (analytic) = 1.0258795975836656567339292952864 y[1] (numeric) = 1.0258795975836656677218682638753 absolute error = 1.09879389685889e-17 relative error = 1.0710749092261558640738636621016e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.229 y[1] (analytic) = 1.0261061143422431599152290573844 y[1] (numeric) = 1.0261061143422431709505189469045 absolute error = 1.10352898895201e-17 relative error = 1.0754530876754365942052740732433e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.23 y[1] (analytic) = 1.0263336049946251630322693519284 y[1] (numeric) = 1.0263336049946251741148991418726 absolute error = 1.10826297899442e-17 relative error = 1.0798272351222718614403136115307e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.231 y[1] (analytic) = 1.0265620693133210326606007951267 y[1] (numeric) = 1.0265620693133210437905594176479 absolute error = 1.11299586225212e-17 relative error = 1.0841973374260900834334096247966e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.232 y[1] (analytic) = 1.0267915070698664691430463486806 y[1] (numeric) = 1.0267915070698664803203226886028 absolute error = 1.11772763399222e-17 relative error = 1.0885633804878811879059428441720e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.233 y[1] (analytic) = 1.0270219180348237350539819382704 y[1] (numeric) = 1.0270219180348237462785648331 absolute error = 1.12245828948296e-17 relative error = 1.0929253502503149666656896207963e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.234 y[1] (analytic) = 1.027253301977781884637054759369 y[1] (numeric) = 1.0272533019777818959089329993057 absolute error = 1.12718782399367e-17 relative error = 1.0972832326978001434060177017227e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.235 y[1] (analytic) = 1.0274856586673569942161098326828 y[1] (numeric) = 1.027485658667357005535272160631 absolute error = 1.13191623279482e-17 relative error = 1.1016370138566302340693385223682e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.236 y[1] (analytic) = 1.0277189878711923935790943983139 y[1] (numeric) = 1.0277189878711924049455295098941 absolute error = 1.13664351115802e-17 relative error = 1.1059866797950798365105314111757e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.237 y[1] (analytic) = 1.0279532893559588983347087647578 y[1] (numeric) = 1.0279532893559589097484053083175 absolute error = 1.14136965435597e-17 relative error = 1.1103322166234514255104261113191e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.238 y[1] (analytic) = 1.0281885628873550432415712561047 y[1] (numeric) = 1.0281885628873550547025178327301 absolute error = 1.14609465766254e-17 relative error = 1.1146736104942477955319234449033e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.239 y[1] (analytic) = 1.0284248082301073165096639283 y[1] (numeric) = 1.0284248082301073280178490918271 absolute error = 1.15081851635271e-17 relative error = 1.1190108476022074106880661251532e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.24 y[1] (analytic) = 1.0286620251479703950738247530366 y[1] (numeric) = 1.0286620251479704066292370100631 absolute error = 1.15554122570265e-17 relative error = 1.1233439141844750779191508822471e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.241 y[1] (analytic) = 1.0289002134037273808390509958078 y[1] (numeric) = 1.0289002134037273924416788057041 absolute error = 1.16026278098963e-17 relative error = 1.1276727965206064306814245618820e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.242 y[1] (analytic) = 1.0291393727591900378973775428355 y[1] (numeric) = 1.0291393727591900495472093177564 absolute error = 1.16498317749209e-17 relative error = 1.1319974809327271462615337248835e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.243 y[1] (analytic) = 1.0293795029751990307160929600163 y[1] (numeric) = 1.0293795029751990424131170649128 absolute error = 1.16970241048965e-17 relative error = 1.1363179537856329228546816921657e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.244 y[1] (analytic) = 1.0296206038116241632970550956892 y[1] (numeric) = 1.0296206038116241750412598483199 absolute error = 1.17442047526307e-17 relative error = 1.1406342014868400225575506566546e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.245 y[1] (analytic) = 1.0298626750273646193068670679285 y[1] (numeric) = 1.0298626750273646310982407388714 absolute error = 1.17913736709429e-17 relative error = 1.1449462104867126899449880695300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.246 y[1] (analytic) = 1.0301057163803492031776735062069 y[1] (numeric) = 1.0301057163803492150162043188711 absolute error = 1.18385308126642e-17 relative error = 1.1492539672785411175184924661272e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.247 y[1] (analytic) = 1.0303497276275365821783359466519 y[1] (numeric) = 1.0303497276275365940640120772892 absolute error = 1.18856761306373e-17 relative error = 1.1535574583986185645975358724871e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.248 y[1] (analytic) = 1.0305947085249155294557453097401 y[1] (numeric) = 1.0305947085249155413885548874572 absolute error = 1.19328095777171e-17 relative error = 1.1578566704263855513696926783043e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.249 y[1] (analytic) = 1.0308406588275051680460284191387 y[1] (numeric) = 1.0308406588275051800259595259087 absolute error = 1.19799311067700e-17 relative error = 1.1621515899844469980490050374069e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.25 y[1] (analytic) = 1.0310875782893552158554045505058 y[1] (numeric) = 1.0310875782893552278824452211804 absolute error = 1.20270406706746e-17 relative error = 1.1664422037387243786136735269837e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.251 y[1] (analytic) = 1.0313354666635462316104470294153 y[1] (numeric) = 1.0313354666635462436845852517365 absolute error = 1.20741382223212e-17 relative error = 1.1707284983984905612164066875177e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=2.65 NO POLE x[1] = 0.252 y[1] (analytic) = 1.0315843237021898617775039281638 y[1] (numeric) = 1.0315843237021898738987276427762 absolute error = 1.21212237146124e-17 relative error = 1.1750104607165104883067831295166e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.253 y[1] (analytic) = 1.0318341491564290884510309420608 y[1] (numeric) = 1.0318341491564291006193280425234 absolute error = 1.21682971004626e-17 relative error = 1.1792880774890743037592714564710e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.254 y[1] (analytic) = 1.0320849427764384782105885568886 y[1] (numeric) = 1.032084942776438490425946889687 absolute error = 1.22153583327984e-17 relative error = 1.1835613355561168896037598085624e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.255 y[1] (analytic) = 1.0323367043114244319462546505563 y[1] (numeric) = 1.0323367043114244442086620151151 absolute error = 1.22624073645588e-17 relative error = 1.1878302218013171097391604053614e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.256 y[1] (analytic) = 1.0325894335096254356522027035565 y[1] (numeric) = 1.0325894335096254479616468522511 absolute error = 1.23094441486946e-17 relative error = 1.1920947231521186866289668314084e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.257 y[1] (analytic) = 1.032843130118312312188194824666 y[1] (numeric) = 1.0328431301183123245446634628349 absolute error = 1.23564686381689e-17 relative error = 1.1963548265798568019422565189612e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.258 y[1] (analytic) = 1.0330977938837884740087378304194 y[1] (numeric) = 1.0330977938837884864122186163768 absolute error = 1.24034807859574e-17 relative error = 1.2006105190998644031038911090368e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.259 y[1] (analytic) = 1.0333534245513901768596496492213 y[1] (numeric) = 1.0333534245513901893101301942692 absolute error = 1.24504805450479e-17 relative error = 1.2048617877715001849640543234032e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.26 y[1] (analytic) = 1.0336100218654867744417823535499 y[1] (numeric) = 1.0336100218654867869392502219905 absolute error = 1.24974678684406e-17 relative error = 1.2091086196982531778178291791034e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.261 y[1] (analytic) = 1.0338675855694809740416471565521 y[1] (numeric) = 1.0338675855694809865860898657003 absolute error = 1.25444427091482e-17 relative error = 1.2133510020278270833984841862593e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.262 y[1] (analytic) = 1.0341261154058090931286857424248 y[1] (numeric) = 1.0341261154058091057200907626208 absolute error = 1.25914050201960e-17 relative error = 1.2175889219522237321886353904889e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.263 y[1] (analytic) = 1.0343856111159413169189313333344 y[1] (numeric) = 1.0343856111159413295572860879559 absolute error = 1.26383547546215e-17 relative error = 1.2218223667077773240243718481899e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.264 y[1] (analytic) = 1.0346460724403819569048019292326 y[1] (numeric) = 1.0346460724403819695900937947076 absolute error = 1.26852918654750e-17 relative error = 1.2260513235752845141601172477931e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.265 y[1] (analytic) = 1.0349074991186697103507671907983 y[1] (numeric) = 1.0349074991186697230829834966178 absolute error = 1.27322163058195e-17 relative error = 1.2302757798800659087214405860783e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.266 y[1] (analytic) = 1.0351698908893779207546294698607 y[1] (numeric) = 1.0351698908893779335337574985911 absolute error = 1.27791280287304e-17 relative error = 1.2344957229920073899221367788621e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.267 y[1] (analytic) = 1.0354332474901148392741585260421 y[1] (numeric) = 1.0354332474901148521001855133383 absolute error = 1.28260269872962e-17 relative error = 1.2387111403256971992441356185331e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.268 y[1] (analytic) = 1.0356975686575238871188185030108 y[1] (numeric) = 1.0356975686575238999917316376286 absolute error = 1.28729131346178e-17 relative error = 1.2429220193404268788026266840797e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.269 y[1] (analytic) = 1.0359628541272839189063247726353 y[1] (numeric) = 1.0359628541272839318261111964443 absolute error = 1.29197864238090e-17 relative error = 1.2471283475403072864868383684542e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.27 y[1] (analytic) = 1.0362291036341094869837672905078 y[1] (numeric) = 1.0362291036341094999504140985045 absolute error = 1.29666468079967e-17 relative error = 1.2513301124743547222409435692315e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.271 y[1] (analytic) = 1.0364963169117511067130361417346 y[1] (numeric) = 1.036496316911751119726530382055 absolute error = 1.30134942403204e-17 relative error = 1.2555273017365086255967997062914e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.272 y[1] (analytic) = 1.0367644936929955227202839915894 y[1] (numeric) = 1.036764493692995535780612665522 absolute error = 1.30603286739326e-17 relative error = 1.2597199029657352929457575883229e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.273 y[1] (analytic) = 1.0370336337096659761091591915901 y[1] (numeric) = 1.0370336337096659892163092535892 absolute error = 1.31071500619991e-17 relative error = 1.2639079038461210290418432370001e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.274 y[1] (analytic) = 1.0373037366926224726375423277883 y[1] (numeric) = 1.0373037366926224857915006854866 absolute error = 1.31539583576983e-17 relative error = 1.2680912921068679865728403515018e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.275 y[1] (analytic) = 1.0375748023717620518575180345561 y[1] (numeric) = 1.0375748023717620650582715487781 absolute error = 1.32007535142220e-17 relative error = 1.2722700555224338164315806220354e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=2.90 NO POLE x[1] = 0.276 y[1] (analytic) = 1.0378468304760190572183129339225 y[1] (numeric) = 1.0378468304760190704658484186975 absolute error = 1.32475354847750e-17 relative error = 1.2764441819125547109241399096467e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.277 y[1] (analytic) = 1.0381198207333654071319295975428 y[1] (numeric) = 1.0381198207333654204262338201182 absolute error = 1.32943042225754e-17 relative error = 1.2806136591423350750440072727843e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.278 y[1] (analytic) = 1.0383937728708108670012054656899 y[1] (numeric) = 1.0383937728708108803422651465443 absolute error = 1.33410596808544e-17 relative error = 1.2847784751222881392380631285945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.279 y[1] (analytic) = 1.0386686866144033222100246952314 y[1] (numeric) = 1.038668686614403335597826508088 absolute error = 1.33878018128566e-17 relative error = 1.2889386178084238799259488489212e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.28 y[1] (analytic) = 1.0389445616892290520754099464035 y[1] (numeric) = 1.0389445616892290655099405182433 absolute error = 1.34345305718398e-17 relative error = 1.2930940752022879075488978303081e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.281 y[1] (analytic) = 1.0392213978194130047612201563121 y[1] (numeric) = 1.0392213978194130182424660673874 absolute error = 1.34812459110753e-17 relative error = 1.2972448353510476377864877085795e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.282 y[1] (analytic) = 1.0394991947281190731531793854871 y[1] (numeric) = 1.0394991947281190866811271693349 absolute error = 1.35279477838478e-17 relative error = 1.3013908863475390766129206209429e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.283 y[1] (analytic) = 1.0397779521375503716949608624835 y[1] (numeric) = 1.0397779521375503852695970059389 absolute error = 1.35746361434554e-17 relative error = 1.3055322163303223786611106206690e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.284 y[1] (analytic) = 1.0400576697689495141850493904688 y[1] (numeric) = 1.0400576697689495278063603336784 absolute error = 1.36213109432096e-17 relative error = 1.3096688134837365466590975349957e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.285 y[1] (analytic) = 1.040338347342598892534104318956 y[1] (numeric) = 1.0403383473425989062020764553919 absolute error = 1.36679721364359e-17 relative error = 1.3138006660380109460723442985934e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.286 y[1] (analytic) = 1.0406199845778209564825443233454 y[1] (numeric) = 1.0406199845778209701971639998182 absolute error = 1.37146196764728e-17 relative error = 1.3179277622692221138727418370657e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.287 y[1] (analytic) = 1.0409025811929784942780742747098 y[1] (numeric) = 1.0409025811929785080393277913828 absolute error = 1.37612535166730e-17 relative error = 1.3220500904994612211219237486844e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.288 y[1] (analytic) = 1.0411861369054749143128735223236 y[1] (numeric) = 1.0411861369054749281207471327261 absolute error = 1.38078736104025e-17 relative error = 1.3261676390967987981587187885165e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.289 y[1] (analytic) = 1.0414706514317545277201639517677 y[1] (numeric) = 1.0414706514317545415746438628091 absolute error = 1.38544799110414e-17 relative error = 1.3302803964754119755645097367945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.29 y[1] (analytic) = 1.0417561244873028319298752220681 y[1] (numeric) = 1.0417561244873028458309475940514 absolute error = 1.39010723719833e-17 relative error = 1.3343883510955763554665592981956e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.291 y[1] (analytic) = 1.0420425557866467951831236262249 y[1] (numeric) = 1.0420425557866468091307745728605 absolute error = 1.39476509466356e-17 relative error = 1.3384914914637434916083315887576e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.292 y[1] (analytic) = 1.0423299450433551420052200606774 y[1] (numeric) = 1.0423299450433551559994356490973 absolute error = 1.39942155884199e-17 relative error = 1.3425898061326270620579351029185e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.293 y[1] (analytic) = 1.0426182919700386396369216307212 y[1] (numeric) = 1.0426182919700386536776878814928 absolute error = 1.40407662507716e-17 relative error = 1.3466832837012113951650348540287e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.294 y[1] (analytic) = 1.0429075962783503854236404606493 y[1] (numeric) = 1.0429075962783503995109433477892 absolute error = 1.40873028871399e-17 relative error = 1.3507719128147975608843614462022e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.295 y[1] (analytic) = 1.043197857678986095162322319432 y[1] (numeric) = 1.0431978576789861092961477704202 absolute error = 1.41338254509882e-17 relative error = 1.3548556821650869542173945884513e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.296 y[1] (analytic) = 1.0434890758816843924057067150814 y[1] (numeric) = 1.0434890758816844065860406108755 absolute error = 1.41803338957941e-17 relative error = 1.3589345804902256308542295644602e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.297 y[1] (analytic) = 1.0437812505952270987236791534653 y[1] (numeric) = 1.0437812505952271129505073285142 absolute error = 1.42268281750489e-17 relative error = 1.3630085965747998898479429615160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.298 y[1] (analytic) = 1.0440743815274395249214253002402 y[1] (numeric) = 1.0440743815274395391947335424988 absolute error = 1.42733082422586e-17 relative error = 1.3670777192499747556090332609914e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.299 y[1] (analytic) = 1.0443684683851907632140958277764 y[1] (numeric) = 1.0443684683851907775338698787193 absolute error = 1.43197740509429e-17 relative error = 1.3711419373934399469637825828625e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=3.15 NO POLE x[1] = 0.3 y[1] (analytic) = 1.044663510874393980357689772432 y[1] (numeric) = 1.044663510874393994723915327068 absolute error = 1.43662255546360e-17 relative error = 1.3752012399295274648055718362085e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.301 y[1] (analytic) = 1.0449595087000067117358632713184 y[1] (numeric) = 1.0449595087000067261485259782051 absolute error = 1.44126627068867e-17 relative error = 1.3792556158292612154691603318577e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.302 y[1] (analytic) = 1.0452564615660311564023695917739 y[1] (numeric) = 1.0452564615660311708614550530314 absolute error = 1.44590854612575e-17 relative error = 1.3833050541103101017470761481076e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.303 y[1] (analytic) = 1.0455543691755144730788354111266 y[1] (numeric) = 1.0455543691755144875843291824524 absolute error = 1.45054937713258e-17 relative error = 1.3873495438371412666702380553958e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304 y[1] (analytic) = 1.0458532312305490771075773489994 y[1] (numeric) = 1.0458532312305490916594649396827 absolute error = 1.45518875906833e-17 relative error = 1.3913890741210001894269970199959e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.305 y[1] (analytic) = 1.0461530474322729383591617993617 y[1] (numeric) = 1.0461530474322729529574286722978 absolute error = 1.45982668729361e-17 relative error = 1.3954236341199569487304148740260e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.306 y[1] (analytic) = 1.0464538174808698800944101547946 y[1] (numeric) = 1.0464538174808698947390417264996 absolute error = 1.46446315717050e-17 relative error = 1.3994532130389707405962026417600e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.307 y[1] (analytic) = 1.0467555410755698787805505609892 y[1] (numeric) = 1.0467555410755698934715322016146 absolute error = 1.46909816406254e-17 relative error = 1.4034778001299152929661812346049e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.308 y[1] (analytic) = 1.0470582179146493648612163853508 y[1] (numeric) = 1.0470582179146493795985334186978 absolute error = 1.47373170333470e-17 relative error = 1.4074973846915843563338553335589e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.309 y[1] (analytic) = 1.0473618476954315244799906297348 y[1] (numeric) = 1.0473618476954315392636283332695 absolute error = 1.47836377035347e-17 relative error = 1.4115119560698109796323693919798e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.31 y[1] (analytic) = 1.0476664301142866021571945637978 y[1] (numeric) = 1.0476664301142866169871381686653 absolute error = 1.48299436048675e-17 relative error = 1.4155215036573948991250521213064e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.311 y[1] (analytic) = 1.0479719648666322044196179021966 y[1] (numeric) = 1.0479719648666322192958525932363 absolute error = 1.48762346910397e-17 relative error = 1.4195260168942487460933043099293e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.312 y[1] (analytic) = 1.0482784516469336043828868959338 y[1] (numeric) = 1.048278451646933619305397811694 absolute error = 1.49225109157602e-17 relative error = 1.4235254852673619701117822203200e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.313 y[1] (analytic) = 1.0485858901487040472861657555049 y[1] (numeric) = 1.0485858901487040622549379882577 absolute error = 1.49687722327528e-17 relative error = 1.4275198983108594123268618759886e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.314 y[1] (analytic) = 1.0488942800645050569788858711721 y[1] (numeric) = 1.0488942800645050719939044669283 absolute error = 1.50150185957562e-17 relative error = 1.4315092456060303947375717221699e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.315 y[1] (analytic) = 1.0492036210859467433591963436608 y[1] (numeric) = 1.0492036210859467584204463021848 absolute error = 1.50612499585240e-17 relative error = 1.4354935167813569784843532311850e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.316 y[1] (analytic) = 1.0495139129036881107638283868539 y[1] (numeric) = 1.0495139129036881258712946616787 absolute error = 1.51074662748248e-17 relative error = 1.4394727015125509206913863240767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.317 y[1] (analytic) = 1.0498251552074373673090652126448 y[1] (numeric) = 1.0498251552074373824627327110872 absolute error = 1.51536674984424e-17 relative error = 1.4434467895225993114355405428388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.318 y[1] (analytic) = 1.0501373476859522351825080570062 y[1] (numeric) = 1.0501373476859522503823616401816 absolute error = 1.51998535831754e-17 relative error = 1.4474157705817522142949123953204e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.319 y[1] (analytic) = 1.0504504900270402618853280555329 y[1] (numeric) = 1.0504504900270402771313525383708 absolute error = 1.52460244828379e-17 relative error = 1.4513796345076142661306030654504e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.32 y[1] (analytic) = 1.0507645819175591324246927262339 y[1] (numeric) = 1.0507645819175591477168728774929 absolute error = 1.52921801512590e-17 relative error = 1.4553383711651211307524706203901e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.321 y[1] (analytic) = 1.0510796230434169824560548671731 y[1] (numeric) = 1.051079623043416997794375409456 absolute error = 1.53383205422829e-17 relative error = 1.4592919704665722989855651431798e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.322 y[1] (analytic) = 1.0513956130895727123749907266948 y[1] (numeric) = 1.0513956130895727277594363364641 absolute error = 1.53844456097693e-17 relative error = 1.4632404223716915837192489060769e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=53.4MB, alloc=4.3MB, time=3.39 x[1] = 0.323 y[1] (analytic) = 1.051712551740036302358273354424 y[1] (numeric) = 1.0517125517400363177888286620171 absolute error = 1.54305553075931e-17 relative error = 1.4671837168876201680645511184351e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.324 y[1] (analytic) = 1.0520304386778691283538660919921 y[1] (numeric) = 1.0520304386778691438305156816367 absolute error = 1.54766495896446e-17 relative error = 1.4711218440689564134632427872118e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.325 y[1] (analytic) = 1.0523492735851842790195202135225 y[1] (numeric) = 1.0523492735851842945422486233521 absolute error = 1.55227284098296e-17 relative error = 1.4750547940177853136108123709810e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.326 y[1] (analytic) = 1.0526690561431468736096597773046 y[1] (numeric) = 1.0526690561431468891784514993737 absolute error = 1.55687917220691e-17 relative error = 1.4789825568836691166676433252307e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.327 y[1] (analytic) = 1.0529897860319743808102358017967 y[1] (numeric) = 1.0529897860319743964250752820967 absolute error = 1.56148394803000e-17 relative error = 1.4829051228637321529499674735795e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.328 y[1] (analytic) = 1.0533114629309369385212309311322 y[1] (numeric) = 1.0533114629309369541821025696066 absolute error = 1.56608716384744e-17 relative error = 1.4868224822026118142572374240488e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.329 y[1] (analytic) = 1.0536340865183576745864948076487 y[1] (numeric) = 1.053634086518357690293382958209 absolute error = 1.57068881505603e-17 relative error = 1.4907346251925417172386582755701e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.33 y[1] (analytic) = 1.0539576564716130284705894216338 y[1] (numeric) = 1.0539576564716130442234783921749 absolute error = 1.57528889705411e-17 relative error = 1.4946415421733200786367154754268e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.331 y[1] (analytic) = 1.0542821724671330738823227614669 y[1] (numeric) = 1.0542821724671330896811968138829 absolute error = 1.57988740524160e-17 relative error = 1.4985432235323627360416018540031e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.332 y[1] (analytic) = 1.0546076341804018423446481406519 y[1] (numeric) = 1.0546076341804018581894914908518 absolute error = 1.58448433501999e-17 relative error = 1.5024396597047078813176924973591e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.333 y[1] (analytic) = 1.0549340412859576477106056318672 y[1] (numeric) = 1.0549340412859576636014024497906 absolute error = 1.58907968179234e-17 relative error = 1.5063308411730294861005652097449e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.334 y[1] (analytic) = 1.0552613934573934116249810921192 y[1] (numeric) = 1.0552613934573934275617155017524 absolute error = 1.59367344096332e-17 relative error = 1.5102167584676878295984852838191e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.335 y[1] (analytic) = 1.0555896903673569899313573173679 y[1] (numeric) = 1.0555896903673570059140133967597 absolute error = 1.59826560793918e-17 relative error = 1.5140974021667128407413192905303e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.336 y[1] (analytic) = 1.0559189316875515000242309195995 y[1] (numeric) = 1.0559189316875515160527927008768 absolute error = 1.60285617812773e-17 relative error = 1.5179727628957961639908027444788e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.337 y[1] (analytic) = 1.056249117088735649145867574257 y[1] (numeric) = 1.0562491170887356652203190436411 absolute error = 1.60744514693841e-17 relative error = 1.5218428313283676699765631524667e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.338 y[1] (analytic) = 1.0565802462407240636275673412012 y[1] (numeric) = 1.0565802462407240797478924390237 absolute error = 1.61203250978225e-17 relative error = 1.5257075981855669361599200656694e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.339 y[1] (analytic) = 1.0569123188123876190750108179637 y[1] (numeric) = 1.0569123188123876352411934386826 absolute error = 1.61661826207189e-17 relative error = 1.5295670542362707732141485432481e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.34 y[1] (analytic) = 1.0572453344716537714973559399734 y[1] (numeric) = 1.0572453344716537877093799321892 absolute error = 1.62120239922158e-17 relative error = 1.5334211902971010059831652685117e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.341 y[1] (analytic) = 1.0575792928855068893797542986879 y[1] (numeric) = 1.0575792928855069056376034651597 absolute error = 1.62578491664718e-17 relative error = 1.5372699972324314635066494051129e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.342 y[1] (analytic) = 1.0579141937199885866989549051396 y[1] (numeric) = 1.0579141937199886030026130028014 absolute error = 1.63036580976618e-17 relative error = 1.5411134659544130850929553281818e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.343 y[1] (analytic) = 1.0582500366401980568816623833228 y[1] (numeric) = 1.0582500366401980732311131232995 absolute error = 1.63494507399767e-17 relative error = 1.5449515874229509553785520021448e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.344 y[1] (analytic) = 1.0585868213102924077053156350886 y[1] (numeric) = 1.0585868213102924241005426827127 absolute error = 1.63952270476241e-17 relative error = 1.5487843526457750735602855334836e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.345 y[1] (analytic) = 1.0589245473934869971409520758003 y[1] (numeric) = 1.0589245473934870135819390506277 absolute error = 1.64409869748274e-17 relative error = 1.5526117526783591160937002200486e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.346 y[1] (analytic) = 1.0592632145520557701378215979091 y[1] (numeric) = 1.059263214552055786624552073736 absolute error = 1.64867304758269e-17 relative error = 1.5564337786240273908664148397628e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=57.2MB, alloc=4.3MB, time=3.64 x[1] = 0.347 y[1] (analytic) = 1.0596028224473315963494134778678 y[1] (numeric) = 1.0596028224473316128818709827469 absolute error = 1.65324575048791e-17 relative error = 1.5602504216338909374721032151827e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.348 y[1] (analytic) = 1.0599433707397066088005585003816 y[1] (numeric) = 1.0599433707397066253787265166384 absolute error = 1.65781680162568e-17 relative error = 1.5640616729068584522389525083699e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.349 y[1] (analytic) = 1.0602848590886325434952676329222 y[1] (numeric) = 1.0602848590886325601191295971719 absolute error = 1.66238619642497e-17 relative error = 1.5678675236896935764992902518008e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.35 y[1] (analytic) = 1.0606272871526210799649676426963 y[1] (numeric) = 1.0606272871526210966345069458601 absolute error = 1.66695393031638e-17 relative error = 1.5716679652769581608860562721814e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.351 y[1] (analytic) = 1.0609706545892441827567931078597 y[1] (numeric) = 1.0609706545892441994719930951814 absolute error = 1.67151999873217e-17 relative error = 1.5754629890110396951437408881376e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.352 y[1] (analytic) = 1.0613149610551344438615933347137 y[1] (numeric) = 1.0613149610551344606224373057764 absolute error = 1.67608439710627e-17 relative error = 1.5792525862821590686483785624714e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.353 y[1] (analytic) = 1.0616602062059854260813117529063 y[1] (numeric) = 1.0616602062059854428877829616492 absolute error = 1.68064712087429e-17 relative error = 1.5830367485283775446058376473118e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.354 y[1] (analytic) = 1.0620063896965520073353944212866 y[1] (numeric) = 1.0620063896965520241874760760217 absolute error = 1.68520816547351e-17 relative error = 1.5868154672355841175887710085651e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.355 y[1] (analytic) = 1.062353511180650725905883338033 y[1] (numeric) = 1.0623535111806507428035586014617 absolute error = 1.68976752634287e-17 relative error = 1.5905887339374821255675917068671e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.356 y[1] (analytic) = 1.0627015703111601266208493099901 y[1] (numeric) = 1.0627015703111601435641012992203 absolute error = 1.69432519892302e-17 relative error = 1.5943565402156315785509988970633e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.357 y[1] (analytic) = 1.0630505667400211079758181978111 y[1] (numeric) = 1.063050566740021124964629984374 absolute error = 1.69888117865629e-17 relative error = 1.5981188776994153798774305287428e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.358 y[1] (analytic) = 1.0634005001182372701928434155077 y[1] (numeric) = 1.0634005001182372872271980253746 absolute error = 1.70343546098669e-17 relative error = 1.6018757380660330567297325730945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.359 y[1] (analytic) = 1.0637513700958752642168766253644 y[1] (numeric) = 1.0637513700958752812967570389639 absolute error = 1.70798804135995e-17 relative error = 1.6056271130405313379793421327402e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.36 y[1] (analytic) = 1.0641031763220651416490876318753 y[1] (numeric) = 1.0641031763220651587744767841102 absolute error = 1.71253891522349e-17 relative error = 1.6093729943957681210733559774159e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.361 y[1] (analytic) = 1.064455918445000705616783541413 y[1] (numeric) = 1.0644559184450007227876643216774 absolute error = 1.71708807802644e-17 relative error = 1.6131133739524227158754933762230e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.362 y[1] (analytic) = 1.0648095961119398625795763177395 y[1] (numeric) = 1.0648095961119398797959315699357 absolute error = 1.72163552521962e-17 relative error = 1.6168482435789677366898382216452e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.363 y[1] (analytic) = 1.0651642089692049750714469272204 y[1] (numeric) = 1.0651642089692049923332594497763 absolute error = 1.72618125225559e-17 relative error = 1.6205775951917060024334550060336e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.364 y[1] (analytic) = 1.0655197566621832153783533317088 y[1] (numeric) = 1.0655197566621832326856058775951 absolute error = 1.73072525458863e-17 relative error = 1.6243014207547409026745423276160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.365 y[1] (analytic) = 1.0658762388353269201510286515192 y[1] (numeric) = 1.0658762388353269375037039282665 absolute error = 1.73526752767473e-17 relative error = 1.6280197122799554405640301198872e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.366 y[1] (analytic) = 1.0662336551321539459526148857234 y[1] (numeric) = 1.0662336551321539633506955554396 absolute error = 1.73980806697162e-17 relative error = 1.6317324618270280695937924603617e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.367 y[1] (analytic) = 1.0665920051952480257407766421643 y[1] (numeric) = 1.066592005195248043184245321552 absolute error = 1.74434686793877e-17 relative error = 1.6354396615034196087690468762990e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.368 y[1] (analytic) = 1.0669512886662591262839383951033 y[1] (numeric) = 1.066951288666259143772777655477 absolute error = 1.74888392603737e-17 relative error = 1.6391413034643406769081405873740e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.369 y[1] (analytic) = 1.0673115051859038065112878542941 y[1] (numeric) = 1.0673115051859038240454802215977 absolute error = 1.75341923673036e-17 relative error = 1.6428373799127652780199218295709e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.37 y[1] (analytic) = 1.0676726543939655767961870955091 y[1] (numeric) = 1.0676726543939655943757150503335 absolute error = 1.75795279548244e-17 relative error = 1.6465278830994248662509344033261e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=61.0MB, alloc=4.3MB, time=3.89 x[1] = 0.371 y[1] (analytic) = 1.0680347359292952591726321691378 y[1] (numeric) = 1.0680347359292952767974781467382 absolute error = 1.76248459776004e-17 relative error = 1.6502128053227642108358820726683e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.372 y[1] (analytic) = 1.0683977494298113484844009704265 y[1] (numeric) = 1.0683977494298113661545473607402 absolute error = 1.76701463903137e-17 relative error = 1.6538921389289714700804639556698e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.373 y[1] (analytic) = 1.0687616945325003744665282222431 y[1] (numeric) = 1.0687616945325003921819573699069 absolute error = 1.77154291476638e-17 relative error = 1.6575658763119232360520603338693e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.374 y[1] (analytic) = 1.0691265708734172647587454889206 y[1] (numeric) = 1.0691265708734172825194396932885 absolute error = 1.77606942043679e-17 relative error = 1.6612340099131944077841176950546e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.375 y[1] (analytic) = 1.0694923780876857088505232077704 y[1] (numeric) = 1.0694923780876857266564647229316 absolute error = 1.78059415151612e-17 relative error = 1.6648965322220672875233245257205e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.376 y[1] (analytic) = 1.0698591158094985229573507932542 y[1] (numeric) = 1.0698591158094985408085218280503 absolute error = 1.78511710347961e-17 relative error = 1.6685534357754370847832340996014e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.377 y[1] (analytic) = 1.070226783672118015827889937563 y[1] (numeric) = 1.0702267836721180337242726556061 absolute error = 1.78963827180431e-17 relative error = 1.6722047131578757043069466375293e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.378 y[1] (analytic) = 1.0705953813078763554816353004824 y[1] (numeric) = 1.0705953813078763734232118201731 absolute error = 1.79415765196907e-17 relative error = 1.6758503570016012424340448280506e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.379 y[1] (analytic) = 1.070964908348175936876715850913 y[1] (numeric) = 1.070964908348175954863468245458 absolute error = 1.79867523945450e-17 relative error = 1.6794903599864187804333882747342e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.38 y[1] (analytic) = 1.0713353644234897505074691922754 y[1] (numeric) = 1.0713353644234897685393794897056 absolute error = 1.80319102974302e-17 relative error = 1.6831247148397445549455056995802e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.381 y[1] (analytic) = 1.0717067491633617519314202742562 y[1] (numeric) = 1.0717067491633617700084704574445 absolute error = 1.80770501831883e-17 relative error = 1.6867534143365546792480594861933e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.382 y[1] (analytic) = 1.0720790621964072322252949639468 y[1] (numeric) = 1.0720790621964072503474669706262 absolute error = 1.81221720066794e-17 relative error = 1.6903764512993891860761579401315e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.383 y[1] (analytic) = 1.072452303150313189369698020393 y[1] (numeric) = 1.0724523031503132075369737431748 absolute error = 1.81672757227818e-17 relative error = 1.6939938185983366631400952334698e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.384 y[1] (analytic) = 1.0728264716518387005620840879077 y[1] (numeric) = 1.0728264716518387187744453742995 absolute error = 1.82123612863918e-17 relative error = 1.6976055091509902078543915747221e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.385 y[1] (analytic) = 1.0732015673268152954576493952072 y[1] (numeric) = 1.073201567326815313715078047631 absolute error = 1.82574286524238e-17 relative error = 1.7012115159224306795927881821201e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.386 y[1] (analytic) = 1.0735775898001473303377709195101 y[1] (numeric) = 1.0735775898001473486402486953204 absolute error = 1.83024777758103e-17 relative error = 1.7048118319251999251232568903181e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.387 y[1] (analytic) = 1.0739545386958123632056188471909 y[1] (numeric) = 1.0739545386958123815531274586932 absolute error = 1.83475086115023e-17 relative error = 1.7084064502193105594542206651281e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.388 y[1] (analytic) = 1.0743324136368615298085672354074 y[1] (numeric) = 1.0743324136368615482010883498765 absolute error = 1.83925211144691e-17 relative error = 1.7119953639121991319028574079474e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.389 y[1] (analytic) = 1.0747112142454199205870268523226 y[1] (numeric) = 1.0747112142454199390245420920206 absolute error = 1.84375152396980e-17 relative error = 1.7155785661586693414111281222010e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.39 y[1] (analytic) = 1.0750909401426869585493232471189 y[1] (numeric) = 1.0750909401426869770318141893138 absolute error = 1.84824909421949e-17 relative error = 1.7191560501609183423412262849750e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.391 y[1] (analytic) = 1.0754715909489367780722421749589 y[1] (numeric) = 1.075471590948936796599690351943 absolute error = 1.85274481769841e-17 relative error = 1.7227278091684878661203897179609e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.392 y[1] (analytic) = 1.0758531662835186046268635763786 y[1] (numeric) = 1.0758531662835186231992504754871 absolute error = 1.85723868991085e-17 relative error = 1.7262938364782518847053623124932e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.393 y[1] (analytic) = 1.0762356657648571354293043853106 y[1] (numeric) = 1.07623566576485715404661144894 absolute error = 1.86173070636294e-17 relative error = 1.7298541254343663930796290123430e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.394 y[1] (analytic) = 1.0766190890104529210159895150267 y[1] (numeric) = 1.076619089010452939678198140653 absolute error = 1.86622086256263e-17 relative error = 1.7334086694282185591918622875753e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=64.8MB, alloc=4.3MB, time=4.15 x[1] = 0.395 y[1] (analytic) = 1.0770034356368827477430694467592 y[1] (numeric) = 1.0770034356368827664501609869571 absolute error = 1.87070915401979e-17 relative error = 1.7369574618984866644861387630783e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.396 y[1] (analytic) = 1.0773887052598000212096019216175 y[1] (numeric) = 1.0773887052598000399615576840789 absolute error = 1.87519557624614e-17 relative error = 1.7405004963310413896884808861996e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.397 y[1] (analytic) = 1.0777748974939351506041143126486 y[1] (numeric) = 1.077774897493935169400915560201 absolute error = 1.87968012475524e-17 relative error = 1.7440377662589022457661175272349e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.398 y[1] (analytic) = 1.0781620119530959339741623305114 y[1] (numeric) = 1.0781620119530959528157902811368 absolute error = 1.88416279506254e-17 relative error = 1.7475692652622490136506359789358e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.399 y[1] (analytic) = 1.0785500482501679444184997932385 y[1] (numeric) = 1.0785500482501679633049356200924 absolute error = 1.88864358268539e-17 relative error = 1.7510949869683953383205234953046e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4 y[1] (analytic) = 1.0789390059971149172014732679482 y[1] (numeric) = 1.078939005997114936132698099378 absolute error = 1.89312248314298e-17 relative error = 1.7546149250516967678692903994661e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.401 y[1] (analytic) = 1.0793288848049791377892544701431 y[1] (numeric) = 1.0793288848049791567652493897073 absolute error = 1.89759949195642e-17 relative error = 1.7581290732335879695648034994197e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.402 y[1] (analytic) = 1.0797196842838818308075223843972 y[1] (numeric) = 1.0797196842838818498282684308841 absolute error = 1.90207460464869e-17 relative error = 1.7616374252824987327838271944083e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.403 y[1] (analytic) = 1.0801114040430235499202061487794 y[1] (numeric) = 1.0801114040430235689856843162264 absolute error = 1.90654781674470e-17 relative error = 1.7651399750138712656058941818750e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.404 y[1] (analytic) = 1.0805040436906845686288988243055 y[1] (numeric) = 1.0805040436906845877390900620178 absolute error = 1.91101912377123e-17 relative error = 1.7686367162900656657218670689240e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.405 y[1] (analytic) = 1.0808976028342252719925512500355 y[1] (numeric) = 1.0808976028342252911474364626051 absolute error = 1.91548852125696e-17 relative error = 1.7721276430203481337687631508781e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.406 y[1] (analytic) = 1.0812920810800865492670542641556 y[1] (numeric) = 1.0812920810800865684666143114807 absolute error = 1.91995600473251e-17 relative error = 1.7756127491608877343522475121381e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.407 y[1] (analytic) = 1.0816874780337901874643166514964 y[1] (numeric) = 1.0816874780337902067085323488003 absolute error = 1.92442156973039e-17 relative error = 1.7790920287146692353902426366225e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.408 y[1] (analytic) = 1.0820837932999392658304452584406 y[1] (numeric) = 1.0820837932999392851192973762909 absolute error = 1.92888521178503e-17 relative error = 1.7825654757314793457168078114833e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.409 y[1] (analytic) = 1.0824810264822185512426327970737 y[1] (numeric) = 1.0824810264822185705761020614016 absolute error = 1.93334692643279e-17 relative error = 1.7860330843078737840284750294211e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.41 y[1] (analytic) = 1.082879177183394894524357941723 y[1] (numeric) = 1.0828791771833949139024250338427 absolute error = 1.93780670921197e-17 relative error = 1.7894948485871436984806652128701e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.411 y[1] (analytic) = 1.0832782450053176276785014027179 y[1] (numeric) = 1.0832782450053176471011469593456 absolute error = 1.94226455566277e-17 relative error = 1.7929507627592352834499702229514e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.412 y[1] (analytic) = 1.0836782295489189620379807442877 y[1] (numeric) = 1.0836782295489189815051853575612 absolute error = 1.94672046132735e-17 relative error = 1.7964008210607611329055782108663e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.413 y[1] (analytic) = 1.084079130414214387333505795996 y[1] (numeric) = 1.0840791304142144068452500134941 absolute error = 1.95117442174981e-17 relative error = 1.7998450177749370552563737652351e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.414 y[1] (analytic) = 1.0844809472003030716780555899898 y[1] (numeric) = 1.0844809472003030912343199147516 absolute error = 1.95562643247618e-17 relative error = 1.8032833472315275322616058217767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.415 y[1] (analytic) = 1.0848836795053682624676768396186 y[1] (numeric) = 1.0848836795053682820684417301632 absolute error = 1.96007648905446e-17 relative error = 1.8067158038068366714338292026479e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.416 y[1] (analytic) = 1.0852873269266776881982030586595 y[1] (numeric) = 1.0852873269266777078434489290054 absolute error = 1.96452458703459e-17 relative error = 1.8101423819236339651214337759036e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.417 y[1] (analytic) = 1.0856918890605839611974925044623 y[1] (numeric) = 1.085691889060583980887199724147 absolute error = 1.96897072196847e-17 relative error = 1.8135630760511255555408441127696e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.418 y[1] (analytic) = 1.0860973655025249812727822128099 y[1] (numeric) = 1.0860973655025250010069311069096 absolute error = 1.97341488940997e-17 relative error = 1.8169778807049156449483723330738e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=4.39 NO POLE x[1] = 0.419 y[1] (analytic) = 1.0865037558470243402727544771743 y[1] (numeric) = 1.0865037558470243600513253263234 absolute error = 1.97785708491491e-17 relative error = 1.8203867904469396700616501538578e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.42 y[1] (analytic) = 1.0869110596876917275639112103343 y[1] (numeric) = 1.0869110596876917473868842507454 absolute error = 1.98229730404111e-17 relative error = 1.8237897998854613197962936444359e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.421 y[1] (analytic) = 1.087319276617223336420850712016 y[1] (numeric) = 1.0873192766172233562882061354994 absolute error = 1.98673554234834e-17 relative error = 1.8271869036749768823644465579641e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.422 y[1] (analytic) = 1.0877284062274022713300404523114 y[1] (numeric) = 1.0877284062274022912417584062951 absolute error = 1.99117179539837e-17 relative error = 1.8305780965162110356849424774556e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.423 y[1] (analytic) = 1.0881384481090989562066785671374 y[1] (numeric) = 1.088138448109098976162739154687 absolute error = 1.99560605875496e-17 relative error = 1.8339633731560568019441905205842e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.424 y[1] (analytic) = 1.088549401852271543524235848908 y[1] (numeric) = 1.0885494018522715635246191287461 absolute error = 2.00003832798381e-17 relative error = 1.8373427283874781874912566676584e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.425 y[1] (analytic) = 1.0889612670459663243562691029099 y[1] (numeric) = 1.0889612670459663444009550894367 absolute error = 2.00446859865268e-17 relative error = 1.8407161570495684527200308203967e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.426 y[1] (analytic) = 1.0893740432783181393300958276049 y[1] (numeric) = 1.0893740432783181594190644909179 absolute error = 2.00889686633130e-17 relative error = 1.8440836540274147771685484746661e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.427 y[1] (analytic) = 1.089787730136550790491919265217 y[1] (numeric) = 1.0897877301365508106251505311309 absolute error = 2.01332312659139e-17 relative error = 1.8474452142520634689136824671958e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.428 y[1] (analytic) = 1.0902023272069774540829919575135 y[1] (numeric) = 1.0902023272069774742604657075805 absolute error = 2.01774737500670e-17 relative error = 1.8508008327005028999841498055876e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.429 y[1] (analytic) = 1.0906178340750010942264050306518 y[1] (numeric) = 1.0906178340750011144481011021816 absolute error = 2.02216960715298e-17 relative error = 1.8541505043955815995852224157597e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.43 y[1] (analytic) = 1.0910342503251148775240895223366 y[1] (numeric) = 1.0910342503251148977899877084164 absolute error = 2.02658981860798e-17 relative error = 1.8574942244059533353151423271170e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.431 y[1] (analytic) = 1.09145157554090258856361515432 y[1] (numeric) = 1.0914515755409026088736952038352 absolute error = 2.03100800495152e-17 relative error = 1.8608319878460857605084994801327e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.432 y[1] (analytic) = 1.0918698093050390463343710434825 y[1] (numeric) = 1.0918698093050390666886126611364 absolute error = 2.03542416176539e-17 relative error = 1.8641637898761126522961894138350e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.433 y[1] (analytic) = 1.0922889511992905215527119353457 y[1] (numeric) = 1.0922889511992905419510947816802 absolute error = 2.03983828463345e-17 relative error = 1.8674896257018688990653314327739e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.434 y[1] (analytic) = 1.0927090008045151548956526349088 y[1] (numeric) = 1.0927090008045151753381563263245 absolute error = 2.04425036914157e-17 relative error = 1.8708094905747782922168438660939e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.435 y[1] (analytic) = 1.0931299577006633761426924011461 y[1] (numeric) = 1.0931299577006633966292965099227 absolute error = 2.04866041087766e-17 relative error = 1.8741233797918232199788737473854e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.436 y[1] (analytic) = 1.0935518214667783242253501633781 y[1] (numeric) = 1.093551821466778344756034217695 absolute error = 2.05306840543169e-17 relative error = 1.8774312886955045994244407820411e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.437 y[1] (analytic) = 1.0939745916809962681839905100158 y[1] (numeric) = 1.0939745916809962887587339939723 absolute error = 2.05747434839565e-17 relative error = 1.8807332126737463692330778804809e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.438 y[1] (analytic) = 1.0943982679205470290315194928856 y[1] (numeric) = 1.0943982679205470496503018465218 absolute error = 2.06187823536362e-17 relative error = 1.8840291471599000311402782905692e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.439 y[1] (analytic) = 1.0948228497617544025235283834771 y[1] (numeric) = 1.094822849761754423186329002794 absolute error = 2.06628006193169e-17 relative error = 1.8873190876326114893032976225487e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.44 y[1] (analytic) = 1.0952483367800365828344626110016 y[1] (numeric) = 1.0952483367800366035412608479822 absolute error = 2.07067982369806e-17 relative error = 1.8906030296158518640122988495613e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.441 y[1] (analytic) = 1.0956747285499065871393922061318 y[1] (numeric) = 1.0956747285499066078901673687612 absolute error = 2.07507751626294e-17 relative error = 1.8938809686787650176281278465391e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.442 y[1] (analytic) = 1.0961020246449726811009591686834 y[1] (numeric) = 1.0961020246449727018956905209699 absolute error = 2.07947313522865e-17 relative error = 1.8971529004356972224216304472924e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=4.64 NO POLE x[1] = 0.443 y[1] (analytic) = 1.0965302246379388052610762723304 y[1] (numeric) = 1.0965302246379388260997430343262 absolute error = 2.08386667619958e-17 relative error = 1.9004188205460984066091353570758e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.444 y[1] (analytic) = 1.0969593281006050023369509146883 y[1] (numeric) = 1.0969593281006050232195322625101 absolute error = 2.08825813478218e-17 relative error = 1.9036787247144503040784562161671e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.445 y[1] (analytic) = 1.0973893346038678454210067167782 y[1] (numeric) = 1.0973893346038678663474817826281 absolute error = 2.09264750658499e-17 relative error = 1.9069326086902305487754729437309e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.446 y[1] (analytic) = 1.0978202437177208670842746719854 y[1] (numeric) = 1.0978202437177208880546225441718 absolute error = 2.09703478721864e-17 relative error = 1.9101804682678488540380774340109e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.447 y[1] (analytic) = 1.0982520550112549893828247411573 y[1] (numeric) = 1.0982520550112550103970244641159 absolute error = 2.10141997229586e-17 relative error = 1.9134222992865917763629127061006e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.448 y[1] (analytic) = 1.0986847680526589547668078874449 y[1] (numeric) = 1.0986847680526589758248384617595 absolute error = 2.10580305743146e-17 relative error = 1.9166580976305396343980599880300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.449 y[1] (analytic) = 1.0991183824092197578916776418816 y[1] (numeric) = 1.0991183824092197789935180243051 absolute error = 2.11018403824235e-17 relative error = 1.9198878592285193489442832606190e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.45 y[1] (analytic) = 1.0995528976473230783311593885136 y[1] (numeric) = 1.099552897647323099476788491989 absolute error = 2.11456291034754e-17 relative error = 1.9231115800540385389254446316629e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.451 y[1] (analytic) = 1.0999883133324537141915346561489 y[1] (numeric) = 1.0999883133324537353809313498308 absolute error = 2.11893966936819e-17 relative error = 1.9263292561252645636475409851752e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.452 y[1] (analytic) = 1.1004246290291960166268068024775 y[1] (numeric) = 1.1004246290291960378599499117526 absolute error = 2.12331431092751e-17 relative error = 1.9295408835048666402422808968722e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.453 y[1] (analytic) = 1.100861844301234325254313575431 y[1] (numeric) = 1.1008618443012343465311818819397 absolute error = 2.12768683065087e-17 relative error = 1.9327464583000484343667747287228e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.454 y[1] (analytic) = 1.101299958711353404470351136208 y[1] (numeric) = 1.1012999587113534257909233778656 absolute error = 2.13205722416576e-17 relative error = 1.9359459766624437105721670405853e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.455 y[1] (analytic) = 1.1017389718214388806653732283767 y[1] (numeric) = 1.1017389718214389020296280993944 absolute error = 2.13642548710177e-17 relative error = 1.9391394347880297258121010576694e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.456 y[1] (analytic) = 1.1021788831924776803383282778904 y[1] (numeric) = 1.1021788831924777017462444287968 absolute error = 2.14079161509064e-17 relative error = 1.9423268289171036835325894005051e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.457 y[1] (analytic) = 1.1026196923845584691096963097179 y[1] (numeric) = 1.1026196923845584905612523473805 absolute error = 2.14515560376626e-17 relative error = 1.9455081553342132421703980479111e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.458 y[1] (analytic) = 1.1030613989568720916327866680871 y[1] (numeric) = 1.1030613989568721131279611557333 absolute error = 2.14951744876462e-17 relative error = 1.9486834103680412077941471463952e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.459 y[1] (analytic) = 1.1035040024677120124028566290802 y[1] (numeric) = 1.103504002467712033941628086319 absolute error = 2.15387714572388e-17 relative error = 1.9518525903913985959738371117902e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.46 y[1] (analytic) = 1.1039475024744747574636100964996 y[1] (numeric) = 1.1039475024744747790459569993432 absolute error = 2.15823469028436e-17 relative error = 1.9550156918211445926036531023548e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.461 y[1] (analytic) = 1.104391898533660357010634674543 y[1] (numeric) = 1.104391898533660378636535455428 absolute error = 2.16259007808850e-17 relative error = 1.9581727111180788940342657410312e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.462 y[1] (analytic) = 1.1048371902008727888913345138855 y[1] (numeric) = 1.1048371902008728105607675616947 absolute error = 2.16694330478092e-17 relative error = 1.9613236447869241707487538669646e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.463 y[1] (analytic) = 1.1052833770308204230009154312754 y[1] (numeric) = 1.1052833770308204447138590913593 absolute error = 2.17129436600839e-17 relative error = 1.9644684893762265006772605765975e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.464 y[1] (analytic) = 1.1057304585773164665739779066934 y[1] (numeric) = 1.1057304585773164883304104808919 absolute error = 2.17564325741985e-17 relative error = 1.9676072414783006183088933105014e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.465 y[1] (analytic) = 1.1061784343932794103712726665209 y[1] (numeric) = 1.106178434393279432171172413185 absolute error = 2.17998997466641e-17 relative error = 1.9707398977291565738714583419380e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.466 y[1] (analytic) = 1.1066273040307334757611726659979 y[1] (numeric) = 1.1066273040307334976045178000113 absolute error = 2.18433451340134e-17 relative error = 1.9738664548084168933133008056427e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=4.89 NO POLE x[1] = 0.467 y[1] (analytic) = 1.1070770670408090626954143895363 y[1] (numeric) = 1.1070770670408090845821830823375 absolute error = 2.18867686928012e-17 relative error = 1.9769869094392874974662252546968e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.468 y[1] (analytic) = 1.107527722973743198578660493185 y[1] (numeric) = 1.1075277229737432205088308727889 absolute error = 2.19301703796039e-17 relative error = 1.9801012583884377633187694740039e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.469 y[1] (analytic) = 1.1079792713788799880314349197206 y[1] (numeric) = 1.1079792713788800100049850707404 absolute error = 2.19735501510198e-17 relative error = 1.9832094984659524455646534272052e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.47 y[1] (analytic) = 1.1084317118046710635459807234666 y[1] (numeric) = 1.1084317118046710855628886871357 absolute error = 2.20169079636691e-17 relative error = 1.9863116265252560163809454438021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.471 y[1] (analytic) = 1.1088850437986760370345899490213 y[1] (numeric) = 1.1088850437986760590948337232153 absolute error = 2.20602437741940e-17 relative error = 1.9894076394630455760122615726981e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.472 y[1] (analytic) = 1.109339266907562952269954015601 y[1] (numeric) = 1.1093392669075629743735115548598 absolute error = 2.21035575392588e-17 relative error = 1.9924975342192232970624858229198e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.473 y[1] (analytic) = 1.1097943806771087382170821666872 y[1] (numeric) = 1.1097943806771087603639313822367 absolute error = 2.21468492155495e-17 relative error = 1.9955813077767833521392201721556e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.474 y[1] (analytic) = 1.1102503846521996632563346530956 y[1] (numeric) = 1.1102503846521996854464534128702 absolute error = 2.21901187597746e-17 relative error = 1.9986589571618065760334046992767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.475 y[1] (analytic) = 1.1107072783768317902971164264731 y[1] (numeric) = 1.1107072783768318125304825551377 absolute error = 2.22333661286646e-17 relative error = 2.0017304794433374728810068440964e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.476 y[1] (analytic) = 1.1111650613941114327817762295659 y[1] (numeric) = 1.111165061394111455058367508538 absolute error = 2.22765912789721e-17 relative error = 2.0047958717333148999689373647552e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.477 y[1] (analytic) = 1.1116237332462556115792550793985 y[1] (numeric) = 1.1116237332462556338990492468703 absolute error = 2.23197941674718e-17 relative error = 2.0078551311864933048412386251498e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.478 y[1] (analytic) = 1.1120832934745925127680272497516 y[1] (numeric) = 1.1120832934745925351310020007126 absolute error = 2.23629747509610e-17 relative error = 2.0109082550004084975615106498371e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.479 y[1] (analytic) = 1.1125437416195619463078759700387 y[1] (numeric) = 1.1125437416195619687140089562978 absolute error = 2.24061329862591e-17 relative error = 2.0139552404152530048446693629628e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.48 y[1] (analytic) = 1.1130050772207158056000451688413 y[1] (numeric) = 1.1130050772207158280493139990491 absolute error = 2.24492688302078e-17 relative error = 2.0169960847138140091972406969851e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.481 y[1] (analytic) = 1.1134672998167185279353077019906 y[1] (numeric) = 1.113467299816718550427689941662 absolute error = 2.24923822396714e-17 relative error = 2.0200307852214198081357019662012e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.482 y[1] (analytic) = 1.1139304089453475558294896171662 y[1] (numeric) = 1.1139304089453475783649627887024 absolute error = 2.25354731715362e-17 relative error = 2.0230593393058049980885656286752e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.483 y[1] (analytic) = 1.1143944041434937992459891195241 y[1] (numeric) = 1.1143944041434938218245307022356 absolute error = 2.25785415827115e-17 relative error = 2.0260817443771189584297178933042e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.484 y[1] (analytic) = 1.1148592849471620987048280158762 y[1] (numeric) = 1.1148592849471621213264154460051 absolute error = 2.26215874301289e-17 relative error = 2.0290979978877812187128402264347e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.485 y[1] (analytic) = 1.1153250508914716892777725284065 y[1] (numeric) = 1.1153250508914717119423831991489 absolute error = 2.26646106707424e-17 relative error = 2.0321080973324083070455897748276e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.486 y[1] (analytic) = 1.115791701510656665469059482842 y[1] (numeric) = 1.1157917015106566881766707443709 absolute error = 2.27076112615289e-17 relative error = 2.0351120402477760243451894258324e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.487 y[1] (analytic) = 1.1162592363380664469812629903921 y[1] (numeric) = 1.1162592363380664697318521498799 absolute error = 2.27505891594878e-17 relative error = 2.0381098242127005820096128864849e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.488 y[1] (analytic) = 1.1167276549061662453658358576272 y[1] (numeric) = 1.1167276549061662681593801792684 absolute error = 2.27935443216412e-17 relative error = 2.0411014468479731634719569452733e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.489 y[1] (analytic) = 1.117196956746537531557859073795 y[1] (numeric) = 1.1171969567465375543943357788289 absolute error = 2.28364767050339e-17 relative error = 2.0440869058162761473207730771241e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.49 y[1] (analytic) = 1.1176671413898785042945318408633 y[1] (numeric) = 1.1176671413898785271739181075968 absolute error = 2.28793862667335e-17 relative error = 2.0470661988221078892855666748913e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=5.13 NO POLE x[1] = 0.491 y[1] (analytic) = 1.1181382083660045594169337278386 y[1] (numeric) = 1.1181382083660045823392066916691 absolute error = 2.29222729638305e-17 relative error = 2.0500393236117070963861636678289e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.492 y[1] (analytic) = 1.1186101572038487600545896476376 y[1] (numeric) = 1.1186101572038487830197264010758 absolute error = 2.29651367534382e-17 relative error = 2.0530062779729589169561993543880e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.493 y[1] (analytic) = 1.1190829874314623076923674719854 y[1] (numeric) = 1.1190829874314623307003450646782 absolute error = 2.30079775926928e-17 relative error = 2.0559670597353185460115550261008e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.494 y[1] (analytic) = 1.1195566985760150141192372174827 y[1] (numeric) = 1.1195566985760150371700326562361 absolute error = 2.30507954387534e-17 relative error = 2.0589216667697254999096375740971e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.495 y[1] (analytic) = 1.1200312901637957742584198541208 y[1] (numeric) = 1.1200312901637957973520101029231 absolute error = 2.30935902488023e-17 relative error = 2.0618700969885443031180656989125e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.496 y[1] (analytic) = 1.1205067617202130398784529061372 y[1] (numeric) = 1.1205067617202130630148148861819 absolute error = 2.31363619800447e-17 relative error = 2.0648123483454511898474440072582e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.497 y[1] (analytic) = 1.1209831127697952941846991341835 y[1] (numeric) = 1.1209831127697953173638097238922 absolute error = 2.31791105897087e-17 relative error = 2.0677484188353472693732226079357e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.498 y[1] (analytic) = 1.1214603428361915272908237073372 y[1] (numeric) = 1.121460342836191550512659742383 absolute error = 2.32218360350458e-17 relative error = 2.0706783064943159125679912972366e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.499 y[1] (analytic) = 1.1219384514421717125697643935207 y[1] (numeric) = 1.1219384514421717358343026668513 absolute error = 2.32645382733306e-17 relative error = 2.0736020093995083588731684406010e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5 y[1] (analytic) = 1.1224174381096272838837184173962 y[1] (numeric) = 1.1224174381096273071909356792569 absolute error = 2.33072172618607e-17 relative error = 2.0765195256690468528424583220050e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.501 y[1] (analytic) = 1.1228973023595716136926687557886 y[1] (numeric) = 1.1228973023595716370425417137459 absolute error = 2.33498729579573e-17 relative error = 2.0794308534619897879658000244582e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.502 y[1] (analytic) = 1.1233780437121404920409717621522 y[1] (numeric) = 1.1233780437121405154334770811168 absolute error = 2.33925053189646e-17 relative error = 2.0823359909781895414793749566977e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.503 y[1] (analytic) = 1.1238596616865926064215271335312 y[1] (numeric) = 1.1238596616865926298566414357816 absolute error = 2.34351143022504e-17 relative error = 2.0852349364582568730313187189158e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.504 y[1] (analytic) = 1.1243421558013100225170503558855 y[1] (numeric) = 1.124342155801310045994750221091 absolute error = 2.34776998652055e-17 relative error = 2.0881276881834181118676182059851e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.505 y[1] (analytic) = 1.1248255255737986658179668865485 y[1] (numeric) = 1.1248255255737986893382288517929 absolute error = 2.35202619652444e-17 relative error = 2.0910142444754877129176110346729e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.506 y[1] (analytic) = 1.1253097705206888041164464559634 y[1] (numeric) = 1.1253097705206888276792470157685 absolute error = 2.35628005598051e-17 relative error = 2.0938946036967603354721191805586e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.507 y[1] (analytic) = 1.1257948901577355308760949947039 y[1] (numeric) = 1.1257948901577355544814106010529 absolute error = 2.36053156063490e-17 relative error = 2.0967687642499115143848508100926e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.508 y[1] (analytic) = 1.1262808839998192494768208161278 y[1] (numeric) = 1.1262808839998192731246278784886 absolute error = 2.36478070623608e-17 relative error = 2.0996367245778980214285992294797e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.509 y[1] (analytic) = 1.126767751560946158334390809836 y[1] (numeric) = 1.1267677515609461820246656951854 absolute error = 2.36902748853494e-17 relative error = 2.1024984831639466694013505372486e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.51 y[1] (analytic) = 1.1272554923542487368941915264245 y[1] (numeric) = 1.1272554923542487606269105592713 absolute error = 2.37327190328468e-17 relative error = 2.1053540385313651602374972986630e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.511 y[1] (analytic) = 1.1277441058919862324987091598053 y[1] (numeric) = 1.1277441058919862562738486222142 absolute error = 2.37751394624089e-17 relative error = 2.1082033892435213407634365137227e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.512 y[1] (analytic) = 1.1282335916855451481282415596589 y[1] (numeric) = 1.1282335916855451719457776912742 absolute error = 2.38175361316153e-17 relative error = 2.1110465339037333193613043416340e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.513 y[1] (analytic) = 1.1287239492454397310143545333464 y[1] (numeric) = 1.1287239492454397548742635314157 absolute error = 2.38599089980693e-17 relative error = 2.1138834711551770303085712941195e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.514 y[1] (analytic) = 1.1292151780813124621255938238659 y[1] (numeric) = 1.1292151780813124860278518432639 absolute error = 2.39022580193980e-17 relative error = 2.1167141996808023393462996095889e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.3MB, time=5.38 NO POLE x[1] = 0.515 y[1] (analytic) = 1.1297072777019345465249632781811 y[1] (numeric) = 1.1297072777019345704695464314335 absolute error = 2.39445831532524e-17 relative error = 2.1195387182032488146890998682984e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.516 y[1] (analytic) = 1.1302002476152064045986788484863 y[1] (numeric) = 1.1302002476152064285855632057936 absolute error = 2.39868843573073e-17 relative error = 2.1223570254847434704876545231942e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.517 y[1] (analytic) = 1.1306940873281581641557071976931 y[1] (numeric) = 1.1306940873281581881848687869548 absolute error = 2.40291615892617e-17 relative error = 2.1251691203270424487088332514926e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.518 y[1] (analytic) = 1.1311887963469501533975968096429 y[1] (numeric) = 1.1311887963469501774690116164812 absolute error = 2.40714148068383e-17 relative error = 2.1279750015712927435842360222432e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.519 y[1] (analytic) = 1.1316843741768733947581086342535 y[1] (numeric) = 1.1316843741768734188717526020373 absolute error = 2.41136439677838e-17 relative error = 2.1307746680979644338439286717244e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.52 y[1] (analytic) = 1.1321808203223500996121524280115 y[1] (numeric) = 1.1321808203223501237680014578806 absolute error = 2.41558490298691e-17 relative error = 2.1335681188267737165578169963604e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.521 y[1] (analytic) = 1.1326781342869341638535340809147 y[1] (numeric) = 1.1326781342869341880515640318039 absolute error = 2.41980299508892e-17 relative error = 2.1363553527165791152937066346173e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.522 y[1] (analytic) = 1.1331763155733116643410183521593 y[1] (numeric) = 1.1331763155733116885812050408223 absolute error = 2.42401866886630e-17 relative error = 2.1391363687652685965032559615504e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.523 y[1] (analytic) = 1.133675363683301356212210568549 y[1] (numeric) = 1.133675363683301380494529769583 absolute error = 2.42823192010340e-17 relative error = 2.1419111660097258331082537979865e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.524 y[1] (analytic) = 1.134175278117855171064759971788 y[1] (numeric) = 1.1341752781178551953891874176575 absolute error = 2.43244274458695e-17 relative error = 2.1446797435256637660088878733993e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.525 y[1] (analytic) = 1.1346760583770587160043865334936 y[1] (numeric) = 1.1346760583770587403708979145549 absolute error = 2.43665113810613e-17 relative error = 2.1474421004275902672822677431917e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.526 y[1] (analytic) = 1.135177703960131773559232189945 y[1] (numeric) = 1.1351777039601317979678031544705 absolute error = 2.44085709645255e-17 relative error = 2.1501982358686940790727092799537e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.527 y[1] (analytic) = 1.1356802143654288024600365822581 y[1] (numeric) = 1.1356802143654288269106427364606 absolute error = 2.44506061542025e-17 relative error = 2.1529481490407481345250301699393e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.528 y[1] (analytic) = 1.1361835890904394392856365218521 y[1] (numeric) = 1.1361835890904394637782534299092 absolute error = 2.44926169080571e-17 relative error = 2.1556918391740214079016053816359e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.529 y[1] (analytic) = 1.1366878276317890009732875357502 y[1] (numeric) = 1.1366878276317890255078907198289 absolute error = 2.45346031840787e-17 relative error = 2.1584293055371992695609170720943e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.53 y[1] (analytic) = 1.1371929294852389881933049814358 y[1] (numeric) = 1.1371929294852390127698699217166 absolute error = 2.45765649402808e-17 relative error = 2.1611605474372419727191810670716e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.531 y[1] (analytic) = 1.1376988941456875895875213566629 y[1] (numeric) = 1.1376988941456876142060234913647 absolute error = 2.46185021347018e-17 relative error = 2.1638855642193572599233345051654e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.532 y[1] (analytic) = 1.138205721107170186871055565808 y[1] (numeric) = 1.1382057211071702115314702912124 absolute error = 2.46604147254044e-17 relative error = 2.1666043552668495209315582720118e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.533 y[1] (analytic) = 1.1387134098628598607968890410339 y[1] (numeric) = 1.13871340986285988549919171151 absolute error = 2.47023026704761e-17 relative error = 2.1693169200010654343524504850944e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.534 y[1] (analytic) = 1.1392219599050678979827427537335 y[1] (numeric) = 1.1392219599050679227269086817624 absolute error = 2.47441659280289e-17 relative error = 2.1720232578812690140743425224979e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.535 y[1] (analytic) = 1.1397313707252442985997482894172 y[1] (numeric) = 1.1397313707252443233857527456168 absolute error = 2.47860044561996e-17 relative error = 2.1747233684045691188029213140681e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.536 y[1] (analytic) = 1.1402416418139782849224052974161 y[1] (numeric) = 1.1402416418139783097502235105658 absolute error = 2.48278182131497e-17 relative error = 2.1774172511058115622567700937188e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.537 y[1] (analytic) = 1.1407527726609988107393167654858 y[1] (numeric) = 1.1407527726609988356089239225512 absolute error = 2.48696071570654e-17 relative error = 2.1801049055574797675263114590701e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.538 y[1] (analytic) = 1.1412647627551750716241927086173 y[1] (numeric) = 1.1412647627551750965355639547751 absolute error = 2.49113712461578e-17 relative error = 2.1827863313696127033033233063495e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=5.63 NO POLE x[1] = 0.539 y[1] (analytic) = 1.1417776115845170160666120010952 y[1] (numeric) = 1.1417776115845170410197224397579 absolute error = 2.49531104386627e-17 relative error = 2.1854615281896875001993588878506e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.54 y[1] (analytic) = 1.1422913186361758574620312210822 y[1] (numeric) = 1.1422913186361758824568559139231 absolute error = 2.49948246928409e-17 relative error = 2.1881304957025456492680911715365e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.541 y[1] (analytic) = 1.1428058833964445869605285177651 y[1] (numeric) = 1.1428058833964446119970424847434 absolute error = 2.50365139669783e-17 relative error = 2.1907932336303013950948610131872e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.542 y[1] (analytic) = 1.1433213053507584871737696523608 y[1] (numeric) = 1.1433213053507585122519478717465 absolute error = 2.50781782193857e-17 relative error = 2.1934497417322236349809902996225e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.543 y[1] (analytic) = 1.1438375839836956467396825060591 y[1] (numeric) = 1.1438375839836956718594999144576 absolute error = 2.51198174083985e-17 relative error = 2.1961000198046088949966559133889e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.544 y[1] (analytic) = 1.1443547187789774757443254902696 y[1] (numeric) = 1.1443547187789775009057569826475 absolute error = 2.51614314923779e-17 relative error = 2.1987440676807852303976008591540e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.545 y[1] (analytic) = 1.1448727092194692220004344373497 y[1] (numeric) = 1.1448727092194692472034548670593 absolute error = 2.52030204297096e-17 relative error = 2.2013818852308972545545457024857e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.546 y[1] (analytic) = 1.1453915547871804881821316933069 y[1] (numeric) = 1.1453915547871805134267158721116 absolute error = 2.52445841788047e-17 relative error = 2.2040134723618833310047067634551e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.547 y[1] (analytic) = 1.1459112549632657498152802778119 y[1] (numeric) = 1.1459112549632657751014029759114 absolute error = 2.52861226980995e-17 relative error = 2.2066388290173563421474907615574e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.548 y[1] (analytic) = 1.1464318092280248741229651212096 y[1] (numeric) = 1.146431809228024899450601067265 absolute error = 2.53276359460554e-17 relative error = 2.2092579551774930146460135732834e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.549 y[1] (analytic) = 1.1469532170609036397255825330915 y[1] (numeric) = 1.1469532170609036650947064142507 absolute error = 2.53691238811592e-17 relative error = 2.2118708508589579330503489326643e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.55 y[1] (analytic) = 1.1474754779404942571950182023822 y[1] (numeric) = 1.1474754779404942826056046643053 absolute error = 2.54105864619231e-17 relative error = 2.2144775161148011299996968563797e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.551 y[1] (analytic) = 1.1479985913445358904623931748063 y[1] (numeric) = 1.1479985913445359159144168216906 absolute error = 2.54520236468843e-17 relative error = 2.2170779510343206282871232280249e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.552 y[1] (analytic) = 1.1485225567499151790788564000321 y[1] (numeric) = 1.1485225567499152045722917946378 absolute error = 2.54934353946057e-17 relative error = 2.2196721557430206515070144035300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.553 y[1] (analytic) = 1.1490473736326667613289015877443 y[1] (numeric) = 1.1490473736326667868637232514199 absolute error = 2.55348216636756e-17 relative error = 2.2222601304024824400933719579519e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.554 y[1] (analytic) = 1.1495730414679737981956852593716 y[1] (numeric) = 1.1495730414679738237718676720793 absolute error = 2.55761824127077e-17 relative error = 2.2248418752102610392313848054898e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.555 y[1] (analytic) = 1.150099559730168498177822030195 y[1] (numeric) = 1.1500995597301685237953396305363 absolute error = 2.56175176003413e-17 relative error = 2.2274173903997992831476383997727e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.556 y[1] (analytic) = 1.1506269278927326429571323050854 y[1] (numeric) = 1.1506269278927326686159594903265 absolute error = 2.56588271852411e-17 relative error = 2.2299866762403067773511266141482e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.557 y[1] (analytic) = 1.1511551454282981139168167201663 y[1] (numeric) = 1.151155145428298139616927846264 absolute error = 2.57001111260977e-17 relative error = 2.2325497330366995494033855005632e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.558 y[1] (analytic) = 1.1516842118086474195095308122717 y[1] (numeric) = 1.1516842118086474452509001938987 absolute error = 2.57413693816270e-17 relative error = 2.2351065611294438827848563929601e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.559 y[1] (analytic) = 1.1522141265047142234748325481675 y[1] (numeric) = 1.1522141265047142492574344587383 absolute error = 2.57826019105708e-17 relative error = 2.2376571608945042595634970075271e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.56 y[1] (analytic) = 1.1527448889865838739054744961337 y[1] (numeric) = 1.1527448889865838997292831678303 absolute error = 2.58238086716966e-17 relative error = 2.2402015327432215804345521283969e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.561 y[1] (analytic) = 1.153276498723493933162011573659 y[1] (numeric) = 1.1532764987234939590270011974566 absolute error = 2.58649896237976e-17 relative error = 2.2427396771222085980116395256501e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.562 y[1] (analytic) = 1.1538089551838347086351944566842 y[1] (numeric) = 1.1538089551838347345413391823772 absolute error = 2.59061447256930e-17 relative error = 2.2452715945132711772164866933506e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=5.87 NO POLE x[1] = 0.563 y[1] (analytic) = 1.1543422578351497843556178880455 y[1] (numeric) = 1.154342257835149810302891824273 absolute error = 2.59472739362275e-17 relative error = 2.2477972854332600091198685396194e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.564 y[1] (analytic) = 1.1548764061441365534500922755128 y[1] (numeric) = 1.1548764061441365794384694897847 absolute error = 2.59883772142719e-17 relative error = 2.2503167504340175250072857347615e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.565 y[1] (analytic) = 1.1554113995766467514442061230971 y[1] (numeric) = 1.1554113995766467774736606418202 absolute error = 2.60294545187231e-17 relative error = 2.2528299901022725712709032119909e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.566 y[1] (analytic) = 1.1559472375976869904105459931083 y[1] (numeric) = 1.155947237597687016481051801612 absolute error = 2.60705058085037e-17 relative error = 2.2553370050595003179063378941668e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.567 y[1] (analytic) = 1.1564839196714192939620398507875 y[1] (numeric) = 1.1564839196714193200735708933499 absolute error = 2.61115310425624e-17 relative error = 2.2578377959618512785861621853049e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.568 y[1] (analytic) = 1.157021445261161633089888798216 y[1] (numeric) = 1.1570214452611616592424189780899 absolute error = 2.61525301798739e-17 relative error = 2.2603323635000368628624702955362e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.569 y[1] (analytic) = 1.1575598138293884628455513596132 y[1] (numeric) = 1.1575598138293884890390545390523 absolute error = 2.61935031794391e-17 relative error = 2.2628207083992407146270480756400e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.57 y[1] (analytic) = 1.158099024837731259866243636084 y[1] (numeric) = 1.1580990248377312861006936363692 absolute error = 2.62344500002852e-17 relative error = 2.2653028314190212158030231090306e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.571 y[1] (analytic) = 1.158639077746979060743417804361 y[1] (numeric) = 1.1586390777469790870187884058261 absolute error = 2.62753706014651e-17 relative error = 2.2677787333531534011828980782966e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.572 y[1] (analytic) = 1.1591799720170790012336805911064 y[1] (numeric) = 1.1591799720170790275499455331648 absolute error = 2.63162649420584e-17 relative error = 2.2702484150296089005572880127153e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.573 y[1] (analytic) = 1.1597217071071368563116125119018 y[1] (numeric) = 1.1597217071071368826687454930725 absolute error = 2.63571329811707e-17 relative error = 2.2727118773103889088133639109807e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.574 y[1] (analytic) = 1.1602642824754175810639478221502 y[1] (numeric) = 1.1602642824754176074619225000841 absolute error = 2.63979746779339e-17 relative error = 2.2751691210914433716398052509724e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.575 y[1] (analytic) = 1.1608076975793458524245742857562 y[1] (numeric) = 1.1608076975793458788633642772626 absolute error = 2.64387899915064e-17 relative error = 2.2776201473025813458761047146203e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.576 y[1] (analytic) = 1.1613519518755066117498110266296 y[1] (numeric) = 1.1613519518755066382293899077025 absolute error = 2.64795788810729e-17 relative error = 2.2800649569073467333491998192395e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.577 y[1] (analytic) = 1.1618970448196456082334218877795 y[1] (numeric) = 1.1618970448196456347537631936239 absolute error = 2.65203413058444e-17 relative error = 2.2825035509029111435842831518829e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.578 y[1] (analytic) = 1.162442975866669943160820883031 y[1] (numeric) = 1.1624429758666699697218981080896 absolute error = 2.65610772250586e-17 relative error = 2.2849359303200010367333909998906e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.579 y[1] (analytic) = 1.1629897444706486150019254872046 y[1] (numeric) = 1.1629897444706486416037120851841 absolute error = 2.66017865979795e-17 relative error = 2.2873620962227558538167632710177e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.58 y[1] (analytic) = 1.16353735008481306534211267195 y[1] (numeric) = 1.1635373500848130919845820558478 absolute error = 2.66424693838978e-17 relative error = 2.2897820497086548750659900757028e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.581 y[1] (analytic) = 1.1640857921615577256507317563242 y[1] (numeric) = 1.1640857921615577523338572984549 absolute error = 2.66831255421307e-17 relative error = 2.2921957919083923164256798483829e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.582 y[1] (analytic) = 1.1646350701524405648866273036464 y[1] (numeric) = 1.1646350701524405916103823356684 absolute error = 2.67237550320220e-17 relative error = 2.2946033239857781142558890126848e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.583 y[1] (analytic) = 1.165185183508183637940124459152 y[1] (numeric) = 1.1651851835081836647044822720943 absolute error = 2.67643578129423e-17 relative error = 2.2970046471376471511929778629224e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.584 y[1] (analytic) = 1.1657361316786736349109282865074 y[1] (numeric) = 1.1657361316786736617158621307961 absolute error = 2.68049338442887e-17 relative error = 2.2993997625937254277376350897578e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.585 y[1] (analytic) = 1.1662879141129624312213878253303 y[1] (numeric) = 1.1662879141129624580668709108155 absolute error = 2.68454830854852e-17 relative error = 2.3017886716165562146915509593124e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.586 y[1] (analytic) = 1.1668405302592676385645747564984 y[1] (numeric) = 1.1668405302592676654505802524811 absolute error = 2.68860054959827e-17 relative error = 2.3041713755013917185630037295337e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=6.12 NO POLE x[1] = 0.587 y[1] (analytic) = 1.1673939795649731566866257272142 y[1] (numeric) = 1.1673939795649731836131267624727 absolute error = 2.69265010352585e-17 relative error = 2.3065478755760418100348736064321e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.588 y[1] (analytic) = 1.1679482614766297260027965535271 y[1] (numeric) = 1.1679482614766297529697662163445 absolute error = 2.69669696628174e-17 relative error = 2.3089181732008597628661537559322e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.589 y[1] (analytic) = 1.1685033754399554810466756843086 y[1] (numeric) = 1.1685033754399555080540870224992 absolute error = 2.70074113381906e-17 relative error = 2.3112822697685393481805988201206e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.59 y[1] (analytic) = 1.1690593208998365047520034775093 y[1] (numeric) = 1.1690593208998365317998294984458 absolute error = 2.70478260209365e-17 relative error = 2.3136401667040746222690931015165e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.591 y[1] (analytic) = 1.1696160973003273835665430069271 y[1] (numeric) = 1.1696160973003274106547566775674 absolute error = 2.70882136706403e-17 relative error = 2.3159918654646168251937238465629e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.592 y[1] (analytic) = 1.1701737040846517633974472856612 y[1] (numeric) = 1.1701737040846517905260215325757 absolute error = 2.71285742469145e-17 relative error = 2.3183373675394081951508228647807e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.593 y[1] (analytic) = 1.1707321406952029063875669609314 y[1] (numeric) = 1.1707321406952029335564746703298 absolute error = 2.71689077093984e-17 relative error = 2.3206766744496301529201919416373e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.594 y[1] (analytic) = 1.1712914065735442485221417040005 y[1] (numeric) = 1.1712914065735442757313557217591 absolute error = 2.72092140177586e-17 relative error = 2.3230097877483368959135863520524e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.595 y[1] (analytic) = 1.1718515011604099580653176885558 y[1] (numeric) = 1.1718515011604099853148108202447 absolute error = 2.72494931316889e-17 relative error = 2.3253367090203375828745930908170e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.596 y[1] (analytic) = 1.172412423895705494825932721079 y[1] (numeric) = 1.172412423895705522115677731989 absolute error = 2.72897450109100e-17 relative error = 2.3276574398820614006963439078890e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.597 y[1] (analytic) = 1.1729741742185081702520097574644 y[1] (numeric) = 1.1729741742185081975819793726345 absolute error = 2.73299696151701e-17 relative error = 2.3299719819814993518167382334032e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.598 y[1] (analytic) = 1.1735367515670677083533987114403 y[1] (numeric) = 1.173536751567067735723565615685 absolute error = 2.73701669042447e-17 relative error = 2.3322803369980776461092760809517e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.599 y[1] (analytic) = 1.1741001553788068074520056321979 y[1] (numeric) = 1.1741001553788068348623424701343 absolute error = 2.74103368379364e-17 relative error = 2.3345825066425310657807059694496e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6 y[1] (analytic) = 1.1746643850903217027590475010446 y[1] (numeric) = 1.1746643850903217302095268771198 absolute error = 2.74504793760752e-17 relative error = 2.3368784926568188712065530424257e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.601 y[1] (analytic) = 1.1752294401373827297787700698751 y[1] (numeric) = 1.1752294401373827572693645483937 absolute error = 2.74905944785186e-17 relative error = 2.3391682968140235441785164793617e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.602 y[1] (analytic) = 1.1757953199549348885380653377883 y[1] (numeric) = 1.17579531995493491606874744294 absolute error = 2.75306821051517e-17 relative error = 2.3414519209182494380050278946711e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.603 y[1] (analytic) = 1.1763620239770984086414244362806 y[1] (numeric) = 1.1763620239770984362121666521673 absolute error = 2.75707422158867e-17 relative error = 2.3437293668044703321820673084113e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.604 y[1] (analytic) = 1.1769295516371693151506608681084 y[1] (numeric) = 1.1769295516371693427614356387719 absolute error = 2.76107747706635e-17 relative error = 2.3460006363384705098641899464283e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.605 y[1] (analytic) = 1.177497902367619995288838220145 y[1] (numeric) = 1.1774979023676200229396179495947 absolute error = 2.76507797294497e-17 relative error = 2.3482657314167346710734434608052e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.606 y[1] (analytic) = 1.1780670756000997659678356463513 y[1] (numeric) = 1.1780670756000997936585926985914 absolute error = 2.76907570522401e-17 relative error = 2.3505246539662953446459729791033e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.607 y[1] (analytic) = 1.1786370707654354421389835933405 y[1] (numeric) = 1.178637070765435469869690292398 absolute error = 2.77307066990575e-17 relative error = 2.3527774059446906637902665118109e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.608 y[1] (analytic) = 1.1792078872936319059662014179512 y[1] (numeric) = 1.1792078872936319337368300479035 absolute error = 2.77706286299523e-17 relative error = 2.3550239893398201274191625261911e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.609 y[1] (analytic) = 1.1797795246138726768210677237362 y[1] (numeric) = 1.1797795246138727046315905287386 absolute error = 2.78105228050024e-17 relative error = 2.3572644061698258368904395248988e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.61 y[1] (analytic) = 1.1803519821545204820992534213452 y[1] (numeric) = 1.1803519821545205099496426056591 absolute error = 2.78503891843139e-17 relative error = 2.3594986584830414846362826088381e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.3MB, time=6.37 NO POLE x[1] = 0.611 y[1] (analytic) = 1.1809252593431178288577466964165 y[1] (numeric) = 1.1809252593431178567479744244368 absolute error = 2.78902277280203e-17 relative error = 2.3617267483578141042609377715714e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.612 y[1] (analytic) = 1.1814993556063875762722982477992 y[1] (numeric) = 1.1814993556063876042023366440822 absolute error = 2.79300383962830e-17 relative error = 2.3639486779024360032550656657878e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.613 y[1] (analytic) = 1.1820742703702335089145143387088 y[1] (numeric) = 1.1820742703702335368843354880002 absolute error = 2.79698211492914e-17 relative error = 2.3661644492550426914237175986224e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.614 y[1] (analytic) = 1.1826500030597409108480243837716 y[1] (numeric) = 1.1826500030597409388576003310342 absolute error = 2.80095759472626e-17 relative error = 2.3683740645834769225066711144518e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.615 y[1] (analytic) = 1.1832265530991771405431489758368 y[1] (numeric) = 1.1832265530991771685924517262789 absolute error = 2.80493027504421e-17 relative error = 2.3705775260852372872053134309594e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.616 y[1] (analytic) = 1.1838039199119922066094934379379 y[1] (numeric) = 1.1838039199119922346984949570407 absolute error = 2.80890015191028e-17 relative error = 2.3727748359872829932238794208833e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.617 y[1] (analytic) = 1.1843821029208193443458911678558 y[1] (numeric) = 1.184382102920819372474563381402 absolute error = 2.81286722135462e-17 relative error = 2.3749659965460246107439941624209e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.618 y[1] (analytic) = 1.1849611015474755931071202253905 y[1] (numeric) = 1.1849611015474756212754350194919 absolute error = 2.81683147941014e-17 relative error = 2.3771510100471288304925194616960e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.619 y[1] (analytic) = 1.1855409152129623744868157956707 y[1] (numeric) = 1.1855409152129624026947450167966 absolute error = 2.82079292211259e-17 relative error = 2.3793298788054752706043539071446e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.62 y[1] (analytic) = 1.1861215433374660713160003456393 y[1] (numeric) = 1.1861215433374660995635158006445 absolute error = 2.82475154550052e-17 relative error = 2.3815026051650118895160674816305e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.621 y[1] (analytic) = 1.1867029853403586074766524752305 y[1] (numeric) = 1.1867029853403586357637259313837 absolute error = 2.82870734561532e-17 relative error = 2.3836691914986778880450123174037e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.622 y[1] (analytic) = 1.1872852406401980285297346497202 y[1] (numeric) = 1.1872852406401980568563378347321 absolute error = 2.83266031850119e-17 relative error = 2.3858296402082675330242132777745e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.623 y[1] (analytic) = 1.1878683086547290831570991852689 y[1] (numeric) = 1.1878683086547291115232037873204 absolute error = 2.83661046020515e-17 relative error = 2.3879839537243277100580800662601e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.624 y[1] (analytic) = 1.1884521888008838054166910457999 y[1] (numeric) = 1.1884521888008838338222687135705 absolute error = 2.84055776677706e-17 relative error = 2.3901321345060638490473839156874e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.625 y[1] (analytic) = 1.1890368804947820978104651960589 y[1] (numeric) = 1.1890368804947821262554875387551 absolute error = 2.84450223426962e-17 relative error = 2.3922741850412289652340133762027e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.626 y[1] (analytic) = 1.189622383151732315164435442986 y[1] (numeric) = 1.1896223831517323436488740303695 absolute error = 2.84844385873835e-17 relative error = 2.3944101078459958758891320351839e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.627 y[1] (analytic) = 1.1902086961862318493202708853993 y[1] (numeric) = 1.1902086961862318778440972478157 absolute error = 2.85238263624164e-17 relative error = 2.3965399054648882698429273579352e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.628 y[1] (analytic) = 1.1907958190119677146378552804441 y[1] (numeric) = 1.1907958190119677432010409088511 absolute error = 2.85631856284070e-17 relative error = 2.3986635804706276674932726748706e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.629 y[1] (analytic) = 1.1913837510418171343082238242947 y[1] (numeric) = 1.1913837510418171629107401702907 absolute error = 2.86025163459960e-17 relative error = 2.4007811354640560418501540176261e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.63 y[1] (analytic) = 1.1919724916878481274762910342229 y[1] (numeric) = 1.1919724916878481561181095100758 absolute error = 2.86418184758529e-17 relative error = 2.4028925730740415577965999329371e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.631 y[1] (analytic) = 1.1925620403613200971727826093538 y[1] (numeric) = 1.1925620403613201258538745880292 absolute error = 2.86810919786754e-17 relative error = 2.4049978959573171778403783818987e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.632 y[1] (analytic) = 1.1931523964726844190547833382246 y[1] (numeric) = 1.1931523964726844477751201534147 absolute error = 2.87203368151901e-17 relative error = 2.4070971067984283731552219247111e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.633 y[1] (analytic) = 1.1937435594315850309543123126502 y[1] (numeric) = 1.1937435594315850597138652588022 absolute error = 2.87595529461520e-17 relative error = 2.4091902083095801393738734526272e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.634 y[1] (analytic) = 1.1943355286468590232343358993664 y[1] (numeric) = 1.1943355286468590520330762317117 absolute error = 2.87987403323453e-17 relative error = 2.4112772032305929892517083048887e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.3MB, time=6.62 NO POLE x[1] = 0.635 y[1] (analytic) = 1.1949283035265372299516281134903 y[1] (numeric) = 1.1949283035265372587895270480726 absolute error = 2.88378989345823e-17 relative error = 2.4133580943286997480474160373181e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.636 y[1] (analytic) = 1.1955218834778448208258872309833 y[1] (numeric) = 1.1955218834778448497029159446878 absolute error = 2.88770287137045e-17 relative error = 2.4154328843985266525963122390651e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.637 y[1] (analytic) = 1.1961162679072018940145166710524 y[1] (numeric) = 1.1961162679072019229306463016345 absolute error = 2.89161296305821e-17 relative error = 2.4175015762619404215761644969583e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.638 y[1] (analytic) = 1.1967114562202240696924773737563 y[1] (numeric) = 1.1967114562202240986476790198706 absolute error = 2.89552016461143e-17 relative error = 2.4195641727679623140424978954741e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.639 y[1] (analytic) = 1.1973074478217230844366180930148 y[1] (numeric) = 1.1973074478217231134308628142439 absolute error = 2.89942447212291e-17 relative error = 2.4216206767926403686107373939151e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.64 y[1] (analytic) = 1.1979042421157073864138892207397 y[1] (numeric) = 1.1979042421157074154471480376229 absolute error = 2.90332588168832e-17 relative error = 2.4236710912389300584059911545274e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.641 y[1] (analytic) = 1.198501838505382731372844953923 y[1] (numeric) = 1.1985018385053827604450888479857 absolute error = 2.90722438940627e-17 relative error = 2.4257154190366417410484078491662e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.642 y[1] (analytic) = 1.1991002363931527794378378132311 y[1] (numeric) = 1.1991002363931528085490377270136 absolute error = 2.91111999137825e-17 relative error = 2.4277536631422795412953455302388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.643 y[1] (analytic) = 1.1996994351806196927053087189588 y[1] (numeric) = 1.1996994351806197218554355560454 absolute error = 2.91501268370866e-17 relative error = 2.4297858265389554265071561996711e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.644 y[1] (analytic) = 1.2002994342685847336415750281037 y[1] (numeric) = 1.2002994342685847628305996531517 absolute error = 2.91890246250480e-17 relative error = 2.4318119122362699083682249056272e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.645 y[1] (analytic) = 1.2009002330570488642815181348221 y[1] (numeric) = 1.200900233057048893509411373591 absolute error = 2.92278932387689e-17 relative error = 2.4338319232702177791361383532667e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.646 y[1] (analytic) = 1.2015018309452133462275714356296 y[1] (numeric) = 1.2015018309452133754943040750103 absolute error = 2.92667326393807e-17 relative error = 2.4358458627030771823458969446853e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.647 y[1] (analytic) = 1.2021042273314803414484086604078 y[1] (numeric) = 1.2021042273314803707539514484519 absolute error = 2.93055427880441e-17 relative error = 2.4378537336233070345715274584658e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.648 y[1] (analytic) = 1.2027074216134535138767317705792 y[1] (numeric) = 1.2027074216134535432210554165281 absolute error = 2.93443236459489e-17 relative error = 2.4398555391454195127641392637949e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.649 y[1] (analytic) = 1.203311413187938631805556826712 y[1] (numeric) = 1.2033114131879386611886320010263 absolute error = 2.93830751743143e-17 relative error = 2.4418512824098941799958147131743e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.65 y[1] (analytic) = 1.2039162014509441710823954293201 y[1] (numeric) = 1.2039162014509442005041927637087 absolute error = 2.94217973343886e-17 relative error = 2.4438409665830422370626524944639e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.651 y[1] (analytic) = 1.2045217857976819191007285387257 y[1] (numeric) = 1.2045217857976819485612186261755 absolute error = 2.94604900874498e-17 relative error = 2.4458245948569456079955828773293e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.652 y[1] (analytic) = 1.2051281656225675795881686825627 y[1] (numeric) = 1.2051281656225676090873220773678 absolute error = 2.94991533948051e-17 relative error = 2.4478021704493046409156908964155e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.653 y[1] (analytic) = 1.2057353403192213781907057628076 y[1] (numeric) = 1.2057353403192214077284929805988 absolute error = 2.95377872177912e-17 relative error = 2.4497736966033523279784915227968e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.654 y[1] (analytic) = 1.2063433092804686688524308781435 y[1] (numeric) = 1.2063433092804686984288223959179 absolute error = 2.95763915177744e-17 relative error = 2.4517391765877519172853291428726e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.655 y[1] (analytic) = 1.2069520718983405409901317819836 y[1] (numeric) = 1.2069520718983405706050980381338 absolute error = 2.96149662561502e-17 relative error = 2.4536986136964531211655644329372e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.656 y[1] (analytic) = 1.207561627564074427462152801609 y[1] (numeric) = 1.207561627564074457115664195953 absolute error = 2.96535113943440e-17 relative error = 2.4556520112486395675345848205212e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.657 y[1] (analytic) = 1.2081719756681147133309112496125 y[1] (numeric) = 1.2081719756681147430229381434231 absolute error = 2.96920268938106e-17 relative error = 2.4575993725885768039775592891913e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.658 y[1] (analytic) = 1.2087831156001133454184615651814 y[1] (numeric) = 1.2087831156001133751489742812159 absolute error = 2.97305127160345e-17 relative error = 2.4595407010855266634649311853581e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.3MB, time=6.87 NO POLE x[1] = 0.659 y[1] (analytic) = 1.2093950467489304426544976297072 y[1] (numeric) = 1.2093950467489304724234664522371 absolute error = 2.97689688225299e-17 relative error = 2.4614760001336368047570893729932e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.66 y[1] (analytic) = 1.2100077685026349072161829087698 y[1] (numeric) = 1.2100077685026349370235780836105 absolute error = 2.98073951748407e-17 relative error = 2.4634052731518303104757208943682e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.661 y[1] (analytic) = 1.2106212802485050364591972807178 y[1] (numeric) = 1.2106212802485050663049890152584 absolute error = 2.98457917345406e-17 relative error = 2.4653285235837036049481409516718e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.662 y[1] (analytic) = 1.2112355813730291356393886208484 y[1] (numeric) = 1.2112355813730291655235470840814 absolute error = 2.98841584632330e-17 relative error = 2.4672457548974078962766773759363e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.663 y[1] (analytic) = 1.2118506712619061314244164195866 y[1] (numeric) = 1.2118506712619061613469117421377 absolute error = 2.99224953225511e-17 relative error = 2.4691569705855472105063576473650e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.664 y[1] (analytic) = 1.2124665493000461861947739230711 y[1] (numeric) = 1.2124665493000462161555761972293 absolute error = 2.99608022741582e-17 relative error = 2.4710621741650929610855578737093e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.665 y[1] (analytic) = 1.2130832148715713131335744951767 y[1] (numeric) = 1.213083214871571343132653774924 absolute error = 2.99990792797473e-17 relative error = 2.4729613691772408056234054318110e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.666 y[1] (analytic) = 1.213700667359815992104487111237 y[1] (numeric) = 1.2137006673598160221418134122783 absolute error = 3.00373263010413e-17 relative error = 2.4748545591873171076305442761021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.667 y[1] (analytic) = 1.2143189061473277863172051055833 y[1] (numeric) = 1.2143189061473278163927484053766 absolute error = 3.00755432997933e-17 relative error = 2.4767417477846936536286420560054e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.668 y[1] (analytic) = 1.2149379306158679597798315074841 y[1] (numeric) = 1.2149379306158679898935617452702 absolute error = 3.01137302377861e-17 relative error = 2.4786229385826365201649610452178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.669 y[1] (analytic) = 1.2155577401464120955375635131482 y[1] (numeric) = 1.2155577401464121256894505899812 absolute error = 3.01518870768330e-17 relative error = 2.4804981352182620876945554832764e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.67 y[1] (analytic) = 1.2161783341191507146970578551619 y[1] (numeric) = 1.216178334119150744887071633939 absolute error = 3.01900137787771e-17 relative error = 2.4823673413523695918243761303967e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.671 y[1] (analytic) = 1.2167997119134898962358580450436 y[1] (numeric) = 1.2167997119134899264639683505353 absolute error = 3.02281103054917e-17 relative error = 2.4842305606693643296798867538666e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.672 y[1] (analytic) = 1.2174218729080518975962636795423 y[1] (numeric) = 1.2174218729080519278624402984225 absolute error = 3.02661766188802e-17 relative error = 2.4860877968771397746456773813143e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.673 y[1] (analytic) = 1.2180448164806757760630212168607 y[1] (numeric) = 1.2180448164806758063672338977371 absolute error = 3.03042126808764e-17 relative error = 2.4879390537069926370934882669366e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.674 y[1] (analytic) = 1.2186685420084180109242148451658 y[1] (numeric) = 1.21866854200841804126643329861 absolute error = 3.03422184534442e-17 relative error = 2.4897843349134886984468983358834e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.675 y[1] (analytic) = 1.219293048867553126414735282546 y[1] (numeric) = 1.2192930488675531567949291811238 absolute error = 3.03801938985778e-17 relative error = 2.4916236442743698129909244188139e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.676 y[1] (analytic) = 1.2199183364335743154417035649992 y[1] (numeric) = 1.219918336433574345859842543301 absolute error = 3.04181389783018e-17 relative error = 2.4934569855904527484610951362392e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.677 y[1] (analytic) = 1.2205444040811940640912260970796 y[1] (numeric) = 1.2205444040811940945472797517507 absolute error = 3.04560536546711e-17 relative error = 2.4952843626855117034564506490214e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.678 y[1] (analytic) = 1.2211712511843447769158564585004 y[1] (numeric) = 1.2211712511843448074097943482714 absolute error = 3.04939378897710e-17 relative error = 2.4971057794061773176807880598624e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.679 y[1] (analytic) = 1.221798877116179403002138679282 y[1] (numeric) = 1.2217988771161794335339303249993 absolute error = 3.05317916457173e-17 relative error = 2.4989212396218357485291507481794e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.68 y[1] (analytic) = 1.2224272812490720628176059159557 y[1] (numeric) = 1.2224272812490720933872208006119 absolute error = 3.05696148846562e-17 relative error = 2.5007307472245114547941587552550e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.681 y[1] (analytic) = 1.2230564629546186758366076818755 y[1] (numeric) = 1.2230564629546187064440152506401 absolute error = 3.06074075687646e-17 relative error = 2.5025343061287828054888749315950e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.682 y[1] (analytic) = 1.223686421603637588944338005864 y[1] (numeric) = 1.2236864216036376195895076661136 absolute error = 3.06451696602496e-17 relative error = 2.5043319202716323332731398691473e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.3MB, time=7.11 NO POLE x[1] = 0.683 y[1] (analytic) = 1.2243171565661702056184361152149 y[1] (numeric) = 1.2243171565661702363013372365643 absolute error = 3.06829011213494e-17 relative error = 2.5061235936124115618447209899295e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.684 y[1] (analytic) = 1.2249486672114816158875304615069 y[1] (numeric) = 1.2249486672114816466081323758392 absolute error = 3.07206019143323e-17 relative error = 2.5079093301326505973202001633411e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.685 y[1] (analytic) = 1.2255809529080612270660961307334 y[1] (numeric) = 1.225580952908061257824368132231 absolute error = 3.07582720014976e-17 relative error = 2.5096891338360231022702879800158e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.686 y[1] (analytic) = 1.2262140130236233952649949029474 y[1] (numeric) = 1.2262140130236234260609062481226 absolute error = 3.07959113451752e-17 relative error = 2.5114630087482051280806295910917e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.687 y[1] (analytic) = 1.2268478469251080576770664509304 y[1] (numeric) = 1.2268478469251080885105863586562 absolute error = 3.08335199077258e-17 relative error = 2.5132309589167830589341260773887e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.688 y[1] (analytic) = 1.2274824539786813656371383923497 y[1] (numeric) = 1.2274824539786813965082360438905 absolute error = 3.08710976515408e-17 relative error = 2.5149929884111371712895357393700e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.689 y[1] (analytic) = 1.2281178335497363184558221354451 y[1] (numeric) = 1.2281178335497363493644666744875 absolute error = 3.09086445390424e-17 relative error = 2.5167491013223416116310535175980e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.69 y[1] (analytic) = 1.2287539850028933980264606845022 y[1] (numeric) = 1.2287539850028934289726212171861 absolute error = 3.09461605326839e-17 relative error = 2.5184993017630807350672690516518e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.691 y[1] (analytic) = 1.2293909077020012042045937982186 y[1] (numeric) = 1.2293909077020012351882393931677 absolute error = 3.09836455949491e-17 relative error = 2.5202435938674922721029261681513e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.692 y[1] (analytic) = 1.2300286010101370909593051215486 y[1] (numeric) = 1.2300286010101371219804048099016 absolute error = 3.10210996883530e-17 relative error = 2.5219819817911164483994424287184e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.693 y[1] (analytic) = 1.2306670642896078032958151397345 y[1] (numeric) = 1.2306670642896078343543379151761 absolute error = 3.10585227754416e-17 relative error = 2.5237144697107719105101526898875e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.694 y[1] (analytic) = 1.2313062969019501149486830319832 y[1] (numeric) = 1.231306296901950146044597850775 absolute error = 3.10959148187918e-17 relative error = 2.5254410618244399393465963931802e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.695 y[1] (analytic) = 1.2319462982079314668449797316401 y[1] (numeric) = 1.2319462982079314979782555126515 absolute error = 3.11332757810114e-17 relative error = 2.5271617623511569234000651758595e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.696 y[1] (analytic) = 1.2325870675675506063367937297397 y[1] (numeric) = 1.2325870675675506375073993544793 absolute error = 3.11706056247396e-17 relative error = 2.5288765755309475157802350945325e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.697 y[1] (analytic) = 1.2332286043400382272024303894814 y[1] (numeric) = 1.233228604340038258410334702128 absolute error = 3.12079043126466e-17 relative error = 2.5305855056246848057079417545797e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.698 y[1] (analytic) = 1.2338709078838576104156647704838 y[1] (numeric) = 1.2338709078838576416608365779174 absolute error = 3.12451718074336e-17 relative error = 2.5322885569139831313026288512516e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.699 y[1] (analytic) = 1.234513977556705265682407193618 y[1] (numeric) = 1.2345139775567052969648152654511 absolute error = 3.12824080718331e-17 relative error = 2.5339857337011153166429407495074e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7 y[1] (analytic) = 1.2351578127155115737441400098081 y[1] (numeric) = 1.235157812715511605063753078417 absolute error = 3.13196130686089e-17 relative error = 2.5356770403089056691176007889228e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.701 y[1] (analytic) = 1.2358024127164414294474832694162 y[1] (numeric) = 1.2358024127164414608042700299721 absolute error = 3.13567867605559e-17 relative error = 2.5373624810806069190842437488106e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.702 y[1] (analytic) = 1.2364477769148948855792462226979 y[1] (numeric) = 1.2364477769148949169731753331985 absolute error = 3.13939291105006e-17 relative error = 2.5390420603798339515860783414102e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.703 y[1] (analytic) = 1.2370939046655077974663208163335 y[1] (numeric) = 1.237093904665507828897360897634 absolute error = 3.14310400813005e-17 relative error = 2.5407157825904086223193753177054e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.704 y[1] (analytic) = 1.2377407953221524683397725861917 y[1] (numeric) = 1.2377407953221524998078922220364 absolute error = 3.14681196358447e-17 relative error = 2.5423836521163018069579323199770e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.705 y[1] (analytic) = 1.2383884482379382954624835822915 y[1] (numeric) = 1.2383884482379383269676513193452 absolute error = 3.15051677370537e-17 relative error = 2.5440456733815108301921894801149e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.706 y[1] (analytic) = 1.2390368627652124170197011983717 y[1] (numeric) = 1.239036862765212448561885546251 absolute error = 3.15421843478793e-17 relative error = 2.5457018508299451495373596390926e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.3MB, time=7.36 NO POLE x[1] = 0.707 y[1] (analytic) = 1.2396860382555603597718460155734 y[1] (numeric) = 1.2396860382555603913510154468783 absolute error = 3.15791694313049e-17 relative error = 2.5473521889253444654287858543521e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.708 y[1] (analytic) = 1.2403359740598066874689310074817 y[1] (numeric) = 1.2403359740598067190850539578272 absolute error = 3.16161229503455e-17 relative error = 2.5489966921511727043346852652610e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.709 y[1] (analytic) = 1.2409866695280156500259436921618 y[1] (numeric) = 1.2409866695280156816789885602093 absolute error = 3.16530448680475e-17 relative error = 2.5506353650104960231162827961088e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.71 y[1] (analytic) = 1.2416381240094918334585420558604 y[1] (numeric) = 1.2416381240094918651484772033495 absolute error = 3.16899351474891e-17 relative error = 2.5522682120259093262103469077702e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.711 y[1] (analytic) = 1.2422903368527808105784143127322 y[1] (numeric) = 1.242290336852780842305208064512 absolute error = 3.17267937517798e-17 relative error = 2.5538952377393903747056521806713e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.712 y[1] (analytic) = 1.2429433074056697924476518052839 y[1] (numeric) = 1.2429433074056698242112724493451 absolute error = 3.17636206440612e-17 relative error = 2.5555164467122587542648695854828e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.713 y[1] (analytic) = 1.2435970350151882805914835912195 y[1] (numeric) = 1.2435970350151883123918993787258 absolute error = 3.18004157875063e-17 relative error = 2.5571318435250141650998101421387e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.714 y[1] (analytic) = 1.2442515190276087199687205040045 y[1] (numeric) = 1.2442515190276087518058996493246 absolute error = 3.18371791453201e-17 relative error = 2.5587414327772795142636184396163e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.715 y[1] (analytic) = 1.2449067587884471526992557167609 y[1] (numeric) = 1.2449067587884471845731663975 absolute error = 3.18739106807391e-17 relative error = 2.5603452190876556411811091156640e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.716 y[1] (analytic) = 1.2455627536424638725479680820458 y[1] (numeric) = 1.2455627536424639044585784390776 absolute error = 3.19106103570318e-17 relative error = 2.5619432070936566019188343595174e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.717 y[1] (analytic) = 1.2462195029336640801643737636656 y[1] (numeric) = 1.2462195029336641121116519011641 absolute error = 3.19472781374985e-17 relative error = 2.5635354014515888048066300536800e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.718 y[1] (analytic) = 1.2468770060052985390773709209283 y[1] (numeric) = 1.2468770060052985710612849063998 absolute error = 3.19839139854715e-17 relative error = 2.5651218068364624264057209670955e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.719 y[1] (analytic) = 1.2475352621998642324444214506442 y[1] (numeric) = 1.2475352621998642644649393149592 absolute error = 3.20205178643150e-17 relative error = 2.5667024279418788799944665777431e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.72 y[1] (analytic) = 1.248194270859105020554513037748 y[1] (numeric) = 1.248194270859105052611602775173 absolute error = 3.20570897374250e-17 relative error = 2.5682772694799184614216872106964e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.721 y[1] (analytic) = 1.2488540313240122990842440116342 y[1] (numeric) = 1.2488540313240123311778735798638 absolute error = 3.20936295682296e-17 relative error = 2.5698463361810602029603839575852e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.722 y[1] (analytic) = 1.249514542934825658106372752177 y[1] (numeric) = 1.2495145429348256902365100723661 absolute error = 3.21301373201891e-17 relative error = 2.5714096327940857992529089306031e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.723 y[1] (analytic) = 1.2501758050310335418501726369398 y[1] (numeric) = 1.2501758050310335740167855937355 absolute error = 3.21666129567957e-17 relative error = 2.5729671640859516680809693103396e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.724 y[1] (analytic) = 1.2508378169513739092129327692739 y[1] (numeric) = 1.2508378169513739414159892108478 absolute error = 3.22030564415739e-17 relative error = 2.5745189348417172067788840806603e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.725 y[1] (analytic) = 1.2515005780338348950219439758613 y[1] (numeric) = 1.2515005780338349272614117139412 absolute error = 3.22394677380799e-17 relative error = 2.5760649498643932011445134823770e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.726 y[1] (analytic) = 1.2521640876156554720463088117698 y[1] (numeric) = 1.2521640876156555043221556216725 absolute error = 3.22758468099027e-17 relative error = 2.5776052139749263111083299349557e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.727 y[1] (analytic) = 1.2528283450333261137579135612673 y[1] (numeric) = 1.2528283450333261460701071819304 absolute error = 3.23121936206631e-17 relative error = 2.5791397320120158168144039431322e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.728 y[1] (analytic) = 1.2534933496225894578408994734763 y[1] (numeric) = 1.2534933496225894901894076074906 absolute error = 3.23485081340143e-17 relative error = 2.5806685088320584238051399915622e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.729 y[1] (analytic) = 1.2541591007184409704489697234547 y[1] (numeric) = 1.2541591007184410028337600370965 absolute error = 3.23847903136418e-17 relative error = 2.5821915493090372644342225896008e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.73 y[1] (analytic) = 1.2548255976551296112098678414497 y[1] (numeric) = 1.2548255976551296436309079647131 absolute error = 3.24210401232634e-17 relative error = 2.5837088583344190580453074177755e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.3MB, time=7.61 NO POLE x[1] = 0.731 y[1] (analytic) = 1.2554928397661584989763626059028 y[1] (numeric) = 1.2554928397661585314336201325322 absolute error = 3.24572575266294e-17 relative error = 2.5852204408170673664356800105472e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.732 y[1] (analytic) = 1.2561608263842855783230736492765 y[1] (numeric) = 1.2561608263842856108165161367987 absolute error = 3.24934424875222e-17 relative error = 2.5867263016831082003461563817539e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.733 y[1] (analytic) = 1.2568295568415242867884712799312 y[1] (numeric) = 1.2568295568415243193180662496882 absolute error = 3.25295949697570e-17 relative error = 2.5882264458758834169931291338633e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.734 y[1] (analytic) = 1.2574990304691442228613832781104 y[1] (numeric) = 1.2574990304691442554270982152917 absolute error = 3.25657149371813e-17 relative error = 2.5897208783558086808988355542746e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.735 y[1] (analytic) = 1.2581692465976718147113406795812 y[1] (numeric) = 1.2581692465976718473131430332564 absolute error = 3.26018023536752e-17 relative error = 2.5912096041002953060735692674571e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.736 y[1] (analytic) = 1.2588402045568909896620938166407 y[1] (numeric) = 1.2588402045568910222999509997919 absolute error = 3.26378571831512e-17 relative error = 2.5926926281036324737891459650757e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.737 y[1] (analytic) = 1.2595119036758438444076291430284 y[1] (numeric) = 1.2595119036758438770815085325828 absolute error = 3.26738793895544e-17 relative error = 2.5941699553769014315629752265256e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.738 y[1] (analytic) = 1.2601843432828313159700166267826 y[1] (numeric) = 1.2601843432828313486798855636453 absolute error = 3.27098689368627e-17 relative error = 2.5956415909478898144393948615493e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.739 y[1] (analytic) = 1.2608575227054138533984167532507 y[1] (numeric) = 1.2608575227054138861442425423372 absolute error = 3.27458257890865e-17 relative error = 2.5971075398609664340937273875009e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.74 y[1] (analytic) = 1.2615314412704120902085754393012 y[1] (numeric) = 1.2615314412704121229903253495702 absolute error = 3.27817499102690e-17 relative error = 2.5985678071770038807241681412357e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.741 y[1] (analytic) = 1.2622060983039075175621344192991 y[1] (numeric) = 1.2622060983039075503797756837853 absolute error = 3.28176412644862e-17 relative error = 2.6000223979732774571225319296504e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.742 y[1] (analytic) = 1.2628814931312431581850839235906 y[1] (numeric) = 1.2628814931312431910385837394371 absolute error = 3.28534998158465e-17 relative error = 2.6014713173433326165497543946012e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.743 y[1] (analytic) = 1.2635576250770242410246837310994 y[1] (numeric) = 1.2635576250770242739140092595909 absolute error = 3.28893255284915e-17 relative error = 2.6029145703969476506962509091408e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.744 y[1] (analytic) = 1.2642344934651188766441779391716 y[1] (numeric) = 1.2642344934651189095692963057671 absolute error = 3.29251183665955e-17 relative error = 2.6043521622599935247169339677672e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.745 y[1] (analytic) = 1.2649120976186587333546280560096 y[1] (numeric) = 1.2649120976186587663155063503751 absolute error = 3.29608782943655e-17 relative error = 2.6057840980743335483253749909333e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.746 y[1] (analytic) = 1.2655904368600397140831882839174 y[1] (numeric) = 1.2655904368600397470797935599592 absolute error = 3.29966052760418e-17 relative error = 2.6072103829977706371130300806465e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.747 y[1] (analytic) = 1.266269510510922633977146125141 y[1] (numeric) = 1.2662695105109226670094454010383 absolute error = 3.30322992758973e-17 relative error = 2.6086310222038919400824018670847e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.748 y[1] (analytic) = 1.2669493178922338987430507063167 y[1] (numeric) = 1.2669493178922339318110109645548 absolute error = 3.30679602582381e-17 relative error = 2.6100460208820164373549700067941e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.749 y[1] (analytic) = 1.2676298583241661837202504824584 y[1] (numeric) = 1.2676298583241662168238386698614 absolute error = 3.31035881874030e-17 relative error = 2.6114553842370557937237963479519e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.75 y[1] (analytic) = 1.2683111311261791136881612469999 y[1] (numeric) = 1.2683111311261791468273442747642 absolute error = 3.31391830277643e-17 relative error = 2.6128591174894780233251351065035e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.751 y[1] (analytic) = 1.2689931356169999434065846406836 y[1] (numeric) = 1.2689931356169999765813293844106 absolute error = 3.31747447437270e-17 relative error = 2.6142572258751450531564779050194e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.752 y[1] (analytic) = 1.2696758711146242388883966190315 y[1] (numeric) = 1.2696758711146242720986699187611 absolute error = 3.32102732997296e-17 relative error = 2.6156497146452766938186016418440e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.753 y[1] (analytic) = 1.270359336936316559403924605769 y[1] (numeric) = 1.2703593369363165926496932660123 absolute error = 3.32457686602433e-17 relative error = 2.6170365890662886466095685221021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.754 y[1] (analytic) = 1.2710435323986111402163313278786 y[1] (numeric) = 1.2710435323986111734975621176515 absolute error = 3.32812307897729e-17 relative error = 2.6184178544197646516853820568219e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.3MB, time=7.86 NO POLE x[1] = 0.755 y[1] (analytic) = 1.2717284568173125760473225969591 y[1] (numeric) = 1.2717284568173126093639822498153 absolute error = 3.33166596528562e-17 relative error = 2.6197935160023106479297643629313e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.756 y[1] (analytic) = 1.2724141095074965052724955712377 y[1] (numeric) = 1.2724141095074965386245507853021 absolute error = 3.33520552140644e-17 relative error = 2.6211635791254878672885483417175e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.757 y[1] (analytic) = 1.2731004897835102948456433029448 y[1] (numeric) = 1.2731004897835103282330607409467 absolute error = 3.33874174380019e-17 relative error = 2.6225280491156988904403673045923e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.758 y[1] (analytic) = 1.2737875969589737259513306468032 y[1] (numeric) = 1.2737875969589737593740769361097 absolute error = 3.34227462893065e-17 relative error = 2.6238869313141053486932441421071e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.759 y[1] (analytic) = 1.274475430346779680385055877114 y[1] (numeric) = 1.2744754303467797138430976097633 absolute error = 3.34580417326493e-17 relative error = 2.6252402310765222298034363721110e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.76 y[1] (analytic) = 1.275163989259094827660311633333 y[1] (numeric) = 1.275163989259094861153615366068 absolute error = 3.34933037327350e-17 relative error = 2.6265879537733437724788548088533e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.761 y[1] (analytic) = 1.2758532730073603128418580871366 y[1] (numeric) = 1.275853273007360346370390341438 absolute error = 3.35285322543014e-17 relative error = 2.6279301047894067771084622680424e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.762 y[1] (analytic) = 1.2765432809022924451045204977583 y[1] (numeric) = 1.2765432809022924786682477598785 absolute error = 3.35637272621202e-17 relative error = 2.6292666895239560776016630799543e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.763 y[1] (analytic) = 1.2772340122538833870168225968583 y[1] (numeric) = 1.2772340122538834206157113178544 absolute error = 3.35988887209961e-17 relative error = 2.6305977133904769070976767759705e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.764 y[1] (analytic) = 1.277925466371401844548766519348 y[1] (numeric) = 1.2779254663714018781827831151159 absolute error = 3.36340165957679e-17 relative error = 2.6319231818166841942897981943794e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.765 y[1] (analytic) = 1.2786176425633937578030692724491 y[1] (numeric) = 1.2786176425633937914721801237568 absolute error = 3.36691108513077e-17 relative error = 2.6332431002443631812052879437537e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.766 y[1] (analytic) = 1.2793105401376829924691650118068 y[1] (numeric) = 1.279310540137683026173336464328 absolute error = 3.37041714525212e-17 relative error = 2.6345574741292964280040041603049e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.767 y[1] (analytic) = 1.2800041584013720319992816707128 y[1] (numeric) = 1.2800041584013720657384800350605 absolute error = 3.37391983643477e-17 relative error = 2.6358663089411675047869940201539e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.768 y[1] (analytic) = 1.2806984966608426705058997664195 y[1] (numeric) = 1.28069849666084270428009131818 absolute error = 3.37741915517605e-17 relative error = 2.6371696101634961178579791188806e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.769 y[1] (analytic) = 1.2813935542217567063799004861449 y[1] (numeric) = 1.2813935542217567401890514659111 absolute error = 3.38091509797662e-17 relative error = 2.6384673832934874925943647604766e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.77 y[1] (analytic) = 1.2820893303890566366287094346757 y[1] (numeric) = 1.2820893303890566704727860480813 absolute error = 3.38440766134056e-17 relative error = 2.6397596338420069335958011910559e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.771 y[1] (analytic) = 1.2827858244669663519337417054856 y[1] (numeric) = 1.2827858244669663858127101232386 absolute error = 3.38789684177530e-17 relative error = 2.6410463673334296314756029182422e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.772 y[1] (analytic) = 1.2834830357589918324264532179796 y[1] (numeric) = 1.2834830357589918663402795758961 absolute error = 3.39138263579165e-17 relative error = 2.6423275893055687651703114655550e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.773 y[1] (analytic) = 1.2841809635679218441823025448716 y[1] (numeric) = 1.2841809635679218781309529439098 absolute error = 3.39486503990382e-17 relative error = 2.6436033053095959463792048668210e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.774 y[1] (analytic) = 1.2848796071958286364319267357915 y[1] (numeric) = 1.2848796071958286704153672420856 absolute error = 3.39834405062941e-17 relative error = 2.6448735209099384708853097113048e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.775 y[1] (analytic) = 1.2855789659440686394888339260045 y[1] (numeric) = 1.2855789659440686735070305708985 absolute error = 3.40181966448940e-17 relative error = 2.6461382416841768022191028872820e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.776 y[1] (analytic) = 1.2862790391132831633929148026071 y[1] (numeric) = 1.286279039113283197445833582689 absolute error = 3.40529187800819e-17 relative error = 2.6473974732229811602137840903335e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.777 y[1] (analytic) = 1.2869798260033990972690742847478 y[1] (numeric) = 1.2869798260033991313566811618834 absolute error = 3.40876068771356e-17 relative error = 2.6486512211299860553272781409686e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.778 y[1] (analytic) = 1.2876813259136296094002840592981 y[1] (numeric) = 1.287681325913629643522544960665 absolute error = 3.41222609013669e-17 relative error = 2.6498994910217117290784829681778e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=8.12 NO POLE x[1] = 0.779 y[1] (analytic) = 1.28838353814247484801435589898 y[1] (numeric) = 1.288383538142474882171236717102 absolute error = 3.41568808181220e-17 relative error = 2.6511422885275012768578331376384e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.78 y[1] (analytic) = 1.2890864619877226427837349762354 y[1] (numeric) = 1.2890864619877226769752015690162 absolute error = 3.41914665927808e-17 relative error = 2.6523796192893725479673501174941e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.781 y[1] (analytic) = 1.289790096746449207037611673102 y[1] (numeric) = 1.2897900967464492412636298638596 absolute error = 3.42260181907576e-17 relative error = 2.6536114889619789794683264258548e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.782 y[1] (analytic) = 1.2904944417150198406856496750424 y[1] (numeric) = 1.2904944417150198749461852525432 absolute error = 3.42605355775008e-17 relative error = 2.6548379032124929745425993987010e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.783 y[1] (analytic) = 1.2911994961890896338526274250576 y[1] (numeric) = 1.2911994961890896681476461435507 absolute error = 3.42950187184931e-17 relative error = 2.6560588677205282933379499439184e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.784 y[1] (analytic) = 1.2919052594636041712232893035015 y[1] (numeric) = 1.2919052594636042055527568827527 absolute error = 3.43294675792512e-17 relative error = 2.6572743881780239038069076242601e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.785 y[1] (analytic) = 1.2926117308328002370967021888034 y[1] (numeric) = 1.2926117308328002714605843141297 absolute error = 3.43638821253263e-17 relative error = 2.6584844702891900128627657058110e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.786 y[1] (analytic) = 1.293318909590206521149412344802 y[1] (numeric) = 1.293318909590206555547674667106 absolute error = 3.43982623223040e-17 relative error = 2.6596891197704077929640514595879e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.787 y[1] (analytic) = 1.2940267950286443249066968715924 y[1] (numeric) = 1.2940267950286443593393050073962 absolute error = 3.44326081358038e-17 relative error = 2.6608883423500984380939976774143e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.788 y[1] (analytic) = 1.2947353864402282689212032486917 y[1] (numeric) = 1.2947353864402283033881227801719 absolute error = 3.44669195314802e-17 relative error = 2.6620821437687161399037041396061e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.789 y[1] (analytic) = 1.2954446831163670006582697919461 y[1] (numeric) = 1.2954446831163670351594662669679 absolute error = 3.45011964750218e-17 relative error = 2.6632705297785866141133443317718e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.79 y[1] (analytic) = 1.296154684347763903087219138915 y[1] (numeric) = 1.2961546843477639376226580710665 absolute error = 3.45354389321515e-17 relative error = 2.6644535061438309388611487152135e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.791 y[1] (analytic) = 1.2968653894244178039779161714986 y[1] (numeric) = 1.2968653894244178385475630401254 absolute error = 3.45696468686268e-17 relative error = 2.6656310786402972709669569768568e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.792 y[1] (analytic) = 1.2975767976356236859018810793109 y[1] (numeric) = 1.2975767976356237205057013295508 absolute error = 3.46038202502399e-17 relative error = 2.6668032530554772911200188628288e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.793 y[1] (analytic) = 1.2982889082699733969372475627432 y[1] (numeric) = 1.2982889082699734315752066055606 absolute error = 3.46379590428174e-17 relative error = 2.6679700351883920329028967488842e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.794 y[1] (analytic) = 1.2990017206153563620768554708199 y[1] (numeric) = 1.2990017206153563967489186830404 absolute error = 3.46720632122205e-17 relative error = 2.6691314308495164985674149878604e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.795 y[1] (analytic) = 1.2997152339589602953387664658126 y[1] (numeric) = 1.2997152339589603300448991901576 absolute error = 3.47061327243450e-17 relative error = 2.6702874458606890562450099813380e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.796 y[1] (analytic) = 1.3004294475872719125784906041565 y[1] (numeric) = 1.300429447587271947318658149278 absolute error = 3.47401675451215e-17 relative error = 2.6714380860550364374111534416855e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.797 y[1] (analytic) = 1.3011443607860776450022110215024 y[1] (numeric) = 1.3011443607860776797763786620174 absolute error = 3.47741676405150e-17 relative error = 2.6725833572768527916761740451595e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.798 y[1] (analytic) = 1.3018599728404643533802932087375 y[1] (numeric) = 1.301859972840464388188426185263 absolute error = 3.48081329765255e-17 relative error = 2.6737232653815558779951831417084e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.799 y[1] (analytic) = 1.3025762830348200429603646655274 y[1] (numeric) = 1.3025762830348200778024281847151 absolute error = 3.48420635191877e-17 relative error = 2.6748578162355742323352359788924e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8 y[1] (analytic) = 1.3032932906528345790792500183577 y[1] (numeric) = 1.3032932906528346139552092529287 absolute error = 3.48759592345710e-17 relative error = 2.6759870157162576529288649461045e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.801 y[1] (analytic) = 1.3040109949775004034730459911998 y[1] (numeric) = 1.3040109949775004383828660799795 absolute error = 3.49098200887797e-17 relative error = 2.6771108697118032462804798009161e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.802 y[1] (analytic) = 1.3047293952911132512846199187868 y[1] (numeric) = 1.3047293952911132862282659667397 absolute error = 3.49436460479529e-17 relative error = 2.6782293841211586532106025684936e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.4MB, time=8.37 x[1] = 0.803 y[1] (analytic) = 1.3054484908752728687678147950589 y[1] (numeric) = 1.3054484908752729037452518733237 absolute error = 3.49774370782648e-17 relative error = 2.6793425648539561655539261633398e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.804 y[1] (analytic) = 1.3061682810108837316876431526351 y[1] (numeric) = 1.3061682810108837666988362985593 absolute error = 3.50111931459242e-17 relative error = 2.6804504178303857440328572043595e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.805 y[1] (analytic) = 1.3068887649781557644157513731752 y[1] (numeric) = 1.3068887649781557994606655903504 absolute error = 3.50449142171752e-17 relative error = 2.6815529489811602094147477825990e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.806 y[1] (analytic) = 1.3076099420566050597204353332294 y[1] (numeric) = 1.3076099420566050947990355915261 absolute error = 3.50786002582967e-17 relative error = 2.6826501642473887119189102237251e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.807 y[1] (analytic) = 1.3083318115250545992504875956188 y[1] (numeric) = 1.3083318115250546343627388312213 absolute error = 3.51122512356025e-17 relative error = 2.6837420695804964136614868711113e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.808 y[1] (analytic) = 1.3090543726616349747121556625597 y[1] (numeric) = 1.3090543726616350098580227780015 absolute error = 3.51458671154418e-17 relative error = 2.6848286709421749291516086806463e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.809 y[1] (analytic) = 1.3097776247437851097384901136346 y[1] (numeric) = 1.3097776247437851449179379778332 absolute error = 3.51794478641986e-17 relative error = 2.6859099743042488829496212887631e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.81 y[1] (analytic) = 1.3105015670482529824503607593199 y[1] (numeric) = 1.3105015670482530176633542076122 absolute error = 3.52129934482923e-17 relative error = 2.6869859856486344150934778214311e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.811 y[1] (analytic) = 1.311226198851096348708418249117 y[1] (numeric) = 1.3112261988510963839549220832942 absolute error = 3.52465038341772e-17 relative error = 2.6880567109672138721061797279655e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.812 y[1] (analytic) = 1.3119515194276834660552778823829 y[1] (numeric) = 1.3119515194276835013352568707258 absolute error = 3.52799789883429e-17 relative error = 2.6891221562617794534250008225834e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.813 y[1] (analytic) = 1.3126775280526938183472016797382 y[1] (numeric) = 1.3126775280526938536606205570526 absolute error = 3.53134188773144e-17 relative error = 2.6901823275439541318266146710877e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.814 y[1] (analytic) = 1.3134042240001188410745540834314 y[1] (numeric) = 1.313404224000118876421377551083 absolute error = 3.53468234676516e-17 relative error = 2.6912372308350670954409901492368e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.815 y[1] (analytic) = 1.3141316065432626473703059662622 y[1] (numeric) = 1.3141316065432626827504986922122 absolute error = 3.53801927259500e-17 relative error = 2.6922868721661208613733871837764e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.816 y[1] (analytic) = 1.314859674954742754705860940622 y[1] (numeric) = 1.3148596749547427901193875594625 absolute error = 3.54135266188405e-17 relative error = 2.6933312575776899944722736632038e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.817 y[1] (analytic) = 1.315588428506490812273477271886 y[1] (numeric) = 1.315588428506490847720302384875 absolute error = 3.54468251129890e-17 relative error = 2.6943703931198049052945468259128e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.818 y[1] (analytic) = 1.316317866469753329054558013794 y[1] (numeric) = 1.3163178664697533645346461888911 absolute error = 3.54800881750971e-17 relative error = 2.6954042848519195469484652703388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.819 y[1] (analytic) = 1.3170479881150924025730812975917 y[1] (numeric) = 1.3170479881150924380863970694934 absolute error = 3.55133157719017e-17 relative error = 2.6964329388427956466316611245398e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.82 y[1] (analytic) = 1.3177787927123864483334420215631 y[1] (numeric) = 1.3177787927123864838799498917383 absolute error = 3.55465078701752e-17 relative error = 2.6974563611704328015405979850834e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.821 y[1] (analytic) = 1.3185102795308309299419755031717 y[1] (numeric) = 1.3185102795308309655216399398973 absolute error = 3.55796644367256e-17 relative error = 2.6984745579219911724279459992861e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.822 y[1] (analytic) = 1.3192424478389390899114329723498 y[1] (numeric) = 1.3192424478389391255242184107461 absolute error = 3.56127854383963e-17 relative error = 2.6994875351936916444573337361917e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.823 y[1] (analytic) = 1.3199752969045426811476781015192 y[1] (numeric) = 1.3199752969045427167935489435854 absolute error = 3.56458708420662e-17 relative error = 2.7004952990907389995075802268521e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.824 y[1] (analytic) = 1.3207088259947926991178730857087 y[1] (numeric) = 1.3207088259947927347967937003587 absolute error = 3.56789206146500e-17 relative error = 2.7014978557272604401957653993353e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.825 y[1] (analytic) = 1.3214430343761601146994221046441 y[1] (numeric) = 1.3214430343761601504113568277421 absolute error = 3.57119347230980e-17 relative error = 2.7024952112262064346925992568455e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.826 y[1] (analytic) = 1.3221779213144366077089393179268 y[1] (numeric) = 1.3221779213144366434538524523227 absolute error = 3.57449131343959e-17 relative error = 2.7034873717192518463274521731572e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=133.5MB, alloc=4.4MB, time=8.62 x[1] = 0.827 y[1] (analytic) = 1.3229134860747353011105078643946 y[1] (numeric) = 1.32291348607473533688836367996 absolute error = 3.57778558155654e-17 relative error = 2.7044743433467578208695780299045e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.828 y[1] (analytic) = 1.3236497279214914959024956574681 y[1] (numeric) = 1.3236497279214915317132583911319 absolute error = 3.58107627336638e-17 relative error = 2.7054561322576582086865873702895e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.829 y[1] (analytic) = 1.3243866461184634066821930897261 y[1] (numeric) = 1.3243866461184634425258269455103 absolute error = 3.58436338557842e-17 relative error = 2.7064327446093916271014209638027e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.83 y[1] (analytic) = 1.3251242399287328978875370821356 y[1] (numeric) = 1.325124239928732933764006231191 absolute error = 3.58764691490554e-17 relative error = 2.7074041865678110685107064345876e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.831 y[1] (analytic) = 1.3258625086147062207151852362717 y[1] (numeric) = 1.325862508614706256624453816914 absolute error = 3.59092685806423e-17 relative error = 2.7083704643071314809281353612941e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.832 y[1] (analytic) = 1.3266014514381147507142031715169 y[1] (numeric) = 1.3266014514381147866562352892623 absolute error = 3.59420321177454e-17 relative error = 2.7093315840098096413656229608894e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.833 y[1] (analytic) = 1.3273410676600157260546274536119 y[1] (numeric) = 1.327341067660015762029387181213 absolute error = 3.59747597276011e-17 relative error = 2.7102875518664846626327002378584e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.834 y[1] (analytic) = 1.3280813565407929864701658460576 y[1] (numeric) = 1.3280813565407930224776172235393 absolute error = 3.60074513774817e-17 relative error = 2.7112383740758960723268970341674e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.835 y[1] (analytic) = 1.3288223173401577128742959417292 y[1] (numeric) = 1.3288223173401577489144029764249 absolute error = 3.60401070346957e-17 relative error = 2.7121840568448247052803937632007e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.836 y[1] (analytic) = 1.3295639493171491676490225586661 y[1] (numeric) = 1.3295639493171492037217492252536 absolute error = 3.60727266665875e-17 relative error = 2.7131246063879886302151589499092e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.837 y[1] (analytic) = 1.3303062517301354356055536113409 y[1] (numeric) = 1.3303062517301354717108638518782 absolute error = 3.61053102405373e-17 relative error = 2.7140600289279544237209380453126e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.838 y[1] (analytic) = 1.3310492238368141656161534967937 y[1] (numeric) = 1.3310492238368142017540112207553 absolute error = 3.61378577239616e-17 relative error = 2.7149903306950937844944449805015e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.839 y[1] (analytic) = 1.3317928648942133129164323638407 y[1] (numeric) = 1.3317928648942133490868014481537 absolute error = 3.61703690843130e-17 relative error = 2.7159155179274876991028185676328e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.84 y[1] (analytic) = 1.3325371741586918820773289631291 y[1] (numeric) = 1.3325371741586919182801732522092 absolute error = 3.62028442890801e-17 relative error = 2.7168355968708384009689798444108e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.841 y[1] (analytic) = 1.3332821508859406706460441061175 y[1] (numeric) = 1.333282150885940706881327411905 absolute error = 3.62352833057875e-17 relative error = 2.7177505737783890934249009446076e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.842 y[1] (analytic) = 1.3340277943309830134551810921098 y[1] (numeric) = 1.3340277943309830497228671941063 absolute error = 3.62676861019965e-17 relative error = 2.7186604549108963842714044931368e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.843 y[1] (analytic) = 1.334774103748175527599348794266 y[1] (numeric) = 1.3347741037481755638994014395701 absolute error = 3.63000526453041e-17 relative error = 2.7195652465364754209886850237608e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.844 y[1] (analytic) = 1.3355210783912088580784824280462 y[1] (numeric) = 1.3355210783912088944108653313901 absolute error = 3.63323829033439e-17 relative error = 2.7204649549305877833094556287828e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.845 y[1] (analytic) = 1.3362687175131084241071363588314 y[1] (numeric) = 1.336268717513108460471813202617 absolute error = 3.63646768437856e-17 relative error = 2.7213595863759246196630081625316e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.846 y[1] (analytic) = 1.3370170203662351660890026394896 y[1] (numeric) = 1.3370170203662352024859370738248 absolute error = 3.63969344343352e-17 relative error = 2.7222491471623425044008442798328e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.847 y[1] (analytic) = 1.3377659862022862932559083034306 y[1] (numeric) = 1.3377659862022863296850639461658 absolute error = 3.64291556427352e-17 relative error = 2.7231336435867994846733758992180e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.848 y[1] (analytic) = 1.3385156142722960319705437742155 y[1] (numeric) = 1.3385156142722960684318842109797 absolute error = 3.64613404367642e-17 relative error = 2.7240130819532464914139427552856e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.849 y[1] (analytic) = 1.3392659038266363746921740890535 y[1] (numeric) = 1.3392659038266364111856628732911 absolute error = 3.64934887842376e-17 relative error = 2.7248874685726012256544468046123e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.85 y[1] (analytic) = 1.3400168541150178296045839705385 y[1] (numeric) = 1.3400168541150178661301846235455 absolute error = 3.65256006530070e-17 relative error = 2.7257568097626250958416587060081e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=137.3MB, alloc=4.4MB, time=8.87 x[1] = 0.851 y[1] (analytic) = 1.3407684643864901709055071187424 y[1] (numeric) = 1.3407684643864902074631831297029 absolute error = 3.65576760109605e-17 relative error = 2.7266211118478676721675591128424e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.852 y[1] (analytic) = 1.3415207338894431897567894342973 y[1] (numeric) = 1.3415207338894432263465042603202 absolute error = 3.65897148260229e-17 relative error = 2.7274803811596038521920764805763e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.853 y[1] (analytic) = 1.3422736618716074458945352223685 y[1] (numeric) = 1.3422736618716074825162522885237 absolute error = 3.66217170661552e-17 relative error = 2.7283346240357190669769090370961e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.854 y[1] (analytic) = 1.3430272475800550198984847674316 y[1] (numeric) = 1.3430272475800550565521674667868 absolute error = 3.66536826993552e-17 relative error = 2.7291838468206767583366900518746e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.855 y[1] (analytic) = 1.3437814902612002661198710095412 y[1] (numeric) = 1.3437814902612003028054827031986 absolute error = 3.66856116936574e-17 relative error = 2.7300280558654338550929396993792e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.856 y[1] (analytic) = 1.3445363891608005662670023942965 y[1] (numeric) = 1.3445363891608006029845064114292 absolute error = 3.67175040171327e-17 relative error = 2.7308672575273416408736466019191e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.857 y[1] (analytic) = 1.3452919435239570836478183109831 y[1] (numeric) = 1.3452919435239571203971779488718 absolute error = 3.67493596378887e-17 relative error = 2.7317014581700915386963750624349e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.858 y[1] (analytic) = 1.3460481525951155180686628763995 y[1] (numeric) = 1.3460481525951155548498414004693 absolute error = 3.67811785240698e-17 relative error = 2.7325306641636462037635517198253e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.859 y[1] (analytic) = 1.3468050156180668613885221656564 y[1] (numeric) = 1.3468050156180668982014828095138 absolute error = 3.68129606438574e-17 relative error = 2.7333548818841782580478817271606e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.86 y[1] (analytic) = 1.3475625318359481537279693357761 y[1] (numeric) = 1.3475625318359481905726753012451 absolute error = 3.68447059654690e-17 relative error = 2.7341741177139275879185473836355e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.861 y[1] (analytic) = 1.3483207004912432403320614332074 y[1] (numeric) = 1.3483207004912432772084758903669 absolute error = 3.68764144571595e-17 relative error = 2.7349883780412222751608730440554e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.862 y[1] (analytic) = 1.3490795208257835290864310224247 y[1] (numeric) = 1.349079520825783565994517109645 absolute error = 3.69080860872203e-17 relative error = 2.7357976692603363705437962785945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.863 y[1] (analytic) = 1.3498389920807487486858151195816 y[1] (numeric) = 1.3498389920807487856255359435615 absolute error = 3.69397208239799e-17 relative error = 2.7366019977714592593639144544170e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.864 y[1] (analytic) = 1.3505991134966677074542632627533 y[1] (numeric) = 1.3505991134966677444255818985568 absolute error = 3.69713186358035e-17 relative error = 2.7374013699805910780200403678056e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.865 y[1] (analytic) = 1.3513598843134190528162658986232 y[1] (numeric) = 1.3513598843134190898191453897165 absolute error = 3.70028794910933e-17 relative error = 2.7381957922994902728309855686070e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.866 y[1] (analytic) = 1.3521213037702320314180436145485 y[1] (numeric) = 1.352121303770232068452446972837 absolute error = 3.70344033582885e-17 relative error = 2.7389852711455991390303715786423e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.867 y[1] (analytic) = 1.3528833711056872498982370947791 y[1] (numeric) = 1.3528833711056872869641273006442 absolute error = 3.70658902058651e-17 relative error = 2.7397698129419548191903656130732e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.868 y[1] (analytic) = 1.3536460855577174363072370302028 y[1] (numeric) = 1.353646085557717473404577032539 absolute error = 3.70973400023362e-17 relative error = 2.7405494241171375316378322225974e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.869 y[1] (analytic) = 1.3544094463636082021743925623504 y[1] (numeric) = 1.3544094463636082393031452786027 absolute error = 3.71287527162523e-17 relative error = 2.7413241111052189666903109908884e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.87 y[1] (analytic) = 1.3551734527599988052223361945172 y[1] (numeric) = 1.3551734527599988423824645107176 absolute error = 3.71601283162004e-17 relative error = 2.7420938803456223012918403493577e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.871 y[1] (analytic) = 1.3559381039828829127276624557362 y[1] (numeric) = 1.3559381039828829499191292265414 absolute error = 3.71914667708052e-17 relative error = 2.7428587382831375556644775204428e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.872 y[1] (analytic) = 1.3567033992676093655271969569926 y[1] (numeric) = 1.3567033992676094027499650057205 absolute error = 3.72227680487279e-17 relative error = 2.7436186913677599939104415417773e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.873 y[1] (analytic) = 1.3574693378488829426690918334692 y[1] (numeric) = 1.3574693378488829799231239521367 absolute error = 3.72540321186675e-17 relative error = 2.7443737460547132333975335134916e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.874 y[1] (analytic) = 1.3582359189607651267079829217956 y[1] (numeric) = 1.3582359189607651639932418711554 absolute error = 3.72852589493598e-17 relative error = 2.7451239088043029354849681829725e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=141.1MB, alloc=4.4MB, time=9.11 x[1] = 0.875 y[1] (analytic) = 1.359003141836674869643443377204 y[1] (numeric) = 1.359003141836674906959891886782 absolute error = 3.73164485095780e-17 relative error = 2.7458691860818887221961084397752e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.876 y[1] (analytic) = 1.3597710057093893595009677922045 y[1] (numeric) = 1.3597710057093893968485685603371 absolute error = 3.73476007681326e-17 relative error = 2.7466095843578047070897776296289e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.877 y[1] (analytic) = 1.3605395098110447875547202358586 y[1] (numeric) = 1.3605395098110448249334359297297 absolute error = 3.73787156938711e-17 relative error = 2.7473451101072655941765475783438e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.878 y[1] (analytic) = 1.3613086533731371161912789909656 y[1] (numeric) = 1.3613086533731371536010722466446 absolute error = 3.74097932556790e-17 relative error = 2.7480757698103685910955787017063e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.879 y[1] (analytic) = 1.3620784356265228474136101254846 y[1] (numeric) = 1.362078435626522884854443547963 absolute error = 3.74408334224784e-17 relative error = 2.7488015699519191150094978345872e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.88 y[1] (analytic) = 1.3628488558014197919845013942779 y[1] (numeric) = 1.3628488558014198294563375575071 absolute error = 3.74718361632292e-17 relative error = 2.7495225170214478672706288886954e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.881 y[1] (analytic) = 1.3636199131274078392086873278103 y[1] (numeric) = 1.3636199131274078767114887747391 absolute error = 3.75028014469288e-17 relative error = 2.7502386175131178510696669127575e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.882 y[1] (analytic) = 1.3643916068334297273528957257406 y[1] (numeric) = 1.3643916068334297648866249683524 absolute error = 3.75337292426118e-17 relative error = 2.7509498779256317070005185787441e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.883 y[1] (analytic) = 1.3651639361477918147030451354242 y[1] (numeric) = 1.3651639361477918522676646547746 absolute error = 3.75646195193504e-17 relative error = 2.7516563047621906423406429826258e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.884 y[1] (analytic) = 1.3659369002981648512578222581931 y[1] (numeric) = 1.3659369002981648888532945044474 absolute error = 3.75954722462543e-17 relative error = 2.7523579045304168990437236815457e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.885 y[1] (analytic) = 1.3667104985115847510578675899006 y[1] (numeric) = 1.3667104985115847886841549823715 absolute error = 3.76262873924709e-17 relative error = 2.7530546837422984402721693770534e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.886 y[1] (analytic) = 1.3674847300144533651497969666091 y[1] (numeric) = 1.3674847300144534028068618937941 absolute error = 3.76570649271850e-17 relative error = 2.7537466489140972668508077627597e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.887 y[1] (analytic) = 1.3682595940325392551842860514642 y[1] (numeric) = 1.3682595940325392928720908710832 absolute error = 3.76878048196190e-17 relative error = 2.7544338065662945941528073331121e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.888 y[1] (analytic) = 1.3690350897909784676474441647341 y[1] (numeric) = 1.3690350897909785053659512037672 absolute error = 3.77185070390331e-17 relative error = 2.7551161632235362223230362048845e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.889 y[1] (analytic) = 1.369811216514275308724703225707 y[1] (numeric) = 1.3698112165142753464738747804321 absolute error = 3.77491715547251e-17 relative error = 2.7557937254145488987446229489962e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.89 y[1] (analytic) = 1.3705879734263031197964469426198 y[1] (numeric) = 1.3705879734263031575762452786501 absolute error = 3.77797983360303e-17 relative error = 2.7564664996720642692925536190550e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.891 y[1] (analytic) = 1.3713653597503050535646047550548 y[1] (numeric) = 1.371365359750305091374992107377 absolute error = 3.78103873523222e-17 relative error = 2.7571344925328014333307635135595e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.892 y[1] (analytic) = 1.3721433747088948508094344022757 y[1] (numeric) = 1.3721433747088948886503729752873 absolute error = 3.78409385730116e-17 relative error = 2.7577977105373329619897560275535e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.893 y[1] (analytic) = 1.3729220175240576177757163607833 y[1] (numeric) = 1.3729220175240576556471683283307 absolute error = 3.78714519675474e-17 relative error = 2.7584561602300752060348647186132e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.894 y[1] (analytic) = 1.373701287417150604187582764963 y[1] (numeric) = 1.373701287417150642089510270379 absolute error = 3.79019275054160e-17 relative error = 2.7591098481591767336099829127390e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.895 y[1] (analytic) = 1.3744811836089039818912027960585 y[1] (numeric) = 1.3744811836089040198235679522006 absolute error = 3.79323651561421e-17 relative error = 2.7597587808765090160314564661391e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.896 y[1] (analytic) = 1.3752617053194216241245458968532 y[1] (numeric) = 1.375261705319421662087310786141 absolute error = 3.79627648892878e-17 relative error = 2.7604029649375335450800188706859e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.897 y[1] (analytic) = 1.3760428517681818854134435423582 y[1] (numeric) = 1.3760428517681819234065702168118 absolute error = 3.79931266744536e-17 relative error = 2.7610424069013074929016737777650e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.898 y[1] (analytic) = 1.3768246221740383820931696705131 y[1] (numeric) = 1.3768246221740384201166201517908 absolute error = 3.80234504812777e-17 relative error = 2.7616771133303658941481712851021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=144.9MB, alloc=4.4MB, time=9.36 x[1] = 0.899 y[1] (analytic) = 1.3776070157552207734547592513822 y[1] (numeric) = 1.3776070157552208115084955308183 absolute error = 3.80537362794361e-17 relative error = 2.7623070907906623155323509442103e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9 y[1] (analytic) = 1.3783900317293355435152838485929 y[1] (numeric) = 1.3783900317293355815992678872361 absolute error = 3.80839840386432e-17 relative error = 2.7629323458515460170521245417304e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.901 y[1] (analytic) = 1.3791736693133667834113024028072 y[1] (numeric) = 1.3791736693133668215254961314584 absolute error = 3.81141937286512e-17 relative error = 2.7635528850856521983191114339897e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.902 y[1] (analytic) = 1.3799579277236769744147048438388 y[1] (numeric) = 1.3799579277236770125590701630892 absolute error = 3.81443653192504e-17 relative error = 2.7641687150688578547563114152154e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.903 y[1] (analytic) = 1.380742806176007771570165515639 y[1] (numeric) = 1.3807428061760078097446642959082 absolute error = 3.81744987802692e-17 relative error = 2.7647798423802160741155038180496e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.904 y[1] (analytic) = 1.3815283038854807879534227767624 y[1] (numeric) = 1.3815283038854808261580168583365 absolute error = 3.82045940815741e-17 relative error = 2.7653862736018905748436326818427e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.905 y[1] (analytic) = 1.3823144200665983795496005180982 y[1] (numeric) = 1.3823144200665984177842517111682 absolute error = 3.82346511930700e-17 relative error = 2.7659880153191121889086069971163e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.906 y[1] (analytic) = 1.3831011539332444307507867196122 y[1] (numeric) = 1.3831011539332444690154568043117 absolute error = 3.82646700846995e-17 relative error = 2.7665850741200632108642299171638e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.907 y[1] (analytic) = 1.3838885046986851404720835485838 y[1] (numeric) = 1.3838885046986851787667342750277 absolute error = 3.82946507264439e-17 relative error = 2.7671774565958850034837208313468e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.908 y[1] (analytic) = 1.3846764715755698088853428833566 y[1] (numeric) = 1.3846764715755698472099359716791 absolute error = 3.83245930883225e-17 relative error = 2.7677651693405628255548971283166e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.909 y[1] (analytic) = 1.3854650537759316247698005289301 y[1] (numeric) = 1.3854650537759316631242976693231 absolute error = 3.83544971403930e-17 relative error = 2.7683482189508904693685204477299e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.91 y[1] (analytic) = 1.3862542505111884534788217738253 y[1] (numeric) = 1.3862542505111884918631846265766 absolute error = 3.83843628527513e-17 relative error = 2.7689266120263917585117414426913e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.911 y[1] (analytic) = 1.3870440609921436255219703215436 y[1] (numeric) = 1.3870440609921436639361605170752 absolute error = 3.84141901955316e-17 relative error = 2.7695003551692639646486658618680e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.912 y[1] (analytic) = 1.387834484428986725761612014616 y[1] (numeric) = 1.3878344844289867642055911535227 absolute error = 3.84439791389067e-17 relative error = 2.7700694549843358513737699131723e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.913 y[1] (analytic) = 1.3886255200312943832232641547054 y[1] (numeric) = 1.388625520031294421696993807793 absolute error = 3.84737296530876e-17 relative error = 2.7706339180789754752571900576274e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.914 y[1] (analytic) = 1.3894171670080310615189006084766 y[1] (numeric) = 1.3894171670080311000223423168004 absolute error = 3.85034417083238e-17 relative error = 2.7711937510630487067419541372034e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.915 y[1] (analytic) = 1.390209424567549849882422275997 y[1] (numeric) = 1.3902094245675498884155375509002 absolute error = 3.85331152749032e-17 relative error = 2.7717489605488491448528266374744e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.916 y[1] (analytic) = 1.3910022919175932548165018862618 y[1] (numeric) = 1.3910022919175932933792522094142 absolute error = 3.85627503231524e-17 relative error = 2.7722995531510570529303231685558e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.917 y[1] (analytic) = 1.3917957682652939923500114730661 y[1] (numeric) = 1.3917957682652940309423582965022 absolute error = 3.85923468234361e-17 relative error = 2.7728455354866337959154115686168e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.918 y[1] (analytic) = 1.3925898528171757809052402738607 y[1] (numeric) = 1.3925898528171758195271450200187 absolute error = 3.86219047461580e-17 relative error = 2.7733869141748243779797508554960e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.919 y[1] (analytic) = 1.3933845447791541347741101844421 y[1] (numeric) = 1.3933845447791541734255342462022 absolute error = 3.86514240617601e-17 relative error = 2.7739236958370451702388662935039e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.92 y[1] (analytic) = 1.3941798433565371582025952933256 y[1] (numeric) = 1.3941798433565371968835000340488 absolute error = 3.86809047407232e-17 relative error = 2.7744558870968581220952465241987e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.921 y[1] (analytic) = 1.3949757477540263400825514114488 y[1] (numeric) = 1.3949757477540263787928981650152 absolute error = 3.87103467535664e-17 relative error = 2.7749834945798734031986359802269e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.922 y[1] (analytic) = 1.3957722571757173492501609054418 y[1] (numeric) = 1.3957722571757173879899109762897 absolute error = 3.87397500708479e-17 relative error = 2.7755065249137455456786822735371e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=148.7MB, alloc=4.4MB, time=9.61 x[1] = 0.923 y[1] (analytic) = 1.3965693708251008303901975360864 y[1] (numeric) = 1.3965693708251008691593121992507 absolute error = 3.87691146631643e-17 relative error = 2.7760249847280622228718509174103e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.924 y[1] (analytic) = 1.3973670879050632005453153977649 y[1] (numeric) = 1.3973670879050632393437558989159 absolute error = 3.87984405011510e-17 relative error = 2.7765388806543121580167150025001e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.925 y[1] (analytic) = 1.3981654076178874462295654496762 y[1] (numeric) = 1.3981654076178874850572930051584 absolute error = 3.88277275554822e-17 relative error = 2.7770482193258245644067805883089e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.926 y[1] (analytic) = 1.3989643291652539211453425253694 y[1] (numeric) = 1.3989643291652539600023183222401 absolute error = 3.88569757968707e-17 relative error = 2.7775530073776945275791928236775e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.927 y[1] (analytic) = 1.3997638517482411445029651037137 y[1] (numeric) = 1.3997638517482411833891502997822 absolute error = 3.88861851960685e-17 relative error = 2.7780532514467658271075671896951e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.928 y[1] (analytic) = 1.4005639745673265999420895217925 y[1] (numeric) = 1.4005639745673266388574452456586 absolute error = 3.89153557238661e-17 relative error = 2.7785489581715210295619926150983e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.929 y[1] (analytic) = 1.4013646968223875350541597083728 y[1] (numeric) = 1.4013646968223875739986470594657 absolute error = 3.89444873510929e-17 relative error = 2.7790401341920504854970446475500e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.93 y[1] (analytic) = 1.402166017712701761505092915567 y[1] (numeric) = 1.4021660177127018004786729641844 absolute error = 3.89735800486174e-17 relative error = 2.7795267861500072022928652737774e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.931 y[1] (analytic) = 1.4029679364369484557574013260696 y[1] (numeric) = 1.4029679364369484947600351134164 absolute error = 3.90026337873468e-17 relative error = 2.7800089206885191388389303738383e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.932 y[1] (analytic) = 1.4037704521932089603909488139114 y[1] (numeric) = 1.4037704521932089994225973521388 absolute error = 3.90316485382274e-17 relative error = 2.7804865444521588244438818741600e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.933 y[1] (analytic) = 1.4045735641789675860215415380431 y[1] (numeric) = 1.4045735641789676250821658102876 absolute error = 3.90606242722445e-17 relative error = 2.7809596640868775187164881652275e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.934 y[1] (analytic) = 1.4053772715911124138165504502244 y[1] (numeric) = 1.4053772715911124529061114106466 absolute error = 3.90895609604222e-17 relative error = 2.7814282862399325169270382156095e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.935 y[1] (analytic) = 1.4061815736259360986067632016613 y[1] (numeric) = 1.4061815736259361377252217754854 absolute error = 3.91184585738241e-17 relative error = 2.7818924175598787436313765917215e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.936 y[1] (analytic) = 1.4069864694791366725936623366093 y[1] (numeric) = 1.4069864694791367117409794201616 absolute error = 3.91473170835523e-17 relative error = 2.7823520646964395858289107815148e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.937 y[1] (analytic) = 1.4077919583458183496513260657285 y[1] (numeric) = 1.4077919583458183888274625264771 absolute error = 3.91761364607486e-17 relative error = 2.7828072343005344791409996881145e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.938 y[1] (analytic) = 1.4085980394204923302221473173594 y[1] (numeric) = 1.4085980394204923694270639939527 absolute error = 3.92049166765933e-17 relative error = 2.7832579330241360545678026468112e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.939 y[1] (analytic) = 1.409404711897077606805566171065 y[1] (numeric) = 1.4094047118970776460392238733714 absolute error = 3.92336577023064e-17 relative error = 2.7837041675202980979295237493328e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.94 y[1] (analytic) = 1.410211974968901770039010184776 y[1] (numeric) = 1.4102119749689018093013696939228 absolute error = 3.92623595091468e-17 relative error = 2.7841459444430416291318522399771e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.941 y[1] (analytic) = 1.4110198278287018153702365346646 y[1] (numeric) = 1.4110198278287018546612586030773 absolute error = 3.92910220684127e-17 relative error = 2.7845832704473264561226539330395e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.942 y[1] (analytic) = 1.4118282696686249503202692954725 y[1] (numeric) = 1.4118282696686249896399146469141 absolute error = 3.93196453514416e-17 relative error = 2.7850161521889945338681173399150e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.943 y[1] (analytic) = 1.4126372996802294023361245984231 y[1] (numeric) = 1.4126372996802294416843539280333 absolute error = 3.93482293296102e-17 relative error = 2.7854445963247064786738701763649e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.944 y[1] (analytic) = 1.41344691705448522723251581406 y[1] (numeric) = 1.4134469170544852666092897883944 absolute error = 3.93767739743344e-17 relative error = 2.7858686095118854157653605440063e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.945 y[1] (analytic) = 1.4142571209817751182217303183736 y[1] (numeric) = 1.4142571209817751576270095754432 absolute error = 3.94052792570696e-17 relative error = 2.7862881984086822731410424009382e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.946 y[1] (analytic) = 1.4150679106518952155308688124071 y[1] (numeric) = 1.4150679106518952549646139617178 absolute error = 3.94337451493107e-17 relative error = 2.7867033696739200355450230725294e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=152.5MB, alloc=4.4MB, time=9.85 x[1] = 0.947 y[1] (analytic) = 1.4158792852540559166056375781701 y[1] (numeric) = 1.4158792852540559560678092007617 absolute error = 3.94621716225916e-17 relative error = 2.7871141299670029179265158697160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.948 y[1] (analytic) = 1.4166912439768826868998834671338 y[1] (numeric) = 1.4166912439768827263904421156198 absolute error = 3.94905586484860e-17 relative error = 2.7875204859479176563941881753507e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.949 y[1] (analytic) = 1.4175037860084168712500608318425 y[1] (numeric) = 1.4175037860084169107689670304492 absolute error = 3.95189061986067e-17 relative error = 2.7879224442771290176514311696376e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.95 y[1] (analytic) = 1.4183169105361165058338190262395 y[1] (numeric) = 1.4183169105361165453810332708458 absolute error = 3.95472142446063e-17 relative error = 2.7883200116155744192785126998448e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.951 y[1] (analytic) = 1.4191306167468571307118985161905 y[1] (numeric) = 1.4191306167468571702873812743671 absolute error = 3.95754827581766e-17 relative error = 2.7887131946245670067936041713016e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.952 y[1] (analytic) = 1.419944903826932602952523058373 y[1] (numeric) = 1.4199449038269326425562347694222 absolute error = 3.96037117110492e-17 relative error = 2.7891019999657836183438215238921e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.953 y[1] (analytic) = 1.4207597709620559103374748232099 y[1] (numeric) = 1.4207597709620559499693758982051 absolute error = 3.96319010749952e-17 relative error = 2.7894864343011894889692241854829e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.954 y[1] (analytic) = 1.4215752173373599856490387558386 y[1] (numeric) = 1.4215752173373600253090895776638 absolute error = 3.96600508218252e-17 relative error = 2.7898665042929843621134152587651e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.955 y[1] (analytic) = 1.4223912421373985215370018882395 y[1] (numeric) = 1.4223912421373985612251628116288 absolute error = 3.96881609233893e-17 relative error = 2.7902422166035488319665465208024e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.956 y[1] (analytic) = 1.4232078445461467859648927355918 y[1] (numeric) = 1.4232078445461468256811240871694 absolute error = 3.97162313515776e-17 relative error = 2.7906135778954260482296942908073e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.957 y[1] (analytic) = 1.4240250237470024382346453306867 y[1] (numeric) = 1.4240250237470024779789074090063 absolute error = 3.97442620783196e-17 relative error = 2.7909805948312262842838353708451e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.958 y[1] (analytic) = 1.4248427789227863455888718718004 y[1] (numeric) = 1.4248427789227863853611249473851 absolute error = 3.97722530755847e-17 relative error = 2.7913432740736090819653489345568e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.959 y[1] (analytic) = 1.4256611092557434003899273818234 y[1] (numeric) = 1.425661109255743440190131697205 absolute error = 3.98002043153816e-17 relative error = 2.7917016222851883478310617631329e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.96 y[1] (analytic) = 1.4264800139275433378749491996481 y[1] (numeric) = 1.4264800139275433777030649694075 absolute error = 3.98281157697594e-17 relative error = 2.7920556461285569981956138756960e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.961 y[1] (analytic) = 1.4272994921192815544860535488458 y[1] (numeric) = 1.4272994921192815943420409596522 absolute error = 3.98559874108064e-17 relative error = 2.7924053522661504238989231172196e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.962 y[1] (analytic) = 1.4281195430114799267748708535018 y[1] (numeric) = 1.4281195430114799666586900641529 absolute error = 3.98838192106511e-17 relative error = 2.7927507473602645222815484660859e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.963 y[1] (analytic) = 1.4289401657840876308806008967442 y[1] (numeric) = 1.4289401657840876707922120382058 absolute error = 3.99116111414616e-17 relative error = 2.7930918380729617449401238441872e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.964 y[1] (analytic) = 1.4297613596164819625807683439772 y[1] (numeric) = 1.4297613596164820025201315194232 absolute error = 3.99393631754460e-17 relative error = 2.7934286310660474600160836981897e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.965 y[1] (analytic) = 1.4305831236874691579138585801337 y[1] (numeric) = 1.4305831236874691978809338649861 absolute error = 3.99670752848524e-17 relative error = 2.7937611330010184850218747895319e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.966 y[1] (analytic) = 1.4314054571752852143730132383785 y[1] (numeric) = 1.4314054571752852543677606803471 absolute error = 3.99947474419686e-17 relative error = 2.7940893505389908885986730241902e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.967 y[1] (analytic) = 1.4322283592575967126699642266353 y[1] (numeric) = 1.4322283592575967526923438457577 absolute error = 4.00223796191224e-17 relative error = 2.7944132903406699842947217561736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.968 y[1] (analytic) = 1.4330518291115016390683844880724 y[1] (numeric) = 1.433051829111501679118356276754 absolute error = 4.00499717886816e-17 relative error = 2.7947329590662995443590975022818e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.969 y[1] (analytic) = 1.4338758659135302082858331622636 y[1] (numeric) = 1.4338758659135302483633570853178 absolute error = 4.00775239230542e-17 relative error = 2.7950483633756251880538403702358e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.97 y[1] (analytic) = 1.4347004688396456869634722451501 y[1] (numeric) = 1.434700468839645727068508239838 absolute error = 4.01050359946879e-17 relative error = 2.7953595099278091571493023077040e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=156.4MB, alloc=4.4MB, time=10.11 x[1] = 0.971 y[1] (analytic) = 1.4355256370652452177027312781524 y[1] (numeric) = 1.435525637065245257835239254223 absolute error = 4.01325079760706e-17 relative error = 2.7956664053814150981663571486684e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.972 y[1] (analytic) = 1.4363513697651606436680960298383 y[1] (numeric) = 1.4363513697651606838280358695688 absolute error = 4.01599398397305e-17 relative error = 2.7959690563943651012966093475331e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.973 y[1] (analytic) = 1.4371776661136593337551965674268 y[1] (numeric) = 1.4371776661136593739425281256624 absolute error = 4.01873315582356e-17 relative error = 2.7962674696238551917499831669037e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.974 y[1] (analytic) = 1.4380045252844450083233695501071 y[1] (numeric) = 1.4380045252844450485380526543014 absolute error = 4.02146831041943e-17 relative error = 2.7965616517263476606221965419045e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.975 y[1] (analytic) = 1.4388319464506585654918690116816 y[1] (numeric) = 1.4388319464506586057338634619366 absolute error = 4.02419944502550e-17 relative error = 2.7968516093574939750700576648748e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.976 y[1] (analytic) = 1.4396599287848789079988993363884 y[1] (numeric) = 1.4396599287848789482681649054948 absolute error = 4.02692655691064e-17 relative error = 2.7971373491721066309062823000041e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.977 y[1] (analytic) = 1.4404884714591237706226435689417 y[1] (numeric) = 1.4404884714591238109191400024189 absolute error = 4.02964964334772e-17 relative error = 2.7974188778240895041515675942701e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.978 y[1] (analytic) = 1.4413175736448505481634596378282 y[1] (numeric) = 1.4413175736448505884871466539649 absolute error = 4.03236870161367e-17 relative error = 2.7976962019664309404538967086592e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.979 y[1] (analytic) = 1.4421472345129571239864165097351 y[1] (numeric) = 1.4421472345129571643372537996294 absolute error = 4.03508372898943e-17 relative error = 2.7979693282511206483221666613767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.98 y[1] (analytic) = 1.4429774532337826991233417326401 y[1] (numeric) = 1.4429774532337827395012889602398 absolute error = 4.03779472275997e-17 relative error = 2.7982382633291154453046794142633e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.981 y[1] (analytic) = 1.4438082289771086219335512655861 y[1] (numeric) = 1.4438082289771086623385680677291 absolute error = 4.04050168021430e-17 relative error = 2.7985030138502982521165166431710e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.982 y[1] (analytic) = 1.4446395609121592183224319344801 y[1] (numeric) = 1.4446395609121592587544779209348 absolute error = 4.04320459864547e-17 relative error = 2.7987635864634303623128188582759e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.983 y[1] (analytic) = 1.4454714482076026225170462954026 y[1] (numeric) = 1.445471448207602662976081048908 absolute error = 4.04590347535054e-17 relative error = 2.7990199878160831787330815287517e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.984 y[1] (analytic) = 1.4463038900315516083979291298914 y[1] (numeric) = 1.4463038900315516488839122061979 absolute error = 4.04859830763065e-17 relative error = 2.7992722245546393842387107753136e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.985 y[1] (analytic) = 1.4471368855515644213862442404742 y[1] (numeric) = 1.4471368855515644618991351683839 absolute error = 4.05128909279097e-17 relative error = 2.7995203033242112433185188677212e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.986 y[1] (analytic) = 1.4479704339346456108854696593607 y[1] (numeric) = 1.4479704339346456514252279407677 absolute error = 4.05397582814070e-17 relative error = 2.7997642307685937743163852457289e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.987 y[1] (analytic) = 1.4488045343472468632767788286789 y[1] (numeric) = 1.4488045343472469038433639386102 absolute error = 4.05665851099313e-17 relative error = 2.8000040135302595547642218952852e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.988 y[1] (analytic) = 1.4496391859552678354672847569453 y[1] (numeric) = 1.4496391859552678760606561436008 absolute error = 4.05933713866555e-17 relative error = 2.8002396582502501288785418442477e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.989 y[1] (analytic) = 1.4504743879240569889903136035916 y[1] (numeric) = 1.4504743879240570296104306883851 absolute error = 4.06201170847935e-17 relative error = 2.8004711715681988402091751279308e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.99 y[1] (analytic) = 1.4513101394184124246568735913464 y[1] (numeric) = 1.4513101394184124653036957689458 absolute error = 4.06468221775994e-17 relative error = 2.8006985601222296185765455108838e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.991 y[1] (analytic) = 1.4521464396025827177574845950707 y[1] (numeric) = 1.452146439602582758430971233439 absolute error = 4.06734866383683e-17 relative error = 2.8009218305489663574635774816234e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.992 y[1] (analytic) = 1.4529832876402677538135332052885 y[1] (numeric) = 1.4529832876402677945136436457243 absolute error = 4.07001104404358e-17 relative error = 2.8011409894834528475539249660865e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.993 y[1] (analytic) = 1.4538206826946195648773175151265 y[1] (numeric) = 1.4538206826946196056040110723045 absolute error = 4.07266935571780e-17 relative error = 2.8013560435591074387787042498041e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.994 y[1] (analytic) = 1.4546586239282431663799453306873 y[1] (numeric) = 1.454658623928243207133181292699 absolute error = 4.07532359620117e-17 relative error = 2.8015669994076916681806531738709e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=160.2MB, alloc=4.4MB, time=10.35 x[1] = 0.995 y[1] (analytic) = 1.4554971105031973945262489570286 y[1] (numeric) = 1.4554971105031974353059865854232 absolute error = 4.07797376283946e-17 relative error = 2.8017738636592790567305962573527e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.996 y[1] (analytic) = 1.4563361415809957442358791649033 y[1] (numeric) = 1.4563361415809957850420776947282 absolute error = 4.08061985298249e-17 relative error = 2.8019766429421828754864747950088e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.997 y[1] (analytic) = 1.4571757163226072076297403972349 y[1] (numeric) = 1.4571757163226072484623590370769 absolute error = 4.08326186398420e-17 relative error = 2.8021753438829597109625527266021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.998 y[1] (analytic) = 1.4580158338884571130609287289657 y[1] (numeric) = 1.4580158338884571539199266609912 absolute error = 4.08589979320255e-17 relative error = 2.8023699731062964828347974079823e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.999 y[1] (analytic) = 1.4588564934384279646893335494061 y[1] (numeric) = 1.4588564934384280055746699294024 absolute error = 4.08853363799963e-17 relative error = 2.8025605372350418621616920097980e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1 y[1] (analytic) = 1.459697694131860282599063392557 y[1] (numeric) = 1.4596976941318603235106973499728 absolute error = 4.09116339574158e-17 relative error = 2.8027470428901074792482484943784e-15 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sin(x); Iterations = 1000 Total Elapsed Time = 10 Seconds Elapsed Time(since restart) = 10 Seconds Expected Time Remaining = 41 Seconds Optimized Time Remaining = 41 Seconds Time to Timeout = 14 Minutes 49 Seconds Percent Done = 20.02 % > quit memory used=161.1MB, alloc=4.4MB, time=10.41