|\^/| 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, > DEBUGL, > glob_iolevel, > ALWAYS, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_relerr, > glob_almost_1, > hours_in_day, > glob_max_opt_iter, > glob_iter, > glob_abserr, > glob_h, > glob_initial_pass, > min_in_hour, > glob_max_minutes, > MAX_UNCHANGED, > glob_start, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_last_good_h, > glob_dump, > glob_unchanged_h_cnt, > glob_max_iter, > glob_hmax, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_max_sec, > glob_warned, > glob_no_eqs, > glob_large_float, > days_in_year, > glob_optimal_expect_sec, > glob_current_iter, > glob_reached_optimal_h, > glob_small_float, > glob_clock_start_sec, > centuries_in_millinium, > sec_in_min, > glob_normmax, > glob_orig_start_sec, > glob_optimal_start, > glob_log10_abserr, > glob_not_yet_finished, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_log10_relerr, > glob_clock_sec, > years_in_century, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_last_rel_error, > array_norms, > array_y_init, > array_pole, > array_m1, > array_type_pole, > array_1st_rel_error, > array_fact_2, > array_y_higher_work, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_real_pole, > array_y_higher_work2, > array_poles, > 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, DEBUGL, glob_iolevel, ALWAYS, glob_max_terms, INFO, glob_relerr, glob_almost_1, hours_in_day, glob_max_opt_iter, glob_iter, glob_abserr, glob_h, glob_initial_pass, min_in_hour, glob_max_minutes, MAX_UNCHANGED, glob_start, glob_max_trunc_err, glob_max_rel_trunc_err, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_max_hours, glob_last_good_h, glob_dump, glob_unchanged_h_cnt, glob_max_iter, glob_hmax, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_max_sec, glob_warned, glob_no_eqs, glob_large_float, days_in_year, glob_optimal_expect_sec, glob_current_iter, glob_reached_optimal_h, glob_small_float, glob_clock_start_sec, centuries_in_millinium, sec_in_min, glob_normmax, glob_orig_start_sec, glob_optimal_start, glob_log10_abserr, glob_not_yet_finished, djd_debug, glob_log10normmin, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_log10_relerr, glob_clock_sec, years_in_century, djd_debug2, glob_log10abserr, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, array_const_0D0, array_const_1, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_y, array_x, array_last_rel_error, array_norms, array_y_init, array_pole, array_m1, array_type_pole, array_1st_rel_error, array_fact_2, array_y_higher_work, array_y_set_initial, array_y_higher, array_complex_pole, array_real_pole, array_y_higher_work2, array_poles, 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, > DEBUGL, > glob_iolevel, > ALWAYS, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_relerr, > glob_almost_1, > hours_in_day, > glob_max_opt_iter, > glob_iter, > glob_abserr, > glob_h, > glob_initial_pass, > min_in_hour, > glob_max_minutes, > MAX_UNCHANGED, > glob_start, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_last_good_h, > glob_dump, > glob_unchanged_h_cnt, > glob_max_iter, > glob_hmax, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_max_sec, > glob_warned, > glob_no_eqs, > glob_large_float, > days_in_year, > glob_optimal_expect_sec, > glob_current_iter, > glob_reached_optimal_h, > glob_small_float, > glob_clock_start_sec, > centuries_in_millinium, > sec_in_min, > glob_normmax, > glob_orig_start_sec, > glob_optimal_start, > glob_log10_abserr, > glob_not_yet_finished, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_log10_relerr, > glob_clock_sec, > years_in_century, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_last_rel_error, > array_norms, > array_y_init, > array_pole, > array_m1, > array_type_pole, > array_1st_rel_error, > array_fact_2, > array_y_higher_work, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_real_pole, > array_y_higher_work2, > array_poles, > 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, DEBUGL, glob_iolevel, ALWAYS, glob_max_terms, INFO, glob_relerr, glob_almost_1, hours_in_day, glob_max_opt_iter, glob_iter, glob_abserr, glob_h, glob_initial_pass, min_in_hour, glob_max_minutes, MAX_UNCHANGED, glob_start, glob_max_trunc_err, glob_max_rel_trunc_err, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_max_hours, glob_last_good_h, glob_dump, glob_unchanged_h_cnt, glob_max_iter, glob_hmax, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_max_sec, glob_warned, glob_no_eqs, glob_large_float, days_in_year, glob_optimal_expect_sec, glob_current_iter, glob_reached_optimal_h, glob_small_float, glob_clock_start_sec, centuries_in_millinium, sec_in_min, glob_normmax, glob_orig_start_sec, glob_optimal_start, glob_log10_abserr, glob_not_yet_finished, djd_debug, glob_log10normmin, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_log10_relerr, glob_clock_sec, years_in_century, djd_debug2, glob_log10abserr, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, array_const_0D0, array_const_1, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_y, array_x, array_last_rel_error, array_norms, array_y_init, array_pole, array_m1, array_type_pole, array_1st_rel_error, array_fact_2, array_y_higher_work, array_y_set_initial, array_y_higher, array_complex_pole, array_real_pole, array_y_higher_work2, array_poles, 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, > DEBUGL, > glob_iolevel, > ALWAYS, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_relerr, > glob_almost_1, > hours_in_day, > glob_max_opt_iter, > glob_iter, > glob_abserr, > glob_h, > glob_initial_pass, > min_in_hour, > glob_max_minutes, > MAX_UNCHANGED, > glob_start, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_last_good_h, > glob_dump, > glob_unchanged_h_cnt, > glob_max_iter, > glob_hmax, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_max_sec, > glob_warned, > glob_no_eqs, > glob_large_float, > days_in_year, > glob_optimal_expect_sec, > glob_current_iter, > glob_reached_optimal_h, > glob_small_float, > glob_clock_start_sec, > centuries_in_millinium, > sec_in_min, > glob_normmax, > glob_orig_start_sec, > glob_optimal_start, > glob_log10_abserr, > glob_not_yet_finished, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_log10_relerr, > glob_clock_sec, > years_in_century, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_last_rel_error, > array_norms, > array_y_init, > array_pole, > array_m1, > array_type_pole, > array_1st_rel_error, > array_fact_2, > array_y_higher_work, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_real_pole, > array_y_higher_work2, > array_poles, > 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, DEBUGL, glob_iolevel, ALWAYS, glob_max_terms, INFO, glob_relerr, glob_almost_1, hours_in_day, glob_max_opt_iter, glob_iter, glob_abserr, glob_h, glob_initial_pass, min_in_hour, glob_max_minutes, MAX_UNCHANGED, glob_start, glob_max_trunc_err, glob_max_rel_trunc_err, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_max_hours, glob_last_good_h, glob_dump, glob_unchanged_h_cnt, glob_max_iter, glob_hmax, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_max_sec, glob_warned, glob_no_eqs, glob_large_float, days_in_year, glob_optimal_expect_sec, glob_current_iter, glob_reached_optimal_h, glob_small_float, glob_clock_start_sec, centuries_in_millinium, sec_in_min, glob_normmax, glob_orig_start_sec, glob_optimal_start, glob_log10_abserr, glob_not_yet_finished, djd_debug, glob_log10normmin, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_log10_relerr, glob_clock_sec, years_in_century, djd_debug2, glob_log10abserr, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, array_const_0D0, array_const_1, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_y, array_x, array_last_rel_error, array_norms, array_y_init, array_pole, array_m1, array_type_pole, array_1st_rel_error, array_fact_2, array_y_higher_work, array_y_set_initial, array_y_higher, array_complex_pole, array_real_pole, array_y_higher_work2, array_poles, 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, > DEBUGL, > glob_iolevel, > ALWAYS, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_relerr, > glob_almost_1, > hours_in_day, > glob_max_opt_iter, > glob_iter, > glob_abserr, > glob_h, > glob_initial_pass, > min_in_hour, > glob_max_minutes, > MAX_UNCHANGED, > glob_start, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_last_good_h, > glob_dump, > glob_unchanged_h_cnt, > glob_max_iter, > glob_hmax, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_max_sec, > glob_warned, > glob_no_eqs, > glob_large_float, > days_in_year, > glob_optimal_expect_sec, > glob_current_iter, > glob_reached_optimal_h, > glob_small_float, > glob_clock_start_sec, > centuries_in_millinium, > sec_in_min, > glob_normmax, > glob_orig_start_sec, > glob_optimal_start, > glob_log10_abserr, > glob_not_yet_finished, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_log10_relerr, > glob_clock_sec, > years_in_century, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_last_rel_error, > array_norms, > array_y_init, > array_pole, > array_m1, > array_type_pole, > array_1st_rel_error, > array_fact_2, > array_y_higher_work, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_real_pole, > array_y_higher_work2, > array_poles, > 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, DEBUGL, glob_iolevel, ALWAYS, glob_max_terms, INFO, glob_relerr, glob_almost_1, hours_in_day, glob_max_opt_iter, glob_iter, glob_abserr, glob_h, glob_initial_pass, min_in_hour, glob_max_minutes, MAX_UNCHANGED, glob_start, glob_max_trunc_err, glob_max_rel_trunc_err, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_max_hours, glob_last_good_h, glob_dump, glob_unchanged_h_cnt, glob_max_iter, glob_hmax, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_max_sec, glob_warned, glob_no_eqs, glob_large_float, days_in_year, glob_optimal_expect_sec, glob_current_iter, glob_reached_optimal_h, glob_small_float, glob_clock_start_sec, centuries_in_millinium, sec_in_min, glob_normmax, glob_orig_start_sec, glob_optimal_start, glob_log10_abserr, glob_not_yet_finished, djd_debug, glob_log10normmin, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_log10_relerr, glob_clock_sec, years_in_century, djd_debug2, glob_log10abserr, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, array_const_0D0, array_const_1, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_y, array_x, array_last_rel_error, array_norms, array_y_init, array_pole, array_m1, array_type_pole, array_1st_rel_error, array_fact_2, array_y_higher_work, array_y_set_initial, array_y_higher, array_complex_pole, array_real_pole, array_y_higher_work2, array_poles, 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, > DEBUGL, > glob_iolevel, > ALWAYS, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_relerr, > glob_almost_1, > hours_in_day, > glob_max_opt_iter, > glob_iter, > glob_abserr, > glob_h, > glob_initial_pass, > min_in_hour, > glob_max_minutes, > MAX_UNCHANGED, > glob_start, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_last_good_h, > glob_dump, > glob_unchanged_h_cnt, > glob_max_iter, > glob_hmax, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_max_sec, > glob_warned, > glob_no_eqs, > glob_large_float, > days_in_year, > glob_optimal_expect_sec, > glob_current_iter, > glob_reached_optimal_h, > glob_small_float, > glob_clock_start_sec, > centuries_in_millinium, > sec_in_min, > glob_normmax, > glob_orig_start_sec, > glob_optimal_start, > glob_log10_abserr, > glob_not_yet_finished, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_log10_relerr, > glob_clock_sec, > years_in_century, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_last_rel_error, > array_norms, > array_y_init, > array_pole, > array_m1, > array_type_pole, > array_1st_rel_error, > array_fact_2, > array_y_higher_work, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_real_pole, > array_y_higher_work2, > array_poles, > 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, DEBUGL, glob_iolevel, ALWAYS, glob_max_terms, INFO, glob_relerr, glob_almost_1, hours_in_day, glob_max_opt_iter, glob_iter, glob_abserr, glob_h, glob_initial_pass, min_in_hour, glob_max_minutes, MAX_UNCHANGED, glob_start, glob_max_trunc_err, glob_max_rel_trunc_err, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_max_hours, glob_last_good_h, glob_dump, glob_unchanged_h_cnt, glob_max_iter, glob_hmax, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_max_sec, glob_warned, glob_no_eqs, glob_large_float, days_in_year, glob_optimal_expect_sec, glob_current_iter, glob_reached_optimal_h, glob_small_float, glob_clock_start_sec, centuries_in_millinium, sec_in_min, glob_normmax, glob_orig_start_sec, glob_optimal_start, glob_log10_abserr, glob_not_yet_finished, djd_debug, glob_log10normmin, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_log10_relerr, glob_clock_sec, years_in_century, djd_debug2, glob_log10abserr, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, array_const_0D0, array_const_1, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_y, array_x, array_last_rel_error, array_norms, array_y_init, array_pole, array_m1, array_type_pole, array_1st_rel_error, array_fact_2, array_y_higher_work, array_y_set_initial, array_y_higher, array_complex_pole, array_real_pole, array_y_higher_work2, array_poles, 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, > DEBUGL, > glob_iolevel, > ALWAYS, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_relerr, > glob_almost_1, > hours_in_day, > glob_max_opt_iter, > glob_iter, > glob_abserr, > glob_h, > glob_initial_pass, > min_in_hour, > glob_max_minutes, > MAX_UNCHANGED, > glob_start, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_last_good_h, > glob_dump, > glob_unchanged_h_cnt, > glob_max_iter, > glob_hmax, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_max_sec, > glob_warned, > glob_no_eqs, > glob_large_float, > days_in_year, > glob_optimal_expect_sec, > glob_current_iter, > glob_reached_optimal_h, > glob_small_float, > glob_clock_start_sec, > centuries_in_millinium, > sec_in_min, > glob_normmax, > glob_orig_start_sec, > glob_optimal_start, > glob_log10_abserr, > glob_not_yet_finished, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_log10_relerr, > glob_clock_sec, > years_in_century, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_last_rel_error, > array_norms, > array_y_init, > array_pole, > array_m1, > array_type_pole, > array_1st_rel_error, > array_fact_2, > array_y_higher_work, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_real_pole, > array_y_higher_work2, > array_poles, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre exp $eq_no = 1 i = 1 > array_tmp1[1] := exp(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre exp $eq_no = 1 i = 2 > array_tmp1[2] := att(1,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre exp $eq_no = 1 i = 3 > array_tmp1[3] := att(2,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre exp $eq_no = 1 i = 4 > array_tmp1[4] := att(3,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre exp $eq_no = 1 i = 5 > array_tmp1[5] := att(4,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit exp $eq_no = 1 > array_tmp1[kkk] := att(kkk-1,array_tmp1,array_x,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGMASSIVE, DEBUGL, glob_iolevel, ALWAYS, glob_max_terms, INFO, glob_relerr, glob_almost_1, hours_in_day, glob_max_opt_iter, glob_iter, glob_abserr, glob_h, glob_initial_pass, min_in_hour, glob_max_minutes, MAX_UNCHANGED, glob_start, glob_max_trunc_err, glob_max_rel_trunc_err, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_max_hours, glob_last_good_h, glob_dump, glob_unchanged_h_cnt, glob_max_iter, glob_hmax, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_max_sec, glob_warned, glob_no_eqs, glob_large_float, days_in_year, glob_optimal_expect_sec, glob_current_iter, glob_reached_optimal_h, glob_small_float, glob_clock_start_sec, centuries_in_millinium, sec_in_min, glob_normmax, glob_orig_start_sec, glob_optimal_start, glob_log10_abserr, glob_not_yet_finished, djd_debug, glob_log10normmin, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_log10_relerr, glob_clock_sec, years_in_century, djd_debug2, glob_log10abserr, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, array_const_0D0, array_const_1, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_y, array_x, array_last_rel_error, array_norms, array_y_init, array_pole, array_m1, array_type_pole, array_1st_rel_error, array_fact_2, array_y_higher_work, array_y_set_initial, array_y_higher, array_complex_pole, array_real_pole, array_y_higher_work2, array_poles, glob_last; array_tmp1[1] := exp(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := att(1, array_tmp1, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := att(2, array_tmp1, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := att(3, array_tmp1, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := att(4, array_tmp1, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := att(kkk - 1, array_tmp1, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > if (nnn <= glob_max_terms) then # if number 13 > ret := array_fact_1[nnn]; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; Warning, `ret` is implicitly declared local to procedure `factorial_1` factorial_1 := proc(nnn) local ret; if nnn <= glob_max_terms then ret := array_fact_1[nnn] else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > ret := array_fact_2[mmm,nnn]; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; Warning, `ret` is implicitly declared local to procedure `factorial_3` factorial_3 := proc(mmm, nnn) local ret; if nnn <= glob_max_terms and mmm <= glob_max_terms then ret := array_fact_2[mmm, nnn] else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0 + exp(x) > end; exact_soln_y := proc(x) 1.0 + exp(x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > DEBUGL, > glob_iolevel, > ALWAYS, > glob_max_terms, > INFO, > #Top Generate Globals Decl > glob_relerr, > glob_almost_1, > hours_in_day, > glob_max_opt_iter, > glob_iter, > glob_abserr, > glob_h, > glob_initial_pass, > min_in_hour, > glob_max_minutes, > MAX_UNCHANGED, > glob_start, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_look_poles, > glob_hmin, > glob_disp_incr, > glob_display_flag, > glob_html_log, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_max_hours, > glob_last_good_h, > glob_dump, > glob_unchanged_h_cnt, > glob_max_iter, > glob_hmax, > glob_not_yet_start_msg, > glob_curr_iter_when_opt, > glob_max_sec, > glob_warned, > glob_no_eqs, > glob_large_float, > days_in_year, > glob_optimal_expect_sec, > glob_current_iter, > glob_reached_optimal_h, > glob_small_float, > glob_clock_start_sec, > centuries_in_millinium, > sec_in_min, > glob_normmax, > glob_orig_start_sec, > glob_optimal_start, > glob_log10_abserr, > glob_not_yet_finished, > djd_debug, > glob_log10normmin, > glob_percent_done, > glob_log10relerr, > glob_smallish_float, > glob_log10_relerr, > glob_clock_sec, > years_in_century, > djd_debug2, > glob_log10abserr, > glob_warned2, > glob_dump_analytic, > glob_hmin_init, > glob_optimal_done, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_fact_1, > array_tmp0, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_last_rel_error, > array_norms, > array_y_init, > array_pole, > array_m1, > array_type_pole, > array_1st_rel_error, > array_fact_2, > array_y_higher_work, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_real_pole, > array_y_higher_work2, > array_poles, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > DEBUGL := 3; > glob_iolevel := 5; > ALWAYS := 1; > glob_max_terms := 30; > INFO := 2; > glob_relerr := 0.1e-10; > glob_almost_1 := 0.9990; > hours_in_day := 24.0; > glob_max_opt_iter := 10; > glob_iter := 0; > glob_abserr := 0.1e-10; > glob_h := 0.1; > glob_initial_pass := true; > min_in_hour := 60.0; > glob_max_minutes := 0.0; > MAX_UNCHANGED := 10; > glob_start := 0; > glob_max_trunc_err := 0.1e-10; > glob_max_rel_trunc_err := 0.1e-10; > glob_look_poles := false; > glob_hmin := 0.00000000001; > glob_disp_incr := 0.1; > glob_display_flag := true; > glob_html_log := true; > glob_subiter_method := 3; > glob_optimal_clock_start_sec := 0.0; > glob_max_hours := 0.0; > glob_last_good_h := 0.1; > glob_dump := false; > glob_unchanged_h_cnt := 0; > glob_max_iter := 1000; > glob_hmax := 1.0; > glob_not_yet_start_msg := true; > glob_curr_iter_when_opt := 0; > glob_max_sec := 10000.0; > glob_warned := false; > glob_no_eqs := 0; > glob_large_float := 9.0e100; > days_in_year := 365.0; > glob_optimal_expect_sec := 0.1; > glob_current_iter := 0; > glob_reached_optimal_h := false; > glob_small_float := 0.1e-50; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > sec_in_min := 60.0; > glob_normmax := 0.0; > glob_orig_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_log10_abserr := 0.1e-10; > glob_not_yet_finished := true; > djd_debug := true; > glob_log10normmin := 0.1; > glob_percent_done := 0.0; > glob_log10relerr := 0.0; > glob_smallish_float := 0.1e-100; > glob_log10_relerr := 0.1e-10; > glob_clock_sec := 0.0; > years_in_century := 100.0; > djd_debug2 := true; > glob_log10abserr := 0.0; > glob_warned2 := false; > glob_dump_analytic := false; > glob_hmin_init := 0.001; > glob_optimal_done := false; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/exppostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = exp ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 1.0;"); > omniout_str(ALWAYS,"x_end := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"1.0 + exp(x)"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > max_terms := 30; > Digits := 32; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_fact_1:= 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_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > 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_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_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_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_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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_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_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_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 > temp1 := iiif !; > temp2 := jjjf !; > array_fact_1[iiif] := temp1; > array_fact_2[iiif,jjjf] := temp1/temp2; > 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 := 1.0; > x_end := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > 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 ) = exp ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-16T21:59:55-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"exp") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = exp ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 091 ") > ; > logitem_str(html_log_file,"exp diffeq.mxt") > ; > logitem_str(html_log_file,"exp maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly for speeding 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; Warning, `iiif` is implicitly declared local to procedure `mainprog` Warning, `jjjf` is implicitly declared local to procedure `mainprog` Warning, `temp1` is implicitly declared local to procedure `mainprog` Warning, `temp2` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, iiif, jjjf, temp1, temp2; global DEBUGMASSIVE, DEBUGL, glob_iolevel, ALWAYS, glob_max_terms, INFO, glob_relerr, glob_almost_1, hours_in_day, glob_max_opt_iter, glob_iter, glob_abserr, glob_h, glob_initial_pass, min_in_hour, glob_max_minutes, MAX_UNCHANGED, glob_start, glob_max_trunc_err, glob_max_rel_trunc_err, glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_html_log, glob_subiter_method, glob_optimal_clock_start_sec, glob_max_hours, glob_last_good_h, glob_dump, glob_unchanged_h_cnt, glob_max_iter, glob_hmax, glob_not_yet_start_msg, glob_curr_iter_when_opt, glob_max_sec, glob_warned, glob_no_eqs, glob_large_float, days_in_year, glob_optimal_expect_sec, glob_current_iter, glob_reached_optimal_h, glob_small_float, glob_clock_start_sec, centuries_in_millinium, sec_in_min, glob_normmax, glob_orig_start_sec, glob_optimal_start, glob_log10_abserr, glob_not_yet_finished, djd_debug, glob_log10normmin, glob_percent_done, glob_log10relerr, glob_smallish_float, glob_log10_relerr, glob_clock_sec, years_in_century, djd_debug2, glob_log10abserr, glob_warned2, glob_dump_analytic, glob_hmin_init, glob_optimal_done, array_const_0D0, array_const_1, array_fact_1, array_tmp0, array_tmp1, array_tmp2, array_y, array_x, array_last_rel_error, array_norms, array_y_init, array_pole, array_m1, array_type_pole, array_1st_rel_error, array_fact_2, array_y_higher_work, array_y_set_initial, array_y_higher, array_complex_pole, array_real_pole, array_y_higher_work2, array_poles, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; DEBUGL := 3; glob_iolevel := 5; ALWAYS := 1; glob_max_terms := 30; INFO := 2; glob_relerr := 0.1*10^(-10); glob_almost_1 := 0.9990; hours_in_day := 24.0; glob_max_opt_iter := 10; glob_iter := 0; glob_abserr := 0.1*10^(-10); glob_h := 0.1; glob_initial_pass := true; min_in_hour := 60.0; glob_max_minutes := 0.; MAX_UNCHANGED := 10; glob_start := 0; glob_max_trunc_err := 0.1*10^(-10); glob_max_rel_trunc_err := 0.1*10^(-10); glob_look_poles := false; glob_hmin := 0.1*10^(-10); glob_disp_incr := 0.1; glob_display_flag := true; glob_html_log := true; glob_subiter_method := 3; glob_optimal_clock_start_sec := 0.; glob_max_hours := 0.; glob_last_good_h := 0.1; glob_dump := false; glob_unchanged_h_cnt := 0; glob_max_iter := 1000; glob_hmax := 1.0; glob_not_yet_start_msg := true; glob_curr_iter_when_opt := 0; glob_max_sec := 10000.0; glob_warned := false; glob_no_eqs := 0; glob_large_float := 0.90*10^101; days_in_year := 365.0; glob_optimal_expect_sec := 0.1; glob_current_iter := 0; glob_reached_optimal_h := false; glob_small_float := 0.1*10^(-50); glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; sec_in_min := 60.0; glob_normmax := 0.; glob_orig_start_sec := 0.; glob_optimal_start := 0.; glob_log10_abserr := 0.1*10^(-10); glob_not_yet_finished := true; djd_debug := true; glob_log10normmin := 0.1; glob_percent_done := 0.; glob_log10relerr := 0.; glob_smallish_float := 0.1*10^(-100); glob_log10_relerr := 0.1*10^(-10); glob_clock_sec := 0.; years_in_century := 100.0; djd_debug2 := true; glob_log10abserr := 0.; glob_warned2 := false; glob_dump_analytic := false; glob_hmin_init := 0.001; glob_optimal_done := false; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/exppostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 1.0;"); omniout_str(ALWAYS, "x_end := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "1.0 +\texp(x)"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; max_terms := 30; Digits := 32; glob_max_terms := max_terms; glob_html_log := true; array_fact_1 := 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_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); 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_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_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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_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_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_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 temp1 := iiif!; temp2 := jjjf!; array_fact_1[iiif] := temp1; array_fact_2[iiif, jjjf] := temp1/temp2; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 1.0; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_h := 0.001; 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 ) = exp ( x ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-16T21:59:55-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "exp"); logitem_str(html_log_file, "diff ( y , x , 1 ) = exp ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 091 "); logitem_str(html_log_file, "exp diffeq.mxt"); logitem_str(html_log_file, "exp maple results"); logitem_str(html_log_file, "Test of revised logic - mostly for speeding 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/exppostode.ode################# diff ( y , x , 1 ) = exp ( x ) ; ! #BEGIN FIRST INPUT BLOCK max_terms := 30; Digits := 32; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 1.0; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0 + exp(x) end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 1 y[1] (analytic) = 3.7182818284590452353602874713527 y[1] (numeric) = 3.7182818284590452353602874713527 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.001 y[1] (analytic) = 3.7210014698815787659270832730755 y[1] (numeric) = 3.7210014698815787660592478657163 absolute error = 1.321645926408e-19 relative error = 3.5518554268404024852199337764816e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.002 y[1] (analytic) = 3.7237238323058089282026934709967 y[1] (numeric) = 3.7237238323058089284671548869753 absolute error = 2.644614159786e-19 relative error = 7.1020684639451328825125368089241e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.003 y[1] (analytic) = 3.726448918454098373280823255358 y[1] (numeric) = 3.7264489184540983736777138576682 absolute error = 3.968906023102e-19 relative error = 1.0650638476344615867209846449000e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.004 y[1] (analytic) = 3.7291767310515334765414376314268 y[1] (numeric) = 3.7291767310515334770708899154916 absolute error = 5.294522840648e-19 relative error = 1.4197564831300120575009738071130e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.005 y[1] (analytic) = 3.7319072728259270627373638900002 y[1] (numeric) = 3.7319072728259270633995104838043 absolute error = 6.621465938041e-19 relative error = 1.7742846898301952926092618257928e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.006 y[1] (analytic) = 3.7346405465078211338073436779749 y[1] (numeric) = 3.7346405465078211346023173421973 absolute error = 7.949736642224e-19 relative error = 2.1286484049067643131465786198319e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.007 y[1] (analytic) = 3.7373765548304895994182624822638 y[1] (numeric) = 3.7373765548304896003461961104105 absolute error = 9.279336281467e-19 relative error = 2.4828475657540128400185660708560e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.008 y[1] (analytic) = 3.7401153005299410102392870695142 y[1] (numeric) = 3.7401153005299410113003136880515 absolute error = 1.0610266185373e-18 relative error = 2.8368821099899299437913521620847e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.009 y[1] (analytic) = 3.7428567863449212939506441559956 y[1] (numeric) = 3.7428567863449212951448969244824 absolute error = 1.1942527684868e-18 relative error = 3.1907519754530735336425858900753e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.01 y[1] (analytic) = 3.7456010150169164939897763166604 y[1] (numeric) = 3.745601015016916495317388527882 absolute error = 1.3276122112216e-18 relative error = 3.5444571002061307944106649588401e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.011 y[1] (analytic) = 3.748347989290155511037613879765 y[1] (numeric) = 3.7483479892901555124987189598661 absolute error = 1.4611050801011e-18 relative error = 3.8979974225333256713912698485350e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.012 y[1] (analytic) = 3.7510977119116128472477042935493 y[1] (numeric) = 3.7510977119116128488424358021675 absolute error = 1.5947315086182e-18 relative error = 4.2513728809413021081639918468126e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.013 y[1] (analytic) = 3.7538501856310113532209431943337 y[1] (numeric) = 3.7538501856310113549494348247329 absolute error = 1.7284916303992e-18 relative error = 4.6045834141584037640045549437544e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.014 y[1] (analytic) = 3.7566054132008249777286541509929 y[1] (numeric) = 3.7566054132008249795910397301973 absolute error = 1.8623855792044e-18 relative error = 4.9576289611358189975256175073641e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.015 y[1] (analytic) = 3.7593633973762815201867668091167 y[1] (numeric) = 3.7593633973762815221831802980444 absolute error = 1.9964134889277e-18 relative error = 5.3105094610460595030981999618964e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.016 y[1] (analytic) = 3.7621241409153653858838459092636 y[1] (numeric) = 3.7621241409153653880144214028606 absolute error = 2.1305754935970e-18 relative error = 5.6632248532835708065781948318822e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.017 y[1] (analytic) = 3.7648876465788203439657264075669 y[1] (numeric) = 3.7648876465788203462305981349413 absolute error = 2.2648717273744e-18 relative error = 6.0157750774648075647889800695076e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.44 NO POLE x[1] = 1.018 y[1] (analytic) = 3.7676539171301522881795126835586 y[1] (numeric) = 3.7676539171301522905788150081146 absolute error = 2.3993023245560e-18 relative error = 6.3681600734272455722875330332834e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.019 y[1] (analytic) = 3.7704229553356320003797025794385 y[1] (numeric) = 3.770422955335632002913569999011 absolute error = 2.5338674195725e-18 relative error = 6.7203797812305186039040262108193e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.02 y[1] (analytic) = 3.7731947639642979167991997771454 y[1] (numeric) = 3.7731947639642979194677669241345 absolute error = 2.6685671469891e-18 relative error = 7.0724341411556937674526362314428e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.021 y[1] (analytic) = 3.7759693457879588970879807844716 y[1] (numeric) = 3.7759693457879588998913824259769 absolute error = 2.8034016415053e-18 relative error = 7.4243230937042839163886133273449e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.022 y[1] (analytic) = 3.7787467035811969961221855691182 y[1] (numeric) = 3.778746703581196999060556607074 absolute error = 2.9383710379558e-18 relative error = 7.7760465796001741390682950024868e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.023 y[1] (analytic) = 3.7815268401213702385864036500145 y[1] (numeric) = 3.7815268401213702416598791213244 absolute error = 3.0734754713099e-18 relative error = 8.1276045397875718099808713699292e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.024 y[1] (analytic) = 3.784309758188615396331930228417 y[1] (numeric) = 3.7843097581886153995406453050892 absolute error = 3.2087150766722e-18 relative error = 8.4789969154323996107452111094608e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.025 y[1] (analytic) = 3.787095460565850768513769717277 y[1] (numeric) = 3.7870954605658507718578597065592 absolute error = 3.3440899892822e-18 relative error = 8.8302236479207765105228072337208e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.026 y[1] (analytic) = 3.7898839500387789645091668061106 y[1] (numeric) = 3.7898839500387789679887671506254 absolute error = 3.4796003445148e-18 relative error = 9.1812846788598788855500274090782e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.027 y[1] (analytic) = 3.7926752293958896896204479801354 y[1] (numeric) = 3.7926752293958896932356942580158 absolute error = 3.6152462778804e-18 relative error = 9.5321799500777418762099509698071e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.028 y[1] (analytic) = 3.795469301428462533564959196747 y[1] (numeric) = 3.7954693014284625373159871217719 absolute error = 3.7510279250249e-18 relative error = 9.8829094036227968420948681334882e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.029 y[1] (analytic) = 3.7982661689305697617548882095049 y[1] (numeric) = 3.7982661689305697656418336312349 absolute error = 3.8869454217300e-18 relative error = 1.0233472981764199387049013022675e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.03 y[1] (analytic) = 3.8010658346990791093697628196836 y[1] (numeric) = 3.8010658346990791133927617235969 absolute error = 4.0229989039133e-18 relative error = 1.0583870626991628461333800507542e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.031 y[1] (analytic) = 3.8038683015336565782244191281195 y[1] (numeric) = 3.8038683015336565823836076357477 absolute error = 4.1591885076282e-18 relative error = 1.0934102282014559260164117248218e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.032 y[1] (analytic) = 3.8066735722367692364352366555551 y[1] (numeric) = 3.8066735722367692407307510246193 absolute error = 4.2955143690642e-18 relative error = 1.1284167889762588811997535819323e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.033 y[1] (analytic) = 3.8094816496136880208874399979479 y[1] (numeric) = 3.8094816496136880253194166224953 absolute error = 4.4319766245474e-18 relative error = 1.1634067393386283826795164498629e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.034 y[1] (analytic) = 3.8122925364724905425062694842819 y[1] (numeric) = 3.8122925364724905470748448948218 absolute error = 4.5685754105399e-18 relative error = 1.1983800736255138078637672033167e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.035 y[1] (analytic) = 3.8151062356240638943348261082825 y[1] (numeric) = 3.8151062356240638990401369719231 absolute error = 4.7053108636406e-18 relative error = 1.2333367861959207125932562443730e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.036 y[1] (analytic) = 3.8179227498821074624213988121168 y[1] (numeric) = 3.8179227498821074672635819327017 absolute error = 4.8421831205849e-18 relative error = 1.2682768714307853344401021752874e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.037 y[1] (analytic) = 3.820742082063135739519085009639 y[1] (numeric) = 3.8207420820631357444982773278841 absolute error = 4.9791923182451e-18 relative error = 1.3032003237330327296925362017391e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.038 y[1] (analytic) = 3.8235642349864811416005180490368 y[1] (numeric) = 3.8235642349864811467168566426672 absolute error = 5.1163385936304e-18 relative error = 1.3381071375275299071614971306486e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.039 y[1] (analytic) = 3.8263892114742968271905181298406 y[1] (numeric) = 3.8263892114742968324441402137277 absolute error = 5.2536220838871e-18 relative error = 1.3729973072610913060158478096189e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.04 y[1] (analytic) = 3.8292170143515595195194860071813 y[1] (numeric) = 3.82921701435155952491052893348 absolute error = 5.3910429262987e-18 relative error = 1.4078708274024580024423997428967e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.041 y[1] (analytic) = 3.832047646446072331500361636926 y[1] (numeric) = 3.832047646446072337028962895212 absolute error = 5.5286012582860e-18 relative error = 1.4427276924422768762495018521059e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.042 y[1] (analytic) = 3.834881110588467593531972738885 y[1] (numeric) = 3.8348811105884675991982699562924 absolute error = 5.6662972174074e-18 relative error = 1.4775678968931318904525831981255e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.043 y[1] (analytic) = 3.8377174096122096841316010816751 y[1] (numeric) = 3.8377174096122096899357320230339 absolute error = 5.8041309413588e-18 relative error = 1.5123914352894708712821992570441e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.044 y[1] (analytic) = 3.8405565463535978633995971220407 y[1] (numeric) = 3.8405565463535978693416996900148 absolute error = 5.9421025679741e-18 relative error = 1.5471983021876887074717605419025e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.045 y[1] (analytic) = 3.843398523651769109318876463484 y[1] (numeric) = 3.8433985236517691153990886987087 absolute error = 6.0802122352247e-18 relative error = 1.5819884921659498617412271100100e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.046 y[1] (analytic) = 3.8462433443487009568921344339362 y[1] (numeric) = 3.8462433443487009631105945151567 absolute error = 6.2184600812205e-18 relative error = 1.6167619998244015274126634416453e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.047 y[1] (analytic) = 3.8490910112892143401196179199226 y[1] (numeric) = 3.8490910112892143464764641641318 absolute error = 6.3568462442092e-18 relative error = 1.6515188197849440443747323023050e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.048 y[1] (analytic) = 3.8519415273209764368202964352279 y[1] (numeric) = 3.851941527320976443315667297805 absolute error = 6.4953708625771e-18 relative error = 1.6862589466913916140904729068560e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=7.6MB, alloc=4.1MB, time=0.99 x[1] = 1.049 y[1] (analytic) = 3.8547948952945035162992772454722 y[1] (numeric) = 3.854794895294503522933311320321 absolute error = 6.6340340748488e-18 relative error = 1.7209823752093468098804684298691e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.05 y[1] (analytic) = 3.8576511180631637898643122162488 y[1] (numeric) = 3.8576511180631637966371482359362 absolute error = 6.7728360196874e-18 relative error = 1.7556891000262051231505070874175e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.051 y[1] (analytic) = 3.8605101984831802641942469015675 y[1] (numeric) = 3.8605101984831802711060237374625 absolute error = 6.9117768358950e-18 relative error = 1.7903791158512370664109658942131e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.052 y[1] (analytic) = 3.8633721394136335975622652412928 y[1] (numeric) = 3.8633721394136336046131219037052 absolute error = 7.0508566624124e-18 relative error = 1.8250524174154627051434387278947e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.053 y[1] (analytic) = 3.8662369437164649589167860910568 y[1] (numeric) = 3.8662369437164649661068617293763 absolute error = 7.1900756383195e-18 relative error = 1.8597089994717076676840200581456e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.054 y[1] (analytic) = 3.8691046142564788898228706657838 y[1] (numeric) = 3.8691046142564788971523045686189 absolute error = 7.3294339028351e-18 relative error = 1.8943488567945036981292957836730e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.055 y[1] (analytic) = 3.8719751539013461692670028384709 y[1] (numeric) = 3.8719751539013461767359344337885 absolute error = 7.4689315953176e-18 relative error = 1.9289719841802219569759174377644e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.056 y[1] (analytic) = 3.8748485655216066813281070992449 y[1] (numeric) = 3.8748485655216066889366759545096 absolute error = 7.6085688552647e-18 relative error = 1.9635783764469475207823702720283e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.057 y[1] (analytic) = 3.8777248519906722857176718459518 y[1] (numeric) = 3.8777248519906722934660176682654 absolute error = 7.7483458223136e-18 relative error = 1.9981680284344832469452682607227e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.058 y[1] (analytic) = 3.8806040161848296911918485466416 y[1] (numeric) = 3.8806040161848296990801111828829 absolute error = 7.8882626362413e-18 relative error = 2.0327409350043792565899646031491e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.059 y[1] (analytic) = 3.8834860609832433318384001862864 y[1] (numeric) = 3.8834860609832433398667196232512 absolute error = 8.0283194369648e-18 relative error = 2.0672970910399364019620197662997e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.06 y[1] (analytic) = 3.8863709892679582462413752849215 y[1] (numeric) = 3.8863709892679582544098916494622 absolute error = 8.1685163645407e-18 relative error = 2.1018364914460551979655562583124e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.061 y[1] (analytic) = 3.8892588039239029595263866521213 y[1] (numeric) = 3.8892588039239029678352402112873 absolute error = 8.3088535591660e-18 relative error = 2.1363591311493938337741046015819e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.062 y[1] (analytic) = 3.8921495078388923682893769233309 y[1] (numeric) = 3.8921495078388923767387080845088 absolute error = 8.4493311611779e-18 relative error = 2.1708650050982684192754426216116e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.063 y[1] (analytic) = 3.8950431039036306284117558070577 y[1] (numeric) = 3.8950431039036306370017051181118 absolute error = 8.5899493110541e-18 relative error = 2.2053541082626819088323052626979e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.064 y[1] (analytic) = 3.8979395950117140457647968583027 y[1] (numeric) = 3.8979395950117140544955050077154 absolute error = 8.7307081494127e-18 relative error = 2.2398264356342501430240297423508e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.065 y[1] (analytic) = 3.9008389840596339698061844828672 y[1] (numeric) = 3.9008389840596339786777922998797 absolute error = 8.8716078170125e-18 relative error = 2.2742819822262306269397074832123e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.066 y[1] (analytic) = 3.9037412739467796900716047693244 y[1] (numeric) = 3.9037412739467796990842532240776 absolute error = 9.0126484547532e-18 relative error = 2.3087207430735254288997452549609e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.067 y[1] (analytic) = 3.9066464675754413355642766404877 y[1] (numeric) = 3.9066464675754413447181068441632 absolute error = 9.1538302036755e-18 relative error = 2.3431427132326583335240138135980e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.068 y[1] (analytic) = 3.9095545678508127770453227141486 y[1] (numeric) = 3.9095545678508127863404759191097 absolute error = 9.2951532049611e-18 relative error = 2.3775478877817263828046188984422e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.069 y[1] (analytic) = 3.9124655776809945322278821636965 y[1] (numeric) = 3.9124655776809945416644997636295 absolute error = 9.4366175999330e-18 relative error = 2.4119362618204281759021673795726e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.07 y[1] (analytic) = 3.9153794999769966738778707729755 y[1] (numeric) = 3.9153794999769966834560943030313 absolute error = 9.5782235300558e-18 relative error = 2.4463078304700919072645249181572e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.071 y[1] (analytic) = 3.9182963376527417408242962863816 y[1] (numeric) = 3.9182963376527417505442674233168 absolute error = 9.7199711369352e-18 relative error = 2.4806625888734989732709965475296e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.072 y[1] (analytic) = 3.9212160936250676518820400647562 y[1] (numeric) = 3.9212160936250676617439006270751 absolute error = 9.8618605623189e-18 relative error = 2.5150005321950652625914206279988e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.073 y[1] (analytic) = 3.9241387708137306226900189701024 y[1] (numeric) = 3.9241387708137306326939109181987 absolute error = 1.00038919480963e-17 relative error = 2.5493216556207157020939412171652e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.074 y[1] (analytic) = 3.9270643721414080854676443175278 y[1] (numeric) = 3.9270643721414080956137097538268 absolute error = 1.01460654362990e-17 relative error = 2.5836259543579629410336859789663e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.075 y[1] (analytic) = 3.9299929005337016116924976511169 y[1] (numeric) = 3.9299929005337016219808788202172 absolute error = 1.02883811691003e-17 relative error = 2.6179134236357310942048231031575e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.076 y[1] (analytic) = 3.9329243589191398377021460216515 y[1] (numeric) = 3.9329243589191398481329853104674 absolute error = 1.04308392888159e-17 relative error = 2.6521840587044852528348933244430e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.077 y[1] (analytic) = 3.9358587502291813932230223682388 y[1] (numeric) = 3.9358587502291814037964623061429 absolute error = 1.05734399379041e-17 relative error = 2.6864378548362332437924924378454e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.078 y[1] (analytic) = 3.938796077398217832829299532972 y[1] (numeric) = 3.9387960773982178435454827919374 absolute error = 1.07161832589654e-17 relative error = 2.7206748073243749131504010468342e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.079 y[1] (analytic) = 3.9417363433635765703346893677405 y[1] (numeric) = 3.9417363433635765811937587624837 absolute error = 1.08590693947432e-17 relative error = 2.7548949114838310118932835671196e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.08 y[1] (analytic) = 3.9446795510655238161201013252344 y[1] (numeric) = 3.9446795510655238271221998133582 absolute error = 1.10020984881238e-17 relative error = 2.7890981626509939146257266708400e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=1.56 NO POLE x[1] = 1.081 y[1] (analytic) = 3.9476257034472675174000978620467 y[1] (numeric) = 3.9476257034472675285453685441828 absolute error = 1.11452706821361e-17 relative error = 2.8232845561836024264131515185204e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.082 y[1] (analytic) = 3.9505748034549603014310869205724 y[1] (numeric) = 3.9505748034549603127196730405248 absolute error = 1.12885861199524e-17 relative error = 2.8574540874608954536592025126206e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.083 y[1] (analytic) = 3.9535268540377024216641946981439 y[1] (numeric) = 3.953526854037702433096239643032 absolute error = 1.14320449448881e-17 relative error = 2.8916067518834866178838547408199e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.084 y[1] (analytic) = 3.9564818581475447068457648565196 y[1] (numeric) = 3.9564818581475447184214121569217 absolute error = 1.15756473004021e-17 relative error = 2.9257425448734162182301278665910e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.085 y[1] (analytic) = 3.9594398187394915130684332724717 y[1] (numeric) = 3.9594398187394915247878266025684 absolute error = 1.17193933300967e-17 relative error = 2.9598614618740765436949986027863e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.086 y[1] (analytic) = 3.9624007387715036787757303807931 y[1] (numeric) = 3.9624007387715036906390135585111 absolute error = 1.18632831777180e-17 relative error = 2.9939634983502635686472851348089e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.087 y[1] (analytic) = 3.9653646212045014827231661145728 y[1] (numeric) = 3.9653646212045014947304831017286 absolute error = 1.20073169871558e-17 relative error = 3.0280486497881021875794992472315e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.088 y[1] (analytic) = 3.9683314690023676048987554040703 y[1] (numeric) = 3.9683314690023676170502503065143 absolute error = 1.21514949024440e-17 relative error = 3.0621169116950976448281439963942e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.089 y[1] (analytic) = 3.9713012851319500904059451549626 y[1] (numeric) = 3.9713012851319501027017622227231 absolute error = 1.22958170677605e-17 relative error = 3.0961682796000606928503920637490e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.09 y[1] (analytic) = 3.9742740725630653163119065891359 y[1] (numeric) = 3.9742740725630653287521902165633 absolute error = 1.24402836274274e-17 relative error = 3.1302027490531084336812722804704e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.091 y[1] (analytic) = 3.9772498342685009614641597965635 y[1] (numeric) = 3.9772498342685009740490545224748 absolute error = 1.25848947259113e-17 relative error = 3.1642203156256901620050642806138e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.092 y[1] (analytic) = 3.9802285732240189792785003151405 y[1] (numeric) = 3.9802285732240189920081508229639 absolute error = 1.27296505078234e-17 relative error = 3.1982209749105627059407187409531e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.093 y[1] (analytic) = 3.9832102924083585735012005266506 y[1] (numeric) = 3.9832102924083585863757516445701 absolute error = 1.28745511179195e-17 relative error = 3.2322047225217406347892561439814e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.094 y[1] (analytic) = 3.9861949948032391769484616313138 y[1] (numeric) = 3.9861949948032391899680583324138 absolute error = 1.30195967011000e-17 relative error = 3.2661715540944465520837235101352e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.095 y[1] (analytic) = 3.9891826833933634332260949406148 y[1] (numeric) = 3.9891826833933634463908823430255 absolute error = 1.31647874024107e-17 relative error = 3.3001214652852620162525302535179e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.096 y[1] (analytic) = 3.9921733611664201814324142083434 y[1] (numeric) = 3.9921733611664201947425375753857 absolute error = 1.33101233670423e-17 relative error = 3.3340544517719520079805881605781e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.097 y[1] (analytic) = 3.9951670311130874438473237029863 y[1] (numeric) = 3.9951670311130874573029284433171 absolute error = 1.34556047403308e-17 relative error = 3.3679705092535153192085276973092e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.098 y[1] (analytic) = 3.9981636962270354166105897108083 y[1] (numeric) = 3.9981636962270354302118213785657 absolute error = 1.36012316677574e-17 relative error = 3.4018696334501095201067375892058e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.099 y[1] (analytic) = 4.0011633595049294633922861481429 y[1] (numeric) = 4.0011633595049294771392904430922 absolute error = 1.37470042949493e-17 relative error = 3.4357518201032010593112652357111e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.1 y[1] (analytic) = 4.0041660239464331120584079535887 y[1] (numeric) = 4.0041660239464331259513307212676 absolute error = 1.38929227676789e-17 relative error = 3.4696170649753149667401923360125e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.101 y[1] (analytic) = 4.0071716925542110543346489259728 y[1] (numeric) = 4.0071716925542110683736361578377 absolute error = 1.40389872318649e-17 relative error = 3.5034653638502596925601417820200e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.102 y[1] (analytic) = 4.0101803683339321484713436721111 y[1] (numeric) = 4.0101803683339321626565415056827 absolute error = 1.41851978335716e-17 relative error = 3.5372967125329019387896188297022e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.103 y[1] (analytic) = 4.0131920542942724249125763295557 y[1] (numeric) = 4.0131920542942724392441310485654 absolute error = 1.43315547190097e-17 relative error = 3.5711111068493161316707862874850e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104 y[1] (analytic) = 4.0162067534469180949724617336901 y[1] (numeric) = 4.0162067534469181094505197682262 absolute error = 1.44780580345361e-17 relative error = 3.6049085426466840915573727235363e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.105 y[1] (analytic) = 4.0192244688065685625216077057034 y[1] (numeric) = 4.0192244688065685771463156323574 absolute error = 1.46247079266540e-17 relative error = 3.6386890157932696559878872072480e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.106 y[1] (analytic) = 4.0222452033909394386867701481565 y[1] (numeric) = 4.02224520339093945345827469017 absolute error = 1.47715045420135e-17 relative error = 3.6724525221785175866056510618617e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.107 y[1] (analytic) = 4.0252689602207655595667156480479 y[1] (numeric) = 4.025268960220765574485163675459 absolute error = 1.49184480274111e-17 relative error = 3.7061990577128786174721557214225e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.108 y[1] (analytic) = 4.0282957423198040069673093034912 y[1] (numeric) = 4.0282957423198040220328478332815 absolute error = 1.50655385297903e-17 relative error = 3.7399286183279082199240926990425e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.109 y[1] (analytic) = 4.0313255527148371321588485093454 y[1] (numeric) = 4.0313255527148371473716247055872 absolute error = 1.52127761962418e-17 relative error = 3.7736411999762655603093030923188e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.11 y[1] (analytic) = 4.0343583944356755826586664593838 y[1] (numeric) = 4.0343583944356755980188276333868 absolute error = 1.53601611740030e-17 relative error = 3.8073367986315388126319306066626e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.111 y[1] (analytic) = 4.0373942705151613320420321478555 y[1] (numeric) = 4.0373942705151613475497257583146 absolute error = 1.55076936104591e-17 relative error = 3.8410154102884674141180223389637e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.112 y[1] (analytic) = 4.0404331839891707127843766815947 y[1] (numeric) = 4.0404331839891707284397503347372 absolute error = 1.56553736531425e-17 relative error = 3.8746770309627424321332556760007e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.2MB, time=2.13 NO POLE x[1] = 1.113 y[1] (analytic) = 4.0434751378966174521378787451541 y[1] (numeric) = 4.0434751378966174679410801948873 absolute error = 1.58032014497332e-17 relative error = 3.9083216566910550027804889718880e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.114 y[1] (analytic) = 4.0465201352794557110454450958028 y[1] (numeric) = 4.0465201352794557269966222438618 absolute error = 1.59511771480590e-17 relative error = 3.9419492835310949861530183630722e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.115 y[1] (analytic) = 4.0495681791826831260951250026217 y[1] (numeric) = 4.0495681791826831421944258987173 absolute error = 1.60993008960956e-17 relative error = 3.9755599075615247934088960715295e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.116 y[1] (analytic) = 4.052619272654343854518000584364 y[1] (numeric) = 4.0526192726543438707655734263308 absolute error = 1.62475728419668e-17 relative error = 4.0091535248819778669735097283740e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.117 y[1] (analytic) = 4.0556734187455316222325980442257 y[1] (numeric) = 4.0556734187455316386285911781703 absolute error = 1.63959931339446e-17 relative error = 4.0427301316130323703322236728140e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.118 y[1] (analytic) = 4.058730620510392774938867846191 y[1] (numeric) = 4.0587306205103927914834297666403 absolute error = 1.65445619204493e-17 relative error = 4.0762897238961848560340855461324e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.119 y[1] (analytic) = 4.0617908810061293322647849271863 y[1] (numeric) = 4.0617908810061293489580642772359 absolute error = 1.66932793500496e-17 relative error = 4.1098322978938239120768916332469e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.12 y[1] (analytic) = 4.0648542032930020449686230918988 y[1] (numeric) = 4.0648542032930020618107686633619 absolute error = 1.68421455714631e-17 relative error = 4.1433578497893021913570801194349e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.121 y[1] (analytic) = 4.0679205904343334551999607927883 y[1] (numeric) = 4.0679205904343334721911215263442 absolute error = 1.69911607335559e-17 relative error = 4.1768663757867867315217151433325e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.122 y[1] (analytic) = 4.0709900454965109598224785565521 y[1] (numeric) = 4.0709900454965109769628035418953 absolute error = 1.71403249853432e-17 relative error = 4.2103578721113554508143884407618e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.123 y[1] (analytic) = 4.0740625715489898768016113800976 y[1] (numeric) = 4.0740625715489898940912498560869 absolute error = 1.72896384759893e-17 relative error = 4.2438323350089457939345782558252e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.124 y[1] (analytic) = 4.0771381716642965146601224839288 y[1] (numeric) = 4.0771381716642965320992238387365 absolute error = 1.74391013548077e-17 relative error = 4.2772897607463279957957512970303e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.125 y[1] (analytic) = 4.080216848918031245004667878777 y[1] (numeric) = 4.0802168489180312625933816500383 absolute error = 1.75887137712613e-17 relative error = 4.3107301456111028336074078222816e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.126 y[1] (analytic) = 4.0832986063888715781264242722967 y[1] (numeric) = 4.0832986063888715958649001472591 absolute error = 1.77384758749624e-17 relative error = 4.3441534859116502679574370928369e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.127 y[1] (analytic) = 4.0863834471585752416788559167095 y[1] (numeric) = 4.0863834471585752595672437323828 absolute error = 1.78883878156733e-17 relative error = 4.3775597779772250042211035552913e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.128 y[1] (analytic) = 4.0894713743119832624356990754214 y[1] (numeric) = 4.0894713743119832804741488187272 absolute error = 1.80384497433058e-17 relative error = 4.4109490181577824965299760469980e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.129 y[1] (analytic) = 4.0925623909370230511322458668527 y[1] (numeric) = 4.0925623909370230693209076747747 absolute error = 1.81886618079220e-17 relative error = 4.4443212028241232472250733625214e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.13 y[1] (analytic) = 4.0956565001247114903930123270235 y[1] (numeric) = 4.0956565001247115087320364867574 absolute error = 1.83390241597339e-17 relative error = 4.4776763283677433182181531750472e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.131 y[1] (analytic) = 4.0987537049691580257488786188181 y[1] (numeric) = 4.0987537049691580442384155679219 absolute error = 1.84895369491038e-17 relative error = 4.5110143912008805588136346805502e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.132 y[1] (analytic) = 4.1018540085675677597467924053276 y[1] (numeric) = 4.1018540085675677783869927318722 absolute error = 1.86402003265446e-17 relative error = 4.5443353877565361035231051088356e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.133 y[1] (analytic) = 4.1049574140202445491551294972316 y[1] (numeric) = 4.1049574140202445679461439399512 absolute error = 1.87910144427196e-17 relative error = 4.5776393144883738264972380102687e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.134 y[1] (analytic) = 4.1080639244305941052678089798371 y[1] (numeric) = 4.1080639244305941242097884282801 absolute error = 1.89419794484430e-17 relative error = 4.6109261678707905062992758272317e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.135 y[1] (analytic) = 4.1111735429051270973102631241492 y[1] (numeric) = 4.1111735429051271164033586188289 absolute error = 1.90930954946797e-17 relative error = 4.6441959443988152630279318400678e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.136 y[1] (analytic) = 4.1142862725534622589503654882003 y[1] (numeric) = 4.1142862725534622781947282207463 absolute error = 1.92443627325460e-17 relative error = 4.6774486405882280593176290989084e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.137 y[1] (analytic) = 4.1174021164883294979174237198279 y[1] (numeric) = 4.1174021164883295173132050331368 absolute error = 1.93957813133089e-17 relative error = 4.7106842529753375013559251821831e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.138 y[1] (analytic) = 4.120521077825573008732346680149 y[1] (numeric) = 4.1205210778255730282796980685361 absolute error = 1.95473513883871e-17 relative error = 4.7439027781171720749181519653594e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.139 y[1] (analytic) = 4.1236431596841543885520986181606 y[1] (numeric) = 4.1236431596841544082511717275113 absolute error = 1.96990731093507e-17 relative error = 4.7771042125913551164248319750528e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.14 y[1] (analytic) = 4.1267683651861557561315562411795 y[1] (numeric) = 4.1267683651861557759825028691009 absolute error = 1.98509466279214e-17 relative error = 4.8102885529961013688264136927425e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.141 y[1] (analytic) = 4.1298966974567828739058876432372 y[1] (numeric) = 4.1298966974567828939088597392099 absolute error = 2.00029720959727e-17 relative error = 4.8434557959502134108439984054920e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.142 y[1] (analytic) = 4.1330281596243682731965751740702 y[1] (numeric) = 4.1330281596243682933517248396004 absolute error = 2.01551496655302e-17 relative error = 4.8766059380931021552647121059579e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.143 y[1] (analytic) = 4.1361627548203743825442074549888 y[1] (numeric) = 4.1361627548203744028516869437602 absolute error = 2.03074794887714e-17 relative error = 4.9097389760846862263102561182708e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.144 y[1] (analytic) = 4.1393004861793966591711688746769 y[1] (numeric) = 4.139300486179396679631130592703 absolute error = 2.04599617180261e-17 relative error = 4.9428549066054366034703876122624e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=2.71 NO POLE x[1] = 1.145 y[1] (analytic) = 4.1424413568391667235773580278727 y[1] (numeric) = 4.1424413568391667441899545336494 absolute error = 2.06125965057767e-17 relative error = 4.9759537263563967795567163013271e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.146 y[1] (analytic) = 4.1455853699405554972720696929117 y[1] (numeric) = 4.1455853699405555180374536975696 absolute error = 2.07653840046579e-17 relative error = 5.0090354320590579516651792494146e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.147 y[1] (analytic) = 4.1487325286275763436451780802733 y[1] (numeric) = 4.1487325286275763645635024477304 absolute error = 2.09183243674571e-17 relative error = 5.0421000204554033628627601782096e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.148 y[1] (analytic) = 4.1518828360473882119807622235773 y[1] (numeric) = 4.1518828360473882330521799706921 absolute error = 2.10714177471148e-17 relative error = 5.0751474883079522995938486034468e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.149 y[1] (analytic) = 4.1550362953502987846163175269177 y[1] (numeric) = 4.1550362953502988058409818236421 absolute error = 2.12246642967244e-17 relative error = 5.1081778323996593424959201232655e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.15 y[1] (analytic) = 4.1581929096897676272507006280068 y[1] (numeric) = 4.1581929096897676486287647975392 absolute error = 2.13780641695324e-17 relative error = 5.1411910495339101278142397818911e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.151 y[1] (analytic) = 4.1613526822224093424039578853379 y[1] (numeric) = 4.1613526822224093639355754042767 absolute error = 2.15316175189388e-17 relative error = 5.1741871365345650463875605566276e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.152 y[1] (analytic) = 4.1645156161079967260321909494573 y[1] (numeric) = 4.1645156161079967477175154479541 absolute error = 2.16853244984968e-17 relative error = 5.2071660902458345134820130104128e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.153 y[1] (analytic) = 4.1676817145094639273006160334744 y[1] (numeric) = 4.1676817145094639491398012953878 absolute error = 2.18391852619134e-17 relative error = 5.2401279075323706105525790453075e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.154 y[1] (analytic) = 4.1708509805929096115179766561321 y[1] (numeric) = 4.1708509805929096335111766191817 absolute error = 2.19931999630496e-17 relative error = 5.2730725852792622626752250400961e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.155 y[1] (analytic) = 4.1740234175276001262354727921153 y[1] (numeric) = 4.1740234175276001483828415480352 absolute error = 2.21473687559199e-17 relative error = 5.3060001203918625899447893454062e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.156 y[1] (analytic) = 4.177199028485972670513372528788 y[1] (numeric) = 4.1771990284859726928150643234811 absolute error = 2.23016917946931e-17 relative error = 5.3389105097959281153798453074939e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.157 y[1] (analytic) = 4.1803778166436384673584754962368 y[1] (numeric) = 4.1803778166436384898146447299293 absolute error = 2.24561692336925e-17 relative error = 5.3718037504376136673857575903041e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.158 y[1] (analytic) = 4.1835597851793859393356005083486 y[1] (numeric) = 4.1835597851793859619464017357438 absolute error = 2.26108012273952e-17 relative error = 5.4046798392832520332255730977970e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.159 y[1] (analytic) = 4.1867449372751838873562730266726 y[1] (numeric) = 4.186744937275183910121860957106 absolute error = 2.27655879304334e-17 relative error = 5.4375387733196121717092910245362e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.16 y[1] (analytic) = 4.1899332761161846726477912360218 y[1] (numeric) = 4.1899332761161846955683207336156 absolute error = 2.29205294975938e-17 relative error = 5.4703805495537026367174203026765e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.161 y[1] (analytic) = 4.1931248048907274019058527011435 y[1] (numeric) = 4.1931248048907274249814787849615 absolute error = 2.30756260838180e-17 relative error = 5.5032051650128142384796201687274e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.162 y[1] (analytic) = 4.1963195267903411156339267573512 y[1] (numeric) = 4.1963195267903411388648046015537 absolute error = 2.32308778442025e-17 relative error = 5.5360126167444670447430279214131e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.163 y[1] (analytic) = 4.199517445009747979672560974756 y[1] (numeric) = 4.1995174450097480030588459087552 absolute error = 2.33862849339992e-17 relative error = 5.5688029018164765410356794974462e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.164 y[1] (analytic) = 4.2027185627468664799218132256705 y[1] (numeric) = 4.2027185627468665034636607342857 absolute error = 2.35418475086152e-17 relative error = 5.6015760173168527857117338601396e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.165 y[1] (analytic) = 4.2059228832028146202600040778825 y[1] (numeric) = 4.2059228832028146439575698014955 absolute error = 2.36975657236130e-17 relative error = 5.6343319603537949849381583915114e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.166 y[1] (analytic) = 4.2091304095819131236619874328181 y[1] (numeric) = 4.209130409581913147515427167529 absolute error = 2.38534397347109e-17 relative error = 5.6670707280557334641193519787128e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.167 y[1] (analytic) = 4.2123411450916886365201405271318 y[1] (numeric) = 4.2123411450916886605296102249146 absolute error = 2.40094696977828e-17 relative error = 5.6997923175712288644546433600812e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.168 y[1] (analytic) = 4.2155550929428769361712776189791 y[1] (numeric) = 4.215555092942876960336933387838 absolute error = 2.41656557688589e-17 relative error = 5.7324967260690851505807105886237e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.169 y[1] (analytic) = 4.2187722563494261416326948861554 y[1] (numeric) = 4.2187722563494261659546929902804 absolute error = 2.43219981041250e-17 relative error = 5.7651839507381301068959240571564e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.17 y[1] (analytic) = 4.2219926385284999275505572724101 y[1] (numeric) = 4.2219926385284999520290541323337 absolute error = 2.44784968599236e-17 relative error = 5.7978539887874230317350774668288e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.171 y[1] (analytic) = 4.2252162427004807413638412305939 y[1] (numeric) = 4.2252162427004807659989934233475 absolute error = 2.46351521927536e-17 relative error = 5.8305068374461299933578144027091e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.172 y[1] (analytic) = 4.2284430720889730236870505268483 y[1] (numeric) = 4.2284430720889730484790147861184 absolute error = 2.47919642592701e-17 relative error = 5.8631424939634231604014934815532e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.173 y[1] (analytic) = 4.2316731299208064319149254888211 y[1] (numeric) = 4.2316731299208064568638587051064 absolute error = 2.49489332162853e-17 relative error = 5.8957609556086403929434211346263e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.174 y[1] (analytic) = 4.2349064194260390670523693028876 y[1] (numeric) = 4.2349064194260390921584285236559 absolute error = 2.51060592207683e-17 relative error = 5.9283622196711842124846668151650e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.175 y[1] (analytic) = 4.2381429438379607037728181905713 y[1] (numeric) = 4.2381429438379607290361606204162 absolute error = 2.52633424298449e-17 relative error = 5.9609462834604210887654198101703e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.176 y[1] (analytic) = 4.2413827063930960237082855228031 y[1] (numeric) = 4.2413827063930960491290685236015 memory used=22.8MB, alloc=4.2MB, time=3.28 absolute error = 2.54207830007984e-17 relative error = 5.9935131443058168151379357567836e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.177 y[1] (analytic) = 4.2446257103312078519743131623343 y[1] (numeric) = 4.2446257103312078775526942534036 absolute error = 2.55783810910693e-17 relative error = 6.0260627995568119678322525764143e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.178 y[1] (analytic) = 4.2478719588953003969330665595226 y[1] (numeric) = 4.2478719588953004226692034177785 absolute error = 2.57361368582559e-17 relative error = 6.0585952465829096609690067102143e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.179 y[1] (analytic) = 4.2511214553316224931978133648575 y[1] (numeric) = 4.2511214553316225190918638249713 absolute error = 2.58940504601138e-17 relative error = 6.0911104827735039989252233653754e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.18 y[1] (analytic) = 4.2543742028896708478820285629729 y[1] (numeric) = 4.2543742028896708739341506175296 absolute error = 2.60521220545567e-17 relative error = 6.1236085055380147373271404177237e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.181 y[1] (analytic) = 4.2576302048221932900963723775236 y[1] (numeric) = 4.2576302048221933163067241771799 absolute error = 2.62103517996563e-17 relative error = 6.1560893123058097964837182449771e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.182 y[1] (analytic) = 4.2608894643851920236967904441737 y[1] (numeric) = 4.2608894643851920500655302978158 absolute error = 2.63687398536421e-17 relative error = 6.1885529005261045148979972490662e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.183 y[1] (analytic) = 4.2641519848379268832869890000679 y[1] (numeric) = 4.2641519848379269098142753749703 absolute error = 2.65272863749024e-17 relative error = 6.2209992676681426354882458157229e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.184 y[1] (analytic) = 4.2674177694429185934785410925333 y[1] (numeric) = 4.267417769442918620164532614517 absolute error = 2.66859915219837e-17 relative error = 6.2534284112210013820381704915360e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.185 y[1] (analytic) = 4.2706868214659520314118830673888 y[1] (numeric) = 4.2706868214659520582567385209798 absolute error = 2.68448554535910e-17 relative error = 6.2858403286936080227537889436312e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.186 y[1] (analytic) = 4.2739591441760794925414638581296 y[1] (numeric) = 4.273959144176079519545342186718 absolute error = 2.70038783285884e-17 relative error = 6.3182350176148264051680589499109e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.187 y[1] (analytic) = 4.2772347408456239596883128614104 y[1] (numeric) = 4.2772347408456239868513731674091 absolute error = 2.71630603059987e-17 relative error = 6.3506124755333091519764295736997e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.188 y[1] (analytic) = 4.2805136147501823753632954516656 y[1] (numeric) = 4.2805136147501824026856969966696 absolute error = 2.73224015450040e-17 relative error = 6.3829727000175840062219555268604e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.189 y[1] (analytic) = 4.2837957691686289173643284583956 y[1] (numeric) = 4.2837957691686289448462306633411 absolute error = 2.74819022049455e-17 relative error = 6.4153156886559528839367401234785e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.19 y[1] (analytic) = 4.2870812073831182776508312036078 y[1] (numeric) = 4.2870812073831183052923936489316 absolute error = 2.76415624453238e-17 relative error = 6.4476414390565078738333644911353e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.191 y[1] (analytic) = 4.2903699326790889444986909741357 y[1] (numeric) = 4.2903699326790889723000733999349 absolute error = 2.78013824257992e-17 relative error = 6.4799499488471470177255205418913e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.192 y[1] (analytic) = 4.2936619483452664879390250840762 y[1] (numeric) = 4.2936619483452665159003873902679 absolute error = 2.79613623061917e-17 relative error = 6.5122412156755200018024208975302e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.193 y[1] (analytic) = 4.2969572576736668484840249663801 y[1] (numeric) = 4.2969572576736668766055272128613 absolute error = 2.81215022464812e-17 relative error = 6.5445152372090204958009704674524e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.194 y[1] (analytic) = 4.3002558639595996291431710197145 y[1] (numeric) = 4.3002558639595996574249734265222 absolute error = 2.82818024068077e-17 relative error = 6.5767720111347783812453300156330e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.195 y[1] (analytic) = 4.3035577705016713907331102270859 y[1] (numeric) = 4.3035577705016714191753731745573 absolute error = 2.84422629474714e-17 relative error = 6.6090115351596286325175324147413e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.196 y[1] (analytic) = 4.3068629806017889504844918563765 y[1] (numeric) = 4.3068629806017889790873758853092 absolute error = 2.86028840289327e-17 relative error = 6.6412338070100569759378069365052e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.197 y[1] (analytic) = 4.3101714975651626839490598499039 y[1] (numeric) = 4.3101714975651627127127256617167 absolute error = 2.87636658118128e-17 relative error = 6.6734388244322848582964380102963e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.198 y[1] (analytic) = 4.3134833247003098302103038103722 y[1] (numeric) = 4.3134833247003098591349122672657 absolute error = 2.89246084568935e-17 relative error = 6.7056265851921684129525507352106e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.199 y[1] (analytic) = 4.3167984653190578004009737941409 y[1] (numeric) = 4.3167984653190578294866859192583 absolute error = 2.90857121251174e-17 relative error = 6.7377970870751904054547288791483e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.2 y[1] (analytic) = 4.3201169227365474895307674296016 y[1] (numeric) = 4.3201169227365475187777444071899 absolute error = 2.92469769775883e-17 relative error = 6.7699503278864983649503187724673e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.201 y[1] (analytic) = 4.3234387002712365916275011886262 y[1] (numeric) = 4.3234387002712366210359043641971 absolute error = 2.94084031755709e-17 relative error = 6.8020863054507804851155697757712e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.202 y[1] (analytic) = 4.3267638012449029181950809525336 y[1] (numeric) = 4.326763801244902947765071833025 absolute error = 2.95699908804914e-17 relative error = 6.8342050176123499577284345681502e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.203 y[1] (analytic) = 4.3300922289826477199915903308224 y[1] (numeric) = 4.3300922289826477497233305847602 absolute error = 2.97317402539378e-17 relative error = 6.8663064622351594886447526702580e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204 y[1] (analytic) = 4.3334239868128990121308185110351 y[1] (numeric) = 4.3334239868128990420244699686943 absolute error = 2.98936514576592e-17 relative error = 6.8983906372025848351238463726878e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.205 y[1] (analytic) = 4.3367590780674149025105527415571 y[1] (numeric) = 4.336759078067414932566277395124 absolute error = 3.00557246535669e-17 relative error = 6.9304575404176242507329849704320e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.206 y[1] (analytic) = 4.3400975060812869235709638759227 y[1] (numeric) = 4.3400975060812869537889238796569 absolute error = 3.02179600037342e-17 relative error = 6.9625071698027973318592884185516e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.207 y[1] (analytic) = 4.3434392741929433673864167372895 y[1] (numeric) = 4.3434392741929433977667744076859 absolute error = 3.03803576703964e-17 relative error = 6.9945395233000902296158356508562e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=26.7MB, alloc=4.3MB, time=3.85 x[1] = 1.208 y[1] (analytic) = 4.3467843857441526240940403951701 y[1] (numeric) = 4.3467843857441526546369582111212 absolute error = 3.05429178159511e-17 relative error = 7.0265545988709699841507368159249e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.209 y[1] (analytic) = 4.3501328440800265236623967832695 y[1] (numeric) = 4.350132844080026554368037386228 absolute error = 3.07056406029585e-17 relative error = 7.0585523944963986460224906363074e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.21 y[1] (analytic) = 4.3534846525490236810035894273757 y[1] (numeric) = 4.3534846525490237118721156215172 absolute error = 3.08685261941415e-17 relative error = 7.0905329081768012449801756252400e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.211 y[1] (analytic) = 4.3568398145029528444321573956904 y[1] (numeric) = 4.356839814502952875463732148076 absolute error = 3.10315747523856e-17 relative error = 7.1224961379319878543439263218918e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.212 y[1] (analytic) = 4.360198333296976247474102930773 y[1] (numeric) = 4.3601983332969762786688893715124 absolute error = 3.11947864407394e-17 relative error = 7.1544420818012134765374826958965e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.213 y[1] (analytic) = 4.363560212289612964029404572405 y[1] (numeric) = 4.3635602122896129953875659948196 absolute error = 3.13581614224146e-17 relative error = 7.1863707378431229196474931203572e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.214 y[1] (analytic) = 4.3669254548427422668913709341673 y[1] (numeric) = 4.3669254548427422984130707949535 absolute error = 3.15216998607862e-17 relative error = 7.2182821041357415799155133246992e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.215 y[1] (analytic) = 4.3702940643216069896261936533644 y[1] (numeric) = 4.370294064321607021311595572757 absolute error = 3.16854019193926e-17 relative error = 7.2501761787764432377299561225271e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.216 y[1] (analytic) = 4.3736660440948168918160613941278 y[1] (numeric) = 4.3736660440948169236653291560639 absolute error = 3.18492677619361e-17 relative error = 7.2820529598820093115239316748562e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.217 y[1] (analytic) = 4.3770413975343520276692001470946 y[1] (numeric) = 4.3770413975343520596824976993769 absolute error = 3.20132975522823e-17 relative error = 7.3139124455884363787991883433410e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.218 y[1] (analytic) = 4.3804201280155661180002084359801 y[1] (numeric) = 4.3804201280155661501776998904411 absolute error = 3.21774914544610e-17 relative error = 7.3457546340510868724977657768967e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.219 y[1] (analytic) = 4.3838022389171899255840594116627 y[1] (numeric) = 4.3838022389171899579259090443289 absolute error = 3.23418496326662e-17 relative error = 7.3775795234446336321938197754252e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.22 y[1] (analytic) = 4.3871877336213346338871451880633 y[1] (numeric) = 4.3871877336213346663935174393195 absolute error = 3.25063722512562e-17 relative error = 7.4093871119630273572932422229927e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.221 y[1] (analytic) = 4.3905766155134952291787421511456 y[1] (numeric) = 4.390576615513495261849801625899 absolute error = 3.26710594747534e-17 relative error = 7.4411773978193957348235576186074e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.222 y[1] (analytic) = 4.3939688879825538860262793527837 y[1] (numeric) = 4.393968887982553918862190820629 absolute error = 3.28359114678453e-17 relative error = 7.4729503792462159882358020962956e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.223 y[1] (analytic) = 4.3973645544207833561777954850489 y[1] (numeric) = 4.3973645544207833891787238804326 absolute error = 3.30009283953837e-17 relative error = 7.5047060544950771437135979835983e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.224 y[1] (analytic) = 4.4007636182238503608349733176533 y[1] (numeric) = 4.400763618223850394001083740039 absolute error = 3.31661104223857e-17 relative error = 7.5364444218368522689325456871476e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.225 y[1] (analytic) = 4.4041660827908189863201438718694 y[1] (numeric) = 4.4041660827908190196516015859025 absolute error = 3.33314577140331e-17 relative error = 7.5681654795615064743487264170225e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.226 y[1] (analytic) = 4.4075719515241540831406559982103 y[1] (numeric) = 4.4075719515241541166376264338838 absolute error = 3.34969704356735e-17 relative error = 7.5998692259782913556045682632008e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.227 y[1] (analytic) = 4.4109812278297246684540104225264 y[1] (numeric) = 4.4109812278297247021166591753458 absolute error = 3.36626487528194e-17 relative error = 7.6315556594154849733853015663569e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.228 y[1] (analytic) = 4.4143939151168073319371607259328 y[1] (numeric) = 4.4143939151168073657656535570821 absolute error = 3.38284928311493e-17 relative error = 7.6632247782205859532182943237418e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.229 y[1] (analytic) = 4.4178100167980896450633871281557 y[1] (numeric) = 4.4178100167980896790578899646628 absolute error = 3.39945028365071e-17 relative error = 7.6948765807601217319650769900405e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.23 y[1] (analytic) = 4.4212295362896735737901523514522 y[1] (numeric) = 4.4212295362896736079508312863553 absolute error = 3.41606789349031e-17 relative error = 7.7265110654198194352130292274253e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.231 y[1] (analytic) = 4.4246524770110788946613522532473 y[1] (numeric) = 4.4246524770110789289883735457604 absolute error = 3.43270212925131e-17 relative error = 7.7581282306043464019974085083341e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.232 y[1] (analytic) = 4.4280788423852466143273773300196 y[1] (numeric) = 4.4280788423852466488209074056993 absolute error = 3.44935300756797e-17 relative error = 7.7897280747375485941441238879277e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.233 y[1] (analytic) = 4.431508635838542392486404612786 y[1] (numeric) = 4.4315086358385424271466100636976 absolute error = 3.46602054509116e-17 relative error = 7.8213105962622364381855698326537e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.234 y[1] (analytic) = 4.4349418608007599682503428957595 y[1] (numeric) = 4.4349418608007600030773904806437 absolute error = 3.48270475848842e-17 relative error = 7.8528757936402646389620844810745e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.235 y[1] (analytic) = 4.4383785207051245899388576644125 y[1] (numeric) = 4.4383785207051246249329143088522 absolute error = 3.49940566444397e-17 relative error = 7.8844236653524988211379713826054e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.236 y[1] (analytic) = 4.4418186189882964483049055172559 y[1] (numeric) = 4.441818618988296483466138313843 absolute error = 3.51612327965871e-17 relative error = 7.9159542098987596637186213153466e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.237 y[1] (analytic) = 4.4452621590903741131952113071546 y[1] (numeric) = 4.4452621590903741485237875156572 absolute error = 3.53285762085026e-17 relative error = 7.9474674257978571290930447550909e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.238 y[1] (analytic) = 4.4487091444548979736491246629424 y[1] (numeric) = 4.448709144454898009145211710472 absolute error = 3.54960870475296e-17 relative error = 7.9789633115875344710416342037198e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.239 y[1] (analytic) = 4.4521595785288536814392959904806 y[1] (numeric) = 4.4521595785288537171030614716595 absolute error = 3.56637654811789e-17 relative error = 8.0104418658244572762938086843145e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.3MB, time=4.43 x[1] = 1.24 y[1] (analytic) = 4.455613464762675598057615494122 y[1] (numeric) = 4.4556134647626756338892271712511 absolute error = 3.58316116771291e-17 relative error = 8.0419030870842472958144911012957e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.241 y[1] (analytic) = 4.4590708066102502451498622048078 y[1] (numeric) = 4.4590708066102502811494880080341 absolute error = 3.59996258032263e-17 relative error = 8.0733469739613589867628987993466e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.242 y[1] (analytic) = 4.4625316075289197584025134497329 y[1] (numeric) = 4.4625316075289197945703214772176 absolute error = 3.61678080274847e-17 relative error = 8.1047735250691581589538159168993e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.243 y[1] (analytic) = 4.4659958709794853448851686506773 y[1] (numeric) = 4.4659958709794853812213271687638 absolute error = 3.63361585180865e-17 relative error = 8.1361827390398433672986811098183e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.244 y[1] (analytic) = 4.4694636004262107438520447937159 y[1] (numeric) = 4.4694636004262107803567222370982 absolute error = 3.65046774433823e-17 relative error = 8.1675746145244793912353248876178e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.245 y[1] (analytic) = 4.4729347993368256910060043720902 y[1] (numeric) = 4.472934799336825727679369343981 absolute error = 3.66733649718908e-17 relative error = 8.1989491501928739129298434737938e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.246 y[1] (analytic) = 4.476409471182529386228580066558 y[1] (numeric) = 4.4764094711825294230708013388577 absolute error = 3.68422212722997e-17 relative error = 8.2303063447337226926402786380277e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.247 y[1] (analytic) = 4.4798876194379939647794638935359 y[1] (numeric) = 4.4798876194379940017907104070013 absolute error = 3.70112465134654e-17 relative error = 8.2616461968544860559446378401569e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.248 y[1] (analytic) = 4.4833692475813679719689320208126 y[1] (numeric) = 4.4833692475813680091493728852256 absolute error = 3.71804408644130e-17 relative error = 8.2929687052813327204875596288289e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.249 y[1] (analytic) = 4.4868543590942798413066799235461 y[1] (numeric) = 4.4868543590942798786564844178831 absolute error = 3.73498044943370e-17 relative error = 8.3242738687592397470684286001175e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.25 y[1] (analytic) = 4.4903429574618413761305460296723 y[1] (numeric) = 4.4903429574618414136498836022732 absolute error = 3.75193375726009e-17 relative error = 8.3555616860518469063052792592418e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.251 y[1] (analytic) = 4.4938350461726512347186054837364 y[1] (numeric) = 4.4938350461726512724076457524743 absolute error = 3.76890402687379e-17 relative error = 8.3868321559415563543359722788336e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.252 y[1] (analytic) = 4.4973306287187984188881191415326 y[1] (numeric) = 4.4973306287187984567470318939833 absolute error = 3.78589127524507e-17 relative error = 8.4180852772294315766419409646991e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.253 y[1] (analytic) = 4.5008297085958657660848263947917 y[1] (numeric) = 4.5008297085958658041137815884035 absolute error = 3.80289551936118e-17 relative error = 8.4493210487352077441448372752707e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.254 y[1] (analytic) = 4.5043322893029334449660739154997 y[1] (numeric) = 4.5043322893029334831652416777633 absolute error = 3.81991677622636e-17 relative error = 8.4805394692972574704723392053595e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.255 y[1] (analytic) = 4.5078383743425824544812759032684 y[1] (numeric) = 4.507838374342582492850826531887 absolute error = 3.83695506286186e-17 relative error = 8.5117405377725787634155524533494e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.256 y[1] (analytic) = 4.5113479672208981264532049165091 y[1] (numeric) = 4.511347967220898164993308879569 absolute error = 3.85401039630599e-17 relative error = 8.5429242530368493825545146403929e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.257 y[1] (analytic) = 4.5148610714474736316636158689929 y[1] (numeric) = 4.5148610714474736703744438051336 absolute error = 3.87108279361407e-17 relative error = 8.5740906139842593031912014550519e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.258 y[1] (analytic) = 4.5183776905354134894467092777124 y[1] (numeric) = 4.5183776905354135283284319962974 absolute error = 3.88817227185850e-17 relative error = 8.6052396195276093946417413696119e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.259 y[1] (analytic) = 4.5218978280013370807939433558024 y[1] (numeric) = 4.5218978280013371198467318370901 absolute error = 3.90527884812877e-17 relative error = 8.6363712685982768016330759583690e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.26 y[1] (analytic) = 4.5254214873653821649737080556228 y[1] (numeric) = 4.5254214873653822041977334509372 absolute error = 3.92240253953144e-17 relative error = 8.6674855601461140455214929203230e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.261 y[1] (analytic) = 4.5289486721512083996693776819714 y[1] (numeric) = 4.5289486721512084390648113138736 absolute error = 3.93954336319022e-17 relative error = 8.6985824931395692492008662500876e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.262 y[1] (analytic) = 4.5324793858860008646392622137731 y[1] (numeric) = 4.5324793858860009042062755762324 absolute error = 3.95670133624593e-17 relative error = 8.7296620665655408956734531635696e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.263 y[1] (analytic) = 4.5360136321004735889019809944896 y[1] (numeric) = 4.536013632100473628640745753055 absolute error = 3.97387647585654e-17 relative error = 8.7607242794294094816038255324743e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.264 y[1] (analytic) = 4.5395514143288730814507859769173 y[1] (numeric) = 4.5395514143288731213614739688893 absolute error = 3.99106879919720e-17 relative error = 8.7917691307550468453764030110890e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.265 y[1] (analytic) = 4.5430927361089818655003652369921 y[1] (numeric) = 4.5430927361089819055831484715943 absolute error = 4.00827832346022e-17 relative error = 8.8227966195847152448413814385390e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.266 y[1] (analytic) = 4.546637600982122016269661003697 y[1] (numeric) = 4.5466376009821220565247116622483 absolute error = 4.02550506585513e-17 relative error = 8.8538067449791427115192026892182e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.267 y[1] (analytic) = 4.5501860124931587023042399881873 y[1] (numeric) = 4.5501860124931587427317304242742 absolute error = 4.04274904360869e-17 relative error = 8.8847995060174880176698725966608e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.268 y[1] (analytic) = 4.5537379741905037303417573347981 y[1] (numeric) = 4.5537379741905037709418600744467 absolute error = 4.06001027396486e-17 relative error = 8.9157749017972178173289456013128e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.269 y[1] (analytic) = 4.5572934896261190937240590596928 y[1] (numeric) = 4.5572934896261191344969468015416 absolute error = 4.07728877418488e-17 relative error = 8.9467329314342255838812422059935e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.27 y[1] (analytic) = 4.5608525623555205243594713895519 y[1] (numeric) = 4.5608525623555205653053170050245 absolute error = 4.09458456154726e-17 relative error = 8.9776735940627525105054317116032e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.271 y[1] (analytic) = 4.5644151959377810482388289628871 y[1] (numeric) = 4.5644151959377810893578054963648 absolute error = 4.11189765334777e-17 relative error = 9.0085968888353086306880044730202e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.272 memory used=34.3MB, alloc=4.3MB, time=5.00 y[1] (analytic) = 4.5679813939355345445087974103041 y[1] (numeric) = 4.5679813939355345858010780792993 absolute error = 4.12922806689952e-17 relative error = 9.0395028149227911820995490061047e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.273 y[1] (analytic) = 4.5715511599149793081060493873352 y[1] (numeric) = 4.5715511599149793495718075826643 absolute error = 4.14657581953291e-17 relative error = 9.0703913715143178995190479171812e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.274 y[1] (analytic) = 4.5751244974458816159558566943127 y[1] (numeric) = 4.5751244974458816575952659802697 absolute error = 4.16394092859570e-17 relative error = 9.1012625578173232262715141371826e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.275 y[1] (analytic) = 4.578701410101579296738664682174 y[1] (numeric) = 4.5787014101015793385518987967041 absolute error = 4.18132341145301e-17 relative error = 9.1321163730575010439672181720524e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.276 y[1] (analytic) = 4.5822819014589853042282187110692 y[1] (numeric) = 4.5822819014589853462154515659423 absolute error = 4.19872328548731e-17 relative error = 9.1629528164787256972167017698647e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.277 y[1] (analytic) = 4.5858659750985912942048160001958 y[1] (numeric) = 4.5858659750985913363662216811806 absolute error = 4.21614056809848e-17 relative error = 9.1937718873431258816941302809532e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.278 y[1] (analytic) = 4.5894536346044712049472597824105 y[1] (numeric) = 4.5894536346044712472830125494486 absolute error = 4.23357527670381e-17 relative error = 9.2245735849310273018855991569172e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.279 y[1] (analytic) = 4.5930448835642848413070962558706 y[1] (numeric) = 4.5930448835642848838173705432507 absolute error = 4.25102742873801e-17 relative error = 9.2553579085409172195408329138076e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.28 y[1] (analytic) = 4.5966397255692814623687184072408 y[1] (numeric) = 4.5966397255692815050536888237731 absolute error = 4.26849704165323e-17 relative error = 9.2861248574894307735614215518678e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.281 y[1] (analytic) = 4.6002381642143033726989243668673 y[1] (numeric) = 4.6002381642143034155587656960582 absolute error = 4.28598413291909e-17 relative error = 9.3168744311113589523275959470665e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.282 y[1] (analytic) = 4.6038402030977895171895215457785 y[1] (numeric) = 4.6038402030977895602244087460051 absolute error = 4.30348872002266e-17 relative error = 9.3476066287595477737514410980642e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.283 y[1] (analytic) = 4.6074458458217790794965713974139 y[1] (numeric) = 4.6074458458217791227066796020994 absolute error = 4.32101082046855e-17 relative error = 9.3783214498050365325034582497695e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.284 y[1] (analytic) = 4.611055095991915084079873243628 y[1] (numeric) = 4.6110550959919151274653777614166 absolute error = 4.33855045177886e-17 relative error = 9.4090188936368916305496988893368e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.285 y[1] (analytic) = 4.6146679572174480018462892047514 y[1] (numeric) = 4.6146679572174480454073655196836 absolute error = 4.35610763149322e-17 relative error = 9.4396989596622360673979369056236e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.286 y[1] (analytic) = 4.6182844331112393594005158773358 y[1] (numeric) = 4.6182844331112394031373396490239 absolute error = 4.37368237716881e-17 relative error = 9.4703616473062353362120085124342e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.287 y[1] (analytic) = 4.6219045272897653519069120106541 y[1] (numeric) = 4.6219045272897653958196590744579 absolute error = 4.39127470638038e-17 relative error = 9.5010069560120832361626884421182e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.288 y[1] (analytic) = 4.6255282433731204595659950440859 y[1] (numeric) = 4.6255282433731205036548414112885 absolute error = 4.40888463672026e-17 relative error = 9.5316348852409659821860091796743e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.289 y[1] (analytic) = 4.6291555849850210677092229821847 y[1] (numeric) = 4.6291555849850211119743448401685 absolute error = 4.42651218579838e-17 relative error = 9.5622454344720479354790898593183e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.29 y[1] (analytic) = 4.6327865557528090905156817025115 y[1] (numeric) = 4.6327865557528091349572554149344 absolute error = 4.44415737124229e-17 relative error = 9.5928386032024572510570661782303e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.291 y[1] (analytic) = 4.6364211593074555983543014132237 y[1] (numeric) = 4.6364211593074556429725035201955 absolute error = 4.46182021069718e-17 relative error = 9.6234143909472714426933516531664e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.292 y[1] (analytic) = 4.6400593992835644487552296029379 y[1] (numeric) = 4.6400593992835644935502368211968 absolute error = 4.47950072182589e-17 relative error = 9.6539727972394813141168593292234e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.293 y[1] (analytic) = 4.6437012793193759210139914545421 y[1] (numeric) = 4.6437012793193759659859806776314 absolute error = 4.49719892230893e-17 relative error = 9.6845138216299764441941391547097e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.294 y[1] (analytic) = 4.6473468030567703544320723274211 y[1] (numeric) = 4.6473468030567703995812206258662 absolute error = 4.51491482984451e-17 relative error = 9.7150374636875521079689900374148e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.295 y[1] (analytic) = 4.6509959741412717901975605489803 y[1] (numeric) = 4.6509959741412718355240451704656 absolute error = 4.53264846214853e-17 relative error = 9.7455437229988300118454061143622e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.296 y[1] (analytic) = 4.6546487962220516169094923964141 y[1] (numeric) = 4.6546487962220516624134907659603 absolute error = 4.55039983695462e-17 relative error = 9.7760325991682866709660073723682e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.297 y[1] (analytic) = 4.658305272951932219749544793368 y[1] (numeric) = 4.6583052729519322654312345135097 absolute error = 4.56816897201417e-17 relative error = 9.8065040918182600360701414108569e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.298 y[1] (analytic) = 4.6619654079873906333047248934913 y[1] (numeric) = 4.6619654079873906791642837444544 absolute error = 4.58595588509631e-17 relative error = 9.8369582005888486878101945730395e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.299 y[1] (analytic) = 4.665629204988562198044709373874 y[1] (numeric) = 4.6656292049885622440823153137534 absolute error = 4.60376059398794e-17 relative error = 9.8673949251379185219602909455545e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.3 y[1] (analytic) = 4.6692966676192442204574899160115 y[1] (numeric) = 4.6692966676192442666733210809494 absolute error = 4.62158311649379e-17 relative error = 9.8978142651411735028121807295543e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.301 y[1] (analytic) = 4.6729677995468996368469850102494 y[1] (numeric) = 4.6729677995468996832412197146132 absolute error = 4.63942347043638e-17 relative error = 9.9282162202920119361567106192049e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.302 y[1] (analytic) = 4.6766426044426606807962818816229 y[1] (numeric) = 4.6766426044426607273690986181836 absolute error = 4.65728167365607e-17 relative error = 9.9586007903015757144196588501059e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.303 y[1] (analytic) = 4.6803210859813325543001760006409 y[1] (numeric) = 4.6803210859813326010517534407514 absolute error = 4.67515774401105e-17 relative error = 9.9889679748986709834609628829257e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304 y[1] (analytic) = 4.684003247841397102570679311858 y[1] (numeric) = 4.6840032478413971495011963056321 absolute error = 4.69305169937741e-17 memory used=38.1MB, alloc=4.3MB, time=5.57 relative error = 1.0019317773829859827030270871205e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.305 y[1] (analytic) = 4.6876890937050164925191719860508 y[1] (numeric) = 4.6876890937050165396288075625417 absolute error = 4.71096355764909e-17 relative error = 1.0049650186859295379087936075204e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.306 y[1] (analytic) = 4.6913786272580368949188761784555 y[1] (numeric) = 4.691378627258036942207809545835 absolute error = 4.72889333673795e-17 relative error = 1.0079965213768813351280335586134e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.307 y[1] (analytic) = 4.6950718521899921702513339558475 y[1] (numeric) = 4.6950718521899922177197445015853 absolute error = 4.74684105457378e-17 relative error = 1.0110262854357895185304418037534e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.308 y[1] (analytic) = 4.6987687721941075582405752392492 y[1] (numeric) = 4.6987687721941076058886425302922 absolute error = 4.76480672910430e-17 relative error = 1.0140543108443609946164577538019e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.309 y[1] (analytic) = 4.70246939096730337107866529674 y[1] (numeric) = 4.7024693909673034189065690796919 absolute error = 4.78279037829519e-17 relative error = 1.0170805975860620135363175228821e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.31 y[1] (analytic) = 4.7061737122101986903463250122245 y[1] (numeric) = 4.7061737122101987383542452135254 absolute error = 4.80079202013009e-17 relative error = 1.0201051456461123580322357747496e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.311 y[1] (analytic) = 4.7098817396271150676323208510871 y[1] (numeric) = 4.7098817396271151158204375771935 absolute error = 4.81881167261064e-17 relative error = 1.0231279550114880375548326595203e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.312 y[1] (analytic) = 4.7135934769260802288553251424314 y[1] (numeric) = 4.7135934769260802772238186799964 absolute error = 4.83684935375650e-17 relative error = 1.0261490256709197115892744754350e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.313 y[1] (analytic) = 4.7173089278188317822919510000733 y[1] (numeric) = 4.7173089278188318308410018161269 absolute error = 4.85490508160536e-17 relative error = 1.0291683576148889855090299137015e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.314 y[1] (analytic) = 4.721028096020820930314669910632 y[1] (numeric) = 4.7210280960208209790444586527614 absolute error = 4.87297887421294e-17 relative error = 1.0321859508356225906785771011069e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.315 y[1] (analytic) = 4.724750985251216184843323726945 y[1] (numeric) = 4.7247509852512162337540312234753 absolute error = 4.89107074965303e-17 relative error = 1.0352018053270950430677154654039e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.316 y[1] (analytic) = 4.7284775992329070865139465186297 y[1] (numeric) = 4.728477599232907135605753778805 absolute error = 4.90918072601753e-17 relative error = 1.0382159210850312742800607163162e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.317 y[1] (analytic) = 4.7322079416925079275686154489233 y[1] (numeric) = 4.7322079416925079768417036630872 absolute error = 4.92730882141639e-17 relative error = 1.0412282981068881032825692557653e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.318 y[1] (analytic) = 4.7359420163603614784700535679605 y[1] (numeric) = 4.7359420163603615279246041077378 absolute error = 4.94545505397773e-17 relative error = 1.0442389363918737878833498236720e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.319 y[1] (analytic) = 4.7396798269705427182447111374053 y[1] (numeric) = 4.7396798269705427678809055558829 absolute error = 4.96361944184776e-17 relative error = 1.0472478359409252718223593971034e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.32 y[1] (analytic) = 4.7434213772608625685580558298259 y[1] (numeric) = 4.7434213772608626183760758617348 absolute error = 4.98180200319089e-17 relative error = 1.0502549967567255798335345677702e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.321 y[1] (analytic) = 4.7471666709728716315258058784167 y[1] (numeric) = 4.7471666709728716815258334403134 absolute error = 5.00000275618967e-17 relative error = 1.0532604188436853045856909473004e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.322 y[1] (analytic) = 4.7509157118518639312648439886101 y[1] (numeric) = 4.7509157118518639814470611790587 absolute error = 5.01822171904486e-17 relative error = 1.0562641022079515292497689679558e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.323 y[1] (analytic) = 4.7546685036468806591875535628052 y[1] (numeric) = 4.7546685036468807095521426625595 absolute error = 5.03645890997543e-17 relative error = 1.0592660468574019704594934224954e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.324 y[1] (analytic) = 4.7584250501107139230433225328607 y[1] (numeric) = 4.7584250501107139735904660050464 absolute error = 5.05471434721857e-17 relative error = 1.0622662528016412354410837033867e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.325 y[1] (analytic) = 4.7621853549999104997109638421691 y[1] (numeric) = 4.7621853549999105504408443324662 absolute error = 5.07298804902971e-17 relative error = 1.0652647200519991816866911253780e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.326 y[1] (analytic) = 4.7659494220747755917458053700446 y[1] (numeric) = 4.7659494220747756426586057068701 absolute error = 5.09128003368255e-17 relative error = 1.0682614486215313675731436941110e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.327 y[1] (analytic) = 4.7697172550993765876852058458285 y[1] (numeric) = 4.7697172550993766387811090405194 absolute error = 5.10959031946909e-17 relative error = 1.0712564385250194857941484154776e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.328 y[1] (analytic) = 4.7734888578415468261162570585405 y[1] (numeric) = 4.7734888578415468773954463055367 absolute error = 5.12791892469962e-17 relative error = 1.0742496897789634000417526480156e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.329 y[1] (analytic) = 4.777264234072889363509436430093 y[1] (numeric) = 4.7772642340728894149720951071203 absolute error = 5.14626586770273e-17 relative error = 1.0772412024015773908332676582876e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.33 y[1] (analytic) = 4.7810433875687807458219777860331 y[1] (numeric) = 4.7810433875687807974682894542868 absolute error = 5.16463116682537e-17 relative error = 1.0802309764127968620703767955289e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.331 y[1] (analytic) = 4.7848263221083747838747319274995 y[1] (numeric) = 4.784826322108374835704880331828 absolute error = 5.18301484043285e-17 relative error = 1.0832190118342724611235032484293e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.332 y[1] (analytic) = 4.7886130414746063325062923815678 y[1] (numeric) = 4.7886130414746063845204614506562 absolute error = 5.20141690690884e-17 relative error = 1.0862053086893642116893018859968e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.333 y[1] (analytic) = 4.792403549454195073508165484426 y[1] (numeric) = 4.7924035494541951257065393309801 absolute error = 5.21983738465541e-17 relative error = 1.0891898670031440059540273954064e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.334 y[1] (analytic) = 4.7961978498376493023447677328647 y[1] (numeric) = 4.796197849837649354727530653795 absolute error = 5.23827629209303e-17 relative error = 1.0921726868023897299529370873640e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.335 y[1] (analytic) = 4.7999959464192697186620371243952 y[1] (numeric) = 4.7999959464192697712293736010014 absolute error = 5.25673364766062e-17 relative error = 1.0951537681155898184065897154862e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.336 y[1] (analytic) = 4.8037978429971532205884489949236 y[1] (numeric) = 4.8037978429971532733405436930788 absolute error = 5.27520946981552e-17 relative error = 1.0981331109729311193937892351495e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=6.14 NO POLE x[1] = 1.337 y[1] (analytic) = 4.8076035433731967028322306553107 y[1] (numeric) = 4.8076035433731967557692684256465 absolute error = 5.29370377703358e-17 relative error = 1.1011107154063117620006974373314e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.338 y[1] (analytic) = 4.811413051353100858578572924352 y[1] (numeric) = 4.8114130513531009117007388024429 absolute error = 5.31221658780909e-17 relative error = 1.1040865814493206935737605574814e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.339 y[1] (analytic) = 4.8152263707463739851906404557028 y[1] (numeric) = 4.8152263707463740384981196622515 absolute error = 5.33074792065487e-17 relative error = 1.1070607091372505269514990328846e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.34 y[1] (analytic) = 4.8190435053663357937181865600786 y[1] (numeric) = 4.8190435053663358472111645011011 absolute error = 5.34929779410225e-17 relative error = 1.1100330985070874855704271416954e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.341 y[1] (analytic) = 4.8228644590301212222175820316614 y[1] (numeric) = 4.8228644590301212758962442986725 absolute error = 5.36786622670111e-17 relative error = 1.1130037495975138219677202125651e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.342 y[1] (analytic) = 4.8266892355586842528870712990595 y[1] (numeric) = 4.8266892355586843067516036692582 absolute error = 5.38645323701987e-17 relative error = 1.1159726624488998506731789993333e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.343 y[1] (analytic) = 4.8305178387768017330210730363942 y[1] (numeric) = 4.8305178387768017870716614728497 absolute error = 5.40505884364555e-17 relative error = 1.1189398371033104950914439098001e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.344 y[1] (analytic) = 4.8343502725130771997873461891328 y[1] (numeric) = 4.8343502725130772540241768409706 absolute error = 5.42368306518378e-17 relative error = 1.1219052736045014455651644438348e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.345 y[1] (analytic) = 4.8381865405999447088308461921537 y[1] (numeric) = 4.8381865405999447632541053947412 absolute error = 5.44232592025875e-17 relative error = 1.1248689719979029192458265270699e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.346 y[1] (analytic) = 4.8420266468736726667080999842164 y[1] (numeric) = 4.8420266468736727213179742593497 absolute error = 5.46098742751333e-17 relative error = 1.1278309323306385914000210404846e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.347 y[1] (analytic) = 4.8458705951743676671559322535332 y[1] (numeric) = 4.8458705951743677219526083096235 absolute error = 5.47966760560903e-17 relative error = 1.1307911546515114038704231938870e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.348 y[1] (analytic) = 4.8497183893459783311983791834874 y[1] (numeric) = 4.8497183893459783861820439157477 absolute error = 5.49836647322603e-17 relative error = 1.1337496390110038597332270928090e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.349 y[1] (analytic) = 4.853570033236299151095629805732 y[1] (numeric) = 4.853570033236299206266470296364 absolute error = 5.51708404906320e-17 relative error = 1.1367063854612762411685424772812e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.35 y[1] (analytic) = 4.8574255306969743381388389099302 y[1] (numeric) = 4.8574255306969743934970424283114 absolute error = 5.53582035183812e-17 relative error = 1.1396613940561648207451402849612e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.351 y[1] (analytic) = 4.8612848855835016742946593052721 y[1] (numeric) = 4.861284885583501729840413308143 absolute error = 5.55457540028709e-17 relative error = 1.1426146648511780090801460255278e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.352 y[1] (analytic) = 4.8651481017552363677033450786199 y[1] (numeric) = 4.8651481017552364234368372102714 absolute error = 5.57334921316515e-17 relative error = 1.1455661979034945612093779513618e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.353 y[1] (analytic) = 4.8690151830753949120342813477067 y[1] (numeric) = 4.869015183075394967955699440168 absolute error = 5.59214180924613e-17 relative error = 1.1485159932719679378574849494665e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.354 y[1] (analytic) = 4.8728861334110589497027998652402 y[1] (numeric) = 4.8728861334110590058123319384664 absolute error = 5.61095320732262e-17 relative error = 1.1514640510171142134850237573791e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.355 y[1] (analytic) = 4.8767609566331791389521436910487 y[1] (numeric) = 4.8767609566331791952499779531089 absolute error = 5.62978342620602e-17 relative error = 1.1544103712011164311752360825886e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.356 y[1] (analytic) = 4.8806396566165790248044480145565 y[1] (numeric) = 4.8806396566165790812907728618221 absolute error = 5.64863248472656e-17 relative error = 1.1573549538878227750029266518568e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.357 y[1] (analytic) = 4.884522237239958913884608078892 y[1] (numeric) = 4.8845222372399589705596120962248 absolute error = 5.66750040173328e-17 relative error = 1.1602977991427365468937280220063e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.358 y[1] (analytic) = 4.888408702385899753120909030819 y[1] (numeric) = 4.8884087023858998099847809917601 absolute error = 5.68638719609411e-17 relative error = 1.1632389070330266327545947017908e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.359 y[1] (analytic) = 4.892299055940867012326296397445 y[1] (numeric) = 4.8922990559408670693792252644035 absolute error = 5.70529288669585e-17 relative error = 1.1661782776275174633797547816675e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.36 y[1] (analytic) = 4.8961933017952145706641697713002 y[1] (numeric) = 4.8961933017952146279063446957421 absolute error = 5.72421749244419e-17 relative error = 1.1691159109966871777271196604068e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.361 y[1] (analytic) = 4.9000914438431886070025861699043 y[1] (numeric) = 4.9000914438431886644341964925417 absolute error = 5.74316103226374e-17 relative error = 1.1720518072126678206852979625941e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.362 y[1] (analytic) = 4.9039934859829314941607634243494 y[1] (numeric) = 4.9039934859829315517819986753297 absolute error = 5.76212352509803e-17 relative error = 1.1749859663492394073762546232321e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.363 y[1] (analytic) = 4.9078994321164856970517778437259 y[1] (numeric) = 4.9078994321164857548628277428216 absolute error = 5.78110498990957e-17 relative error = 1.1779183884818362259073254908424e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.364 y[1] (analytic) = 4.9118092861497976747253542984159 y[1] (numeric) = 4.911809286149797732726408755214 absolute error = 5.80010544567981e-17 relative error = 1.1808490736875327358872579487985e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.365 y[1] (analytic) = 4.9157230519927217863146507653665 y[1] (numeric) = 4.9157230519927218445058998794586 absolute error = 5.81912491140921e-17 relative error = 1.1837780220450518963452101216304e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.366 y[1] (analytic) = 4.9196407335590242008909432824553 y[1] (numeric) = 4.9196407335590242592725773436279 absolute error = 5.83816340611726e-17 relative error = 1.1867052336347632755227507202506e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.367 y[1] (analytic) = 4.9235623347663868112301211669584 y[1] (numeric) = 4.9235623347663868698023306553828 absolute error = 5.85722094884244e-17 relative error = 1.1896307085386689682847873968469e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.368 y[1] (analytic) = 4.9274878595364111514949062649416 y[1] (numeric) = 4.9274878595364112102578818513644 absolute error = 5.87629755864228e-17 relative error = 1.1925544468404098600438509505898e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=6.71 NO POLE x[1] = 1.369 y[1] (analytic) = 4.9314173117946223188367139141204 y[1] (numeric) = 4.9314173117946223777906464600546 absolute error = 5.89539325459342e-17 relative error = 1.1954764486252718457634312331616e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.37 y[1] (analytic) = 4.9353506954704728989210772223787 y[1] (numeric) = 4.935350695470472958066157780294 absolute error = 5.91450805579153e-17 relative error = 1.1983967139801636373717226557475e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.371 y[1] (analytic) = 4.9392880144973468953805601876939 y[1] (numeric) = 4.9392880144973469547169800012082 absolute error = 5.93364198135143e-17 relative error = 1.2013152429936351538142501801342e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.372 y[1] (analytic) = 4.9432292728125636631990891127129 y[1] (numeric) = 4.9432292728125637227270396167833 absolute error = 5.95279505040704e-17 relative error = 1.2042320357558614177272012207797e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.373 y[1] (analytic) = 4.9471744743573818460316356986353 y[1] (numeric) = 4.9471744743573819057513085197496 absolute error = 5.97196728211143e-17 relative error = 1.2071470923586467275463924535169e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.374 y[1] (analytic) = 4.9511236230770033174631891384162 y[1] (numeric) = 4.9511236230770033773747760947846 absolute error = 5.99115869563684e-17 relative error = 1.2100604128954227354133217600686e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.375 y[1] (analytic) = 4.9550767229205771262109584685895 y[1] (numeric) = 4.9550767229205771863146515703363 absolute error = 6.01036931017468e-17 relative error = 1.2129719974612424829378380276150e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.376 y[1] (analytic) = 4.9590337778412034452737503822416 y[1] (numeric) = 4.9590337778412035055697418315973 absolute error = 6.02959914493557e-17 relative error = 1.2158818461527825165225671804535e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.377 y[1] (analytic) = 4.9629947917959375250324716528437 y[1] (numeric) = 4.9629947917959375855209538443372 absolute error = 6.04884821914935e-17 relative error = 1.2187899590683389327870682585885e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.378 y[1] (analytic) = 4.966959768745793650305709269774 y[1] (numeric) = 4.9669597687457937109868747904248 absolute error = 6.06811655206508e-17 relative error = 1.2216963363078214145462106849180e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.379 y[1] (analytic) = 4.9709287126557491013643453414388 y[1] (numeric) = 4.9709287126557491622383869709499 absolute error = 6.08740416295111e-17 relative error = 1.2246009779727613621759102935250e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.38 y[1] (analytic) = 4.9749016274947481189091677809396 y[1] (numeric) = 4.97490162749474817997627849189 absolute error = 6.10671107109504e-17 relative error = 1.2275038841662978600149568650492e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.381 y[1] (analytic) = 4.9788785172357058730154417522248 y[1] (numeric) = 4.9788785172357059342758147102628 absolute error = 6.12603729580380e-17 relative error = 1.2304050549931877967028168105291e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.382 y[1] (analytic) = 4.982859385855512436048410821631 y[1] (numeric) = 4.9828593858555124975022393856669 absolute error = 6.14538285640359e-17 relative error = 1.2333044905597878256987481957378e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.383 y[1] (analytic) = 4.9868442373350367595537007306426 y[1] (numeric) = 4.9868442373350368212011784530425 absolute error = 6.16474777223999e-17 relative error = 1.2362021909740704868506327711642e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.384 y[1] (analytic) = 4.9908330756591306551266026806085 y[1] (numeric) = 4.9908330756591307169679233073877 absolute error = 6.18413206267792e-17 relative error = 1.2390981563456101806093269122510e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.385 y[1] (analytic) = 4.9948259048166327792642169990288 y[1] (numeric) = 4.9948259048166328412995744700453 absolute error = 6.20353574710165e-17 relative error = 1.2419923867855792047150186469594e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.386 y[1] (analytic) = 4.9988227288003726222044420398869 y[1] (numeric) = 4.9988227288003726844340304890358 absolute error = 6.22295884491489e-17 relative error = 1.2448848824067597986494217573397e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.387 y[1] (analytic) = 5.0028235516071745007557971573507 y[1] (numeric) = 5.0028235516071745631798109127579 absolute error = 6.24240137554072e-17 relative error = 1.2477756433235241333639023663922e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.388 y[1] (analytic) = 5.0068283772378615551220725829952 y[1] (numeric) = 5.0068283772378616177407061672121 absolute error = 6.26186335842169e-17 relative error = 1.2506646696518483355117363112296e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.389 y[1] (analytic) = 5.010837209697259749725803031533 y[1] (numeric) = 5.0108372096972598125392511617308 absolute error = 6.28134481301978e-17 relative error = 1.2535519615092984899741006652741e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.39 y[1] (analytic) = 5.0148500529942018780345658588566 y[1] (numeric) = 5.014850052994201941043023447021 absolute error = 6.30084575881644e-17 relative error = 1.2564375190150326470742826489806e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.391 y[1] (analytic) = 5.0188669111415315713941085990267 y[1] (numeric) = 5.0188669111415316345977707521529 absolute error = 6.32036621531262e-17 relative error = 1.2593213422898008126790087707449e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.392 y[1] (analytic) = 5.0228877881561073118723147136667 y[1] (numeric) = 5.0228877881561073752713767339545 absolute error = 6.33990620202878e-17 relative error = 1.2622034314559409415338110714216e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.393 y[1] (analytic) = 5.026912688058806449118020398064 y[1] (numeric) = 5.0269126880588065127126777831131 absolute error = 6.35946573850491e-17 relative error = 1.2650837866373769240750092217113e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.394 y[1] (analytic) = 5.0309416148745292212386993031302 y[1] (numeric) = 5.0309416148745292850291477461356 absolute error = 6.37904484430054e-17 relative error = 1.2679624079596145801757126729723e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.395 y[1] (analytic) = 5.0349745726322027797010360512387 y[1] (numeric) = 5.0349745726322028436874714411866 absolute error = 6.39864353899479e-17 relative error = 1.2708392955497456015355114560954e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.396 y[1] (analytic) = 5.0390115653647852182584134468501 y[1] (numeric) = 5.0390115653647852824410318687136 absolute error = 6.41826184218635e-17 relative error = 1.2737144495364375684910649101531e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.397 y[1] (analytic) = 5.0430525971092696059093423097474 y[1] (numeric) = 5.0430525971092696702883400446825 absolute error = 6.43789977349351e-17 relative error = 1.2765878700499339143678173754638e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.398 y[1] (analytic) = 5.0470976719066880238908668896466 y[1] (numeric) = 5.0470976719066880884664404151888 absolute error = 6.45755735255422e-17 relative error = 1.2794595572220598190230757383992e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.399 y[1] (analytic) = 5.0511467938021156067109828559262 y[1] (numeric) = 5.0511467938021156714833288461869 absolute error = 6.47723459902607e-17 relative error = 1.2823295111862122210415580981855e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.4 y[1] (analytic) = 5.0551999668446745872241088952286 y[1] (numeric) = 5.0551999668446746521934242210914 absolute error = 6.49693153258628e-17 relative error = 1.2851977320773518410322370099763e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=7.28 NO POLE x[1] = 1.401 y[1] (analytic) = 5.0592571950875383457536569927423 y[1] (numeric) = 5.0592571950875384109201387220604 absolute error = 6.51664817293181e-17 relative error = 1.2880642200320189471913025777346e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.402 y[1] (analytic) = 5.063318482587935463265750520074 y[1] (numeric) = 5.0633184825879355286295959178669 absolute error = 6.53638453977929e-17 relative error = 1.2909289751883134802440575286073e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.403 y[1] (analytic) = 5.0673838334071537785981433037646 y[1] (numeric) = 5.0673838334071538441595498324156 absolute error = 6.55614065286510e-17 relative error = 1.2937919976859048599767168178183e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404 y[1] (analytic) = 5.071453251610544449748396903708 y[1] (numeric) = 5.0714532516105445155075622231614 absolute error = 6.57591653194534e-17 relative error = 1.2966532876660200395816485055160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.405 y[1] (analytic) = 5.0755267412675260192253773899867 y[1] (numeric) = 5.0755267412675260851824993579456 absolute error = 6.59571219679589e-17 relative error = 1.2995128452714493345967153819461e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.406 y[1] (analytic) = 5.0796043064515884834681369699611 y[1] (numeric) = 5.0796043064515885496234136420854 absolute error = 6.61552766721243e-17 relative error = 1.3023706706465443341817157982801e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.407 y[1] (analytic) = 5.0836859512402973663362498848331 y[1] (numeric) = 5.0836859512402974326898795149373 absolute error = 6.63536296301042e-17 relative error = 1.3052267639372079390972400359799e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.408 y[1] (analytic) = 5.0877716797152977966756760663581 y[1] (numeric) = 5.0877716797152978632278571066098 absolute error = 6.65521810402517e-17 relative error = 1.3080811252909021221049134944864e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.409 y[1] (analytic) = 5.091861495962318589964230119911 y[1] (numeric) = 5.091861495962318656715161221029 absolute error = 6.67509311011180e-17 relative error = 1.3109337548566340329117397229043e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.41 y[1] (analytic) = 5.0959554040711763340407372797126 y[1] (numeric) = 5.0959554040711764009906172911661 absolute error = 6.69498800114535e-17 relative error = 1.3137846527849715901273187081913e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.411 y[1] (analytic) = 5.100053408135779478921962065716 y[1] (numeric) = 5.1000534081357795460709900359229 absolute error = 6.71490279702069e-17 relative error = 1.3166338192280197678459657960470e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.412 y[1] (analytic) = 5.1041555122541324307113994594197 y[1] (numeric) = 5.1041555122541324980597746359458 absolute error = 6.73483751765261e-17 relative error = 1.3194812543394322468199502984195e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.413 y[1] (analytic) = 5.1082617205283396496040225077407 y[1] (numeric) = 5.1082617205283397171519443374993 absolute error = 6.75479218297586e-17 relative error = 1.3223269582744132064954854418479e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.414 y[1] (analytic) = 5.1123720370646097519910843600381 y[1] (numeric) = 5.112372037064609819738752489489 absolute error = 6.77476681294509e-17 relative error = 1.3251709311896995329704404286747e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.415 y[1] (analytic) = 5.1164864659732596166690768434283 y[1] (numeric) = 5.1164864659732596846166911187777 absolute error = 6.79476142753494e-17 relative error = 1.3280131732435724147034319136448e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.416 y[1] (analytic) = 5.1206050113687184951569517856954 y[1] (numeric) = 5.1206050113687185633047122530955 absolute error = 6.81477604674001e-17 relative error = 1.3308536845958454326368535685771e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.417 y[1] (analytic) = 5.1247276773695321261257154033581 y[1] (numeric) = 5.1247276773695321944738223091075 absolute error = 6.83481069057494e-17 relative error = 1.3336924654078741573022673452912e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.418 y[1] (analytic) = 5.1288544680983668539445101848329 y[1] (numeric) = 5.1288544680983669224931639755765 absolute error = 6.85486537907436e-17 relative error = 1.3365295158425403378637239046331e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.419 y[1] (analytic) = 5.1329853876820137513473028151164 y[1] (numeric) = 5.1329853876820138200967041380461 absolute error = 6.87494013229297e-17 relative error = 1.3393648360642614788205996063070e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.42 y[1] (analytic) = 5.1371204402513927462243008090194 y[1] (numeric) = 5.1371204402513928151746505120746 absolute error = 6.89503497030552e-17 relative error = 1.3421984262389808893890461227156e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.421 y[1] (analytic) = 5.1412596299415567525422246447136 y[1] (numeric) = 5.1412596299415568216937237767821 absolute error = 6.91514991320685e-17 relative error = 1.3450302865341694361920638805764e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.422 y[1] (analytic) = 5.1454029608916958053975663182059 y[1] (numeric) = 5.145402960891695874750416129325 absolute error = 6.93528498111191e-17 relative error = 1.3478604171188233855631262545603e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.423 y[1] (analytic) = 5.1495504372451412002069693723453 y[1] (numeric) = 5.149550437245141269761371313903 absolute error = 6.95544019415577e-17 relative error = 1.3506888181634602993615219792308e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.424 y[1] (analytic) = 5.1537020631493696360388695910856 y[1] (numeric) = 5.153702063149369705795025316022 absolute error = 6.97561557249364e-17 relative error = 1.3535154898401168759820118166615e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.425 y[1] (analytic) = 5.1578578427560073630905396909911 y[1] (numeric) = 5.157857842756007433048651054 absolute error = 6.99581113630089e-17 relative error = 1.3563404323223467868323812550889e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.426 y[1] (analytic) = 5.1620177802208343343146854873748 y[1] (numeric) = 5.1620177802208344044749545451059 absolute error = 7.01602690577311e-17 relative error = 1.3591636457852262572133756924318e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.427 y[1] (analytic) = 5.1661818797037883611997451620123 y[1] (numeric) = 5.1661818797037884315623741732728 absolute error = 7.03626290112605e-17 relative error = 1.3619851304053363772587393849407e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.428 y[1] (analytic) = 5.1703501453689692737080474130754 y[1] (numeric) = 5.1703501453689693442732388390325 absolute error = 7.05651914259571e-17 relative error = 1.3648048863607744949595228718765e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.429 y[1] (analytic) = 5.1745225813846430843759884257915 y[1] (numeric) = 5.1745225813846431551439449301749 absolute error = 7.07679565043834e-17 relative error = 1.3676229138311481462951819584108e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.43 y[1] (analytic) = 5.1786991919232461565803917643529 y[1] (numeric) = 5.1786991919232462275513162136574 absolute error = 7.09709244493045e-17 relative error = 1.3704392129975709306984028237073e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.431 y[1] (analytic) = 5.1828799811613893769752194517818 y[1] (numeric) = 5.18287998116138944814931491547 absolute error = 7.11740954636882e-17 relative error = 1.3732537840426583915072319330217e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.432 y[1] (analytic) = 5.1870649532798623321028066748111 y[1] (numeric) = 5.1870649532798624034802764255169 absolute error = 7.13774697507058e-17 relative error = 1.3760666271505373965184675517406e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=7.84 NO POLE x[1] = 1.433 y[1] (analytic) = 5.1912541124636374891837967253638 y[1] (numeric) = 5.1912541124636375607648442390952 absolute error = 7.15810475137314e-17 relative error = 1.3788777425068265634484727672323e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.434 y[1] (analytic) = 5.1954474629018743810899569689131 y[1] (numeric) = 5.195447462901874452874785925256 absolute error = 7.17848289563429e-17 relative error = 1.3816871302986494860838507625302e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.435 y[1] (analytic) = 5.1996450087879237955040608128896 y[1] (numeric) = 5.1996450087879238674928750952112 absolute error = 7.19888142823216e-17 relative error = 1.3844947907146209566090700175417e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.436 y[1] (analytic) = 5.2038467543193319682710248353648 y[1] (numeric) = 5.2038467543193320404640285310178 absolute error = 7.21930036956530e-17 relative error = 1.3873007239448562995171689416143e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.437 y[1] (analytic) = 5.2080527036978447809444944254994 y[1] (numeric) = 5.2080527036978448533418918260259 absolute error = 7.23973974005265e-17 relative error = 1.3901049301809595242700074848267e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.438 y[1] (analytic) = 5.2122628611294119625330754826903 y[1] (numeric) = 5.2122628611294120351350710840261 absolute error = 7.26019956013358e-17 relative error = 1.3929074096160249502226184357487e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.439 y[1] (analytic) = 5.2164772308241912954504139209989 y[1] (numeric) = 5.2164772308241913682572124236781 absolute error = 7.28067985026792e-17 relative error = 1.3957081624446368917676724850484e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.44 y[1] (analytic) = 5.2206958169965528256733289292909 y[1] (numeric) = 5.2206958169965528986851352386503 absolute error = 7.30118063093594e-17 relative error = 1.3985071888628597527954984818235e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.441 y[1] (analytic) = 5.2249186238650830771122101455705 y[1] (numeric) = 5.2249186238650831503292293719549 absolute error = 7.32170192263844e-17 relative error = 1.4013044890682492071849605019463e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.442 y[1] (analytic) = 5.2291456556525892701978931162592 y[1] (numeric) = 5.2291456556525893436203305752263 absolute error = 7.34224374589671e-17 relative error = 1.4041000632598384495435223191992e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.443 y[1] (analytic) = 5.2333769165861035446892316276445 y[1] (numeric) = 5.2333769165861036183172928401703 absolute error = 7.36280612125258e-17 relative error = 1.4068939116381416949306516424405e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.444 y[1] (analytic) = 5.2376124108968871867055897174241 y[1] (numeric) = 5.2376124108968872605394804101082 absolute error = 7.38338906926841e-17 relative error = 1.4096860344051461911180650494252e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.445 y[1] (analytic) = 5.2418521428204348599884803991883 y[1] (numeric) = 5.24185214282043493402840650446 absolute error = 7.40399261052717e-17 relative error = 1.4124764317643214241712219901862e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.446 y[1] (analytic) = 5.2460961165964788413965823618339 y[1] (numeric) = 5.2460961165964789156427500181578 absolute error = 7.42461676563239e-17 relative error = 1.4152651039206034841440988764803e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.447 y[1] (analytic) = 5.2503443364689932606383701392776 y[1] (numeric) = 5.2503443364689933350909856913599 absolute error = 7.44526155520823e-17 relative error = 1.4180520510804023473116589691940e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.448 y[1] (analytic) = 5.2545968066861983442465974834531 y[1] (numeric) = 5.2545968066861984189058674824479 absolute error = 7.46592699989948e-17 relative error = 1.4208372734515957865319162436789e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.449 y[1] (analytic) = 5.2588535315005646637988779154288 y[1] (numeric) = 5.2588535315005647386650091191447 absolute error = 7.48661312037159e-17 relative error = 1.4236207712435290008964852496561e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.45 y[1] (analytic) = 5.2631145151688173883886106755809 y[1] (numeric) = 5.2631145151688174634618100486878 absolute error = 7.50731993731069e-17 relative error = 1.4264025446670123322631991775634e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.451 y[1] (analytic) = 5.2673797619519405413505045441019 y[1] (numeric) = 5.2673797619519406166309792583377 absolute error = 7.52804747142358e-17 relative error = 1.4291825939343132825317949392178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.452 y[1] (analytic) = 5.271649276115181261244956257723 y[1] (numeric) = 5.2716492761151813367329136921011 absolute error = 7.54879574343781e-17 relative error = 1.4319609192591656272518388852806e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.453 y[1] (analytic) = 5.2759230619280540671055445073843 y[1] (numeric) = 5.2759230619280541428011922484008 absolute error = 7.56956477410165e-17 relative error = 1.4347375208567576206623457621431e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.454 y[1] (analytic) = 5.280201123664345127953904764702 y[1] (numeric) = 5.2802011236643452038574506065434 absolute error = 7.59035458418414e-17 relative error = 1.4375123989437353940330957194727e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.455 y[1] (analytic) = 5.2844834656021165365862544524633 y[1] (numeric) = 5.284483465602116612697906397214 absolute error = 7.61116519447507e-17 relative error = 1.4402855537381930763005885411170e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.456 y[1] (analytic) = 5.2887700920237105876358422460295 y[1] (numeric) = 5.2887700920237106639558085038803 absolute error = 7.63199662578508e-17 relative error = 1.4430569854596856374150634555355e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.457 y[1] (analytic) = 5.2930610072157540599155995684554 y[1] (numeric) = 5.2930610072157541364440885579111 absolute error = 7.65284889894557e-17 relative error = 1.4458266943292057583427969127132e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.458 y[1] (analytic) = 5.2973562154691625030452766223299 y[1] (numeric) = 5.2973562154691625797824969704183 absolute error = 7.67372203480884e-17 relative error = 1.4485946805692042164784040694944e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.459 y[1] (analytic) = 5.3016557210791445283673495858346 y[1] (numeric) = 5.3016557210791446053135101283148 absolute error = 7.69461605424802e-17 relative error = 1.4513609444035705468556562135415e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.46 y[1] (analytic) = 5.3059595283452061041559898892827 y[1] (numeric) = 5.305959528345206181311299670854 absolute error = 7.71553097815713e-17 relative error = 1.4541254860576382832153610605597e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.461 y[1] (analytic) = 5.3102676415711548551233907814661 y[1] (numeric) = 5.3102676415711549324880590559771 absolute error = 7.73646682745110e-17 relative error = 1.4568883057581826261840806811647e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.462 y[1] (analytic) = 5.3145800650651043662277506924963 y[1] (numeric) = 5.3145800650651044438019869231542 absolute error = 7.75742362306579e-17 relative error = 1.4596494037334181079187903096477e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.463 y[1] (analytic) = 5.3188968031394784907872172014803 y[1] (numeric) = 5.3188968031394785685712310610601 absolute error = 7.77840138595798e-17 relative error = 1.4624087802129906129750336582228e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.464 y[1] (analytic) = 5.3232178601110156629040997233343 y[1] (numeric) = 5.3232178601110157408981010943886 absolute error = 7.79940013710543e-17 relative error = 1.4651664354279825731021509783583e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=8.43 NO POLE x[1] = 1.465 y[1] (analytic) = 5.327543240300773214203663339308 y[1] (numeric) = 5.3275432403007732924078623143771 absolute error = 7.82041989750691e-17 relative error = 1.4679223696109124908183134613139e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.466 y[1] (analytic) = 5.3318729480341316948918205103728 y[1] (numeric) = 5.3318729480341317733064273921946 absolute error = 7.84146068818218e-17 relative error = 1.4706765829957250728519506289752e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.467 y[1] (analytic) = 5.3362069876407991991360417315254 y[1] (numeric) = 5.3362069876407992777612670332457 absolute error = 7.86252253017203e-17 relative error = 1.4734290758177926407021887817066e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.468 y[1] (analytic) = 5.3405453634548156947738105082782 y[1] (numeric) = 5.3405453634548157736098649536612 absolute error = 7.88360544453830e-17 relative error = 1.4761798483139127745815590692960e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.469 y[1] (analytic) = 5.3448880798145573573529523641522 y[1] (numeric) = 5.3448880798145574364000468877912 absolute error = 7.90470945236390e-17 relative error = 1.4789289007223059539980185278718e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.47 y[1] (analytic) = 5.3492351410627409085081719198621 y[1] (numeric) = 5.3492351410627409877665176673907 absolute error = 7.92583457475286e-17 relative error = 1.4816762332826188032792784682679e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.471 y[1] (analytic) = 5.3535865515464279586781364210939 y[1] (numeric) = 5.3535865515464280381479447493968 absolute error = 7.94698083283029e-17 relative error = 1.4844218462359104952750171617793e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.472 y[1] (analytic) = 5.3579423156170293541674484323179 y[1] (numeric) = 5.3579423156170294338489309097423 absolute error = 7.96814824774244e-17 relative error = 1.4871657398246578703630622625037e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.473 y[1] (analytic) = 5.3623024376303095285578547589738 y[1] (numeric) = 5.3623024376303096084512231655412 absolute error = 7.98933684065674e-17 relative error = 1.4899079142927567859872122680843e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.474 y[1] (analytic) = 5.3666669219463908584730430095994 y[1] (numeric) = 5.3666669219463909385785093372173 absolute error = 8.01054663276179e-17 relative error = 1.4926483698855141280018447497508e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.475 y[1] (analytic) = 5.3710357729297580237013815630615 y[1] (numeric) = 5.3710357729297581040191580157353 absolute error = 8.03177764526738e-17 relative error = 1.4953871068496454316422577270523e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.476 y[1] (analytic) = 5.3754089949492623716809630639933 y[1] (numeric) = 5.3754089949492624522112620580384 absolute error = 8.05302989940451e-17 relative error = 1.4981241254332724993053325144477e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.477 y[1] (analytic) = 5.3797865923781262863513159318443 y[1] (numeric) = 5.3797865923781263670943500960989 absolute error = 8.07430341642546e-17 relative error = 1.5008594258859303092137200309134e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.478 y[1] (analytic) = 5.3841685695939475613761527356201 y[1] (numeric) = 5.3841685695939476423321349116574 absolute error = 8.09559821760373e-17 relative error = 1.5035930084585497306935843439166e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.479 y[1] (analytic) = 5.3885549309787037777415286574228 y[1] (numeric) = 5.3885549309787038589106718997641 absolute error = 8.11691432423413e-17 relative error = 1.5063248734034681457527604381005e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.48 y[1] (analytic) = 5.3929456809187566857337876433172 y[1] (numeric) = 5.3929456809187567671163052196449 absolute error = 8.13825175763277e-17 relative error = 1.5090550209744214613227124403236e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.481 y[1] (analytic) = 5.3973408238048565913016782198325 y[1] (numeric) = 5.3973408238048566728977836112032 absolute error = 8.15961053913707e-17 relative error = 1.5117834514265398511963766176346e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.482 y[1] (analytic) = 5.4017403640321467468070253385816 y[1] (numeric) = 5.40174036403214682861693223964 absolute error = 8.18099069010584e-17 relative error = 1.5145101650163564627758464076075e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.483 y[1] (analytic) = 5.4061443060001677461683490000368 y[1] (numeric) = 5.4061443060001678281922713192289 absolute error = 8.20239223191921e-17 relative error = 1.5172351620017883203014688127847e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.484 y[1] (analytic) = 5.4105526541128619244018248004439 y[1] (numeric) = 5.4105526541128620066399766602313 absolute error = 8.22381518597874e-17 relative error = 1.5199584426421505748740849874602e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.485 y[1] (analytic) = 5.4149654127785777615639859432053 y[1] (numeric) = 5.414965412778577844016581680279 absolute error = 8.24525957370737e-17 relative error = 1.5226800071981411223864410680950e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.486 y[1] (analytic) = 5.4193825864100742911005706577984 y[1] (numeric) = 5.4193825864100743737678248232934 absolute error = 8.26672541654950e-17 relative error = 1.5253998559318492697820825708832e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.487 y[1] (analytic) = 5.4238041794245255126059233754456 y[1] (numeric) = 5.4238041794245255954880507351553 absolute error = 8.28821273597097e-17 relative error = 1.5281179891067459069768392280204e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.488 y[1] (analytic) = 5.4282301962435248089973624213046 y[1] (numeric) = 5.4282301962435248920945779558956 absolute error = 8.30972155345910e-17 relative error = 1.5308344069876847653554693682306e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.489 y[1] (analytic) = 5.4326606412930893681089313979137 y[1] (numeric) = 5.4326606412930894514214503031409 absolute error = 8.33125189052272e-17 relative error = 1.5335491098409018146570285390826e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.49 y[1] (analytic) = 5.4370955190036646087089558540139 y[1] (numeric) = 5.4370955190036646922369935409355 absolute error = 8.35280376869216e-17 relative error = 1.5362620979340072911705401741681e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.491 y[1] (analytic) = 5.4415348338101286109458312566713 y[1] (numeric) = 5.4415348338101286946896033518643 absolute error = 8.37437720951930e-17 relative error = 1.5389733715359887764656576497859e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.492 y[1] (analytic) = 5.4459785901517965512264727128585 y[1] (numeric) = 5.4459785901517966351861950586343 absolute error = 8.39597223457758e-17 relative error = 1.5416829309172069014693000491710e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.493 y[1] (analytic) = 5.450426792472425141531861319313 y[1] (numeric) = 5.4504267924724252257077499739334 absolute error = 8.41758886546204e-17 relative error = 1.5443907763493965609624933658917e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.494 y[1] (analytic) = 5.4548794452202170731741264565905 y[1] (numeric) = 5.4548794452202171575663976944835 absolute error = 8.43922712378930e-17 relative error = 1.5470969081056571080610254832700e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.495 y[1] (analytic) = 5.4593365528478254649996077847639 y[1] (numeric) = 5.45933655284782554960847809674 absolute error = 8.46088703119761e-17 relative error = 1.5498013264604554040207952815486e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.496 y[1] (analytic) = 5.4637981198123583160423451442017 y[1] (numeric) = 5.4637981198123584008680312376708 absolute error = 8.48256860934691e-17 relative error = 1.5525040316896306686487330642640e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=61.0MB, alloc=4.3MB, time=8.99 x[1] = 1.497 y[1] (analytic) = 5.4682641505753829626324490152875 y[1] (numeric) = 5.4682641505753830476751678144751 absolute error = 8.50427187991876e-17 relative error = 1.5552050240703755186642763319280e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.498 y[1] (analytic) = 5.4727346496029305399638086458202 y[1] (numeric) = 5.4727346496029306252237772919845 absolute error = 8.52599686461643e-17 relative error = 1.5579043038812463200148366496913e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.499 y[1] (analytic) = 5.4772096213655004481255994141773 y[1] (numeric) = 5.4772096213655005336030352658265 absolute error = 8.54774358516492e-17 relative error = 1.5606018714021606946010403929989e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.5 y[1] (analytic) = 5.4816890703380648226020554601193 y[1] (numeric) = 5.4816890703380649082971760932287 absolute error = 8.56951206331094e-17 relative error = 1.5632977269143877274448349861262e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.501 y[1] (analytic) = 5.4861730010000730092449780833807 y[1] (numeric) = 5.4861730010000730951580012916105 absolute error = 8.59130232082298e-17 relative error = 1.5659918707005546120064612844196e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.502 y[1] (analytic) = 5.4906614178354560437234548829297 y[1] (numeric) = 5.4906614178354561298545986778425 absolute error = 8.61311437949128e-17 relative error = 1.5686843030446350355111040790735e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.503 y[1] (analytic) = 5.4951543253326311354552690869872 y[1] (numeric) = 5.4951543253326312218047516982664 absolute error = 8.63494826112792e-17 relative error = 1.5713750242319594439167406557412e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.504 y[1] (analytic) = 5.4996517279845061560244830055907 y[1] (numeric) = 5.4996517279845062425925228812585 absolute error = 8.65680398756678e-17 relative error = 1.5740640345492016040181477690507e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.505 y[1] (analytic) = 5.5041536302884841320896840236577 y[1] (numeric) = 5.5041536302884842188764998302936 absolute error = 8.67868158066359e-17 relative error = 1.5767513342843815679991691907467e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.506 y[1] (analytic) = 5.5086600367464677427873860431718 y[1] (numeric) = 5.5086600367464678297931966661312 absolute error = 8.70058106229594e-17 relative error = 1.5794369237268613474971315139212e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.507 y[1] (analytic) = 5.5131709518648638216350837782652 y[1] (numeric) = 5.5131709518648639088601083218982 absolute error = 8.72250245436330e-17 relative error = 1.5821208031673424080414161068554e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.508 y[1] (analytic) = 5.5176863801545878629384618066287 y[1] (numeric) = 5.5176863801545879503829195944996 absolute error = 8.74444577878709e-17 relative error = 1.5848029728978722228937551408309e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.509 y[1] (analytic) = 5.5222063261310685327072647848338 y[1] (numeric) = 5.52220632613106862037137535994 absolute error = 8.76641105751062e-17 relative error = 1.5874834332118272387260009505782e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.51 y[1] (analytic) = 5.5267307943142521840843397438116 y[1] (numeric) = 5.5267307943142522719683228688034 absolute error = 8.78839831249918e-17 relative error = 1.5901621844039230510243561850239e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.511 y[1] (analytic) = 5.5312597892286073772923658939088 y[1] (numeric) = 5.531259789228607465396441551309 absolute error = 8.81040756574002e-17 relative error = 1.5928392267702046279568922764011e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.512 y[1] (analytic) = 5.535793315403129404102791886626 y[1] (numeric) = 5.5357933154031294924271802790499 absolute error = 8.83243883924239e-17 relative error = 1.5955145606080474061096246003446e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.513 y[1] (analytic) = 5.5403313773713448168315050023532 y[1] (numeric) = 5.5403313773713449053764265527289 absolute error = 8.85449215503757e-17 relative error = 1.5981881862161565612661522455336e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.514 y[1] (analytic) = 5.5448739796713159618657612601491 y[1] (numeric) = 5.544873979671316050631436611938 absolute error = 8.87656753517889e-17 relative error = 1.6008601038945644646438046582106e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.515 y[1] (analytic) = 5.5494211268456455177269099768721 y[1] (numeric) = 5.5494211268456456067135599942893 absolute error = 8.89866500174172e-17 relative error = 1.6035303139446227309932046807608e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.516 y[1] (analytic) = 5.5539728234414810376734508387651 y[1] (numeric) = 5.5539728234414811268812966070004 absolute error = 8.92078457682353e-17 relative error = 1.6061988166690068947258689187949e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.517 y[1] (analytic) = 5.5585290740105194968489660889309 y[1] (numeric) = 5.5585290740105195862782289143698 absolute error = 8.94292628254389e-17 relative error = 1.6088656123717102542333928785198e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.518 y[1] (analytic) = 5.5630898831090118439794749790081 y[1] (numeric) = 5.5630898831090119336303763894533 absolute error = 8.96509014104452e-17 relative error = 1.6115307013580467196300776944196e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.519 y[1] (analytic) = 5.5676552552977675576247621827822 y[1] (numeric) = 5.567655255297767647497523927675 absolute error = 8.98727617448928e-17 relative error = 1.6141940839346428553422424553447e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.52 y[1] (analytic) = 5.5722251951421592069882364234397 y[1] (numeric) = 5.5722251951421592970830804740815 absolute error = 9.00948440506418e-17 relative error = 1.6168557604094335364143216289500e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.521 y[1] (analytic) = 5.5767997072121270172898801247029 y[1] (numeric) = 5.5767997072121271076070286744778 absolute error = 9.03171485497749e-17 relative error = 1.6195157310916755430301279226914e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.522 y[1] (analytic) = 5.5813787960821834397068554591782 y[1] (numeric) = 5.5813787960821835302465309237745 absolute error = 9.05396754645963e-17 relative error = 1.6221739962919216567686466133399e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.523 y[1] (analytic) = 5.5859624663314177258863367349008 y[1] (numeric) = 5.585962466331417816648761752534 absolute error = 9.07624250176332e-17 relative error = 1.6248305563220414148900079016148e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.524 y[1] (analytic) = 5.5905507225435005070351436332935 y[1] (numeric) = 5.5905507225435005980205410649285 absolute error = 9.09853974316350e-17 relative error = 1.6274854114952006071183015538827e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.525 y[1] (analytic) = 5.5951435693066883775907543885512 y[1] (numeric) = 5.5951435693066884687993473181255 absolute error = 9.12085929295743e-17 relative error = 1.6301385621258730294313723661616e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.526 y[1] (analytic) = 5.5997410112138284834782825798487 y[1] (numeric) = 5.599741011213828574910294314495 absolute error = 9.14320117346463e-17 relative error = 1.6327900085298235927000045579937e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.527 y[1] (analytic) = 5.6043430528623631149580057937283 y[1] (numeric) = 5.6043430528623632066136598639984 absolute error = 9.16556540702701e-17 relative error = 1.6354397510241254021615323794227e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.528 y[1] (analytic) = 5.6089496988543343040680390045818 y[1] (numeric) = 5.6089496988543343959475591646698 absolute error = 9.18795201600880e-17 relative error = 1.6380877899271410809486357157296e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=64.8MB, alloc=4.3MB, time=9.57 x[1] = 1.529 y[1] (analytic) = 5.6135609537963884266667501162807 y[1] (numeric) = 5.6135609537963885187703603442467 absolute error = 9.21036102279660e-17 relative error = 1.6407341255585255477616971729594e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.53 y[1] (analytic) = 5.6181768222997808090795197077546 y[1] (numeric) = 5.618176822299780901407444205749 absolute error = 9.23279244979944e-17 relative error = 1.6433787582392305462811129465574e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.531 y[1] (analytic) = 5.6227973089803803393544516296622 y[1] (numeric) = 5.6227973089803804319069148241495 absolute error = 9.25524631944873e-17 relative error = 1.6460216882914895744714264294249e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.532 y[1] (analytic) = 5.6274224184586740831316457082485 y[1] (numeric) = 5.6274224184586741759088722502319 absolute error = 9.27772265419834e-17 relative error = 1.6486629160388259747293678472174e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.533 y[1] (analytic) = 5.6320521553597719041306484260459 y[1] (numeric) = 5.6320521553597719971328631912922 absolute error = 9.30022147652463e-17 relative error = 1.6513024418060520918979038423388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.534 y[1] (analytic) = 5.6366865243134110892607020672563 y[1] (numeric) = 5.6366865243134111824881301565202 absolute error = 9.32274280892639e-17 relative error = 1.6539402659192524540124864066112e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.535 y[1] (analytic) = 5.6413255299539609783584174384459 y[1] (numeric) = 5.6413255299539610718112841776957 absolute error = 9.34528667392498e-17 relative error = 1.6565763887058024740881352978406e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.536 y[1] (analytic) = 5.6459691769204275985574999026145 y[1] (numeric) = 5.6459691769204276922360308432572 absolute error = 9.36785309406427e-17 relative error = 1.6592108104943516216950811208269e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.537 y[1] (analytic) = 5.6506174698564583032951630967493 y[1] (numeric) = 5.6506174698564583971995840158559 absolute error = 9.39044209191066e-17 relative error = 1.6618435316148208206679312956298e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.538 y[1] (analytic) = 5.6552704134103464159598693396639 y[1] (numeric) = 5.6552704134103465100904062401955 absolute error = 9.41305369005316e-17 relative error = 1.6644745523984104547481175465937e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.539 y[1] (analytic) = 5.6599280122350358781850403782506 y[1] (numeric) = 5.6599280122350359725419194892844 absolute error = 9.43568791110338e-17 relative error = 1.6671038731775924179620153064311e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.54 y[1] (analytic) = 5.6645902709881259027933867662438 y[1] (numeric) = 5.6645902709881259973768345431991 absolute error = 9.45834477769553e-17 relative error = 1.6697314942861039550149128107439e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.541 y[1] (analytic) = 5.6692571943318756313965088202109 y[1] (numeric) = 5.6692571943318757262067519450757 absolute error = 9.48102431248648e-17 relative error = 1.6723574160589521009875004221362e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.542 y[1] (analytic) = 5.6739287869332087966544267527608 y[1] (numeric) = 5.6739287869332088916916921343186 absolute error = 9.50372653815578e-17 relative error = 1.6749816388324110348477937448610e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.543 y[1] (analytic) = 5.6786050534637183891997022428884 y[1] (numeric) = 5.6786050534637184844642170169447 absolute error = 9.52645147740563e-17 relative error = 1.6776041629440106265204791274383e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.544 y[1] (analytic) = 5.6832859985996713292308183679645 y[1] (numeric) = 5.6832859985996714247228098975745 absolute error = 9.54919915296100e-17 relative error = 1.6802249887325514192080104562020e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.545 y[1] (analytic) = 5.6879716270220131427794894911426 y[1] (numeric) = 5.6879716270220132384991853668381 absolute error = 9.57196958756955e-17 relative error = 1.6828441165380843613316820253670e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.546 y[1] (analytic) = 5.6926619434163726426565773718797 y[1] (numeric) = 5.6926619434163727386042054118969 absolute error = 9.59476280400172e-17 relative error = 1.6854615467019204870609122463379e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.547 y[1] (analytic) = 5.6973569524730666140812944458789 y[1] (numeric) = 5.6973569524730667102570826963862 absolute error = 9.61757882505073e-17 relative error = 1.6880772795666247377943564981041e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.548 y[1] (analytic) = 5.7020566588871045049983799040469 y[1] (numeric) = 5.702056658887104601402556639373 absolute error = 9.64041767353261e-17 relative error = 1.6906913154760150609291946292267e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.549 y[1] (analytic) = 5.7067610673581931210879388880337 y[1] (numeric) = 5.7067610673581932177207326108957 absolute error = 9.66327937228620e-17 relative error = 1.6933036547751562416948957207884e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.55 y[1] (analytic) = 5.7114701825907413254726398125845 y[1] (numeric) = 5.7114701825907414223342792543165 absolute error = 9.68616394417320e-17 relative error = 1.6959142978103625053335707389311e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.551 y[1] (analytic) = 5.7161840092938647431269695222932 y[1] (numeric) = 5.7161840092938648402176836430751 absolute error = 9.70907141207819e-17 relative error = 1.6985232449291948437228300953109e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.552 y[1] (analytic) = 5.7209025521813904699932506924041 y[1] (numeric) = 5.7209025521813905673132686814906 absolute error = 9.73200179890865e-17 relative error = 1.7011304964804583407495100728885e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.553 y[1] (analytic) = 5.725625815971861786809130590073 y[1] (numeric) = 5.7256258159718618843586818660224 absolute error = 9.75495512759494e-17 relative error = 1.7037360528141925103187805127345e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.554 y[1] (analytic) = 5.7303538053885428776512550239667 y[1] (numeric) = 5.7303538053885429754305692348709 absolute error = 9.77793142109042e-17 relative error = 1.7063399142816860990407551027117e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.555 y[1] (analytic) = 5.7350865251594235531998460262716 y[1] (numeric) = 5.7350865251594236512091530499852 absolute error = 9.80093070237136e-17 relative error = 1.7089420812354551845574298150353e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.556 y[1] (analytic) = 5.7398239800172239787289065320789 y[1] (numeric) = 5.7398239800172240769684364764495 absolute error = 9.82395299443706e-17 relative error = 1.7115425540292579542579948073733e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.557 y[1] (analytic) = 5.7445661746993994068267800467483 y[1] (numeric) = 5.7445661746993995052967632498465 absolute error = 9.84699832030982e-17 relative error = 1.7141413330180832848510044009932e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.558 y[1] (analytic) = 5.7493131139481449148517980222023 y[1] (numeric) = 5.7493131139481450135524650525518 absolute error = 9.87006670303495e-17 relative error = 1.7167384185581463213505407776487e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.559 y[1] (analytic) = 5.7540648025104001471277523981938 y[1] (numeric) = 5.7540648025104002460593340550022 absolute error = 9.89315816568084e-17 relative error = 1.7193338110068944909842817262273e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.56 y[1] (analytic) = 5.758821245137854061883935504415 y[1] (numeric) = 5.7588212451378541610466628178045 absolute error = 9.91627273133895e-17 relative error = 1.7219275107229995812063342832362e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.561 y[1] (analytic) = 5.7635824465869496829444942638827 y[1] (numeric) = 5.7635824465869497823385984951213 absolute error = 9.93941042312386e-17 relative error = 1.7245195180663602527113668362377e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=10.14 NO POLE x[1] = 1.562 y[1] (analytic) = 5.7683484116188888561718503873506 y[1] (numeric) = 5.7683484116188889557975630290832 absolute error = 9.96257126417326e-17 relative error = 1.7271098333980941240210218711662e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.563 y[1] (analytic) = 5.7731191449996370106689430025646 y[1] (numeric) = 5.7731191449996371105264957790445 absolute error = 9.98575527764799e-17 relative error = 1.7296984570805385417151071087542e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.564 y[1] (analytic) = 5.7778946514999279247450549210009 y[1] (numeric) = 5.7778946514999280248346797883216 absolute error = 1.000896248673207e-16 relative error = 1.7322853894772496017550631189860e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.565 y[1] (analytic) = 5.7826749358952684966499885083104 y[1] (numeric) = 5.7826749358952685969719176546374 absolute error = 1.003219291463270e-16 relative error = 1.7348706309529959733668643912292e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.566 y[1] (analytic) = 5.7874600029659435200813618930423 y[1] (numeric) = 5.7874600029659436206358277388455 absolute error = 1.005544658458032e-16 relative error = 1.7374541818737631064116638897222e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.567 y[1] (analytic) = 5.7922498574970204644698010213417 y[1] (numeric) = 5.7922498574970205652570362196278 absolute error = 1.007872351982861e-16 relative error = 1.7400360426067470448744835808691e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.568 y[1] (analytic) = 5.7970445042783542600468078432117 y[1] (numeric) = 5.7970445042783543610670452797565 absolute error = 1.010202374365448e-16 relative error = 1.7426162135203465316263464448547e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.569 y[1] (analytic) = 5.8018439481045920877000896986054 y[1] (numeric) = 5.8018439481045921889535624921872 absolute error = 1.012534727935818e-16 relative error = 1.7451946949841758210985380661736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.57 y[1] (analytic) = 5.8066481937751781736211397590791 y[1] (numeric) = 5.8066481937751782751080812617115 absolute error = 1.014869415026324e-16 relative error = 1.7477714873690481372881338477876e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.571 y[1] (analytic) = 5.8114572460943585887498631729837 y[1] (numeric) = 5.811457246094358690470506970149 absolute error = 1.017206437971653e-16 relative error = 1.7503465910469798483045870266849e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.572 y[1] (analytic) = 5.8162711098711860530210483592228 y[1] (numeric) = 5.8162711098711861549756282701057 absolute error = 1.019545799108829e-16 relative error = 1.7529200063911894479694599808354e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.573 y[1] (analytic) = 5.8210897899195247444174876964477 y[1] (numeric) = 5.8210897899195248466062377741689 absolute error = 1.021887500777212e-16 relative error = 1.7554917337760896565638817369494e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.574 y[1] (analytic) = 5.8259132910580551128345566612112 y[1] (numeric) = 5.8259132910580552152577111930617 absolute error = 1.024231545318505e-16 relative error = 1.7580617735772932782162221566295e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.575 y[1] (analytic) = 5.8307416181102786987610652800608 y[1] (numeric) = 5.8307416181102788014188587877361 absolute error = 1.026577935076753e-16 relative error = 1.7606301261716052945301794684141e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.576 y[1] (analytic) = 5.835574775904522956781200576824 y[1] (numeric) = 5.8355747759045230596738678166584 absolute error = 1.028926672398344e-16 relative error = 1.7631967919370184103878612009893e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.577 y[1] (analytic) = 5.8404127692739460839023835174292 y[1] (numeric) = 5.840412769273946187030159480631 absolute error = 1.031277759632018e-16 relative error = 1.7657617712527223052615684744767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.578 y[1] (analytic) = 5.8452556030565418527138687805241 y[1] (numeric) = 5.8452556030565419560769886934102 absolute error = 1.033631199128861e-16 relative error = 1.7683250644990871624425779797951e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.579 y[1] (analytic) = 5.8501032820951444493809205128911 y[1] (numeric) = 5.8501032820951445529796198371223 absolute error = 1.035986993242312e-16 relative error = 1.7708866720576694875984690830602e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.58 y[1] (analytic) = 5.8549558112374333164794020642401 y[1] (numeric) = 5.8549558112374334203139164970569 absolute error = 1.038345144328168e-16 relative error = 1.7734465943112144682783478064199e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.581 y[1] (analytic) = 5.859813195335938000675622536373 y[1] (numeric) = 5.8598131953359381047461880108307 absolute error = 1.040705654744577e-16 relative error = 1.7760048316436378289133141395414e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.582 y[1] (analytic) = 5.8646754392480430052562878269677 y[1] (numeric) = 5.8646754392480431095631405121728 absolute error = 1.043068526852051e-16 relative error = 1.7785613844400418642111165158595e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.583 y[1] (analytic) = 5.8695425478359926475134086983399 y[1] (numeric) = 5.8695425478359927520567849996862 absolute error = 1.045433763013463e-16 relative error = 1.7811162530867041192695666008155e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.584 y[1] (analytic) = 5.8744145259668959209890232564936 y[1] (numeric) = 5.8744145259668960257691598158985 absolute error = 1.047801365594049e-16 relative error = 1.7836694379710746231400795320654e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.585 y[1] (analytic) = 5.879291378512731362584596085589 y[1] (numeric) = 5.8792913785127314676017297817301 absolute error = 1.050171336961411e-16 relative error = 1.7862209394817748227994649752007e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.586 y[1] (analytic) = 5.8841731103503519245399611476319 y[1] (numeric) = 5.8841731103503520297943290961841 absolute error = 1.052543679485522e-16 relative error = 1.7887707580085999071449619371652e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.587 y[1] (analytic) = 5.8890597263614898512866804267341 y[1] (numeric) = 5.8890597263614899567785199806064 absolute error = 1.054918395538723e-16 relative error = 1.7913188939425075206686233035591e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.588 y[1] (analytic) = 5.8939512314327615611806951717089 y[1] (numeric) = 5.893951231432761666910243921282 absolute error = 1.057295487495731e-16 relative error = 1.7938653476756251822457514184782e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.589 y[1] (analytic) = 5.8988476304556725331191514700612 y[1] (numeric) = 5.8988476304556726390866472434251 absolute error = 1.059674957733639e-16 relative error = 1.7964101196012440908361661222624e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.59 y[1] (analytic) = 5.9037489283266221980462867706038 y[1] (numeric) = 5.9037489283266223042519676337954 absolute error = 1.062056808631916e-16 relative error = 1.7989532101138129477599293413377e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.591 y[1] (analytic) = 5.9086551299469088353532688609937 y[1] (numeric) = 5.9086551299469089417973731182352 absolute error = 1.064441042572415e-16 relative error = 1.8014946196089453349868904601139e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.592 y[1] (analytic) = 5.9135662402227344741768837004377 y[1] (numeric) = 5.9135662402227345808596498943745 absolute error = 1.066827661939368e-16 relative error = 1.8040343484834050591430445877861e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.593 y[1] (analytic) = 5.9184822640652097996019734066604 y[1] (numeric) = 5.9184822640652099065236403185999 absolute error = 1.069216669119395e-16 relative error = 1.8065723971351152089920941294043e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=10.70 NO POLE x[1] = 1.594 y[1] (analytic) = 5.9234032063903590637725305999839 y[1] (numeric) = 5.9234032063903591709333372501344 absolute error = 1.071608066501505e-16 relative error = 1.8091087659631536479024462291642e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.595 y[1] (analytic) = 5.928329072119125001916360216022 y[1] (numeric) = 5.9283290721191251093165458637314 absolute error = 1.074001856477094e-16 relative error = 1.8116434553677434540879946816738e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.596 y[1] (analytic) = 5.9332598661773737532882248120596 y[1] (numeric) = 5.9332598661773738609280289560549 absolute error = 1.076398041439953e-16 relative error = 1.8141764657502602484431127237809e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.597 y[1] (analytic) = 5.9381955934958997870363943106745 y[1] (numeric) = 5.9381955934958998949160566893011 absolute error = 1.078796623786266e-16 relative error = 1.8167077975132226315849875946190e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.598 y[1] (analytic) = 5.9431362590104308329975260475596 y[1] (numeric) = 5.9431362590104309411172866390212 absolute error = 1.081197605914616e-16 relative error = 1.8192374510602961152745707365790e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.599 y[1] (analytic) = 5.948081867661632817424805918838 y[1] (numeric) = 5.9480818676616329257849049414367 absolute error = 1.083600990225987e-16 relative error = 1.8217654267962902952394193115724e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.6 y[1] (analytic) = 5.953032424395114803654286356424 y[1] (numeric) = 5.9530324243951149122549642688001 absolute error = 1.086006779123761e-16 relative error = 1.8242917251271476248250731399640e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.601 y[1] (analytic) = 5.9579879341614339377143617981767 y[1] (numeric) = 5.9579879341614340465558592995496 absolute error = 1.088414975013729e-16 relative error = 1.8268163464599557283544518040527e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.602 y[1] (analytic) = 5.9629484019161003988833272627379 y[1] (numeric) = 5.9629484019161005079658852931466 absolute error = 1.090825580304087e-16 relative error = 1.8293392912029344836244288259214e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.603 y[1] (analytic) = 5.9679138326195823551999705870222 y[1] (numeric) = 5.9679138326195824645238303275662 absolute error = 1.093238597405440e-16 relative error = 1.8318605597654365596715931834983e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604 y[1] (analytic) = 5.972884231237310923932153837366 y[1] (numeric) = 5.9728842312373110334975567104464 absolute error = 1.095654028730804e-16 relative error = 1.8343801525579445892919515486483e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.605 y[1] (analytic) = 5.9778596027396851370083443633297 y[1] (numeric) = 5.9778596027396852468155320328908 absolute error = 1.098071876695611e-16 relative error = 1.8368980699920733600774770894061e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.606 y[1] (analytic) = 5.982839952102076911417060926098 y[1] (numeric) = 5.9828399521020770214662752978692 absolute error = 1.100492143717712e-16 relative error = 1.8394143124805686375087653304684e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.607 y[1] (analytic) = 5.9878252843048360245792053013396 y[1] (numeric) = 5.9878252843048361348706885230767 absolute error = 1.102914832217371e-16 relative error = 1.8419288804372909492744427700393e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.608 y[1] (analytic) = 5.9928156043332950946982547292702 y[1] (numeric) = 5.9928156043332952052322491909979 absolute error = 1.105339944617277e-16 relative error = 1.8444417742772294724149256218595e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.609 y[1] (analytic) = 5.9978109171777745660932955625286 y[1] (numeric) = 5.997810917177774676870043896783 absolute error = 1.107767483342544e-16 relative error = 1.8469529944164958297939112094286e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.61 y[1] (analytic) = 6.0028112278335876995198834453142 y[1] (numeric) = 6.0028112278335878105396285273853 absolute error = 1.110197450820711e-16 relative error = 1.8494625412723179034049959186844e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.611 y[1] (analytic) = 6.0078165413010455674837203450615 y[1] (numeric) = 6.007816541301045678746705293236 absolute error = 1.112629849481745e-16 relative error = 1.8519704152630386579865567344309e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.612 y[1] (analytic) = 6.0128268625854620545521437507452 y[1] (numeric) = 6.0128268625854621660586119265496 absolute error = 1.115064681758044e-16 relative error = 1.8544766168081149564629876114413e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.613 y[1] (analytic) = 6.0178421966971588626684283497218 y[1] (numeric) = 6.017842196697158974418623358166 absolute error = 1.117501950084442e-16 relative error = 1.8569811463281196906993760184548e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.614 y[1] (analytic) = 6.0228625486514705214739054978273 y[1] (numeric) = 6.022862548651470633468071187648 absolute error = 1.119941656898207e-16 relative error = 1.8594840042447322651538449764704e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.615 y[1] (analytic) = 6.0278879234687494036429108052661 y[1] (numeric) = 6.0278879234687495158812912691706 absolute error = 1.122383804639045e-16 relative error = 1.8619851909807390677551997310027e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.616 y[1] (analytic) = 6.0329183261743707452355751736583 y[1] (numeric) = 6.0329183261743708577184147485689 absolute error = 1.124828395749106e-16 relative error = 1.8644847069600372395571935864270e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.617 y[1] (analytic) = 6.0379537617987376710734796374546 y[1] (numeric) = 6.0379537617987377838010229047525 absolute error = 1.127275432672979e-16 relative error = 1.8669825526076201933993858666736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.618 y[1] (analytic) = 6.0429942353772862251431993857913 y[1] (numeric) = 6.0429942353772863381156911715616 absolute error = 1.129724917857703e-16 relative error = 1.8694787283495896678768674397483e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.619 y[1] (analytic) = 6.0480397519504904060327673687502 y[1] (numeric) = 6.0480397519504905192504527440264 absolute error = 1.132176853752762e-16 relative error = 1.8719732346131412521779376911064e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.62 y[1] (analytic) = 6.053090316563867207406092924905 y[1] (numeric) = 6.0530903165638673208692172059143 absolute error = 1.134631242810093e-16 relative error = 1.8744660718265714459069839460607e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.621 y[1] (analytic) = 6.0581459342679816635203759049944 y[1] (numeric) = 6.058145934267981777229184653403 absolute error = 1.137088087484086e-16 relative error = 1.8769572404192714642446296496139e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.622 y[1] (analytic) = 6.0632066101184518997915618095556 y[1] (numeric) = 6.063206610118452013746300832714 absolute error = 1.139547390231584e-16 relative error = 1.8794467408217210600699962056642e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.623 y[1] (analytic) = 6.0682723491759541884128885063939 y[1] (numeric) = 6.068272349175954302613803857583 absolute error = 1.142009153511891e-16 relative error = 1.8819345734654955463469299917468e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.624 y[1] (analytic) = 6.0733431565062280090315801468578 y[1] (numeric) = 6.0733431565062281234789181255348 absolute error = 1.144473379786770e-16 relative error = 1.8844207387832563039894090244326e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.625 y[1] (analytic) = 6.0784190371800811144887489580334 y[1] (numeric) = 6.0784190371800812291827561100782 absolute error = 1.146940071520448e-16 relative error = 1.8869052372087528393855269786888e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=11.28 NO POLE x[1] = 1.626 y[1] (analytic) = 6.0834999962733946016275706511838 y[1] (numeric) = 6.0834999962733947165684937691455 absolute error = 1.149409231179617e-16 relative error = 1.8893880691768182424944179908292e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.627 y[1] (analytic) = 6.0885860388671279871748042550302 y[1] (numeric) = 6.0885860388671281023628903783738 absolute error = 1.151880861233436e-16 relative error = 1.8918692351233662961255075713717e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.628 y[1] (analytic) = 6.0936771700473242887007322558178 y[1] (numeric) = 6.0936771700473244041362286711715 absolute error = 1.154354964153537e-16 relative error = 1.8943487354853951499275144694626e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.629 y[1] (analytic) = 6.0987733949051151106626020045313 y[1] (numeric) = 6.0987733949051152263457562459334 absolute error = 1.156831542414021e-16 relative error = 1.8968265707009745652721038845097e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.63 y[1] (analytic) = 6.1038747185367257355366544351225 y[1] (numeric) = 6.1038747185367258514677142842693 absolute error = 1.159310598491468e-16 relative error = 1.8993027412092561463378446042253e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.631 y[1] (analytic) = 6.1089811460434802200438312262063 y[1] (numeric) = 6.1089811460434803362230447126997 absolute error = 1.161792134864934e-16 relative error = 1.9017772474504622258669681994449e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.632 y[1] (analytic) = 6.1140926825318064964742566323543 y[1] (numeric) = 6.1140926825318066129018720339498 absolute error = 1.164276154015955e-16 relative error = 1.9042500898658862416141624810804e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.633 y[1] (analytic) = 6.1192093331132414791155953098944 y[1] (numeric) = 6.1192093331132415957918611527495 absolute error = 1.166762658428551e-16 relative error = 1.9067212688978930970081977173881e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.634 y[1] (analytic) = 6.124331102904436175790392565999 y[1] (numeric) = 6.1243311029044362927155576249216 absolute error = 1.169251650589226e-16 relative error = 1.9091907849899129747556658950866e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.635 y[1] (analytic) = 6.1294579970271608045075085688286 y[1] (numeric) = 6.1294579970271609216818218675259 absolute error = 1.171743132986973e-16 relative error = 1.9116586385864433248733564388007e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.636 y[1] (analytic) = 6.1345900206083099152327631705911 y[1] (numeric) = 6.1345900206083100326564739819185 absolute error = 1.174237108113274e-16 relative error = 1.9141248301330426783494883991079e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.637 y[1] (analytic) = 6.1397271787799075167839131145883 y[1] (numeric) = 6.1397271787799076344572709607988 absolute error = 1.176733578462105e-16 relative error = 1.9165893600763326216135003515369e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.638 y[1] (analytic) = 6.1448694766791122088550885216543 y[1] (numeric) = 6.1448694766791123267783431746479 absolute error = 1.179232546529936e-16 relative error = 1.9190522288639916103480623047894e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.639 y[1] (analytic) = 6.15001691944822231917582068085 y[1] (numeric) = 6.1500169194482224373492221624236 absolute error = 1.181734014815736e-16 relative error = 1.9215134369447569305077417418680e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.64 y[1] (analytic) = 6.1551695122346810458097983038692 y[1] (numeric) = 6.1551695122346811642335968859664 absolute error = 1.184237985820972e-16 relative error = 1.9239729847684168877240092461060e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.641 y[1] (analytic) = 6.1603272601910816045984945423413 y[1] (numeric) = 6.1603272601910817232729407473029 absolute error = 1.186744462049616e-16 relative error = 1.9264308727858160083657646404182e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.642 y[1] (analytic) = 6.165490168475172381754812212087 y[1] (numeric) = 6.1654901684751725006801568129015 absolute error = 1.189253446008145e-16 relative error = 1.9288871014488488471251770883842e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.643 y[1] (analytic) = 6.170658242249862091611899818401 y[1] (numeric) = 6.1706582422498622107883938389552 absolute error = 1.191764940205542e-16 relative error = 1.9313416712104554323840210962567e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.644 y[1] (analytic) = 6.1758314866832249395322961316073 y[1] (numeric) = 6.1758314866832250589601908469377 absolute error = 1.194278947153304e-16 relative error = 1.9337945825246280551261027648185e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.645 y[1] (analytic) = 6.1810099069485057899825662224634 y[1] (numeric) = 6.1810099069485059096621131590069 absolute error = 1.196795469365435e-16 relative error = 1.9362458358463937420310068767300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.646 y[1] (analytic) = 6.1861935082241253397785970324779 y[1] (numeric) = 6.1861935082241254597100479683238 absolute error = 1.199314509358459e-16 relative error = 1.9386954316318291328267810245273e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.647 y[1] (analytic) = 6.19138229569368529650672572487 y[1] (numeric) = 6.1913822956936854166903326900116 absolute error = 1.201836069651416e-16 relative error = 1.9411433703380478115969717231520e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.648 y[1] (analytic) = 6.1965762745459735621258792377303 y[1] (numeric) = 6.196576274545973682561894514317 absolute error = 1.204360152765867e-16 relative error = 1.9435896524232022120277551146537e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.649 y[1] (analytic) = 6.2017754499749694217559086419538 y[1] (numeric) = 6.2017754499749695424445847645432 absolute error = 1.206886761225894e-16 relative error = 1.9460342783464774370813176353104e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.65 y[1] (analytic) = 6.2069798271798487376573070927123 y[1] (numeric) = 6.206979827179848858598896848523 absolute error = 1.209415897558107e-16 relative error = 1.9484772485680963735619766004515e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.651 y[1] (analytic) = 6.2121894113649891484075053546177 y[1] (numeric) = 6.2121894113649892696022617837818 absolute error = 1.211947564291641e-16 relative error = 1.9509185635493086697960865204457e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.652 y[1] (analytic) = 6.2174042077399752732789440773031 y[1] (numeric) = 6.2174042077399753947271204731196 absolute error = 1.214481763958165e-16 relative error = 1.9533582237523990555898476614950e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.653 y[1] (analytic) = 6.22262422151960392182412719993 y[1] (numeric) = 6.2226242215196040435259771091178 absolute error = 1.217018499091878e-16 relative error = 1.9557962296406747150720905032449e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.654 y[1] (analytic) = 6.2278494579238893086728660701076 y[1] (numeric) = 6.2278494579238894306286432930591 absolute error = 1.219557772229515e-16 relative error = 1.9582325816784687661554047984346e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.655 y[1] (analytic) = 6.2330799221780682735469290749028 y[1] (numeric) = 6.2330799221780683957568876659377 absolute error = 1.222099585910349e-16 relative error = 1.9606672803311372913904827631011e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.656 y[1] (analytic) = 6.2383156195126055064973167990266 y[1] (numeric) = 6.2383156195126056289617110666461 absolute error = 1.224643942676195e-16 relative error = 1.9631003260650595759881466133308e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.657 y[1] (analytic) = 6.2435565551631987783693879479068 y[1] (numeric) = 6.2435565551631989010884724550477 absolute error = 1.227190845071409e-16 relative error = 1.9655317193476303226272584065343e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=80.1MB, alloc=4.3MB, time=11.86 x[1] = 1.658 y[1] (analytic) = 6.2488027343707841765010665012086 y[1] (numeric) = 6.2488027343707842994750960654981 absolute error = 1.229740295642895e-16 relative error = 1.9679614606472646941502999236983e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.659 y[1] (analytic) = 6.2540541623815413456593657954475 y[1] (numeric) = 6.2540541623815414688885954894577 absolute error = 1.232292296940102e-16 relative error = 1.9703895504333873275231946404892e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.66 y[1] (analytic) = 6.2593108444468987342204704726538 y[1] (numeric) = 6.259310844446898857705155624157 absolute error = 1.234846851515032e-16 relative error = 1.9728159891764389631880605243081e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.661 y[1] (analytic) = 6.2645727858235388455986224756095 y[1] (numeric) = 6.2645727858235389693390186678334 absolute error = 1.237403961922239e-16 relative error = 1.9752407773478686608385555784999e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.662 y[1] (analytic) = 6.2698399917734034949290625189798 y[1] (numeric) = 6.2698399917734036189254255908634 absolute error = 1.239963630718836e-16 relative error = 1.9776639154201388001608047344880e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.663 y[1] (analytic) = 6.2751124675636990710102837197202 y[1] (numeric) = 6.2751124675636991952628697661693 absolute error = 1.242525860464491e-16 relative error = 1.9800854038667125131096573388667e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.664 y[1] (analytic) = 6.2803902184669018035108593294496 y[1] (numeric) = 6.2803902184669019280199247015929 absolute error = 1.245090653721433e-16 relative error = 1.9825052431620570883606679780201e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.665 y[1] (analytic) = 6.2856732497607630354461117760574 y[1] (numeric) = 6.285673249760763160211913081503 absolute error = 1.247658013054456e-16 relative error = 1.9849234337816441631244196958398e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.666 y[1] (analytic) = 6.2909615667283145009298954916526 y[1] (numeric) = 6.2909615667283146259526895947446 absolute error = 1.250227941030920e-16 relative error = 1.9873399762019451315551798028951e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.667 y[1] (analytic) = 6.2962551746578736082067712790772 y[1] (numeric) = 6.2962551746578737334868153011525 absolute error = 1.252800440220753e-16 relative error = 1.9897548709004281508546332248678e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.668 y[1] (analytic) = 6.3015540788430487279698552495994 y[1] (numeric) = 6.3015540788430488535074065692449 absolute error = 1.255375513196455e-16 relative error = 1.9921681183555583226271959821564e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.669 y[1] (analytic) = 6.3068582845827444869696306500752 y[1] (numeric) = 6.3068582845827446127649469033849 absolute error = 1.257953162533097e-16 relative error = 1.9945797190467899317878581908602e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.67 y[1] (analytic) = 6.3121677971811670669190161888314 y[1] (numeric) = 6.3121677971811671929723552696645 absolute error = 1.260533390808331e-16 relative error = 1.9969896734545761376236542588285e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.671 y[1] (analytic) = 6.3174826219478295086999897657817 y[1] (numeric) = 6.3174826219478296350116098260202 absolute error = 1.263116200602385e-16 relative error = 1.9993979820603548587059869179497e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.672 y[1] (analytic) = 6.322802764197557021877071813839 y[1] (numeric) = 6.3228027641975571484472312636457 absolute error = 1.265701594498067e-16 relative error = 2.0018046453465489495198885577094e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.673 y[1] (analytic) = 6.3281282292504922995229777655511 y[1] (numeric) = 6.3281282292504924263519352736285 absolute error = 1.268289575080774e-16 relative error = 2.0042096637965742638540047752017e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.674 y[1] (analytic) = 6.3334590224321008383617544710559 y[1] (numeric) = 6.3334590224321009654497689649044 absolute error = 1.270880144938485e-16 relative error = 2.0066130378948224012142381311260e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.675 y[1] (analytic) = 6.3387951490731762642347207109341 y[1] (numeric) = 6.3387951490731763915820513771112 absolute error = 1.273473306661771e-16 relative error = 2.0090147681266703456417544833163e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.676 y[1] (analytic) = 6.3441366145098456628945372703451 y[1] (numeric) = 6.3441366145098457905014435547244 absolute error = 1.276069062843793e-16 relative error = 2.0114148549784711272151652689005e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.677 y[1] (analytic) = 6.3494834240835749161327373689596 y[1] (numeric) = 6.3494834240835750439994789769903 absolute error = 1.278667416080307e-16 relative error = 2.0138132989375555415946074651079e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.678 y[1] (analytic) = 6.3548355831411740432460535746645 y[1] (numeric) = 6.3548355831411741713728904716313 absolute error = 1.281268368969668e-16 relative error = 2.0162101004922322737110505628835e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.679 y[1] (analytic) = 6.360193097034802547846882667812 y[1] (numeric) = 6.3601930970348026762340750790948 absolute error = 1.283871924112828e-16 relative error = 2.0186052601317785735539429553959e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.68 y[1] (analytic) = 6.3655559711219747700232352669232 y[1] (numeric) = 6.3655559711219748986710436782576 absolute error = 1.286478084113344e-16 relative error = 2.0209987783464466750180041328602e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.681 y[1] (analytic) = 6.370924210765565243853522376242 y[1] (numeric) = 6.3709242107655653727622075339795 absolute error = 1.289086851577375e-16 relative error = 2.0233906556274529028361538930491e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.682 y[1] (analytic) = 6.3762978213338140602815363703721 y[1] (numeric) = 6.3762978213338141894513592817409 absolute error = 1.291698229113688e-16 relative error = 2.0257808924669809357458560087327e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.683 y[1] (analytic) = 6.3816768082003322353569892914251 y[1] (numeric) = 6.3816768082003323647882112247912 absolute error = 1.294312219333661e-16 relative error = 2.0281694893581803386922680758108e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.684 y[1] (analytic) = 6.3870611767441070838469766996656 y[1] (numeric) = 6.3870611767441072135398591847941 absolute error = 1.296928824851285e-16 relative error = 2.0305564467951635232291960396326e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.685 y[1] (analytic) = 6.3924509323495075982237406895646 y[1] (numeric) = 6.3924509323495077281785455178812 absolute error = 1.299548048283166e-16 relative error = 2.0329417652730027097360441993715e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.686 y[1] (analytic) = 6.3978460804062898330341110594726 y[1] (numeric) = 6.3978460804062899632511002843253 absolute error = 1.302169892248527e-16 relative error = 2.0353254452877268914640678096787e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.687 y[1] (analytic) = 6.4032466263096022946560090048022 y[1] (numeric) = 6.4032466263096024251354449417234 absolute error = 1.304794359369212e-16 relative error = 2.0377074873363219238407239074866e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.688 y[1] (analytic) = 6.4086525754599913364474030916731 y[1] (numeric) = 6.408652575459991467189548318642 absolute error = 1.307421452269689e-16 relative error = 2.0400878919167290394310474192422e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.689 y[1] (analytic) = 6.4140639332634065592931126604252 y[1] (numeric) = 6.4140639332634066902982300181304 absolute error = 1.310051173577052e-16 relative error = 2.0424666595278417978224530102973e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=83.9MB, alloc=4.3MB, time=12.44 x[1] = 1.69 y[1] (analytic) = 6.4194807051312062175548592062532 y[1] (numeric) = 6.4194807051312063488232117983552 absolute error = 1.312683525921020e-16 relative error = 2.0448437906694983641571230207084e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.691 y[1] (analytic) = 6.4249028964801626304299716874637 y[1] (numeric) = 6.4249028964801627619618228808585 absolute error = 1.315318511933948e-16 relative error = 2.0472192858424924905889037904958e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.692 y[1] (analytic) = 6.4303305127324675987241571205134 y[1] (numeric) = 6.4303305127324677305197705455954 absolute error = 1.317956134250820e-16 relative error = 2.0495931455485564363660436687960e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.693 y[1] (analytic) = 6.435763559315737827043753235047 y[1] (numeric) = 6.4357635593157379591033927859731 absolute error = 1.320596395509261e-16 relative error = 2.0519653702903734833766734086736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.694 y[1] (analytic) = 6.4412020416630203514128853816428 y[1] (numeric) = 6.4412020416630204837368152165958 absolute error = 1.323239298349530e-16 relative error = 2.0543359605715608773126072260405e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.695 y[1] (analytic) = 6.4466459652127979723209553098721 y[1] (numeric) = 6.4466459652127981049094398513254 absolute error = 1.325884845414533e-16 relative error = 2.0567049168966838655955022304312e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.696 y[1] (analytic) = 6.4520953354089946932058948646169 y[1] (numeric) = 6.4520953354089948260591987995983 absolute error = 1.328533039349814e-16 relative error = 2.0590722397712355533577974827893e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.697 y[1] (analytic) = 6.4575501577009811643786230843498 y[1] (numeric) = 6.4575501577009812974970113647067 absolute error = 1.331183882803569e-16 relative error = 2.0614379297016524651894356931572e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.698 y[1] (analytic) = 6.4630104375435801323941506262894 y[1] (numeric) = 6.4630104375435802657778884689535 absolute error = 1.333837378426641e-16 relative error = 2.0638019871953006166196088003080e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.699 y[1] (analytic) = 6.4684761803970718948747808899881 y[1] (numeric) = 6.4684761803970720285241337772408 absolute error = 1.336493528872527e-16 relative error = 2.0661644127604801941934888932506e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.7 y[1] (analytic) = 6.4739473917271997607908626630091 y[1] (numeric) = 6.4739473917271998947060963427468 absolute error = 1.339152336797377e-16 relative error = 2.0685252069064178412239716097759e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.701 y[1] (analytic) = 6.4794240770051755162045545698991 y[1] (numeric) = 6.479424077005175650385935055899 absolute error = 1.341813804859999e-16 relative error = 2.0708843701432682292983004469799e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.702 y[1] (analytic) = 6.484906241707684895482067068678 y[1] (numeric) = 6.4849062417076850299298606408641 absolute error = 1.344477935721861e-16 relative error = 2.0732419029821109823165233570830e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.703 y[1] (analytic) = 6.490393891316893057979853207542 y[1] (numeric) = 6.4903938913168931926943264122515 absolute error = 1.347144732047095e-16 relative error = 2.0755978059349506842035513013560e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704 y[1] (analytic) = 6.495887031320450070210224828429 y[1] (numeric) = 6.4958870313204502051916444786786 absolute error = 1.349814196502496e-16 relative error = 2.0779520795147091760170773140891e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.705 y[1] (analytic) = 6.5013856672114963934918763835174 y[1] (numeric) = 6.5013856672114965287405095592704 absolute error = 1.352486331757530e-16 relative error = 2.0803047242352317219424134253439e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.706 y[1] (analytic) = 6.5068898044886683770908040156412 y[1] (numeric) = 6.5068898044886685126069180640744 absolute error = 1.355161140484332e-16 relative error = 2.0826557406112777623422375086428e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.707 y[1] (analytic) = 6.5123994486561037568571130439972 y[1] (numeric) = 6.5123994486561038926409755797683 absolute error = 1.357838625357711e-16 relative error = 2.0850051291585224490506011738678e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.708 y[1] (analytic) = 6.5179146052234471593632124924101 y[1] (numeric) = 6.5179146052234472954150913979254 absolute error = 1.360518789055153e-16 relative error = 2.0873528903935550910846842979048e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.709 y[1] (analytic) = 6.5234352797058556115489007988092 y[1] (numeric) = 6.5234352797058557478690642244913 absolute error = 1.363201634256821e-16 relative error = 2.0896990248338729960859852257069e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.71 y[1] (analytic) = 6.528961477624004055878852351461 y[1] (numeric) = 6.528961477624004192467568716017 absolute error = 1.365887163645560e-16 relative error = 2.0920435329978829878665245692982e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.711 y[1] (analytic) = 6.5344932045040908710180200099042 y[1] (numeric) = 6.5344932045040910078755580005942 absolute error = 1.368575379906900e-16 relative error = 2.0943864154048998422694258810792e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.712 y[1] (analytic) = 6.5400304658778433980304742864492 y[1] (numeric) = 6.540030465877843535157102859355 absolute error = 1.371266285729058e-16 relative error = 2.0967276725751431885970746182580e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.713 y[1] (analytic) = 6.5455732672825234721072053875428 y[1] (numeric) = 6.5455732672825236095031937678368 absolute error = 1.373959883802940e-16 relative error = 2.0990673050297344134512282812951e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.714 y[1] (analytic) = 6.5511216142609329598284198432597 y[1] (numeric) = 6.5511216142609330974940375254741 absolute error = 1.376656176822144e-16 relative error = 2.1014053132906950934530294375080e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.715 y[1] (analytic) = 6.5566755123614193019658689876804 y[1] (numeric) = 6.5566755123614194399013857359766 absolute error = 1.379355167482962e-16 relative error = 2.1037416978809438974773191751753e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.716 y[1] (analytic) = 6.562234967137881061830752092944 y[1] (numeric) = 6.5622349671378812000364379413827 absolute error = 1.382056858484387e-16 relative error = 2.1060764593243011107029161934136e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.717 y[1] (analytic) = 6.567799984149773479172742505344 y[1] (numeric) = 6.5677999841497736176488677581549 absolute error = 1.384761252528109e-16 relative error = 2.1084095981454763740205502730602e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.718 y[1] (analytic) = 6.573370568962114029635690682953 y[1] (numeric) = 6.5733705689621141683825259148053 absolute error = 1.387468352318523e-16 relative error = 2.1107411148700747279176703386401e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.719 y[1] (analytic) = 6.5789467271454879897755635909454 y[1] (numeric) = 6.5789467271454881287933796472182 absolute error = 1.390178160562728e-16 relative error = 2.1130710100245889324250949775494e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.72 y[1] (analytic) = 6.5845284642760540076461854730193 y[1] (numeric) = 6.5845284642760541469352534700727 absolute error = 1.392890679970534e-16 relative error = 2.1153992841364039625240921222222e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.721 y[1] (analytic) = 6.5901157859355496789583505851238 y[1] (numeric) = 6.5901157859355498185189419105697 absolute error = 1.395605913254459e-16 relative error = 2.1177259377337862932299579152370e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.722 y[1] (analytic) = 6.5957086977112971288178840510681 y[1] (numeric) = 6.5957086977112972686502703640419 absolute error = 1.398323863129738e-16 relative error = 2.1200509713458914195485582194383e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=13.02 NO POLE x[1] = 1.723 y[1] (analytic) = 6.6013072051962085990482325785396 y[1] (numeric) = 6.6013072051962087391526858099715 absolute error = 1.401044532314319e-16 relative error = 2.1223743855027516319269149362994e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.724 y[1] (analytic) = 6.6069113139887920411031723585858 y[1] (numeric) = 6.6069113139887921814799647114731 absolute error = 1.403767923528873e-16 relative error = 2.1246961807352850305660887743878e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.725 y[1] (analytic) = 6.6125210296931567145752270617358 y[1] (numeric) = 6.612521029693156855224631011415 absolute error = 1.406494039496792e-16 relative error = 2.1270163575752863333140332532557e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.726 y[1] (analytic) = 6.6181363579190187913053944396445 y[1] (numeric) = 6.6181363579190189322276827340636 absolute error = 1.409222882944191e-16 relative error = 2.1293349165554237610735981889272e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.727 y[1] (analytic) = 6.6237573042817069650997856424531 y[1] (numeric) = 6.6237573042817071062952313024445 absolute error = 1.411954456599914e-16 relative error = 2.1316518582092419647588217041050e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.728 y[1] (analytic) = 6.6293838744021680670587869689742 y[1] (numeric) = 6.6293838744021682085276632885277 absolute error = 1.414688763195535e-16 relative error = 2.1339671830711573820106390251313e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.729 y[1] (analytic) = 6.6350160739069726865243593793293 y[1] (numeric) = 6.6350160739069728282669399258654 absolute error = 1.417425805465361e-16 relative error = 2.1362808916764566186613893640793e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.73 y[1] (analytic) = 6.640653908428320797651096717808 y[1] (numeric) = 6.6406539084283209396676553324514 absolute error = 1.420165586146434e-16 relative error = 2.1385929845612933193990610957630e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.731 y[1] (analytic) = 6.6462973836040473916066692174754 y[1] (numeric) = 6.6462973836040475338974800153289 absolute error = 1.422908107978535e-16 relative error = 2.1409034622626880504029556298844e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.732 y[1] (analytic) = 6.6519465050776281144072844874402 y[1] (numeric) = 6.6519465050776282569726218578589 absolute error = 1.425653373704187e-16 relative error = 2.1432123253185266661147136197930e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.733 y[1] (analytic) = 6.6576012784981849103938038187158 y[1] (numeric) = 6.6576012784981850532339424255812 absolute error = 1.428401386068654e-16 relative error = 2.1455195742675526630036445326435e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.734 y[1] (analytic) = 6.6632617095204916713541572852586 y[1] (numeric) = 6.6632617095204918144693720672536 absolute error = 1.431152147819950e-16 relative error = 2.1478252096493745668144225313595e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.735 y[1] (analytic) = 6.668927803804979891297706763072 y[1] (numeric) = 6.6689278038049800346882729339557 absolute error = 1.433905661708837e-16 relative error = 2.1501292320044567746754823670657e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.736 y[1] (analytic) = 6.6745995670177443268872116422082 y[1] (numeric) = 6.6745995670177444705534046910911 absolute error = 1.436661930488829e-16 relative error = 2.1524316418741194200158686406963e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.737 y[1] (analytic) = 6.6802770048305486635340576641065 y[1] (numeric) = 6.680277004830548807476153355726 absolute error = 1.439420956916195e-16 relative error = 2.1547324398005367281398717369994e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.738 y[1] (analytic) = 6.6859601229208311871624149799684 y[1] (numeric) = 6.6859601229208313313806893549646 absolute error = 1.442182743749962e-16 relative error = 2.1570316263267353670857981186311e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.739 y[1] (analytic) = 6.6916489269717104616479971948011 y[1] (numeric) = 6.6916489269717106061427265699927 absolute error = 1.444947293751916e-16 relative error = 2.1593292019965898049980711636950e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.74 y[1] (analytic) = 6.6973434226719910119370988363601 y[1] (numeric) = 6.6973434226719911567085598050208 absolute error = 1.447714609686607e-16 relative error = 2.1616251673548236506066586218322e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.741 y[1] (analytic) = 6.7030436157161690128515943685033 y[1] (numeric) = 6.7030436157161691579000638006386 absolute error = 1.450484694321353e-16 relative error = 2.1639195229470094819546757807152e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.742 y[1] (analytic) = 6.7087495118044379835855875544297 y[1] (numeric) = 6.7087495118044381289113425970534 absolute error = 1.453257550426237e-16 relative error = 2.1662122693195582287779673893423e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.743 y[1] (analytic) = 6.7144611166426944878994056669249 y[1] (numeric) = 6.7144611166426946335027237443365 absolute error = 1.456033180774116e-16 relative error = 2.1685034070197264678473923931570e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.744 y[1] (analytic) = 6.7201784359425438400166387400849 y[1] (numeric) = 6.7201784359425439858977975541471 absolute error = 1.458811588140622e-16 relative error = 2.1707929365956117636421325621687e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.745 y[1] (analytic) = 6.7259014754213058162299297600317 y[1] (numeric) = 6.7259014754213059623892072904478 absolute error = 1.461592775304161e-16 relative error = 2.1730808585961450461382969539464e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.746 y[1] (analytic) = 6.7316302408020203722212274008865 y[1] (numeric) = 6.7316302408020205186589019054786 absolute error = 1.464376745045921e-16 relative error = 2.1753671735710963841850395341568e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.747 y[1] (analytic) = 6.7373647378134533661022186267307 y[1] (numeric) = 6.7373647378134535128185686417178 absolute error = 1.467163500149871e-16 relative error = 2.1776518820710673580874976787631e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.748 y[1] (analytic) = 6.7431049721901022871806642004637 y[1] (numeric) = 6.7431049721901024341759685407404 absolute error = 1.469953043402767e-16 relative error = 2.1799349846474938390612622545589e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.749 y[1] (analytic) = 6.7488509496722019904583658663702 y[1] (numeric) = 6.7488509496722021377329036257855 absolute error = 1.472745377594153e-16 relative error = 2.1822164818526413328390729082314e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.75 y[1] (analytic) = 6.7546026760057304368664997048427 y[1] (numeric) = 6.754602676005730584420550256479 absolute error = 1.475540505516363e-16 relative error = 2.1844963742396018145068348724333e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.751 y[1] (analytic) = 6.7603601569424144392440558950701 y[1] (numeric) = 6.7603601569424145870778988915226 absolute error = 1.478338429964525e-16 relative error = 2.1867746623622935249452602515155e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.752 y[1] (analytic) = 6.7661233982397354140651308646117 y[1] (numeric) = 6.7661233982397355621790462382681 absolute error = 1.481139153736564e-16 relative error = 2.1890513467754592773938872372601e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.753 y[1] (analytic) = 6.7718924056609351389208235536275 y[1] (numeric) = 6.7718924056609352873150915169479 absolute error = 1.483942679633204e-16 relative error = 2.1913264280346632829979285185715e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.754 y[1] (analytic) = 6.7776671849750215157614932761416 y[1] (numeric) = 6.7776671849750216644363943219387 absolute error = 1.486749010457971e-16 relative error = 2.1935999066962894550413075625540e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=13.60 NO POLE x[1] = 1.755 y[1] (analytic) = 6.7834477419567743399051424210758 y[1] (numeric) = 6.7834477419567744888609573227953 absolute error = 1.489558149017195e-16 relative error = 2.1958717833175382347211089727246e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.756 y[1] (analytic) = 6.7892340823867510748176930019174 y[1] (numeric) = 6.7892340823867512240547028139191 absolute error = 1.492370098120017e-16 relative error = 2.1981420584564307848076343927935e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.757 y[1] (analytic) = 6.7950262120512926326709318357798 y[1] (numeric) = 6.7950262120512927821894178936183 absolute error = 1.495184860578385e-16 relative error = 2.2004107326717969606213329982338e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.758 y[1] (analytic) = 6.8008241367425291606839049102811 y[1] (numeric) = 6.8008241367425293104841488309872 absolute error = 1.498002439207061e-16 relative error = 2.2026778065232795040570366223272e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.759 y[1] (analytic) = 6.8066278622583858332535472801182 y[1] (numeric) = 6.8066278622583859833358309624808 absolute error = 1.500822836823626e-16 relative error = 2.2049432805713352649824600400684e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.76 y[1] (analytic) = 6.8124373944025886498803406244497 y[1] (numeric) = 6.8124373944025888002449462492973 absolute error = 1.503646056248476e-16 relative error = 2.2072071553772231923296345678203e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.761 y[1] (analytic) = 6.8182527389846702388947963912265 y[1] (numeric) = 6.8182527389846703895420064217096 absolute error = 1.506472100304831e-16 relative error = 2.2094694315030114401504574666115e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.762 y[1] (analytic) = 6.8240739018199756669905682554387 y[1] (numeric) = 6.8240739018199758179206654373123 absolute error = 1.509300971818736e-16 relative error = 2.2117301095115727012772462651973e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.763 y[1] (analytic) = 6.8299008887296682545700034248743 y[1] (numeric) = 6.8299008887296684057832707867805 absolute error = 1.512132673619062e-16 relative error = 2.2139891899665795519403780488751e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.764 y[1] (analytic) = 6.8357337055407353969079481394257 y[1] (numeric) = 6.8357337055407355484046689931768 absolute error = 1.514967208537511e-16 relative error = 2.2162466734325056589365127016151e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.765 y[1] (analytic) = 6.8415723580859943911396285282354 y[1] (numeric) = 6.8415723580859945429200864690973 absolute error = 1.517804579408619e-16 relative error = 2.2185025604746240444673928546846e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.766 y[1] (analytic) = 6.8474168522040982690784338130463 y[1] (numeric) = 6.8474168522040984211429127200219 absolute error = 1.520644789069756e-16 relative error = 2.2207568516590009657750460694300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.767 y[1] (analytic) = 6.8532671937395416358694346760262 y[1] (numeric) = 6.8532671937395417882182187121395 absolute error = 1.523487840361133e-16 relative error = 2.2230095475525000273617162464029e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.768 y[1] (analytic) = 6.8591233885426665144844754460723 y[1] (numeric) = 6.8591233885426666671178490586523 absolute error = 1.526333736125800e-16 relative error = 2.2252606487227731381259925518784e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.769 y[1] (analytic) = 6.8649854424696681960646845991733 y[1] (numeric) = 6.8649854424696683489829325201387 absolute error = 1.529182479209654e-16 relative error = 2.2275101557382660686257932964459e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.77 y[1] (analytic) = 6.8708533613826010961162539158285 y[1] (numeric) = 6.8708533613826012493196611619725 absolute error = 1.532034072461440e-16 relative error = 2.2297580691682137791242230373739e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.771 y[1] (analytic) = 6.8767271511493846165653424917908 y[1] (numeric) = 6.8767271511493847700541943650656 absolute error = 1.534888518732748e-16 relative error = 2.2320043895826299419931773155428e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.772 y[1] (analytic) = 6.8826068176438090136779676575249 y[1] (numeric) = 6.8826068176438091674525497453276 absolute error = 1.537745820878027e-16 relative error = 2.2342491175523212049434975690596e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.773 y[1] (analytic) = 6.8884923667455412718507507267631 y[1] (numeric) = 6.888492366745541425911348902221 absolute error = 1.540605981754579e-16 relative error = 2.2364922536488723345026739515481e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.774 y[1] (analytic) = 6.8943838043401309832783913653911 y[1] (numeric) = 6.8943838043401311376252917876475 absolute error = 1.543469004222564e-16 relative error = 2.2387337984446473777769471647784e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.775 y[1] (analytic) = 6.9002811363190162335037502486301 y[1] (numeric) = 6.9002811363190163881372393631307 absolute error = 1.546334891145006e-16 relative error = 2.2409737525127922547433730598043e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.776 y[1] (analytic) = 6.906184368579529492856425557088 y[1] (numeric) = 6.9061843685795296477767900958671 absolute error = 1.549203645387791e-16 relative error = 2.2432121164272257406664039446137e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.777 y[1] (analytic) = 6.9120935070249035137857147507459 y[1] (numeric) = 6.9120935070249036689932417327134 absolute error = 1.552075269819675e-16 relative error = 2.2454488907626449493565531094993e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.778 y[1] (analytic) = 6.9180085575642772340938589543353 y[1] (numeric) = 6.9180085575642773895888356855635 absolute error = 1.554949767312282e-16 relative error = 2.2476840760945163205620729230051e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.779 y[1] (analytic) = 6.9239295261127016860754731878399 y[1] (numeric) = 6.9239295261127018418581872618509 absolute error = 1.557827140740110e-16 relative error = 2.2499176729990781949391549528931e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.78 y[1] (analytic) = 6.9298564185911459115690715820469 y[1] (numeric) = 6.9298564185911460676398108801 absolute error = 1.560707392980531e-16 relative error = 2.2521496820533347049229709917343e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.781 y[1] (analytic) = 6.9357892409265028829266026311638 y[1] (numeric) = 6.9357892409265030392856553225437 absolute error = 1.563590526913799e-16 relative error = 2.2543801038350612185823054208724e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.782 y[1] (analytic) = 6.9417279990515954299069154525317 y[1] (numeric) = 6.9417279990515955865545699948365 absolute error = 1.566476545423048e-16 relative error = 2.2566089389227953372110352633924e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.783 y[1] (analytic) = 6.947672698905182172499083947393 y[1] (numeric) = 6.9476726989051823294356290868227 absolute error = 1.569365451394297e-16 relative error = 2.2588361878958380016825738452061e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.784 y[1] (analytic) = 6.9536233464319634596815216865335 y[1] (numeric) = 6.9536233464319636169072464581786 absolute error = 1.572257247716451e-16 relative error = 2.2610618513342488280560589662960e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.785 y[1] (analytic) = 6.9595799475825873141228262804083 y[1] (numeric) = 6.9595799475825874716380200085391 absolute error = 1.575151937281308e-16 relative error = 2.2632859298188500756444938695668e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.786 y[1] (analytic) = 6.9655425083136553828302979350911 y[1] (numeric) = 6.9655425083136555406352502334468 absolute error = 1.578049522983557e-16 relative error = 2.2655084239312176613001568400447e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=14.17 NO POLE x[1] = 1.787 y[1] (analytic) = 6.9715110345877288937520828430617 y[1] (numeric) = 6.9715110345877290518470836151401 absolute error = 1.580950007720784e-16 relative error = 2.2677293342536836824075426376448e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.788 y[1] (analytic) = 6.9774855323733346183388980114707 y[1] (numeric) = 6.9774855323733347767242374508182 absolute error = 1.583853394393475e-16 relative error = 2.2699486613693346147462548428557e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.789 y[1] (analytic) = 6.9834660076449708400713000901046 y[1] (numeric) = 6.9834660076449709987472686806061 absolute error = 1.586759685905015e-16 relative error = 2.2721664058620037791256333710430e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.79 y[1] (analytic) = 6.9894524663831133289584667268155 y[1] (numeric) = 6.9894524663831134879253552429852 absolute error = 1.589668885161697e-16 relative error = 2.2743825683162781413394969226074e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.791 y[1] (analytic) = 6.9954449145742213220144649496965 y[1] (numeric) = 6.9954449145742214812725644569685 absolute error = 1.592580995072720e-16 relative error = 2.2765971493174893400675199727806e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.792 y[1] (analytic) = 7.0014433582107435097179870527682 y[1] (numeric) = 7.0014433582107436692675889077878 absolute error = 1.595496018550196e-16 relative error = 2.2788101494517176027011392731896e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.793 y[1] (analytic) = 7.0074478032911240284615404454122 y[1] (numeric) = 7.0074478032911241883029362963268 absolute error = 1.598413958509146e-16 relative error = 2.2810215693057799308642294387352e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.794 y[1] (analytic) = 7.0134582558198084589960839152395 y[1] (numeric) = 7.0134582558198086191295657019906 absolute error = 1.601334817867511e-16 relative error = 2.2832314094672397214793439332559e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.795 y[1] (analytic) = 7.0194747218072498308771087495312 y[1] (numeric) = 7.0194747218072499913029687041463 absolute error = 1.604258599546151e-16 relative error = 2.2854396705243992305402795649945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.796 y[1] (analytic) = 7.0254972072699146329181691618323 y[1] (numeric) = 7.0254972072699147936366998087171 absolute error = 1.607185306468848e-16 relative error = 2.2876463530662977565347883903698e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.797 y[1] (analytic) = 7.0315257182302888296578724777299 y[1] (numeric) = 7.0315257182302889906693666339608 absolute error = 1.610114941562309e-16 relative error = 2.2898514576827098206341048683569e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.798 y[1] (analytic) = 7.0375602607168838838463455473078 y[1] (numeric) = 7.0375602607168840451510963229248 absolute error = 1.613047507756170e-16 relative error = 2.2920549849641447646218132354088e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.799 y[1] (analytic) = 7.0436008407642427849571998712453 y[1] (numeric) = 7.043600840764242946555500669545 absolute error = 1.615983007982997e-16 relative error = 2.2942569355018420791438120915780e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.8 y[1] (analytic) = 7.0496474644129460837310239530277 y[1] (numeric) = 7.0496474644129462456231684708568 absolute error = 1.618921445178291e-16 relative error = 2.2964573098877724174699754759222e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.801 y[1] (analytic) = 7.0557001377096179327564374212646 y[1] (numeric) = 7.0557001377096180949427196493133 absolute error = 1.621862822280487e-16 relative error = 2.2986561087146300877463108548399e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.802 y[1] (analytic) = 7.0617588667069321330947475036717 y[1] (numeric) = 7.0617588667069322955754617267682 absolute error = 1.624807142230965e-16 relative error = 2.3008533325758425642714378577014e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.803 y[1] (analytic) = 7.0678236574636181869542544778789 y[1] (numeric) = 7.0678236574636183497296952752834 absolute error = 1.627754407974045e-16 relative error = 2.3030489820655572995244475137879e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804 y[1] (analytic) = 7.0738945160444673564202587738724 y[1] (numeric) = 7.0738945160444675194907210195715 absolute error = 1.630704622456991e-16 relative error = 2.3052430577786413143221416346237e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.805 y[1] (analytic) = 7.0799714485203387282468284585835 y[1] (numeric) = 7.0799714485203388916126073215855 absolute error = 1.633657788630020e-16 relative error = 2.3074355603106878398016427483763e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.806 y[1] (analytic) = 7.0860544609681652847163918948979 y[1] (numeric) = 7.0860544609681654483777828395276 absolute error = 1.636613909446297e-16 relative error = 2.3096264902580031556052759215907e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.807 y[1] (analytic) = 7.0921435594709599805732264351825 y[1] (numeric) = 7.0921435594709601445305252213768 absolute error = 1.639572987861943e-16 relative error = 2.3118158482176118134377088611361e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.808 y[1] (analytic) = 7.098238750117821826036920083326 y[1] (numeric) = 7.0982387501178219902904227669297 absolute error = 1.642535026836037e-16 relative error = 2.3140036347872533684913451917332e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.809 y[1] (analytic) = 7.1043400390039419759018891392612 y[1] (numeric) = 7.1043400390039421404518920723231 absolute error = 1.645500029330619e-16 relative error = 2.3161898505653805228036708088406e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.81 y[1] (analytic) = 7.1104474322306098247290409259947 y[1] (numeric) = 7.1104474322306099895758407570638 absolute error = 1.648467998310691e-16 relative error = 2.3183744961511544529461481158634e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.811 y[1] (analytic) = 7.1165609359052191081356767913138 y[1] (numeric) = 7.116560935905219273279570465736 absolute error = 1.651438936744222e-16 relative error = 2.3205575721444457700221902684318e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.812 y[1] (analytic) = 7.122680556141274010189736674583 y[1] (numeric) = 7.1226805561412741756310214347981 absolute error = 1.654412847602151e-16 relative error = 2.3227390791458326543634834403948e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.813 y[1] (analytic) = 7.1288062990583952769144926333827 y[1] (numeric) = 7.1288062990583954426534660192216 absolute error = 1.657389733858389e-16 relative error = 2.3249190177565975846350223953917e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.814 y[1] (analytic) = 7.1349381707823263359098048351939 y[1] (numeric) = 7.1349381707823265019467646841762 absolute error = 1.660369598489823e-16 relative error = 2.3270973885787268744738021029313e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.815 y[1] (analytic) = 7.1410761774449394220960596358944 y[1] (numeric) = 7.1410761774449395884313040835262 absolute error = 1.663352444476318e-16 relative error = 2.3292741922149073984052296115938e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.816 y[1] (analytic) = 7.147220325184241709586915489515 y[1] (numeric) = 7.147220325184241876220742969587 absolute error = 1.666338274800720e-16 relative error = 2.3314494292685247213693707703586e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.817 y[1] (analytic) = 7.1533706201443814496969885625129 y[1] (numeric) = 7.1533706201443816166296978073988 absolute error = 1.669327092448859e-16 relative error = 2.3336231003436612255001546647309e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.818 y[1] (analytic) = 7.1595270684756541150906160607592 y[1] (numeric) = 7.1595270684756542823225061017144 absolute error = 1.672318900409552e-16 relative error = 2.3357952060450942341818544112300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=99.1MB, alloc=4.3MB, time=14.74 x[1] = 1.819 y[1] (analytic) = 7.1656896763345085500778414185157 y[1] (numeric) = 7.1656896763345087176092115859767 absolute error = 1.675313701674610e-16 relative error = 2.3379657469782997155634334380985e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.82 y[1] (analytic) = 7.1718584498835531270637716458996 y[1] (numeric) = 7.1718584498835532948949215697828 absolute error = 1.678311499238832e-16 relative error = 2.3401347237494378281866545522298e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.821 y[1] (analytic) = 7.1780333952915619091574632847049 y[1] (numeric) = 7.1780333952915620772886928947066 absolute error = 1.681312296100017e-16 relative error = 2.3423021369653636052946745216561e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.822 y[1] (analytic) = 7.1842145187334808189464995819814 y[1] (numeric) = 7.1842145187334809873781091078777 absolute error = 1.684316095258963e-16 relative error = 2.3444679872336194764959875129655e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.823 y[1] (analytic) = 7.1904018263904338134434276564624 y[1] (numeric) = 7.1904018263904339821757176284091 absolute error = 1.687322899719467e-16 relative error = 2.3466322751624292063672640038992e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.824 y[1] (analytic) = 7.1965953244497290652102306047914 y[1] (numeric) = 7.1965953244497292342435018536249 absolute error = 1.690332712488335e-16 relative error = 2.3487950013607057474818195686527e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.825 y[1] (analytic) = 7.2027950191048651496670156725373 y[1] (numeric) = 7.2027950191048653190015693300753 absolute error = 1.693345536575380e-16 relative error = 2.3509561664380423804124754418542e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.826 y[1] (analytic) = 7.2090009165555372385911057991999 y[1] (numeric) = 7.2090009165555374082272432985425 absolute error = 1.696361374993426e-16 relative error = 2.3531157710047122100394613565368e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.827 y[1] (analytic) = 7.2152130230076432998127280368143 y[1] (numeric) = 7.2152130230076434697507511126456 absolute error = 1.699380230758313e-16 relative error = 2.3552738156716690381333670407615e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.828 y[1] (analytic) = 7.2214313446732903031134985383596 y[1] (numeric) = 7.2214313446732904733537092272491 absolute error = 1.702402106888895e-16 relative error = 2.3574303010505385257646973212324e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.829 y[1] (analytic) = 7.2276558877708004323339100149724 y[1] (numeric) = 7.2276558877708006028766106556774 absolute error = 1.705427006407050e-16 relative error = 2.3595852277536259919507146781115e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.83 y[1] (analytic) = 7.2338866585247173036960337699729 y[1] (numeric) = 7.2338866585247174745415270037406 absolute error = 1.708454932337677e-16 relative error = 2.3617385963939061888001914834590e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.831 y[1] (analytic) = 7.2401236631658121903476546329209 y[1] (numeric) = 7.2401236631658123614962434037912 absolute error = 1.711485887708703e-16 relative error = 2.3638904075850269290872078605496e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.832 y[1] (analytic) = 7.2463669079310902531340633383577 y[1] (numeric) = 7.246366907931090424586050893466 absolute error = 1.714519875551083e-16 relative error = 2.3660406619413030228373427003296e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.833 y[1] (analytic) = 7.2526163990637967776037371215442 y[1] (numeric) = 7.2526163990637969493594270114246 absolute error = 1.717556898898804e-16 relative error = 2.3681893600777157482297424673454e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.834 y[1] (analytic) = 7.2588721428134234172541455373957 y[1] (numeric) = 7.2588721428134235893138416162848 absolute error = 1.720596960788891e-16 relative error = 2.3703365026099150682636177259215e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.835 y[1] (analytic) = 7.2651341454357144430239247489402 y[1] (numeric) = 7.2651341454357146153879311750809 absolute error = 1.723640064261407e-16 relative error = 2.3724820901542135651101897188717e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.836 y[1] (analytic) = 7.2714024131926729990376697779945 y[1] (numeric) = 7.2714024131926731717062910139399 absolute error = 1.726686212359454e-16 relative error = 2.3746261233275817688162487510920e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.837 y[1] (analytic) = 7.2776769523525673646096004633717 y[1] (numeric) = 7.2776769523525675375831412762898 absolute error = 1.729735408129181e-16 relative error = 2.3767686027476531164174732033360e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.838 y[1] (analytic) = 7.2839577691899372225123631308089 y[1] (numeric) = 7.2839577691899373957911285927872 absolute error = 1.732787654619783e-16 relative error = 2.3789095290327165173117208312280e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.839 y[1] (analytic) = 7.2902448699855999335172362439372 y[1] (numeric) = 7.290244869985600107101531732288 absolute error = 1.735842954883508e-16 relative error = 2.3810489028017199184283444327467e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.84 y[1] (analytic) = 7.2965382610266568172120145770248 y[1] (numeric) = 7.2965382610266569911021457745905 absolute error = 1.738901311975657e-16 relative error = 2.3831867246742642451961862504929e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.841 y[1] (analytic) = 7.3028379486064994391028527278992 y[1] (numeric) = 7.3028379486064996132991256233578 absolute error = 1.741962728954586e-16 relative error = 2.3853229952706001003117486140586e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.842 y[1] (analytic) = 7.3091439390248159040063550734161 y[1] (numeric) = 7.3091439390248160785090759615874 absolute error = 1.745027208881713e-16 relative error = 2.3874577152116313081845953709456e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.843 y[1] (analytic) = 7.3154562385875971557382055600903 y[1] (numeric) = 7.3154562385875973305476810422421 absolute error = 1.748094754821518e-16 relative error = 2.3895908851189088601210750677110e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.844 y[1] (analytic) = 7.3217748536071432831046370190424 y[1] (numeric) = 7.3217748536071434582211740031971 absolute error = 1.751165369841547e-16 relative error = 2.3917225056146303418251100226871e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.845 y[1] (analytic) = 7.3280997904020698322030459972565 y[1] (numeric) = 7.328099790402070007626951698498 absolute error = 1.754239057012415e-16 relative error = 2.3938525773216379871264634922096e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.846 y[1] (analytic) = 7.3344310552973141250380654062898 y[1] (numeric) = 7.3344310552973143007696473470709 absolute error = 1.757315819407811e-16 relative error = 2.3959811008634194565196647970549e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.847 y[1] (analytic) = 7.3407686546241415844594136050335 y[1] (numeric) = 7.340768654624141760498979615483 absolute error = 1.760395660104495e-16 relative error = 2.3981080768640977015049689687442e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.848 y[1] (analytic) = 7.3471125947201520654278448549001 y[1] (numeric) = 7.3471125947201522417757030731312 absolute error = 1.763478582182311e-16 relative error = 2.4002335059484426465537995930257e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.849 y[1] (analytic) = 7.3534628819292861926155324139173 y[1] (numeric) = 7.3534628819292863692719912863352 absolute error = 1.766564588724179e-16 relative error = 2.4023573887418542405387698807106e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.85 y[1] (analytic) = 7.3598195226018317043472218706367 y[1] (numeric) = 7.3598195226018318813125901522474 absolute error = 1.769653682816107e-16 relative error = 2.4044797258703727583757851734162e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=103.0MB, alloc=4.3MB, time=15.30 x[1] = 1.851 y[1] (analytic) = 7.3661825230944298028884986595428 y[1] (numeric) = 7.3661825230944299801630854142616 absolute error = 1.772745867547188e-16 relative error = 2.4066005179606686739518381167146e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.852 y[1] (analytic) = 7.3725518897700815110875200467554 y[1] (numeric) = 7.3725518897700816886716346477163 absolute error = 1.775841146009609e-16 relative error = 2.4087197656400488499958978088614e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.853 y[1] (analytic) = 7.3789276289981540353765682282906 y[1] (numeric) = 7.3789276289981542132705203581553 absolute error = 1.778939521298647e-16 relative error = 2.4108374695364450660994019147625e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.854 y[1] (analytic) = 7.3853097471543871351397875429606 y[1] (numeric) = 7.3853097471543873133438871942285 absolute error = 1.782040996512679e-16 relative error = 2.4129536302784215506507941711139e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.855 y[1] (analytic) = 7.3916982506208994984534751681827 y[1] (numeric) = 7.3916982506208996769680326435006 absolute error = 1.785145574753179e-16 relative error = 2.4150682484951648744290176339220e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.856 y[1] (analytic) = 7.398093145786195124205301039518 y[1] (numeric) = 7.3980931457861953030306269519907 absolute error = 1.788253259124727e-16 relative error = 2.4171813248164901049119144938849e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.857 y[1] (analytic) = 7.4044944390451697105988391136926 y[1] (numeric) = 7.4044944390451698897352443871932 absolute error = 1.791364052735006e-16 relative error = 2.4192928598728307103082296484614e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.858 y[1] (analytic) = 7.4109021367991170500497984801639 y[1] (numeric) = 7.410902136799117229497594349645 absolute error = 1.794477958694811e-16 relative error = 2.4214028542952446962515687506165e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.859 y[1] (analytic) = 7.417316245455735430480349217997 y[1] (numeric) = 7.4173162454557356102398472298017 absolute error = 1.797594980118047e-16 relative error = 2.4235113087154058685344068131924e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.86 y[1] (analytic) = 7.4237367714291340430179442929097 y[1] (numeric) = 7.4237367714291342230894563050835 absolute error = 1.800715120121738e-16 relative error = 2.4256182237656099464652555520167e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.861 y[1] (analytic) = 7.430163721139839396105045193843 y[1] (numeric) = 7.4301637211398395764888833764451 absolute error = 1.803838381826021e-16 relative error = 2.4277236000787604445647746031458e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.862 y[1] (analytic) = 7.4365971010148017360261654193154 y[1] (numeric) = 7.4365971010148019167226422547315 absolute error = 1.806964768354161e-16 relative error = 2.4298274382883828542198337942926e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.863 y[1] (analytic) = 7.4430369174874014738586523411422 y[1] (numeric) = 7.4430369174874016548680806243966 absolute error = 1.810094282832544e-16 relative error = 2.4319297390286091820115001764186e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.864 y[1] (analytic) = 7.4494831769974556188536343968346 y[1] (numeric) = 7.449483176997455800176327235903 absolute error = 1.813226928390684e-16 relative error = 2.4340305029341813494938166390279e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.865 y[1] (analytic) = 7.4559358859912242182535669921635 y[1] (numeric) = 7.4559358859912243998898378082861 absolute error = 1.816362708161226e-16 relative error = 2.4361297306404491985759139901260e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.866 y[1] (analytic) = 7.4623950509214168035528169319699 y[1] (numeric) = 7.4623950509214169855029794599652 absolute error = 1.819501625279953e-16 relative error = 2.4382274227833738555243227034973e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.867 y[1] (analytic) = 7.4688606782471988432077316403445 y[1] (numeric) = 7.4688606782471990254720999289224 absolute error = 1.822643682885779e-16 relative error = 2.4403235799995123210640200126952e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.868 y[1] (analytic) = 7.4753327744341982018026458807814 y[1] (numeric) = 7.4753327744341983843815342928579 absolute error = 1.825788884120765e-16 relative error = 2.4424182029260328963971105041528e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.869 y[1] (analytic) = 7.4818113459545116056782851428534 y[1] (numeric) = 7.4818113459545117885720083558644 absolute error = 1.828937232130110e-16 relative error = 2.4445112922006971028995937527419e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.87 y[1] (analytic) = 7.4882963992867111150290313243491 y[1] (numeric) = 7.4882963992867112982379043305654 absolute error = 1.832088730062163e-16 relative error = 2.4466028484618697275051990332675e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.871 y[1] (analytic) = 7.4947879409158506024755228066778 y[1] (numeric) = 7.4947879409158507859998609135201 absolute error = 1.835243381068423e-16 relative error = 2.4486928723485127929559666897547e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.872 y[1] (analytic) = 7.501285977333472238119067496682 y[1] (numeric) = 7.501285977333472421959186327036 absolute error = 1.838401188303540e-16 relative error = 2.4507813645001808805508525846157e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.873 y[1] (analytic) = 7.5077905150376129810843538898108 y[1] (numeric) = 7.5077905150376131652405693823431 absolute error = 1.841562154925323e-16 relative error = 2.4528683255570257889738700028351e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.874 y[1] (analytic) = 7.5143015605328110775569516979066 y[1] (numeric) = 7.5143015605328112620295801073803 absolute error = 1.844726284094737e-16 relative error = 2.4549537561597865183132227259605e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.875 y[1] (analytic) = 7.5208191203301125653221000796462 y[1] (numeric) = 7.5208191203301127501114579772375 absolute error = 1.847893578975913e-16 relative error = 2.4570376569497965796006672940543e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.876 y[1] (analytic) = 7.5273432009470777848112880129684 y[1] (numeric) = 7.5273432009470779699176922865831 absolute error = 1.851064042736147e-16 relative error = 2.4591200285689766411551186227192e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.877 y[1] (analytic) = 7.5338738089077878966631378566094 y[1] (numeric) = 7.5338738089077880820869057111994 absolute error = 1.854237678545900e-16 relative error = 2.4612008716598285286079273763138e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.878 y[1] (analytic) = 7.5404109507428514058051096621729 y[1] (numeric) = 7.5404109507428515915465586200539 absolute error = 1.857414489578810e-16 relative error = 2.4632801868654451585685964289416e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.879 y[1] (analytic) = 7.5469546329894106920625503189842 y[1] (numeric) = 7.546954632989410878121998220153 absolute error = 1.860594479011688e-16 relative error = 2.4653579748294992082499135498468e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.88 y[1] (analytic) = 7.5535048621911485473016181413198 y[1] (numeric) = 7.5535048621911487336793831437722 absolute error = 1.863777650024524e-16 relative error = 2.4674342361962450710326702401302e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.881 y[1] (analytic) = 7.5600616448982947191126200414837 y[1] (numeric) = 7.5600616448982949058090206215326 absolute error = 1.866964005800489e-16 relative error = 2.4695089716105154991248159721277e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.882 y[1] (analytic) = 7.566624987667632461040304972611 y[1] (numeric) = 7.5666249876676326480556599252049 absolute error = 1.870153549525939e-16 relative error = 2.4715821817177208950736693539496e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.883 y[1] (analytic) = 7.5731948970625050893676638720398 y[1] (numeric) = 7.5731948970625052767022923110816 absolute error = 1.873346284390418e-16 relative error = 2.4736538671638472747426318334749e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.3MB, time=15.88 NO POLE x[1] = 1.884 y[1] (analytic) = 7.5797713796528225464597928895968 y[1] (numeric) = 7.5797713796528227341140142482629 absolute error = 1.876542213586661e-16 relative error = 2.4757240285954542291110728316299e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.885 y[1] (analytic) = 7.5863544420150679706743832452064 y[1] (numeric) = 7.5863544420150681586485172762662 absolute error = 1.879741340310598e-16 relative error = 2.4777926666596742030737785780623e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.886 y[1] (analytic) = 7.5929440907323042728454076268625 y[1] (numeric) = 7.592944090732304461139774402998 absolute error = 1.882943667761355e-16 relative error = 2.4798597820042078152034486430276e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.887 y[1] (analytic) = 7.5995403323941807193465796131947 y[1] (numeric) = 7.5995403323941809079614995273208 absolute error = 1.886149199141261e-16 relative error = 2.4819253752773270853414892631904e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.888 y[1] (analytic) = 7.6061431735969395217411691846394 y[1] (numeric) = 7.606143173596939710676962950224 absolute error = 1.889357937655846e-16 relative error = 2.4839894471278668011238315317477e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.889 y[1] (analytic) = 7.6127526209434224330247639735788 y[1] (numeric) = 7.6127526209434226222817526249639 absolute error = 1.892569886513851e-16 relative error = 2.4860519982052316807356265004225e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.89 y[1] (analytic) = 7.6193686810430773504675724967601 y[1] (numeric) = 7.6193686810430775400460773894824 absolute error = 1.895785048927223e-16 relative error = 2.4881130291593838000080321611356e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.891 y[1] (analytic) = 7.6259913605119649250628722128465 y[1] (numeric) = 7.6259913605119651149632150239591 absolute error = 1.899003428111126e-16 relative error = 2.4901725406408510541293328425875e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.892 y[1] (analytic) = 7.6326206659727651775882118541011 y[1] (numeric) = 7.6326206659727653678107145824951 absolute error = 1.902225027283940e-16 relative error = 2.4922305333007198416407821475533e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.893 y[1] (analytic) = 7.6392566040547841212859840939558 y[1] (numeric) = 7.6392566040547843118309690606821 absolute error = 1.905449849667263e-16 relative error = 2.4942870077906317018963097629949e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.894 y[1] (analytic) = 7.6458991813939603911699912315898 y[1] (numeric) = 7.6458991813939605820377810801815 absolute error = 1.908677898485917e-16 relative error = 2.4963419647627851899435068785877e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.895 y[1] (analytic) = 7.6525484046328718799646332006366 y[1] (numeric) = 7.6525484046328720711555508974319 absolute error = 1.911909176967953e-16 relative error = 2.4983954048699364232371554469896e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.896 y[1] (analytic) = 7.6592042804207423806833538417607 y[1] (numeric) = 7.6592042804207425721977226762255 absolute error = 1.915143688344648e-16 relative error = 2.5004473287653891688761586877571e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.897 y[1] (analytic) = 7.6658668154134482358529880181017 y[1] (numeric) = 7.6658668154134484276911316031533 absolute error = 1.918381435850516e-16 relative error = 2.5024977371030032336100100526974e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.898 y[1] (analytic) = 7.6725360162735249933906587984906 y[1] (numeric) = 7.6725360162735251855529010708209 absolute error = 1.921622422723303e-16 relative error = 2.5045466305371819449059358504588e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.899 y[1] (analytic) = 7.6792118896701740691398805858861 y[1] (numeric) = 7.6792118896701742616265458062858 absolute error = 1.924866652203997e-16 relative error = 2.5065940097228792188654202966268e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.9 y[1] (analytic) = 7.6858944422792694160725307276929 y[1] (numeric) = 7.6858944422792696088839434813755 absolute error = 1.928114127536826e-16 relative error = 2.5086398753155909666973212666143e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.901 y[1] (analytic) = 7.6925836807833642001633588104863 y[1] (numeric) = 7.6925836807833643932998440074131 absolute error = 1.931364851969268e-16 relative error = 2.5106842279713621338068374304837e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.902 y[1] (analytic) = 7.6992796118716974829437095142116 y[1] (numeric) = 7.6992796118716976764055923894162 absolute error = 1.934618828752046e-16 relative error = 2.5127270683467742082497009574875e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.903 y[1] (analytic) = 7.7059822422402009107411415801352 y[1] (numeric) = 7.705982242240201104528747694049 absolute error = 1.937876061139138e-16 relative error = 2.5147683970989522481063862911583e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904 y[1] (analytic) = 7.7126915785915054106116321327263 y[1] (numeric) = 7.7126915785915056047252873715039 absolute error = 1.941136552387776e-16 relative error = 2.5168082148855575984531336037712e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.905 y[1] (analytic) = 7.7194076276349478929710622882295 y[1] (numeric) = 7.7194076276349480874110928640747 absolute error = 1.944400305758452e-16 relative error = 2.5188465223647897027820719144786e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.906 y[1] (analytic) = 7.7261303960865779609326866819739 y[1] (numeric) = 7.7261303960865781556994191334658 absolute error = 1.947667324514919e-16 relative error = 2.5208833201953814218783815068704e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.907 y[1] (analytic) = 7.7328598906691646263572962524467 y[1] (numeric) = 7.7328598906691648214510574448664 absolute error = 1.950937611924197e-16 relative error = 2.5229186090366008314750616049320e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.908 y[1] (analytic) = 7.7395961181122030326227903328538 y[1] (numeric) = 7.7395961181122032280439074585111 absolute error = 1.954211171256573e-16 relative error = 2.5249523895482452466474460332970e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.909 y[1] (analytic) = 7.7463390851519211841198808202997 y[1] (numeric) = 7.7463390851519213798686813988603 absolute error = 1.957488005785606e-16 relative error = 2.5269846623906417205123982053373e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.91 y[1] (analytic) = 7.7530887985312866824806579188518 y[1] (numeric) = 7.753088798531286878557469797665 absolute error = 1.960768118788132e-16 relative error = 2.5290154282246475288204388461228e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.911 y[1] (analytic) = 7.7598452650000134695467536856162 y[1] (numeric) = 7.7598452650000136659519050400427 absolute error = 1.964051513544265e-16 relative error = 2.5310446877116454857525104529750e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.912 y[1] (analytic) = 7.7666084913145685770838463485505 y[1] (numeric) = 7.7666084913145687738176656822902 absolute error = 1.967338193337397e-16 relative error = 2.5330724415135379850863634520445e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.913 y[1] (analytic) = 7.7733784842381788832492551110796 y[1] (numeric) = 7.7733784842381790803120712565007 absolute error = 1.970628161454211e-16 relative error = 2.5350986902927577847526074097940e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.914 y[1] (analytic) = 7.780155250540837875819381911674 y[1] (numeric) = 7.7801552505408380732115240301415 absolute error = 1.973921421184675e-16 relative error = 2.5371234347122543024933403605914e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.915 y[1] (analytic) = 7.7869387969993124221837633663945 y[1] (numeric) = 7.7869387969993126199055609485993 absolute error = 1.977217975822048e-16 relative error = 2.5391466754354953819892210520730e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=16.45 NO POLE x[1] = 1.916 y[1] (analytic) = 7.7937291303971495461125028890197 y[1] (numeric) = 7.7937291303971497441642857553081 absolute error = 1.980517828662884e-16 relative error = 2.5411684131264664721715052229472e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.917 y[1] (analytic) = 7.8005262575246832113038597567535 y[1] (numeric) = 7.8005262575246834096859580574574 absolute error = 1.983820983007039e-16 relative error = 2.5431886484496736452662007077971e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.918 y[1] (analytic) = 7.8073301851790411117187786696674 y[1] (numeric) = 7.8073301851790413104315228854339 absolute error = 1.987127442157665e-16 relative error = 2.5452073820701299365833496742431e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.919 y[1] (analytic) = 7.8141409201641514687091501389713 y[1] (numeric) = 7.8141409201641516677528710810936 absolute error = 1.990437209421223e-16 relative error = 2.5472246146533660591281672151851e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.92 y[1] (analytic) = 7.8209584692907498349465988329418 y[1] (numeric) = 7.8209584692907500343216276436897 absolute error = 1.993750288107479e-16 relative error = 2.5492403468654193143637915636626e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.921 y[1] (analytic) = 7.8277828393763859051586038098615 y[1] (numeric) = 7.8277828393763861048652719628128 absolute error = 1.997066681529513e-16 relative error = 2.5512545793728391569975592299717e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.922 y[1] (analytic) = 7.8346140372454303336787613746585 y[1] (numeric) = 7.8346140372454305337174006750304 absolute error = 2.000386393003719e-16 relative error = 2.5532673128426812318078134750021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.923 y[1] (analytic) = 7.841452069729081558818008110076 y[1] (numeric) = 7.8414520697290817591889506950569 absolute error = 2.003709425849809e-16 relative error = 2.5552785479425065313182954390384e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.924 y[1] (analytic) = 7.8482969436653726340636284541646 y[1] (numeric) = 7.8482969436653728347672067932461 absolute error = 2.007035783390815e-16 relative error = 2.5572882853403779981726683763615e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.925 y[1] (analytic) = 7.8551486658991780661128780236733 y[1] (numeric) = 7.8551486658991782671494249189828 absolute error = 2.010365468953095e-16 relative error = 2.5592965257048622261062317351976e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.926 y[1] (analytic) = 7.862007243282220659748060717533 y[1] (numeric) = 7.8620072432822208611179093041666 absolute error = 2.013698485866336e-16 relative error = 2.5613032697050273248405072845613e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.927 y[1] (analytic) = 7.8688726826730783695599044760802 y[1] (numeric) = 7.8688726826730785712633882224355 absolute error = 2.017034837463553e-16 relative error = 2.5633085180104357014450575018572e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.928 y[1] (analytic) = 7.8757449909371911585260874199663 y[1] (numeric) = 7.8757449909371913605635401280763 absolute error = 2.020374527081100e-16 relative error = 2.5653122712911521047721806047916e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.929 y[1] (analytic) = 7.8826241749468678634517729478523 y[1] (numeric) = 7.8826241749468680658235287537189 absolute error = 2.023717558058666e-16 relative error = 2.5673145302177325872803996715061e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.93 y[1] (analytic) = 7.8895102415812930672790192339938 y[1] (numeric) = 7.8895102415812932699854126079221 absolute error = 2.027063933739283e-16 relative error = 2.5693152954612287233222748268948e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.931 y[1] (analytic) = 7.8964031977265339782719354357008 y[1] (numeric) = 7.8964031977265341813133011826334 absolute error = 2.030413657469326e-16 relative error = 2.5713145676931816628645350688661e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.932 y[1] (analytic) = 7.9033030502755473160844637963994 y[1] (numeric) = 7.9033030502755475194611370562513 absolute error = 2.033766732598519e-16 relative error = 2.5733123475856237967713727683029e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.933 y[1] (analytic) = 7.9102098061281862047176737126536 y[1] (numeric) = 7.9102098061281864084299899606473 absolute error = 2.037123162479937e-16 relative error = 2.5753086358110753453255154380962e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.934 y[1] (analytic) = 7.9171234721912070723734607230139 y[1] (numeric) = 7.917123472191207276421755770015 absolute error = 2.040482950470011e-16 relative error = 2.5773034330425447425622599112618e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.935 y[1] (analytic) = 7.9240440553782765582115502729679 y[1] (numeric) = 7.9240440553782767625961602658209 absolute error = 2.043846099928530e-16 relative error = 2.5792967399535252213592228027934e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.936 y[1] (analytic) = 7.9309715626099784260167130135715 y[1] (numeric) = 7.9309715626099786307379744354358 absolute error = 2.047212614218643e-16 relative error = 2.5812885572179914051207661552745e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.937 y[1] (analytic) = 7.9379060008138204847831053015525 y[1] (numeric) = 7.9379060008138206898413549722389 absolute error = 2.050582496706864e-16 relative error = 2.5832788855103996853910800342521e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.938 y[1] (analytic) = 7.9448473769242415162226554858033 y[1] (numeric) = 7.944847376924241721618230562111 absolute error = 2.053955750763077e-16 relative error = 2.5852677255056885862494542743582e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.939 y[1] (analytic) = 7.9517956978826182092044234892275 y[1] (numeric) = 7.951795697882618414937661465281 absolute error = 2.057332379760535e-16 relative error = 2.5872550778792715700737835616522e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.94 y[1] (analytic) = 7.958750970637272101131868125876 y[1] (numeric) = 7.9587509706372723072031068334628 absolute error = 2.060712387075868e-16 relative error = 2.5892409433070411780608913347779e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.941 y[1] (analytic) = 7.9657132021434765262649635312202 y[1] (numeric) = 7.9657132021434767326745411401286 absolute error = 2.064095776089084e-16 relative error = 2.5912253224653643501792320185123e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.942 y[1] (analytic) = 7.9726823993634635709941130282566 y[1] (numeric) = 7.9726823993634637777423680466137 absolute error = 2.067482550183571e-16 relative error = 2.5932082160310790126922840587816e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.943 y[1] (analytic) = 7.9796585692664310360728157039367 y[1] (numeric) = 7.9796585692664312431600869785471 absolute error = 2.070872712746104e-16 relative error = 2.5951896246814969383047405222039e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.944 y[1] (analytic) = 7.9866417188285494058160479291685 y[1] (numeric) = 7.9866417188285496132426746458531 absolute error = 2.074266267166846e-16 relative error = 2.5971695490943990675824507458498e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.945 y[1] (analytic) = 7.9936318550329688242713290213531 y[1] (numeric) = 7.9936318550329690320376507052883 absolute error = 2.077663216839352e-16 relative error = 2.5991479899480345966801125841655e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.946 y[1] (analytic) = 8.0006289848698260783694472211019 y[1] (numeric) = 8.0006289848698262864758037371591 absolute error = 2.081063565160572e-16 relative error = 2.6011249479211188087760026780217e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.947 y[1] (analytic) = 8.007633115336251588061829134443 y[1] (numeric) = 8.0076331153362517965085606875284 absolute error = 2.084467315530854e-16 relative error = 2.6031004236928309057087545322279e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=17.04 NO POLE x[1] = 1.948 y[1] (analytic) = 8.014644253436376403451542778469 y[1] (numeric) = 8.014644253436376612238989913864 absolute error = 2.087874471353950e-16 relative error = 2.6050744179428155829806227751741e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.949 y[1] (analytic) = 8.0216624061813392089249313620124 y[1] (numeric) = 8.0216624061813394180534349657137 absolute error = 2.091285036037013e-16 relative error = 2.6070469313511733657267311808813e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.95 y[1] (analytic) = 8.0286875805892933342908819335644 y[1] (numeric) = 8.0286875805892935437607832326255 absolute error = 2.094699012990611e-16 relative error = 2.6090179645984721583122002837076e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.951 y[1] (analytic) = 8.0357197836854137729347400362931 y[1] (numeric) = 8.0357197836854139827463805991652 absolute error = 2.098116405628721e-16 relative error = 2.6109875183657338333485574866590e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.952 y[1] (analytic) = 8.0427590225019042069938885246578 y[1] (numeric) = 8.0427590225019044171476102615312 absolute error = 2.101537217368734e-16 relative error = 2.6129555933344345568056527495015e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.953 y[1] (analytic) = 8.0498053040780040395620157187845 y[1] (numeric) = 8.0498053040780042500581608819309 absolute error = 2.104961451631464e-16 relative error = 2.6149221901865100694148538473755e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.954 y[1] (analytic) = 8.0568586354599954339291051014579 y[1] (numeric) = 8.0568586354599956447680162855723 absolute error = 2.108389111841144e-16 relative error = 2.6168873096043447939278608192363e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.955 y[1] (analytic) = 8.0639190237012103598641857983045 y[1] (numeric) = 8.063919023701210571046205940848 absolute error = 2.111820201425435e-16 relative error = 2.6188509522707771096286643250584e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.956 y[1] (analytic) = 8.0709864758620376469478901245053 y[1] (numeric) = 8.070986475862037858473362506048 absolute error = 2.115254723815427e-16 relative error = 2.6208131188690946760532050785965e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.957 y[1] (analytic) = 8.0780609990099300449618715311838 y[1] (numeric) = 8.0780609990099302568311397757481 absolute error = 2.118692682445643e-16 relative error = 2.6227738100830334839293847690835e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.958 y[1] (analytic) = 8.0851426002194112913421433414748 y[1] (numeric) = 8.085142600219411503555551416879 absolute error = 2.122134080754042e-16 relative error = 2.6247330265967756632030249147492e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.959 y[1] (analytic) = 8.0922312865720831857034057302022 y[1] (numeric) = 8.0922312865720833982612979484044 absolute error = 2.125578922182022e-16 relative error = 2.6266907690949472915199168527089e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.96 y[1] (analytic) = 8.099327065156632671441435472082 y[1] (numeric) = 8.0993270651566328843441564895244 absolute error = 2.129027210174424e-16 relative error = 2.6286470382626174378501047710173e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.961 y[1] (analytic) = 8.1064299430688389244206200614307 y[1] (numeric) = 8.1064299430688391376685148793846 absolute error = 2.132478948179539e-16 relative error = 2.6306018347853009008745676653559e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.962 y[1] (analytic) = 8.1135399274115804487537248915043 y[1] (numeric) = 8.1135399274115806623471388564145 absolute error = 2.135934139649102e-16 relative error = 2.6325551593489448993434684700161e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.963 y[1] (analytic) = 8.1206570252948421796809892738246 y[1] (numeric) = 8.1206570252948423936202680776554 absolute error = 2.139392788038308e-16 relative error = 2.6345070126399429127482930079474e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.964 y[1] (analytic) = 8.1277812438357225935556541771839 y[1] (numeric) = 8.1277812438357228078411438577641 absolute error = 2.142854896805802e-16 relative error = 2.6364573953451164492374852892513e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.965 y[1] (analytic) = 8.1349125901584408249430316724443 y[1] (numeric) = 8.1349125901584410395750786138139 absolute error = 2.146320469413696e-16 relative error = 2.6384063081517300885960154188176e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.966 y[1] (analytic) = 8.1420510713943437908402331827983 y[1] (numeric) = 8.1420510713943440058191841155546 absolute error = 2.149789509327563e-16 relative error = 2.6403537517474781867990898398445e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.967 y[1] (analytic) = 8.1491966946819133220236807598096 y[1] (numeric) = 8.1491966946819135373498827614537 absolute error = 2.153262020016441e-16 relative error = 2.6422997268204839105705330584477e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.968 y[1] (analytic) = 8.1563494671667733015315327333406 y[1] (numeric) = 8.1563494671667735172053332286248 absolute error = 2.156738004952842e-16 relative error = 2.6442442340593043962850360799429e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.969 y[1] (analytic) = 8.1635093960016968102881622183876 y[1] (numeric) = 8.1635093960016970263099089796628 absolute error = 2.160217467612752e-16 relative error = 2.6461872741529248461232264600437e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.97 y[1] (analytic) = 8.1706764883466132798778341038975 y[1] (numeric) = 8.1706764883466134962478752514608 absolute error = 2.163700411475633e-16 relative error = 2.6481288477907550920682268796672e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.971 y[1] (analytic) = 8.1778507513686156524747332978382 y[1] (numeric) = 8.1778507513686158691934173002811 absolute error = 2.167186840024429e-16 relative error = 2.6500689556626310583062124394090e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.972 y[1] (analytic) = 8.1850321922419675479365041591486 y[1] (numeric) = 8.1850321922419677650041798337056 absolute error = 2.170676756745570e-16 relative error = 2.6520075984588137615344327906024e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.973 y[1] (analytic) = 8.1922208181481104380684682107047 y[1] (numeric) = 8.192220818148110655485484723602 absolute error = 2.174170165128973e-16 relative error = 2.6539447768699846435814498396745e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.974 y[1] (analytic) = 8.1994166362756708280656943981172 y[1] (numeric) = 8.1994166362756710458324012649217 absolute error = 2.177667068668045e-16 relative error = 2.6558804915872433568627138999319e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.975 y[1] (analytic) = 8.2066196538204674451401033370288 y[1] (numeric) = 8.2066196538204676632568504229978 absolute error = 2.181167470859690e-16 relative error = 2.6578147433021104247229109256708e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.976 y[1] (analytic) = 8.2138298779855184343397941766155 y[1] (numeric) = 8.2138298779855186528069316970467 absolute error = 2.184671375204312e-16 relative error = 2.6597475327065250070588885865453e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.977 y[1] (analytic) = 8.2210473159810485615677898992182 y[1] (numeric) = 8.2210473159810487803856684197997 absolute error = 2.188178785205815e-16 relative error = 2.6616788604928390176231586570069e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.978 y[1] (analytic) = 8.228271975024496423807404075449 y[1] (numeric) = 8.22827197502449664297637451261 absolute error = 2.191689704371610e-16 relative error = 2.6636087273538197686711298356681e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.979 y[1] (analytic) = 8.2355038623405216665614393007418 y[1] (numeric) = 8.2355038623405218860818529220032 absolute error = 2.195204136212614e-16 relative error = 2.6655371339826428768001988617007e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=118.2MB, alloc=4.4MB, time=17.61 x[1] = 1.98 y[1] (analytic) = 8.2427429851610122085124347531447 y[1] (numeric) = 8.242742985161012428384643177471 absolute error = 2.198722084243263e-16 relative error = 2.6674640810729021799263172965638e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.981 y[1] (analytic) = 8.2499893507250914734111875332068 y[1] (numeric) = 8.2499893507250916936355427313569 absolute error = 2.202243551981501e-16 relative error = 2.6693895693185905002500794617042e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.982 y[1] (analytic) = 8.2572429662791256292007796750797 y[1] (numeric) = 8.2572429662791258497776339699596 absolute error = 2.205768542948799e-16 relative error = 2.6713135994141168294127843073068e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.983 y[1] (analytic) = 8.2645038390767308343833499534677 y[1] (numeric) = 8.2645038390767310553130560204824 absolute error = 2.209297060670147e-16 relative error = 2.6732361720542907425243343535559e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.984 y[1] (analytic) = 8.2717719763787804916368568537996 y[1] (numeric) = 8.271771976378780712919767721206 absolute error = 2.212829108674064e-16 relative error = 2.6751572879343286441761453080208e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.985 y[1] (analytic) = 8.2790473854534125086890863229911 y[1] (numeric) = 8.2790473854534127303255553722509 absolute error = 2.216364690492598e-16 relative error = 2.6770769477498478920913942081924e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.986 y[1] (analytic) = 8.2863300735760365664561651754097 y[1] (numeric) = 8.2863300735760367884465461415428 absolute error = 2.219903809661331e-16 relative error = 2.6789951521968669749580955533175e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.987 y[1] (analytic) = 8.2936200480293413944528482931621 y[1] (numeric) = 8.2936200480293416167974952651003 absolute error = 2.223446469719382e-16 relative error = 2.6809119019718032670588178317431e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.988 y[1] (analytic) = 8.3009173161033020534818550315964 y[1] (numeric) = 8.3009173161033022761811224525375 absolute error = 2.226992674209411e-16 relative error = 2.6828271977714719886427111273965e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.989 y[1] (analytic) = 8.3082218850951872256095375199637 y[1] (numeric) = 8.3082218850951874486637801877261 absolute error = 2.230542426677624e-16 relative error = 2.6847410402930863646396749461416e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.99 y[1] (analytic) = 8.315533762309566511435170833514 y[1] (numeric) = 8.3155337623095667348447439008913 absolute error = 2.234095730673773e-16 relative error = 2.6866534302342517589272037348858e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.991 y[1] (analytic) = 8.3228529550583177346611623069249 y[1] (numeric) = 8.3228529550583179584264212820411 absolute error = 2.237652589751162e-16 relative error = 2.6885643682929670378335352068178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.992 y[1] (analytic) = 8.330179470660634253971484559881 y[1] (numeric) = 8.3301794706606344780927853065462 absolute error = 2.241213007466652e-16 relative error = 2.6904738551676247152765788187010e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.993 y[1] (analytic) = 8.3375133164430322822256441138471 y[1] (numeric) = 8.3375133164430325067033428519131 absolute error = 2.244776987380660e-16 relative error = 2.6923818915570038900026032543096e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.994 y[1] (analytic) = 8.3448544997393582129755047946128 y[1] (numeric) = 8.3448544997393584378099581003293 absolute error = 2.248344533057165e-16 relative error = 2.6942884781602715977501106593635e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.995 y[1] (analytic) = 8.3522030278907959543122924380423 y[1] (numeric) = 8.3522030278907961795038572444138 absolute error = 2.251915648063715e-16 relative error = 2.6961936156769853428890204596272e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.996 y[1] (analytic) = 8.3595589082458742700511147466471 y[1] (numeric) = 8.3595589082458744956001483437895 absolute error = 2.255490335971424e-16 relative error = 2.6980973048070836436354326194226e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.997 y[1] (analytic) = 8.3669221481604741282603374821105 y[1] (numeric) = 8.3669221481604743541671975176085 absolute error = 2.259068600354980e-16 relative error = 2.6999995462508897634494975239270e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.998 y[1] (analytic) = 8.3742927549978360571431655237545 y[1] (numeric) = 8.3742927549978362834082100030195 absolute error = 2.262650444792650e-16 relative error = 2.7019003407091118297000778927474e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.999 y[1] (analytic) = 8.381670736128567508278784675143 y[1] (numeric) = 8.3816707361285677349023719617706 absolute error = 2.266235872866276e-16 relative error = 2.7037996888828322032901413942782e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2 y[1] (analytic) = 8.389056098930650227230427460575 y[1] (numeric) = 8.3890560989306504542129162767037 absolute error = 2.269824888161287e-16 relative error = 2.7056975914735159661914031077789e-15 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = exp ( x ) ; Iterations = 1000 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 17 Seconds Expected Time Remaining = 2 Minutes 22 Seconds Optimized Time Remaining = 2 Minutes 22 Seconds Time to Timeout = 14 Minutes 42 Seconds Percent Done = 11.12 % > quit memory used=120.7MB, alloc=4.4MB, time=17.96