|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_not_yet_finished, > glob_clock_start_sec, > glob_clock_sec, > djd_debug2, > glob_max_opt_iter, > glob_curr_iter_when_opt, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > glob_start, > glob_warned2, > glob_warned, > glob_last_good_h, > glob_hmin, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_dump_analytic, > glob_look_poles, > glob_h, > glob_almost_1, > centuries_in_millinium, > days_in_year, > glob_log10normmin, > glob_max_minutes, > glob_log10abserr, > glob_max_hours, > glob_hmax, > glob_orig_start_sec, > glob_abserr, > glob_initial_pass, > sec_in_min, > glob_subiter_method, > glob_iter, > glob_unchanged_h_cnt, > glob_large_float, > glob_display_flag, > glob_html_log, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_not_yet_start_msg, > glob_log10relerr, > glob_small_float, > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_log10_relerr, > glob_disp_incr, > glob_optimal_done, > hours_in_day, > djd_debug, > glob_optimal_clock_start_sec, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_fact_1, > array_y, > array_x, > array_type_pole, > array_norms, > array_m1, > array_pole, > array_tmp1_g, > array_1st_rel_error, > array_y_init, > array_y_set_initial, > array_poles, > array_fact_2, > array_y_higher_work2, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_complex_pole, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2, glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec, glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h, glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin, years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic, glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium, days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr, glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr, glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter, glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_not_yet_start_msg, glob_log10relerr, glob_small_float, glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr, glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug, glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1, array_y, array_x, array_type_pole, array_norms, array_m1, array_pole, array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial, array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work, array_real_pole, array_y_higher, array_complex_pole, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_not_yet_finished, > glob_clock_start_sec, > glob_clock_sec, > djd_debug2, > glob_max_opt_iter, > glob_curr_iter_when_opt, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > glob_start, > glob_warned2, > glob_warned, > glob_last_good_h, > glob_hmin, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_dump_analytic, > glob_look_poles, > glob_h, > glob_almost_1, > centuries_in_millinium, > days_in_year, > glob_log10normmin, > glob_max_minutes, > glob_log10abserr, > glob_max_hours, > glob_hmax, > glob_orig_start_sec, > glob_abserr, > glob_initial_pass, > sec_in_min, > glob_subiter_method, > glob_iter, > glob_unchanged_h_cnt, > glob_large_float, > glob_display_flag, > glob_html_log, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_not_yet_start_msg, > glob_log10relerr, > glob_small_float, > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_log10_relerr, > glob_disp_incr, > glob_optimal_done, > hours_in_day, > djd_debug, > glob_optimal_clock_start_sec, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_fact_1, > array_y, > array_x, > array_type_pole, > array_norms, > array_m1, > array_pole, > array_tmp1_g, > array_1st_rel_error, > array_y_init, > array_y_set_initial, > array_poles, > array_fact_2, > array_y_higher_work2, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_complex_pole, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2, glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec, glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h, glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin, years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic, glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium, days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr, glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr, glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter, glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_not_yet_start_msg, glob_log10relerr, glob_small_float, glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr, glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug, glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1, array_y, array_x, array_type_pole, array_norms, array_m1, array_pole, array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial, array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work, array_real_pole, array_y_higher, array_complex_pole, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_not_yet_finished, > glob_clock_start_sec, > glob_clock_sec, > djd_debug2, > glob_max_opt_iter, > glob_curr_iter_when_opt, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > glob_start, > glob_warned2, > glob_warned, > glob_last_good_h, > glob_hmin, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_dump_analytic, > glob_look_poles, > glob_h, > glob_almost_1, > centuries_in_millinium, > days_in_year, > glob_log10normmin, > glob_max_minutes, > glob_log10abserr, > glob_max_hours, > glob_hmax, > glob_orig_start_sec, > glob_abserr, > glob_initial_pass, > sec_in_min, > glob_subiter_method, > glob_iter, > glob_unchanged_h_cnt, > glob_large_float, > glob_display_flag, > glob_html_log, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_not_yet_start_msg, > glob_log10relerr, > glob_small_float, > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_log10_relerr, > glob_disp_incr, > glob_optimal_done, > hours_in_day, > djd_debug, > glob_optimal_clock_start_sec, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_fact_1, > array_y, > array_x, > array_type_pole, > array_norms, > array_m1, > array_pole, > array_tmp1_g, > array_1st_rel_error, > array_y_init, > array_y_set_initial, > array_poles, > array_fact_2, > array_y_higher_work2, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_complex_pole, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2, glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec, glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h, glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin, years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic, glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium, days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr, glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr, glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter, glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_not_yet_start_msg, glob_log10relerr, glob_small_float, glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr, glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug, glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1, array_y, array_x, array_type_pole, array_norms, array_m1, array_pole, array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial, array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work, array_real_pole, array_y_higher, array_complex_pole, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_not_yet_finished, > glob_clock_start_sec, > glob_clock_sec, > djd_debug2, > glob_max_opt_iter, > glob_curr_iter_when_opt, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > glob_start, > glob_warned2, > glob_warned, > glob_last_good_h, > glob_hmin, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_dump_analytic, > glob_look_poles, > glob_h, > glob_almost_1, > centuries_in_millinium, > days_in_year, > glob_log10normmin, > glob_max_minutes, > glob_log10abserr, > glob_max_hours, > glob_hmax, > glob_orig_start_sec, > glob_abserr, > glob_initial_pass, > sec_in_min, > glob_subiter_method, > glob_iter, > glob_unchanged_h_cnt, > glob_large_float, > glob_display_flag, > glob_html_log, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_not_yet_start_msg, > glob_log10relerr, > glob_small_float, > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_log10_relerr, > glob_disp_incr, > glob_optimal_done, > hours_in_day, > djd_debug, > glob_optimal_clock_start_sec, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_fact_1, > array_y, > array_x, > array_type_pole, > array_norms, > array_m1, > array_pole, > array_tmp1_g, > array_1st_rel_error, > array_y_init, > array_y_set_initial, > array_poles, > array_fact_2, > array_y_higher_work2, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_complex_pole, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2, glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec, glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h, glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin, years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic, glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium, days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr, glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr, glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter, glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_not_yet_start_msg, glob_log10relerr, glob_small_float, glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr, glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug, glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1, array_y, array_x, array_type_pole, array_norms, array_m1, array_pole, array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial, array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work, array_real_pole, array_y_higher, array_complex_pole, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_not_yet_finished, > glob_clock_start_sec, > glob_clock_sec, > djd_debug2, > glob_max_opt_iter, > glob_curr_iter_when_opt, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > glob_start, > glob_warned2, > glob_warned, > glob_last_good_h, > glob_hmin, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_dump_analytic, > glob_look_poles, > glob_h, > glob_almost_1, > centuries_in_millinium, > days_in_year, > glob_log10normmin, > glob_max_minutes, > glob_log10abserr, > glob_max_hours, > glob_hmax, > glob_orig_start_sec, > glob_abserr, > glob_initial_pass, > sec_in_min, > glob_subiter_method, > glob_iter, > glob_unchanged_h_cnt, > glob_large_float, > glob_display_flag, > glob_html_log, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_not_yet_start_msg, > glob_log10relerr, > glob_small_float, > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_log10_relerr, > glob_disp_incr, > glob_optimal_done, > hours_in_day, > djd_debug, > glob_optimal_clock_start_sec, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_fact_1, > array_y, > array_x, > array_type_pole, > array_norms, > array_m1, > array_pole, > array_tmp1_g, > array_1st_rel_error, > array_y_init, > array_y_set_initial, > array_poles, > array_fact_2, > array_y_higher_work2, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_complex_pole, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2, glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec, glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h, glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin, years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic, glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium, days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr, glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr, glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter, glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_not_yet_start_msg, glob_log10relerr, glob_small_float, glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr, glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug, glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1, array_y, array_x, array_type_pole, array_norms, array_m1, array_pole, array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial, array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work, array_real_pole, array_y_higher, array_complex_pole, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_not_yet_finished, > glob_clock_start_sec, > glob_clock_sec, > djd_debug2, > glob_max_opt_iter, > glob_curr_iter_when_opt, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > glob_start, > glob_warned2, > glob_warned, > glob_last_good_h, > glob_hmin, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_dump_analytic, > glob_look_poles, > glob_h, > glob_almost_1, > centuries_in_millinium, > days_in_year, > glob_log10normmin, > glob_max_minutes, > glob_log10abserr, > glob_max_hours, > glob_hmax, > glob_orig_start_sec, > glob_abserr, > glob_initial_pass, > sec_in_min, > glob_subiter_method, > glob_iter, > glob_unchanged_h_cnt, > glob_large_float, > glob_display_flag, > glob_html_log, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_not_yet_start_msg, > glob_log10relerr, > glob_small_float, > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_log10_relerr, > glob_disp_incr, > glob_optimal_done, > hours_in_day, > djd_debug, > glob_optimal_clock_start_sec, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_fact_1, > array_y, > array_x, > array_type_pole, > array_norms, > array_m1, > array_pole, > array_tmp1_g, > array_1st_rel_error, > array_y_init, > array_y_set_initial, > array_poles, > array_fact_2, > array_y_higher_work2, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_complex_pole, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre cos $eq_no = 1 > array_tmp1_g[1] := sin(array_x[1]); > array_tmp1[1] := cos(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre cos $eq_no = 1 > array_tmp1_g[2] := (att(1,array_tmp1,array_x,1)); > array_tmp1[2] := (-att(1,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre cos $eq_no = 1 > array_tmp1_g[3] := (att(2,array_tmp1,array_x,1)); > array_tmp1[3] := (-att(2,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre cos $eq_no = 1 > array_tmp1_g[4] := (att(3,array_tmp1,array_x,1)); > array_tmp1[4] := (-att(3,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre cos $eq_no = 1 > array_tmp1_g[5] := (att(4,array_tmp1,array_x,1)); > array_tmp1[5] := (-att(4,array_tmp1_g,array_x,1)); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit cos $eq_no = 1 > array_tmp1_g[kkk] := (att(kkk-1,array_tmp1,array_x,1)); > array_tmp1[kkk] := (-att(kkk-1,array_tmp1_g,array_x,1)); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2, glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec, glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h, glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin, years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic, glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium, days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr, glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr, glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter, glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_not_yet_start_msg, glob_log10relerr, glob_small_float, glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr, glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug, glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1, array_y, array_x, array_type_pole, array_norms, array_m1, array_pole, array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial, array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work, array_real_pole, array_y_higher, array_complex_pole, glob_last; array_tmp1_g[1] := sin(array_x[1]); array_tmp1[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1_g[2] := att(1, array_tmp1, array_x, 1); array_tmp1[2] := -att(1, array_tmp1_g, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1_g[3] := att(2, array_tmp1, array_x, 1); array_tmp1[3] := -att(2, array_tmp1_g, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1_g[4] := att(3, array_tmp1, array_x, 1); array_tmp1[4] := -att(3, array_tmp1_g, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1_g[5] := att(4, array_tmp1, array_x, 1); array_tmp1[5] := -att(4, array_tmp1_g, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1); array_tmp1[kkk] := -att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 13 > if array_fact_1[nnn] = 0 then # if number 14 > ret := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > if array_fact_2[mmm,nnn] = 0 then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0 + sin(x); > end; exact_soln_y := proc(x) 1.0 + sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > INFO, > glob_max_terms, > DEBUGMASSIVE, > ALWAYS, > DEBUGL, > glob_iolevel, > #Top Generate Globals Decl > glob_optimal_start, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_not_yet_finished, > glob_clock_start_sec, > glob_clock_sec, > djd_debug2, > glob_max_opt_iter, > glob_curr_iter_when_opt, > glob_max_sec, > glob_smallish_float, > glob_max_iter, > glob_relerr, > glob_reached_optimal_h, > glob_start, > glob_warned2, > glob_warned, > glob_last_good_h, > glob_hmin, > years_in_century, > glob_normmax, > MAX_UNCHANGED, > glob_dump_analytic, > glob_look_poles, > glob_h, > glob_almost_1, > centuries_in_millinium, > days_in_year, > glob_log10normmin, > glob_max_minutes, > glob_log10abserr, > glob_max_hours, > glob_hmax, > glob_orig_start_sec, > glob_abserr, > glob_initial_pass, > sec_in_min, > glob_subiter_method, > glob_iter, > glob_unchanged_h_cnt, > glob_large_float, > glob_display_flag, > glob_html_log, > glob_optimal_expect_sec, > glob_percent_done, > glob_current_iter, > glob_not_yet_start_msg, > glob_log10relerr, > glob_small_float, > glob_log10_abserr, > glob_hmin_init, > glob_dump, > glob_log10_relerr, > glob_disp_incr, > glob_optimal_done, > hours_in_day, > djd_debug, > glob_optimal_clock_start_sec, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_last_rel_error, > array_fact_1, > array_y, > array_x, > array_type_pole, > array_norms, > array_m1, > array_pole, > array_tmp1_g, > array_1st_rel_error, > array_y_init, > array_y_set_initial, > array_poles, > array_fact_2, > array_y_higher_work2, > array_y_higher_work, > array_real_pole, > array_y_higher, > array_complex_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > ALWAYS := 1; > DEBUGL := 3; > glob_iolevel := 5; > glob_optimal_start := 0.0; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_max_rel_trunc_err := 0.1e-10; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > glob_clock_sec := 0.0; > djd_debug2 := true; > glob_max_opt_iter := 10; > glob_curr_iter_when_opt := 0; > glob_max_sec := 10000.0; > glob_smallish_float := 0.1e-100; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_reached_optimal_h := false; > glob_start := 0; > glob_warned2 := false; > glob_warned := false; > glob_last_good_h := 0.1; > glob_hmin := 0.00000000001; > years_in_century := 100.0; > glob_normmax := 0.0; > MAX_UNCHANGED := 10; > glob_dump_analytic := false; > glob_look_poles := false; > glob_h := 0.1; > glob_almost_1 := 0.9990; > centuries_in_millinium := 10.0; > days_in_year := 365.0; > glob_log10normmin := 0.1; > glob_max_minutes := 0.0; > glob_log10abserr := 0.0; > glob_max_hours := 0.0; > glob_hmax := 1.0; > glob_orig_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_initial_pass := true; > sec_in_min := 60.0; > glob_subiter_method := 3; > glob_iter := 0; > glob_unchanged_h_cnt := 0; > glob_large_float := 9.0e100; > glob_display_flag := true; > glob_html_log := true; > glob_optimal_expect_sec := 0.1; > glob_percent_done := 0.0; > glob_current_iter := 0; > glob_not_yet_start_msg := true; > glob_log10relerr := 0.0; > glob_small_float := 0.1e-50; > glob_log10_abserr := 0.1e-10; > glob_hmin_init := 0.001; > glob_dump := false; > glob_log10_relerr := 0.1e-10; > glob_disp_incr := 0.1; > glob_optimal_done := false; > hours_in_day := 24.0; > djd_debug := true; > glob_optimal_clock_start_sec := 0.0; > min_in_hour := 60.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/cospostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 1.6;"); > omniout_str(ALWAYS,"x_end := 10.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > 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 + sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[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_m1[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_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_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 <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_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[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 1.6; > x_end := 10.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > 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 ) = cos ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-17T19:54:25-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"cos") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 092 ") > ; > logitem_str(html_log_file,"cos diffeq.mxt") > ; > logitem_str(html_log_file,"cos maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel, glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2, glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec, glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h, glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin, years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic, glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium, days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr, glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr, glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter, glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log, glob_optimal_expect_sec, glob_percent_done, glob_current_iter, glob_not_yet_start_msg, glob_log10relerr, glob_small_float, glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr, glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug, glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1, array_y, array_x, array_type_pole, array_norms, array_m1, array_pole, array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial, array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work, array_real_pole, array_y_higher, array_complex_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; glob_max_terms := 30; DEBUGMASSIVE := 4; ALWAYS := 1; DEBUGL := 3; glob_iolevel := 5; glob_optimal_start := 0.; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_max_rel_trunc_err := 0.1*10^(-10); glob_not_yet_finished := true; glob_clock_start_sec := 0.; glob_clock_sec := 0.; djd_debug2 := true; glob_max_opt_iter := 10; glob_curr_iter_when_opt := 0; glob_max_sec := 10000.0; glob_smallish_float := 0.1*10^(-100); glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_reached_optimal_h := false; glob_start := 0; glob_warned2 := false; glob_warned := false; glob_last_good_h := 0.1; glob_hmin := 0.1*10^(-10); years_in_century := 100.0; glob_normmax := 0.; MAX_UNCHANGED := 10; glob_dump_analytic := false; glob_look_poles := false; glob_h := 0.1; glob_almost_1 := 0.9990; centuries_in_millinium := 10.0; days_in_year := 365.0; glob_log10normmin := 0.1; glob_max_minutes := 0.; glob_log10abserr := 0.; glob_max_hours := 0.; glob_hmax := 1.0; glob_orig_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_initial_pass := true; sec_in_min := 60.0; glob_subiter_method := 3; glob_iter := 0; glob_unchanged_h_cnt := 0; glob_large_float := 0.90*10^101; glob_display_flag := true; glob_html_log := true; glob_optimal_expect_sec := 0.1; glob_percent_done := 0.; glob_current_iter := 0; glob_not_yet_start_msg := true; glob_log10relerr := 0.; glob_small_float := 0.1*10^(-50); glob_log10_abserr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_dump := false; glob_log10_relerr := 0.1*10^(-10); glob_disp_incr := 0.1; glob_optimal_done := false; hours_in_day := 24.0; djd_debug := true; glob_optimal_clock_start_sec := 0.; min_in_hour := 60.0; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/cospostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 1.6;"); omniout_str(ALWAYS, "x_end := 10.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); 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 + sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_type_pole[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_m1[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_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 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 <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_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[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 1.6; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; glob_h := 0.001; 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 ) = cos ( x ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-17T19:54:25-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "cos"); logitem_str(html_log_file, "diff ( y , x , 1 ) = cos ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 092 "); logitem_str(html_log_file, "cos diffeq.mxt"); logitem_str(html_log_file, "cos maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/cospostode.ode################# diff ( y , x , 1 ) = cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 1.6; x_end := 10.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; 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 + sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 1.6 y[1] (analytic) = 1.9995736030415051643421138255462 y[1] (numeric) = 1.9995736030415051643421138255462 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.601 y[1] (analytic) = 1.9995439037373105905689497577459 y[1] (numeric) = 1.9995439037373105905203596539172 absolute error = 4.85901038287e-20 relative error = 2.4300593619315451943525779077936e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.602 y[1] (analytic) = 1.9995132048892955748077300527509 y[1] (numeric) = 1.9995132048892955747105512983293 absolute error = 9.71787544216e-20 relative error = 4.8601206625679858234868036479976e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.603 y[1] (analytic) = 1.9994815065281589625152332224708 y[1] (numeric) = 1.9994815065281589623694673192807 absolute error = 1.457659031901e-19 relative error = 7.2901851162006313613202679888312e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604 y[1] (analytic) = 1.9994488086855991121865415527359 y[1] (numeric) = 1.9994488086855991119921900511887 absolute error = 1.943515015472e-19 relative error = 9.7202539371319590846331854485445e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.605 y[1] (analytic) = 1.9994151113943138636566852497442 y[1] (numeric) = 1.9994151113943138634137497488371 absolute error = 2.429355009071e-19 relative error = 1.2150328339655604957410507896997e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.606 y[1] (analytic) = 1.9993804146880005054028053298515 y[1] (numeric) = 1.9993804146880005051112874771657 absolute error = 2.915178526858e-19 relative error = 1.4580409538086367824555820386130e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.607 y[1] (analytic) = 1.9993447186013557408468679505378 y[1] (numeric) = 1.9993447186013557405067694422367 absolute error = 3.400985083011e-19 relative error = 1.7010498746760206722874537872622e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.608 y[1] (analytic) = 1.9993080231700756536589638798324 y[1] (numeric) = 1.9993080231700756532702864606601 absolute error = 3.886774191723e-19 relative error = 1.9440597180019232947922611852500e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.609 y[1] (analytic) = 1.9992703284308556720612278008973 y[1] (numeric) = 1.9992703284308556716239732641768 absolute error = 4.372545367205e-19 relative error = 2.1870706052226711307153605676759e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.61 y[1] (analytic) = 1.9992316344213905321324131478443 y[1] (numeric) = 1.9992316344213905316465833354758 absolute error = 4.858298123685e-19 relative error = 2.4300826577762055238237271325293e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.611 y[1] (analytic) = 1.9991919411803742401131591682098 y[1] (numeric) = 1.9991919411803742395787559706687 absolute error = 5.344031975411e-19 relative error = 2.6730959971035829324468618932402e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.612 y[1] (analytic) = 1.9991512487475000337119879068157 y[1] (numeric) = 1.9991512487475000331290132631508 absolute error = 5.829746436649e-19 relative error = 2.9161107446479742887706458619264e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.613 y[1] (analytic) = 1.9991095571634603424120698050174 y[1] (numeric) = 1.9991095571634603417805257028489 absolute error = 6.315441021685e-19 relative error = 3.1591270218556651196501936631896e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.20 NO POLE x[1] = 1.614 y[1] (analytic) = 1.9990668664699467467787976085685 y[1] (numeric) = 1.9990668664699467460986860840861 absolute error = 6.801115244824e-19 relative error = 3.4021449501755550825057211513167e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.615 y[1] (analytic) = 1.999023176709649936768209276527 y[1] (numeric) = 1.9990231767096499360395324144878 absolute error = 7.286768620392e-19 relative error = 3.6451646510601581619008939038156e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.616 y[1] (analytic) = 1.9989784879262596690363015827741 y[1] (numeric) = 1.9989784879262596682590615165005 absolute error = 7.772400662736e-19 relative error = 3.8881862459656024775720365963546e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.617 y[1] (analytic) = 1.9989328001644647232492771008306 y[1] (numeric) = 1.9989328001644647224234760122083 absolute error = 8.258010886223e-19 relative error = 4.1312098563511298200172240044787e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.618 y[1] (analytic) = 1.9988861134699528573947682617194 y[1] (numeric) = 1.998886113469952856520408381195 absolute error = 8.743598805244e-19 relative error = 4.3742356036810965023359185227469e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.619 y[1] (analytic) = 1.9988384278894107620940831736458 y[1] (numeric) = 1.9988384278894107611711667802247 absolute error = 9.229163934211e-19 relative error = 4.6172636094234724527603812027227e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.62 y[1] (analytic) = 1.9987897434705240139155188912468 y[1] (numeric) = 1.998789743470524012944048312491 absolute error = 9.714705787558e-19 relative error = 4.8602939950503413007755365015686e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.621 y[1] (analytic) = 1.9987400602619770276887888210922 y[1] (numeric) = 1.9987400602619770266687664331178 absolute error = 1.0200223879744e-18 relative error = 5.1033268820394011576067692770123e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.622 y[1] (analytic) = 1.9986893783134530078206119490054 y[1] (numeric) = 1.9986893783134530067520401764804 absolute error = 1.0685717725250e-18 relative error = 5.3463623918724636497110433165149e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.623 y[1] (analytic) = 1.9986376976756338986115125736116 y[1] (numeric) = 1.9986376976756338974943938897533 absolute error = 1.1171186838583e-18 relative error = 5.5894006460374551069102581717758e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.624 y[1] (analytic) = 1.9985850184002003335738802293083 y[1] (numeric) = 1.9985850184002003324082171558809 absolute error = 1.1656630734274e-18 relative error = 5.8324417660274159323682056334826e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.625 y[1] (analytic) = 1.9985313405398315837513404805954 y[1] (numeric) = 1.9985313405398315825371355879076 absolute error = 1.2142048926878e-18 relative error = 6.0754858733405005492361714050315e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.626 y[1] (analytic) = 1.9984766641482055050394882683887 y[1] (numeric) = 1.9984766641482055037767441752909 absolute error = 1.2627440930978e-18 relative error = 6.3185330894819788660612577477140e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.627 y[1] (analytic) = 1.9984209892799984845080364875794 y[1] (numeric) = 1.9984209892799984831967558614612 absolute error = 1.3112806261182e-18 relative error = 6.5615835359627353042965616999604e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.628 y[1] (analytic) = 1.9983643159908853857244334736866 y[1] (numeric) = 1.9983643159908853843646190304742 absolute error = 1.3598144432124e-18 relative error = 6.8046373342997692141472674443570e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.629 y[1] (analytic) = 1.998306644337539493079004074981 y[1] (numeric) = 1.9983066443375394916706585791343 absolute error = 1.4083454958467e-18 relative error = 7.0476946060176962186535949265605e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.63 y[1] (analytic) = 1.9982479743776324551116699849331 y[1] (numeric) = 1.9982479743776324536547962494432 absolute error = 1.4568737354899e-18 relative error = 7.2907554726467467501836511924238e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.631 y[1] (analytic) = 1.9981883061698342268403060082628 y[1] (numeric) = 1.9981883061698342253349068946489 absolute error = 1.5053991136139e-18 relative error = 7.5338200557257687683023718661394e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.632 y[1] (analytic) = 1.9981276397738130110907899322266 y[1] (numeric) = 1.9981276397738130095368683505334 absolute error = 1.5539215816932e-18 relative error = 7.7768884767997258611817527186720e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.633 y[1] (analytic) = 1.9980659752502351988288046730904 y[1] (numeric) = 1.998065975250235197226363581885 absolute error = 1.6024410912054e-18 relative error = 8.0199608574221997350431459316914e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.634 y[1] (analytic) = 1.9980033126607653084934523659789 y[1] (numeric) = 1.9980033126607653068424947723478 absolute error = 1.6509575936311e-18 relative error = 8.2630373191548901680277642017783e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.635 y[1] (analytic) = 1.9979396520680659243327410644828 y[1] (numeric) = 1.9979396520680659226332700240291 absolute error = 1.6994710404537e-18 relative error = 8.5061179835666143618662145784570e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.1MB, time=0.44 NO POLE x[1] = 1.636 y[1] (analytic) = 1.9978749935357976337410057145331 y[1] (numeric) = 1.9978749935357976319930243313733 absolute error = 1.7479813831598e-18 relative error = 8.7492029722353092941268659050419e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.637 y[1] (analytic) = 1.9978093371286189635983260651146 y[1] (numeric) = 1.9978093371286189618018374918756 absolute error = 1.7964885732390e-18 relative error = 8.9922924067470311709085278518649e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.638 y[1] (analytic) = 1.9977426829121863156120051763966 y[1] (numeric) = 1.9977426829121863137670126142126 absolute error = 1.8449925621840e-18 relative error = 9.2353864086964563830638480648078e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.639 y[1] (analytic) = 1.9976750309531539006601731837968 y[1] (numeric) = 1.9976750309531538987666798823057 absolute error = 1.8934933014911e-18 relative error = 9.4784850996893848920370858896511e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.64 y[1] (analytic) = 1.9976063813191736721375819743679 y[1] (numeric) = 1.9976063813191736701955912317085 absolute error = 1.9419907426594e-18 relative error = 9.7215886013387363459267284203104e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.641 y[1] (analytic) = 1.9975367340788952583036574297089 y[1] (numeric) = 1.9975367340788952563131725925174 absolute error = 1.9904848371915e-18 relative error = 9.9646970352680546266664237682618e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.642 y[1] (analytic) = 1.997466089301965893632876887341 y[1] (numeric) = 1.9974660893019658915939013507478 absolute error = 2.0389755365932e-18 relative error = 1.0207810523110006786880676957981e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.643 y[1] (analytic) = 1.9973944470590303491675404701666 y[1] (numeric) = 1.9973944470590303470800776777926 absolute error = 2.0874627923740e-18 relative error = 1.0450929186508886895386037250447e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.644 y[1] (analytic) = 1.9973218074217308618730059312328 y[1] (numeric) = 1.9973218074217308597370593751864 absolute error = 2.1359465560464e-18 relative error = 1.0694053147117112384960091060431e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.645 y[1] (analytic) = 1.9972481704627070629954576585605 y[1] (numeric) = 1.9972481704627070608110308794336 absolute error = 2.1844267791269e-18 relative error = 1.0937182526600231355160820095760e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.646 y[1] (analytic) = 1.9971735362555959054222814822617 y[1] (numeric) = 1.9971735362555959031893780691266 absolute error = 2.2329034131351e-18 relative error = 1.1180317446632417544370794732926e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.647 y[1] (analytic) = 1.9970979048750315900451179235668 y[1] (numeric) = 1.9970979048750315877637415139723 absolute error = 2.2813764095945e-18 relative error = 1.1423458028900476657431586414841e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.648 y[1] (analytic) = 1.9970212763966454911256675227001 y[1] (numeric) = 1.9970212763966454887958218026681 absolute error = 2.3298457200320e-18 relative error = 1.1666604395101343912740645321155e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.649 y[1] (analytic) = 1.9969436508970660806643228797941 y[1] (numeric) = 1.9969436508970660782860115838157 absolute error = 2.3783112959784e-18 relative error = 1.1909756666944588679364201593550e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.65 y[1] (analytic) = 1.9968650284539188517717030402022 y[1] (numeric) = 1.9968650284539188493449299512342 absolute error = 2.4267730889680e-18 relative error = 1.2152914966150412642153728666333e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.651 y[1] (analytic) = 1.9967854091458262410431668526709 y[1] (numeric) = 1.9967854091458262385679358021318 absolute error = 2.4752310505391e-18 relative error = 1.2396079414452154750955445039782e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.652 y[1] (analytic) = 1.9967047930524075499363829258502 y[1] (numeric) = 1.9967047930524075474126977936165 absolute error = 2.5236851322337e-18 relative error = 1.2639250133594790177610995731693e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.653 y[1] (analytic) = 1.9966231802542788651520348055667 y[1] (numeric) = 1.9966231802542788625798995199689 absolute error = 2.5721352855978e-18 relative error = 1.2882427245336433998353258474280e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.654 y[1] (analytic) = 1.996540570833052978017740992147 y[1] (numeric) = 1.9965405708330529753971595299658 absolute error = 2.6205814621812e-18 relative error = 1.3125610871447340924927338748199e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.655 y[1] (analytic) = 1.9964569648713393028752704138649 y[1] (numeric) = 1.9964569648713393002062468003272 absolute error = 2.6690236135377e-18 relative error = 1.3368801133710908350877035156857e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.656 y[1] (analytic) = 1.9963723624527437944711349692902 y[1] (numeric) = 1.9963723624527437917536732780651 absolute error = 2.7174616912251e-18 relative error = 1.3611998153923677844152858380524e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.657 y[1] (analytic) = 1.9962867636618688643506417479393 y[1] (numeric) = 1.9962867636618688615847461011339 absolute error = 2.7658956468054e-18 relative error = 1.3855202053896338514788294164142e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.658 y[1] (analytic) = 1.9962001685843132962554885351691 y[1] (numeric) = 1.9962001685843132934411631033244 absolute error = 2.8143254318447e-18 relative error = 1.4098412955453227801766240716554e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=0.69 NO POLE x[1] = 1.659 y[1] (analytic) = 1.9961125773066721605249872037106 y[1] (numeric) = 1.9961125773066721576622362057975 absolute error = 2.8627509979131e-18 relative error = 1.4341630980431832148001580152034e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.66 y[1] (analytic) = 1.996023989916536727501000590613 y[1] (numeric) = 1.9960239899165367245898282940278 absolute error = 2.9111722965852e-18 relative error = 1.4584856250685293532774464046202e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.661 y[1] (analytic) = 1.9959344065024943799366794546528 y[1] (numeric) = 1.9959344065024943769770901752132 absolute error = 2.9595892794396e-18 relative error = 1.4828088888079906503970712485268e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.662 y[1] (analytic) = 1.995843827154128524409087105465 y[1] (numeric) = 1.9958438271541285214010852074058 absolute error = 3.0080018980592e-18 relative error = 1.5071329014496622885369564814974e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.663 y[1] (analytic) = 1.9957522519620185017358002917634 y[1] (numeric) = 1.9957522519620184986793901877318 absolute error = 3.0564101040316e-18 relative error = 1.5314576751833057969319881542690e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.664 y[1] (analytic) = 1.9956596810177394963955759320416 y[1] (numeric) = 1.9956596810177394932907620830932 absolute error = 3.1048138489484e-18 relative error = 1.5557832221999985322835640415286e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.665 y[1] (analytic) = 1.9955661144138624449531742670819 y[1] (numeric) = 1.9955661144138624417999611826758 absolute error = 3.1532130844061e-18 relative error = 1.5801095546925848413163901830978e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.666 y[1] (analytic) = 1.9954715522439539434884300094387 y[1] (numeric) = 1.9954715522439539402868222474334 absolute error = 3.2016077620053e-18 relative error = 1.6044366848552754229653142913305e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.667 y[1] (analytic) = 1.9953759946025761540296640608207 y[1] (numeric) = 1.9953759946025761507796662274693 absolute error = 3.2499978333514e-18 relative error = 1.6287646248839983170198607817332e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.668 y[1] (analytic) = 1.9952794415852867099915293639491 y[1] (numeric) = 1.9952794415852867066931461138948 absolute error = 3.2983832500543e-18 relative error = 1.6530933869762488121722280789148e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.669 y[1] (analytic) = 1.9951818932886386206173854510412 y[1] (numeric) = 1.9951818932886386172706214873126 absolute error = 3.3467639637286e-18 relative error = 1.6774229833311899166776298497319e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.67 y[1] (analytic) = 1.9950833498101801744262972465342 y[1] (numeric) = 1.9950833498101801710311573205407 absolute error = 3.3951399259935e-18 relative error = 1.7017534261496024908037895233429e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.671 y[1] (analytic) = 1.9949838112484548416647546770444 y[1] (numeric) = 1.9949838112484548382212435885712 absolute error = 3.4435110884732e-18 relative error = 1.7260847276340859952450621476253e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.672 y[1] (analytic) = 1.9948832777030011757632106368326 y[1] (numeric) = 1.9948832777030011722713332340362 absolute error = 3.4918774027964e-18 relative error = 1.7504168999888081478122860560104e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.673 y[1] (analytic) = 1.9947817492743527137975358522306 y[1] (numeric) = 1.9947817492743527102572970316337 absolute error = 3.5402388205969e-18 relative error = 1.7747499554198059456069950571306e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.674 y[1] (analytic) = 1.9946792260640378759554901835647 y[1] (numeric) = 1.9946792260640378723668948900514 absolute error = 3.5885952935133e-18 relative error = 1.7990839061348355808190577978220e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.675 y[1] (analytic) = 1.9945757081745798640083108980974 y[1] (numeric) = 1.9945757081745798603713641249084 absolute error = 3.6369467731890e-18 relative error = 1.8234187643433727209971273216407e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.676 y[1] (analytic) = 1.99447119570949655878751944239 y[1] (numeric) = 1.9944711957094965551022262311175 absolute error = 3.6852932112725e-18 relative error = 1.8477545422567632072444236656160e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.677 y[1] (analytic) = 1.994365688773300416667049237271 y[1] (numeric) = 1.9943656887733004129334146778535 absolute error = 3.7336345594175e-18 relative error = 1.8720912520882735196361842827374e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.678 y[1] (analytic) = 1.9942591874714983650507980132736 y[1] (numeric) = 1.9942591874714983612688272439909 absolute error = 3.7819707692827e-18 relative error = 1.8964289060529908299030648515190e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.679 y[1] (analytic) = 1.9941516919105916968657091989816 y[1] (numeric) = 1.9941516919105916930354074064498 absolute error = 3.8303017925318e-18 relative error = 1.9207675163678233182041766234038e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.68 y[1] (analytic) = 1.9940432021980759640604878691936 y[1] (numeric) = 1.9940432021980759601818602883598 absolute error = 3.8786275808338e-18 relative error = 1.9451070952516509403626923193668e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.681 y[1] (analytic) = 1.9939337184424408701100577541801 y[1] (numeric) = 1.9939337184424408661831096683173 absolute error = 3.9269480858628e-18 relative error = 1.9694476549252254863161256120610e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.93 NO POLE x[1] = 1.682 y[1] (analytic) = 1.9938232407531701615258668055684 y[1] (numeric) = 1.9938232407531701575506035462699 absolute error = 3.9752632592985e-18 relative error = 1.9937892076114216927548580167245e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.683 y[1] (analytic) = 1.9937117692407415183721498085394 y[1] (numeric) = 1.9937117692407415143485767557138 absolute error = 4.0235730528256e-18 relative error = 2.0181317655349367075387174006506e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.684 y[1] (analytic) = 1.9935993040166264437882575240663 y[1] (numeric) = 1.993599304016626439716380105932 absolute error = 4.0718774181343e-18 relative error = 2.0424753409225412222331159309791e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.685 y[1] (analytic) = 1.9934858451932901525171628388552 y[1] (numeric) = 1.9934858451932901483969865319349 absolute error = 4.1201763069203e-18 relative error = 2.0668199460030798750976586080533e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.686 y[1] (analytic) = 1.9933713928841914584402553944733 y[1] (numeric) = 1.9933713928841914542717857235886 absolute error = 4.1684696708847e-18 relative error = 2.0911655930074214913177034566937e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.687 y[1] (analytic) = 1.9932559472037826611185371608599 y[1] (numeric) = 1.9932559472037826569017796991258 absolute error = 4.2167574617341e-18 relative error = 2.1155122941685096475296554078247e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.688 y[1] (analytic) = 1.993139508267509431340332413016 y[1] (numeric) = 1.9931395082675094270752927818351 absolute error = 4.2650396311809e-18 relative error = 2.1398600617215136010143196046725e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.689 y[1] (analytic) = 1.9930220761918106956756265631518 y[1] (numeric) = 1.9930220761918106913623104322092 absolute error = 4.3133161309426e-18 relative error = 2.1642089079034775246451640190922e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.69 y[1] (analytic) = 1.9929036510941185200371492939456 y[1] (numeric) = 1.9929036510941185156755623812026 absolute error = 4.3615869127430e-18 relative error = 2.1885588449539230035254342975087e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.691 y[1] (analytic) = 1.9927842330928579922483184318185 y[1] (numeric) = 1.9927842330928579878384665035073 absolute error = 4.4098519283112e-18 relative error = 2.2129098851143477664407156434940e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.692 y[1] (analytic) = 1.9926638223074471036181619922741 y[1] (numeric) = 1.9926638223074470991600508628919 absolute error = 4.4581111293822e-18 relative error = 2.2372620406285271864457529440189e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.693 y[1] (analytic) = 1.9925424188582966295233368223692 y[1] (numeric) = 1.9925424188582966250169723546724 absolute error = 4.5063644676968e-18 relative error = 2.2616153237424645834332809706531e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.694 y[1] (analytic) = 1.9924200228668100089973632582879 y[1] (numeric) = 1.9924200228668100044427513632862 absolute error = 4.5546118950017e-18 relative error = 2.2859697467044418926700700031705e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.695 y[1] (analytic) = 1.9922966344553832233271962087742 y[1] (numeric) = 1.9922966344553832187243428457248 absolute error = 4.6028533630494e-18 relative error = 2.3103253217649699688446224824434e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.696 y[1] (analytic) = 1.992172253747404673657254067842 y[1] (numeric) = 1.9921722537474046690061652442435 absolute error = 4.6510888235985e-18 relative error = 2.3346820611769396609363397933797e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.697 y[1] (analytic) = 1.9920468808672550576010278527229 y[1] (numeric) = 1.9920468808672550529017096243093 absolute error = 4.6993182284136e-18 relative error = 2.3590399771955721487308203529947e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.698 y[1] (analytic) = 1.991920515940307244860393955433 y[1] (numeric) = 1.9919205159403072401128524261679 absolute error = 4.7475415292651e-18 relative error = 2.3833990820783190617062066090170e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.699 y[1] (analytic) = 1.9917931590929261518527548886357 y[1] (numeric) = 1.9917931590929261470569962107058 absolute error = 4.7957586779299e-18 relative error = 2.4077593880852144173258992377833e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.7 y[1] (analytic) = 1.9916648104524686153461333986479 y[1] (numeric) = 1.9916648104524686105021637724571 absolute error = 4.8439696261908e-18 relative error = 2.4321209074785739778365558481927e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.701 y[1] (analytic) = 1.991535470147283265102346310487 y[1] (numeric) = 1.9915354701472832602101719846502 absolute error = 4.8921743258368e-18 relative error = 2.4564836525231464077242136542966e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.702 y[1] (analytic) = 1.9914051383067103955283854617728 y[1] (numeric) = 1.9914051383067103905880127331096 absolute error = 4.9403727286632e-18 relative error = 2.4808476354861640617472278411498e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.703 y[1] (analytic) = 1.9912738150610818363361340740934 y[1] (numeric) = 1.9912738150610818313475692876217 absolute error = 4.9885647864717e-18 relative error = 2.5052128686373937968800708407976e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704 y[1] (analytic) = 1.9911415005417208222105479021069 y[1] (numeric) = 1.9911415005417208171737974510367 absolute error = 5.0367504510702e-18 relative error = 2.5295793642490371412338985244327e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=1.18 NO POLE x[1] = 1.705 y[1] (analytic) = 1.9910081948809418614864314921887 y[1] (numeric) = 1.9910081948809418564015018179157 absolute error = 5.0849296742730e-18 relative error = 2.5539471345958313304215414742205e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.706 y[1] (analytic) = 1.9908738982120506038339408738353 y[1] (numeric) = 1.9908738982120505987008384659343 absolute error = 5.1331024079010e-18 relative error = 2.5783161919551503882447723733601e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.707 y[1] (analytic) = 1.9907386106693437069529449983121 y[1] (numeric) = 1.9907386106693437017716763945308 absolute error = 5.1812686037813e-18 relative error = 2.6026865486068048569766549971839e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.708 y[1] (analytic) = 1.9906023323881087022763792301723 y[1] (numeric) = 1.9906023323881086970469510164245 absolute error = 5.2294282137478e-18 relative error = 2.6270582168333438105609091870476e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.709 y[1] (analytic) = 1.9904650635046238596827251882821 y[1] (numeric) = 1.9904650635046238544051439986412 absolute error = 5.2775811896409e-18 relative error = 2.6514312089199048401843783209907e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.71 y[1] (analytic) = 1.9903268041561580512177522238611 y[1] (numeric) = 1.9903268041561580458920247405535 absolute error = 5.3257274833076e-18 relative error = 2.6758055371542649545106157812819e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.711 y[1] (analytic) = 1.9901875544809706138256568137853 y[1] (numeric) = 1.9901875544809706084517897671836 absolute error = 5.3738670466017e-18 relative error = 2.7001812138269417517144963173211e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.712 y[1] (analytic) = 1.9900473146183112110897371380016 y[1] (numeric) = 1.9900473146183112056677373066181 absolute error = 5.4219998313835e-18 relative error = 2.7245582512310433881456937370575e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.713 y[1] (analytic) = 1.9899060847084196939827411003679 y[1] (numeric) = 1.9899060847084196885126153108477 absolute error = 5.4701257895202e-18 relative error = 2.7489366616624702632785834061216e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.714 y[1] (analytic) = 1.9897638648925259606270270425593 y[1] (numeric) = 1.9897638648925259551087821696732 absolute error = 5.5182448728861e-18 relative error = 2.7733164574200162802426169851699e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.715 y[1] (analytic) = 1.9896206553128498150646773908669 y[1] (numeric) = 1.9896206553128498094983203575051 absolute error = 5.5663570333618e-18 relative error = 2.7976976508049675466094231503008e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.716 y[1] (analytic) = 1.989476456112600825037706465766 y[1] (numeric) = 1.9894764561126008194232442429307 absolute error = 5.6144622228353e-18 relative error = 2.8220802541216559313046131465644e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.717 y[1] (analytic) = 1.9893312674359781787785046740318 y[1] (numeric) = 1.9893312674359781731159442808303 absolute error = 5.6625603932015e-18 relative error = 2.8464642796772085759351121839802e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.718 y[1] (analytic) = 1.9891850894281705408106622929473 y[1] (numeric) = 1.9891850894281705351000107965852 absolute error = 5.7106514963621e-18 relative error = 2.8708497397814983894299675799702e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.719 y[1] (analytic) = 1.9890379222353559067603170457685 y[1] (numeric) = 1.9890379222353559010015815615424 absolute error = 5.7587354842261e-18 relative error = 2.8952366467473961784621353464680e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.72 y[1] (analytic) = 1.9888897660047014571781706570855 y[1] (numeric) = 1.9888897660047014513713583483761 absolute error = 5.8068123087094e-18 relative error = 2.9196250128905703806741690633546e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.721 y[1] (analytic) = 1.9887406208843634103723205660523 y[1] (numeric) = 1.9887406208843634045174386443171 absolute error = 5.8548819217352e-18 relative error = 2.9440148505296889780421977168262e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.722 y[1] (analytic) = 1.9885904870234868742520539646404 y[1] (numeric) = 1.9885904870234868683491096894065 absolute error = 5.9029442752339e-18 relative error = 2.9684061719863700713305963089952e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.723 y[1] (analytic) = 1.9884393645722056971827523171103 y[1] (numeric) = 1.988439364572205691231752995967 absolute error = 5.9509993211433e-18 relative error = 2.9927989895852833094670702128445e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.724 y[1] (analytic) = 1.9882872536816423178520555057834 y[1] (numeric) = 1.9882872536816423118530084943752 absolute error = 5.9990470114082e-18 relative error = 3.0171933156539496030807743883569e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.725 y[1] (analytic) = 1.9881341545039076141474357369385 y[1] (numeric) = 1.9881341545039076081003484389576 absolute error = 6.0470872979809e-18 relative error = 3.0415891625229934367378415941216e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.726 y[1] (analytic) = 1.9879800671921007510453323292455 y[1] (numeric) = 1.9879800671921007449502121964243 absolute error = 6.0951201328212e-18 relative error = 3.0659865425261437907998128983480e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.727 y[1] (analytic) = 1.9878249919003090275119994955896 y[1] (numeric) = 1.9878249919003090213688540276934 absolute error = 6.1431454678962e-18 relative error = 3.0903854680001344568404128240982e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.2MB, time=1.43 NO POLE x[1] = 1.728 y[1] (analytic) = 1.9876689287836077224162202174247 y[1] (numeric) = 1.987668928783607716225056962244 absolute error = 6.1911632551807e-18 relative error = 3.1147859512849061727142895776758e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.729 y[1] (analytic) = 1.9875118779980599394540402989299 y[1] (numeric) = 1.9875118779980599332148668522731 absolute error = 6.2391734466568e-18 relative error = 3.1391880047234063447415099354565e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.73 y[1] (analytic) = 1.9873538397007164510856776762221 y[1] (numeric) = 1.9873538397007164447985016819078 absolute error = 6.2871759943143e-18 relative error = 3.1635916406617912256294251085231e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.731 y[1] (analytic) = 1.9871948140496155414847630447017 y[1] (numeric) = 1.9871948140496155351495921945511 absolute error = 6.3351708501506e-18 relative error = 3.1879968714493765828493696224118e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.732 y[1] (analytic) = 1.987034801203782848500068855279 y[1] (numeric) = 1.9870348012037828421169108891079 absolute error = 6.3831579661711e-18 relative error = 3.2124037094388399801148554022546e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.733 y[1] (analytic) = 1.986873801323231204629884717737 y[1] (numeric) = 1.9868738013232311981987474233486 absolute error = 6.4311372943884e-18 relative error = 3.2368121669858191985412897853997e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.734 y[1] (analytic) = 1.9867118145689604770091982368449 y[1] (numeric) = 1.9867118145689604705300894500215 absolute error = 6.4791087868234e-18 relative error = 3.2612222564494668220347621770476e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.735 y[1] (analytic) = 1.986548841102957406409841294025 y[1] (numeric) = 1.9865488411029573998827688985205 absolute error = 6.5270723955045e-18 relative error = 3.2856339901920486665536801373982e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.736 y[1] (analytic) = 1.9863848810881954452537627744158 y[1] (numeric) = 1.9863848810881954386787347019477 absolute error = 6.5750280724681e-18 relative error = 3.3100473805791964731827651292729e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.737 y[1] (analytic) = 1.9862199346886345946395897260435 y[1] (numeric) = 1.9862199346886345880166139562849 absolute error = 6.6229757697586e-18 relative error = 3.3344624399799089969779238361123e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.738 y[1] (analytic) = 1.986054002069221240382639924528 y[1] (numeric) = 1.9860540020692212337117244850998 absolute error = 6.6709154394282e-18 relative error = 3.3588791807664524002262858601909e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.739 y[1] (analytic) = 1.9858870833958879880685498032969 y[1] (numeric) = 1.9858870833958879813497027697596 absolute error = 6.7188470335373e-18 relative error = 3.3832976153145627333918236610803e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.74 y[1] (analytic) = 1.9857191788355534971206826956656 y[1] (numeric) = 1.9857191788355534903539121915113 absolute error = 6.7667705041543e-18 relative error = 3.4077177560033463663164352210633e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.741 y[1] (analytic) = 1.9855502885561223138814833213618 y[1] (numeric) = 1.9855502885561223070667975180061 absolute error = 6.8146858033557e-18 relative error = 3.4321396152153314666498872600237e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.742 y[1] (analytic) = 1.9853804127264847037079454361259 y[1] (numeric) = 1.9853804127264846968453525528998 absolute error = 6.8625928832261e-18 relative error = 3.4565632053364691420776186515284e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.743 y[1] (analytic) = 1.9852095515165164820813605489057 y[1] (numeric) = 1.985209551516516475170868853047 absolute error = 6.9104916958587e-18 relative error = 3.4809885387563864515157248892276e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.744 y[1] (analytic) = 1.985037705097078844731516596882 y[1] (numeric) = 1.9850377050970788377731344035275 absolute error = 6.9583821933545e-18 relative error = 3.5054156278679846539956641047407e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.745 y[1] (analytic) = 1.9848648736400181967755164541134 y[1] (numeric) = 1.9848648736400181897692521262904 absolute error = 7.0062643278230e-18 relative error = 3.5298444850677929740202066261438e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.746 y[1] (analytic) = 1.9846910573181659808713871349669 y[1] (numeric) = 1.9846910573181659738172490835847 absolute error = 7.0541380513822e-18 relative error = 3.5542751227559698573688776053055e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.747 y[1] (analytic) = 1.9845162563053385043866515387101 y[1] (numeric) = 1.9845162563053384972846482225519 absolute error = 7.1020033161582e-18 relative error = 3.5787075533361026738937135812870e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.748 y[1] (analytic) = 1.9843404707763367655820355666807 y[1] (numeric) = 1.9843404707763367584321754923948 absolute error = 7.1498600742859e-18 relative error = 3.6031417892155616608610125758470e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.749 y[1] (analytic) = 1.9841637009069462788104844283096 y[1] (numeric) = 1.9841637009069462716127761504011 absolute error = 7.1977082779085e-18 relative error = 3.6275778428052492717069739457932e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.75 memory used=26.7MB, alloc=4.2MB, time=1.68 y[1] (analytic) = 1.983985946873936898731662936968 y[1] (numeric) = 1.9839859468739368914861150577902 absolute error = 7.2455478791778e-18 relative error = 3.6520157265197526262346147192831e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.751 y[1] (analytic) = 1.9838072088550626435421155811236 y[1] (numeric) = 1.9838072088550626362487367508695 absolute error = 7.2933788302541e-18 relative error = 3.6764554527772944162442125584815e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.752 y[1] (analytic) = 1.9836274870290615172212631406304 y[1] (numeric) = 1.9836274870290615098800620573238 absolute error = 7.3412010833066e-18 relative error = 3.7008970339999358544441712433654e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.753 y[1] (analytic) = 1.9834467815756553307934136021408 y[1] (numeric) = 1.9834467815756553234043990116279 absolute error = 7.3890145905129e-18 relative error = 3.7253404826133259847535736610913e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.754 y[1] (analytic) = 1.9832650926755495226059661116152 y[1] (numeric) = 1.9832650926755495151691468075555 absolute error = 7.4368193040597e-18 relative error = 3.7497858110470559250243365464492e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.755 y[1] (analytic) = 1.9830824205104329776239876857083 y[1] (numeric) = 1.9830824205104329701393725095662 absolute error = 7.4846151761421e-18 relative error = 3.7742330317343073392607893205934e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.756 y[1] (analytic) = 1.9828987652629778457413433874426 y[1] (numeric) = 1.9828987652629778382089412284782 absolute error = 7.5324021589644e-18 relative error = 3.7986821571122571906319883570811e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.757 y[1] (analytic) = 1.9827141271168393591085616550214 y[1] (numeric) = 1.982714127116839351528381450282 absolute error = 7.5801802047394e-18 relative error = 3.8231331996217261870397379794907e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.758 y[1] (analytic) = 1.9825285062566556484776174559031 y[1] (numeric) = 1.9825285062566556408496681902138 absolute error = 7.6279492656893e-18 relative error = 3.8475861717076340873692655938337e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.759 y[1] (analytic) = 1.982341902868047558563816921336 y[1] (numeric) = 1.9823419028680475508881076272911 absolute error = 7.6757092940449e-18 relative error = 3.8720410858185976985903290220929e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.76 y[1] (analytic) = 1.982154317137618462424968099456 y[1] (numeric) = 1.9821543171376184547015078574098 absolute error = 7.7234602420462e-18 relative error = 3.8964979544072349552955835141270e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.761 y[1] (analytic) = 1.9819657492529540748580234477586 y[1] (numeric) = 1.9819657492529540670868213858164 absolute error = 7.7712020619422e-18 relative error = 3.9209567899300655385064148671822e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.762 y[1] (analytic) = 1.9817761994026222648133806682892 y[1] (numeric) = 1.981776199402622256994445962298 absolute error = 7.8189347059912e-18 relative error = 3.9454176048476637438421722816505e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.763 y[1] (analytic) = 1.9815856677761728668270294712338 y[1] (numeric) = 1.9815856677761728589603713447733 absolute error = 7.8666581264605e-18 relative error = 3.9698804116245086566570009927476e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.764 y[1] (analytic) = 1.9813941545641374914707328347483 y[1] (numeric) = 1.9813941545641374835563605591216 absolute error = 7.9143722756267e-18 relative error = 3.9943452227291370649625319293833e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.765 y[1] (analytic) = 1.9812016599580293348204323108292 y[1] (numeric) = 1.9812016599580293268583552050535 absolute error = 7.9620771057757e-18 relative error = 4.0188120506341450445770258098671e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.766 y[1] (analytic) = 1.9810081841503429869430679088044 y[1] (numeric) = 1.9810081841503429789332953396018 absolute error = 8.0097725692026e-18 relative error = 4.0432809078161390731887266359232e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.767 y[1] (analytic) = 1.9808137273345542394020040696088 y[1] (numeric) = 1.9808137273345542313445454513969 absolute error = 8.0574586182119e-18 relative error = 4.0677518067558385757363405963580e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.768 y[1] (analytic) = 1.9806182897051198917812542254018 y[1] (numeric) = 1.9806182897051198836761190202842 absolute error = 8.1051352051176e-18 relative error = 4.0922247599381280479167877153301e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.769 y[1] (analytic) = 1.9804218714574775572286974202867 y[1] (numeric) = 1.9804218714574775490758951380434 absolute error = 8.1528022822433e-18 relative error = 4.1166997798521092180310205400125e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.77 y[1] (analytic) = 1.9802244727880454670184814488984 y[1] (numeric) = 1.9802244727880454588180216469768 absolute error = 8.2004598019216e-18 relative error = 4.1411768789907997523169473140485e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.771 y[1] (analytic) = 1.9800260938942222741328079504419 y[1] (numeric) = 1.9800260938942222658847002339466 absolute error = 8.2481077164953e-18 relative error = 4.1656560698517408659028420163101e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.772 y[1] (analytic) = 1.9798267349743868558632958763769 y[1] (numeric) = 1.9798267349743868475675498980607 absolute error = 8.2957459783162e-18 relative error = 4.1901373649363930790038075948637e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.773 memory used=30.5MB, alloc=4.2MB, time=1.92 y[1] (analytic) = 1.9796263962278981154321207303721 y[1] (numeric) = 1.9796263962278981070887461906259 absolute error = 8.3433745397462e-18 relative error = 4.2146207767506934514109480126318e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.774 y[1] (analytic) = 1.9794250778550947826331279593709 y[1] (numeric) = 1.9794250778550947742421346062141 absolute error = 8.3909933531568e-18 relative error = 4.2391063178048048466842682869193e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.775 y[1] (analytic) = 1.9792227800572952134931198546392 y[1] (numeric) = 1.9792227800572952050545174837102 absolute error = 8.4386023709290e-18 relative error = 4.2635940006130671512819235706054e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.776 y[1] (analytic) = 1.9790195030367971889535163014928 y[1] (numeric) = 1.9790195030367971804673147560389 absolute error = 8.4862015454539e-18 relative error = 4.2880838376943021813038915941883e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.777 y[1] (analytic) = 1.9788152469968777125725906960248 y[1] (numeric) = 1.9788152469968777040387998668925 absolute error = 8.5337908291323e-18 relative error = 4.3125758415716134318475302040028e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.778 y[1] (analytic) = 1.9786100121417928072484833265824 y[1] (numeric) = 1.9786100121417927986671131522074 absolute error = 8.5813701743750e-18 relative error = 4.3370700247725394942327080983244e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.779 y[1] (analytic) = 1.978403798676777310963195496961 y[1] (numeric) = 1.9784037986767773023342559633584 absolute error = 8.6289395336026e-18 relative error = 4.3615663998289548473341205960918e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.78 y[1] (analytic) = 1.9781966068080446715477686473056 y[1] (numeric) = 1.9781966068080446628712697880598 absolute error = 8.6764988592458e-18 relative error = 4.3860649792772233501813850344438e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.781 y[1] (analytic) = 1.9779884367427867404688537075226 y[1] (numeric) = 1.9779884367427867317448056037775 absolute error = 8.7240481037451e-18 relative error = 4.4105657756580485002772163241947e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.782 y[1] (analytic) = 1.9777792886891735656368768966163 y[1] (numeric) = 1.9777792886891735568652896770648 absolute error = 8.7715872195515e-18 relative error = 4.4350688015168292227629883757092e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.783 y[1] (analytic) = 1.9775691628563531832360091597658 y[1] (numeric) = 1.97756916285635317441689300064 absolute error = 8.8191161591258e-18 relative error = 4.4595740694033079535802925279379e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.784 y[1] (analytic) = 1.9773580594544514085761474131563 y[1] (numeric) = 1.9773580594544513997095125382174 absolute error = 8.8666348749389e-18 relative error = 4.4840815918717242320165553576322e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.785 y[1] (analytic) = 1.9771459786945716259671167445668 y[1] (numeric) = 1.9771459786945716170529734250945 absolute error = 8.9141433194723e-18 relative error = 4.5085913814810695547657555881129e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.786 y[1] (analytic) = 1.9769329207887945776153036954926 y[1] (numeric) = 1.9769329207887945686536622502751 absolute error = 8.9616414452175e-18 relative error = 4.5331034507947859850721951505442e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.787 y[1] (analytic) = 1.9767188859501781515429317281535 y[1] (numeric) = 1.9767188859501781425338025234772 absolute error = 9.0091292046763e-18 relative error = 4.5576178123809198755101473773138e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.788 y[1] (analytic) = 1.9765038743927571685301909580939 y[1] (numeric) = 1.9765038743927571594735844077329 absolute error = 9.0566065503610e-18 relative error = 4.5821344788122251038285332472894e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.789 y[1] (analytic) = 1.976287886331543168080435210227 y[1] (numeric) = 1.9762878863315431589763617754327 absolute error = 9.1040734347943e-18 relative error = 4.6066534626661145848560696508633e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.79 y[1] (analytic) = 1.9760709219825241934086604331086 y[1] (numeric) = 1.9760709219825241842571306225993 absolute error = 9.1515298105093e-18 relative error = 4.6311747765246623646665022077830e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.791 y[1] (analytic) = 1.9758529815626645754534794829444 y[1] (numeric) = 1.9758529815626645662545038528947 absolute error = 9.1989756300497e-18 relative error = 4.6556984329747069464632686717536e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.792 y[1] (analytic) = 1.9756340652899047159128092653371 y[1] (numeric) = 1.9756340652899047066663984193676 absolute error = 9.2464108459695e-18 relative error = 4.6802244446077016099526603075993e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.793 y[1] (analytic) = 1.9754141733831608693034871990695 y[1] (numeric) = 1.9754141733831608600096517882359 absolute error = 9.2938354108336e-18 relative error = 4.7047528240200202401253363461212e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.794 y[1] (analytic) = 1.9751933060623249240450349422872 y[1] (numeric) = 1.9751933060623249147037856650698 absolute error = 9.3412492772174e-18 relative error = 4.7292835838127570891288952509911e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.795 y[1] (analytic) = 1.9749714635482641825677882973008 y[1] (numeric) = 1.9749714635482641731791358995936 absolute error = 9.3886523977072e-18 relative error = 4.7538167365919314819159762754090e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.796 memory used=34.3MB, alloc=4.3MB, time=2.17 y[1] (analytic) = 1.9747486460628211404456131858575 y[1] (numeric) = 1.9747486460628211310095684609579 absolute error = 9.4360447248996e-18 relative error = 4.7783522949681862748719593172821e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.797 y[1] (analytic) = 1.9745248538288132645534285621498 y[1] (numeric) = 1.9745248538288132550700023507474 absolute error = 9.4834262114024e-18 relative error = 4.8028902715572457951425623775253e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.798 y[1] (analytic) = 1.9743000870700327702497581060178 y[1] (numeric) = 1.9743000870700327607189612961836 absolute error = 9.5307968098342e-18 relative error = 4.8274306789797156385185226387056e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.799 y[1] (analytic) = 1.9740743460112463975845335137761 y[1] (numeric) = 1.9740743460112463880063770409517 absolute error = 9.5781564728244e-18 relative error = 4.8519735298610849667632273396935e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.8 y[1] (analytic) = 1.9738476308781951865323731788434 y[1] (numeric) = 1.9738476308781951769068680258302 absolute error = 9.6255051530132e-18 relative error = 4.8765188368317288150858576797441e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.801 y[1] (analytic) = 1.9736199418975942512515610288767 y[1] (numeric) = 1.9736199418975942415787182258247 absolute error = 9.6728428030520e-18 relative error = 4.9010666125271130829107798093087e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.802 y[1] (analytic) = 1.9733912792971325533689512604129 y[1] (numeric) = 1.9733912792971325436487818848097 absolute error = 9.7201693756032e-18 relative error = 4.9256168695876956303414510973038e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.803 y[1] (analytic) = 1.9731616433054726742910256860942 y[1] (numeric) = 1.973161643305472664523540862754 absolute error = 9.7674848233402e-18 relative error = 4.9501696206589286754055987421268e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804 y[1] (analytic) = 1.9729310341522505865413313834007 y[1] (numeric) = 1.9729310341522505767265422844531 absolute error = 9.8147890989476e-18 relative error = 4.9747248783913625737934241498398e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.805 y[1] (analytic) = 1.9726994520680754241245273074336 y[1] (numeric) = 1.9726994520680754142624451523126 absolute error = 9.8620821551210e-18 relative error = 4.9992826554405469125220255061726e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.806 y[1] (analytic) = 1.9724668972845292519172695036838 y[1] (numeric) = 1.9724668972845292420079055591163 absolute error = 9.9093639445675e-18 relative error = 5.0238429644672864284678970893286e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.807 y[1] (analytic) = 1.9722333700341668340861655298801 y[1] (numeric) = 1.9722333700341668241295311098749 absolute error = 9.9566344200052e-18 relative error = 5.0484058181373900777330763050882e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.808 y[1] (analytic) = 1.9719988705505154015330296689451 y[1] (numeric) = 1.9719988705505153915291361347815 absolute error = 1.00038935341636e-17 relative error = 5.0729712291218763258391031440000e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.809 y[1] (analytic) = 1.9717633990680744183676714877829 y[1] (numeric) = 1.9717633990680744083165302479991 absolute error = 1.00511412397838e-17 relative error = 5.0975392100970771611154355966154e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.81 y[1] (analytic) = 1.9715269558223153474084512690904 y[1] (numeric) = 1.9715269558223153373100737794725 absolute error = 1.00983774896179e-17 relative error = 5.1221097737443364155978289800338e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.811 y[1] (analytic) = 1.9712895410496814147108368156187 y[1] (numeric) = 1.971289541049681404565234579189 absolute error = 1.01456022364297e-17 relative error = 5.1466829327503673448612098806709e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.812 y[1] (analytic) = 1.9710511549875873731241970983066 y[1] (numeric) = 1.9710511549875873629313816653122 absolute error = 1.01928154329944e-17 relative error = 5.1712586998071031315871430125385e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.813 y[1] (analytic) = 1.970811797874419264877069191474 y[1] (numeric) = 1.970811797874419254637052159375 absolute error = 1.02400170320990e-17 relative error = 5.1958370876119024740287710422902e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.814 y[1] (analytic) = 1.9705714699495341831911359097873 y[1] (numeric) = 1.9705714699495341729039289232455 absolute error = 1.02872069865418e-17 relative error = 5.2204181088672986136086572918922e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.815 y[1] (analytic) = 1.9703301714532600329241525330003 y[1] (numeric) = 1.9703301714532600225897672838676 absolute error = 1.03343852491327e-17 relative error = 5.2450017762811542117910173968632e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.816 y[1] (analytic) = 1.9700879026268952902420619755244 y[1] (numeric) = 1.9700879026268952798605102028307 absolute error = 1.03815517726937e-17 relative error = 5.2695881025669178679039446091106e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.817 y[1] (analytic) = 1.9698446637127087613205387286904 y[1] (numeric) = 1.9698446637127087508918322186323 absolute error = 1.04287065100581e-17 relative error = 5.2941771004432208858549729686757e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.818 y[1] (analytic) = 1.9696004549539393400762028741411 y[1] (numeric) = 1.9696004549539393296003534600699 absolute error = 1.04758494140712e-17 relative error = 5.3187687826342353277483498294900e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.819 memory used=38.1MB, alloc=4.3MB, time=2.41 y[1] (analytic) = 1.9693552765947957649277464371182 y[1] (numeric) = 1.9693552765947957544047659995281 absolute error = 1.05229804375901e-17 relative error = 5.3433631618695753405791490774626e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.82 y[1] (analytic) = 1.969109128880456374587215318498 y[1] (numeric) = 1.9691091288804563640171157850141 absolute error = 1.05700995334839e-17 relative error = 5.3679602508844015569349597893964e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.821 y[1] (analytic) = 1.9688620120570688628816910142727 y[1] (numeric) = 1.9688620120570688522644843596393 absolute error = 1.06172066546334e-17 relative error = 5.3925600624192716301016789846217e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.822 y[1] (analytic) = 1.9686139263717500326056173007762 y[1] (numeric) = 1.9686139263717500219413155468447 absolute error = 1.06643017539315e-17 relative error = 5.4171626092203462464952639934502e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.823 y[1] (analytic) = 1.9683648720725855484040180333065 y[1] (numeric) = 1.9683648720725855376926332490235 absolute error = 1.07113847842830e-17 relative error = 5.4417679040392904819111831419327e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.824 y[1] (analytic) = 1.9681148494086296886868531749068 y[1] (numeric) = 1.9681148494086296779283974763017 absolute error = 1.07584556986051e-17 relative error = 5.4663759596335307632088558297255e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.825 y[1] (analytic) = 1.9678638586299050965747611409276 y[1] (numeric) = 1.9678638586299050857692466911009 absolute error = 1.08055144498267e-17 relative error = 5.4909867887659022378018981828576e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.826 y[1] (analytic) = 1.9676118999874025298764365136082 y[1] (numeric) = 1.9676118999874025190238755227191 absolute error = 1.08525609908891e-17 relative error = 5.5156004042050074058331763851054e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.827 y[1] (analytic) = 1.9673589737330806100978931492779 y[1] (numeric) = 1.9673589737330805991982978745321 absolute error = 1.08995952747458e-17 relative error = 5.5402168187251175713393216706128e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.828 y[1] (analytic) = 1.9671050801198655704838636688928 y[1] (numeric) = 1.9671050801198655595372464145304 absolute error = 1.09466172543624e-17 relative error = 5.5648360451061250641496928182009e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.829 y[1] (analytic) = 1.9668502194016510030915872904893 y[1] (numeric) = 1.9668502194016509920979604077722 absolute error = 1.09936268827171e-17 relative error = 5.5894580961338004909612617981843e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.83 y[1] (analytic) = 1.9665943918332976048972389297428 y[1] (numeric) = 1.9665943918332975938566148169426 absolute error = 1.10406241128002e-17 relative error = 5.6140829845995417034822912755886e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.831 y[1] (analytic) = 1.966337597670632922935253462184 y[1] (numeric) = 1.9663375976706329118476445645695 absolute error = 1.10876088976145e-17 relative error = 5.6387107233005802848647737233113e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.832 y[1] (analytic) = 1.9660798371704510984708000077252 y[1] (numeric) = 1.9660798371704510873362188175501 absolute error = 1.11345811901751e-17 relative error = 5.6633413250398830320398000723803e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.833 y[1] (analytic) = 1.9658211105905126102056620650027 y[1] (numeric) = 1.9658211105905125990241211214928 absolute error = 1.11815409435099e-17 relative error = 5.6879748026264094562078659606492e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.834 y[1] (analytic) = 1.9655614181895440165177802896318 y[1] (numeric) = 1.9655614181895440052892921789729 absolute error = 1.12284881106589e-17 relative error = 5.7126111688747589846348655361358e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.835 y[1] (analytic) = 1.9653007602272376967347156768128 y[1] (numeric) = 1.9653007602272376854592930321376 absolute error = 1.12754226446752e-17 relative error = 5.7372504366056829007665385116668e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.836 y[1] (analytic) = 1.9650391369642515914412918748 y[1] (numeric) = 1.9650391369642515801189473761759 absolute error = 1.13223444986241e-17 relative error = 5.7618926186456298001980958021406e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.837 y[1] (analytic) = 1.9647765486622089418216763215732 y[1] (numeric) = 1.9647765486622089304524226959893 absolute error = 1.13692536255839e-17 relative error = 5.7865377278271559328711876521268e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.838 y[1] (analytic) = 1.9645129955836980280361608626057 y[1] (numeric) = 1.9645129955836980166200108839603 absolute error = 1.14161499786454e-17 relative error = 5.8111857769886741428350417371684e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.839 y[1] (analytic) = 1.9642484779922719066329034729287 y[1] (numeric) = 1.9642484779922718951698699620165 absolute error = 1.14630335109122e-17 relative error = 5.8358367789746098973446941085230e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.84 y[1] (analytic) = 1.9639829961524481469948936717271 y[1] (numeric) = 1.9639829961524481354849894962264 absolute error = 1.15099041755007e-17 relative error = 5.8604907466354047014339383100565e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.841 y[1] (analytic) = 1.9637165503297085668224051824804 y[1] (numeric) = 1.96371655032970855526564325694 absolute error = 1.15567619255404e-17 relative error = 5.8851476928276722975419256508356e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.842 memory used=41.9MB, alloc=4.3MB, time=2.66 y[1] (analytic) = 1.9634491407904989666512003561727 y[1] (numeric) = 1.9634491407904989550475936419991 absolute error = 1.16036067141736e-17 relative error = 5.9098076304140494186930224985672e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.843 y[1] (analytic) = 1.9631807678022288634067518393463 y[1] (numeric) = 1.9631807678022288517563133447909 absolute error = 1.16504384945554e-17 relative error = 5.9344705722631992440930822917206e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.844 y[1] (analytic) = 1.962911431633271222994747932755 y[1] (numeric) = 1.962911431633271211297490712901 absolute error = 1.16972572198540e-17 relative error = 5.9591365312499677021151613133355e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.845 y[1] (analytic) = 1.9626411325529621919281490500886 y[1] (numeric) = 1.962641132552962180184086206838 absolute error = 1.17440628432506e-17 relative error = 5.9838055202553361056573693870971e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.846 y[1] (analytic) = 1.962369870831600827991063649691 y[1] (numeric) = 1.9623698708316008162002083317512 absolute error = 1.17908553179398e-17 relative error = 6.0084775521666285533891286056400e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.847 y[1] (analytic) = 1.962097646740448829939712975372 y[1] (numeric) = 1.9620976467404488181020783782429 absolute error = 1.18376345971291e-17 relative error = 6.0331526398772608215825726049717e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.848 y[1] (analytic) = 1.961824460551730266240754905327 y[1] (numeric) = 1.9618244605517302543563542712879 absolute error = 1.18844006340391e-17 relative error = 6.0578307962868458689332552396586e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.849 y[1] (analytic) = 1.9615503125386313028472381708177 y[1] (numeric) = 1.9615503125386312909160847889139 absolute error = 1.19311533819038e-17 relative error = 6.0825120343013504200040414731900e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.85 y[1] (analytic) = 1.9612752029752999300124591686361 y[1] (numeric) = 1.9612752029752999180345663746656 absolute error = 1.19778927939705e-17 relative error = 6.1071963668330477421981821528784e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.851 y[1] (analytic) = 1.9609991321368456881419945534734 y[1] (numeric) = 1.9609991321368456761173757299736 absolute error = 1.20246188234998e-17 relative error = 6.1318838068005213889363564841572e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.852 y[1] (analytic) = 1.9607221002993393926841837581374 y[1] (numeric) = 1.9607221002993393806128523343718 absolute error = 1.20713314237656e-17 relative error = 6.1565743671286689571809749381790e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.853 y[1] (analytic) = 1.9604441077398128580593365511139 y[1] (numeric) = 1.9604441077398128459413060030586 absolute error = 1.21180305480553e-17 relative error = 6.1812680607488078769014003296251e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.854 y[1] (analytic) = 1.9601651547362586206279417022404 y[1] (numeric) = 1.9601651547362586084632255525705 absolute error = 1.21647161496699e-17 relative error = 6.2059649005987302856725293578974e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.855 y[1] (analytic) = 1.9598852415676296606981537882613 y[1] (numeric) = 1.9598852415676296484867656063377 absolute error = 1.22113881819236e-17 relative error = 6.2306648996225028448506910710341e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.856 y[1] (analytic) = 1.9596043685138391235728361307546 y[1] (numeric) = 1.95960436851383911131478953261 absolute error = 1.22580465981446e-17 relative error = 6.2553680707708787638758666412222e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.857 y[1] (analytic) = 1.9593225358557600396364388193626 y[1] (numeric) = 1.9593225358557600273317474676883 absolute error = 1.23046913516743e-17 relative error = 6.2800744270008935815306842789948e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.858 y[1] (analytic) = 1.9590397438752250434819917334276 y[1] (numeric) = 1.9590397438752250311306693375595 absolute error = 1.23513223958681e-17 relative error = 6.3047839812762773367803519915699e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.859 y[1] (analytic) = 1.9587559928550260920784934350135 y[1] (numeric) = 1.9587559928550260796805537509186 absolute error = 1.23979396840949e-17 relative error = 6.3294967465672034212003603672229e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.86 y[1] (analytic) = 1.9584712830789141819789777659032 y[1] (numeric) = 1.9584712830789141695344345961658 absolute error = 1.24445431697374e-17 relative error = 6.3542127358504457069590638211742e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.861 y[1] (analytic) = 1.9581856148315990655695409404804 y[1] (numeric) = 1.9581856148315990530784081342883 absolute error = 1.24911328061921e-17 relative error = 6.3789319621093826200370395921465e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.862 y[1] (analytic) = 1.9578989883987489663596128854452 y[1] (numeric) = 1.9578989883987489538219043385757 absolute error = 1.25377085468695e-17 relative error = 6.4036544383341033790810299275210e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.863 y[1] (analytic) = 1.9576114040669902933137575360685 y[1] (numeric) = 1.9576114040669902807294871908748 absolute error = 1.25842703451937e-17 relative error = 6.4283801775212078435437585688668e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.864 y[1] (analytic) = 1.9573228621239073542252877571615 y[1] (numeric) = 1.9573228621239073415944696025586 absolute error = 1.26308181546029e-17 relative error = 6.4531091926740660087425442842958e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.865 y[1] (analytic) = 1.9570333628580420681319815151212 y[1] (numeric) = 1.9570333628580420554546295865718 absolute error = 1.26773519285494e-17 memory used=45.7MB, alloc=4.3MB, time=2.91 relative error = 6.4778414968028222530894880422890e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.866 y[1] (analytic) = 1.9567429065588936767741868853113 y[1] (numeric) = 1.9567429065588936640503152648119 absolute error = 1.27238716204994e-17 relative error = 6.5025771029242973907779171311029e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.867 y[1] (analytic) = 1.9564514935169184550956044366501 y[1] (numeric) = 1.9564514935169184423252272527169 absolute error = 1.27703771839332e-17 relative error = 6.5273160240620951009292611197118e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.868 y[1] (analytic) = 1.956159124023529420787036492599 y[1] (numeric) = 1.9561591240235294079701679202537 absolute error = 1.28168685723453e-17 relative error = 6.5520582732466573429266665696374e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.869 y[1] (analytic) = 1.9558657983710960428733937247771 y[1] (numeric) = 1.9558657983710960300100479855329 absolute error = 1.28633457392442e-17 relative error = 6.5768038635151664488051313121808e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.87 y[1] (analytic) = 1.9555715168529439493442504921726 y[1] (numeric) = 1.9555715168529439364344418540198 absolute error = 1.29098086381528e-17 relative error = 6.6015528079117539551108507426145e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.871 y[1] (analytic) = 1.9552762797633546338282412953696 y[1] (numeric) = 1.9552762797633546208719840727613 absolute error = 1.29562572226083e-17 relative error = 6.6263051194874539169303009436544e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.872 y[1] (analytic) = 1.9549800873975651613115916713705 y[1] (numeric) = 1.9549800873975651483089002252086 absolute error = 1.30026914461619e-17 relative error = 6.6510608113000538893275634175812e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.873 y[1] (analytic) = 1.9546829400517678729010778104589 y[1] (numeric) = 1.9546829400517678598519665480794 absolute error = 1.30491112623795e-17 relative error = 6.6758198964144573769554309080332e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.874 y[1] (analytic) = 1.9543848380231100896317101321172 y[1] (numeric) = 1.9543848380231100765361935072759 absolute error = 1.30955166248413e-17 relative error = 6.7005823879024837893420636999350e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.875 y[1] (analytic) = 1.9540857816096938153194370122924 y[1] (numeric) = 1.9540857816096938021775295251504 absolute error = 1.31419074871420e-17 relative error = 6.7253482988429752748537814325949e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.876 y[1] (analytic) = 1.9537857711105754384591658092802 y[1] (numeric) = 1.9537857711105754252708820063896 absolute error = 1.31882838028906e-17 relative error = 6.7501176423216989341301368160497e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.877 y[1] (analytic) = 1.953484806825765433168399290183 y[1] (numeric) = 1.9534848068257654199337537644721 absolute error = 1.32346455257109e-17 relative error = 6.7748904314316072895119488617970e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.878 y[1] (analytic) = 1.9531828890562280591767865142787 y[1] (numeric) = 1.9531828890562280458957939050376 absolute error = 1.32809926092411e-17 relative error = 6.7996666792726382212205805631169e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.879 y[1] (analytic) = 1.9528800181038810608618881837261 y[1] (numeric) = 1.9528800181038810475345631765919 absolute error = 1.33273250071342e-17 relative error = 6.8244463989519243820138168336913e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.88 y[1] (analytic) = 1.9525761942715953653314574258151 y[1] (numeric) = 1.9525761942715953519578147527574 absolute error = 1.33736426730577e-17 relative error = 6.8492296035836443182486464341963e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.881 y[1] (analytic) = 1.952271417863194779552537924457 y[1] (numeric) = 1.9522714178631947661325923637629 absolute error = 1.34199455606941e-17 relative error = 6.8740163062892832435768182626277e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.882 y[1] (analytic) = 1.9519656891834556865276822717902 y[1] (numeric) = 1.9519656891834556730614486480498 absolute error = 1.34662336237404e-17 relative error = 6.8988065201973817653592673245054e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.883 y[1] (analytic) = 1.9516590085381067405185943636589 y[1] (numeric) = 1.9516590085381067270060875477504 absolute error = 1.35125068159085e-17 relative error = 6.9236002584437455337869854707570e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.884 y[1] (analytic) = 1.9513513762338285613175006152962 y[1] (numeric) = 1.9513513762338285477587355243709 absolute error = 1.35587650909253e-17 relative error = 6.9483975341715013611790483689309e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.885 y[1] (analytic) = 1.9510427925782534275665557258151 y[1] (numeric) = 1.9510427925782534139615473232826 absolute error = 1.36050084025325e-17 relative error = 6.9731983605309996434570577363492e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.886 y[1] (analytic) = 1.9507332578799649691255896720762 y[1] (numeric) = 1.9507332578799649554743529675894 absolute error = 1.36512367044868e-17 relative error = 6.9980027506799217529089119615767e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.887 y[1] (analytic) = 1.9504227724484978584885035641592 y[1] (numeric) = 1.9504227724484978447910536135993 absolute error = 1.36974499505599e-17 relative error = 7.0228107177832850038648370034056e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.888 y[1] (analytic) = 1.9501113365943375012486229460171 y[1] (numeric) = 1.9501113365943374875049748514786 absolute error = 1.37436480945385e-17 memory used=49.5MB, alloc=4.3MB, time=3.15 relative error = 7.0476222750134476359581410987812e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.889 y[1] (analytic) = 1.9497989506289197256133180759338 y[1] (numeric) = 1.9497989506289197118234869857093 absolute error = 1.37898310902245e-17 relative error = 7.0724374355502163895494963542063e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.89 y[1] (analytic) = 1.9494856148646304709682016721383 y[1] (numeric) = 1.9494856148646304571322027807033 absolute error = 1.38359988914350e-17 relative error = 7.0972562125808516062915779126325e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.891 y[1] (analytic) = 1.9491713296148054754912155593528 y[1] (numeric) = 1.9491713296148054616090641073507 absolute error = 1.38821514520021e-17 relative error = 7.1220786192999697401025449331943e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.892 y[1] (analytic) = 1.9488560951937299628169186021618 y[1] (numeric) = 1.9488560951937299488886298763885 absolute error = 1.39282887257733e-17 relative error = 7.1469046689097536594850793589299e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.893 y[1] (analytic) = 1.9485399119166383277512892608872 y[1] (numeric) = 1.948539911916638313776878594276 absolute error = 1.39744106666112e-17 relative error = 7.1717343746198039234168217419611e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.894 y[1] (analytic) = 1.9482227800997138210373570551425 y[1] (numeric) = 1.9482227800997138070168398267484 absolute error = 1.40205172283941e-17 relative error = 7.1965677496474518850089816686015e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.895 y[1] (analytic) = 1.9479047000600882331719781694058 y[1] (numeric) = 1.9479047000600882191053698043906 absolute error = 1.40666083650152e-17 relative error = 7.2214048072173543932178404561030e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.896 y[1] (analytic) = 1.9475856721158415772740713838128 y[1] (numeric) = 1.9475856721158415631613873534293 absolute error = 1.41126840303835e-17 relative error = 7.2462455605619609862016200358016e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.897 y[1] (analytic) = 1.9472656965860017710046314619044 y[1] (numeric) = 1.947265696586001756845887283481 absolute error = 1.41587441784234e-17 relative error = 7.2710900229213139537759328211345e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.898 y[1] (analytic) = 1.9469447737905443175388380752907 y[1] (numeric) = 1.9469447737905443033340493122162 absolute error = 1.42047887630745e-17 relative error = 7.2959382075429509416867389994772e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.899 y[1] (analytic) = 1.9466229040503919855905792930964 y[1] (numeric) = 1.9466229040503919713397615548039 absolute error = 1.42508177382925e-17 relative error = 7.3207901276823725533305318280661e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.9 y[1] (analytic) = 1.946300087687414488489709611635 y[1] (numeric) = 1.9463000876874144741928785535868 absolute error = 1.42968310580482e-17 relative error = 7.3456457966025342175828014804252e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.901 y[1] (analytic) = 1.9459763250244281623123634470302 y[1] (numeric) = 1.9459763250244281479695347707018 absolute error = 1.43428286763284e-17 relative error = 7.3705052275743139382626822928270e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.902 y[1] (analytic) = 1.9456516163851956430646459604419 y[1] (numeric) = 1.9456516163851956286758354133063 absolute error = 1.43888105471356e-17 relative error = 7.3953684338763637633742804561963e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.903 y[1] (analytic) = 1.9453259620944255429200240321793 y[1] (numeric) = 1.9453259620944255284852474076915 absolute error = 1.44347766244878e-17 relative error = 7.4202354287950125250225975324275e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904 y[1] (analytic) = 1.9449993624777721255107411472845 y[1] (numeric) = 1.9449993624777721110300142848656 absolute error = 1.44807268624189e-17 relative error = 7.4451062256244769780701563473538e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.905 y[1] (analytic) = 1.9446718178618349802735809011434 y[1] (numeric) = 1.9446718178618349657469196861648 absolute error = 1.45266612149786e-17 relative error = 7.4699808376668160518343091986152e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.906 y[1] (analytic) = 1.9443433285741586958503047793337 y[1] (numeric) = 1.944343328574158681277725143101 absolute error = 1.45725796362327e-17 relative error = 7.4948592782320907942183687107320e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.907 y[1] (analytic) = 1.9440138949432325325430908112447 y[1] (numeric) = 1.9440138949432325179246087309819 absolute error = 1.46184820802628e-17 relative error = 7.5197415606382158520157580630044e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.908 y[1] (analytic) = 1.9436835172984900938253006420035 y[1] (numeric) = 1.9436835172984900791609321408371 absolute error = 1.46643685011664e-17 relative error = 7.5446276982110166088752357494944e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.909 y[1] (analytic) = 1.9433521959703089969079035119126 y[1] (numeric) = 1.9433521959703089821976646588556 absolute error = 1.47102388530570e-17 relative error = 7.5695177042842863947671088320214e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.91 y[1] (analytic) = 1.9430199312900105423618865769482 y[1] (numeric) = 1.9430199312900105276057934868838 absolute error = 1.47560930900644e-17 relative error = 7.5944115921999466999943475464671e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.911 y[1] (analytic) = 1.94268672358985938279698194788 y[1] (numeric) = 1.9426867235898593679950507815457 absolute error = 1.48019311663343e-17 relative error = 7.6193093753078472418950356612450e-16 % h = 0.001 memory used=53.4MB, alloc=4.3MB, time=3.40 TOP MAIN SOLVE Loop NO POLE x[1] = 1.912 y[1] (analytic) = 1.9423525732030631905970417692598 y[1] (numeric) = 1.9423525732030631757492887332311 absolute error = 1.48477530360287e-17 relative error = 7.6442110669659777113723171845811e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.913 y[1] (analytic) = 1.9420174804637723247123936028736 y[1] (numeric) = 1.9420174804637723098188349495481 absolute error = 1.48935586533255e-17 relative error = 7.6691166805402678088022383608109e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.914 y[1] (analytic) = 1.9416814457070794965095093232775 y[1] (numeric) = 1.9416814457070794815701613508581 absolute error = 1.49393479724194e-17 relative error = 7.6940262294050566093663804339307e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.915 y[1] (analytic) = 1.9413444692690194346783216757165 y[1] (numeric) = 1.9413444692690194196932007281956 absolute error = 1.49851209475209e-17 relative error = 7.7189397269425837266708525827412e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.916 y[1] (analytic) = 1.9410065514865685491975235890855 y[1] (numeric) = 1.9410065514865685341666460562284 absolute error = 1.50308775328571e-17 relative error = 7.7438571865434073146261923731935e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.917 y[1] (analytic) = 1.9406676926976445943581862786025 y[1] (numeric) = 1.9406676926976445792815685959312 absolute error = 1.50766176826713e-17 relative error = 7.7687786216062041753570812557445e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.918 y[1] (analytic) = 1.9403278932411063308460331145497 y[1] (numeric) = 1.9403278932411063157236917633262 absolute error = 1.51223413512235e-17 relative error = 7.7937040455380335110610298056494e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.919 y[1] (analytic) = 1.939987153456753186882707174779 y[1] (numeric) = 1.9399871534567531717146586819891 absolute error = 1.51680484927899e-17 relative error = 7.8186334717540854997138821655922e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.92 y[1] (analytic) = 1.939645473685324918426371339687 y[1] (numeric) = 1.9396454736853249032126322780236 absolute error = 1.52137390616634e-17 relative error = 7.8435669136779451781350751047671e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.921 y[1] (analytic) = 1.9393028542685012684319807290311 y[1] (numeric) = 1.9393028542685012531725677168775 absolute error = 1.52594130121536e-17 relative error = 7.8685043847415987931270680279177e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.922 y[1] (analytic) = 1.9389592955489016251715682202849 y[1] (numeric) = 1.9389592955489016098664979216985 absolute error = 1.53050702985864e-17 relative error = 7.8934458983852338778326420636651e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.923 y[1] (analytic) = 1.9386147978700846796148847282204 y[1] (numeric) = 1.9386147978700846642641738529159 absolute error = 1.53507108753045e-17 relative error = 7.9183914680575033785063750514598e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.924 y[1] (analytic) = 1.9382693615765480818707368650469 y[1] (numeric) = 1.9382693615765480664744021683796 absolute error = 1.53963346966673e-17 relative error = 7.9433411072154805221573842531385e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.925 y[1] (analytic) = 1.9379229870137280966893655397411 y[1] (numeric) = 1.93792298701372808124742382269 absolute error = 1.54419417170511e-17 relative error = 7.9682948293247684553801404996870e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.926 y[1] (analytic) = 1.9375756745279992580262099941604 y[1] (numeric) = 1.9375756745279992425386781033116 absolute error = 1.54875318908488e-17 relative error = 7.9932526478593519608330011326806e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.927 y[1] (analytic) = 1.9372274244666740226674027121474 y[1] (numeric) = 1.9372274244666740071342975396771 absolute error = 1.55331051724703e-17 relative error = 8.0182145763018103697187956565281e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.928 y[1] (analytic) = 1.936878237178002422917341576101 y[1] (numeric) = 1.9368782371780024073386800597587 absolute error = 1.55786615163423e-17 relative error = 8.0431806281432209412700842460273e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.929 y[1] (analytic) = 1.9365281130111717183486865834136 y[1] (numeric) = 1.9365281130111717027244857065052 absolute error = 1.56242008769084e-17 relative error = 8.0681508168832170687310105253146e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.93 y[1] (analytic) = 1.9361770523163060466151293727488 y[1] (numeric) = 1.9361770523163060309454061641194 absolute error = 1.56697232086294e-17 relative error = 8.0931251560301498590092014170319e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.931 y[1] (analytic) = 1.9358250554444660733272847473596 y[1] (numeric) = 1.9358250554444660576120562813768 absolute error = 1.57152284659828e-17 relative error = 8.1181036591008366423770607315754e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.932 y[1] (analytic) = 1.9354721227476486409920543195285 y[1] (numeric) = 1.9354721227476486252313377160652 absolute error = 1.57607166034633e-17 relative error = 8.1430863396208258920618684212744e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.933 y[1] (analytic) = 1.9351182545787864170158133367354 y[1] (numeric) = 1.9351182545787864012096257611524 absolute error = 1.58061875755830e-17 relative error = 8.1680732111245074184548503143910e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.934 y[1] (analytic) = 1.9347634512917475407717726863362 y[1] (numeric) = 1.9347634512917475249201313494654 absolute error = 1.58516413368708e-17 relative error = 8.1930642871548092123007277021997e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=3.64 NO POLE x[1] = 1.935 y[1] (analytic) = 1.9344077132413352697318690113633 y[1] (numeric) = 1.9344077132413352538347911694904 absolute error = 1.58970778418729e-17 relative error = 8.2180595812634626184843028218595e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.936 y[1] (analytic) = 1.9340510407832876246635368055256 y[1] (numeric) = 1.9340510407832876087210397603728 absolute error = 1.59424970451528e-17 relative error = 8.2430591070110092917238687156979e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.937 y[1] (analytic) = 1.9336934342742770338917172906085 y[1] (numeric) = 1.9336934342742770179038183893171 absolute error = 1.59878989012914e-17 relative error = 8.2680628779668598894363489725111e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.938 y[1] (analytic) = 1.9333348940719099766264598142336 y[1] (numeric) = 1.9333348940719099605931764493468 absolute error = 1.60332833648868e-17 relative error = 8.2930709077091976724364949677085e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.939 y[1] (analytic) = 1.9329754205347266253564724403485 y[1] (numeric) = 1.932975420534726609277822049794 absolute error = 1.60786503905545e-17 relative error = 8.3180832098250889479887415876654e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.94 y[1] (analytic) = 1.9326150140222004873089793388657 y[1] (numeric) = 1.9326150140222004711849794059381 absolute error = 1.61239999329276e-17 relative error = 8.3430997979105936506084381370994e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.941 y[1] (analytic) = 1.9322536748947380449762435145626 y[1] (numeric) = 1.9322536748947380288069115679062 absolute error = 1.61693319466564e-17 relative error = 8.3681206855705655434905021757915e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.942 y[1] (analytic) = 1.9318914035136783957091143486912 y[1] (numeric) = 1.9318914035136783794944679622823 absolute error = 1.62146463864089e-17 relative error = 8.3931458864189180752370570421538e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.943 y[1] (analytic) = 1.9315282002412928903779603597194 y[1] (numeric) = 1.9315282002412928741180171528486 absolute error = 1.62599432068708e-17 relative error = 8.4181754140786316879185526077695e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.944 y[1] (analytic) = 1.9311640654407847711013485222403 y[1] (numeric) = 1.9311640654407847547961261594951 absolute error = 1.63052223627452e-17 relative error = 8.4432092821816058021941288154370e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.945 y[1] (analytic) = 1.9307989994762888080428324153414 y[1] (numeric) = 1.9307989994762887916923486065884 absolute error = 1.63504838087530e-17 relative error = 8.4682475043688731941032351341904e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.946 y[1] (analytic) = 1.9304330027128709352762124036138 y[1] (numeric) = 1.9304330027128709188804849039812 absolute error = 1.63957274996326e-17 relative error = 8.4932900942904520168946921254563e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.947 y[1] (analytic) = 1.9300660755165278857196319855127 y[1] (numeric) = 1.9300660755165278692786785953721 absolute error = 1.64409533901406e-17 relative error = 8.5183370656057157865206793840408e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.948 y[1] (analytic) = 1.9296982182541868251388753749397 y[1] (numeric) = 1.9296982182541868086527139398889 absolute error = 1.64861614350508e-17 relative error = 8.5433884319828828377692352128053e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.949 y[1] (analytic) = 1.9293294312937049852202323127222 y[1] (numeric) = 1.9293294312937049686888807235668 absolute error = 1.65313515891554e-17 relative error = 8.5684442070996455041344431963637e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.95 y[1] (analytic) = 1.9289597150038692957132970350915 y[1] (numeric) = 1.9289597150038692791367732278273 absolute error = 1.65765238072642e-17 relative error = 8.5935044046427632057857240251719e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.951 y[1] (analytic) = 1.9285890697543960156440692563316 y[1] (numeric) = 1.9285890697543959990223912121268 absolute error = 1.66216780442048e-17 relative error = 8.6185690383081735992909830931023e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.952 y[1] (analytic) = 1.9282174959159303635987259524672 y[1] (numeric) = 1.928217495915930346931911697644 absolute error = 1.66668142548232e-17 relative error = 8.6436381218013113153932441867812e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.953 y[1] (analytic) = 1.9278449938600461470784336621868 y[1] (numeric) = 1.9278449938600461303665012682037 absolute error = 1.67119323939831e-17 relative error = 8.6687116688367527529134143515847e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.954 y[1] (analytic) = 1.9274715639592453909255719501591 y[1] (numeric) = 1.9274715639592453741685395335928 absolute error = 1.67570324165663e-17 relative error = 8.6937896931384311723724856767281e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.955 y[1] (analytic) = 1.9270972065869579648217396064882 y[1] (numeric) = 1.9270972065869579480196253290153 absolute error = 1.68021142774729e-17 relative error = 8.7188722084397482713144357703005e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.956 y[1] (analytic) = 1.9267219221175412098579160842691 y[1] (numeric) = 1.9267219221175411930107381526482 absolute error = 1.68471779316209e-17 relative error = 8.7439592284833744956662062949583e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.957 y[1] (analytic) = 1.9263457109262795641771516050526 y[1] (numeric) = 1.9263457109262795472849282711058 absolute error = 1.68922233339468e-17 relative error = 8.7690507670215682507351937176153e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=3.89 NO POLE x[1] = 1.958 y[1] (analytic) = 1.9259685733893841876901602894971 y[1] (numeric) = 1.925968573389384170752909850092 absolute error = 1.69372504394051e-17 relative error = 8.7941468378159243604277931848654e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.959 y[1] (analytic) = 1.9255905098839925858641915975835 y[1] (numeric) = 1.9255905098839925688819323946147 absolute error = 1.69822592029688e-17 relative error = 8.8192474546376415678514758637211e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.96 y[1] (analytic) = 1.92521152078816823258555628949 y[1] (numeric) = 1.925211520788168215558306709861 absolute error = 1.70272495796290e-17 relative error = 8.8443526312673228852539901134864e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.961 y[1] (analytic) = 1.92483160648090019209618404457 y[1] (numeric) = 1.9248316064809001750239625201745 absolute error = 1.70722215243955e-17 relative error = 8.8694623814952952497128907297788e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.962 y[1] (analytic) = 1.9244507673421027400045908018431 y[1] (numeric) = 1.924450767342102722887415809547 absolute error = 1.71171749922961e-17 relative error = 8.8945767191212540555513080351845e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.963 y[1] (analytic) = 1.9240690037526149833716348110015 y[1] (numeric) = 1.9240690037526149662095248726239 absolute error = 1.71621099383776e-17 relative error = 8.9196956579547908244683217729896e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.964 y[1] (analytic) = 1.9236863160942004798714413081424 y[1] (numeric) = 1.9236863160942004626644149904375 absolute error = 1.72070263177049e-17 relative error = 8.9448192118149338324262144507508e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.965 y[1] (analytic) = 1.923302704749546856027876655272 y[1] (numeric) = 1.9233027047495468387759525699103 absolute error = 1.72519240853617e-17 relative error = 8.9699473945305201066749006799461e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.966 y[1] (analytic) = 1.9229181701022654245269537070733 y[1] (numeric) = 1.9229181701022654072301505106231 absolute error = 1.72968031964502e-17 relative error = 8.9950802199400478402332777820281e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.967 y[1] (analytic) = 1.9225327125368908006055510925018 y[1] (numeric) = 1.9225327125368907832638874864104 absolute error = 1.73416636060914e-17 relative error = 9.0202177018918407336805437051190e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.968 y[1] (analytic) = 1.9221463324388805175168300224568 y[1] (numeric) = 1.9221463324388805001303247530321 absolute error = 1.73865052694247e-17 relative error = 9.0453598542438483742056229904458e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.969 y[1] (analytic) = 1.9217590301946146410727331580806 y[1] (numeric) = 1.921759030194614623641405016472 absolute error = 1.74313281416086e-17 relative error = 9.0705066908640187817978794188080e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.97 y[1] (analytic) = 1.9213708061913953832639509971532 y[1] (numeric) = 1.921370806191395365787818819333 absolute error = 1.74761321778202e-17 relative error = 9.0956582256300468676256282750260e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.971 y[1] (analytic) = 1.9209816608174467149577421585852 y[1] (numeric) = 1.9209816608174466974368248253298 absolute error = 1.75209173332554e-17 relative error = 9.1208144724294870008147207993639e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.972 y[1] (analytic) = 1.9205915944619139776739948671558 y[1] (numeric) = 1.9205915944619139601083113040267 absolute error = 1.75656835631291e-17 relative error = 9.1459754451598657275064177521600e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.973 y[1] (analytic) = 1.9202006075148634944399178624018 y[1] (numeric) = 1.9202006075148634768294870397268 absolute error = 1.76104308226750e-17 relative error = 9.1711411577285863317770038199178e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.974 y[1] (analytic) = 1.9198087003672821797237498769349 y[1] (numeric) = 1.9198087003672821620685908097889 absolute error = 1.76551590671460e-17 relative error = 9.1963116240531458271331421628844e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.975 y[1] (analytic) = 1.9194158734110771484478777504443 y[1] (numeric) = 1.9194158734110771307480094986306 absolute error = 1.76998682518137e-17 relative error = 9.2214868580608833372603626882783e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.976 y[1] (analytic) = 1.9190221270390753240817541662356 y[1] (numeric) = 1.9190221270390753063371958342666 absolute error = 1.77445583319690e-17 relative error = 9.2466668736893013924245230612917e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.977 y[1] (analytic) = 1.9186274616450230458150069173535 y[1] (numeric) = 1.9186274616450230280257776544317 absolute error = 1.77892292629218e-17 relative error = 9.2718516848859185518922795602469e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.978 y[1] (analytic) = 1.9182318776235856748111325291483 y[1] (numeric) = 1.918231877623585656977251529147 absolute error = 1.78338810000013e-17 relative error = 9.2970413056084346489541689914960e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.979 y[1] (analytic) = 1.9178353753703471995421679845577 y[1] (numeric) = 1.9178353753703471816636544860022 absolute error = 1.78785134985555e-17 relative error = 9.3222357498244791196327899876995e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.98 y[1] (analytic) = 1.917437955281809840204735217402 y[1] (numeric) = 1.9174379552818098222816085034499 absolute error = 1.79231267139521e-17 relative error = 9.3474350315120891760200053241944e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=4.14 NO POLE x[1] = 1.981 y[1] (analytic) = 1.9170396177553936522178539576119 y[1] (numeric) = 1.9170396177553936342501333560341 absolute error = 1.79677206015778e-17 relative error = 9.3726391646593539701938641433956e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.982 y[1] (analytic) = 1.9166403631894361288029194305462 y[1] (numeric) = 1.9166403631894361107906243137074 absolute error = 1.80122951168388e-17 relative error = 9.3978481632646844268057979155873e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.983 y[1] (analytic) = 1.9162401919831918026462423303861 y[1] (numeric) = 1.9162401919831917845893921152256 absolute error = 1.80568502151605e-17 relative error = 9.4230620413366659446768817658177e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.984 y[1] (analytic) = 1.915839104536831846644549405035 y[1] (numeric) = 1.9158391045368318285431635530471 absolute error = 1.81013858519879e-17 relative error = 9.4482808128942763053643680464320e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.985 y[1] (analytic) = 1.9154371012514436737338439069878 y[1] (numeric) = 1.9154371012514436555879419242025 absolute error = 1.81459019827853e-17 relative error = 9.4735044919667384198828937419768e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.986 y[1] (analytic) = 1.9150341825290305358020260812782 y[1] (numeric) = 1.9150341825290305176116275182416 absolute error = 1.81903985630366e-17 relative error = 9.4987330925936862168159074477216e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.987 y[1] (analytic) = 1.9146303487725111216856747778477 y[1] (numeric) = 1.9146303487725111034507992296025 absolute error = 1.82348755482452e-17 relative error = 9.5239666288251218384371762361612e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.988 y[1] (analytic) = 1.9142256003857191542513921915236 y[1] (numeric) = 1.9142256003857191359720592975894 absolute error = 1.82793328939342e-17 relative error = 9.5492051147215295205416451888703e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.989 y[1] (analytic) = 1.9138199377734029865621146482255 y[1] (numeric) = 1.9138199377734029682383440925794 absolute error = 1.83237705556461e-17 relative error = 9.5744485643537283756718830374049e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.99 y[1] (analytic) = 1.9134133613412251971287932710576 y[1] (numeric) = 1.9134133613412251787606047821142 absolute error = 1.83681884889434e-17 relative error = 9.5996969918031953690299703610344e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.991 y[1] (analytic) = 1.9130058714957621842478492745711 y[1] (numeric) = 1.913005871495762165835262625163 absolute error = 1.84125866494081e-17 relative error = 9.6249504111618137113836302909360e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.992 y[1] (analytic) = 1.9125974686445037594248095497085 y[1] (numeric) = 1.9125974686445037409678445570665 absolute error = 1.84569649926420e-17 relative error = 9.6502088365320392265732014051260e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.993 y[1] (analytic) = 1.9121881531958527398845291157598 y[1] (numeric) = 1.9121881531958527213832056414929 absolute error = 1.85013234742669e-17 relative error = 9.6754722820270146521968289624658e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.994 y[1] (analytic) = 1.9117779255591245401684079290744 y[1] (numeric) = 1.9117779255591245216227458791503 absolute error = 1.85456620499241e-17 relative error = 9.7007407617703179527414198627920e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.995 y[1] (analytic) = 1.9113667861445467628190104512782 y[1] (numeric) = 1.9113667861445467442290297760029 absolute error = 1.85899806752753e-17 relative error = 9.7260142898964427852436442449348e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.996 y[1] (analytic) = 1.9109547353632587881524972923409 y[1] (numeric) = 1.9109547353632587695182179863393 absolute error = 1.86342793060016e-17 relative error = 9.7512928805502853343573461541360e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.997 y[1] (analytic) = 1.9105417736273113631192791560302 y[1] (numeric) = 1.9105417736273113444407212582255 absolute error = 1.86785578978047e-17 relative error = 9.7765765478877820061694819059925e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.998 y[1] (analytic) = 1.9101279013496661892533042270611 y[1] (numeric) = 1.9101279013496661705304878206555 absolute error = 1.87228164064056e-17 relative error = 9.8018653060752391527160351463259e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.999 y[1] (analytic) = 1.9097131189441955097103910506228 y[1] (numeric) = 1.9097131189441954909433362630767 absolute error = 1.87670547875461e-17 relative error = 9.8271591692901281307253210029136e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2 y[1] (analytic) = 1.9092974268256816953960198659117 y[1] (numeric) = 1.909297426825681676584746868924 absolute error = 1.88112729969877e-17 relative error = 9.8524581517205196554164657468563e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.001 y[1] (analytic) = 1.9088808254098168301829962658482 y[1] (numeric) = 1.9088808254098168113275252753359 absolute error = 1.88554709905123e-17 relative error = 9.8777622675654603938960503697145e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.002 y[1] (analytic) = 1.9084633151132022952194019652766 y[1] (numeric) = 1.9084633151132022763197532413547 absolute error = 1.88996487239219e-17 relative error = 9.9030715310348260862247386745968e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.003 y[1] (analytic) = 1.908044896353348352327248369664 y[1] (numeric) = 1.9080448963533483333834422166254 absolute error = 1.89438061530386e-17 relative error = 9.9283859563493317198417597312565e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=4.38 NO POLE x[1] = 2.004 y[1] (analytic) = 1.9076255695486737264922495456098 y[1] (numeric) = 1.9076255695486737075043063119047 absolute error = 1.89879432337051e-17 relative error = 9.9537055577408038397013842799379e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.005 y[1] (analytic) = 1.9072053351185051874451321033573 y[1] (numeric) = 1.907205335118505168413072181573 absolute error = 1.90320599217843e-17 relative error = 9.9790303494519813399733022636852e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.006 y[1] (analytic) = 1.9067841934830771303349004099636 y[1] (numeric) = 1.906784193483077111258744236804 absolute error = 1.90761561731596e-17 relative error = 1.0004360345736683119936714831730e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.007 y[1] (analytic) = 1.9063621450635311554944764598267 y[1] (numeric) = 1.9063621450635311363742445160921 absolute error = 1.91202319437346e-17 relative error = 1.0029695560859661243305250679026e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.008 y[1] (analytic) = 1.9059391902819156472991346368961 y[1] (numeric) = 1.9059391902819156281348474474625 absolute error = 1.91642871894336e-17 relative error = 1.0055036009096873659898534029795e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.009 y[1] (analytic) = 1.9055153295611853521181525100957 y[1] (numeric) = 1.9055153295611853329098306438942 absolute error = 1.92083218662015e-17 relative error = 1.0080381704735442431879097347767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.01 y[1] (analytic) = 1.9050905633252009553600997102737 y[1] (numeric) = 1.9050905633252009361077637802703 absolute error = 1.92523359300034e-17 relative error = 1.0105732662073454449041826957654e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.011 y[1] (analytic) = 1.9046648919987286576121878433562 y[1] (numeric) = 1.9046648919987286383158585065308 absolute error = 1.92963293368254e-17 relative error = 1.0131088895420391926217875068385e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.012 y[1] (analytic) = 1.9042383160074397498741053003172 y[1] (numeric) = 1.9042383160074397305338032576432 absolute error = 1.93403020426740e-17 relative error = 1.0156450419096828292826541174936e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.013 y[1] (analytic) = 1.9038108357779101878867617300969 y[1] (numeric) = 1.9038108357779101685025077265204 absolute error = 1.93842540035765e-17 relative error = 1.0181817247434648953460463462731e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.014 y[1] (analytic) = 1.9033824517376201655563678466871 y[1] (numeric) = 1.9033824517376201461281826711061 absolute error = 1.94281851755810e-17 relative error = 1.0207189394777062210478130151570e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.015 y[1] (analytic) = 1.9029531643149536874742771462688 y[1] (numeric) = 1.9029531643149536680021816315125 absolute error = 1.94720955147563e-17 relative error = 1.0232566875478557668926887869544e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.016 y[1] (analytic) = 1.9025229739391981405330170145245 y[1] (numeric) = 1.9025229739391981210170320373325 absolute error = 1.95159849771920e-17 relative error = 1.0257949703904969725908923345417e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.017 y[1] (analytic) = 1.9020918810405438646389376080588 y[1] (numeric) = 1.90209188104054384507908408906 absolute error = 1.95598535189988e-17 relative error = 1.0283337894433646310470542705521e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.018 y[1] (analytic) = 1.9016598860500837225219077972415 y[1] (numeric) = 1.9016598860500837029182067009335 absolute error = 1.96037010963080e-17 relative error = 1.0308731461453197185404434106443e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.019 y[1] (analytic) = 1.9012269893998126686424883607435 y[1] (numeric) = 1.9012269893998126489949606954713 absolute error = 1.96475276652722e-17 relative error = 1.0334130419363873094552737028502e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.02 y[1] (analytic) = 1.9007931915226273171970135245537 y[1] (numeric) = 1.900793191522627297505680342489 absolute error = 1.96913331820647e-17 relative error = 1.0359534782577261520278930232235e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.021 y[1] (analytic) = 1.9003584928523255092210128403617 y[1] (numeric) = 1.9003584928523254894858952374817 absolute error = 1.97351176028800e-17 relative error = 1.0384944565516560880011110716573e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.022 y[1] (analytic) = 1.8999228938236058787914062998471 y[1] (numeric) = 1.8999228938236058590125254159134 absolute error = 1.97788808839337e-17 relative error = 1.0410359782616539313789610558426e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.023 y[1] (analytic) = 1.8994863948720674183279064826446 y[1] (numeric) = 1.899486394872067398505283501182 absolute error = 1.98226229814626e-17 relative error = 1.0435780448323598724442138210676e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.024 y[1] (analytic) = 1.899048996434209042994062436546 y[1] (numeric) = 1.8990489964342090231277185848215 absolute error = 1.98663438517245e-17 relative error = 1.0461206577095680949769498592349e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.025 y[1] (analytic) = 1.8986106989474291541983808888597 y[1] (numeric) = 1.8986106989474291342883374378612 absolute error = 1.99100434509985e-17 relative error = 1.0486638183402437172780843302654e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.026 y[1] (analytic) = 1.8981715028500252021959612877695 y[1] (numeric) = 1.8981715028500251822422395521844 absolute error = 1.99537217355851e-17 relative error = 1.0512075281725292219223451266159e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=4.63 NO POLE x[1] = 2.027 y[1] (analytic) = 1.8977314085811932477910820720215 y[1] (numeric) = 1.8977314085811932277937034102155 absolute error = 1.99973786618060e-17 relative error = 1.0537517886557350878736741710399e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.028 y[1] (analytic) = 1.8972904165810275231411764663162 y[1] (numeric) = 1.8972904165810275031001622803119 absolute error = 2.00410141860043e-17 relative error = 1.0562966012403514940218174918743e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.029 y[1] (analytic) = 1.896848527290519991662636998393 y[1] (numeric) = 1.8968485272905199715780087338487 absolute error = 2.00846282645443e-17 relative error = 1.0588419673780389531679679379544e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.03 y[1] (analytic) = 1.8964057411515599070388888319676 y[1] (numeric) = 1.8964057411515598869106679781553 absolute error = 2.01282208538123e-17 relative error = 1.0613878885216716659810264408866e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.031 y[1] (analytic) = 1.895962058606933371331172907409 y[1] (numeric) = 1.8959620586069333511593809971937 absolute error = 2.01717919102153e-17 relative error = 1.0639343661252701757877136413673e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.032 y[1] (analytic) = 1.8955174801003228921924807793401 y[1] (numeric) = 1.8955174801003228719771393891576 absolute error = 2.02153413901825e-17 relative error = 1.0664814016440816474652478557475e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.033 y[1] (analytic) = 1.8950720060763069391850839371867 y[1] (numeric) = 1.8950720060763069189262146870223 absolute error = 2.02588692501644e-17 relative error = 1.0690289965345336167528971647253e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.034 y[1] (analytic) = 1.8946256369803594992021012911108 y[1] (numeric) = 1.8946256369803594788997258444777 absolute error = 2.03023754466331e-17 relative error = 1.0715771522542510132379569628321e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.035 y[1] (analytic) = 1.8941783732588496309935494017223 y[1] (numeric) = 1.89417837325884961064768946564 absolute error = 2.03458599360823e-17 relative error = 1.0741258702620573711101289881933e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.036 y[1] (analytic) = 1.8937302153590410187973209274834 y[1] (numeric) = 1.8937302153590409984079982524557 absolute error = 2.03893226750277e-17 relative error = 1.0766751520179971657186120951732e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.037 y[1] (analytic) = 1.893281163729091525075537658788 y[1] (numeric) = 1.8932811637290915046427740387815 absolute error = 2.04327636200065e-17 relative error = 1.0792249989833106471316074996545e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.038 y[1] (analytic) = 1.892831218818052742356725402327 y[1] (numeric) = 1.8928312188180527218805426747493 absolute error = 2.04761827275777e-17 relative error = 1.0817754126204509044037554346178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.039 y[1] (analytic) = 1.8923803810758695441842588735278 y[1] (numeric) = 1.8923803810758695236646789192056 absolute error = 2.05195799543222e-17 relative error = 1.0843263943930903872071136820798e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.04 y[1] (analytic) = 1.8919286509533796351715256485842 y[1] (numeric) = 1.8919286509533796146085703917413 absolute error = 2.05629552568429e-17 relative error = 1.0868779457661274385741302573273e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.041 y[1] (analytic) = 1.8914760289023131001642591208761 y[1] (numeric) = 1.8914760289023130795579505291117 absolute error = 2.06063085917644e-17 relative error = 1.0894300682056716913068803182184e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.042 y[1] (analytic) = 1.891022515375291952510491299409 y[1] (numeric) = 1.8910225153752919318608513836756 absolute error = 2.06496399157334e-17 relative error = 1.0919827631790664621984824554859e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.043 y[1] (analytic) = 1.8905681108258296814385771792814 y[1] (numeric) = 1.8905681108258296607456279938629 absolute error = 2.06929491854185e-17 relative error = 1.0945360321548794437469336350821e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.044 y[1] (analytic) = 1.8901128157083307985437433061198 y[1] (numeric) = 1.8901128157083307778075069486092 absolute error = 2.07362363575106e-17 relative error = 1.0970898766029251283773731982594e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.045 y[1] (analytic) = 1.889656630478090383383614047893 y[1] (numeric) = 1.8896566304780903626041126591706 absolute error = 2.07795013887224e-17 relative error = 1.0996442979942396391805472292151e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.046 y[1] (analytic) = 1.8891995555912936281831699785436 y[1] (numeric) = 1.8891995555912936073604257427547 absolute error = 2.08227442357889e-17 relative error = 1.1021992978011084584562271588344e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.047 y[1] (analytic) = 1.8887415915050153816495936684384 y[1] (numeric) = 1.8887415915050153607836288129712 absolute error = 2.08659648554672e-17 relative error = 1.1047548774970571365532944364575e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.048 y[1] (analytic) = 1.8882827386772196918974590667558 y[1] (numeric) = 1.888282738677219670988295862219 absolute error = 2.09091632045368e-17 relative error = 1.1073110385568684680915947232685e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.049 y[1] (analytic) = 1.8878229975667593484847215505806 y[1] (numeric) = 1.8878229975667593275323823107813 absolute error = 2.09523392397993e-17 relative error = 1.1098677824565679123945606322126e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=4.88 NO POLE x[1] = 2.05 y[1] (analytic) = 1.8873623686333754235599666046803 y[1] (numeric) = 1.8873623686333754025644736866017 absolute error = 2.09954929180786e-17 relative error = 1.1124251106734354864219005513940e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.051 y[1] (analytic) = 1.8869008523376968121213759846744 y[1] (numeric) = 1.8869008523376967910827517884532 absolute error = 2.10386241962212e-17 relative error = 1.1149830246860229765766625332653e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.052 y[1] (analytic) = 1.886438449141239771387871104592 y[1] (numeric) = 1.8864384491412397503061380734964 absolute error = 2.10817330310956e-17 relative error = 1.1175415259741234686607907360637e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.053 y[1] (analytic) = 1.8859751595064074592828942776381 y[1] (numeric) = 1.8859751595064074381580748980449 absolute error = 2.11248193795932e-17 relative error = 1.1201006160188203692563611470011e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.054 y[1] (analytic) = 1.8855109838964894720312893263458 y[1] (numeric) = 1.8855109838964894508634061277182 absolute error = 2.11678831986276e-17 relative error = 1.1226602963024516435274056896873e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.055 y[1] (analytic) = 1.8850459227756613808697439651976 y[1] (numeric) = 1.8850459227756613596588195200628 absolute error = 2.12109244451348e-17 relative error = 1.1252205683086217462466128671881e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.056 y[1] (analytic) = 1.8845799766089842678712572452345 y[1] (numeric) = 1.8845799766089842466173141691608 absolute error = 2.12539430760737e-17 relative error = 1.1277814335222294908792282001270e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.057 y[1] (analytic) = 1.8841131458624042608840962361454 y[1] (numeric) = 1.8841131458624042395871571877197 absolute error = 2.12969390484257e-17 relative error = 1.1303428934294481940182981794305e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.058 y[1] (analytic) = 1.8836454310027520675857070068426 y[1] (numeric) = 1.8836454310027520462457946876479 absolute error = 2.13399123191947e-17 relative error = 1.1329049495177270275823715947066e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.059 y[1] (analytic) = 1.883176832497742508652045850574 y[1] (numeric) = 1.8831768324977424872691830051664 absolute error = 2.13828628454076e-17 relative error = 1.1354676032758189256718552987195e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.06 y[1] (analytic) = 1.8827073508159740500427975851999 y[1] (numeric) = 1.8827073508159740286170070010861 absolute error = 2.14257905841138e-17 relative error = 1.1380308561937554199264738796314e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.061 y[1] (analytic) = 1.8822369864269283344029486433794 y[1] (numeric) = 1.8822369864269283129342531509939 absolute error = 2.14686954923855e-17 relative error = 1.1405947097628639416886508208066e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.062 y[1] (analytic) = 1.881765739800969711581183551053 y[1] (numeric) = 1.8817657398009696900696060237351 absolute error = 2.15115775273179e-17 relative error = 1.1431591654757798377247839470139e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.063 y[1] (analytic) = 1.8812936114093447682655742757855 y[1] (numeric) = 1.8812936114093447467111376297566 absolute error = 2.15544366460289e-17 relative error = 1.1457242248264318283979807454300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.064 y[1] (analytic) = 1.880820601724181856737032809242 y[1] (numeric) = 1.8808206017241818351397600035825 absolute error = 2.15972728056595e-17 relative error = 1.1482898893100646635713213827737e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.065 y[1] (analytic) = 1.8803467112184906227409982303038 y[1] (numeric) = 1.8803467112184906011009122669303 absolute error = 2.16400859633735e-17 relative error = 1.1508561604232245873425071225910e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.066 y[1] (analytic) = 1.8798719403661615324778303770984 y[1] (numeric) = 1.8798719403661615107949543007408 absolute error = 2.16828760763576e-17 relative error = 1.1534230396637660606825580301679e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.067 y[1] (analytic) = 1.8793962896419653987123831375107 y[1] (numeric) = 1.8793962896419653769867400356889 absolute error = 2.17256431018218e-17 relative error = 1.1559905285308744586139483769303e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.068 y[1] (analytic) = 1.8789197595215529060032312485622 y[1] (numeric) = 1.8789197595215528842348442515631 absolute error = 2.17683869969991e-17 relative error = 1.1585586285250515482591405758392e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.069 y[1] (analytic) = 1.8784423504814541350520253753917 y[1] (numeric) = 1.8784423504814541132409176562462 absolute error = 2.18111077191455e-17 relative error = 1.1611273411481169173396646305821e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.07 y[1] (analytic) = 1.8779640629990780861734511204438 y[1] (numeric) = 1.8779640629990780643196458949034 absolute error = 2.18538052255404e-17 relative error = 1.1636966679032307063098730064085e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.071 y[1] (analytic) = 1.877484897552712201886268492865 y[1] (numeric) = 1.8774848975527121799897890193787 absolute error = 2.18964794734863e-17 relative error = 1.1662666102948790931538890383997e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.072 y[1] (analytic) = 1.8770048546215218886259092470293 y[1] (numeric) = 1.8770048546215218666867788267204 absolute error = 2.19391304203089e-17 relative error = 1.1688371698288810683660550664693e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=5.13 NO POLE x[1] = 2.073 y[1] (analytic) = 1.8765239346855500375791103775557 y[1] (numeric) = 1.8765239346855500155973523541984 absolute error = 2.19817580233573e-17 relative error = 1.1714083480124005511349983106697e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.074 y[1] (analytic) = 1.8760421382257165446410629361442 y[1] (numeric) = 1.8760421382257165226167006961404 absolute error = 2.20243622400038e-17 relative error = 1.1739801463539372045212451053196e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.075 y[1] (analytic) = 1.8755594657238178294955562130413 y[1] (numeric) = 1.875559465723817807428613185397 absolute error = 2.20669430276443e-17 relative error = 1.1765525663633492287739616945864e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.076 y[1] (analytic) = 1.8750759176625263538185982029511 y[1] (numeric) = 1.8750759176625263317090978592531 absolute error = 2.21095003436980e-17 relative error = 1.1791256095518388598713404150095e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.077 y[1] (analytic) = 1.8745914945253901386059941517309 y[1] (numeric) = 1.8745914945253901164539600061234 absolute error = 2.21520341456075e-17 relative error = 1.1816992774319591854711679528759e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.078 y[1] (analytic) = 1.8741061967968322806253658562534 y[1] (numeric) = 1.8741061967968322584308214654143 absolute error = 2.21945443908391e-17 relative error = 1.1842735715176316449909748124174e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.079 y[1] (analytic) = 1.8736200249621504679930952653746 y[1] (numeric) = 1.8736200249621504457560642284921 absolute error = 2.22370310368825e-17 relative error = 1.1868484933241315351736905015198e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.08 y[1] (analytic) = 1.8731329795075164948766768050246 y[1] (numeric) = 1.8731329795075164725971827637735 absolute error = 2.22794940412511e-17 relative error = 1.1894240443681055268421805767368e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.081 y[1] (analytic) = 1.8726450609199757753229637250282 y[1] (numeric) = 1.8726450609199757530010303635463 absolute error = 2.23219333614819e-17 relative error = 1.1920002261675678506563030441283e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.082 y[1] (analytic) = 1.8721562696874468562127946393678 y[1] (numeric) = 1.8721562696874468338484456842323 absolute error = 2.23643489551355e-17 relative error = 1.1945770402419018202062915100402e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.083 y[1] (analytic) = 1.8716666062987209293424873052228 y[1] (numeric) = 1.8716666062987209069357465254263 absolute error = 2.24067407797965e-17 relative error = 1.1971544881118827306494609329972e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.084 y[1] (analytic) = 1.8711760712434613426326875592491 y[1] (numeric) = 1.8711760712434613201835787661763 absolute error = 2.24491087930728e-17 relative error = 1.1997325712996420086173828588765e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.085 y[1] (analytic) = 1.8706846650122031104650622022118 y[1] (numeric) = 1.8706846650122030879736092496152 absolute error = 2.24914529525966e-17 relative error = 1.2023112913287221833822666313177e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.086 y[1] (analytic) = 1.8701923880963524231473254952341 y[1] (numeric) = 1.8701923880963524006135522792104 absolute error = 2.25337732160237e-17 relative error = 1.2048906497240410467714582806433e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.087 y[1] (analytic) = 1.8696992409881861555070898025979 y[1] (numeric) = 1.8696992409881861329310202615641 absolute error = 2.25760695410338e-17 relative error = 1.2074706480119092429290696820724e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.088 y[1] (analytic) = 1.869205224180851374615031787203 y[1] (numeric) = 1.8692052241808513519966899018725 absolute error = 2.26183418853305e-17 relative error = 1.2100512877200318381204903526732e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.089 y[1] (analytic) = 1.868710338168364846637866435478 y[1] (numeric) = 1.8687103381683648239772762288363 absolute error = 2.26605902066417e-17 relative error = 1.2126325703775313000169773586393e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.09 y[1] (analytic) = 1.8682145834456125428216220587275 y[1] (numeric) = 1.8682145834456125201188075960086 absolute error = 2.27028144627189e-17 relative error = 1.2152144975149116356558707506280e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.091 y[1] (analytic) = 1.8677179605083491446057102876003 y[1] (numeric) = 1.8677179605083491218606956762624 absolute error = 2.27450146113379e-17 relative error = 1.2177970706640974319401877706578e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.092 y[1] (analytic) = 1.8672204698531975478682859455666 y[1] (numeric) = 1.867220469853197525081095335268 absolute error = 2.27871906102986e-17 relative error = 1.2203802913584247602558857989536e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.093 y[1] (analytic) = 1.8667221119776483663033925560026 y[1] (numeric) = 1.8667221119776483434740501385777 absolute error = 2.28293424174249e-17 relative error = 1.2229641611326374254432764304463e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.094 y[1] (analytic) = 1.8662228873800594339303901056974 y[1] (numeric) = 1.8662228873800594110589201151324 absolute error = 2.28714699905650e-17 relative error = 1.2255486815229046442651782337980e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.095 y[1] (analytic) = 1.8657227965596553067361625553108 y[1] (numeric) = 1.8657227965596552838225892677193 absolute error = 2.29135732875915e-17 relative error = 1.2281338540668280343985054978584e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=83.9MB, alloc=4.3MB, time=5.37 x[1] = 2.096 y[1] (analytic) = 1.8652218400165267634506034545341 y[1] (numeric) = 1.8652218400165267404949511881332 absolute error = 2.29556522664009e-17 relative error = 1.2307196803034164488282118381973e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.097 y[1] (analytic) = 1.8647200182516303054558788864271 y[1] (numeric) = 1.8647200182516302824581720015128 absolute error = 2.29977068849143e-17 relative error = 1.2333061617731251243490490294635e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.098 y[1] (analytic) = 1.8642173317667876558299678316255 y[1] (numeric) = 1.8642173317667876327902307305484 absolute error = 2.30397371010771e-17 relative error = 1.2358933000178412533079043480245e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.099 y[1] (analytic) = 1.8637137810646852575249809088376 y[1] (numeric) = 1.8637137810646852344432380359785 absolute error = 2.30817428728591e-17 relative error = 1.2384810965808909964420359206138e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.1 y[1] (analytic) = 1.863209366648873770680759313269 y[1] (numeric) = 1.8632093666488737475570351550145 absolute error = 2.31237241582545e-17 relative error = 1.2410695530070411418612612969826e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.101 y[1] (analytic) = 1.8627040890237675690742566393353 y[1] (numeric) = 1.8627040890237675459085757240532 absolute error = 2.31656809152821e-17 relative error = 1.2436586708425115056672602849903e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.102 y[1] (analytic) = 1.8621979486946442357052071382378 y[1] (numeric) = 1.8621979486946442124975940362528 absolute error = 2.32076131019850e-17 relative error = 1.2462484516349605046472938422996e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.103 y[1] (analytic) = 1.8616909461676440575185848246937 y[1] (numeric) = 1.8616909461676440342690641482626 absolute error = 2.32495206764311e-17 relative error = 1.2488388969335136789836609148731e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.104 y[1] (analytic) = 1.8611830819497695192643587103173 y[1] (numeric) = 1.8611830819497694959729551136046 absolute error = 2.32914035967127e-17 relative error = 1.2514300082887439070990605373963e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.105 y[1] (analytic) = 1.8606743565488847964950503038573 y[1] (numeric) = 1.8606743565488847731617884829102 absolute error = 2.33332618209471e-17 relative error = 1.2540217872527053339490639841463e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.106 y[1] (analytic) = 1.8601647704737152477016003806879 y[1] (numeric) = 1.8601647704737152243265050734118 absolute error = 2.33750953072761e-17 relative error = 1.2566142353789082223195331921881e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.107 y[1] (analytic) = 1.8596543242338469055880528856467 y[1] (numeric) = 1.8596543242338468821711488717807 absolute error = 2.34169040138660e-17 relative error = 1.2592073542223206514166076358773e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.108 y[1] (analytic) = 1.8591430183397259674855646944923 y[1] (numeric) = 1.8591430183397259440268767955841 absolute error = 2.34586878989082e-17 relative error = 1.2618011453394024929851727293105e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.109 y[1] (analytic) = 1.8586308533026582849062508199289 y[1] (numeric) = 1.85863085330265826140580389931 absolute error = 2.35004469206189e-17 relative error = 1.2643956102880910226379493265167e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.11 y[1] (analytic) = 1.8581178296348088522373755083107 y[1] (numeric) = 1.8581178296348088286951944710718 absolute error = 2.35421810372389e-17 relative error = 1.2669907506277918911237144029608e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.111 y[1] (analytic) = 1.8576039478492012945764005327927 y[1] (numeric) = 1.8576039478492012709925103257585 absolute error = 2.35838902070342e-17 relative error = 1.2695865679194131486984965435312e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.112 y[1] (analytic) = 1.8570892084597173547074028478361 y[1] (numeric) = 1.8570892084597173310818284595405 absolute error = 2.36255743882956e-17 relative error = 1.2721830637253454801405667696313e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.113 y[1] (analytic) = 1.8565736119810963792193746286086 y[1] (numeric) = 1.8565736119810963555521410892696 absolute error = 2.36672335393390e-17 relative error = 1.2747802396094801126733952299841e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.114 y[1] (analytic) = 1.8560571589289348037669195769361 y[1] (numeric) = 1.856057158928934780058051958431 absolute error = 2.37088676185051e-17 relative error = 1.2773780971371944290089040238878e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.115 y[1] (analytic) = 1.8555398498196856374738602330676 y[1] (numeric) = 1.8555398498196856137233836489076 absolute error = 2.37504765841600e-17 relative error = 1.2799766378753860616396095632971e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.116 y[1] (analytic) = 1.8550216851706579464802718896016 y[1] (numeric) = 1.8550216851706579226882114949069 absolute error = 2.37920603946947e-17 relative error = 1.2825758633924477475573462862353e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.117 y[1] (analytic) = 1.8545026655000163366334595604984 y[1] (numeric) = 1.8545026655000163127998405519731 absolute error = 2.38336190085253e-17 relative error = 1.2851757752582798887082152317249e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.118 y[1] (analytic) = 1.8539827913267804353233953141574 y[1] (numeric) = 1.8539827913267804114482429300642 absolute error = 2.38751523840932e-17 relative error = 1.2877763750443031353702778958426e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.119 memory used=87.7MB, alloc=4.3MB, time=5.61 y[1] (analytic) = 1.8534620631708243724631341350795 y[1] (numeric) = 1.8534620631708243485464736552143 absolute error = 2.39166604798652e-17 relative error = 1.2903776643234655972839834925653e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.12 y[1] (analytic) = 1.8529404815528762606147273336542 y[1] (numeric) = 1.8529404815528762366565840793212 absolute error = 2.39581432543330e-17 relative error = 1.2929796446702176879062804510488e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.121 y[1] (analytic) = 1.8524180469945176742611533781168 y[1] (numeric) = 1.8524180469945176502615527121029 absolute error = 2.39996006660139e-17 relative error = 1.2955823176605517082218887510757e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.122 y[1] (analytic) = 1.8518947600181831282247868766995 y[1] (numeric) = 1.851894760018183104183754203249 absolute error = 2.40410326734505e-17 relative error = 1.2981856848719875006463055612204e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.123 y[1] (analytic) = 1.8513706211471595552329272914649 y[1] (numeric) = 1.8513706211471595311504880562541 absolute error = 2.40824392352108e-17 relative error = 1.3007897478835796861496706168372e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.124 y[1] (analytic) = 1.8508456309055857826309098182495 y[1] (numeric) = 1.8508456309055857585070895083612 absolute error = 2.41238203098883e-17 relative error = 1.3033945082759249155458290010164e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.125 y[1] (analytic) = 1.8503197898184520082433217195624 y[1] (numeric) = 1.8503197898184519840781458634607 absolute error = 2.41651758561017e-17 relative error = 1.3059999676311475171314692961904e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.126 y[1] (analytic) = 1.8497930984115992753838482491804 y[1] (numeric) = 1.8497930984115992511773424166847 absolute error = 2.42065058324957e-17 relative error = 1.3086061275329445878084773230798e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.127 y[1] (analytic) = 1.8492655572117189470142731585474 y[1] (numeric) = 1.8492655572117189227664629608071 absolute error = 2.42478101977403e-17 relative error = 1.3112129895665500498680043745224e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.128 y[1] (analytic) = 1.8487371667463521790531596259367 y[1] (numeric) = 1.8487371667463521547640707154057 absolute error = 2.42890889105310e-17 relative error = 1.3138205553187473300642351457911e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.129 y[1] (analytic) = 1.8482079275438893928347382996491 y[1] (numeric) = 1.8482079275438893685043963700599 absolute error = 2.43303419295892e-17 relative error = 1.3164288263778928835376544282032e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.13 y[1] (analytic) = 1.8476778401335697467185299963159 y[1] (numeric) = 1.8476778401335697223469607826541 absolute error = 2.43715692136618e-17 relative error = 1.3190378043338964624714855711149e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.131 y[1] (analytic) = 1.84714690504548060685023144464 y[1] (numeric) = 1.8471469050454805824374607231183 absolute error = 2.44127707215217e-17 relative error = 1.3216474907782500764752760796322e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.132 y[1] (analytic) = 1.8466151228105570170743933136445 y[1] (numeric) = 1.8466151228105569926204469016773 absolute error = 2.44539464119672e-17 relative error = 1.3242578873039974363589305283794e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.133 y[1] (analytic) = 1.846082493960581167999420612708 y[1] (numeric) = 1.8460824939605811435043243688853 absolute error = 2.44950962438227e-17 relative error = 1.3268689955057737663702798874819e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.134 y[1] (analytic) = 1.8455490190281818652154263983403 y[1] (numeric) = 1.8455490190281818406792062224019 absolute error = 2.45362201759384e-17 relative error = 1.3294808169797915027958303957006e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.135 y[1] (analytic) = 1.8450146985468339966654705698019 y[1] (numeric) = 1.8450146985468339720881524026115 absolute error = 2.45773181671904e-17 relative error = 1.3320933533238476497331467788315e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.136 y[1] (analytic) = 1.844479533050857999170716382283 y[1] (numeric) = 1.8444795330508579745523262058024 absolute error = 2.46183901764806e-17 relative error = 1.3347066061373203063521976672364e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.137 y[1] (analytic) = 1.8439435230754193241100381524421 y[1] (numeric) = 1.8439435230754192994506019897052 absolute error = 2.46594361627369e-17 relative error = 1.3373205770211814594511397489958e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.138 y[1] (analytic) = 1.8434066691565279022546144766512 y[1] (numeric) = 1.8434066691565278775541583917377 absolute error = 2.47004560849135e-17 relative error = 1.3399352675780152249243260921596e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.139 y[1] (analytic) = 1.8428689718310376077580421273097 y[1] (numeric) = 1.8428689718310375830165922253192 absolute error = 2.47414499019905e-17 relative error = 1.3425506794119981387909096911091e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.14 y[1] (analytic) = 1.8423304316366457213025066370689 y[1] (numeric) = 1.8423304316366456965200890640949 absolute error = 2.47824175729740e-17 relative error = 1.3451668141289065551708880229655e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.141 y[1] (analytic) = 1.8417910491118923924015464247522 y[1] (numeric) = 1.8417910491118923675781873678558 absolute error = 2.48233590568964e-17 relative error = 1.3477836733361349180661999886912e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.142 y[1] (analytic) = 1.8412508247961601008599481601604 y[1] (numeric) = 1.8412508247961600759956738473443 absolute error = 2.48642743128161e-17 relative error = 1.3504012586426814805963892784073e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=5.86 NO POLE x[1] = 2.143 y[1] (analytic) = 1.840709759229673117391311907824 y[1] (numeric) = 1.840709759229673092486148608006 absolute error = 2.49051632998180e-17 relative error = 1.3530195716591774624722784341085e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.144 y[1] (analytic) = 1.8401678529534969633938254320903 y[1] (numeric) = 1.8401678529534969384477994550774 absolute error = 2.49460259770129e-17 relative error = 1.3556386139978564836343144589556e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.145 y[1] (analytic) = 1.8396251065095378698847878877284 y[1] (numeric) = 1.83962510650953784489792558419 absolute error = 2.49868623035384e-17 relative error = 1.3582583872726054841067000039552e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.146 y[1] (analytic) = 1.8390815204405422355944239614801 y[1] (numeric) = 1.8390815204405422105667517229222 absolute error = 2.50276722385579e-17 relative error = 1.3608788930989124234476240195022e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.147 y[1] (analytic) = 1.8385370952900960842195303707013 y[1] (numeric) = 1.8385370952900960591510746294396 absolute error = 2.50684557412617e-17 relative error = 1.3635001330939281105756764517580e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.148 y[1] (analytic) = 1.8379918316026245208374974653982 y[1] (numeric) = 1.837991831602624495728284694532 absolute error = 2.51092127708662e-17 relative error = 1.3661221088764247716250230597869e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.149 y[1] (analytic) = 1.8374457299233911874812495195948 y[1] (numeric) = 1.8374457299233911623313062329804 absolute error = 2.51499432866144e-17 relative error = 1.3687448220668252963638430314703e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.15 y[1] (analytic) = 1.8368987907984977178756481370438 y[1] (numeric) = 1.836898790798497692685000889268 absolute error = 2.51906472477758e-17 relative error = 1.3713682742871998748578875284809e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.151 y[1] (analytic) = 1.8363510147748831913359040348326 y[1] (numeric) = 1.8363510147748831661045794211862 absolute error = 2.52313246136464e-17 relative error = 1.3739924671612680756112699641066e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.152 y[1] (analytic) = 1.8358024024003235858285433064282 y[1] (numeric) = 1.8358024024003235605565679628794 absolute error = 2.52719753435488e-17 relative error = 1.3766174023144063765047423704213e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.153 y[1] (analytic) = 1.8352529542234312301954751031475 y[1] (numeric) = 1.8352529542234312048828757063151 absolute error = 2.53125993968324e-17 relative error = 1.3792430813736611599482460845736e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.154 y[1] (analytic) = 1.8347026707936542555417085099405 y[1] (numeric) = 1.8347026707936542301885117770675 absolute error = 2.53531967328730e-17 relative error = 1.3818695059677290304403347771299e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.155 y[1] (analytic) = 1.8341515526612760457872672277244 y[1] (numeric) = 1.834151552661276020393499916651 absolute error = 2.53937673110734e-17 relative error = 1.3844966777269916196909155578409e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.156 y[1] (analytic) = 1.8335996003774146873838515103066 y[1] (numeric) = 1.8335996003774146619495404194437 absolute error = 2.54343110908629e-17 relative error = 1.3871245982834904650810274155925e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.157 y[1] (analytic) = 1.8330468144940224181967976391905 y[1] (numeric) = 1.8330468144940223927219696074926 absolute error = 2.54748280316979e-17 relative error = 1.3897532692709618540150683599747e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.158 y[1] (analytic) = 1.8324931955638850755528860542571 y[1] (numeric) = 1.8324931955638850500375679611958 absolute error = 2.55153180930613e-17 relative error = 1.3923826923248062486474312562703e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.159 y[1] (analytic) = 1.8319387441406215434545500924698 y[1] (numeric) = 1.8319387441406215178987688580067 absolute error = 2.55557812344631e-17 relative error = 1.3950128690821231614340002291503e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.16 y[1] (analytic) = 1.8313834607786831989610381203463 y[1] (numeric) = 1.8313834607786831733648207049062 absolute error = 2.55962174154401e-17 relative error = 1.3976438011816969526894007583817e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.161 y[1] (analytic) = 1.8308273460333533577370826789904 y[1] (numeric) = 1.8308273460333533321004560834341 absolute error = 2.56366265955563e-17 relative error = 1.4002754902640208382832158543894e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.162 y[1] (analytic) = 1.8302704004607467187696310929671 y[1] (numeric) = 1.8302704004607466930926223585648 absolute error = 2.56770087344023e-17 relative error = 1.4029079379712663062484482628682e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.163 y[1] (analytic) = 1.8297126246178088082531928262459 y[1] (numeric) = 1.8297126246178087825358290346498 absolute error = 2.57173637915961e-17 relative error = 1.4055411459473289941467079849994e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.164 y[1] (analytic) = 1.8291540190623154226443596998165 y[1] (numeric) = 1.8291540190623153968866679730338 absolute error = 2.57576917267827e-17 relative error = 1.4081751158378090481068979630203e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.165 y[1] (analytic) = 1.8285945843528720708860559164118 y[1] (numeric) = 1.8285945843528720450880634167779 absolute error = 2.57979924996339e-17 relative error = 1.4108098492900023851621516200157e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=6.11 NO POLE x[1] = 2.166 y[1] (analytic) = 1.8280343210489134158020756680418 y[1] (numeric) = 1.8280343210489133899638095981925 absolute error = 2.58382660698493e-17 relative error = 1.4134453479529575856262424426532e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.167 y[1] (analytic) = 1.8274732297107027146624669317521 y[1] (numeric) = 1.8274732297107026887839545345971 absolute error = 2.58785123971550e-17 relative error = 1.4160816134774070351746863268702e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.168 y[1] (analytic) = 1.8269113108993312589203208881803 y[1] (numeric) = 1.8269113108993312330015894468754 absolute error = 2.59187314413049e-17 relative error = 1.4187186475158402586471723137474e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.169 y[1] (analytic) = 1.82634856517671781312052722607 y[1] (numeric) = 1.8263485651767177871616040639901 absolute error = 2.59589231620799e-17 relative error = 1.4213564517224624074905735258651e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.17 y[1] (analytic) = 1.8257849931056080529810564239434 y[1] (numeric) = 1.8257849931056080269819689046552 absolute error = 2.59990875192882e-17 relative error = 1.4239950277532129204351926541938e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.171 y[1] (analytic) = 1.8252205952495740026473309276027 y[1] (numeric) = 1.8252205952495739766081064548372 absolute error = 2.60392244727655e-17 relative error = 1.4266343772657787417479240239397e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.172 y[1] (analytic) = 1.824655372173013471120247969041 y[1] (numeric) = 1.8246553721730134450409139866661 absolute error = 2.60793339823749e-17 relative error = 1.4292745019195911244324706488208e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.173 y[1] (analytic) = 1.8240893244411494878584175986943 y[1] (numeric) = 1.8240893244411494617390015906875 absolute error = 2.61194160080068e-17 relative error = 1.4319154033758224293758195829332e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.174 y[1] (analytic) = 1.8235224526200297375551803287493 y[1] (numeric) = 1.82352245262002971139570981917 absolute error = 2.61594705095793e-17 relative error = 1.4345570832974103398290276170946e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.175 y[1] (analytic) = 1.8229547572765259940909696104411 y[1] (numeric) = 1.8229547572765259678914721634034 absolute error = 2.61994974470377e-17 relative error = 1.4371995433490327525272318903657e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.176 y[1] (analytic) = 1.8223862389783335536615851929335 y[1] (numeric) = 1.8223862389783335274220884125782 absolute error = 2.62394967803553e-17 relative error = 1.4398427851971539587779052879252e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.177 y[1] (analytic) = 1.8218168982939706670829442354582 y[1] (numeric) = 1.8218168982939706408034757659256 absolute error = 2.62794684695326e-17 relative error = 1.4424868105099830894509749439041e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.178 y[1] (analytic) = 1.8212467357927779712728778679176 y[1] (numeric) = 1.8212467357927779449534653933195 absolute error = 2.63194124745981e-17 relative error = 1.4451316209575203358236969003474e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.179 y[1] (analytic) = 1.8206757520449179199105417181047 y[1] (numeric) = 1.8206757520449178935512129624971 absolute error = 2.63593287556076e-17 relative error = 1.4477772182115208720943453444187e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.18 y[1] (analytic) = 1.8201039476213742132740097460839 y[1] (numeric) = 1.820103947621374186874792473439 absolute error = 2.63992172726449e-17 relative error = 1.4504236039455356305451102344516e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.181 y[1] (analytic) = 1.8195313230939512272566215480908 y[1] (numeric) = 1.8195313230939512008175435622692 absolute error = 2.64390779858216e-17 relative error = 1.4530707798349026921059356567308e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.182 y[1] (analytic) = 1.8189578790352734415626541135548 y[1] (numeric) = 1.818957879035273415083743258278 absolute error = 2.64789108552768e-17 relative error = 1.4557187475567331649170077000243e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.183 y[1] (analytic) = 1.8183836160187848670828898395281 y[1] (numeric) = 1.8183836160187848405641739983504 absolute error = 2.65187158411777e-17 relative error = 1.4583675087899465324864517887702e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.184 y[1] (analytic) = 1.8178085346187484724506534269022 y[1] (numeric) = 1.8178085346187484458921605231828 absolute error = 2.65584929037194e-17 relative error = 1.4610170652152620616279491518144e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.185 y[1] (analytic) = 1.8172326354102456097788911023289 y[1] (numeric) = 1.8172326354102455831806490992041 absolute error = 2.65982420031248e-17 relative error = 1.4636674185151956988587419550262e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.186 y[1] (analytic) = 1.8166559189691754395788664287185 y[1] (numeric) = 1.8166559189691754129409033290739 absolute error = 2.66379630996446e-17 relative error = 1.4663185703740624673400937446021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.187 y[1] (analytic) = 1.8160783858722543548610477855718 y[1] (numeric) = 1.8160783858722543281833916320138 absolute error = 2.66776561535580e-17 relative error = 1.4689705224780174147637579119332e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.188 y[1] (analytic) = 1.8155000366970154044187634182087 y[1] (numeric) = 1.815500036697015377701442293037 absolute error = 2.67173211251717e-17 relative error = 1.4716232765150030031549002272264e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.3MB, time=6.36 NO POLE x[1] = 2.189 y[1] (analytic) = 1.8149208720218077152952007721934 y[1] (numeric) = 1.8149208720218076885382427973724 absolute error = 2.67569579748210e-17 relative error = 1.4742768341748121074746259116835e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.19 y[1] (analytic) = 1.814340892425795914434327645905 y[1] (numeric) = 1.8143408924257958876377609830361 absolute error = 2.67965666628689e-17 relative error = 1.4769311971490409038046075655113e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.191 y[1] (analytic) = 1.8137600984889595495163135102877 y[1] (numeric) = 1.813760098488959522680166360581 absolute error = 2.68361471497067e-17 relative error = 1.4795863671311243701520037371118e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.192 y[1] (analytic) = 1.8131784907920925089780301603084 y[1] (numeric) = 1.8131784907920924821023307645544 absolute error = 2.68756993957540e-17 relative error = 1.4822423458163387661789740293163e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.193 y[1] (analytic) = 1.8125960699168024412192116775739 y[1] (numeric) = 1.8125960699168024143039883161154 absolute error = 2.69152233614585e-17 relative error = 1.4848991349017930856815405425997e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.194 y[1] (analytic) = 1.8120128364455101729948544978995 y[1] (numeric) = 1.8120128364455101460401354906033 absolute error = 2.69547190072962e-17 relative error = 1.4875567360864425693099603706683e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.195 y[1] (analytic) = 1.8114287909614491269944391913796 y[1] (numeric) = 1.8114287909614491000002528976081 absolute error = 2.69941862937715e-17 relative error = 1.4902151510710967246848316573226e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.196 y[1] (analytic) = 1.8108439340486647386085563756909 y[1] (numeric) = 1.8108439340486647115749311942738 absolute error = 2.70336251814171e-17 relative error = 1.4928743815584163192972594484907e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.197 y[1] (analytic) = 1.810258266292013871883519995953 y[1] (numeric) = 1.8102582662920138448104843651588 absolute error = 2.70730356307942e-17 relative error = 1.4955344292529269416294120061283e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.198 y[1] (analytic) = 1.809671788277164234664552016485 y[1] (numeric) = 1.8096717882771642075521344139927 absolute error = 2.71124176024923e-17 relative error = 1.4981952958610104869716026942670e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.199 y[1] (analytic) = 1.8090845005905937929281233812238 y[1] (numeric) = 1.8090845005905937657763523240945 absolute error = 2.71517710571293e-17 relative error = 1.5008569830909132114689375912601e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.2 y[1] (analytic) = 1.8084964038195901843040369104161 y[1] (numeric) = 1.8084964038195901571129409550641 absolute error = 2.71910959553520e-17 relative error = 1.5035194926527759214525788100942e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.201 y[1] (analytic) = 1.8079074985522501307878386114497 y[1] (numeric) = 1.8079074985522501035574463536143 absolute error = 2.72303922578354e-17 relative error = 1.5061828262585978484659688811900e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.202 y[1] (analytic) = 1.8073177853774788506441446913663 y[1] (numeric) = 1.8073177853774788233744847660832 absolute error = 2.72696599252831e-17 relative error = 1.5088469856222613191788108735754e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.203 y[1] (analytic) = 1.8067272648849894695014723676786 y[1] (numeric) = 1.8067272648849894421925734492512 absolute error = 2.73088989184274e-17 relative error = 1.5115119724595398707327569825238e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.204 y[1] (analytic) = 1.806135937665302430639163382612 y[1] (numeric) = 1.8061359376653024032910541845824 absolute error = 2.73481091980296e-17 relative error = 1.5141777884881174571850747867841e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.205 y[1] (analytic) = 1.8055438043097449044669899337976 y[1] (numeric) = 1.8055438043097448770796992089185 absolute error = 2.73872907248791e-17 relative error = 1.5168444354275412335868263205898e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.206 y[1] (analytic) = 1.8049508654104501971980335417633 y[1] (numeric) = 1.8049508654104501697715900819688 absolute error = 2.74264434597945e-17 relative error = 1.5195119149992850552437513959346e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.207 y[1] (analytic) = 1.8043571215603571587154281812924 y[1] (numeric) = 1.8043571215603571312498608176692 absolute error = 2.74655673636232e-17 relative error = 1.5221802289267299718024154764799e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.208 y[1] (analytic) = 1.8037625733532095896335598098588 y[1] (numeric) = 1.8037625733532095621288974126176 absolute error = 2.75046623972412e-17 relative error = 1.5248493789351557726402193673376e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.209 y[1] (analytic) = 1.8031672213835556475543152318894 y[1] (numeric) = 1.8031672213835556200105867103361 absolute error = 2.75437285215533e-17 relative error = 1.5275193667517547004775400059674e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.21 y[1] (analytic) = 1.802571066246747252518974042556 y[1] (numeric) = 1.8025710662467472249362083450623 absolute error = 2.75827656974937e-17 relative error = 1.5301901941056673844186462628787e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.211 y[1] (analytic) = 1.8019741085389394916563381991531 y[1] (numeric) = 1.8019741085389394640345643131281 absolute error = 2.76217738860250e-17 relative error = 1.5328618627279300546542712645501e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.3MB, time=6.60 NO POLE x[1] = 2.212 y[1] (analytic) = 1.8013763488570900230276945718856 y[1] (numeric) = 1.8013763488570899953669415237466 absolute error = 2.76607530481390e-17 relative error = 1.5355343743515215776149614427177e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.213 y[1] (analytic) = 1.8007777877989584786692066290518 y[1] (numeric) = 1.8007777877989584509695034841951 absolute error = 2.76997031448567e-17 relative error = 1.5382077307113661612450988236563e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.214 y[1] (analytic) = 1.8001784259631058668323322141805 y[1] (numeric) = 1.8001784259631058390937080769525 absolute error = 2.77386241372280e-17 relative error = 1.5408819335443194025100696009771e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.215 y[1] (analytic) = 1.7995782639488939734228651746556 y[1] (numeric) = 1.7995782639488939456453491883238 absolute error = 2.77775159863318e-17 relative error = 1.5435569845891765362407914402825e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.216 y[1] (analytic) = 1.7989773023564847626391994027364 y[1] (numeric) = 1.7989773023564847348228207494602 absolute error = 2.78163786532762e-17 relative error = 1.5462328855866862609235443154844e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.217 y[1] (analytic) = 1.798375541786839776810414650659 y[1] (numeric) = 1.7983755417868397489552025514602 absolute error = 2.78552120991988e-17 relative error = 1.5489096382795701545390418156368e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.218 y[1] (analytic) = 1.7977729828417195354347842816829 y[1] (numeric) = 1.797772982841719507540767996417 absolute error = 2.78940162852659e-17 relative error = 1.5515872444124809444080239524627e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.219 y[1] (analytic) = 1.7971696261236829334193059185266 y[1] (numeric) = 1.7971696261236829054865147458532 absolute error = 2.79327911726734e-17 relative error = 1.5542657057320552880310206625325e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.22 y[1] (analytic) = 1.7965654722360866385208567496092 y[1] (numeric) = 1.7965654722360866105493200269628 absolute error = 2.79715367226464e-17 relative error = 1.5569450239868943016874140636603e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.221 y[1] (analytic) = 1.7959605217830844879895760518937 y[1] (numeric) = 1.7959605217830844599793231554544 absolute error = 2.80102528964393e-17 relative error = 1.5596252009275718918077446381575e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.222 y[1] (analytic) = 1.7953547753696268844150782868996 y[1] (numeric) = 1.7953547753696268563661386315635 absolute error = 2.80489396553361e-17 relative error = 1.5623062383066542447759221059967e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.223 y[1] (analytic) = 1.7947482336014601907761009236199 y[1] (numeric) = 1.79474823360146016268850396297 absolute error = 2.80875969606499e-17 relative error = 1.5649881378786747834782001585173e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.224 y[1] (analytic) = 1.7941408970851261246941919386457 y[1] (numeric) = 1.7941408970851260965679671649223 absolute error = 2.81262247737234e-17 relative error = 1.5676709014001648117873282582053e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.225 y[1] (analytic) = 1.7935327664279611518920427397597 y[1] (numeric) = 1.7935327664279611237272196838308 absolute error = 2.81648230559289e-17 relative error = 1.5703545306296563450644225130007e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.226 y[1] (analytic) = 1.7929238422380958788570730546151 y[1] (numeric) = 1.7929238422380958506536812859471 absolute error = 2.82033917686680e-17 relative error = 1.5730390273276682157657109667094e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.227 y[1] (analytic) = 1.7923141251244544447108751208649 y[1] (numeric) = 1.7923141251244544164689442474928 absolute error = 2.82419308733721e-17 relative error = 1.5757243932567367874868766128554e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.228 y[1] (analytic) = 1.7917036156967539122851253082462 y[1] (numeric) = 1.7917036156967538840046849767441 absolute error = 2.82804403315021e-17 relative error = 1.5784106301814020831948134521231e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.229 y[1] (analytic) = 1.7910923145655036584045720966571 y[1] (numeric) = 1.7910923145655036300856519921088 absolute error = 2.83189201045483e-17 relative error = 1.5810977398682050532261563693295e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.23 y[1] (analytic) = 1.7904802223420047633777101271885 y[1] (numeric) = 1.7904802223420047350203399731573 absolute error = 2.83573701540312e-17 relative error = 1.5837857240857351052007671193261e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.231 y[1] (analytic) = 1.7898673396383493996957508353839 y[1] (numeric) = 1.7898673396383493712999603938832 absolute error = 2.83957904415007e-17 relative error = 1.5864745846045883411055948444562e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.232 y[1] (analytic) = 1.7892536670674202199405009677075 y[1] (numeric) = 1.789253667067420191506320039171 absolute error = 2.84341809285365e-17 relative error = 1.5891643231973927774034481913989e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.233 y[1] (analytic) = 1.7886392052428897439017610732902 y[1] (numeric) = 1.7886392052428897154292194965421 absolute error = 2.84725415767481e-17 relative error = 1.5918549416388112553401155682878e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.234 y[1] (analytic) = 1.7880239547792197449048568535039 y[1] (numeric) = 1.7880239547792197163939845057291 absolute error = 2.85108723477748e-17 relative error = 1.5945464417055443589740960065527e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=106.8MB, alloc=4.3MB, time=6.86 x[1] = 2.235 y[1] (analytic) = 1.787407916291660635348917041782 y[1] (numeric) = 1.7874079162916606067997438384961 absolute error = 2.85491732032859e-17 relative error = 1.5972388251763445303243859648471e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.236 y[1] (analytic) = 1.7867910903962508514565122753565 y[1] (numeric) = 1.7867910903962508228690681703759 absolute error = 2.85874441049806e-17 relative error = 1.5999320938320134255574691658599e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.237 y[1] (analytic) = 1.786173477709816237235270209222 y[1] (numeric) = 1.7861734777098162086095851946341 absolute error = 2.86256850145879e-17 relative error = 1.6026262494553992674235051244414e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.238 y[1] (analytic) = 1.7855550788499694276520829106602 y[1] (numeric) = 1.7855550788499693989881870167933 absolute error = 2.86638958938669e-17 relative error = 1.6053212938314165958673438465537e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.239 y[1] (analytic) = 1.7849358944351092310205233600656 y[1] (numeric) = 1.7849358944351092023184466554587 absolute error = 2.87020767046069e-17 relative error = 1.6080172287470548564878128622033e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.24 y[1] (analytic) = 1.7843159250844200106020886706045 y[1] (numeric) = 1.7843159250844199818618612619777 absolute error = 2.87402274086268e-17 relative error = 1.6107140559913477778977269263461e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.241 y[1] (analytic) = 1.7836951714178710654218884254138 y[1] (numeric) = 1.7836951714178710366435404576377 absolute error = 2.87783479677761e-17 relative error = 1.6134117773554323883025542092876e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.242 y[1] (analytic) = 1.7830736340562160102993973165972 y[1] (numeric) = 1.7830736340562159814829589726631 absolute error = 2.88164383439341e-17 relative error = 1.6161103946325072077255424848078e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.243 y[1] (analytic) = 1.7824513136209921550948920552174 y[1] (numeric) = 1.7824513136209921262403935562067 absolute error = 2.88544984990107e-17 relative error = 1.6188099096178801185227241039021e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.244 y[1] (analytic) = 1.7818282107345198831721933057926 y[1] (numeric) = 1.7818282107345198542796649108472 absolute error = 2.88925283949454e-17 relative error = 1.6215103241089153180333889866162e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.245 y[1] (analytic) = 1.7812043260199020290783341825072 y[1] (numeric) = 1.7812043260199020001478061887986 absolute error = 2.89305279937086e-17 relative error = 1.6242116399051092876771059822128e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.246 y[1] (analytic) = 1.780579660101023255440777627412 y[1] (numeric) = 1.7805796601010232264722803701115 absolute error = 2.89684972573005e-17 relative error = 1.6269138588080321358166558764386e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.247 y[1] (analytic) = 1.779954213602549429082805773349 y[1] (numeric) = 1.779954213602549400076369625597 absolute error = 2.90064361477520e-17 relative error = 1.6296169826213811812797693305159e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.248 y[1] (analytic) = 1.7793279871499269963577051761557 y[1] (numeric) = 1.7793279871499269673133605490316 absolute error = 2.90443446271241e-17 relative error = 1.6323210131509503500023977557586e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.249 y[1] (analytic) = 1.7787009813693823577023725819146 y[1] (numeric) = 1.7787009813693823286201499244063 absolute error = 2.90822226575083e-17 relative error = 1.6350259522046557295231387296951e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.25 y[1] (analytic) = 1.7780731968879212414109666755878 y[1] (numeric) = 1.7780731968879212122908964745611 absolute error = 2.91200702010267e-17 relative error = 1.6377318015925443069508647430394e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.251 y[1] (analytic) = 1.7774446343333280766292320373338 y[1] (numeric) = 1.7774446343333280474713448175022 absolute error = 2.91578872198316e-17 relative error = 1.6404385631267745968646195144125e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.252 y[1] (analytic) = 1.7768152943341653655701223121308 y[1] (numeric) = 1.7768152943341653363744486360246 absolute error = 2.91956736761062e-17 relative error = 1.6431462386216591382434497687475e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.253 y[1] (analytic) = 1.7761851775197730549513503770291 y[1] (numeric) = 1.7761851775197730257179208449652 absolute error = 2.92334295320639e-17 relative error = 1.6458548298936282627584126774699e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.254 y[1] (analytic) = 1.7755542845202679066554940684325 y[1] (numeric) = 1.7755542845202678773843393184837 absolute error = 2.92711547499488e-17 relative error = 1.6485643387612613721055794915525e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.255 y[1] (analytic) = 1.7749226159665428676132868092489 y[1] (numeric) = 1.7749226159665428383044375172131 absolute error = 2.93088492920358e-17 relative error = 1.6512747670452957474106991962353e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.256 y[1] (analytic) = 1.774290172490266438910723252567 y[1] (numeric) = 1.7742901724902664095642101319368 absolute error = 2.93465131206302e-17 relative error = 1.6539861165686071988354183084681e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.257 y[1] (analytic) = 1.7736569547238820441206108347022 y[1] (numeric) = 1.7736569547238820147364646366338 absolute error = 2.93841461980684e-17 relative error = 1.6566983891562526941533072741020e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=110.6MB, alloc=4.3MB, time=7.11 x[1] = 2.258 y[1] (analytic) = 1.7730229633006073968591989060056 y[1] (numeric) = 1.7730229633006073674374504192883 absolute error = 2.94217484867173e-17 relative error = 1.6594115866354397591767272744729e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.259 y[1] (analytic) = 1.7723881988544338675685178827555 y[1] (numeric) = 1.7723881988544338381091979337812 absolute error = 2.94593199489743e-17 relative error = 1.6621257108355296667946591663153e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.26 y[1] (analytic) = 1.7717526620201258495250616377403 y[1] (numeric) = 1.771752662020125820028201090472 absolute error = 2.94968605472683e-17 relative error = 1.6648407635880970756565101422445e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.261 y[1] (analytic) = 1.7711163534332201240754471207947 y[1] (numeric) = 1.7711163534332200945410768767361 absolute error = 2.95343702440586e-17 relative error = 1.6675567467268712296058484286807e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.262 y[1] (analytic) = 1.7704792737300252250996859735799 y[1] (numeric) = 1.7704792737300251955278369717445 absolute error = 2.95718490018354e-17 relative error = 1.6702736620877674029998660005365e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.263 y[1] (analytic) = 1.7698414235476208027027036752813 y[1] (numeric) = 1.7698414235476207730934068921612 absolute error = 2.96092967831201e-17 relative error = 1.6729915115089071149809350866905e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.264 y[1] (analytic) = 1.769202803523856986134742527652 y[1] (numeric) = 1.7692028035238569564880289771872 absolute error = 2.96467135504648e-17 relative error = 1.6757102968305931709895502962561e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.265 y[1] (analytic) = 1.7685634142973537459412855589463 y[1] (numeric) = 1.7685634142973537162571862924935 absolute error = 2.96840992664528e-17 relative error = 1.6784300198953411948641689181889e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.266 y[1] (analytic) = 1.7679232565075002553431391967656 y[1] (numeric) = 1.7679232565075002256216853030673 absolute error = 2.97214538936983e-17 relative error = 1.6811506825478659800698188624073e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.267 y[1] (analytic) = 1.7672823307944542508473133296815 y[1] (numeric) = 1.7672823307944542210885359348346 absolute error = 2.97587773948469e-17 relative error = 1.6838722866351130800921597967558e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.268 y[1] (analytic) = 1.7666406377991413920893381467019 y[1] (numeric) = 1.766640637799141362293268414127 absolute error = 2.97960697325749e-17 relative error = 1.6865948340062225436409346691066e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.269 y[1] (analytic) = 1.765998178163254620907657912211 y[1] (numeric) = 1.765998178163254591074327042621 absolute error = 2.98333308695900e-17 relative error = 1.6893183265125718476323541328647e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.27 y[1] (analytic) = 1.7653549525292535196507426019347 y[1] (numeric) = 1.7653549525292534897801818333037 absolute error = 2.98705607686310e-17 relative error = 1.6920427660077622795774239967586e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.271 y[1] (analytic) = 1.7647109615403636687175590927679 y[1] (numeric) = 1.7647109615403636388097997002998 absolute error = 2.99077593924681e-17 relative error = 1.6947681543476392916737956306742e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.272 y[1] (analytic) = 1.7640662058405760033320443659369 y[1] (numeric) = 1.7640662058405759733871176620342 absolute error = 2.99449267039027e-17 relative error = 1.6974944933902845574142389995828e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.273 y[1] (analytic) = 1.7634206860746461695522239489724 y[1] (numeric) = 1.763420686074646139570161283205 absolute error = 2.99820626657674e-17 relative error = 1.7002217849960193539210882812228e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.274 y[1] (analytic) = 1.7627744028880938795146195873191 y[1] (numeric) = 1.7627744028880938494954523463927 absolute error = 3.00191672409264e-17 relative error = 1.7029500310274306447100922453397e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.275 y[1] (analytic) = 1.7621273569272022659145909011215 y[1] (numeric) = 1.7621273569272022358583505088466 absolute error = 3.00562403922749e-17 relative error = 1.7056792333493404717990367951807e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.276 y[1] (analytic) = 1.7614795488390172357232565467904 y[1] (numeric) = 1.7614795488390172056299744640505 absolute error = 3.00932820827399e-17 relative error = 1.7084093938288547605129900361085e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.277 y[1] (analytic) = 1.7608309792713468231416411663746 y[1] (numeric) = 1.7608309792713467930113488910948 absolute error = 3.01302922752798e-17 relative error = 1.7111405143353440838606182245907e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.278 y[1] (analytic) = 1.760181648872760541792695170537 y[1] (numeric) = 1.7601816488727605116254242376528 absolute error = 3.01672709328842e-17 relative error = 1.7138725967404357484274622600058e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.279 y[1] (analytic) = 1.7595315582925887361518351630624 y[1] (numeric) = 1.7595315582925887059476171444879 absolute error = 3.02042180185745e-17 relative error = 1.7166056429180513308346691851842e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.28 y[1] (analytic) = 1.7588807081809219322166535763009 y[1] (numeric) = 1.7588807081809219019755200808972 absolute error = 3.02411334954037e-17 relative error = 1.7193396547443988154351450849256e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.281 y[1] (analytic) = 1.758229099188610187416446847784 y[1] (numeric) = 1.7582290991886101571384295213277 absolute error = 3.02780173264563e-17 memory used=114.4MB, alloc=4.3MB, time=7.35 relative error = 1.7220746340979704036383216933838e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.282 y[1] (analytic) = 1.7575767319672624397622122284313 y[1] (numeric) = 1.7575767319672624094473427535828 absolute error = 3.03148694748485e-17 relative error = 1.7248105828595573887895203408196e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.283 y[1] (analytic) = 1.7569236071692458562377640722962 y[1] (numeric) = 1.7569236071692458258860741685681 absolute error = 3.03516899037281e-17 relative error = 1.7275475029122479903465747936825e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.284 y[1] (analytic) = 1.7562697254476851804326212166805 y[1] (numeric) = 1.7562697254476851500441426404058 absolute error = 3.03884785762747e-17 relative error = 1.7302853961414422663514790931362e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.285 y[1] (analytic) = 1.7556150874564620794173178196754 y[1] (numeric) = 1.7556150874564620489920823639758 absolute error = 3.04252354556996e-17 relative error = 1.7330242644348499726554245053318e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.286 y[1] (analytic) = 1.7549596938502144898617907797647 y[1] (numeric) = 1.7549596938502144593998302745188 absolute error = 3.04619605052459e-17 relative error = 1.7357641096824998150917007766846e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.287 y[1] (analytic) = 1.7543035452843359633974976190476 y[1] (numeric) = 1.7543035452843359328988439308589 absolute error = 3.04986536881887e-17 relative error = 1.7385049337767544240944253076407e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.288 y[1] (analytic) = 1.753646642414975011223919467908 y[1] (numeric) = 1.7536466424149749806886045000734 absolute error = 3.05353149678346e-17 relative error = 1.7412467386122854475837747924403e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.289 y[1] (analytic) = 1.7529889858990344479601045445751 y[1] (numeric) = 1.7529889858990344173881602370526 absolute error = 3.05719443075225e-17 relative error = 1.7439895260861227483223223395789e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.29 y[1] (analytic) = 1.7523305763941707347419082779736 y[1] (numeric) = 1.7523305763941707041333666073507 absolute error = 3.06085416706229e-17 relative error = 1.7467332980976181131765546339510e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.291 y[1] (analytic) = 1.7516714145587933215655869765725 y[1] (numeric) = 1.7516714145587932909204799560338 absolute error = 3.06451070205387e-17 relative error = 1.7494780565484945144941201558664e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.292 y[1] (analytic) = 1.7510115010520639888784026995802 y[1] (numeric) = 1.7510115010520639581967623788759 absolute error = 3.06816403207043e-17 relative error = 1.7522238033427983974105764969649e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.293 y[1] (analytic) = 1.7503508365338961884168977398298 y[1] (numeric) = 1.7503508365338961576987562052432 absolute error = 3.07181415345866e-17 relative error = 1.7549705403869604103205390420756e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.294 y[1] (analytic) = 1.749689421664954383293497880022 y[1] (numeric) = 1.7496894216649543525388872543377 absolute error = 3.07546106256843e-17 relative error = 1.7577182695897591141926596121900e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.295 y[1] (analytic) = 1.7490272571066533873321043356696 y[1] (numeric) = 1.7490272571066533565410567781414 absolute error = 3.07910475575282e-17 relative error = 1.7604669928623417856345435459830e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.296 y[1] (analytic) = 1.748364343521157703653335049096 y[1] (numeric) = 1.7483643435211576728258827554145 absolute error = 3.08274522936815e-17 relative error = 1.7632167121182452685545713821909e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.297 y[1] (analytic) = 1.7477006815713808625100767491899 y[1] (numeric) = 1.7477006815713808316462519514505 absolute error = 3.08638247977394e-17 relative error = 1.7659674292733768220675511611002e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.298 y[1] (analytic) = 1.7470362719209847583740099413117 y[1] (numeric) = 1.7470362719209847274738449079822 absolute error = 3.09001650333295e-17 relative error = 1.7687191462460407179852449879696e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.299 y[1] (analytic) = 1.7463711152343789862737697407685 y[1] (numeric) = 1.746371115234378955337296776657 absolute error = 3.09364729641115e-17 relative error = 1.7714718649569248172539154911560e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.3 y[1] (analytic) = 1.7457052121767201773854062116435 y[1] (numeric) = 1.7457052121767201464126576578661 absolute error = 3.09727485537774e-17 relative error = 1.7742255873291157587982684808747e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.301 y[1] (analytic) = 1.7450385634139113338758086204636 y[1] (numeric) = 1.7450385634139113028668168544119 absolute error = 3.10089917660517e-17 relative error = 1.7769803152881141844588804656295e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.302 y[1] (analytic) = 1.7443711696126011629997587612248 y[1] (numeric) = 1.7443711696126011319545561965336 absolute error = 3.10452025646912e-17 relative error = 1.7797360507618270693114780795141e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.303 y[1] (analytic) = 1.7437030314401834104512792546678 y[1] (numeric) = 1.7437030314401833793698983411826 absolute error = 3.10813809134852e-17 relative error = 1.7824927956805829754232305941348e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.304 y[1] (analytic) = 1.7430341495647961929699434703985 y[1] (numeric) = 1.7430341495647961618524166941434 absolute error = 3.11175267762551e-17 relative error = 1.7852505519771129192867215799553e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.3MB, time=7.60 NO POLE x[1] = 2.305 y[1] (analytic) = 1.74236452465532133020281446549 y[1] (numeric) = 1.7423645246553212990491743486347 absolute error = 3.11536401168553e-17 relative error = 1.7880093215866058077309852395980e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.306 y[1] (analytic) = 1.7416941573813836758226810775684 y[1] (numeric) = 1.7416941573813836446329601783961 absolute error = 3.11897208991723e-17 relative error = 1.7907691064466606553780122198609e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.307 y[1] (analytic) = 1.7410230484133504479032600540938 y[1] (numeric) = 1.7410230484133504166774909669686 absolute error = 3.12257690871252e-17 relative error = 1.7935299084973191055623177064604e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.308 y[1] (analytic) = 1.7403511984223305585520338425766 y[1] (numeric) = 1.7403511984223305272902491979105 absolute error = 3.12617846446661e-17 relative error = 1.7962917296810922817438054297114e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.309 y[1] (analytic) = 1.7396786080801739428013944088355 y[1] (numeric) = 1.7396786080801739115036268730561 absolute error = 3.12977675357794e-17 relative error = 1.7990545719429244724336237115423e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.31 y[1] (analytic) = 1.7390052780594708867587641920983 y[1] (numeric) = 1.7390052780594708554250464676162 absolute error = 3.13337177244821e-17 relative error = 1.8018184372302142373139067968397e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.311 y[1] (analytic) = 1.7383312090335513550163660467684 y[1] (numeric) = 1.7383312090335513236467308719444 absolute error = 3.13696351748240e-17 relative error = 1.8045833274928298109630688405380e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.312 y[1] (analytic) = 1.7376564016764843173213147610302 y[1] (numeric) = 1.7376564016764842859157949101425 absolute error = 3.14055198508877e-17 relative error = 1.8073492446831130339497712972435e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.313 y[1] (analytic) = 1.7369808566630770745067034821467 y[1] (numeric) = 1.7369808566630770430653317653582 absolute error = 3.14413717167885e-17 relative error = 1.8101161907558775372688245087598e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.314 y[1] (analytic) = 1.7363045746688745836843591173063 y[1] (numeric) = 1.7363045746688745522071683806317 absolute error = 3.14771907366746e-17 relative error = 1.8128841676684242018720944007267e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.315 y[1] (analytic) = 1.7356275563701587826999415172067 y[1] (numeric) = 1.7356275563701587511869646424798 absolute error = 3.15129768747269e-17 relative error = 1.8156531773805336091676690854657e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.316 y[1] (analytic) = 1.7349498024439479138510619872218 y[1] (numeric) = 1.7349498024439478823023318920625 absolute error = 3.15487300951593e-17 relative error = 1.8184232218544872943588332679510e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.317 y[1] (analytic) = 1.7342713135679958468690974079753 y[1] (numeric) = 1.7342713135679958152846470457566 absolute error = 3.15844503622187e-17 relative error = 1.8211943030550717525032710306623e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.318 y[1] (analytic) = 1.7335920904207914011653769834506 y[1] (numeric) = 1.7335920904207913695452393432659 absolute error = 3.16201376401847e-17 relative error = 1.8239664229495651501319735850852e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.319 y[1] (analytic) = 1.7329121336815576673424193703953 y[1] (numeric) = 1.7329121336815576356866274770253 absolute error = 3.16557918933700e-17 relative error = 1.8267395835077644012446794959575e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.32 y[1] (analytic) = 1.7322314440302513279708986777247 y[1] (numeric) = 1.7322314440302512962794855916042 absolute error = 3.16914130861205e-17 relative error = 1.8295137867019949895397448873645e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.321 y[1] (analytic) = 1.7315500221475619776330185589022 y[1] (numeric) = 1.7315500221475619459060173760874 absolute error = 3.17270011828148e-17 relative error = 1.8322890345070861640246857280865e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.322 y[1] (analytic) = 1.7308678687149114422329743538675 y[1] (numeric) = 1.7308678687149114104704182060025 absolute error = 3.17625561478650e-17 relative error = 1.8350653289004211840415726393300e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.323 y[1] (analytic) = 1.7301849844144530975751839699906 y[1] (numeric) = 1.7301849844144530657771060242746 absolute error = 3.17980779457160e-17 relative error = 1.8378426718619009883806636567357e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.324 y[1] (analytic) = 1.7295013699290711872109689237674 y[1] (numeric) = 1.7295013699290711553774023829213 absolute error = 3.18335665408461e-17 relative error = 1.8406210653739829457096400948187e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.325 y[1] (analytic) = 1.7288170259423801395543676965162 y[1] (numeric) = 1.7288170259423801076853457987495 absolute error = 3.18690218977667e-17 relative error = 1.8434005114216676393453818903410e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.326 y[1] (analytic) = 1.7281319531387238842677642882063 y[1] (numeric) = 1.7281319531387238523633203071839 absolute error = 3.19044439810224e-17 relative error = 1.8461810119925087681976373132865e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.327 y[1] (analytic) = 1.7274461522031751679180155837332 y[1] (numeric) = 1.7274461522031751359781828285421 absolute error = 3.19398327551911e-17 relative error = 1.8489625690766230723895419110694e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.3MB, time=7.85 NO POLE x[1] = 2.328 y[1] (analytic) = 1.7267596238215348689037618754551 y[1] (numeric) = 1.726759623821534836928573690571 absolute error = 3.19751881848841e-17 relative error = 1.8517451846667002836628581843474e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.329 y[1] (analytic) = 1.7260723686803313116546056146241 y[1] (numeric) = 1.7260723686803312796440953798782 absolute error = 3.20105102347459e-17 relative error = 1.8545288607579957201766590780771e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.33 y[1] (analytic) = 1.7253843874668195801028441924754 y[1] (numeric) = 1.7253843874668195480570453230208 absolute error = 3.20457988694546e-17 relative error = 1.8573135993483576395854435743775e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.331 y[1] (analytic) = 1.724695680868980830428443279185 y[1] (numeric) = 1.7246956808689807983473892254635 absolute error = 3.20810540537215e-17 relative error = 1.8600994024382082736995054472549e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.332 y[1] (analytic) = 1.7240062495755216030779379756651 y[1] (numeric) = 1.7240062495755215709616622233738 absolute error = 3.21162757522913e-17 relative error = 1.8628862720305596214628852408134e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.333 y[1] (analytic) = 1.723316094275873134057949759239 y[1] (numeric) = 1.7233160942758731019064858292967 absolute error = 3.21514639299423e-17 relative error = 1.8656742101310292808766997044846e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.334 y[1] (analytic) = 1.7226252156601906655040079296206 y[1] (numeric) = 1.7226252156601906333173893781341 absolute error = 3.21866185514865e-17 relative error = 1.8684632187478505149740861204945e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.335 y[1] (analytic) = 1.7219336144193527555253649863199 y[1] (numeric) = 1.7219336144193527233036254045506 absolute error = 3.22217395817693e-17 relative error = 1.8712532998918591134515228264796e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.336 y[1] (analytic) = 1.7212412912449605873264960926017 y[1] (numeric) = 1.7212412912449605550696691069323 absolute error = 3.22568269856694e-17 relative error = 1.8740444555764918432264235883794e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.337 y[1] (analytic) = 1.720548246829337277605973504441 y[1] (numeric) = 1.7205482468293372453140927763413 absolute error = 3.22918807280997e-17 relative error = 1.8768366878178430172391327962151e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.338 y[1] (analytic) = 1.719854481865527184233407565541 y[1] (numeric) = 1.7198544818655271519065067915348 absolute error = 3.23269007740062e-17 relative error = 1.8796299986346049121821875250312e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.339 y[1] (analytic) = 1.7191599970472952132051465914183 y[1] (numeric) = 1.7191599970472951808432595030493 absolute error = 3.23618870883690e-17 relative error = 1.8824243900481301957202914458698e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.34 y[1] (analytic) = 1.718464793069126124879428686794 y[1] (numeric) = 1.7184647930691260924825890505922 absolute error = 3.23968396362018e-17 relative error = 1.8852198640824072188310813668119e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.341 y[1] (analytic) = 1.7177688706262238394916792610841 y[1] (numeric) = 1.717768870626223807059920878532 absolute error = 3.24317583825521e-17 relative error = 1.8880164227640759997666827065501e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.342 y[1] (analytic) = 1.717072230414510741950648726632 y[1] (numeric) = 1.717072230414510709484005434131 absolute error = 3.24666432925010e-17 relative error = 1.8908140681224209523974718443553e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.343 y[1] (analytic) = 1.7163748731306269859160855834886 y[1] (numeric) = 1.7163748731306269534145912523249 absolute error = 3.25014943311637e-17 relative error = 1.8936128021894043814505814650843e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.344 y[1] (analytic) = 1.7156767994719297971586408130075 y[1] (numeric) = 1.7156767994719297646223293493184 absolute error = 3.25363114636891e-17 relative error = 1.8964126269996476029812950490966e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.345 y[1] (analytic) = 1.7149780101364927762027002202945 y[1] (numeric) = 1.7149780101364927436316055650344 absolute error = 3.25710946552601e-17 relative error = 1.8992135445904528365918104718799e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.346 y[1] (analytic) = 1.71427850582310520025284208262 y[1] (numeric) = 1.7142785058231051676469982115264 absolute error = 3.26058438710936e-17 relative error = 1.9020155570018076520594336785329e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.347 y[1] (analytic) = 1.7135782872312713244046181772782 y[1] (numeric) = 1.713578287231271291764059100838 absolute error = 3.26405590764402e-17 relative error = 1.9048186662763719206134088107812e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.348 y[1] (analytic) = 1.712877355061209682140356978055 y[1] (numeric) = 1.7128773550612096494651167414702 absolute error = 3.26752402365848e-17 relative error = 1.9076228744595172782879477343518e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.349 y[1] (analytic) = 1.7121757100138523851106885244419 y[1] (numeric) = 1.7121757100138523524008012075956 absolute error = 3.27098873168463e-17 relative error = 1.9104281835993141224240759368940e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.35 y[1] (analytic) = 1.7114733527908444222024911820132 y[1] (numeric) = 1.7114733527908443894579908994356 absolute error = 3.27445002825776e-17 relative error = 1.9132345957465361059206336155971e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.3MB, time=8.09 NO POLE x[1] = 2.351 y[1] (analytic) = 1.7107702840945429578939612259616 y[1] (numeric) = 1.7107702840945429251148821267959 absolute error = 3.27790790991657e-17 relative error = 1.9160421129546704887655566086162e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.352 y[1] (analytic) = 1.7100665046280166298975068926636 y[1] (numeric) = 1.7100665046280165970838831606318 absolute error = 3.28136237320318e-17 relative error = 1.9188507372799285159830912057499e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.353 y[1] (analytic) = 1.7093620150950448460911692563224 y[1] (numeric) = 1.7093620150950448132430351096912 absolute error = 3.28481341466312e-17 relative error = 1.9216604707812441218398741572165e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.354 y[1] (analytic) = 1.7086568162001170807392729992091 y[1] (numeric) = 1.7086568162001170478566626907555 absolute error = 3.28826103084536e-17 relative error = 1.9244713155202960419242022875810e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.355 y[1] (analytic) = 1.7079509086484321700030108547919 y[1] (numeric) = 1.7079509086484321370859586717691 absolute error = 3.29170521830228e-17 relative error = 1.9272832735614948510651299675415e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.356 y[1] (analytic) = 1.7072442931458976067416662131113 y[1] (numeric) = 1.7072442931458975737902064772144 absolute error = 3.29514597358969e-17 relative error = 1.9300963469719992569311536194904e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.357 y[1] (analytic) = 1.7065369703991288346051790871192 y[1] (numeric) = 1.7065369703991288016193461544508 absolute error = 3.29858329326684e-17 relative error = 1.9329105378217265751020584906817e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.358 y[1] (analytic) = 1.705828941115448541418761347357 y[1] (numeric) = 1.705828941115448508398589608393 absolute error = 3.30201717389640e-17 relative error = 1.9357258481833456442926173103125e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.359 y[1] (analytic) = 1.7051202060028859518602678402994 y[1] (numeric) = 1.7051202060028859188057917198544 absolute error = 3.30544761204450e-17 relative error = 1.9385422801323049128774703604949e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.36 y[1] (analytic) = 1.7044107657701761194310307129327 y[1] (numeric) = 1.7044107657701760863422846701257 absolute error = 3.30887460428070e-17 relative error = 1.9413598357468195263864408627538e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.361 y[1] (analytic) = 1.7037006211267592177208649726753 y[1] (numeric) = 1.7037006211267591845978835008951 absolute error = 3.31229814717802e-17 relative error = 1.9441785171078936010211691464802e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.362 y[1] (analytic) = 1.702989772782779830967954017575 y[1] (numeric) = 1.7029897727827797978107716444461 absolute error = 3.31571823731289e-17 relative error = 1.9469983262992955774748763591466e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.363 y[1] (analytic) = 1.7022782214490862439143245768393 y[1] (numeric) = 1.7022782214490862107229758641869 absolute error = 3.31913487126524e-17 relative error = 1.9498192654076157564764533879209e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.364 y[1] (analytic) = 1.7015659678372297309576212061635 y[1] (numeric) = 1.7015659678372296977321407499792 absolute error = 3.32254804561843e-17 relative error = 1.9526413365222299484124340913123e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.365 y[1] (analytic) = 1.7008530126594638445998911860238 y[1] (numeric) = 1.7008530126594638113403136164309 absolute error = 3.32595775695929e-17 relative error = 1.9554645417353277058655415529353e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.366 y[1] (analytic) = 1.7001393566287437031940913740907 y[1] (numeric) = 1.7001393566287436699004513553096 absolute error = 3.32936400187811e-17 relative error = 1.9582888831419112185351548827774e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.367 y[1] (analytic) = 1.6994250004587252779890292651966 y[1] (numeric) = 1.6994250004587252446613614955103 absolute error = 3.33276677696863e-17 relative error = 1.9611143628397942061215042728735e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.368 y[1] (analytic) = 1.6987099448637646794734512138577 y[1] (numeric) = 1.6987099448637646461117904255767 absolute error = 3.33616607882810e-17 relative error = 1.9639409829296420168451095153075e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.369 y[1] (analytic) = 1.6979941905589174430199914752009 y[1] (numeric) = 1.6979941905589174096243724346288 absolute error = 3.33956190405721e-17 relative error = 1.9667687455149352670901400749820e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.37 y[1] (analytic) = 1.6972777382599378138296964202892 y[1] (numeric) = 1.697277738259937780400153927688 absolute error = 3.34295424926012e-17 relative error = 1.9695976527019923076564517203065e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.371 y[1] (analytic) = 1.6965605886832780311778389812606 y[1] (numeric) = 1.6965605886832779977144078708156 absolute error = 3.34634311104450e-17 relative error = 1.9724277065999976418135049667587e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.372 y[1] (analytic) = 1.6958427425460876119617390804061 y[1] (numeric) = 1.6958427425460875784644542201912 absolute error = 3.34972848602149e-17 relative error = 1.9752589093209832419725360019295e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.373 y[1] (analytic) = 1.6951242005662126335513064953075 y[1] (numeric) = 1.6951242005662126000202027872505 absolute error = 3.35311037080570e-17 relative error = 1.9780912629798334166802400282223e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.3MB, time=8.33 x[1] = 2.374 y[1] (analytic) = 1.6944049634621950159430233094326 y[1] (numeric) = 1.6944049634621949823781356892801 absolute error = 3.35648876201525e-17 relative error = 1.9809247696943132976937621776215e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.375 y[1] (analytic) = 1.6936850319532718032180837941439 y[1] (numeric) = 1.6936850319532717696194472314263 absolute error = 3.35986365627176e-17 relative error = 1.9837594315850678788351536253004e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.376 y[1] (analytic) = 1.6929644067593744443054102639229 y[1] (numeric) = 1.6929644067593744106730597619196 absolute error = 3.36323505020033e-17 relative error = 1.9865952507756151462658099733841e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.377 y[1] (analytic) = 1.6922430886011280730502641417332 y[1] (numeric) = 1.6922430886011280393842347374375 absolute error = 3.36660294042957e-17 relative error = 1.9894322293923687383861687345487e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.378 y[1] (analytic) = 1.6915210781998507875891721658513 y[1] (numeric) = 1.6915210781998507538894989299355 absolute error = 3.36996732359158e-17 relative error = 1.9922703695646311050886812405926e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.379 y[1] (analytic) = 1.69079837627755292903188836318 y[1] (numeric) = 1.6907983762775528952986063999602 absolute error = 3.37332819632198e-17 relative error = 1.9951096734246162218937117816716e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.38 y[1] (analytic) = 1.6900749835569363594511131070202 y[1] (numeric) = 1.6900749835569363256842575544211 absolute error = 3.37668555525991e-17 relative error = 1.9979501431074546122270503934084e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.381 y[1] (analytic) = 1.6893509007613937391806912695238 y[1] (numeric) = 1.6893509007613937053802972990438 absolute error = 3.38003939704800e-17 relative error = 2.0007917807511806248967368167435e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.382 y[1] (analytic) = 1.6886261286150078034230121705686 y[1] (numeric) = 1.6886261286150077695891149872446 absolute error = 3.38338971833240e-17 relative error = 2.0036345884967552112081494978619e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.383 y[1] (analytic) = 1.6879006678425506381663347155952 y[1] (numeric) = 1.687900667842550604298969557967 absolute error = 3.38673651576282e-17 relative error = 2.0064785684880946857598949482916e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.384 y[1] (analytic) = 1.6871745191694829554127618050192 y[1] (numeric) = 1.6871745191694829215119639450949 absolute error = 3.39007978599243e-17 relative error = 2.0093237228720165830495674146530e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.385 y[1] (analytic) = 1.6864476833219533677175887871863 y[1] (numeric) = 1.6864476833219533337833935304066 absolute error = 3.39341952567797e-17 relative error = 2.0121700537983098967910007329299e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.386 y[1] (analytic) = 1.685720161026797662040751415459 y[1] (numeric) = 1.6857201610267976280731941006619 absolute error = 3.39675573147971e-17 relative error = 2.0150175634197165186121897813111e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.387 y[1] (analytic) = 1.6849919530115380729110994579277 y[1] (numeric) = 1.6849919530115380389102154573133 absolute error = 3.40008840006144e-17 relative error = 2.0178662538919304334729649455768e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.388 y[1] (analytic) = 1.684263060004382554904222795412 y[1] (numeric) = 1.6842630600043825208700475145071 absolute error = 3.40341752809049e-17 relative error = 2.0207161273736147253778377528882e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.389 y[1] (analytic) = 1.6835334827342240544345575298648 y[1] (numeric) = 1.6835334827342240203671264074875 absolute error = 3.40674311223773e-17 relative error = 2.0235671860264067479086603212697e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.39 y[1] (analytic) = 1.682803221930639780862500311013 y[1] (numeric) = 1.6828032219306397467618488192373 absolute error = 3.41006514917757e-17 relative error = 2.0264194320149233086440113397971e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.391 y[1] (analytic) = 1.6820722783238904769172597740602 y[1] (numeric) = 1.6820722783238904427834234181802 absolute error = 3.41338363558800e-17 relative error = 2.0292728675067896476847890812357e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.392 y[1] (analytic) = 1.6813406526449196884361746655369 y[1] (numeric) = 1.6813406526449196542691889840319 absolute error = 3.41669856815050e-17 relative error = 2.0321274946725911729594986966783e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.393 y[1] (analytic) = 1.6806083456253530334212289179227 y[1] (numeric) = 1.6806083456253529992211294824212 absolute error = 3.42000994355015e-17 relative error = 2.0349833156859440743608854194836e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.394 y[1] (analytic) = 1.6798753579974974704134946164617 y[1] (numeric) = 1.6798753579974974361803170317058 absolute error = 3.42331775847559e-17 relative error = 2.0378403327234768305501951863759e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.395 y[1] (analytic) = 1.6791416904943405661862344836678 y[1] (numeric) = 1.679141690494340531920014387478 absolute error = 3.42662200961898e-17 relative error = 2.0406985479648116677894218752080e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.396 y[1] (analytic) = 1.6784073438495497627573961883579 y[1] (numeric) = 1.678407343849549728458169251597 absolute error = 3.42992269367609e-17 relative error = 2.0435579635926234248183333240913e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=133.5MB, alloc=4.3MB, time=8.58 x[1] = 2.397 y[1] (analytic) = 1.6776723187974716437222314666549 y[1] (numeric) = 1.6776723187974716093900333931927 absolute error = 3.43321980734622e-17 relative error = 2.0464185817925972417661001775280e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.398 y[1] (analytic) = 1.6769366160731311999067737222834 y[1] (numeric) = 1.6769366160731311655416402489606 absolute error = 3.43651334733228e-17 relative error = 2.0492804047534815502263080014867e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.399 y[1] (analytic) = 1.6762002364122310943429084526159 y[1] (numeric) = 1.6762002364122310599448753492088 absolute error = 3.43980331034071e-17 relative error = 2.0521434346670457491682329505082e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.4 y[1] (analytic) = 1.6754631805511509265657715253413 y[1] (numeric) = 1.6754631805511508921348745945258 absolute error = 3.44308969308155e-17 relative error = 2.0550076737281272970289755587726e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.401 y[1] (analytic) = 1.6747254492269464962342110082933 y[1] (numeric) = 1.6747254492269464617704860856091 absolute error = 3.44637249226842e-17 relative error = 2.0578731241346251882168043903163e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.402 y[1] (analytic) = 1.6739870431773490660750489319168 y[1] (numeric) = 1.6739870431773490315785318857316 absolute error = 3.44965170461852e-17 relative error = 2.0607397880875053601947065238097e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.403 y[1] (analytic) = 1.6732479631407646241518800400492 y[1] (numeric) = 1.6732479631407645896226067715228 absolute error = 3.45292732685264e-17 relative error = 2.0636076677908120915169395069827e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.404 y[1] (analytic) = 1.6725082098562731454591452601561 y[1] (numeric) = 1.6725082098562731108971517032045 absolute error = 3.45619935569516e-17 relative error = 2.0664767654516734512652279701261e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.405 y[1] (analytic) = 1.6717677840636278528422182988858 y[1] (numeric) = 1.6717677840636278182475404201454 absolute error = 3.45946778787404e-17 relative error = 2.0693470832803007814783726966927e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.406 y[1] (analytic) = 1.6710266865032544772442444427958 y[1] (numeric) = 1.6710266865032544426169182415872 absolute error = 3.46273262012086e-17 relative error = 2.0722186234900181001057592585121e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.407 y[1] (analytic) = 1.6702849179162505172804713173498 y[1] (numeric) = 1.6702849179162504826205328256419 absolute error = 3.46599384917079e-17 relative error = 2.0750913882972496734031117529210e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.408 y[1] (analytic) = 1.6695424790443844981408120297924 y[1] (numeric) = 1.6695424790443844634482973121664 absolute error = 3.46925147176260e-17 relative error = 2.0779653799215315140587093869160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.409 y[1] (analytic) = 1.668799370630095229821381793278 y[1] (numeric) = 1.6687993706300951950963269468915 absolute error = 3.47250548463865e-17 relative error = 2.0808406005855109254699744854886e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.41 y[1] (analytic) = 1.6680555934164910646857498006547 y[1] (numeric) = 1.6680555934164910299281909552052 absolute error = 3.47575588454495e-17 relative error = 2.0837170525149880099315012544749e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.411 y[1] (analytic) = 1.6673111481473491543566487865884 y[1] (numeric) = 1.6673111481473491195666221042775 absolute error = 3.47900266823109e-17 relative error = 2.0865947379388793182108999773604e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.412 y[1] (analytic) = 1.6665660355671147059388853862578 y[1] (numeric) = 1.6665660355671146711164270617549 absolute error = 3.48224583245029e-17 relative error = 2.0894736590892534061865428587057e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.413 y[1] (analytic) = 1.665820256420900237574195067646 y[1] (numeric) = 1.6658202564209002027193413280522 absolute error = 3.48548537395938e-17 relative error = 2.0923538182013244656029614137027e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.414 y[1] (analytic) = 1.665073811454484833328786082513 y[1] (numeric) = 1.6650738114544847984415731873248 absolute error = 3.48872128951882e-17 relative error = 2.0952352175134699607522610602921e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.415 y[1] (analytic) = 1.6643267014143133974143175484422 y[1] (numeric) = 1.6643267014143133624947817895153 absolute error = 3.49195357589269e-17 relative error = 2.0981178592672302873492977993583e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.416 y[1] (analytic) = 1.6635789270474959077430574409217 y[1] (numeric) = 1.6635789270474958727912351424344 absolute error = 3.49518222984873e-17 relative error = 2.1010017457073384862117104838177e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.417 y[1] (analytic) = 1.6628304891018066688179669402382 y[1] (numeric) = 1.6628304891018066338338944586557 absolute error = 3.49840724815825e-17 relative error = 2.1038868790816718572153064335939e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.418 y[1] (analytic) = 1.6620813883256835639584582430401 y[1] (numeric) = 1.6620813883256835289421719670774 absolute error = 3.50162862759627e-17 relative error = 2.1067732616413418232057492771111e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.419 y[1] (analytic) = 1.6613316254682273068625736127459 y[1] (numeric) = 1.6613316254682272718141099633322 absolute error = 3.50484636494137e-17 relative error = 2.1096608956406094782195652595211e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.42 y[1] (analytic) = 1.6605812012792006925063341065602 y[1] (numeric) = 1.6605812012792006574257295368018 absolute error = 3.50806045697584e-17 relative error = 2.1125497833369815665751407421305e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.3MB, time=8.83 NO POLE x[1] = 2.421 y[1] (analytic) = 1.6598301165090278473810070796829 y[1] (numeric) = 1.659830116509027812268298074827 absolute error = 3.51127090048559e-17 relative error = 2.1154399269911621290885494239186e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.422 y[1] (analytic) = 1.6590783719087934790690422293838 y[1] (numeric) = 1.6590783719087934439242653067821 absolute error = 3.51447769226017e-17 relative error = 2.1183313288670703198613079369456e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.423 y[1] (analytic) = 1.6583259682302421251594266029431 y[1] (numeric) = 1.6583259682302420899826183120153 absolute error = 3.51768082909278e-17 relative error = 2.1212239912318522411991907234590e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.424 y[1] (analytic) = 1.6575729062257774015032096540404 y[1] (numeric) = 1.6575729062257773662944065762375 absolute error = 3.52088030778029e-17 relative error = 2.1241179163558988435581687326712e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.425 y[1] (analytic) = 1.6568191866484612498099500920047 y[1] (numeric) = 1.6568191866484612145691888407724 absolute error = 3.52407612512323e-17 relative error = 2.1270131065128457672197281870015e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.426 y[1] (analytic) = 1.6560648102520131845858369274149 y[1] (numeric) = 1.6560648102520131493131541481572 absolute error = 3.52726827792577e-17 relative error = 2.1299095639795671450211407476305e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.427 y[1] (analytic) = 1.6553097777908095394142377758687 y[1] (numeric) = 1.6553097777908095041096701459111 absolute error = 3.53045676299576e-17 relative error = 2.1328072910362056349506658178339e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.428 y[1] (analytic) = 1.6545540900198827125794281393073 y[1] (numeric) = 1.6545540900198826772430123678601 absolute error = 3.53364157714472e-17 relative error = 2.1357062899661723151538223718110e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.429 y[1] (analytic) = 1.6537977476949204120342560411039 y[1] (numeric) = 1.6537977476949203766660288692256 absolute error = 3.53682271718783e-17 relative error = 2.1386065630561465784980649427675e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.43 y[1] (analytic) = 1.6530407515722648997124970471899 y[1] (numeric) = 1.6530407515722648643124952477504 absolute error = 3.54000017994395e-17 relative error = 2.1415081125960941750017978427866e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.431 y[1] (analytic) = 1.6522831024089122351866553607985 y[1] (numeric) = 1.6522831024089121997549157384423 absolute error = 3.54317396223562e-17 relative error = 2.1444109408792731991556358197795e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.432 y[1] (analytic) = 1.6515248009625115186719673329637 y[1] (numeric) = 1.651524800962511483208526724073 absolute error = 3.54634406088907e-17 relative error = 2.1473150502022461485063162752835e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.433 y[1] (analytic) = 1.6507658479913641333773643847066 y[1] (numeric) = 1.6507658479913640978822596573648 absolute error = 3.54951047273418e-17 relative error = 2.1502204428648617262609163395026e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.434 y[1] (analytic) = 1.6500062442544229872041529898842 y[1] (numeric) = 1.6500062442544229516774210438386 absolute error = 3.55267319460456e-17 relative error = 2.1531271211703093203576820086343e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.435 y[1] (analytic) = 1.6492459905112917537931700199558 y[1] (numeric) = 1.6492459905112917182348477865812 absolute error = 3.55583222333746e-17 relative error = 2.1560350874250705553698663389067e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.436 y[1] (analytic) = 1.6484850875222241129211724034511 y[1] (numeric) = 1.6484850875222240773312968457122 absolute error = 3.55898755577389e-17 relative error = 2.1589443439389980997385111224673e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.437 y[1] (analytic) = 1.6477235360481229902472207036835 y[1] (numeric) = 1.6477235360481229546258288160986 absolute error = 3.56213918875849e-17 relative error = 2.1618548930252429665282391615112e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.438 y[1] (analytic) = 1.6469613368505397964098168682653 y[1] (numeric) = 1.646961336850539760756945676869 absolute error = 3.56528711913963e-17 relative error = 2.1647667370003212633019596132731e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.439 y[1] (analytic) = 1.6461984906916736654755570532208 y[1] (numeric) = 1.6461984906916736297912436155269 absolute error = 3.56843134376939e-17 relative error = 2.1676798781841082317350375284355e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.44 y[1] (analytic) = 1.6454349983343706927400610729825 y[1] (numeric) = 1.6454349983343706570243424779472 absolute error = 3.57157185950353e-17 relative error = 2.1705943188998261929103710947943e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.441 y[1] (analytic) = 1.6446708605421231718819406752776 y[1] (numeric) = 1.6446708605421231361348540432621 absolute error = 3.57470866320155e-17 relative error = 2.1735100614740871807969869374817e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.442 y[1] (analytic) = 1.6439060780790688314705694868712 y[1] (numeric) = 1.6439060780790687956921519696048 absolute error = 3.57784175172664e-17 relative error = 2.1764271082368687803895571015089e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.443 y[1] (analytic) = 1.6431406517099900708284181223353 y[1] (numeric) = 1.6431406517099900350187069028781 absolute error = 3.58097112194572e-17 relative error = 2.1793454615215446711108889224944e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.3MB, time=9.08 NO POLE x[1] = 2.444 y[1] (analytic) = 1.642374582200313195248718593442 y[1] (numeric) = 1.642374582200313159407750886148 absolute error = 3.58409677072940e-17 relative error = 2.1822651236648665451635993237834e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.445 y[1] (analytic) = 1.6416078703161076505692228014556 y[1] (numeric) = 1.641607870316107614697035851935 absolute error = 3.58721869495206e-17 relative error = 2.1851860970070190738172943915225e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.446 y[1] (analytic) = 1.6408405168240852571028205384981 y[1] (numeric) = 1.6408405168240852211994516235806 absolute error = 3.59033689149175e-17 relative error = 2.1881083838915653274202075131455e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.447 y[1] (analytic) = 1.6400725224915994429257830673099 y[1] (numeric) = 1.6400725224915994069912694950071 absolute error = 3.59345135723028e-17 relative error = 2.1910319866655078902191768854794e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.448 y[1] (analytic) = 1.6393038880866444765243989910949 y[1] (numeric) = 1.6393038880866444405587781005629 absolute error = 3.59656208905320e-17 relative error = 2.1939569076792830446925892703332e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.449 y[1] (analytic) = 1.638534614377854698800769766752 y[1] (numeric) = 1.6385346143778546628040789282544 absolute error = 3.59966908384976e-17 relative error = 2.1968831492867427329953075389743e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.45 y[1] (analytic) = 1.6377647021345037544385328556338 y[1] (numeric) = 1.637764702134503718410809470504 absolute error = 3.60277233851298e-17 relative error = 2.1998107138452036316592388388470e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.451 y[1] (analytic) = 1.6369941521265038226292811460435 y[1] (numeric) = 1.6369941521265037865705626466476 absolute error = 3.60587184993959e-17 relative error = 2.2027396037154169502940850171118e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.452 y[1] (analytic) = 1.6362229651244048471604479209885 y[1] (numeric) = 1.6362229651244048110707717706877 absolute error = 3.60896761503008e-17 relative error = 2.2056698212616053723457777647501e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.453 y[1] (analytic) = 1.6354511418993937658654272832402 y[1] (numeric) = 1.6354511418993937297448309763532 absolute error = 3.61205963068870e-17 relative error = 2.2086013688514695270698638461252e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.454 y[1] (analytic) = 1.6346786832232937394367005875158 y[1] (numeric) = 1.6346786832232937032852216492815 absolute error = 3.61514789382343e-17 relative error = 2.2115342488561761269878685104108e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.455 y[1] (analytic) = 1.6339055898685633796027400665917 y[1] (numeric) = 1.6339055898685633434204160531316 absolute error = 3.61823240134601e-17 relative error = 2.2144684636503827928261869588192e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.456 y[1] (analytic) = 1.6331318626082959766694614743798 y[1] (numeric) = 1.6331318626082959404563299726606 absolute error = 3.62131315017192e-17 relative error = 2.2174040156122323321938662503187e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.457 y[1] (analytic) = 1.6323575022162187264269982044508 y[1] (numeric) = 1.6323575022162186901830968322467 absolute error = 3.62439013722041e-17 relative error = 2.2203409071233776317879276564427e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.458 y[1] (analytic) = 1.631582509466691956422569977165 y[1] (numeric) = 1.6315825094666919201479363830199 absolute error = 3.62746335941451e-17 relative error = 2.2232791405689943616663066671422e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.459 y[1] (analytic) = 1.6308068851347083516002198224772 y[1] (numeric) = 1.6308068851347083152948916856674 absolute error = 3.63053281368098e-17 relative error = 2.2262187183377569234086025457838e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.46 y[1] (analytic) = 1.6300306299958921793081937186159 y[1] (numeric) = 1.6300306299958921429722087491121 absolute error = 3.63359849695038e-17 relative error = 2.2291596428218879470419051271808e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.461 y[1] (analytic) = 1.6292537448264985136747378791905 y[1] (numeric) = 1.6292537448264984773081338176202 absolute error = 3.63666040615703e-17 relative error = 2.2321019164171404130348277092522e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.462 y[1] (analytic) = 1.6284762304034124593530893128656 y[1] (numeric) = 1.6284762304034124229559039304755 absolute error = 3.63971853823901e-17 relative error = 2.2350455415228042851617970648964e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.463 y[1] (analytic) = 1.6276980875041483746364359105474 y[1] (numeric) = 1.6276980875041483382087070091656 absolute error = 3.64277289013818e-17 relative error = 2.2379905205417254487546362651211e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.464 y[1] (analytic) = 1.6269193169068490939436229450571 y[1] (numeric) = 1.626919316906849057485388357055 absolute error = 3.64582345880021e-17 relative error = 2.2409368558803308489700486274384e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.465 y[1] (analytic) = 1.6261399193902851496763834975192 y[1] (numeric) = 1.626139919390285113187681085774 absolute error = 3.64887024117452e-17 relative error = 2.2438845499485983546332133728877e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.466 y[1] (analytic) = 1.6253598957338539934488709531707 y[1] (numeric) = 1.6253598957338539569297386110275 absolute error = 3.65191323421432e-17 relative error = 2.2468336051600880592898753857184e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=9.32 NO POLE x[1] = 2.467 y[1] (analytic) = 1.6245792467175792166902723369937 y[1] (numeric) = 1.6245792467175791801407479882273 absolute error = 3.65495243487664e-17 relative error = 2.2497840239319675159660446854096e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.468 y[1] (analytic) = 1.6237979731221097706212818864913 y[1] (numeric) = 1.6237979731221097340414034852687 absolute error = 3.65798784012226e-17 relative error = 2.2527358086849754597711458598830e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.469 y[1] (analytic) = 1.6230160757287191856052148850713 y[1] (numeric) = 1.6230160757287191489950204159135 absolute error = 3.66101944691578e-17 relative error = 2.2556889618434716838813519953293e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.47 y[1] (analytic) = 1.6222335553193047898745424048558 y[1] (numeric) = 1.6222335553193047532340698825998 absolute error = 3.66404725222560e-17 relative error = 2.2586434858354315796123533672890e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.471 y[1] (analytic) = 1.6214504126763869276336282323186 y[1] (numeric) = 1.6214504126763868909629157020796 absolute error = 3.66707125302390e-17 relative error = 2.2615993830924406596851233745556e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.472 y[1] (analytic) = 1.6206666485831081765384498739484 y[1] (numeric) = 1.6206666485831081398375354110815 absolute error = 3.67009144628669e-17 relative error = 2.2645566560497322566132248885268e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.473 y[1] (analytic) = 1.61988226382323256455408616215 y[1] (numeric) = 1.6198822638232325278230078722122 absolute error = 3.67310782899378e-17 relative error = 2.2675153071461759431169271352160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.474 y[1] (analytic) = 1.6190972591811447861907546038325 y[1] (numeric) = 1.6190972591811447494295506225448 absolute error = 3.67612039812877e-17 relative error = 2.2704753388242782703625681311476e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.475 y[1] (analytic) = 1.6183116354418494181191822355812 y[1] (numeric) = 1.61831163544184938132789072879 absolute error = 3.67912915067912e-17 relative error = 2.2734367535302329413962990229020e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.476 y[1] (analytic) = 1.6175253933909701341660943699759 y[1] (numeric) = 1.6175253933909700973447535336152 absolute error = 3.68213408363607e-17 relative error = 2.2763995537138783953970654087929e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.477 y[1] (analytic) = 1.616738533814748919690606237503 y[1] (numeric) = 1.6167385338147488828392542975563 absolute error = 3.68513519399467e-17 relative error = 2.2793637418287233052316380871880e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.478 y[1] (analytic) = 1.6159510575000452853423031476038 y[1] (numeric) = 1.6159510575000452484609783600657 absolute error = 3.68813247875381e-17 relative error = 2.2823293203319721481945193481970e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.479 y[1] (analytic) = 1.6151629652343354802017954107127 y[1] (numeric) = 1.6151629652343354432905360615505 absolute error = 3.69112593491622e-17 relative error = 2.2852962916845322763357955131597e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.48 y[1] (analytic) = 1.6143742578057117043045348806656 y[1] (numeric) = 1.6143742578057116673633792857812 absolute error = 3.69411555948844e-17 relative error = 2.2882646583510024232380828919539e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.481 y[1] (analytic) = 1.6135849360028813205486805935955 y[1] (numeric) = 1.6135849360028812835776670987871 absolute error = 3.69710134948084e-17 relative error = 2.2912344227996921627035708319290e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.482 y[1] (analytic) = 1.6127950006151660659878015953853 y[1] (numeric) = 1.6127950006151660289869685763089 absolute error = 3.70008330190764e-17 relative error = 2.2942055875026414232241338540188e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.483 y[1] (analytic) = 1.6120044524325012625092056649077 y[1] (numeric) = 1.6120044524325012254785915270389 absolute error = 3.70306141378688e-17 relative error = 2.2971781549356090412222890257485e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.484 y[1] (analytic) = 1.6112132922454350268986832546588 y[1] (numeric) = 1.6112132922454349898383264332543 absolute error = 3.70603568214045e-17 relative error = 2.3001521275780985182542832900856e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.485 y[1] (analytic) = 1.6104215208451274802924565839752 y[1] (numeric) = 1.6104215208451274432023955440343 absolute error = 3.70900610399409e-17 relative error = 2.3031275079133652240594330771532e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.486 y[1] (analytic) = 1.6096291390233499570171244328196 y[1] (numeric) = 1.6096291390233499198973976690459 absolute error = 3.71197267637737e-17 relative error = 2.3061042984284111942600032061810e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.487 y[1] (analytic) = 1.6088361475724842128183937961245 y[1] (numeric) = 1.6088361475724841756690398328873 absolute error = 3.71493539632372e-17 relative error = 2.3090825016140109896043847381286e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.488 y[1] (analytic) = 1.6080425472855216324793901698958 y[1] (numeric) = 1.6080425472855215953004475611917 absolute error = 3.71789426087041e-17 relative error = 2.3120621199647065365329026675241e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.489 y[1] (analytic) = 1.6072483389560624368293388507008 y[1] (numeric) = 1.6072483389560623996208461801148 absolute error = 3.72084926705860e-17 relative error = 2.3150431559788455036683831823585e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=9.57 NO POLE x[1] = 2.49 y[1] (analytic) = 1.6064535233783148891434102397918 y[1] (numeric) = 1.6064535233783148519054061204592 absolute error = 3.72380041193326e-17 relative error = 2.3180256121585388670498478587025e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.491 y[1] (analytic) = 1.6056581013470945009345227519563 y[1] (numeric) = 1.6056581013470944636670458265237 absolute error = 3.72674769254326e-17 relative error = 2.3210094910097242233847696936892e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.492 y[1] (analytic) = 1.6048620736578232371378975372216 y[1] (numeric) = 1.6048620736578231998409864778085 absolute error = 3.72969110594131e-17 relative error = 2.3239947950421358239885063955388e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.493 y[1] (analytic) = 1.6040654411065287206891598307957 y[1] (numeric) = 1.6040654411065286833628533389557 absolute error = 3.73263064918400e-17 relative error = 2.3269815267693368595464644848306e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.494 y[1] (analytic) = 1.6032682044898434364967823530747 y[1] (numeric) = 1.6032682044898433991411191597568 absolute error = 3.73556631933179e-17 relative error = 2.3299696887087206531725006676028e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.495 y[1] (analytic) = 1.6024703646050039348096667872084 y[1] (numeric) = 1.6024703646050038974246856527184 absolute error = 3.73849811344900e-17 relative error = 2.3329592833815118554064222662579e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.496 y[1] (analytic) = 1.601671922249850033980659966576 y[1] (numeric) = 1.6016719222498499965663996805374 absolute error = 3.74142602860386e-17 relative error = 2.3359503133128051019437564628671e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.497 y[1] (analytic) = 1.6008728782228240226268020085877 y[1] (numeric) = 1.6008728782228239851833013899035 absolute error = 3.74435006186842e-17 relative error = 2.3389427810315163330767842446906e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.498 y[1] (analytic) = 1.6000732333229698611871042345008 y[1] (numeric) = 1.600073233322969823714402131314 absolute error = 3.74727021031868e-17 relative error = 2.3419366890704714592409679677121e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.499 y[1] (analytic) = 1.5992729883499323828786553174019 y[1] (numeric) = 1.5992729883499323453767906070572 absolute error = 3.75018647103447e-17 relative error = 2.3449320399663389697457159819390e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.5 y[1] (analytic) = 1.5984721441039564940518547021862 y[1] (numeric) = 1.5984721441039564565208662911907 absolute error = 3.75309884109955e-17 relative error = 2.3479288362596999687841856862503e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.501 y[1] (analytic) = 1.5976707013858863739455729422307 y[1] (numeric) = 1.5976707013858863363854997662154 absolute error = 3.75600731760153e-17 relative error = 2.3509270804950057561938917647177e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.502 y[1] (analytic) = 1.5968686609971646738430391975371 y[1] (numeric) = 1.5968686609971646362539202212176 absolute error = 3.75891189763195e-17 relative error = 2.3539267752206354747651682163457e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.503 y[1] (analytic) = 1.5960660237398317156292567383872 y[1] (numeric) = 1.5960660237398316780111309555251 absolute error = 3.76181257828621e-17 relative error = 2.3569279229888599483836334012724e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.504 y[1] (analytic) = 1.5952627904165246897507478970316 y[1] (numeric) = 1.5952627904165246521036543303952 absolute error = 3.76470935666364e-17 relative error = 2.3599305263558931689720490594997e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.505 y[1] (analytic) = 1.5944589618304768525784305075974 y[1] (numeric) = 1.5944589618304768149024082089226 absolute error = 3.76760222986748e-17 relative error = 2.3629345878818874916198857720574e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.506 y[1] (analytic) = 1.5936545387855167231744284712725 y[1] (numeric) = 1.5936545387855166854695165212242 absolute error = 3.77049119500483e-17 relative error = 2.3659401101309099886383413719394e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.507 y[1] (analytic) = 1.59284952208606727946361967989 y[1] (numeric) = 1.5928495220860672417298571880227 absolute error = 3.77337624918673e-17 relative error = 2.3689470956710003446781043934382e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.508 y[1] (analytic) = 1.5920439125371451538107251262958 y[1] (numeric) = 1.5920439125371451160481512310145 absolute error = 3.77625738952813e-17 relative error = 2.3719555470741598318643912846400e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.509 y[1] (analytic) = 1.591237710944359828003743624345 y[1] (numeric) = 1.591237710944359790212397492866 absolute error = 3.77913461314790e-17 relative error = 2.3749654669163653871350437729882e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.51 y[1] (analytic) = 1.590430918113912827644537155024 y[1] (numeric) = 1.590430918113912789824457983336 absolute error = 3.78200791716880e-17 relative error = 2.3779768577775585799177018554280e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.511 y[1] (analytic) = 1.5896235348525969159473724480472 y[1] (numeric) = 1.5896235348525968780985994608718 absolute error = 3.78487729871754e-17 relative error = 2.3809897222416911612698501792458e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.512 y[1] (analytic) = 1.5888155619677952869462250003178 y[1] (numeric) = 1.5888155619677952490687974510705 absolute error = 3.78774275492473e-17 relative error = 2.3840040628967015157953381367292e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=152.5MB, alloc=4.4MB, time=9.82 x[1] = 2.513 y[1] (analytic) = 1.5880070002674807581116523238833 y[1] (numeric) = 1.5880070002674807202056094946341 absolute error = 3.79060428292492e-17 relative error = 2.3870198823345477143649669370199e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.514 y[1] (analytic) = 1.5871978505602149623780438064436 y[1] (numeric) = 1.5871978505602149244434250078778 absolute error = 3.79346187985658e-17 relative error = 2.3900371831512028631835804802074e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.515 y[1] (analytic) = 1.5863881136551475395820551570956 y[1] (numeric) = 1.5863881136551475016188997284745 absolute error = 3.79631554286211e-17 relative error = 2.3930559679466693473122274501687e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.516 y[1] (analytic) = 1.5855777903620153273130359988119 y[1] (numeric) = 1.5855777903620152893213833079334 absolute error = 3.79916526908785e-17 relative error = 2.3960762393249931155719419096977e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.517 y[1] (analytic) = 1.5847668814911415511762597571587 y[1] (numeric) = 1.5847668814911415131561492003179 absolute error = 3.80201105568408e-17 relative error = 2.3990979998942716969285687210760e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.518 y[1] (analytic) = 1.5839553878534350144697655819554 y[1] (numeric) = 1.5839553878534349764212365839054 absolute error = 3.80485289980500e-17 relative error = 2.4021212522666496125964944668875e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.519 y[1] (analytic) = 1.583143310260389287275622624967 y[1] (numeric) = 1.5831433102603892491987146388793 absolute error = 3.80769079860877e-17 relative error = 2.4051459990583516709623593604508e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.52 y[1] (analytic) = 1.5823306495240818949664275822971 y[1] (numeric) = 1.5823306495240818568611800897221 absolute error = 3.81052474925750e-17 relative error = 2.4081722428896847636936734185256e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.521 y[1] (analytic) = 1.5815174064571735061278469949155 y[1] (numeric) = 1.5815174064571734679942995057432 absolute error = 3.81335474891723e-17 relative error = 2.4111999863850333419908862948774e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.522 y[1] (analytic) = 1.5807035818729071198980163847122 y[1] (numeric) = 1.5807035818729070817362084371325 absolute error = 3.81618079475797e-17 relative error = 2.4142292321728928342133999374097e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.523 y[1] (analytic) = 1.5798891765851072527246088866095 y[1] (numeric) = 1.5798891765851072145345800470728 absolute error = 3.81900288395367e-17 relative error = 2.4172599828858588574142620934279e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.524 y[1] (analytic) = 1.5790741914081791245403866195961 y[1] (numeric) = 1.5790741914081790863221764827737 absolute error = 3.82182101368224e-17 relative error = 2.4202922411606480571444894131178e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.525 y[1] (analytic) = 1.5782586271571078443580486210646 y[1] (numeric) = 1.5782586271571078061116968098091 absolute error = 3.82463518112555e-17 relative error = 2.4233260096381063370857565773324e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.526 y[1] (analytic) = 1.5774424846474575952851897495358 y[1] (numeric) = 1.5774424846474575570107359148415 absolute error = 3.82744538346943e-17 relative error = 2.4263612909632171116673733801656e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.527 y[1] (analytic) = 1.5766257646953708189601855407438 y[1] (numeric) = 1.5766257646953707806576693617069 absolute error = 3.83025161790369e-17 relative error = 2.4293980877851222670471030082263e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.528 y[1] (analytic) = 1.5758084681175673994098185811278 y[1] (numeric) = 1.5758084681175673610792797649069 absolute error = 3.83305388162209e-17 relative error = 2.4324364027571114549297321977770e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.529 y[1] (analytic) = 1.574990595731343846329462541038 y[1] (numeric) = 1.5749905957313438079709408228145 absolute error = 3.83585217182235e-17 relative error = 2.4354762385366367473861673942731e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.53 y[1] (analytic) = 1.5741721483545724777866405874022 y[1] (numeric) = 1.5741721483545724394001757303402 absolute error = 3.83864648570620e-17 relative error = 2.4385175977853527448047066116961e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.531 y[1] (analytic) = 1.5733531268057006023487754722264 y[1] (numeric) = 1.5733531268057005639344072674332 absolute error = 3.84143682047932e-17 relative error = 2.4415604831690868919655989629797e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.532 y[1] (analytic) = 1.5725335319037497006359491691127 y[1] (numeric) = 1.5725335319037496621937174355989 absolute error = 3.84422317335138e-17 relative error = 2.4446048973578732902959299555778e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.533 y[1] (analytic) = 1.5717133644683146062994905049646 y[1] (numeric) = 1.5717133644683145678294350896044 absolute error = 3.84700554153602e-17 relative error = 2.4476508430259484381973397297107e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.534 y[1] (analytic) = 1.5708926253195626864272098082259 y[1] (numeric) = 1.5708926253195626479293705857171 absolute error = 3.84978392225088e-17 relative error = 2.4506983228517787842608453466377e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.535 y[1] (analytic) = 1.5700713152782330213761001683481 y[1] (numeric) = 1.5700713152782329828505170411724 absolute error = 3.85255831271757e-17 relative error = 2.4537473395180501492267091291167e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=156.4MB, alloc=4.4MB, time=10.06 x[1] = 2.536 y[1] (analytic) = 1.5692494351656355840333254737188 y[1] (numeric) = 1.5692494351656355454800383721018 absolute error = 3.85532871016170e-17 relative error = 2.4567978957116953466941654765766e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.537 y[1] (analytic) = 1.5684269858036504185063159669933 y[1] (numeric) = 1.5684269858036503799253648488644 absolute error = 3.85809511181289e-17 relative error = 2.4598499941239091361078319820796e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.538 y[1] (analytic) = 1.5676039680147268182427926276654 y[1] (numeric) = 1.5676039680147267796342174786182 absolute error = 3.86085751490472e-17 relative error = 2.4629036374501249449387456386149e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.539 y[1] (analytic) = 1.5667803826218825035815422617857 y[1] (numeric) = 1.5667803826218824649453830950377 absolute error = 3.86361591667480e-17 relative error = 2.4659588283900681046897214163502e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.54 y[1] (analytic) = 1.565956230448702798734765747982 y[1] (numeric) = 1.5659562304487027600710626043349 absolute error = 3.86637031436471e-17 relative error = 2.4690155696477262354768072233999e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.541 y[1] (analytic) = 1.5651315123193398082028224573671 y[1] (numeric) = 1.5651315123193397695116154051664 absolute error = 3.86912070522007e-17 relative error = 2.4720738639314025941284195896663e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.542 y[1] (analytic) = 1.5643062290585115926221944325187 y[1] (numeric) = 1.5643062290585115539035235676139 absolute error = 3.87186708649048e-17 relative error = 2.4751337139536864840059923925487e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.543 y[1] (analytic) = 1.5634803814915013440474944775003 y[1] (numeric) = 1.5634803814915013053013999232046 absolute error = 3.87460945542957e-17 relative error = 2.4781951224314939238837660899306e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.544 y[1] (analytic) = 1.5626539704441565606683428768454 y[1] (numeric) = 1.5626539704441565218948647838959 absolute error = 3.87734780929495e-17 relative error = 2.4812580920860444489118522522958e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.545 y[1] (analytic) = 1.56182699674288822096193802656 y[1] (numeric) = 1.5618269967428881821611165730771 absolute error = 3.88008214534829e-17 relative error = 2.4843226256429210705874106983495e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.546 y[1] (analytic) = 1.5609994612146699572821468245029 y[1] (numeric) = 1.5609994612146699184540222159505 absolute error = 3.88281246085524e-17 relative error = 2.4873887258320279256531690408312e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.547 y[1] (analytic) = 1.5601713646870372288859412309866 y[1] (numeric) = 1.5601713646870371900305537001317 absolute error = 3.88553875308549e-17 relative error = 2.4904563953876375207278881498828e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.548 y[1] (analytic) = 1.5593427079880864943980079730907 y[1] (numeric) = 1.5593427079880864555153977799632 absolute error = 3.88826101931275e-17 relative error = 2.4935256370483868204587690251504e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.549 y[1] (analytic) = 1.5585134919464743837143589280114 y[1] (numeric) = 1.5585134919464743448045663598639 absolute error = 3.89097925681475e-17 relative error = 2.4965964535572861526393507923031e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.55 y[1] (analytic) = 1.5576837173914168693457702817662 y[1] (numeric) = 1.5576837173914168304088356530337 absolute error = 3.89369346287325e-17 relative error = 2.4996688476617345581760964676961e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.551 y[1] (analytic) = 1.5568533851526884372018791197471 y[1] (numeric) = 1.5568533851526883982378427720065 absolute error = 3.89640363477406e-17 relative error = 2.5027428221135416099398870351315e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.552 y[1] (analytic) = 1.5560224960606212568167666649541 y[1] (numeric) = 1.5560224960606212178256689668842 absolute error = 3.89910976980699e-17 relative error = 2.5058183796689043115671749488294e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.553 y[1] (analytic) = 1.5551910509461043510168579382599 y[1] (numeric) = 1.5551910509461043119987392856008 absolute error = 3.90181186526591e-17 relative error = 2.5088955230884546495810256189016e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.554 y[1] (analytic) = 1.5543590506405827650319681727342 y[1] (numeric) = 1.5543590506405827259868689882469 absolute error = 3.90450991844873e-17 relative error = 2.5119742551372558264160767625150e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.555 y[1] (analytic) = 1.5535264959760567350503268709131 y[1] (numeric) = 1.5535264959760566959782876043392 absolute error = 3.90720392665739e-17 relative error = 2.5150545785848049148032969770041e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.556 y[1] (analytic) = 1.5526933877850808562184109499206 y[1] (numeric) = 1.5526933877850808171194720779418 absolute error = 3.90989388719788e-17 relative error = 2.5181364962050548383539333073828e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.557 y[1] (analytic) = 1.5518597269007632500864189745387 y[1] (numeric) = 1.5518597269007632109606210007362 absolute error = 3.91257979738025e-17 relative error = 2.5212200107764299754178340369067e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.558 y[1] (analytic) = 1.5510255141567647315002190326836 y[1] (numeric) = 1.5510255141567646923476024874977 absolute error = 3.91526165451859e-17 relative error = 2.5243051250818224675844508899630e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.559 y[1] (analytic) = 1.5501907503872979749406033612695 y[1] (numeric) = 1.5501907503872979357612088019592 absolute error = 3.91793945593103e-17 relative error = 2.5273918419086014142113782561005e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=10.32 NO POLE x[1] = 2.56 y[1] (analytic) = 1.5493554364271266803106833831373 y[1] (numeric) = 1.5493554364271266411045513937395 absolute error = 3.92061319893978e-17 relative error = 2.5304801640486479100834726224491e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.561 y[1] (analytic) = 1.5485195731115647381722593675822 y[1] (numeric) = 1.5485195731115646989394305588713 absolute error = 3.92328288087109e-17 relative error = 2.5335700942983385304542995181408e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.562 y[1] (analytic) = 1.5476831612764753944319994780423 y[1] (numeric) = 1.5476831612764753551725144874895 absolute error = 3.92594849905528e-17 relative error = 2.5366616354585739876742574984904e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.563 y[1] (analytic) = 1.5468462017582704144782635206983 y[1] (numeric) = 1.5468462017582703751921630124309 absolute error = 3.92861005082674e-17 relative error = 2.5397547903347884826073181602332e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.564 y[1] (analytic) = 1.546008695393909246769407257092 y[1] (numeric) = 1.5460086953939092074567319218529 absolute error = 3.93126753352391e-17 relative error = 2.5428495617369461460165217161255e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.565 y[1] (analytic) = 1.5451706430208981858744036923889 y[1] (numeric) = 1.5451706430208981465351942474958 absolute error = 3.93392094448931e-17 relative error = 2.5459459524795698233174989201767e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.566 y[1] (analytic) = 1.544332045477289534966618298594 y[1] (numeric) = 1.5443320454772894956009154878987 absolute error = 3.93657028106953e-17 relative error = 2.5490439653817440478957896068355e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.567 y[1] (analytic) = 1.543492903601680767771575678876 y[1] (numeric) = 1.5434929036016807283794202727237 absolute error = 3.93921554061523e-17 relative error = 2.5521436032671244989345577135554e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.568 y[1] (analytic) = 1.5426532182332136899695557251634 y[1] (numeric) = 1.5426532182332136505509885203517 absolute error = 3.94185672048117e-17 relative error = 2.5552448689639669330616463742198e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.569 y[1] (analytic) = 1.5418129902115736000538578663454 y[1] (numeric) = 1.541812990211573560608919686084 absolute error = 3.94449381802614e-17 relative error = 2.5583477653050913477546064605526e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.57 y[1] (analytic) = 1.5409722203769884496455725487458 y[1] (numeric) = 1.5409722203769884101743042426153 absolute error = 3.94712683061305e-17 relative error = 2.5614522951279498539036742929542e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.571 y[1] (analytic) = 1.5401309095702280032656996340259 y[1] (numeric) = 1.5401309095702279637681420779368 absolute error = 3.94975575560891e-17 relative error = 2.5645584612746233439622608414234e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.572 y[1] (analytic) = 1.539289058632602997565453942329 y[1] (numeric) = 1.5392890586326029580416480384813 absolute error = 3.95238059038477e-17 relative error = 2.5676662665917921590308181685044e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.573 y[1] (analytic) = 1.5384466684059643000155987102919 y[1] (numeric) = 1.5384466684059642604655853871338 absolute error = 3.95500133231581e-17 relative error = 2.5707757139308041562848508549467e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.574 y[1] (analytic) = 1.5376037397327020670556482745177 y[1] (numeric) = 1.5376037397327020274794684867049 absolute error = 3.95761797878128e-17 relative error = 2.5738868061476454414165283961533e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.575 y[1] (analytic) = 1.5367602734557449017037818312394 y[1] (numeric) = 1.536760273455744862101476559594 absolute error = 3.96023052716454e-17 relative error = 2.5769995461029760724238924768251e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.576 y[1] (analytic) = 1.535916270418559010628310662188 y[1] (numeric) = 1.5359162704185589709999209136577 absolute error = 3.96283897485303e-17 relative error = 2.5801139366621203012338603107251e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.577 y[1] (analytic) = 1.5350717314651473606815417551302 y[1] (numeric) = 1.5350717314651473210271085627469 absolute error = 3.96544331923833e-17 relative error = 2.5832299806951154078976632579088e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.578 y[1] (analytic) = 1.5342266574400488348968812851386 y[1] (numeric) = 1.534226657440048795216445707978 absolute error = 3.96804355771606e-17 relative error = 2.5863476810766564045588517319941e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.579 y[1] (analytic) = 1.5333810491883373879500219594245 y[1] (numeric) = 1.5333810491883373482436250825644 absolute error = 3.97063968768601e-17 relative error = 2.5894670406861905473924307208926e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.58 y[1] (analytic) = 1.5325349075556212010850587644716 y[1] (numeric) = 1.5325349075556211613527416989513 absolute error = 3.97323170655203e-17 relative error = 2.5925880624078555535610791853393e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.581 y[1] (analytic) = 1.5316882333880418365063781892878 y[1] (numeric) = 1.5316882333880417967481820720666 absolute error = 3.97581961172212e-17 relative error = 2.5957107491305481837360536607563e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.582 y[1] (analytic) = 1.5308410275322733912371665328125 y[1] (numeric) = 1.5308410275322733514531325267288 absolute error = 3.97840340060837e-17 relative error = 2.5988351037478950621708901816876e-15 % h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=10.57 NO POLE x[1] = 2.583 y[1] (analytic) = 1.529993290835521650445383436903 y[1] (numeric) = 1.5299932908355216106355527306333 absolute error = 3.98098307062697e-17 relative error = 2.6019611291582691470306706121151e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.584 y[1] (analytic) = 1.529145024145523240238047318855 y[1] (numeric) = 1.5291450241455232004024611268722 absolute error = 3.98355861919828e-17 relative error = 2.6050888282648454883262672772441e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.585 y[1] (analytic) = 1.5282962283105447799246799091 y[1] (numeric) = 1.5282962283105447400633794716326 absolute error = 3.98613004374674e-17 relative error = 2.6082182039755524750603965787347e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.586 y[1] (analytic) = 1.5274469041793820337507576305664 y[1] (numeric) = 1.5274469041793819938637842135573 absolute error = 3.98869734170091e-17 relative error = 2.6113492592031080244021445476336e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.587 y[1] (analytic) = 1.5265970526013590621020180861816 y[1] (numeric) = 1.5265970526013590221894129812463 absolute error = 3.99126051049353e-17 relative error = 2.6144819968650689877544783332139e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.588 y[1] (analytic) = 1.525746674426327372180470450136 y[1] (numeric) = 1.5257466744263273322422749745221 absolute error = 3.99381954756139e-17 relative error = 2.6176164198837561879125598967805e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.589 y[1] (analytic) = 1.5248957705046650681529590868315 y[1] (numeric) = 1.5248957705046650281892145833767 absolute error = 3.99637445034548e-17 relative error = 2.6207525311863628195629358805363e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.59 y[1] (analytic) = 1.5240443416872760007731302488759 y[1] (numeric) = 1.5240443416872759607838780859671 absolute error = 3.99892521629088e-17 relative error = 2.6238903337048926091475361086198e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.591 y[1] (analytic) = 1.5231923888255889164776522320893 y[1] (numeric) = 1.5231923888255888764629338036209 absolute error = 4.00147184284684e-17 relative error = 2.6270298303762225003879312529006e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.592 y[1] (analytic) = 1.5223399127715566059575398912282 y[1] (numeric) = 1.522339912771556565917396616561 absolute error = 4.00401432746672e-17 relative error = 2.6301710241420735814782178511562e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.593 y[1] (analytic) = 1.5214869143776550522054349450348 y[1] (numeric) = 1.5214869143776550121399082689544 absolute error = 4.00655266760804e-17 relative error = 2.6333139179490542071422978403991e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.594 y[1] (analytic) = 1.5206333944968825780396940232579 y[1] (numeric) = 1.5206333944968825379488254159332 absolute error = 4.00908686073247e-17 relative error = 2.6364585147486638033788841426160e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.595 y[1] (analytic) = 1.5197793539827589931061369314874 y[1] (numeric) = 1.5197793539827589529899678884292 absolute error = 4.01161690430582e-17 relative error = 2.6396048174972966798544527792486e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.596 y[1] (analytic) = 1.518924793689324740358308131983 y[1] (numeric) = 1.5189247936893247002168801740027 absolute error = 4.01414279579803e-17 relative error = 2.6427528291562458498961946831797e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.597 y[1] (analytic) = 1.5180697144711400420171049601642 y[1] (numeric) = 1.5180697144711400018504596333322 absolute error = 4.01666453268320e-17 relative error = 2.6459025526917332072877725205072e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.598 y[1] (analytic) = 1.5172141171832840450106266170629 y[1] (numeric) = 1.5172141171832840048188054926667 absolute error = 4.01918211243962e-17 relative error = 2.6490539910749397997225731409624e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.599 y[1] (analytic) = 1.5163580026813539658950984978166 y[1] (numeric) = 1.5163580026813539256781431723196 absolute error = 4.02169553254970e-17 relative error = 2.6522071472819702519195094157007e-15 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 2.6 y[1] (analytic) = 1.5155013718214642352577269352094 y[1] (numeric) = 1.5155013718214641950156790302092 absolute error = 4.02420479050002e-17 relative error = 2.6553620242938962444402861513471e-15 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = cos ( x ) ; Iterations = 1000 Total Elapsed Time = 10 Seconds Elapsed Time(since restart) = 10 Seconds Expected Time Remaining = 1 Minutes 19 Seconds Optimized Time Remaining = 1 Minutes 19 Seconds Time to Timeout = 14 Minutes 49 Seconds Percent Done = 11.92 % > quit memory used=167.0MB, alloc=4.4MB, time=10.75