|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_smallish_float, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > days_in_year, > djd_debug2, > glob_optimal_expect_sec, > glob_normmax, > glob_iter, > glob_warned2, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_optimal_done, > djd_debug, > glob_start, > glob_log10_relerr, > glob_hmin, > glob_max_opt_iter, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_abserr, > glob_clock_start_sec, > sec_in_min, > glob_dump, > glob_percent_done, > glob_last_good_h, > glob_hmin_init, > glob_hmax, > centuries_in_millinium, > hours_in_day, > glob_large_float, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > years_in_century, > glob_h, > glob_reached_optimal_h, > glob_almost_1, > min_in_hour, > glob_max_sec, > glob_max_rel_trunc_err, > glob_display_flag, > glob_html_log, > glob_max_minutes, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_optimal_start, > glob_abserr, > glob_clock_sec, > glob_log10normmin, > glob_current_iter, > glob_curr_iter_when_opt, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_m1, > array_type_pole, > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_norms, > array_y, > array_x, > array_fact_1, > array_complex_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_poles, > array_fact_2, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS, glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err, days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter, glob_warned2, glob_warned, glob_max_hours, glob_disp_incr, glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin, glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump, glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax, centuries_in_millinium, hours_in_day, glob_large_float, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1, min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag, glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr, glob_clock_sec, glob_log10normmin, glob_current_iter, glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0, array_pole, array_1st_rel_error, array_m1, array_type_pole, array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_norms, array_y, array_x, array_fact_1, array_complex_pole, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_real_pole, array_poles, array_fact_2, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_smallish_float, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > days_in_year, > djd_debug2, > glob_optimal_expect_sec, > glob_normmax, > glob_iter, > glob_warned2, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_optimal_done, > djd_debug, > glob_start, > glob_log10_relerr, > glob_hmin, > glob_max_opt_iter, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_abserr, > glob_clock_start_sec, > sec_in_min, > glob_dump, > glob_percent_done, > glob_last_good_h, > glob_hmin_init, > glob_hmax, > centuries_in_millinium, > hours_in_day, > glob_large_float, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > years_in_century, > glob_h, > glob_reached_optimal_h, > glob_almost_1, > min_in_hour, > glob_max_sec, > glob_max_rel_trunc_err, > glob_display_flag, > glob_html_log, > glob_max_minutes, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_optimal_start, > glob_abserr, > glob_clock_sec, > glob_log10normmin, > glob_current_iter, > glob_curr_iter_when_opt, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_m1, > array_type_pole, > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_norms, > array_y, > array_x, > array_fact_1, > array_complex_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_poles, > array_fact_2, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS, glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err, days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter, glob_warned2, glob_warned, glob_max_hours, glob_disp_incr, glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin, glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump, glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax, centuries_in_millinium, hours_in_day, glob_large_float, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1, min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag, glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr, glob_clock_sec, glob_log10normmin, glob_current_iter, glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0, array_pole, array_1st_rel_error, array_m1, array_type_pole, array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_norms, array_y, array_x, array_fact_1, array_complex_pole, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_real_pole, array_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_smallish_float, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > days_in_year, > djd_debug2, > glob_optimal_expect_sec, > glob_normmax, > glob_iter, > glob_warned2, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_optimal_done, > djd_debug, > glob_start, > glob_log10_relerr, > glob_hmin, > glob_max_opt_iter, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_abserr, > glob_clock_start_sec, > sec_in_min, > glob_dump, > glob_percent_done, > glob_last_good_h, > glob_hmin_init, > glob_hmax, > centuries_in_millinium, > hours_in_day, > glob_large_float, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > years_in_century, > glob_h, > glob_reached_optimal_h, > glob_almost_1, > min_in_hour, > glob_max_sec, > glob_max_rel_trunc_err, > glob_display_flag, > glob_html_log, > glob_max_minutes, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_optimal_start, > glob_abserr, > glob_clock_sec, > glob_log10normmin, > glob_current_iter, > glob_curr_iter_when_opt, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_m1, > array_type_pole, > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_norms, > array_y, > array_x, > array_fact_1, > array_complex_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_poles, > array_fact_2, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS, glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err, days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter, glob_warned2, glob_warned, glob_max_hours, glob_disp_incr, glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin, glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump, glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax, centuries_in_millinium, hours_in_day, glob_large_float, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1, min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag, glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr, glob_clock_sec, glob_log10normmin, glob_current_iter, glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0, array_pole, array_1st_rel_error, array_m1, array_type_pole, array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_norms, array_y, array_x, array_fact_1, array_complex_pole, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_real_pole, array_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_smallish_float, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > days_in_year, > djd_debug2, > glob_optimal_expect_sec, > glob_normmax, > glob_iter, > glob_warned2, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_optimal_done, > djd_debug, > glob_start, > glob_log10_relerr, > glob_hmin, > glob_max_opt_iter, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_abserr, > glob_clock_start_sec, > sec_in_min, > glob_dump, > glob_percent_done, > glob_last_good_h, > glob_hmin_init, > glob_hmax, > centuries_in_millinium, > hours_in_day, > glob_large_float, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > years_in_century, > glob_h, > glob_reached_optimal_h, > glob_almost_1, > min_in_hour, > glob_max_sec, > glob_max_rel_trunc_err, > glob_display_flag, > glob_html_log, > glob_max_minutes, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_optimal_start, > glob_abserr, > glob_clock_sec, > glob_log10normmin, > glob_current_iter, > glob_curr_iter_when_opt, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_m1, > array_type_pole, > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_norms, > array_y, > array_x, > array_fact_1, > array_complex_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_poles, > array_fact_2, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS, glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err, days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter, glob_warned2, glob_warned, glob_max_hours, glob_disp_incr, glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin, glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump, glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax, centuries_in_millinium, hours_in_day, glob_large_float, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1, min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag, glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr, glob_clock_sec, glob_log10normmin, glob_current_iter, glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0, array_pole, array_1st_rel_error, array_m1, array_type_pole, array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_norms, array_y, array_x, array_fact_1, array_complex_pole, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_real_pole, array_poles, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_smallish_float, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > days_in_year, > djd_debug2, > glob_optimal_expect_sec, > glob_normmax, > glob_iter, > glob_warned2, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_optimal_done, > djd_debug, > glob_start, > glob_log10_relerr, > glob_hmin, > glob_max_opt_iter, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_abserr, > glob_clock_start_sec, > sec_in_min, > glob_dump, > glob_percent_done, > glob_last_good_h, > glob_hmin_init, > glob_hmax, > centuries_in_millinium, > hours_in_day, > glob_large_float, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > years_in_century, > glob_h, > glob_reached_optimal_h, > glob_almost_1, > min_in_hour, > glob_max_sec, > glob_max_rel_trunc_err, > glob_display_flag, > glob_html_log, > glob_max_minutes, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_optimal_start, > glob_abserr, > glob_clock_sec, > glob_log10normmin, > glob_current_iter, > glob_curr_iter_when_opt, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_m1, > array_type_pole, > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_norms, > array_y, > array_x, > array_fact_1, > array_complex_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_poles, > array_fact_2, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS, glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err, days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter, glob_warned2, glob_warned, glob_max_hours, glob_disp_incr, glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin, glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump, glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax, centuries_in_millinium, hours_in_day, glob_large_float, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1, min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag, glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr, glob_clock_sec, glob_log10normmin, glob_current_iter, glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0, array_pole, array_1st_rel_error, array_m1, array_type_pole, array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_norms, array_y, array_x, array_fact_1, array_complex_pole, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_real_pole, array_poles, array_fact_2, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_smallish_float, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > days_in_year, > djd_debug2, > glob_optimal_expect_sec, > glob_normmax, > glob_iter, > glob_warned2, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_optimal_done, > djd_debug, > glob_start, > glob_log10_relerr, > glob_hmin, > glob_max_opt_iter, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_abserr, > glob_clock_start_sec, > sec_in_min, > glob_dump, > glob_percent_done, > glob_last_good_h, > glob_hmin_init, > glob_hmax, > centuries_in_millinium, > hours_in_day, > glob_large_float, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > years_in_century, > glob_h, > glob_reached_optimal_h, > glob_almost_1, > min_in_hour, > glob_max_sec, > glob_max_rel_trunc_err, > glob_display_flag, > glob_html_log, > glob_max_minutes, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_optimal_start, > glob_abserr, > glob_clock_sec, > glob_log10normmin, > glob_current_iter, > glob_curr_iter_when_opt, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_m1, > array_type_pole, > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_norms, > array_y, > array_x, > array_fact_1, > array_complex_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_poles, > array_fact_2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin $eq_no = 1 iii = 1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin $eq_no = 1 iii = 2 > #emit pre sin 2 $eq_no = 1 > array_tmp1[2] := att(1,array_tmp1_g,array_x,1); > array_tmp1_g[2] := -att(1,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin $eq_no = 1 iii = 3 > #emit pre sin 3 $eq_no = 1 > array_tmp1[3] := att(2,array_tmp1_g,array_x,1); > array_tmp1_g[3] := -att(2,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin $eq_no = 1 iii = 4 > #emit pre sin 4 $eq_no = 1 > array_tmp1[4] := att(3,array_tmp1_g,array_x,1); > array_tmp1_g[4] := -att(3,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin $eq_no = 1 iii = 5 > #emit pre sin 5 $eq_no = 1 > array_tmp1[5] := att(4,array_tmp1_g,array_x,1); > array_tmp1_g[5] := -att(4,array_tmp1,array_x,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin $eq_no = 1 > array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1); > array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS, glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err, days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter, glob_warned2, glob_warned, glob_max_hours, glob_disp_incr, glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin, glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump, glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax, centuries_in_millinium, hours_in_day, glob_large_float, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1, min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag, glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr, glob_clock_sec, glob_log10normmin, glob_current_iter, glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0, array_pole, array_1st_rel_error, array_m1, array_type_pole, array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_norms, array_y, array_x, array_fact_1, array_complex_pole, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_real_pole, array_poles, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := att(1, array_tmp1_g, array_x, 1); array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := att(2, array_tmp1_g, array_x, 1); array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := att(3, array_tmp1_g, array_x, 1); array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := att(4, array_tmp1_g, array_x, 1); array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > if (nnn <= glob_max_terms) then # if number 13 > ret := array_fact_1[nnn]; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; Warning, `ret` is implicitly declared local to procedure `factorial_1` factorial_1 := proc(nnn) local ret; if nnn <= glob_max_terms then ret := array_fact_1[nnn] else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > ret := array_fact_2[mmm,nnn]; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; Warning, `ret` is implicitly declared local to procedure `factorial_3` factorial_3 := proc(mmm, nnn) local ret; if nnn <= glob_max_terms and mmm <= glob_max_terms then ret := array_fact_2[mmm, nnn] else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 2.0 - cos(x); > end; exact_soln_y := proc(x) 2.0 - cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGMASSIVE, > glob_iolevel, > DEBUGL, > glob_max_terms, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_smallish_float, > glob_small_float, > glob_no_eqs, > glob_max_trunc_err, > days_in_year, > djd_debug2, > glob_optimal_expect_sec, > glob_normmax, > glob_iter, > glob_warned2, > glob_warned, > glob_max_hours, > glob_disp_incr, > glob_optimal_done, > djd_debug, > glob_start, > glob_log10_relerr, > glob_hmin, > glob_max_opt_iter, > glob_subiter_method, > glob_optimal_clock_start_sec, > glob_log10_abserr, > glob_clock_start_sec, > sec_in_min, > glob_dump, > glob_percent_done, > glob_last_good_h, > glob_hmin_init, > glob_hmax, > centuries_in_millinium, > hours_in_day, > glob_large_float, > glob_unchanged_h_cnt, > glob_max_iter, > glob_relerr, > glob_look_poles, > glob_not_yet_start_msg, > glob_initial_pass, > glob_not_yet_finished, > years_in_century, > glob_h, > glob_reached_optimal_h, > glob_almost_1, > min_in_hour, > glob_max_sec, > glob_max_rel_trunc_err, > glob_display_flag, > glob_html_log, > glob_max_minutes, > glob_log10relerr, > glob_log10abserr, > MAX_UNCHANGED, > glob_orig_start_sec, > glob_optimal_start, > glob_abserr, > glob_clock_sec, > glob_log10normmin, > glob_current_iter, > glob_curr_iter_when_opt, > glob_dump_analytic, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_pole, > array_1st_rel_error, > array_m1, > array_type_pole, > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp1_g, > array_norms, > array_y, > array_x, > array_fact_1, > array_complex_pole, > array_y_set_initial, > array_y_higher_work2, > array_y_higher_work, > array_y_higher, > array_real_pole, > array_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > DEBUGL := 3; > glob_max_terms := 30; > INFO := 2; > ALWAYS := 1; > glob_smallish_float := 0.1e-100; > glob_small_float := 0.1e-50; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > days_in_year := 365.0; > djd_debug2 := true; > glob_optimal_expect_sec := 0.1; > glob_normmax := 0.0; > glob_iter := 0; > glob_warned2 := false; > glob_warned := false; > glob_max_hours := 0.0; > glob_disp_incr := 0.1; > glob_optimal_done := false; > djd_debug := true; > glob_start := 0; > glob_log10_relerr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_max_opt_iter := 10; > glob_subiter_method := 3; > glob_optimal_clock_start_sec := 0.0; > glob_log10_abserr := 0.1e-10; > glob_clock_start_sec := 0.0; > sec_in_min := 60.0; > glob_dump := false; > glob_percent_done := 0.0; > glob_last_good_h := 0.1; > glob_hmin_init := 0.001; > glob_hmax := 1.0; > centuries_in_millinium := 10.0; > hours_in_day := 24.0; > glob_large_float := 9.0e100; > glob_unchanged_h_cnt := 0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_look_poles := false; > glob_not_yet_start_msg := true; > glob_initial_pass := true; > glob_not_yet_finished := true; > years_in_century := 100.0; > glob_h := 0.1; > glob_reached_optimal_h := false; > glob_almost_1 := 0.9990; > min_in_hour := 60.0; > glob_max_sec := 10000.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_display_flag := true; > glob_html_log := true; > glob_max_minutes := 0.0; > glob_log10relerr := 0.0; > glob_log10abserr := 0.0; > MAX_UNCHANGED := 10; > glob_orig_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_abserr := 0.1e-10; > glob_clock_sec := 0.0; > glob_log10normmin := 0.1; > glob_current_iter := 0; > glob_curr_iter_when_opt := 0; > glob_dump_analytic := false; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 16;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.05;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"2.0 - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 16; > 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_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > 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_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[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_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[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_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_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 > temp1 := iiif !; > temp2 := jjjf !; > array_fact_1[iiif] := temp1; > array_fact_2[iiif,jjjf] := temp1/temp2; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.05; > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin(x);"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-17T02:56:25-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x);") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 091 ") > ; > logitem_str(html_log_file,"sin diffeq.mxt") > ; > logitem_str(html_log_file,"sin maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly for speeding factorials") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `iiif` is implicitly declared local to procedure `mainprog` Warning, `jjjf` is implicitly declared local to procedure `mainprog` Warning, `temp1` is implicitly declared local to procedure `mainprog` Warning, `temp2` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, iiif, jjjf, temp1, temp2; global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS, glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err, days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter, glob_warned2, glob_warned, glob_max_hours, glob_disp_incr, glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin, glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec, glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump, glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax, centuries_in_millinium, hours_in_day, glob_large_float, glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles, glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished, years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1, min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag, glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr, MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr, glob_clock_sec, glob_log10normmin, glob_current_iter, glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0, array_pole, array_1st_rel_error, array_m1, array_type_pole, array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp1_g, array_norms, array_y, array_x, array_fact_1, array_complex_pole, array_y_set_initial, array_y_higher_work2, array_y_higher_work, array_y_higher, array_real_pole, array_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; glob_iolevel := 5; DEBUGL := 3; glob_max_terms := 30; INFO := 2; ALWAYS := 1; glob_smallish_float := 0.1*10^(-100); glob_small_float := 0.1*10^(-50); glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); days_in_year := 365.0; djd_debug2 := true; glob_optimal_expect_sec := 0.1; glob_normmax := 0.; glob_iter := 0; glob_warned2 := false; glob_warned := false; glob_max_hours := 0.; glob_disp_incr := 0.1; glob_optimal_done := false; djd_debug := true; glob_start := 0; glob_log10_relerr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_max_opt_iter := 10; glob_subiter_method := 3; glob_optimal_clock_start_sec := 0.; glob_log10_abserr := 0.1*10^(-10); glob_clock_start_sec := 0.; sec_in_min := 60.0; glob_dump := false; glob_percent_done := 0.; glob_last_good_h := 0.1; glob_hmin_init := 0.001; glob_hmax := 1.0; centuries_in_millinium := 10.0; hours_in_day := 24.0; glob_large_float := 0.90*10^101; glob_unchanged_h_cnt := 0; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_look_poles := false; glob_not_yet_start_msg := true; glob_initial_pass := true; glob_not_yet_finished := true; years_in_century := 100.0; glob_h := 0.1; glob_reached_optimal_h := false; glob_almost_1 := 0.9990; min_in_hour := 60.0; glob_max_sec := 10000.0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_display_flag := true; glob_html_log := true; glob_max_minutes := 0.; glob_log10relerr := 0.; glob_log10abserr := 0.; MAX_UNCHANGED := 10; glob_orig_start_sec := 0.; glob_optimal_start := 0.; glob_abserr := 0.1*10^(-10); glob_clock_sec := 0.; glob_log10normmin := 0.1; glob_current_iter := 0; glob_curr_iter_when_opt := 0; glob_dump_analytic := false; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 16;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.05;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "2.0 - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 16; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[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_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[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_fact_1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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 <= 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; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_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 temp1 := iiif!; temp2 := jjjf!; array_fact_1[iiif] := temp1; array_fact_2[iiif, jjjf] := temp1/temp2; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 1000000; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin(x);"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-17T02:56:25-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x);"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 091 "); logitem_str(html_log_file, "sin diffeq.mxt"); logitem_str(html_log_file, "sin maple results"); logitem_str(html_log_file, "Test of revised logic - mostly for speeding factorials"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK Digits := 16; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.05; glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 2.0 - cos(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.001 y[1] (analytic) = 1.000000499999958 y[1] (numeric) = 1.000000499999958 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 1.000001999999333 y[1] (numeric) = 1.000001999999333 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 1.000004499996625 y[1] (numeric) = 1.000004499996625 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.004 y[1] (analytic) = 1.000007999989333 y[1] (numeric) = 1.000007999989333 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 1.000012499973958 y[1] (numeric) = 1.000012499973958 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 1.000017999946 y[1] (numeric) = 1.000017999946 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 1.000024499899958 y[1] (numeric) = 1.000024499899958 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 1.000031999829334 y[1] (numeric) = 1.000031999829333 absolute error = 1e-15 relative error = 9.999680011946223e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 1.000040499726626 y[1] (numeric) = 1.000040499726625 absolute error = 1e-15 relative error = 9.999595019135354e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 1.000049999583335 y[1] (numeric) = 1.000049999583334 absolute error = 1e-15 relative error = 9.999500029164983e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 1.000060499389961 y[1] (numeric) = 1.00006049938996 absolute error = 1e-15 relative error = 9.999395042699938e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 1.000071999136004 y[1] (numeric) = 1.000071999136003 absolute error = 1e-15 relative error = 9.999280060474984e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 1.000084498809965 y[1] (numeric) = 1.000084498809964 absolute error = 1e-15 relative error = 9.999155083294806e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 1.000097998399344 y[1] (numeric) = 1.000097998399343 absolute error = 1e-15 relative error = 9.999020112034012e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.20 NO POLE x[1] = 0.015 y[1] (analytic) = 1.000112497890641 y[1] (numeric) = 1.00011249789064 absolute error = 1e-15 relative error = 9.998875147637108e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 1.000127997269357 y[1] (numeric) = 1.000127997269356 absolute error = 1e-15 relative error = 9.998720191118472e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 1.000144496519992 y[1] (numeric) = 1.000144496519991 absolute error = 1e-15 relative error = 9.998555243562357e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 1.000161995626047 y[1] (numeric) = 1.000161995626046 absolute error = 1e-15 relative error = 9.998380306122854e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 1.000180494570024 y[1] (numeric) = 1.000180494570022 absolute error = 2e-15 relative error = 1.999639076004773e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 1.000199993333422 y[1] (numeric) = 1.000199993333421 absolute error = 1e-15 relative error = 9.998000466559138e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 1.000220491896744 y[1] (numeric) = 1.000220491896743 absolute error = 1e-15 relative error = 9.997795567092153e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 1.000241990239491 y[1] (numeric) = 1.00024199023949 absolute error = 1e-15 relative error = 9.997580683056177e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 1.000264488340164 y[1] (numeric) = 1.000264488340163 absolute error = 1e-15 relative error = 9.997355815954209e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 1.000287986176265 y[1] (numeric) = 1.000287986176264 absolute error = 1e-15 relative error = 9.997120967358952e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 1.000312483724297 y[1] (numeric) = 1.000312483724296 absolute error = 1e-15 relative error = 9.996876138912777e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.026 y[1] (analytic) = 1.000337980959762 y[1] (numeric) = 1.000337980959761 absolute error = 1e-15 relative error = 9.996621332327723e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 1.000364477857163 y[1] (numeric) = 1.000364477857162 absolute error = 1e-15 relative error = 9.996356549385443e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 1.000391974390003 y[1] (numeric) = 1.000391974390002 absolute error = 1e-15 relative error = 9.996081791937185e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 1.000420470530784 y[1] (numeric) = 1.000420470530784 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 1.000449966251012 y[1] (numeric) = 1.000449966251012 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 1.000480461521191 y[1] (numeric) = 1.00048046152119 absolute error = 1e-15 relative error = 9.995197692112243e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 1.000511956310825 y[1] (numeric) = 1.000511956310824 absolute error = 1e-15 relative error = 9.994883056543245e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 1.000544450588419 y[1] (numeric) = 1.000544450588418 absolute error = 1e-15 relative error = 9.994558456767225e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 1.000577944321479 y[1] (numeric) = 1.000577944321478 absolute error = 1e-15 relative error = 9.994223895052265e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 1.000612437476511 y[1] (numeric) = 1.000612437476511 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 1.000647930019023 y[1] (numeric) = 1.000647930019023 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 1.000684421913522 y[1] (numeric) = 1.000684421913522 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 1.000721913123515 y[1] (numeric) = 1.000721913123515 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 1.000760403611512 y[1] (numeric) = 1.000760403611512 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.1MB, time=0.45 NO POLE x[1] = 0.04 y[1] (analytic) = 1.000799893339022 y[1] (numeric) = 1.000799893339022 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.041 y[1] (analytic) = 1.000840382266556 y[1] (numeric) = 1.000840382266555 absolute error = 1e-15 relative error = 9.991603233827828e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 1.000881870353623 y[1] (numeric) = 1.000881870353623 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 1.000924357558738 y[1] (numeric) = 1.000924357558737 absolute error = 1e-15 relative error = 9.990764960890826e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 1.000967843839411 y[1] (numeric) = 1.00096784383941 absolute error = 1e-15 relative error = 9.990330919765628e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 1.001012329152158 y[1] (numeric) = 1.001012329152156 absolute error = 2e-15 relative error = 1.997977389243516e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 1.001057813452492 y[1] (numeric) = 1.00105781345249 absolute error = 2e-15 relative error = 1.997886608668797e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 1.001104296694929 y[1] (numeric) = 1.001104296694927 absolute error = 2e-15 relative error = 1.997793842862178e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 1.001151778832986 y[1] (numeric) = 1.001151778832984 absolute error = 2e-15 relative error = 1.997699092470617e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 1.001200259819182 y[1] (numeric) = 1.001200259819179 absolute error = 3e-15 relative error = 2.996403537232205e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 1.001249739605034 y[1] (numeric) = 1.001249739605031 absolute error = 3e-15 relative error = 2.996255460883734e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 1.001300218141063 y[1] (numeric) = 1.00130021814106 absolute error = 3e-15 relative error = 2.996104410692698e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 1.001351695376791 y[1] (numeric) = 1.001351695376788 absolute error = 3e-15 relative error = 2.995950387711835e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 1.001404171260741 y[1] (numeric) = 1.001404171260737 absolute error = 4e-15 relative error = 3.994391190685882e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 1.001457645740436 y[1] (numeric) = 1.001457645740432 absolute error = 4e-15 relative error = 3.994177903592285e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 1.001512118762402 y[1] (numeric) = 1.001512118762398 absolute error = 4e-15 relative error = 3.993960657154022e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.056 y[1] (analytic) = 1.001567590272166 y[1] (numeric) = 1.001567590272162 absolute error = 4e-15 relative error = 3.993739452884093e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 1.001624060214256 y[1] (numeric) = 1.001624060214253 absolute error = 3e-15 relative error = 2.995135719242082e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 1.001681528532203 y[1] (numeric) = 1.0016815285322 absolute error = 3e-15 relative error = 2.994963882778191e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 1.001739995168539 y[1] (numeric) = 1.001739995168535 absolute error = 4e-15 relative error = 3.993052108623271e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 1.001799460064796 y[1] (numeric) = 1.001799460064792 absolute error = 4e-15 relative error = 3.992815088701766e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.061 y[1] (analytic) = 1.00185992316151 y[1] (numeric) = 1.001859923161506 absolute error = 4e-15 relative error = 3.992574118922171e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 1.001921384398217 y[1] (numeric) = 1.001921384398213 absolute error = 4e-15 relative error = 3.992329200960728e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 1.001983843713457 y[1] (numeric) = 1.001983843713453 absolute error = 4e-15 relative error = 3.992080336520778e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 1.00204730104477 y[1] (numeric) = 1.002047301044766 absolute error = 4e-15 relative error = 3.991827527332750e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 1.002111756328699 y[1] (numeric) = 1.002111756328695 absolute error = 4e-15 relative error = 3.991570775154118e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=0.70 NO POLE x[1] = 0.066 y[1] (analytic) = 1.002177209500788 y[1] (numeric) = 1.002177209500784 absolute error = 4e-15 relative error = 3.991310081769381e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.067 y[1] (analytic) = 1.002243660495585 y[1] (numeric) = 1.002243660495581 absolute error = 4e-15 relative error = 3.991045448990017e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 1.002311109246638 y[1] (numeric) = 1.002311109246634 absolute error = 4e-15 relative error = 3.990776878654473e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 1.002379555686499 y[1] (numeric) = 1.002379555686495 absolute error = 4e-15 relative error = 3.990504372628114e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 1.00244899974672 y[1] (numeric) = 1.002448999746717 absolute error = 3e-15 relative error = 2.992670949602407e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 1.002519441357859 y[1] (numeric) = 1.002519441357856 absolute error = 3e-15 relative error = 2.992460670824159e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 1.002590880449474 y[1] (numeric) = 1.00259088044947 absolute error = 4e-15 relative error = 3.989663259461078e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 1.002663316950125 y[1] (numeric) = 1.002663316950121 absolute error = 4e-15 relative error = 3.989375029862562e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 1.002736750787376 y[1] (numeric) = 1.002736750787372 absolute error = 4e-15 relative error = 3.989082874302844e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 1.002811181887793 y[1] (numeric) = 1.002811181887789 absolute error = 4e-15 relative error = 3.988786794808167e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 1.002886610176944 y[1] (numeric) = 1.002886610176941 absolute error = 3e-15 relative error = 2.991365095073605e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 1.002963035579403 y[1] (numeric) = 1.0029630355794 absolute error = 3e-15 relative error = 2.991137154189263e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 1.003040458018743 y[1] (numeric) = 1.00304045801874 absolute error = 3e-15 relative error = 2.990906275032768e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 1.003118877417542 y[1] (numeric) = 1.003118877417539 absolute error = 3e-15 relative error = 2.990672459203725e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 1.003198293697381 y[1] (numeric) = 1.003198293697377 absolute error = 4e-15 relative error = 3.987247611095536e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 1.003278706778842 y[1] (numeric) = 1.003278706778839 absolute error = 3e-15 relative error = 2.990196024025960e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 1.003360116581514 y[1] (numeric) = 1.003360116581511 absolute error = 3e-15 relative error = 2.989953407975906e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 1.003442523023986 y[1] (numeric) = 1.003442523023983 absolute error = 3e-15 relative error = 2.989707861850587e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 1.003525926023852 y[1] (numeric) = 1.003525926023849 absolute error = 3e-15 relative error = 2.989459387348898e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 1.00361032549771 y[1] (numeric) = 1.003610325497706 absolute error = 4e-15 relative error = 3.985610648252669e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.086 y[1] (analytic) = 1.003695721361158 y[1] (numeric) = 1.003695721361155 absolute error = 3e-15 relative error = 2.988953660110817e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 1.003782113528802 y[1] (numeric) = 1.003782113528799 absolute error = 3e-15 relative error = 2.988696410870963e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 1.00386950191425 y[1] (numeric) = 1.003869501914247 absolute error = 3e-15 relative error = 2.988436240247747e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 1.003957886430112 y[1] (numeric) = 1.00395788643011 absolute error = 2e-15 relative error = 1.992115433359091e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 1.004047266988006 y[1] (numeric) = 1.004047266988003 absolute error = 3e-15 relative error = 2.987907142060710e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 1.004137643498549 y[1] (numeric) = 1.004137643498546 absolute error = 3e-15 memory used=15.2MB, alloc=4.2MB, time=0.96 relative error = 2.987638218150652e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 1.004229015871366 y[1] (numeric) = 1.004229015871363 absolute error = 3e-15 relative error = 2.987366380164698e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 1.004321384015084 y[1] (numeric) = 1.004321384015081 absolute error = 3e-15 relative error = 2.987091629978619e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 1.004414747837335 y[1] (numeric) = 1.004414747837332 absolute error = 3e-15 relative error = 2.986813969487682e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 1.004509107244755 y[1] (numeric) = 1.004509107244752 absolute error = 3e-15 relative error = 2.986533400606622e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 1.004604462142985 y[1] (numeric) = 1.004604462142982 absolute error = 3e-15 relative error = 2.986249925269604e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.097 y[1] (analytic) = 1.00470081243667 y[1] (numeric) = 1.004700812436667 absolute error = 3e-15 relative error = 2.985963545430198e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 1.004798158029459 y[1] (numeric) = 1.004798158029456 absolute error = 3e-15 relative error = 2.985674263061343e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 1.004896498824008 y[1] (numeric) = 1.004896498824004 absolute error = 4e-15 relative error = 3.980509440207073e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 1.004995834721974 y[1] (numeric) = 1.004995834721971 absolute error = 3e-15 relative error = 2.985086998723663e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 1.005096165624023 y[1] (numeric) = 1.00509616562402 absolute error = 3e-15 relative error = 2.984789020797252e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 1.005197491429824 y[1] (numeric) = 1.005197491429821 absolute error = 3e-15 relative error = 2.984488148426144e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 1.00529981203805 y[1] (numeric) = 1.005299812038047 absolute error = 3e-15 relative error = 2.984184383679614e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 1.005403127346382 y[1] (numeric) = 1.005403127346378 absolute error = 4e-15 relative error = 3.978503638194789e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 1.005507437251503 y[1] (numeric) = 1.005507437251499 absolute error = 4e-15 relative error = 3.978090913910862e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 1.005612741649104 y[1] (numeric) = 1.0056127416491 absolute error = 4e-15 relative error = 3.977674341556573e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 1.00571904043388 y[1] (numeric) = 1.005719040433876 absolute error = 4e-15 relative error = 3.977253923992877e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 1.005826333499533 y[1] (numeric) = 1.005826333499529 absolute error = 4e-15 relative error = 3.976829664106082e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 1.00593462073877 y[1] (numeric) = 1.005934620738766 absolute error = 4e-15 relative error = 3.976401564807814e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 1.006043902043303 y[1] (numeric) = 1.006043902043299 absolute error = 4e-15 relative error = 3.975969629034965e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 1.006154177303852 y[1] (numeric) = 1.006154177303847 absolute error = 5e-15 relative error = 4.969417324687042e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 1.00626544641014 y[1] (numeric) = 1.006265446410135 absolute error = 5e-15 relative error = 4.968867824923871e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 1.006377709250899 y[1] (numeric) = 1.006377709250894 absolute error = 5e-15 relative error = 4.968313540769667e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 1.006490965713866 y[1] (numeric) = 1.006490965713861 absolute error = 5e-15 relative error = 4.967754476021242e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 1.006605215685784 y[1] (numeric) = 1.006605215685779 absolute error = 5e-15 relative error = 4.967190634506677e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 1.006720459052404 y[1] (numeric) = 1.006720459052399 absolute error = 5e-15 relative error = 4.966622020085249e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=19.0MB, alloc=4.2MB, time=1.22 x[1] = 0.117 y[1] (analytic) = 1.006836695698482 y[1] (numeric) = 1.006836695698477 absolute error = 5e-15 relative error = 4.966048636647380e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 1.006953925507782 y[1] (numeric) = 1.006953925507777 absolute error = 5e-15 relative error = 4.965470488114561e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 1.007072148363073 y[1] (numeric) = 1.007072148363068 absolute error = 5e-15 relative error = 4.964887578439299e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 1.007191364146134 y[1] (numeric) = 1.007191364146128 absolute error = 6e-15 relative error = 5.957159893926033e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 1.007311572737747 y[1] (numeric) = 1.007311572737741 absolute error = 6e-15 relative error = 5.956448989951291e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 1.007432774017705 y[1] (numeric) = 1.007432774017699 absolute error = 6e-15 relative error = 5.955732387057078e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 1.007554967864806 y[1] (numeric) = 1.0075549678648 absolute error = 6e-15 relative error = 5.955010090134439e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 1.007678154156857 y[1] (numeric) = 1.007678154156851 absolute error = 6e-15 relative error = 5.954282104111219e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 1.007802332770671 y[1] (numeric) = 1.007802332770665 absolute error = 6e-15 relative error = 5.953548433951999e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 1.007927503582069 y[1] (numeric) = 1.007927503582063 absolute error = 6e-15 relative error = 5.952809084658001e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 1.008053666465882 y[1] (numeric) = 1.008053666465875 absolute error = 7e-15 relative error = 6.944074738144825e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 1.008180821295944 y[1] (numeric) = 1.008180821295938 absolute error = 6e-15 relative error = 5.951313368853249e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 1.008308967945104 y[1] (numeric) = 1.008308967945097 absolute error = 7e-15 relative error = 6.942316514615295e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 1.008438106285212 y[1] (numeric) = 1.008438106285205 absolute error = 7e-15 relative error = 6.941427497009144e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 1.008568236187132 y[1] (numeric) = 1.008568236187125 absolute error = 7e-15 relative error = 6.940531883557360e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 1.008699357520732 y[1] (numeric) = 1.008699357520726 absolute error = 6e-15 relative error = 5.948254011727851e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 1.008831470154893 y[1] (numeric) = 1.008831470154887 absolute error = 6e-15 relative error = 5.947475051584957e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 1.008964573957501 y[1] (numeric) = 1.008964573957495 absolute error = 6e-15 relative error = 5.946690453626104e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 1.009098668795452 y[1] (numeric) = 1.009098668795446 absolute error = 6e-15 relative error = 5.945900223178495e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 1.009233754534652 y[1] (numeric) = 1.009233754534646 absolute error = 6e-15 relative error = 5.945104365605114e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 1.009369831040015 y[1] (numeric) = 1.009369831040009 absolute error = 6e-15 relative error = 5.944302886304652e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 1.009506898175464 y[1] (numeric) = 1.009506898175458 absolute error = 6e-15 relative error = 5.943495790711408e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 1.009644955803933 y[1] (numeric) = 1.009644955803927 absolute error = 6e-15 relative error = 5.942683084295193e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 1.009784003787363 y[1] (numeric) = 1.009784003787357 absolute error = 6e-15 relative error = 5.941864772561262e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 1.009924041986707 y[1] (numeric) = 1.009924041986701 absolute error = 6e-15 relative error = 5.941040861050196e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 1.010065070261926 y[1] (numeric) = 1.01006507026192 absolute error = 6e-15 relative error = 5.940211355337834e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=22.8MB, alloc=4.3MB, time=1.49 x[1] = 0.143 y[1] (analytic) = 1.010207088471993 y[1] (numeric) = 1.010207088471987 absolute error = 6e-15 relative error = 5.939376261035159e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 1.010350096474888 y[1] (numeric) = 1.010350096474883 absolute error = 5e-15 relative error = 4.948779653156864e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 1.010494094127605 y[1] (numeric) = 1.0104940941276 absolute error = 5e-15 relative error = 4.948074441065067e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 1.010639081286145 y[1] (numeric) = 1.01063908128614 absolute error = 5e-15 relative error = 4.947364586017168e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 1.010785057805522 y[1] (numeric) = 1.010785057805516 absolute error = 6e-15 relative error = 5.935980111366484e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.148 y[1] (analytic) = 1.010932023539758 y[1] (numeric) = 1.010932023539752 absolute error = 6e-15 relative error = 5.935117159501112e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 1.011079978341888 y[1] (numeric) = 1.011079978341882 absolute error = 6e-15 relative error = 5.934248653444457e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 1.011228922063958 y[1] (numeric) = 1.011228922063951 absolute error = 7e-15 relative error = 6.922270365559486e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 1.011378854557023 y[1] (numeric) = 1.011378854557016 absolute error = 7e-15 relative error = 6.921244169244523e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 1.011529775671151 y[1] (numeric) = 1.011529775671144 absolute error = 7e-15 relative error = 6.920211513650691e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.153 y[1] (analytic) = 1.011681685255421 y[1] (numeric) = 1.011681685255414 absolute error = 7e-15 relative error = 6.919172405728288e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.154 y[1] (analytic) = 1.011834583157923 y[1] (numeric) = 1.011834583157916 absolute error = 7e-15 relative error = 6.918126852467414e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 1.01198846922576 y[1] (numeric) = 1.011988469225753 absolute error = 7e-15 relative error = 6.917074860897848e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.156 y[1] (analytic) = 1.012143343305046 y[1] (numeric) = 1.012143343305038 absolute error = 8e-15 relative error = 7.904018786387365e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 1.012299205240905 y[1] (numeric) = 1.012299205240898 absolute error = 7e-15 relative error = 6.914951591149529e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 1.012456054877477 y[1] (numeric) = 1.01245605487747 absolute error = 7e-15 relative error = 6.913880327227743e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.159 y[1] (analytic) = 1.012613892057912 y[1] (numeric) = 1.012613892057905 absolute error = 7e-15 relative error = 6.912802653510965e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 1.012772716624373 y[1] (numeric) = 1.012772716624366 absolute error = 7e-15 relative error = 6.911718577225682e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 1.012932528418035 y[1] (numeric) = 1.012932528418028 absolute error = 7e-15 relative error = 6.910628105637373e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.162 y[1] (analytic) = 1.013093327279086 y[1] (numeric) = 1.013093327279079 absolute error = 7e-15 relative error = 6.909531246050391e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 1.013255113046728 y[1] (numeric) = 1.013255113046721 absolute error = 7e-15 relative error = 6.908428005807835e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 1.013417885559174 y[1] (numeric) = 1.013417885559167 absolute error = 7e-15 relative error = 6.907318392291456e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.165 y[1] (analytic) = 1.013581644653652 y[1] (numeric) = 1.013581644653646 absolute error = 6e-15 relative error = 5.919602068218434e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 1.013746390166404 y[1] (numeric) = 1.013746390166398 absolute error = 6e-15 relative error = 5.918640064419973e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 1.013912121932683 y[1] (numeric) = 1.013912121932677 absolute error = 6e-15 relative error = 5.917672616994671e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 1.014078839786758 y[1] (numeric) = 1.014078839786752 absolute error = 6e-15 relative error = 5.916699732401170e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=26.7MB, alloc=4.3MB, time=1.75 x[1] = 0.169 y[1] (analytic) = 1.014246543561912 y[1] (numeric) = 1.014246543561905 absolute error = 7e-15 relative error = 6.901674986652497e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.17 y[1] (analytic) = 1.014415233090439 y[1] (numeric) = 1.014415233090433 absolute error = 6e-15 relative error = 5.914737677707051e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 1.014584908203652 y[1] (numeric) = 1.014584908203645 absolute error = 7e-15 relative error = 6.899373274134025e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 1.014755568731874 y[1] (numeric) = 1.014755568731867 absolute error = 7e-15 relative error = 6.898212944766396e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 1.014927214504445 y[1] (numeric) = 1.014927214504438 absolute error = 7e-15 relative error = 6.897046310279369e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 1.015099845349719 y[1] (numeric) = 1.015099845349713 absolute error = 6e-15 relative error = 5.910748610086625e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.175 y[1] (analytic) = 1.015273461095066 y[1] (numeric) = 1.01527346109506 absolute error = 6e-15 relative error = 5.909737848883046e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.176 y[1] (analytic) = 1.01544806156687 y[1] (numeric) = 1.015448061566864 absolute error = 6e-15 relative error = 5.908721703345222e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.177 y[1] (analytic) = 1.015623646590531 y[1] (numeric) = 1.015623646590524 absolute error = 7e-15 relative error = 6.892316876924972e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 1.015800215990463 y[1] (numeric) = 1.015800215990456 absolute error = 7e-15 relative error = 6.891118834006746e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.179 y[1] (analytic) = 1.015977769590096 y[1] (numeric) = 1.01597776959009 absolute error = 6e-15 relative error = 5.905641028366936e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.18 y[1] (analytic) = 1.016156307211879 y[1] (numeric) = 1.016156307211872 absolute error = 7e-15 relative error = 6.888703982172330e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 1.016335828677272 y[1] (numeric) = 1.016335828677265 absolute error = 7e-15 relative error = 6.887487189259354e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 1.016516333806754 y[1] (numeric) = 1.016516333806747 absolute error = 7e-15 relative error = 6.886264162412114e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 1.01669782241982 y[1] (numeric) = 1.016697822419814 absolute error = 6e-15 relative error = 5.901458494048441e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 1.016880294334983 y[1] (numeric) = 1.016880294334976 absolute error = 7e-15 relative error = 6.883799439321266e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 1.017063749369768 y[1] (numeric) = 1.017063749369762 absolute error = 6e-15 relative error = 5.899335222318119e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.186 y[1] (analytic) = 1.017248187340723 y[1] (numeric) = 1.017248187340717 absolute error = 6e-15 relative error = 5.898265609777219e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 1.017433608063409 y[1] (numeric) = 1.017433608063402 absolute error = 7e-15 relative error = 6.880055803664530e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.188 y[1] (analytic) = 1.017620011352404 y[1] (numeric) = 1.017620011352397 absolute error = 7e-15 relative error = 6.878795544416515e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.189 y[1] (analytic) = 1.017807397021306 y[1] (numeric) = 1.017807397021299 absolute error = 7e-15 relative error = 6.877529108636914e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 1.01799576488273 y[1] (numeric) = 1.017995764882722 absolute error = 8e-15 relative error = 7.858578862478446e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 1.018185114748306 y[1] (numeric) = 1.018185114748299 absolute error = 7e-15 relative error = 6.874977740889868e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 1.018375446428686 y[1] (numeric) = 1.018375446428679 absolute error = 7e-15 relative error = 6.873692825713852e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.193 y[1] (analytic) = 1.018566759733538 y[1] (numeric) = 1.018566759733531 absolute error = 7e-15 relative error = 6.872401767588836e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 1.018759054471549 y[1] (numeric) = 1.018759054471541 absolute error = 8e-15 relative error = 7.852690942854748e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.3MB, time=2.00 x[1] = 0.195 y[1] (analytic) = 1.018952330450423 y[1] (numeric) = 1.018952330450415 absolute error = 8e-15 relative error = 7.851201435952983e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 1.019146587476885 y[1] (numeric) = 1.019146587476877 absolute error = 8e-15 relative error = 7.849704937741791e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 1.019341825356677 y[1] (numeric) = 1.01934182535667 absolute error = 7e-15 relative error = 6.867176275780341e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 1.019538043894563 y[1] (numeric) = 1.019538043894556 absolute error = 7e-15 relative error = 6.865854630848788e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 1.019735242894323 y[1] (numeric) = 1.019735242894316 absolute error = 7e-15 relative error = 6.864526894384705e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2 y[1] (analytic) = 1.019933422158758 y[1] (numeric) = 1.019933422158751 absolute error = 7e-15 relative error = 6.863193075077417e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 1.02013258148969 y[1] (numeric) = 1.020132581489683 absolute error = 7e-15 relative error = 6.861853181650140e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.202 y[1] (analytic) = 1.020332720687958 y[1] (numeric) = 1.020332720687951 absolute error = 7e-15 relative error = 6.860507222859872e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.203 y[1] (analytic) = 1.020533839553424 y[1] (numeric) = 1.020533839553417 absolute error = 7e-15 relative error = 6.859155207497219e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.204 y[1] (analytic) = 1.02073593788497 y[1] (numeric) = 1.020735937884962 absolute error = 8e-15 relative error = 7.837482450727179e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.205 y[1] (analytic) = 1.020939015480495 y[1] (numeric) = 1.020939015480487 absolute error = 8e-15 relative error = 7.835923477010895e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.206 y[1] (analytic) = 1.021143072136923 y[1] (numeric) = 1.021143072136915 absolute error = 8e-15 relative error = 7.834357611865868e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.207 y[1] (analytic) = 1.021348107650198 y[1] (numeric) = 1.02134810765019 absolute error = 8e-15 relative error = 7.832784865490664e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.208 y[1] (analytic) = 1.021554121815284 y[1] (numeric) = 1.021554121815275 absolute error = 9e-15 relative error = 8.810105904136685e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.209 y[1] (analytic) = 1.021761114426166 y[1] (numeric) = 1.021761114426157 absolute error = 9e-15 relative error = 8.808321116286084e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.21 y[1] (analytic) = 1.021969085275852 y[1] (numeric) = 1.021969085275843 absolute error = 9e-15 relative error = 8.806528621725090e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.211 y[1] (analytic) = 1.022178034156371 y[1] (numeric) = 1.022178034156362 absolute error = 9e-15 relative error = 8.804728432095417e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.212 y[1] (analytic) = 1.022387960858775 y[1] (numeric) = 1.022387960858766 absolute error = 9e-15 relative error = 8.802920559080402e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.213 y[1] (analytic) = 1.022598865173136 y[1] (numeric) = 1.022598865173127 absolute error = 9e-15 relative error = 8.801105014404854e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.214 y[1] (analytic) = 1.022810746888551 y[1] (numeric) = 1.022810746888542 absolute error = 9e-15 relative error = 8.799281809834827e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.215 y[1] (analytic) = 1.023023605793138 y[1] (numeric) = 1.023023605793128 absolute error = 1.0e-14 relative error = 9.774945507974979e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.216 y[1] (analytic) = 1.023237441674037 y[1] (numeric) = 1.023237441674027 absolute error = 1.0e-14 relative error = 9.772902742534322e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.217 y[1] (analytic) = 1.023452254317413 y[1] (numeric) = 1.023452254317403 absolute error = 1.0e-14 relative error = 9.770851505593152e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.218 y[1] (analytic) = 1.023668043508454 y[1] (numeric) = 1.023668043508444 absolute error = 1.0e-14 relative error = 9.768791810406275e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.219 y[1] (analytic) = 1.023884809031369 y[1] (numeric) = 1.02388480903136 absolute error = 9e-15 relative error = 8.790051303246032e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.22 y[1] (analytic) = 1.024102550669394 y[1] (numeric) = 1.024102550669385 absolute error = 9e-15 relative error = 8.788182388684847e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=34.3MB, alloc=4.3MB, time=2.25 x[1] = 0.221 y[1] (analytic) = 1.024321268204788 y[1] (numeric) = 1.024321268204778 absolute error = 1.0e-14 relative error = 9.762562108591056e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.222 y[1] (analytic) = 1.024540961418832 y[1] (numeric) = 1.024540961418822 absolute error = 1.0e-14 relative error = 9.760468713863362e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.223 y[1] (analytic) = 1.024761630091833 y[1] (numeric) = 1.024761630091823 absolute error = 1.0e-14 relative error = 9.758366927832632e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.224 y[1] (analytic) = 1.024983274003122 y[1] (numeric) = 1.024983274003113 absolute error = 9e-15 relative error = 8.780631087617715e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.225 y[1] (analytic) = 1.025205892931057 y[1] (numeric) = 1.025205892931047 absolute error = 1.0e-14 relative error = 9.754138235988934e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.226 y[1] (analytic) = 1.025429486653017 y[1] (numeric) = 1.025429486653007 absolute error = 1.0e-14 relative error = 9.752011357348243e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.227 y[1] (analytic) = 1.025654054945409 y[1] (numeric) = 1.025654054945399 absolute error = 1.0e-14 relative error = 9.749876141748648e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.228 y[1] (analytic) = 1.025879597583666 y[1] (numeric) = 1.025879597583655 absolute error = 1.1e-14 relative error = 1.072250586317259e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.229 y[1] (analytic) = 1.026106114342243 y[1] (numeric) = 1.026106114342233 absolute error = 1.0e-14 relative error = 9.745580754491677e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.23 y[1] (analytic) = 1.026333604994625 y[1] (numeric) = 1.026333604994615 absolute error = 1.0e-14 relative error = 9.743420610350541e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.231 y[1] (analytic) = 1.026562069313321 y[1] (numeric) = 1.026562069313311 absolute error = 1.0e-14 relative error = 9.741252184282547e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.232 y[1] (analytic) = 1.026791507069866 y[1] (numeric) = 1.026791507069856 absolute error = 1.0e-14 relative error = 9.739075490151644e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.233 y[1] (analytic) = 1.027021918034824 y[1] (numeric) = 1.027021918034813 absolute error = 1.1e-14 relative error = 1.071057959605008e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.234 y[1] (analytic) = 1.027253301977782 y[1] (numeric) = 1.027253301977771 absolute error = 1.1e-14 relative error = 1.070816708870303e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.235 y[1] (analytic) = 1.027485658667357 y[1] (numeric) = 1.027485658667346 absolute error = 1.1e-14 relative error = 1.070574553251375e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.236 y[1] (analytic) = 1.027718987871192 y[1] (numeric) = 1.027718987871181 absolute error = 1.1e-14 relative error = 1.070331494291577e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.237 y[1] (analytic) = 1.027953289355959 y[1] (numeric) = 1.027953289355948 absolute error = 1.1e-14 relative error = 1.070087533538786e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.238 y[1] (analytic) = 1.028188562887355 y[1] (numeric) = 1.028188562887344 absolute error = 1.1e-14 relative error = 1.069842672545379e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.239 y[1] (analytic) = 1.028424808230107 y[1] (numeric) = 1.028424808230096 absolute error = 1.1e-14 relative error = 1.069596912868207e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.24 y[1] (analytic) = 1.02866202514797 y[1] (numeric) = 1.028662025147959 absolute error = 1.1e-14 relative error = 1.069350256068574e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.241 y[1] (analytic) = 1.028900213403727 y[1] (numeric) = 1.028900213403716 absolute error = 1.1e-14 relative error = 1.069102703712215e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.242 y[1] (analytic) = 1.02913937275919 y[1] (numeric) = 1.029139372759179 absolute error = 1.1e-14 relative error = 1.068854257369270e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.243 y[1] (analytic) = 1.029379502975199 y[1] (numeric) = 1.029379502975188 absolute error = 1.1e-14 relative error = 1.068604918614260e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.244 y[1] (analytic) = 1.029620603811624 y[1] (numeric) = 1.029620603811613 absolute error = 1.1e-14 relative error = 1.068354689026068e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.245 y[1] (analytic) = 1.029862675027365 y[1] (numeric) = 1.029862675027353 absolute error = 1.2e-14 relative error = 1.165203894750447e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.246 y[1] (analytic) = 1.030105716380349 y[1] (numeric) = 1.030105716380338 absolute error = 1.1e-14 relative error = 1.067851563687317e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=38.1MB, alloc=4.3MB, time=2.52 x[1] = 0.247 y[1] (analytic) = 1.030349727627537 y[1] (numeric) = 1.030349727627525 absolute error = 1.2e-14 relative error = 1.164653095763024e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.248 y[1] (analytic) = 1.030594708524916 y[1] (numeric) = 1.030594708524904 absolute error = 1.2e-14 relative error = 1.164376248076756e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.249 y[1] (analytic) = 1.030840658827505 y[1] (numeric) = 1.030840658827494 absolute error = 1.1e-14 relative error = 1.067090234150405e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.25 y[1] (analytic) = 1.031087578289355 y[1] (numeric) = 1.031087578289344 absolute error = 1.1e-14 relative error = 1.066834692960782e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.251 y[1] (analytic) = 1.031335466663546 y[1] (numeric) = 1.031335466663535 absolute error = 1.1e-14 relative error = 1.066578272110227e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.252 y[1] (analytic) = 1.03158432370219 y[1] (numeric) = 1.031584323702179 absolute error = 1.1e-14 relative error = 1.066320973211649e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.253 y[1] (analytic) = 1.031834149156429 y[1] (numeric) = 1.031834149156418 absolute error = 1.1e-14 relative error = 1.066062797882101e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.254 y[1] (analytic) = 1.032084942776438 y[1] (numeric) = 1.032084942776427 absolute error = 1.1e-14 relative error = 1.065803747742760e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.255 y[1] (analytic) = 1.032336704311424 y[1] (numeric) = 1.032336704311413 absolute error = 1.1e-14 relative error = 1.065543824418902e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.256 y[1] (analytic) = 1.032589433509625 y[1] (numeric) = 1.032589433509614 absolute error = 1.1e-14 relative error = 1.065283029539878e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.257 y[1] (analytic) = 1.032843130118312 y[1] (numeric) = 1.032843130118301 absolute error = 1.1e-14 relative error = 1.065021364739092e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.258 y[1] (analytic) = 1.033097793883788 y[1] (numeric) = 1.033097793883777 absolute error = 1.1e-14 relative error = 1.064758831653974e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.259 y[1] (analytic) = 1.03335342455139 y[1] (numeric) = 1.033353424551379 absolute error = 1.1e-14 relative error = 1.064495431925958e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.26 y[1] (analytic) = 1.033610021865487 y[1] (numeric) = 1.033610021865476 absolute error = 1.1e-14 relative error = 1.064231167200460e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.261 y[1] (analytic) = 1.033867585569481 y[1] (numeric) = 1.03386758556947 absolute error = 1.1e-14 relative error = 1.063966039126850e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.262 y[1] (analytic) = 1.034126115405809 y[1] (numeric) = 1.034126115405798 absolute error = 1.1e-14 relative error = 1.063700049358430e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.263 y[1] (analytic) = 1.034385611115941 y[1] (numeric) = 1.03438561111593 absolute error = 1.1e-14 relative error = 1.063433199552410e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.264 y[1] (analytic) = 1.034646072440382 y[1] (numeric) = 1.034646072440371 absolute error = 1.1e-14 relative error = 1.063165491369885e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.265 y[1] (analytic) = 1.03490749911867 y[1] (numeric) = 1.034907499118659 absolute error = 1.1e-14 relative error = 1.062896926475809e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.266 y[1] (analytic) = 1.035169890889378 y[1] (numeric) = 1.035169890889367 absolute error = 1.1e-14 relative error = 1.062627506538973e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.267 y[1] (analytic) = 1.035433247490115 y[1] (numeric) = 1.035433247490104 absolute error = 1.1e-14 relative error = 1.062357233231978e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.268 y[1] (analytic) = 1.035697568657524 y[1] (numeric) = 1.035697568657513 absolute error = 1.1e-14 relative error = 1.062086108231214e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.269 y[1] (analytic) = 1.035962854127284 y[1] (numeric) = 1.035962854127273 absolute error = 1.1e-14 relative error = 1.061814133216834e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.27 y[1] (analytic) = 1.03622910363411 y[1] (numeric) = 1.036229103634099 absolute error = 1.1e-14 relative error = 1.061541309872732e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.271 y[1] (analytic) = 1.036496316911751 y[1] (numeric) = 1.036496316911741 absolute error = 1.0e-14 relative error = 9.647887635331961e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.272 y[1] (analytic) = 1.036764493692996 y[1] (numeric) = 1.036764493692985 absolute error = 1.1e-14 relative error = 1.060993124949483e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=41.9MB, alloc=4.3MB, time=2.77 x[1] = 0.273 y[1] (analytic) = 1.037033633709666 y[1] (numeric) = 1.037033633709655 absolute error = 1.1e-14 relative error = 1.060717766756601e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.274 y[1] (analytic) = 1.037303736692622 y[1] (numeric) = 1.037303736692611 absolute error = 1.1e-14 relative error = 1.060441567006479e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.275 y[1] (analytic) = 1.037574802371762 y[1] (numeric) = 1.037574802371751 absolute error = 1.1e-14 relative error = 1.060164527401342e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.276 y[1] (analytic) = 1.037846830476019 y[1] (numeric) = 1.037846830476008 absolute error = 1.1e-14 relative error = 1.059886649647014e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.277 y[1] (analytic) = 1.038119820733365 y[1] (numeric) = 1.038119820733354 absolute error = 1.1e-14 relative error = 1.059607935452885e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.278 y[1] (analytic) = 1.038393772870811 y[1] (numeric) = 1.038393772870799 absolute error = 1.2e-14 relative error = 1.155630967125700e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.279 y[1] (analytic) = 1.038668686614403 y[1] (numeric) = 1.038668686614391 absolute error = 1.2e-14 relative error = 1.155325095927812e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.28 y[1] (analytic) = 1.038944561689229 y[1] (numeric) = 1.038944561689217 absolute error = 1.2e-14 relative error = 1.155018317867615e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.281 y[1] (analytic) = 1.039221397819413 y[1] (numeric) = 1.039221397819401 absolute error = 1.2e-14 relative error = 1.154710634825213e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.282 y[1] (analytic) = 1.039499194728119 y[1] (numeric) = 1.039499194728107 absolute error = 1.2e-14 relative error = 1.154402048684473e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.283 y[1] (analytic) = 1.03977795213755 y[1] (numeric) = 1.039777952137538 absolute error = 1.2e-14 relative error = 1.154092561332994e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.284 y[1] (analytic) = 1.04005766976895 y[1] (numeric) = 1.040057669768937 absolute error = 1.3e-14 relative error = 1.249930689217259e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.285 y[1] (analytic) = 1.040338347342599 y[1] (numeric) = 1.040338347342586 absolute error = 1.3e-14 relative error = 1.249593464780637e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.286 y[1] (analytic) = 1.040619984577821 y[1] (numeric) = 1.040619984577808 absolute error = 1.3e-14 relative error = 1.249255270191077e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.287 y[1] (analytic) = 1.040902581192978 y[1] (numeric) = 1.040902581192966 absolute error = 1.2e-14 relative error = 1.152845637700966e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.288 y[1] (analytic) = 1.041186136905475 y[1] (numeric) = 1.041186136905462 absolute error = 1.3e-14 relative error = 1.248575978800246e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.289 y[1] (analytic) = 1.041470651431754 y[1] (numeric) = 1.041470651431742 absolute error = 1.2e-14 relative error = 1.152216817968235e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.29 y[1] (analytic) = 1.041756124487303 y[1] (numeric) = 1.04175612448729 absolute error = 1.3e-14 relative error = 1.247892831577823e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.291 y[1] (analytic) = 1.042042555786647 y[1] (numeric) = 1.042042555786634 absolute error = 1.3e-14 relative error = 1.247549817213193e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.292 y[1] (analytic) = 1.042329945043355 y[1] (numeric) = 1.042329945043342 absolute error = 1.3e-14 relative error = 1.247205845118388e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.293 y[1] (analytic) = 1.042618291970039 y[1] (numeric) = 1.042618291970025 absolute error = 1.4e-14 relative error = 1.342773295636972e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.294 y[1] (analytic) = 1.04290759627835 y[1] (numeric) = 1.042907596278337 absolute error = 1.3e-14 relative error = 1.246515036077110e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.295 y[1] (analytic) = 1.043197857678986 y[1] (numeric) = 1.043197857678973 absolute error = 1.3e-14 relative error = 1.246168203309364e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.296 y[1] (analytic) = 1.043489075881684 y[1] (numeric) = 1.043489075881671 absolute error = 1.3e-14 relative error = 1.245820421168837e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.297 y[1] (analytic) = 1.043781250595227 y[1] (numeric) = 1.043781250595214 absolute error = 1.3e-14 relative error = 1.245471691754054e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.298 y[1] (analytic) = 1.04407438152744 y[1] (numeric) = 1.044074381527426 absolute error = 1.4e-14 relative error = 1.340900633872325e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.299 y[1] (analytic) = 1.044368468385191 memory used=45.7MB, alloc=4.3MB, time=3.03 y[1] (numeric) = 1.044368468385177 absolute error = 1.4e-14 relative error = 1.340523045630331e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3 y[1] (analytic) = 1.044663510874394 y[1] (numeric) = 1.04466351087438 absolute error = 1.4e-14 relative error = 1.340144444049918e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.301 y[1] (analytic) = 1.044959508700007 y[1] (numeric) = 1.044959508699993 absolute error = 1.4e-14 relative error = 1.339764831406420e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.302 y[1] (analytic) = 1.045256461566031 y[1] (numeric) = 1.045256461566017 absolute error = 1.4e-14 relative error = 1.339384209978939e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.303 y[1] (analytic) = 1.045554369175514 y[1] (numeric) = 1.0455543691755 absolute error = 1.4e-14 relative error = 1.339002582050314e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304 y[1] (analytic) = 1.045853231230549 y[1] (numeric) = 1.045853231230535 absolute error = 1.4e-14 relative error = 1.338619949907085e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.305 y[1] (analytic) = 1.046153047432273 y[1] (numeric) = 1.046153047432259 absolute error = 1.4e-14 relative error = 1.338236315839471e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.306 y[1] (analytic) = 1.04645381748087 y[1] (numeric) = 1.046453817480856 absolute error = 1.4e-14 relative error = 1.337851682141332e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.307 y[1] (analytic) = 1.04675554107557 y[1] (numeric) = 1.046755541075556 absolute error = 1.4e-14 relative error = 1.337466051110139e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.308 y[1] (analytic) = 1.047058217914649 y[1] (numeric) = 1.047058217914635 absolute error = 1.4e-14 relative error = 1.337079425046947e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.309 y[1] (analytic) = 1.047361847695432 y[1] (numeric) = 1.047361847695417 absolute error = 1.5e-14 relative error = 1.432169792417523e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.31 y[1] (analytic) = 1.047666430114287 y[1] (numeric) = 1.047666430114272 absolute error = 1.5e-14 relative error = 1.431753425406949e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.311 y[1] (analytic) = 1.047971964866632 y[1] (numeric) = 1.047971964866618 absolute error = 1.4e-14 relative error = 1.335913599728947e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.312 y[1] (analytic) = 1.048278451646934 y[1] (numeric) = 1.048278451646919 absolute error = 1.5e-14 relative error = 1.430917517805859e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.313 y[1] (analytic) = 1.048585890148704 y[1] (numeric) = 1.048585890148689 absolute error = 1.5e-14 relative error = 1.430497982179866e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.314 y[1] (analytic) = 1.048894280064505 y[1] (numeric) = 1.04889428006449 absolute error = 1.5e-14 relative error = 1.430077395319338e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.315 y[1] (analytic) = 1.049203621085947 y[1] (numeric) = 1.049203621085932 absolute error = 1.5e-14 relative error = 1.429655759715611e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.316 y[1] (analytic) = 1.049513912903688 y[1] (numeric) = 1.049513912903673 absolute error = 1.5e-14 relative error = 1.429233077863592e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.317 y[1] (analytic) = 1.049825155207437 y[1] (numeric) = 1.049825155207422 absolute error = 1.5e-14 relative error = 1.428809352261722e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.318 y[1] (analytic) = 1.050137347685952 y[1] (numeric) = 1.050137347685937 absolute error = 1.5e-14 relative error = 1.428384585411947e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.319 y[1] (analytic) = 1.05045049002704 y[1] (numeric) = 1.050450490027025 absolute error = 1.5e-14 relative error = 1.427958779819683e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.32 y[1] (analytic) = 1.050764581917559 y[1] (numeric) = 1.050764581917544 absolute error = 1.5e-14 relative error = 1.427531937993783e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.321 y[1] (analytic) = 1.051079623043417 y[1] (numeric) = 1.051079623043402 absolute error = 1.5e-14 relative error = 1.427104062446504e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.322 y[1] (analytic) = 1.051395613089573 y[1] (numeric) = 1.051395613089558 absolute error = 1.5e-14 relative error = 1.426675155693472e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.323 y[1] (analytic) = 1.051712551740036 y[1] (numeric) = 1.051712551740022 absolute error = 1.4e-14 relative error = 1.331162205570077e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.324 y[1] (analytic) = 1.052030438677869 y[1] (numeric) = 1.052030438677855 absolute error = 1.4e-14 relative error = 1.330759974739361e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.325 y[1] (analytic) = 1.052349273585184 y[1] (numeric) = 1.05234927358517 absolute error = 1.4e-14 relative error = 1.330356788512265e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=3.29 NO POLE x[1] = 0.326 y[1] (analytic) = 1.052669056143147 y[1] (numeric) = 1.052669056143133 absolute error = 1.4e-14 relative error = 1.329952649248978e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.327 y[1] (analytic) = 1.052989786031974 y[1] (numeric) = 1.052989786031961 absolute error = 1.3e-14 relative error = 1.234579876504638e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.328 y[1] (analytic) = 1.053311462930937 y[1] (numeric) = 1.053311462930924 absolute error = 1.3e-14 relative error = 1.234202840993137e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.329 y[1] (analytic) = 1.053634086518358 y[1] (numeric) = 1.053634086518345 absolute error = 1.3e-14 relative error = 1.233824927110831e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.33 y[1] (analytic) = 1.053957656471613 y[1] (numeric) = 1.0539576564716 absolute error = 1.3e-14 relative error = 1.233446137060264e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.331 y[1] (analytic) = 1.054282172467133 y[1] (numeric) = 1.05428217246712 absolute error = 1.3e-14 relative error = 1.233066473046643e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.332 y[1] (analytic) = 1.054607634180402 y[1] (numeric) = 1.054607634180389 absolute error = 1.3e-14 relative error = 1.232685937277808e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.333 y[1] (analytic) = 1.054934041285958 y[1] (numeric) = 1.054934041285945 absolute error = 1.3e-14 relative error = 1.232304531964205e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.334 y[1] (analytic) = 1.055261393457393 y[1] (numeric) = 1.055261393457381 absolute error = 1.2e-14 relative error = 1.137159008602025e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.335 y[1] (analytic) = 1.055589690367357 y[1] (numeric) = 1.055589690367345 absolute error = 1.2e-14 relative error = 1.136805342976007e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.336 y[1] (analytic) = 1.055918931687552 y[1] (numeric) = 1.05591893168754 absolute error = 1.2e-14 relative error = 1.136450880828683e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.337 y[1] (analytic) = 1.056249117088736 y[1] (numeric) = 1.056249117088724 absolute error = 1.2e-14 relative error = 1.136095624209821e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.338 y[1] (analytic) = 1.056580246240724 y[1] (numeric) = 1.056580246240712 absolute error = 1.2e-14 relative error = 1.135739575171463e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.339 y[1] (analytic) = 1.056912318812388 y[1] (numeric) = 1.056912318812376 absolute error = 1.2e-14 relative error = 1.135382735767896e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.34 y[1] (analytic) = 1.057245334471654 y[1] (numeric) = 1.057245334471642 absolute error = 1.2e-14 relative error = 1.135025108055630e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.341 y[1] (analytic) = 1.057579292885507 y[1] (numeric) = 1.057579292885495 absolute error = 1.2e-14 relative error = 1.134666694093368e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.342 y[1] (analytic) = 1.057914193719989 y[1] (numeric) = 1.057914193719977 absolute error = 1.2e-14 relative error = 1.134307495941981e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.343 y[1] (analytic) = 1.058250036640198 y[1] (numeric) = 1.058250036640186 absolute error = 1.2e-14 relative error = 1.133947515664482e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.344 y[1] (analytic) = 1.058586821310292 y[1] (numeric) = 1.05858682131028 absolute error = 1.2e-14 relative error = 1.133586755326002e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.345 y[1] (analytic) = 1.058924547393487 y[1] (numeric) = 1.058924547393475 absolute error = 1.2e-14 relative error = 1.133225216993757e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.346 y[1] (analytic) = 1.059263214552056 y[1] (numeric) = 1.059263214552044 absolute error = 1.2e-14 relative error = 1.132862902737030e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.347 y[1] (analytic) = 1.059602822447332 y[1] (numeric) = 1.05960282244732 absolute error = 1.2e-14 relative error = 1.132499814627142e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.348 y[1] (analytic) = 1.059943370739707 y[1] (numeric) = 1.059943370739695 absolute error = 1.2e-14 relative error = 1.132135954737423e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.349 y[1] (analytic) = 1.060284859088632 y[1] (numeric) = 1.060284859088621 absolute error = 1.1e-14 relative error = 1.037457048047923e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.35 y[1] (analytic) = 1.060627287152621 y[1] (numeric) = 1.06062728715261 absolute error = 1.1e-14 relative error = 1.037122100594903e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.351 y[1] (analytic) = 1.060970654589244 y[1] (numeric) = 1.060970654589233 absolute error = 1.1e-14 relative error = 1.036786451389521e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=3.55 NO POLE x[1] = 0.352 y[1] (analytic) = 1.061314961055134 y[1] (numeric) = 1.061314961055123 absolute error = 1.1e-14 relative error = 1.036450102339466e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.353 y[1] (analytic) = 1.061660206205985 y[1] (numeric) = 1.061660206205974 absolute error = 1.1e-14 relative error = 1.036113055354150e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.354 y[1] (analytic) = 1.062006389696552 y[1] (numeric) = 1.062006389696541 absolute error = 1.1e-14 relative error = 1.035775312344687e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.355 y[1] (analytic) = 1.062353511180651 y[1] (numeric) = 1.06235351118064 absolute error = 1.1e-14 relative error = 1.035436875223870e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.356 y[1] (analytic) = 1.06270157031116 y[1] (numeric) = 1.062701570311149 absolute error = 1.1e-14 relative error = 1.035097745906143e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.357 y[1] (analytic) = 1.063050566740021 y[1] (numeric) = 1.06305056674001 absolute error = 1.1e-14 relative error = 1.034757926307578e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.358 y[1] (analytic) = 1.063400500118237 y[1] (numeric) = 1.063400500118226 absolute error = 1.1e-14 relative error = 1.034417418345857e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.359 y[1] (analytic) = 1.063751370095875 y[1] (numeric) = 1.063751370095864 absolute error = 1.1e-14 relative error = 1.034076223940241e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.36 y[1] (analytic) = 1.064103176322065 y[1] (numeric) = 1.064103176322054 absolute error = 1.1e-14 relative error = 1.033734345011550e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.361 y[1] (analytic) = 1.064455918445001 y[1] (numeric) = 1.06445591844499 absolute error = 1.1e-14 relative error = 1.033391783482141e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.362 y[1] (analytic) = 1.06480959611194 y[1] (numeric) = 1.064809596111929 absolute error = 1.1e-14 relative error = 1.033048541275881e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.363 y[1] (analytic) = 1.065164208969205 y[1] (numeric) = 1.065164208969194 absolute error = 1.1e-14 relative error = 1.032704620318126e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.364 y[1] (analytic) = 1.065519756662183 y[1] (numeric) = 1.065519756662172 absolute error = 1.1e-14 relative error = 1.032360022535695e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.365 y[1] (analytic) = 1.065876238835327 y[1] (numeric) = 1.065876238835316 absolute error = 1.1e-14 relative error = 1.032014749856850e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.366 y[1] (analytic) = 1.066233655132154 y[1] (numeric) = 1.066233655132143 absolute error = 1.1e-14 relative error = 1.031668804211269e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.367 y[1] (analytic) = 1.066592005195248 y[1] (numeric) = 1.066592005195237 absolute error = 1.1e-14 relative error = 1.031322187530026e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.368 y[1] (analytic) = 1.066951288666259 y[1] (numeric) = 1.066951288666248 absolute error = 1.1e-14 relative error = 1.030974901745565e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.369 y[1] (analytic) = 1.067311505185904 y[1] (numeric) = 1.067311505185893 absolute error = 1.1e-14 relative error = 1.030626948791677e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.37 y[1] (analytic) = 1.067672654393966 y[1] (numeric) = 1.067672654393955 absolute error = 1.1e-14 relative error = 1.030278330603479e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.371 y[1] (analytic) = 1.068034735929295 y[1] (numeric) = 1.068034735929285 absolute error = 1.0e-14 relative error = 9.362991355612623e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.372 y[1] (analytic) = 1.068397749429811 y[1] (numeric) = 1.068397749429801 absolute error = 1.0e-14 relative error = 9.359810057010005e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.373 y[1] (analytic) = 1.0687616945325 y[1] (numeric) = 1.06876169453249 absolute error = 1.0e-14 relative error = 9.356622763668772e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.374 y[1] (analytic) = 1.069126570873417 y[1] (numeric) = 1.069126570873407 absolute error = 1.0e-14 relative error = 9.353429493226939e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.375 y[1] (analytic) = 1.069492378087686 y[1] (numeric) = 1.069492378087675 absolute error = 1.1e-14 relative error = 1.028525328966685e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.376 y[1] (analytic) = 1.069859115809498 y[1] (numeric) = 1.069859115809488 absolute error = 1.0e-14 relative error = 9.347025091648261e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.377 y[1] (analytic) = 1.070226783672118 y[1] (numeric) = 1.070226783672107 absolute error = 1.1e-14 relative error = 1.027819539542568e-12 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=3.81 NO POLE x[1] = 0.378 y[1] (analytic) = 1.070595381307876 y[1] (numeric) = 1.070595381307865 absolute error = 1.1e-14 relative error = 1.027465669295343e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.379 y[1] (analytic) = 1.070964908348176 y[1] (numeric) = 1.070964908348165 absolute error = 1.1e-14 relative error = 1.027111151285626e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.38 y[1] (analytic) = 1.07133536442349 y[1] (numeric) = 1.071335364423479 absolute error = 1.1e-14 relative error = 1.026755987460505e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.381 y[1] (analytic) = 1.071706749163362 y[1] (numeric) = 1.071706749163351 absolute error = 1.1e-14 relative error = 1.026400179768137e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.382 y[1] (analytic) = 1.072079062196407 y[1] (numeric) = 1.072079062196396 absolute error = 1.1e-14 relative error = 1.026043730157728e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.383 y[1] (analytic) = 1.072452303150313 y[1] (numeric) = 1.072452303150302 absolute error = 1.1e-14 relative error = 1.025686640579507e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.384 y[1] (analytic) = 1.072826471651839 y[1] (numeric) = 1.072826471651828 absolute error = 1.1e-14 relative error = 1.025328912984708e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.385 y[1] (analytic) = 1.073201567326815 y[1] (numeric) = 1.073201567326805 absolute error = 1.0e-14 relative error = 9.317914084777670e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.386 y[1] (analytic) = 1.073577589800147 y[1] (numeric) = 1.073577589800137 absolute error = 1.0e-14 relative error = 9.314650468683461e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.387 y[1] (analytic) = 1.073954538695812 y[1] (numeric) = 1.073954538695802 absolute error = 1.0e-14 relative error = 9.311381105706571e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.388 y[1] (analytic) = 1.074332413636862 y[1] (numeric) = 1.074332413636851 absolute error = 1.1e-14 relative error = 1.023891661498183e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.389 y[1] (analytic) = 1.07471121424542 y[1] (numeric) = 1.074711214245409 absolute error = 1.1e-14 relative error = 1.023530773122467e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.39 y[1] (analytic) = 1.075090940142687 y[1] (numeric) = 1.075090940142676 absolute error = 1.1e-14 relative error = 1.023169258457342e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.391 y[1] (analytic) = 1.075471590948937 y[1] (numeric) = 1.075471590948926 absolute error = 1.1e-14 relative error = 1.022807119460422e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.392 y[1] (analytic) = 1.075853166283519 y[1] (numeric) = 1.075853166283508 absolute error = 1.1e-14 relative error = 1.022444358090143e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.393 y[1] (analytic) = 1.076235665764857 y[1] (numeric) = 1.076235665764847 absolute error = 1.0e-14 relative error = 9.291645239143065e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.394 y[1] (analytic) = 1.076619089010453 y[1] (numeric) = 1.076619089010443 absolute error = 1.0e-14 relative error = 9.288336146065592e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.395 y[1] (analytic) = 1.077003435636883 y[1] (numeric) = 1.077003435636873 absolute error = 1.0e-14 relative error = 9.285021448503112e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.396 y[1] (analytic) = 1.0773887052598 y[1] (numeric) = 1.07738870525979 absolute error = 1.0e-14 relative error = 9.281701164287418e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.397 y[1] (analytic) = 1.077774897493935 y[1] (numeric) = 1.077774897493925 absolute error = 1.0e-14 relative error = 9.278375311256749e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.398 y[1] (analytic) = 1.078162011953096 y[1] (numeric) = 1.078162011953086 absolute error = 1.0e-14 relative error = 9.275043907255598e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.399 y[1] (analytic) = 1.078550048250168 y[1] (numeric) = 1.078550048250158 absolute error = 1.0e-14 relative error = 9.271706970134515e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4 y[1] (analytic) = 1.078939005997115 y[1] (numeric) = 1.078939005997105 absolute error = 1.0e-14 relative error = 9.268364517749893e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.401 y[1] (analytic) = 1.079328884804979 y[1] (numeric) = 1.079328884804969 absolute error = 1.0e-14 relative error = 9.265016567963779e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.402 y[1] (analytic) = 1.079719684283882 y[1] (numeric) = 1.079719684283872 absolute error = 1.0e-14 relative error = 9.261663138643660e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.403 y[1] (analytic) = 1.080111404043024 y[1] (numeric) = 1.080111404043014 absolute error = 1.0e-14 relative error = 9.258304247662282e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=4.08 NO POLE x[1] = 0.404 y[1] (analytic) = 1.080504043690685 y[1] (numeric) = 1.080504043690675 absolute error = 1.0e-14 relative error = 9.254939912897440e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.405 y[1] (analytic) = 1.080897602834225 y[1] (numeric) = 1.080897602834216 absolute error = 9e-15 relative error = 8.326413137008604e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.406 y[1] (analytic) = 1.081292081080086 y[1] (numeric) = 1.081292081080077 absolute error = 9e-15 relative error = 8.323375485197338e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.407 y[1] (analytic) = 1.08168747803379 y[1] (numeric) = 1.081687478033781 absolute error = 9e-15 relative error = 8.320332982276472e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.408 y[1] (analytic) = 1.082083793299939 y[1] (numeric) = 1.08208379329993 absolute error = 9e-15 relative error = 8.317285644352426e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.409 y[1] (analytic) = 1.082481026482219 y[1] (numeric) = 1.082481026482209 absolute error = 1.0e-14 relative error = 9.238037208372503e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.41 y[1] (analytic) = 1.082879177183395 y[1] (numeric) = 1.082879177183385 absolute error = 1.0e-14 relative error = 9.234640586598345e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.411 y[1] (analytic) = 1.083278245005318 y[1] (numeric) = 1.083278245005308 absolute error = 1.0e-14 relative error = 9.231238646310033e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.412 y[1] (analytic) = 1.083678229548919 y[1] (numeric) = 1.083678229548909 absolute error = 1.0e-14 relative error = 9.227831405418654e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.413 y[1] (analytic) = 1.084079130414214 y[1] (numeric) = 1.084079130414204 absolute error = 1.0e-14 relative error = 9.224418881838558e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.414 y[1] (analytic) = 1.084480947200303 y[1] (numeric) = 1.084480947200293 absolute error = 1.0e-14 relative error = 9.221001093487174e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.415 y[1] (analytic) = 1.084883679505368 y[1] (numeric) = 1.084883679505358 absolute error = 1.0e-14 relative error = 9.217578058284838e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.416 y[1] (analytic) = 1.085287326926678 y[1] (numeric) = 1.085287326926667 absolute error = 1.1e-14 relative error = 1.013556477357001e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.417 y[1] (analytic) = 1.085691889060584 y[1] (numeric) = 1.085691889060573 absolute error = 1.1e-14 relative error = 1.013178795092405e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.418 y[1] (analytic) = 1.086097365502525 y[1] (numeric) = 1.086097365502514 absolute error = 1.1e-14 relative error = 1.012800541589605e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.419 y[1] (analytic) = 1.086503755847024 y[1] (numeric) = 1.086503755847013 absolute error = 1.1e-14 relative error = 1.012421718820893e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.42 y[1] (analytic) = 1.086911059687692 y[1] (numeric) = 1.08691105968768 absolute error = 1.2e-14 relative error = 1.104046176827755e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.421 y[1] (analytic) = 1.087319276617223 y[1] (numeric) = 1.087319276617212 absolute error = 1.1e-14 relative error = 1.011662373375949e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.422 y[1] (analytic) = 1.087728406227402 y[1] (numeric) = 1.087728406227391 absolute error = 1.1e-14 relative error = 1.011281854645279e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.423 y[1] (analytic) = 1.088138448109099 y[1] (numeric) = 1.088138448109088 absolute error = 1.1e-14 relative error = 1.010900774539778e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.424 y[1] (analytic) = 1.088549401852272 y[1] (numeric) = 1.088549401852261 absolute error = 1.1e-14 relative error = 1.010519135032589e-12 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.425 y[1] (analytic) = 1.088961267045966 y[1] (numeric) = 1.088961267045956 absolute error = 1.0e-14 relative error = 9.183063073608743e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.426 y[1] (analytic) = 1.089374043278318 y[1] (numeric) = 1.089374043278308 absolute error = 1.0e-14 relative error = 9.179583506420261e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.427 y[1] (analytic) = 1.089787730136551 y[1] (numeric) = 1.089787730136541 absolute error = 1.0e-14 relative error = 9.176098907579914e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.428 y[1] (analytic) = 1.090202327206978 y[1] (numeric) = 1.090202327206968 absolute error = 1.0e-14 relative error = 9.172609295028107e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.429 y[1] (analytic) = 1.090617834075001 y[1] (numeric) = 1.090617834074992 absolute error = 9e-15 relative error = 8.252203218034922e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=4.33 NO POLE x[1] = 0.43 y[1] (analytic) = 1.091034250325115 y[1] (numeric) = 1.091034250325106 absolute error = 9e-15 relative error = 8.249053590497373e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.431 y[1] (analytic) = 1.091451575540903 y[1] (numeric) = 1.091451575540894 absolute error = 9e-15 relative error = 8.245899499059102e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.432 y[1] (analytic) = 1.091869809305039 y[1] (numeric) = 1.09186980930503 absolute error = 9e-15 relative error = 8.242740959866253e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.433 y[1] (analytic) = 1.09228895119929 y[1] (numeric) = 1.092288951199281 absolute error = 9e-15 relative error = 8.239577989064484e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.434 y[1] (analytic) = 1.092709000804515 y[1] (numeric) = 1.092709000804506 absolute error = 9e-15 relative error = 8.236410602798809e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.435 y[1] (analytic) = 1.093129957700663 y[1] (numeric) = 1.093129957700654 absolute error = 9e-15 relative error = 8.233238817213454e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.436 y[1] (analytic) = 1.093551821466778 y[1] (numeric) = 1.093551821466769 absolute error = 9e-15 relative error = 8.230062648451653e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.437 y[1] (analytic) = 1.093974591680996 y[1] (numeric) = 1.093974591680987 absolute error = 9e-15 relative error = 8.226882112655509e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.438 y[1] (analytic) = 1.094398267920547 y[1] (numeric) = 1.094398267920538 absolute error = 9e-15 relative error = 8.223697225965819e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.439 y[1] (analytic) = 1.094822849761754 y[1] (numeric) = 1.094822849761745 absolute error = 9e-15 relative error = 8.220508004521922e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.44 y[1] (analytic) = 1.095248336780037 y[1] (numeric) = 1.095248336780027 absolute error = 1.0e-14 relative error = 9.130349404957224e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.441 y[1] (analytic) = 1.095674728549907 y[1] (numeric) = 1.095674728549897 absolute error = 1.0e-14 relative error = 9.126796246578310e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.442 y[1] (analytic) = 1.096102024644973 y[1] (numeric) = 1.096102024644963 absolute error = 1.0e-14 relative error = 9.123238325591996e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.443 y[1] (analytic) = 1.096530224637939 y[1] (numeric) = 1.096530224637929 absolute error = 1.0e-14 relative error = 9.119675659922533e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.444 y[1] (analytic) = 1.096959328100605 y[1] (numeric) = 1.096959328100595 absolute error = 1.0e-14 relative error = 9.116108267491640e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.445 y[1] (analytic) = 1.097389334603868 y[1] (numeric) = 1.097389334603858 absolute error = 1.0e-14 relative error = 9.112536166218316e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.446 y[1] (analytic) = 1.097820243717721 y[1] (numeric) = 1.097820243717711 absolute error = 1.0e-14 relative error = 9.108959374018674e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.447 y[1] (analytic) = 1.098252055011255 y[1] (numeric) = 1.098252055011245 absolute error = 1.0e-14 relative error = 9.105377908805751e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.448 y[1] (analytic) = 1.098684768052659 y[1] (numeric) = 1.098684768052649 absolute error = 1.0e-14 relative error = 9.101791788489334e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.449 y[1] (analytic) = 1.09911838240922 y[1] (numeric) = 1.09911838240921 absolute error = 1.0e-14 relative error = 9.098201030975783e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.45 y[1] (analytic) = 1.099552897647323 y[1] (numeric) = 1.099552897647313 absolute error = 1.0e-14 relative error = 9.094605654167862e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.451 y[1] (analytic) = 1.099988313332454 y[1] (numeric) = 1.099988313332444 absolute error = 1.0e-14 relative error = 9.091005675964540e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.452 y[1] (analytic) = 1.100424629029196 y[1] (numeric) = 1.100424629029186 absolute error = 1.0e-14 relative error = 9.087401114260852e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.453 y[1] (analytic) = 1.100861844301234 y[1] (numeric) = 1.100861844301224 absolute error = 1.0e-14 relative error = 9.083791986947686e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.454 y[1] (analytic) = 1.101299958711353 y[1] (numeric) = 1.101299958711343 absolute error = 1.0e-14 relative error = 9.080178311911629e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.455 y[1] (analytic) = 1.101738971821439 y[1] (numeric) = 1.101738971821428 absolute error = 1.1e-14 relative error = 9.984216117738269e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=4.60 NO POLE x[1] = 0.456 y[1] (analytic) = 1.102178883192478 y[1] (numeric) = 1.102178883192467 absolute error = 1.1e-14 relative error = 9.980231129214100e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.457 y[1] (analytic) = 1.102619692384558 y[1] (numeric) = 1.102619692384548 absolute error = 1.0e-14 relative error = 9.069310179263808e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.458 y[1] (analytic) = 1.103061398956872 y[1] (numeric) = 1.103061398956862 absolute error = 1.0e-14 relative error = 9.065678492109925e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.459 y[1] (analytic) = 1.103504002467712 y[1] (numeric) = 1.103504002467702 absolute error = 1.0e-14 relative error = 9.062042346595472e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.46 y[1] (analytic) = 1.103947502474475 y[1] (numeric) = 1.103947502474465 absolute error = 1.0e-14 relative error = 9.058401760577574e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.461 y[1] (analytic) = 1.10439189853366 y[1] (numeric) = 1.104391898533651 absolute error = 9e-15 relative error = 8.149281076717076e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.462 y[1] (analytic) = 1.104837190200873 y[1] (numeric) = 1.104837190200863 absolute error = 1.0e-14 relative error = 9.051107338432260e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.463 y[1] (analytic) = 1.10528337703082 y[1] (numeric) = 1.105283377030811 absolute error = 9e-15 relative error = 8.142708184191792e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.464 y[1] (analytic) = 1.105730458577316 y[1] (numeric) = 1.105730458577307 absolute error = 9e-15 relative error = 8.139415831576003e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.465 y[1] (analytic) = 1.106178434393279 y[1] (numeric) = 1.10617843439327 absolute error = 9e-15 relative error = 8.136119562786771e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.466 y[1] (analytic) = 1.106627304030734 y[1] (numeric) = 1.106627304030724 absolute error = 1.0e-14 relative error = 9.036465993181633e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.467 y[1] (analytic) = 1.107077067040809 y[1] (numeric) = 1.1070770670408 absolute error = 9e-15 relative error = 8.129515340839630e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.468 y[1] (analytic) = 1.107527722973743 y[1] (numeric) = 1.107527722973734 absolute error = 9e-15 relative error = 8.126207419742729e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.469 y[1] (analytic) = 1.10797927137888 y[1] (numeric) = 1.107979271378871 absolute error = 9e-15 relative error = 8.122895646594093e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.47 y[1] (analytic) = 1.108431711804671 y[1] (numeric) = 1.108431711804662 absolute error = 9e-15 relative error = 8.119580037408736e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.471 y[1] (analytic) = 1.108885043798676 y[1] (numeric) = 1.108885043798667 absolute error = 9e-15 relative error = 8.116260608195197e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.472 y[1] (analytic) = 1.109339266907563 y[1] (numeric) = 1.109339266907554 absolute error = 9e-15 relative error = 8.112937374955407e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.473 y[1] (analytic) = 1.109794380677109 y[1] (numeric) = 1.1097943806771 absolute error = 9e-15 relative error = 8.109610353684536e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.474 y[1] (analytic) = 1.1102503846522 y[1] (numeric) = 1.110250384652191 absolute error = 9e-15 relative error = 8.106279560370847e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.475 y[1] (analytic) = 1.110707278376832 y[1] (numeric) = 1.110707278376823 absolute error = 9e-15 relative error = 8.102945010995553e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.476 y[1] (analytic) = 1.111165061394111 y[1] (numeric) = 1.111165061394103 absolute error = 8e-15 relative error = 7.199650419140148e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.477 y[1] (analytic) = 1.111623733246256 y[1] (numeric) = 1.111623733246247 absolute error = 9e-15 relative error = 8.096264707948842e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.478 y[1] (analytic) = 1.112083293474592 y[1] (numeric) = 1.112083293474584 absolute error = 8e-15 relative error = 7.193705765514027e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.479 y[1] (analytic) = 1.112543741619562 y[1] (numeric) = 1.112543741619553 absolute error = 9e-15 relative error = 8.089569572247506e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.48 y[1] (analytic) = 1.113005077220716 y[1] (numeric) = 1.113005077220707 absolute error = 9e-15 relative error = 8.086216482025304e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.481 y[1] (analytic) = 1.113467299816718 y[1] (numeric) = 1.11346729981671 absolute error = 8e-15 relative error = 7.184764205753360e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=72.4MB, alloc=4.3MB, time=4.86 x[1] = 0.482 y[1] (analytic) = 1.113930408945348 y[1] (numeric) = 1.113930408945339 absolute error = 9e-15 relative error = 8.079499336516955e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.483 y[1] (analytic) = 1.114394404143494 y[1] (numeric) = 1.114394404143485 absolute error = 9e-15 relative error = 8.076135313078190e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.484 y[1] (analytic) = 1.114859284947162 y[1] (numeric) = 1.114859284947153 absolute error = 9e-15 relative error = 8.072767677067469e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.485 y[1] (analytic) = 1.115325050891472 y[1] (numeric) = 1.115325050891463 absolute error = 9e-15 relative error = 8.069396444387543e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.486 y[1] (analytic) = 1.115791701510657 y[1] (numeric) = 1.115791701510648 absolute error = 9e-15 relative error = 8.066021630932555e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.487 y[1] (analytic) = 1.116259236338066 y[1] (numeric) = 1.116259236338058 absolute error = 8e-15 relative error = 7.166794002300332e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.488 y[1] (analytic) = 1.116727654906166 y[1] (numeric) = 1.116727654906158 absolute error = 8e-15 relative error = 7.163787844648843e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.489 y[1] (analytic) = 1.117196956746538 y[1] (numeric) = 1.117196956746529 absolute error = 9e-15 relative error = 8.055875864726204e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.49 y[1] (analytic) = 1.117667141389878 y[1] (numeric) = 1.11766714138987 absolute error = 8e-15 relative error = 7.157766121719905e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.491 y[1] (analytic) = 1.118138208366005 y[1] (numeric) = 1.118138208365996 absolute error = 9e-15 relative error = 8.049094407704912e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.492 y[1] (analytic) = 1.118610157203849 y[1] (numeric) = 1.11861015720384 absolute error = 9e-15 relative error = 8.045698442875745e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.493 y[1] (analytic) = 1.119082987431462 y[1] (numeric) = 1.119082987431454 absolute error = 8e-15 relative error = 7.148710229579786e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.494 y[1] (analytic) = 1.119556698576015 y[1] (numeric) = 1.119556698576007 absolute error = 8e-15 relative error = 7.145685439759638e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.495 y[1] (analytic) = 1.120031290163796 y[1] (numeric) = 1.120031290163788 absolute error = 8e-15 relative error = 7.142657593816027e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.496 y[1] (analytic) = 1.120506761720213 y[1] (numeric) = 1.120506761720205 absolute error = 8e-15 relative error = 7.139626705793655e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.497 y[1] (analytic) = 1.120983112769795 y[1] (numeric) = 1.120983112769787 absolute error = 8e-15 relative error = 7.136592789728206e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.498 y[1] (analytic) = 1.121460342836192 y[1] (numeric) = 1.121460342836183 absolute error = 9e-15 relative error = 8.025250342102021e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.499 y[1] (analytic) = 1.121938451442172 y[1] (numeric) = 1.121938451442163 absolute error = 9e-15 relative error = 8.021830420760730e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5 y[1] (analytic) = 1.122417438109627 y[1] (numeric) = 1.122417438109619 absolute error = 8e-15 relative error = 7.127473013492718e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.501 y[1] (analytic) = 1.122897302359572 y[1] (numeric) = 1.122897302359563 absolute error = 9e-15 relative error = 8.014980516106038e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.502 y[1] (analytic) = 1.12337804371214 y[1] (numeric) = 1.123378043712132 absolute error = 8e-15 relative error = 7.121378279358609e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.503 y[1] (analytic) = 1.123859661686593 y[1] (numeric) = 1.123859661686584 absolute error = 9e-15 relative error = 8.008117300423049e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.504 y[1] (analytic) = 1.12434215580131 y[1] (numeric) = 1.124342155801301 absolute error = 9e-15 relative error = 8.004680740255416e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.505 y[1] (analytic) = 1.124825525573799 y[1] (numeric) = 1.12482552557379 absolute error = 9e-15 relative error = 8.001240899479851e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.506 y[1] (analytic) = 1.125309770520689 y[1] (numeric) = 1.12530977052068 absolute error = 9e-15 relative error = 7.997797793789380e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.507 y[1] (analytic) = 1.125794890157736 y[1] (numeric) = 1.125794890157727 absolute error = 9e-15 relative error = 7.994351438865567e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=76.2MB, alloc=4.3MB, time=5.12 x[1] = 0.508 y[1] (analytic) = 1.126280883999819 y[1] (numeric) = 1.126280883999811 absolute error = 8e-15 relative error = 7.103023867003043e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.509 y[1] (analytic) = 1.126767751560946 y[1] (numeric) = 1.126767751560938 absolute error = 8e-15 relative error = 7.099954705765544e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.51 y[1] (analytic) = 1.127255492354249 y[1] (numeric) = 1.127255492354241 absolute error = 8e-15 relative error = 7.096882698075989e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.511 y[1] (analytic) = 1.127744105891986 y[1] (numeric) = 1.127744105891978 absolute error = 8e-15 relative error = 7.093807857831740e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.512 y[1] (analytic) = 1.128233591685545 y[1] (numeric) = 1.128233591685537 absolute error = 8e-15 relative error = 7.090730198919406e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.513 y[1] (analytic) = 1.12872394924544 y[1] (numeric) = 1.128723949245432 absolute error = 8e-15 relative error = 7.087649735214759e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.514 y[1] (analytic) = 1.129215178081312 y[1] (numeric) = 1.129215178081305 absolute error = 7e-15 relative error = 6.198995670509795e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.515 y[1] (analytic) = 1.129707277701934 y[1] (numeric) = 1.129707277701927 absolute error = 7e-15 relative error = 6.196295392767139e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.516 y[1] (analytic) = 1.130200247615206 y[1] (numeric) = 1.130200247615199 absolute error = 7e-15 relative error = 6.193592697197194e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.517 y[1] (analytic) = 1.130694087328158 y[1] (numeric) = 1.130694087328151 absolute error = 7e-15 relative error = 6.190887595902331e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.518 y[1] (analytic) = 1.13118879634695 y[1] (numeric) = 1.131188796346943 absolute error = 7e-15 relative error = 6.188180100974949e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.519 y[1] (analytic) = 1.131684374176873 y[1] (numeric) = 1.131684374176866 absolute error = 7e-15 relative error = 6.185470224497380e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.52 y[1] (analytic) = 1.13218082032235 y[1] (numeric) = 1.132180820322343 absolute error = 7e-15 relative error = 6.182757978541792e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.521 y[1] (analytic) = 1.132678134286934 y[1] (numeric) = 1.132678134286927 absolute error = 7e-15 relative error = 6.180043375170104e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.522 y[1] (analytic) = 1.133176315573312 y[1] (numeric) = 1.133176315573305 absolute error = 7e-15 relative error = 6.177326426433882e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.523 y[1] (analytic) = 1.133675363683301 y[1] (numeric) = 1.133675363683295 absolute error = 6e-15 relative error = 5.292520409463653e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.524 y[1] (analytic) = 1.134175278117855 y[1] (numeric) = 1.134175278117849 absolute error = 6e-15 relative error = 5.290187606590138e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.525 y[1] (analytic) = 1.134676058377059 y[1] (numeric) = 1.134676058377053 absolute error = 6e-15 relative error = 5.287852824339903e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.526 y[1] (analytic) = 1.135177703960132 y[1] (numeric) = 1.135177703960126 absolute error = 6e-15 relative error = 5.285516073006595e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.527 y[1] (analytic) = 1.135680214365429 y[1] (numeric) = 1.135680214365423 absolute error = 6e-15 relative error = 5.283177362874593e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.528 y[1] (analytic) = 1.136183589090439 y[1] (numeric) = 1.136183589090434 absolute error = 5e-15 relative error = 4.400697253515783e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.529 y[1] (analytic) = 1.136687827631789 y[1] (numeric) = 1.136687827631784 absolute error = 5e-15 relative error = 4.398745089421039e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.53 y[1] (analytic) = 1.137192929485239 y[1] (numeric) = 1.137192929485234 absolute error = 5e-15 relative error = 4.396791318658037e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.531 y[1] (analytic) = 1.137698894145688 y[1] (numeric) = 1.137698894145683 absolute error = 5e-15 relative error = 4.394835949765567e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.532 y[1] (analytic) = 1.13820572110717 y[1] (numeric) = 1.138205721107166 absolute error = 4e-15 relative error = 3.514303193019509e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.533 y[1] (analytic) = 1.13871340986286 y[1] (numeric) = 1.138713409862856 absolute error = 4e-15 relative error = 3.512736361365707e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.534 y[1] (analytic) = 1.139221959905068 y[1] (numeric) = 1.139221959905064 absolute error = 4e-15 relative error = 3.511168271662637e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.3MB, time=5.38 NO POLE x[1] = 0.535 y[1] (analytic) = 1.139731370725244 y[1] (numeric) = 1.13973137072524 absolute error = 4e-15 relative error = 3.509598930715300e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.536 y[1] (analytic) = 1.140241641813978 y[1] (numeric) = 1.140241641813974 absolute error = 4e-15 relative error = 3.508028345322062e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.537 y[1] (analytic) = 1.140752772660999 y[1] (numeric) = 1.140752772660995 absolute error = 4e-15 relative error = 3.506456522274605e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.538 y[1] (analytic) = 1.141264762755175 y[1] (numeric) = 1.141264762755171 absolute error = 4e-15 relative error = 3.504883468357888e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.539 y[1] (analytic) = 1.141777611584517 y[1] (numeric) = 1.141777611584513 absolute error = 4e-15 relative error = 3.503309190350078e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.54 y[1] (analytic) = 1.142291318636176 y[1] (numeric) = 1.142291318636172 absolute error = 4e-15 relative error = 3.501733695022517e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.541 y[1] (analytic) = 1.142805883396445 y[1] (numeric) = 1.142805883396441 absolute error = 4e-15 relative error = 3.500156989139668e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.542 y[1] (analytic) = 1.143321305350758 y[1] (numeric) = 1.143321305350755 absolute error = 3e-15 relative error = 2.623934309594304e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.543 y[1] (analytic) = 1.143837583983696 y[1] (numeric) = 1.143837583983692 absolute error = 4e-15 relative error = 3.496999972731282e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.544 y[1] (analytic) = 1.144354718778978 y[1] (numeric) = 1.144354718778974 absolute error = 4e-15 relative error = 3.495419675699843e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.545 y[1] (analytic) = 1.144872709219469 y[1] (numeric) = 1.144872709219466 absolute error = 3e-15 relative error = 2.620378646325919e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.546 y[1] (analytic) = 1.14539155478718 y[1] (numeric) = 1.145391554787177 absolute error = 3e-15 relative error = 2.619191653248584e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.547 y[1] (analytic) = 1.145911254963266 y[1] (numeric) = 1.145911254963262 absolute error = 4e-15 relative error = 3.490671710112688e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.548 y[1] (analytic) = 1.146431809228025 y[1] (numeric) = 1.146431809228021 absolute error = 4e-15 relative error = 3.489086719159937e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.549 y[1] (analytic) = 1.146953217060904 y[1] (numeric) = 1.1469532170609 absolute error = 4e-15 relative error = 3.487500571514241e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.55 y[1] (analytic) = 1.147475477940494 y[1] (numeric) = 1.147475477940491 absolute error = 3e-15 relative error = 2.614434955407016e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.551 y[1] (analytic) = 1.147998591344536 y[1] (numeric) = 1.147998591344533 absolute error = 3e-15 relative error = 2.613243624703755e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.552 y[1] (analytic) = 1.148522556749915 y[1] (numeric) = 1.148522556749912 absolute error = 3e-15 relative error = 2.612051441540155e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.553 y[1] (analytic) = 1.149047373632667 y[1] (numeric) = 1.149047373632664 absolute error = 3e-15 relative error = 2.610858410924887e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.554 y[1] (analytic) = 1.149573041467974 y[1] (numeric) = 1.149573041467971 absolute error = 3e-15 relative error = 2.609664537861013e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.555 y[1] (analytic) = 1.150099559730168 y[1] (numeric) = 1.150099559730166 absolute error = 2e-15 relative error = 1.738979884897297e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.556 y[1] (analytic) = 1.150626927892733 y[1] (numeric) = 1.15062692789273 absolute error = 3e-15 relative error = 2.607274284371411e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.557 y[1] (analytic) = 1.151155145428298 y[1] (numeric) = 1.151155145428295 absolute error = 3e-15 relative error = 2.606077913923429e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.558 y[1] (analytic) = 1.151684211808647 y[1] (numeric) = 1.151684211808644 absolute error = 3e-15 relative error = 2.604880720982265e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.559 y[1] (analytic) = 1.152214126504714 y[1] (numeric) = 1.152214126504711 absolute error = 3e-15 relative error = 2.603682710522406e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.56 y[1] (analytic) = 1.152744888986584 y[1] (numeric) = 1.152744888986581 absolute error = 3e-15 relative error = 2.602483887512526e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.3MB, time=5.64 NO POLE x[1] = 0.561 y[1] (analytic) = 1.153276498723494 y[1] (numeric) = 1.153276498723491 absolute error = 3e-15 relative error = 2.601284256915453e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.562 y[1] (analytic) = 1.153808955183835 y[1] (numeric) = 1.153808955183832 absolute error = 3e-15 relative error = 2.600083823688137e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.563 y[1] (analytic) = 1.15434225783515 y[1] (numeric) = 1.154342257835147 absolute error = 3e-15 relative error = 2.598882592781617e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.564 y[1] (analytic) = 1.154876406144137 y[1] (numeric) = 1.154876406144134 absolute error = 3e-15 relative error = 2.597680569140987e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.565 y[1] (analytic) = 1.155411399576647 y[1] (numeric) = 1.155411399576644 absolute error = 3e-15 relative error = 2.596477757705374e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.566 y[1] (analytic) = 1.155947237597687 y[1] (numeric) = 1.155947237597684 absolute error = 3e-15 relative error = 2.595274163407891e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.567 y[1] (analytic) = 1.156483919671419 y[1] (numeric) = 1.156483919671416 absolute error = 3e-15 relative error = 2.594069791175620e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.568 y[1] (analytic) = 1.157021445261162 y[1] (numeric) = 1.157021445261158 absolute error = 4e-15 relative error = 3.457152861239424e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.569 y[1] (analytic) = 1.157559813829388 y[1] (numeric) = 1.157559813829385 absolute error = 3e-15 relative error = 2.591658732584654e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.57 y[1] (analytic) = 1.158099024837731 y[1] (numeric) = 1.158099024837728 absolute error = 3e-15 relative error = 2.590452056049654e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.571 y[1] (analytic) = 1.158639077746979 y[1] (numeric) = 1.158639077746976 absolute error = 3e-15 relative error = 2.589244621227192e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.572 y[1] (analytic) = 1.159179972017079 y[1] (numeric) = 1.159179972017076 absolute error = 3e-15 relative error = 2.588036433013699e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.573 y[1] (analytic) = 1.159721707107137 y[1] (numeric) = 1.159721707107134 absolute error = 3e-15 relative error = 2.586827496299382e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.574 y[1] (analytic) = 1.160264282475418 y[1] (numeric) = 1.160264282475415 absolute error = 3e-15 relative error = 2.585617815968199e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.575 y[1] (analytic) = 1.160807697579346 y[1] (numeric) = 1.160807697579343 absolute error = 3e-15 relative error = 2.584407396897829e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.576 y[1] (analytic) = 1.161351951875507 y[1] (numeric) = 1.161351951875504 absolute error = 3e-15 relative error = 2.583196243959635e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.577 y[1] (analytic) = 1.161897044819646 y[1] (numeric) = 1.161897044819643 absolute error = 3e-15 relative error = 2.581984362018643e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.578 y[1] (analytic) = 1.16244297586667 y[1] (numeric) = 1.162442975866667 absolute error = 3e-15 relative error = 2.580771755933509e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.579 y[1] (analytic) = 1.162989744470649 y[1] (numeric) = 1.162989744470646 absolute error = 3e-15 relative error = 2.579558430556489e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.58 y[1] (analytic) = 1.163537350084813 y[1] (numeric) = 1.16353735008481 absolute error = 3e-15 relative error = 2.578344390733416e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.581 y[1] (analytic) = 1.164085792161558 y[1] (numeric) = 1.164085792161555 absolute error = 3e-15 relative error = 2.577129641303658e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.582 y[1] (analytic) = 1.164635070152441 y[1] (numeric) = 1.164635070152438 absolute error = 3e-15 relative error = 2.575914187100106e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.583 y[1] (analytic) = 1.165185183508184 y[1] (numeric) = 1.165185183508181 absolute error = 3e-15 relative error = 2.574698032949137e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.584 y[1] (analytic) = 1.165736131678674 y[1] (numeric) = 1.165736131678671 absolute error = 3e-15 relative error = 2.573481183670583e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.585 y[1] (analytic) = 1.166287914112962 y[1] (numeric) = 1.16628791411296 absolute error = 2e-15 relative error = 1.714842429385141e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.586 y[1] (analytic) = 1.166840530259268 y[1] (numeric) = 1.166840530259265 absolute error = 3e-15 relative error = 2.571045418977185e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=5.90 NO POLE x[1] = 0.587 y[1] (analytic) = 1.167393979564973 y[1] (numeric) = 1.167393979564971 absolute error = 2e-15 relative error = 1.713217675446036e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.588 y[1] (analytic) = 1.16794826147663 y[1] (numeric) = 1.167948261476628 absolute error = 2e-15 relative error = 1.712404620964470e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.589 y[1] (analytic) = 1.168503375439956 y[1] (numeric) = 1.168503375439954 absolute error = 2e-15 relative error = 1.711591119064569e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.59 y[1] (analytic) = 1.169059320899836 y[1] (numeric) = 1.169059320899835 absolute error = 1e-15 relative error = 8.553885864665024e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.591 y[1] (analytic) = 1.169616097300327 y[1] (numeric) = 1.169616097300326 absolute error = 1e-15 relative error = 8.549813928759789e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.592 y[1] (analytic) = 1.170173704084652 y[1] (numeric) = 1.17017370408465 absolute error = 2e-15 relative error = 1.709147960699104e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.593 y[1] (analytic) = 1.170732140695203 y[1] (numeric) = 1.170732140695201 absolute error = 2e-15 relative error = 1.708332700947598e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.594 y[1] (analytic) = 1.171291406573544 y[1] (numeric) = 1.171291406573542 absolute error = 2e-15 relative error = 1.707517009666050e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.595 y[1] (analytic) = 1.17185150116041 y[1] (numeric) = 1.171851501160408 absolute error = 2e-15 relative error = 1.706700890018511e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.596 y[1] (analytic) = 1.172412423895706 y[1] (numeric) = 1.172412423895704 absolute error = 2e-15 relative error = 1.705884345164457e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.597 y[1] (analytic) = 1.172974174218508 y[1] (numeric) = 1.172974174218507 absolute error = 1e-15 relative error = 8.525336891293862e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.598 y[1] (analytic) = 1.173536751567068 y[1] (numeric) = 1.173536751567067 absolute error = 1e-15 relative error = 8.521249962258636e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.599 y[1] (analytic) = 1.174100155378807 y[1] (numeric) = 1.174100155378806 absolute error = 1e-15 relative error = 8.517160954444844e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6 y[1] (analytic) = 1.174664385090322 y[1] (numeric) = 1.174664385090321 absolute error = 1e-15 relative error = 8.513069883557492e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.601 y[1] (analytic) = 1.175229440137383 y[1] (numeric) = 1.175229440137382 absolute error = 1e-15 relative error = 8.508976765278286e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.602 y[1] (analytic) = 1.175795319954935 y[1] (numeric) = 1.175795319954934 absolute error = 1e-15 relative error = 8.504881615265548e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.603 y[1] (analytic) = 1.176362023977098 y[1] (numeric) = 1.176362023977098 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.604 y[1] (analytic) = 1.176929551637169 y[1] (numeric) = 1.176929551637169 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.605 y[1] (analytic) = 1.17749790236762 y[1] (numeric) = 1.17749790236762 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.606 y[1] (analytic) = 1.1780670756001 y[1] (numeric) = 1.1780670756001 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.607 y[1] (analytic) = 1.178637070765435 y[1] (numeric) = 1.178637070765436 absolute error = 1e-15 relative error = 8.484375935592932e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.608 y[1] (analytic) = 1.179207887293632 y[1] (numeric) = 1.179207887293632 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.609 y[1] (analytic) = 1.179779524613873 y[1] (numeric) = 1.179779524613873 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.61 y[1] (analytic) = 1.18035198215452 y[1] (numeric) = 1.180351982154521 absolute error = 1e-15 relative error = 8.472049143973818e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.611 y[1] (analytic) = 1.180925259343118 y[1] (numeric) = 1.180925259343118 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.612 y[1] (analytic) = 1.181499355606388 y[1] (numeric) = 1.181499355606388 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=6.16 NO POLE x[1] = 0.613 y[1] (analytic) = 1.182074270370234 y[1] (numeric) = 1.182074270370234 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.614 y[1] (analytic) = 1.182650003059741 y[1] (numeric) = 1.182650003059741 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.615 y[1] (analytic) = 1.183226553099177 y[1] (numeric) = 1.183226553099177 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.616 y[1] (analytic) = 1.183803919911992 y[1] (numeric) = 1.183803919911992 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.617 y[1] (analytic) = 1.184382102920819 y[1] (numeric) = 1.184382102920819 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.618 y[1] (analytic) = 1.184961101547476 y[1] (numeric) = 1.184961101547475 absolute error = 1e-15 relative error = 8.439095584606703e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.619 y[1] (analytic) = 1.185540915212962 y[1] (numeric) = 1.185540915212962 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.62 y[1] (analytic) = 1.186121543337466 y[1] (numeric) = 1.186121543337466 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.621 y[1] (analytic) = 1.186702985340359 y[1] (numeric) = 1.186702985340359 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.622 y[1] (analytic) = 1.187285240640198 y[1] (numeric) = 1.187285240640198 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.623 y[1] (analytic) = 1.187868308654729 y[1] (numeric) = 1.187868308654729 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.624 y[1] (analytic) = 1.188452188800884 y[1] (numeric) = 1.188452188800884 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.625 y[1] (analytic) = 1.189036880494782 y[1] (numeric) = 1.189036880494782 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.626 y[1] (analytic) = 1.189622383151732 y[1] (numeric) = 1.189622383151732 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.627 y[1] (analytic) = 1.190208696186232 y[1] (numeric) = 1.190208696186232 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.628 y[1] (analytic) = 1.190795819011968 y[1] (numeric) = 1.190795819011968 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.629 y[1] (analytic) = 1.191383751041817 y[1] (numeric) = 1.191383751041817 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.63 y[1] (analytic) = 1.191972491687848 y[1] (numeric) = 1.191972491687848 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.631 y[1] (analytic) = 1.19256204036132 y[1] (numeric) = 1.19256204036132 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.632 y[1] (analytic) = 1.193152396472684 y[1] (numeric) = 1.193152396472684 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.633 y[1] (analytic) = 1.193743559431585 y[1] (numeric) = 1.193743559431585 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.634 y[1] (analytic) = 1.194335528646859 y[1] (numeric) = 1.194335528646859 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.635 y[1] (analytic) = 1.194928303526537 y[1] (numeric) = 1.194928303526537 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.636 y[1] (analytic) = 1.195521883477845 y[1] (numeric) = 1.195521883477845 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.637 y[1] (analytic) = 1.196116267907202 y[1] (numeric) = 1.196116267907202 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.638 y[1] (analytic) = 1.196711456220224 y[1] (numeric) = 1.196711456220224 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=95.3MB, alloc=4.4MB, time=6.42 x[1] = 0.639 y[1] (analytic) = 1.197307447821723 y[1] (numeric) = 1.197307447821723 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.64 y[1] (analytic) = 1.197904242115707 y[1] (numeric) = 1.197904242115707 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.641 y[1] (analytic) = 1.198501838505383 y[1] (numeric) = 1.198501838505382 absolute error = 1e-15 relative error = 8.343750237772443e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.642 y[1] (analytic) = 1.199100236393153 y[1] (numeric) = 1.199100236393152 absolute error = 1e-15 relative error = 8.339586380267601e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.643 y[1] (analytic) = 1.19969943518062 y[1] (numeric) = 1.199699435180619 absolute error = 1e-15 relative error = 8.335421111950808e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.644 y[1] (analytic) = 1.200299434268585 y[1] (numeric) = 1.200299434268584 absolute error = 1e-15 relative error = 8.331254447431781e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.645 y[1] (analytic) = 1.200900233057049 y[1] (numeric) = 1.200900233057048 absolute error = 1e-15 relative error = 8.327086401293877e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.646 y[1] (analytic) = 1.201501830945213 y[1] (numeric) = 1.201501830945212 absolute error = 1e-15 relative error = 8.322916988094034e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.647 y[1] (analytic) = 1.20210422733148 y[1] (numeric) = 1.202104227331479 absolute error = 1e-15 relative error = 8.318746222362715e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.648 y[1] (analytic) = 1.202707421613454 y[1] (numeric) = 1.202707421613452 absolute error = 2e-15 relative error = 1.662914823720771e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.649 y[1] (analytic) = 1.203311413187939 y[1] (numeric) = 1.203311413187937 absolute error = 2e-15 relative error = 1.662080138258965e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.65 y[1] (analytic) = 1.203916201450944 y[1] (numeric) = 1.203916201450943 absolute error = 1e-15 relative error = 8.306225954886338e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.651 y[1] (analytic) = 1.204521785797682 y[1] (numeric) = 1.204521785797681 absolute error = 1e-15 relative error = 8.302049923802419e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.652 y[1] (analytic) = 1.205128165622568 y[1] (numeric) = 1.205128165622567 absolute error = 1e-15 relative error = 8.297872612440362e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.653 y[1] (analytic) = 1.205735340319221 y[1] (numeric) = 1.205735340319221 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.654 y[1] (analytic) = 1.206343309280469 y[1] (numeric) = 1.206343309280468 absolute error = 1e-15 relative error = 8.289514206336969e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.655 y[1] (analytic) = 1.20695207189834 y[1] (numeric) = 1.20695207189834 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.656 y[1] (analytic) = 1.207561627564074 y[1] (numeric) = 1.207561627564074 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.657 y[1] (analytic) = 1.208171975668115 y[1] (numeric) = 1.208171975668114 absolute error = 1e-15 relative error = 8.276967353484618e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.658 y[1] (analytic) = 1.208783115600113 y[1] (numeric) = 1.208783115600113 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.659 y[1] (analytic) = 1.20939504674893 y[1] (numeric) = 1.20939504674893 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.66 y[1] (analytic) = 1.210007768502635 y[1] (numeric) = 1.210007768502634 absolute error = 1e-15 relative error = 8.264409750339734e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.661 y[1] (analytic) = 1.210621280248505 y[1] (numeric) = 1.210621280248504 absolute error = 1e-15 relative error = 8.260221559914504e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.662 y[1] (analytic) = 1.211235581373029 y[1] (numeric) = 1.211235581373028 absolute error = 1e-15 relative error = 8.256032231701969e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.663 y[1] (analytic) = 1.211850671261906 y[1] (numeric) = 1.211850671261905 absolute error = 1e-15 relative error = 8.251841779801922e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.664 y[1] (analytic) = 1.212466549300046 y[1] (numeric) = 1.212466549300045 absolute error = 1e-15 relative error = 8.247650218286827e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.665 y[1] (analytic) = 1.213083214871571 y[1] (numeric) = 1.21308321487157 absolute error = 1e-15 relative error = 8.243457561201767e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=6.68 NO POLE x[1] = 0.666 y[1] (analytic) = 1.213700667359816 y[1] (numeric) = 1.213700667359815 absolute error = 1e-15 relative error = 8.239263822564399e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.667 y[1] (analytic) = 1.214318906147328 y[1] (numeric) = 1.214318906147327 absolute error = 1e-15 relative error = 8.235069016364918e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.668 y[1] (analytic) = 1.214937930615868 y[1] (numeric) = 1.214937930615867 absolute error = 1e-15 relative error = 8.230873156566005e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.669 y[1] (analytic) = 1.215557740146412 y[1] (numeric) = 1.215557740146411 absolute error = 1e-15 relative error = 8.226676257102781e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.67 y[1] (analytic) = 1.216178334119151 y[1] (numeric) = 1.21617833411915 absolute error = 1e-15 relative error = 8.222478331882768e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.671 y[1] (analytic) = 1.21679971191349 y[1] (numeric) = 1.216799711913489 absolute error = 1e-15 relative error = 8.218279394785856e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.672 y[1] (analytic) = 1.217421872908052 y[1] (numeric) = 1.217421872908051 absolute error = 1e-15 relative error = 8.214079459664241e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.673 y[1] (analytic) = 1.218044816480676 y[1] (numeric) = 1.218044816480675 absolute error = 1e-15 relative error = 8.209878540342401e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.674 y[1] (analytic) = 1.218668542008418 y[1] (numeric) = 1.218668542008417 absolute error = 1e-15 relative error = 8.205676650617051e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.675 y[1] (analytic) = 1.219293048867553 y[1] (numeric) = 1.219293048867552 absolute error = 1e-15 relative error = 8.201473804257093e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.676 y[1] (analytic) = 1.219918336433574 y[1] (numeric) = 1.219918336433573 absolute error = 1e-15 relative error = 8.197270015003592e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.677 y[1] (analytic) = 1.220544404081194 y[1] (numeric) = 1.220544404081193 absolute error = 1e-15 relative error = 8.193065296569720e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.678 y[1] (analytic) = 1.221171251184345 y[1] (numeric) = 1.221171251184344 absolute error = 1e-15 relative error = 8.188859662640735e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.679 y[1] (analytic) = 1.221798877116179 y[1] (numeric) = 1.221798877116179 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.68 y[1] (analytic) = 1.222427281249072 y[1] (numeric) = 1.222427281249072 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.681 y[1] (analytic) = 1.223056462954619 y[1] (numeric) = 1.223056462954619 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.682 y[1] (analytic) = 1.223686421603638 y[1] (numeric) = 1.223686421603638 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.683 y[1] (analytic) = 1.22431715656617 y[1] (numeric) = 1.224317156566171 absolute error = 1e-15 relative error = 8.167818237593680e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.684 y[1] (analytic) = 1.224948667211482 y[1] (numeric) = 1.224948667211482 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.685 y[1] (analytic) = 1.225580952908061 y[1] (numeric) = 1.225580952908062 absolute error = 1e-15 relative error = 8.159395734954904e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.686 y[1] (analytic) = 1.226214013023623 y[1] (numeric) = 1.226214013023624 absolute error = 1e-15 relative error = 8.155183266371096e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.687 y[1] (analytic) = 1.226847846925108 y[1] (numeric) = 1.226847846925109 absolute error = 1e-15 relative error = 8.150970004196814e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.688 y[1] (analytic) = 1.227482453978681 y[1] (numeric) = 1.227482453978682 absolute error = 1e-15 relative error = 8.146755961836079e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.689 y[1] (analytic) = 1.228117833549736 y[1] (numeric) = 1.228117833549737 absolute error = 1e-15 relative error = 8.142541152664585e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.69 y[1] (analytic) = 1.228753985002893 y[1] (numeric) = 1.228753985002894 absolute error = 1e-15 relative error = 8.138325590029688e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.691 y[1] (analytic) = 1.229390907702001 y[1] (numeric) = 1.229390907702002 absolute error = 1e-15 relative error = 8.134109287250363e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.4MB, time=6.95 NO POLE x[1] = 0.692 y[1] (analytic) = 1.230028601010137 y[1] (numeric) = 1.230028601010138 absolute error = 1e-15 relative error = 8.129892257617177e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.693 y[1] (analytic) = 1.230667064289608 y[1] (numeric) = 1.230667064289609 absolute error = 1e-15 relative error = 8.125674514392253e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.694 y[1] (analytic) = 1.23130629690195 y[1] (numeric) = 1.231306296901951 absolute error = 1e-15 relative error = 8.121456070809251e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.695 y[1] (analytic) = 1.231946298207932 y[1] (numeric) = 1.231946298207932 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.696 y[1] (analytic) = 1.232587067567551 y[1] (numeric) = 1.232587067567551 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.697 y[1] (analytic) = 1.233228604340038 y[1] (numeric) = 1.233228604340039 absolute error = 1e-15 relative error = 8.108796669820595e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.698 y[1] (analytic) = 1.233870907883858 y[1] (numeric) = 1.233870907883858 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.699 y[1] (analytic) = 1.234513977556705 y[1] (numeric) = 1.234513977556706 absolute error = 1e-15 relative error = 8.100353808704178e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7 y[1] (analytic) = 1.235157812715512 y[1] (numeric) = 1.235157812715512 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.701 y[1] (analytic) = 1.235802412716441 y[1] (numeric) = 1.235802412716442 absolute error = 1e-15 relative error = 8.091908461336314e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.702 y[1] (analytic) = 1.236447776914895 y[1] (numeric) = 1.236447776914895 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.703 y[1] (analytic) = 1.237093904665508 y[1] (numeric) = 1.237093904665508 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.704 y[1] (analytic) = 1.237740795322152 y[1] (numeric) = 1.237740795322153 absolute error = 1e-15 relative error = 8.079236006273234e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.705 y[1] (analytic) = 1.238388448237938 y[1] (numeric) = 1.238388448237939 absolute error = 1e-15 relative error = 8.075010724000752e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.706 y[1] (analytic) = 1.239036862765212 y[1] (numeric) = 1.239036862765213 absolute error = 1e-15 relative error = 8.070784897942882e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.707 y[1] (analytic) = 1.23968603825556 y[1] (numeric) = 1.239686038255561 absolute error = 1e-15 relative error = 8.066558540960603e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.708 y[1] (analytic) = 1.240335974059807 y[1] (numeric) = 1.240335974059807 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.709 y[1] (analytic) = 1.240986669528016 y[1] (numeric) = 1.240986669528016 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.71 y[1] (analytic) = 1.241638124009492 y[1] (numeric) = 1.241638124009492 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.711 y[1] (analytic) = 1.242290336852781 y[1] (numeric) = 1.242290336852781 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.712 y[1] (analytic) = 1.24294330740567 y[1] (numeric) = 1.24294330740567 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.713 y[1] (analytic) = 1.243597035015188 y[1] (numeric) = 1.243597035015188 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.714 y[1] (analytic) = 1.244251519027609 y[1] (numeric) = 1.244251519027608 absolute error = 1e-15 relative error = 8.036960250460508e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.715 y[1] (analytic) = 1.244906758788447 y[1] (numeric) = 1.244906758788446 absolute error = 1e-15 relative error = 8.032730105612149e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.716 y[1] (analytic) = 1.245562753642464 y[1] (numeric) = 1.245562753642463 absolute error = 1e-15 relative error = 8.028499544287495e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.717 y[1] (analytic) = 1.246219502933664 y[1] (numeric) = 1.246219502933663 absolute error = 1e-15 relative error = 8.024268579058097e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=7.22 NO POLE x[1] = 0.718 y[1] (analytic) = 1.246877006005298 y[1] (numeric) = 1.246877006005297 absolute error = 1e-15 relative error = 8.020037222466439e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.719 y[1] (analytic) = 1.247535262199864 y[1] (numeric) = 1.247535262199863 absolute error = 1e-15 relative error = 8.015805487025928e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.72 y[1] (analytic) = 1.248194270859105 y[1] (numeric) = 1.248194270859104 absolute error = 1e-15 relative error = 8.011573385220890e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.721 y[1] (analytic) = 1.248854031324012 y[1] (numeric) = 1.248854031324011 absolute error = 1e-15 relative error = 8.007340929506537e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.722 y[1] (analytic) = 1.249514542934826 y[1] (numeric) = 1.249514542934824 absolute error = 2e-15 relative error = 1.600621626461789e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.723 y[1] (analytic) = 1.250175805031034 y[1] (numeric) = 1.250175805031032 absolute error = 2e-15 relative error = 1.599775001205013e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.724 y[1] (analytic) = 1.250837816951374 y[1] (numeric) = 1.250837816951372 absolute error = 2e-15 relative error = 1.598928312604534e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.725 y[1] (analytic) = 1.251500578033835 y[1] (numeric) = 1.251500578033833 absolute error = 2e-15 relative error = 1.598081563128075e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.726 y[1] (analytic) = 1.252164087615656 y[1] (numeric) = 1.252164087615654 absolute error = 2e-15 relative error = 1.597234755237516e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.727 y[1] (analytic) = 1.252828345033326 y[1] (numeric) = 1.252828345033325 absolute error = 1e-15 relative error = 7.981939456944514e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.728 y[1] (analytic) = 1.25349334962259 y[1] (numeric) = 1.253493349622588 absolute error = 2e-15 relative error = 1.595540974032430e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.729 y[1] (analytic) = 1.254159100718441 y[1] (numeric) = 1.25415910071844 absolute error = 1e-15 relative error = 7.973470028062255e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.73 y[1] (analytic) = 1.25482559765513 y[1] (numeric) = 1.254825597655129 absolute error = 1e-15 relative error = 7.969234942837331e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.731 y[1] (analytic) = 1.255492839766158 y[1] (numeric) = 1.255492839766158 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.732 y[1] (analytic) = 1.256160826384286 y[1] (numeric) = 1.256160826384285 absolute error = 1e-15 relative error = 7.960764091636137e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.733 y[1] (analytic) = 1.256829556841524 y[1] (numeric) = 1.256829556841524 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.734 y[1] (analytic) = 1.257499030469144 y[1] (numeric) = 1.257499030469144 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.735 y[1] (analytic) = 1.258169246597672 y[1] (numeric) = 1.258169246597672 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.736 y[1] (analytic) = 1.258840204556891 y[1] (numeric) = 1.258840204556891 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.737 y[1] (analytic) = 1.259511903675844 y[1] (numeric) = 1.259511903675844 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.738 y[1] (analytic) = 1.260184343282831 y[1] (numeric) = 1.260184343282831 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.739 y[1] (analytic) = 1.260857522705414 y[1] (numeric) = 1.260857522705414 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.74 y[1] (analytic) = 1.261531441270412 y[1] (numeric) = 1.261531441270412 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.741 y[1] (analytic) = 1.262206098303908 y[1] (numeric) = 1.262206098303907 absolute error = 1e-15 relative error = 7.922636416855789e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.742 y[1] (analytic) = 1.262881493131243 y[1] (numeric) = 1.262881493131243 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.743 y[1] (analytic) = 1.263557625077024 y[1] (numeric) = 1.263557625077024 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=110.6MB, alloc=4.4MB, time=7.48 x[1] = 0.744 y[1] (analytic) = 1.264234493465119 y[1] (numeric) = 1.264234493465119 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.745 y[1] (analytic) = 1.264912097618659 y[1] (numeric) = 1.264912097618659 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.746 y[1] (analytic) = 1.26559043686004 y[1] (numeric) = 1.26559043686004 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.747 y[1] (analytic) = 1.266269510510923 y[1] (numeric) = 1.266269510510923 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.748 y[1] (analytic) = 1.266949317892234 y[1] (numeric) = 1.266949317892234 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.749 y[1] (analytic) = 1.267629858324166 y[1] (numeric) = 1.267629858324166 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.75 y[1] (analytic) = 1.268311131126179 y[1] (numeric) = 1.268311131126179 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.751 y[1] (analytic) = 1.268993135617 y[1] (numeric) = 1.268993135617 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.752 y[1] (analytic) = 1.269675871114624 y[1] (numeric) = 1.269675871114624 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.753 y[1] (analytic) = 1.270359336936317 y[1] (numeric) = 1.270359336936316 absolute error = 1e-15 relative error = 7.871788484757915e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.754 y[1] (analytic) = 1.271043532398611 y[1] (numeric) = 1.271043532398611 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.755 y[1] (analytic) = 1.271728456817313 y[1] (numeric) = 1.271728456817312 absolute error = 1e-15 relative error = 7.863313859490466e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.756 y[1] (analytic) = 1.272414109507496 y[1] (numeric) = 1.272414109507496 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.757 y[1] (analytic) = 1.27310048978351 y[1] (numeric) = 1.27310048978351 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.758 y[1] (analytic) = 1.273787596958974 y[1] (numeric) = 1.273787596958973 absolute error = 1e-15 relative error = 7.850602426867624e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.759 y[1] (analytic) = 1.27447543034678 y[1] (numeric) = 1.274475430346779 absolute error = 1e-15 relative error = 7.846365462909738e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.76 y[1] (analytic) = 1.275163989259095 y[1] (numeric) = 1.275163989259094 absolute error = 1e-15 relative error = 7.842128607952827e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.761 y[1] (analytic) = 1.27585327300736 y[1] (numeric) = 1.275853273007359 absolute error = 1e-15 relative error = 7.837891873278373e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.762 y[1] (analytic) = 1.276543280902292 y[1] (numeric) = 1.276543280902291 absolute error = 1e-15 relative error = 7.833655270138397e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.763 y[1] (analytic) = 1.277234012253883 y[1] (numeric) = 1.277234012253882 absolute error = 1e-15 relative error = 7.829418809755470e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.764 y[1] (analytic) = 1.277925466371402 y[1] (numeric) = 1.2779254663714 absolute error = 2e-15 relative error = 1.565036500664541e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.765 y[1] (analytic) = 1.278617642563394 y[1] (numeric) = 1.278617642563392 absolute error = 2e-15 relative error = 1.564189272400752e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.766 y[1] (analytic) = 1.279310540137683 y[1] (numeric) = 1.279310540137681 absolute error = 2e-15 relative error = 1.563342079386569e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.767 y[1] (analytic) = 1.280004158401372 y[1] (numeric) = 1.28000415840137 absolute error = 2e-15 relative error = 1.562494923842941e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.768 y[1] (analytic) = 1.280698496660843 y[1] (numeric) = 1.280698496660841 absolute error = 2e-15 relative error = 1.561647807984929e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.769 y[1] (analytic) = 1.281393554221757 y[1] (numeric) = 1.281393554221755 absolute error = 2e-15 relative error = 1.560800734021705e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.77 memory used=114.4MB, alloc=4.4MB, time=7.74 y[1] (analytic) = 1.282089330389057 y[1] (numeric) = 1.282089330389055 absolute error = 2e-15 relative error = 1.559953704156550e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.771 y[1] (analytic) = 1.282785824466966 y[1] (numeric) = 1.282785824466965 absolute error = 1e-15 relative error = 7.795533602934289e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.772 y[1] (analytic) = 1.283483035758992 y[1] (numeric) = 1.28348303575899 absolute error = 2e-15 relative error = 1.558259785504133e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.773 y[1] (analytic) = 1.284180963567922 y[1] (numeric) = 1.28418096356792 absolute error = 2e-15 relative error = 1.557412901093996e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.774 y[1] (analytic) = 1.284879607195829 y[1] (numeric) = 1.284879607195827 absolute error = 2e-15 relative error = 1.556566069536178e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.775 y[1] (analytic) = 1.285578965944069 y[1] (numeric) = 1.285578965944067 absolute error = 2e-15 relative error = 1.555719293004529e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.776 y[1] (analytic) = 1.286279039113283 y[1] (numeric) = 1.286279039113282 absolute error = 1e-15 relative error = 7.774362868335054e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.777 y[1] (analytic) = 1.286979826003399 y[1] (numeric) = 1.286979826003398 absolute error = 1e-15 relative error = 7.770129568428518e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.778 y[1] (analytic) = 1.28768132591363 y[1] (numeric) = 1.287681325913629 absolute error = 1e-15 relative error = 7.765896576084028e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.779 y[1] (analytic) = 1.288383538142475 y[1] (numeric) = 1.288383538142474 absolute error = 1e-15 relative error = 7.761663902053176e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.78 y[1] (analytic) = 1.289086461987723 y[1] (numeric) = 1.289086461987722 absolute error = 1e-15 relative error = 7.757431557058147e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.781 y[1] (analytic) = 1.289790096746449 y[1] (numeric) = 1.289790096746449 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.782 y[1] (analytic) = 1.29049444171502 y[1] (numeric) = 1.29049444171502 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.783 y[1] (analytic) = 1.29119949618909 y[1] (numeric) = 1.29119949618909 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.784 y[1] (analytic) = 1.291905259463604 y[1] (numeric) = 1.291905259463605 absolute error = 1e-15 relative error = 7.740505680851533e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.785 y[1] (analytic) = 1.2926117308328 y[1] (numeric) = 1.292611730832801 absolute error = 1e-15 relative error = 7.736275140840034e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.786 y[1] (analytic) = 1.293318909590206 y[1] (numeric) = 1.293318909590207 absolute error = 1e-15 relative error = 7.732044993580544e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.787 y[1] (analytic) = 1.294026795028644 y[1] (numeric) = 1.294026795028645 absolute error = 1e-15 relative error = 7.727815249589669e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.788 y[1] (analytic) = 1.294735386440228 y[1] (numeric) = 1.294735386440229 absolute error = 1e-15 relative error = 7.723585919354691e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.789 y[1] (analytic) = 1.295444683116367 y[1] (numeric) = 1.295444683116368 absolute error = 1e-15 relative error = 7.719357013333561e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.79 y[1] (analytic) = 1.296154684347764 y[1] (numeric) = 1.296154684347765 absolute error = 1e-15 relative error = 7.715128541954917e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.791 y[1] (analytic) = 1.296865389424418 y[1] (numeric) = 1.296865389424419 absolute error = 1e-15 relative error = 7.710900515618090e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.792 y[1] (analytic) = 1.297576797635624 y[1] (numeric) = 1.297576797635625 absolute error = 1e-15 relative error = 7.706672944693118e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.793 y[1] (analytic) = 1.298288908269973 y[1] (numeric) = 1.298288908269975 absolute error = 2e-15 relative error = 1.540489167904152e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.794 y[1] (analytic) = 1.299001720615356 y[1] (numeric) = 1.299001720615358 absolute error = 2e-15 relative error = 1.539643842082496e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.795 y[1] (analytic) = 1.29971523395896 y[1] (numeric) = 1.299715233958962 absolute error = 2e-15 relative error = 1.538798613530102e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.796 y[1] (analytic) = 1.300429447587272 y[1] (numeric) = 1.300429447587274 absolute error = 2e-15 relative error = 1.537953484297563e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=8.00 NO POLE x[1] = 0.797 y[1] (analytic) = 1.301144360786078 y[1] (numeric) = 1.30114436078608 absolute error = 2e-15 relative error = 1.537108456429625e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.798 y[1] (analytic) = 1.301859972840464 y[1] (numeric) = 1.301859972840467 absolute error = 3e-15 relative error = 2.304395297947788e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.799 y[1] (analytic) = 1.30257628303482 y[1] (numeric) = 1.302576283034823 absolute error = 3e-15 relative error = 2.303128069405978e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8 y[1] (analytic) = 1.303293290652835 y[1] (numeric) = 1.303293290652838 absolute error = 3e-15 relative error = 2.301861002059839e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.801 y[1] (analytic) = 1.3040109949775 y[1] (numeric) = 1.304010994977504 absolute error = 4e-15 relative error = 3.067458798588595e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.802 y[1] (analytic) = 1.304729395291113 y[1] (numeric) = 1.304729395291117 absolute error = 4e-15 relative error = 3.065769817432154e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.803 y[1] (analytic) = 1.305448490875273 y[1] (numeric) = 1.305448490875277 absolute error = 4e-15 relative error = 3.064081063296563e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.804 y[1] (analytic) = 1.306168281010884 y[1] (numeric) = 1.306168281010888 absolute error = 4e-15 relative error = 3.062392540189597e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.805 y[1] (analytic) = 1.306888764978156 y[1] (numeric) = 1.30688876497816 absolute error = 4e-15 relative error = 3.060704252107377e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.806 y[1] (analytic) = 1.307609942056605 y[1] (numeric) = 1.307609942056609 absolute error = 4e-15 relative error = 3.059016203034379e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.807 y[1] (analytic) = 1.308331811525055 y[1] (numeric) = 1.308331811525059 absolute error = 4e-15 relative error = 3.057328396943437e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.808 y[1] (analytic) = 1.309054372661635 y[1] (numeric) = 1.309054372661639 absolute error = 4e-15 relative error = 3.055640837795759e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.809 y[1] (analytic) = 1.309777624743785 y[1] (numeric) = 1.309777624743789 absolute error = 4e-15 relative error = 3.053953529540916e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.81 y[1] (analytic) = 1.310501567048253 y[1] (numeric) = 1.310501567048257 absolute error = 4e-15 relative error = 3.052266476116864e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.811 y[1] (analytic) = 1.311226198851096 y[1] (numeric) = 1.3112261988511 absolute error = 4e-15 relative error = 3.050579681449946e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.812 y[1] (analytic) = 1.311951519427684 y[1] (numeric) = 1.311951519427687 absolute error = 3e-15 relative error = 2.286669862091168e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.813 y[1] (analytic) = 1.312677528052694 y[1] (numeric) = 1.312677528052697 absolute error = 3e-15 relative error = 2.285405163026127e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.814 y[1] (analytic) = 1.313404224000119 y[1] (numeric) = 1.313404224000122 absolute error = 3e-15 relative error = 2.284140666810988e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.815 y[1] (analytic) = 1.314131606543263 y[1] (numeric) = 1.314131606543266 absolute error = 3e-15 relative error = 2.282876376355716e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.816 y[1] (analytic) = 1.314859674954743 y[1] (numeric) = 1.314859674954746 absolute error = 3e-15 relative error = 2.281612294561592e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.817 y[1] (analytic) = 1.315588428506491 y[1] (numeric) = 1.315588428506494 absolute error = 3e-15 relative error = 2.280348424321215e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.818 y[1] (analytic) = 1.316317866469753 y[1] (numeric) = 1.316317866469757 absolute error = 4e-15 relative error = 3.038779691358017e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.819 y[1] (analytic) = 1.317047988115092 y[1] (numeric) = 1.317047988115096 absolute error = 4e-15 relative error = 3.037095106704992e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.82 y[1] (analytic) = 1.317778792712386 y[1] (numeric) = 1.31777879271239 absolute error = 4e-15 relative error = 3.035410815624673e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.821 y[1] (analytic) = 1.318510279530831 y[1] (numeric) = 1.318510279530834 absolute error = 3e-15 relative error = 2.275295116445734e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.822 y[1] (analytic) = 1.319242447838939 y[1] (numeric) = 1.319242447838942 absolute error = 3e-15 relative error = 2.274032347059726e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=8.25 NO POLE x[1] = 0.823 y[1] (analytic) = 1.319975296904543 y[1] (numeric) = 1.319975296904546 absolute error = 3e-15 relative error = 2.272769806401121e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.824 y[1] (analytic) = 1.320708825994793 y[1] (numeric) = 1.320708825994796 absolute error = 3e-15 relative error = 2.271507497301928e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.825 y[1] (analytic) = 1.32144303437616 y[1] (numeric) = 1.321443034376163 absolute error = 3e-15 relative error = 2.270245422585522e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.826 y[1] (analytic) = 1.322177921314437 y[1] (numeric) = 1.322177921314439 absolute error = 2e-15 relative error = 1.512655723377765e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.827 y[1] (analytic) = 1.322913486074735 y[1] (numeric) = 1.322913486074738 absolute error = 3e-15 relative error = 2.267721987551438e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.828 y[1] (analytic) = 1.323649727921492 y[1] (numeric) = 1.323649727921494 absolute error = 2e-15 relative error = 1.510973755224935e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.829 y[1] (analytic) = 1.324386646118463 y[1] (numeric) = 1.324386646118466 absolute error = 3e-15 relative error = 2.265199523713453e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.83 y[1] (analytic) = 1.325124239928733 y[1] (numeric) = 1.325124239928735 absolute error = 2e-15 relative error = 1.509292441973262e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.831 y[1] (analytic) = 1.325862508614706 y[1] (numeric) = 1.325862508614708 absolute error = 2e-15 relative error = 1.508452035565626e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.832 y[1] (analytic) = 1.326601451438115 y[1] (numeric) = 1.326601451438117 absolute error = 2e-15 relative error = 1.507611798428142e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.833 y[1] (analytic) = 1.327341067660016 y[1] (numeric) = 1.327341067660018 absolute error = 2e-15 relative error = 1.506771732397176e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.834 y[1] (analytic) = 1.328081356540793 y[1] (numeric) = 1.328081356540795 absolute error = 2e-15 relative error = 1.505931839303377e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.835 y[1] (analytic) = 1.328822317340158 y[1] (numeric) = 1.32882231734016 absolute error = 2e-15 relative error = 1.505092120971679e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.836 y[1] (analytic) = 1.329563949317149 y[1] (numeric) = 1.329563949317151 absolute error = 2e-15 relative error = 1.504252579221316e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.837 y[1] (analytic) = 1.330306251730135 y[1] (numeric) = 1.330306251730137 absolute error = 2e-15 relative error = 1.503413215865814e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.838 y[1] (analytic) = 1.331049223836814 y[1] (numeric) = 1.331049223836816 absolute error = 2e-15 relative error = 1.502574032713007e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.839 y[1] (analytic) = 1.331792864894213 y[1] (numeric) = 1.331792864894215 absolute error = 2e-15 relative error = 1.501735031565035e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.84 y[1] (analytic) = 1.332537174158692 y[1] (numeric) = 1.332537174158694 absolute error = 2e-15 relative error = 1.500896214218351e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.841 y[1] (analytic) = 1.333282150885941 y[1] (numeric) = 1.333282150885943 absolute error = 2e-15 relative error = 1.500057582463725e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.842 y[1] (analytic) = 1.334027794330983 y[1] (numeric) = 1.334027794330985 absolute error = 2e-15 relative error = 1.499219138086252e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.843 y[1] (analytic) = 1.334774103748176 y[1] (numeric) = 1.334774103748178 absolute error = 2e-15 relative error = 1.498380882865351e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.844 y[1] (analytic) = 1.335521078391209 y[1] (numeric) = 1.335521078391211 absolute error = 2e-15 relative error = 1.497542818574779e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.845 y[1] (analytic) = 1.336268717513108 y[1] (numeric) = 1.336268717513111 absolute error = 3e-15 relative error = 2.245057420473941e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.846 y[1] (analytic) = 1.337017020366235 y[1] (numeric) = 1.337017020366238 absolute error = 3e-15 relative error = 2.243800904776995e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.847 y[1] (analytic) = 1.337765986202286 y[1] (numeric) = 1.337765986202289 absolute error = 3e-15 relative error = 2.242544683406508e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.848 y[1] (analytic) = 1.338515614272296 y[1] (numeric) = 1.338515614272299 absolute error = 3e-15 relative error = 2.241288758989184e-13 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=8.51 NO POLE x[1] = 0.849 y[1] (analytic) = 1.339265903826636 y[1] (numeric) = 1.339265903826639 absolute error = 3e-15 relative error = 2.240033134143271e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.85 y[1] (analytic) = 1.340016854115018 y[1] (numeric) = 1.34001685411502 absolute error = 2e-15 relative error = 1.492518540985704e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.851 y[1] (analytic) = 1.34076846438649 y[1] (numeric) = 1.340768464386492 absolute error = 2e-15 relative error = 1.491681862397593e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.852 y[1] (analytic) = 1.341520733889443 y[1] (numeric) = 1.341520733889445 absolute error = 2e-15 relative error = 1.490845388726451e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.853 y[1] (analytic) = 1.342273661871607 y[1] (numeric) = 1.342273661871609 absolute error = 2e-15 relative error = 1.490009121695265e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.854 y[1] (analytic) = 1.343027247580055 y[1] (numeric) = 1.343027247580057 absolute error = 2e-15 relative error = 1.489173063021407e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.855 y[1] (analytic) = 1.3437814902612 y[1] (numeric) = 1.343781490261202 absolute error = 2e-15 relative error = 1.488337214416643e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.856 y[1] (analytic) = 1.344536389160801 y[1] (numeric) = 1.344536389160802 absolute error = 1e-15 relative error = 7.437507887935669e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.857 y[1] (analytic) = 1.345291943523957 y[1] (numeric) = 1.345291943523959 absolute error = 2e-15 relative error = 1.486666154233446e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.858 y[1] (analytic) = 1.346048152595116 y[1] (numeric) = 1.346048152595117 absolute error = 1e-15 relative error = 7.429154730252764e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.859 y[1] (analytic) = 1.346805015618067 y[1] (numeric) = 1.346805015618068 absolute error = 1e-15 relative error = 7.424979773639219e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.86 y[1] (analytic) = 1.347562531835948 y[1] (numeric) = 1.347562531835949 absolute error = 1e-15 relative error = 7.420805909745640e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.861 y[1] (analytic) = 1.348320700491243 y[1] (numeric) = 1.348320700491244 absolute error = 1e-15 relative error = 7.416633146963205e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.862 y[1] (analytic) = 1.349079520825784 y[1] (numeric) = 1.349079520825784 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.863 y[1] (analytic) = 1.349838992080749 y[1] (numeric) = 1.349838992080749 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.864 y[1] (analytic) = 1.350599113496668 y[1] (numeric) = 1.350599113496668 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.865 y[1] (analytic) = 1.351359884313419 y[1] (numeric) = 1.351359884313419 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.866 y[1] (analytic) = 1.352121303770232 y[1] (numeric) = 1.352121303770232 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.867 y[1] (analytic) = 1.352883371105687 y[1] (numeric) = 1.352883371105687 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.868 y[1] (analytic) = 1.353646085557717 y[1] (numeric) = 1.353646085557717 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.869 y[1] (analytic) = 1.354409446363608 y[1] (numeric) = 1.354409446363608 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.87 y[1] (analytic) = 1.355173452759999 y[1] (numeric) = 1.355173452759999 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.871 y[1] (analytic) = 1.355938103982883 y[1] (numeric) = 1.355938103982883 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.872 y[1] (analytic) = 1.356703399267609 y[1] (numeric) = 1.356703399267609 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.873 y[1] (analytic) = 1.357469337848883 y[1] (numeric) = 1.357469337848883 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.874 y[1] (analytic) = 1.358235918960765 y[1] (numeric) = 1.358235918960765 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.4MB, time=8.77 x[1] = 0.875 y[1] (analytic) = 1.359003141836675 y[1] (numeric) = 1.359003141836675 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.876 y[1] (analytic) = 1.359771005709389 y[1] (numeric) = 1.359771005709389 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.877 y[1] (analytic) = 1.360539509811045 y[1] (numeric) = 1.360539509811044 absolute error = 1e-15 relative error = 7.350025433211288e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.878 y[1] (analytic) = 1.361308653373137 y[1] (numeric) = 1.361308653373136 absolute error = 1e-15 relative error = 7.345872646310861e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.879 y[1] (analytic) = 1.362078435626523 y[1] (numeric) = 1.362078435626522 absolute error = 1e-15 relative error = 7.341721106832033e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.88 y[1] (analytic) = 1.36284885580142 y[1] (numeric) = 1.362848855801419 absolute error = 1e-15 relative error = 7.337570822642342e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.881 y[1] (analytic) = 1.363619913127408 y[1] (numeric) = 1.363619913127407 absolute error = 1e-15 relative error = 7.333421801582083e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.882 y[1] (analytic) = 1.36439160683343 y[1] (numeric) = 1.364391606833429 absolute error = 1e-15 relative error = 7.329274051464344e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.883 y[1] (analytic) = 1.365163936147792 y[1] (numeric) = 1.365163936147791 absolute error = 1e-15 relative error = 7.325127580075046e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.884 y[1] (analytic) = 1.365936900298165 y[1] (numeric) = 1.365936900298164 absolute error = 1e-15 relative error = 7.320982395172968e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.885 y[1] (analytic) = 1.366710498511585 y[1] (numeric) = 1.366710498511584 absolute error = 1e-15 relative error = 7.316838504489789e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.886 y[1] (analytic) = 1.367484730014453 y[1] (numeric) = 1.367484730014453 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.887 y[1] (analytic) = 1.368259594032539 y[1] (numeric) = 1.368259594032539 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.888 y[1] (analytic) = 1.369035089790978 y[1] (numeric) = 1.369035089790978 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.889 y[1] (analytic) = 1.369811216514275 y[1] (numeric) = 1.369811216514275 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.89 y[1] (analytic) = 1.370587973426303 y[1] (numeric) = 1.370587973426303 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.891 y[1] (analytic) = 1.371365359750305 y[1] (numeric) = 1.371365359750305 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.892 y[1] (analytic) = 1.372143374708895 y[1] (numeric) = 1.372143374708895 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.893 y[1] (analytic) = 1.372922017524058 y[1] (numeric) = 1.372922017524058 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.894 y[1] (analytic) = 1.373701287417151 y[1] (numeric) = 1.373701287417151 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.895 y[1] (analytic) = 1.374481183608904 y[1] (numeric) = 1.374481183608904 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.896 y[1] (analytic) = 1.375261705319422 y[1] (numeric) = 1.375261705319422 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.897 y[1] (analytic) = 1.376042851768182 y[1] (numeric) = 1.376042851768182 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.898 y[1] (analytic) = 1.376824622174038 y[1] (numeric) = 1.376824622174038 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.899 y[1] (analytic) = 1.377607015755221 y[1] (numeric) = 1.37760701575522 absolute error = 1e-15 relative error = 7.258964193440811e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9 y[1] (analytic) = 1.378390031729336 y[1] (numeric) = 1.378390031729335 absolute error = 1e-15 relative error = 7.254840625518702e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.901 y[1] (analytic) = 1.379173669313367 y[1] (numeric) = 1.379173669313366 absolute error = 1e-15 relative error = 7.250718471864811e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.4MB, time=9.04 NO POLE x[1] = 0.902 y[1] (analytic) = 1.379957927723677 y[1] (numeric) = 1.379957927723676 absolute error = 1e-15 relative error = 7.246597739755441e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.903 y[1] (analytic) = 1.380742806176008 y[1] (numeric) = 1.380742806176007 absolute error = 1e-15 relative error = 7.242478436440440e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.904 y[1] (analytic) = 1.381528303885481 y[1] (numeric) = 1.38152830388548 absolute error = 1e-15 relative error = 7.238360569143236e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.905 y[1] (analytic) = 1.382314420066598 y[1] (numeric) = 1.382314420066598 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.906 y[1] (analytic) = 1.383101153933244 y[1] (numeric) = 1.383101153933244 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.907 y[1] (analytic) = 1.383888504698685 y[1] (numeric) = 1.383888504698685 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.908 y[1] (analytic) = 1.38467647157557 y[1] (numeric) = 1.38467647157557 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.909 y[1] (analytic) = 1.385465053775932 y[1] (numeric) = 1.385465053775932 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.91 y[1] (analytic) = 1.386254250511188 y[1] (numeric) = 1.386254250511189 absolute error = 1e-15 relative error = 7.213683922925720e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.911 y[1] (analytic) = 1.387044060992144 y[1] (numeric) = 1.387044060992144 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.912 y[1] (analytic) = 1.387834484428987 y[1] (numeric) = 1.387834484428987 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.913 y[1] (analytic) = 1.388625520031294 y[1] (numeric) = 1.388625520031295 absolute error = 1e-15 relative error = 7.201365563103464e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.914 y[1] (analytic) = 1.389417167008031 y[1] (numeric) = 1.389417167008032 absolute error = 1e-15 relative error = 7.197262447486514e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.915 y[1] (analytic) = 1.39020942456755 y[1] (numeric) = 1.390209424567551 absolute error = 1e-15 relative error = 7.193160845611935e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.916 y[1] (analytic) = 1.391002291917593 y[1] (numeric) = 1.391002291917594 absolute error = 1e-15 relative error = 7.189060764389042e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.917 y[1] (analytic) = 1.391795768265294 y[1] (numeric) = 1.391795768265295 absolute error = 1e-15 relative error = 7.184962210701213e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.918 y[1] (analytic) = 1.392589852817176 y[1] (numeric) = 1.392589852817177 absolute error = 1e-15 relative error = 7.180865191405954e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.919 y[1] (analytic) = 1.393384544779154 y[1] (numeric) = 1.393384544779155 absolute error = 1e-15 relative error = 7.176769713334922e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.92 y[1] (analytic) = 1.394179843356537 y[1] (numeric) = 1.394179843356538 absolute error = 1e-15 relative error = 7.172675783293960e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.921 y[1] (analytic) = 1.394975747754026 y[1] (numeric) = 1.394975747754027 absolute error = 1e-15 relative error = 7.168583408063152e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.922 y[1] (analytic) = 1.395772257175717 y[1] (numeric) = 1.395772257175718 absolute error = 1e-15 relative error = 7.164492594396850e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.923 y[1] (analytic) = 1.396569370825101 y[1] (numeric) = 1.396569370825101 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.924 y[1] (analytic) = 1.397367087905063 y[1] (numeric) = 1.397367087905063 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.925 y[1] (analytic) = 1.398165407617887 y[1] (numeric) = 1.398165407617887 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.926 y[1] (analytic) = 1.398964329165254 y[1] (numeric) = 1.398964329165253 absolute error = 1e-15 relative error = 7.148145089565568e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.927 y[1] (analytic) = 1.399763851748241 y[1] (numeric) = 1.39976385174824 absolute error = 1e-15 relative error = 7.144062184139459e-14 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=9.29 NO POLE x[1] = 0.928 y[1] (analytic) = 1.400563974567327 y[1] (numeric) = 1.400563974567325 absolute error = 2e-15 relative error = 1.427996176053190e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.929 y[1] (analytic) = 1.401364696822388 y[1] (numeric) = 1.401364696822386 absolute error = 2e-15 relative error = 1.427180236904087e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.93 y[1] (analytic) = 1.402166017712702 y[1] (numeric) = 1.4021660177127 absolute error = 2e-15 relative error = 1.426364620690581e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.931 y[1] (analytic) = 1.402967936436948 y[1] (numeric) = 1.402967936436947 absolute error = 1e-15 relative error = 7.127746643587972e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.932 y[1] (analytic) = 1.403770452193209 y[1] (numeric) = 1.403770452193208 absolute error = 1e-15 relative error = 7.123671811424937e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.933 y[1] (analytic) = 1.404573564178968 y[1] (numeric) = 1.404573564178967 absolute error = 1e-15 relative error = 7.119598613437822e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.934 y[1] (analytic) = 1.405377271591112 y[1] (numeric) = 1.405377271591112 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.935 y[1] (analytic) = 1.406181573625936 y[1] (numeric) = 1.406181573625936 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.936 y[1] (analytic) = 1.406986469479137 y[1] (numeric) = 1.406986469479137 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.937 y[1] (analytic) = 1.407791958345818 y[1] (numeric) = 1.407791958345819 absolute error = 1e-15 relative error = 7.103322291846437e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.938 y[1] (analytic) = 1.408598039420492 y[1] (numeric) = 1.408598039420493 absolute error = 1e-15 relative error = 7.099257360967275e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.939 y[1] (analytic) = 1.409404711897078 y[1] (numeric) = 1.409404711897078 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.94 y[1] (analytic) = 1.410211974968902 y[1] (numeric) = 1.410211974968902 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.941 y[1] (analytic) = 1.411019827828702 y[1] (numeric) = 1.411019827828702 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.942 y[1] (analytic) = 1.411828269668625 y[1] (numeric) = 1.411828269668625 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.943 y[1] (analytic) = 1.412637299680229 y[1] (numeric) = 1.412637299680229 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.944 y[1] (analytic) = 1.413446917054485 y[1] (numeric) = 1.413446917054485 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.945 y[1] (analytic) = 1.414257120981775 y[1] (numeric) = 1.414257120981775 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.946 y[1] (analytic) = 1.415067910651895 y[1] (numeric) = 1.415067910651895 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.947 y[1] (analytic) = 1.415879285254056 y[1] (numeric) = 1.415879285254056 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.948 y[1] (analytic) = 1.416691243976883 y[1] (numeric) = 1.416691243976883 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.949 y[1] (analytic) = 1.417503786008417 y[1] (numeric) = 1.417503786008417 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.95 y[1] (analytic) = 1.418316910536116 y[1] (numeric) = 1.418316910536117 absolute error = 1e-15 relative error = 7.050610428257571e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.951 y[1] (analytic) = 1.419130616746857 y[1] (numeric) = 1.419130616746858 absolute error = 1e-15 relative error = 7.046567723923463e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.952 y[1] (analytic) = 1.419944903826933 y[1] (numeric) = 1.419944903826933 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.953 y[1] (analytic) = 1.420759770962056 y[1] (numeric) = 1.420759770962056 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=9.55 NO POLE x[1] = 0.954 y[1] (analytic) = 1.42157521733736 y[1] (numeric) = 1.42157521733736 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.955 y[1] (analytic) = 1.422391242137398 y[1] (numeric) = 1.422391242137399 absolute error = 1e-15 relative error = 7.030414490582216e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.956 y[1] (analytic) = 1.423207844546147 y[1] (numeric) = 1.423207844546147 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.957 y[1] (analytic) = 1.424025023747002 y[1] (numeric) = 1.424025023747003 absolute error = 1e-15 relative error = 7.022348507392971e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.958 y[1] (analytic) = 1.424842778922786 y[1] (numeric) = 1.424842778922787 absolute error = 1e-15 relative error = 7.018318194769693e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.959 y[1] (analytic) = 1.425661109255743 y[1] (numeric) = 1.425661109255744 absolute error = 1e-15 relative error = 7.014289675910732e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.96 y[1] (analytic) = 1.426480013927543 y[1] (numeric) = 1.426480013927544 absolute error = 1e-15 relative error = 7.010262956623480e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.961 y[1] (analytic) = 1.427299492119282 y[1] (numeric) = 1.427299492119282 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.962 y[1] (analytic) = 1.42811954301148 y[1] (numeric) = 1.42811954301148 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.963 y[1] (analytic) = 1.428940165784088 y[1] (numeric) = 1.428940165784088 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.964 y[1] (analytic) = 1.429761359616482 y[1] (numeric) = 1.429761359616482 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.965 y[1] (analytic) = 1.430583123687469 y[1] (numeric) = 1.430583123687469 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.966 y[1] (analytic) = 1.431405457175285 y[1] (numeric) = 1.431405457175285 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.967 y[1] (analytic) = 1.432228359257597 y[1] (numeric) = 1.432228359257596 absolute error = 1e-15 relative error = 6.982126792394721e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.968 y[1] (analytic) = 1.433051829111502 y[1] (numeric) = 1.433051829111501 absolute error = 1e-15 relative error = 6.978114675866288e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.969 y[1] (analytic) = 1.43387586591353 y[1] (numeric) = 1.43387586591353 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.97 y[1] (analytic) = 1.434700468839646 y[1] (numeric) = 1.434700468839645 absolute error = 1e-15 relative error = 6.970096000657042e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.971 y[1] (analytic) = 1.435525637065245 y[1] (numeric) = 1.435525637065245 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.972 y[1] (analytic) = 1.436351369765161 y[1] (numeric) = 1.43635136976516 absolute error = 1e-15 relative error = 6.962084772916650e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.973 y[1] (analytic) = 1.437177666113659 y[1] (numeric) = 1.437177666113659 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.974 y[1] (analytic) = 1.438004525284445 y[1] (numeric) = 1.438004525284445 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.975 y[1] (analytic) = 1.438831946450659 y[1] (numeric) = 1.438831946450659 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.976 y[1] (analytic) = 1.439659928784879 y[1] (numeric) = 1.439659928784879 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.977 y[1] (analytic) = 1.440488471459124 y[1] (numeric) = 1.440488471459124 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.978 y[1] (analytic) = 1.44131757364485 y[1] (numeric) = 1.441317573644851 absolute error = 1e-15 relative error = 6.938096213391529e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.979 y[1] (analytic) = 1.442147234512957 y[1] (numeric) = 1.442147234512958 absolute error = 1e-15 relative error = 6.934104757602789e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=144.9MB, alloc=4.4MB, time=9.82 x[1] = 0.98 y[1] (analytic) = 1.442977453233783 y[1] (numeric) = 1.442977453233784 absolute error = 1e-15 relative error = 6.930115212534687e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.981 y[1] (analytic) = 1.443808228977109 y[1] (numeric) = 1.44380822897711 absolute error = 1e-15 relative error = 6.926127583498172e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.982 y[1] (analytic) = 1.444639560912159 y[1] (numeric) = 1.444639560912161 absolute error = 2e-15 relative error = 1.384428375156209e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.983 y[1] (analytic) = 1.445471448207603 y[1] (numeric) = 1.445471448207604 absolute error = 1e-15 relative error = 6.918158094648003e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.984 y[1] (analytic) = 1.446303890031552 y[1] (numeric) = 1.446303890031553 absolute error = 1e-15 relative error = 6.914176245340697e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.985 y[1] (analytic) = 1.447136885551564 y[1] (numeric) = 1.447136885551566 absolute error = 2e-15 relative error = 1.382039266615554e-13 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.986 y[1] (analytic) = 1.447970433934646 y[1] (numeric) = 1.447970433934647 absolute error = 1e-15 relative error = 6.906218363054883e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.987 y[1] (analytic) = 1.448804534347247 y[1] (numeric) = 1.448804534347248 absolute error = 1e-15 relative error = 6.902242340444813e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.988 y[1] (analytic) = 1.449639185955268 y[1] (numeric) = 1.449639185955269 absolute error = 1e-15 relative error = 6.898268270397440e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.989 y[1] (analytic) = 1.450474387924057 y[1] (numeric) = 1.450474387924058 absolute error = 1e-15 relative error = 6.894296158039830e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.99 y[1] (analytic) = 1.451310139418412 y[1] (numeric) = 1.451310139418413 absolute error = 1e-15 relative error = 6.890326008476266e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.991 y[1] (analytic) = 1.452146439602583 y[1] (numeric) = 1.452146439602583 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.992 y[1] (analytic) = 1.452983287640268 y[1] (numeric) = 1.452983287640268 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.993 y[1] (analytic) = 1.45382068269462 y[1] (numeric) = 1.45382068269462 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.994 y[1] (analytic) = 1.454658623928243 y[1] (numeric) = 1.454658623928244 absolute error = 1e-15 relative error = 6.874465139453428e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.995 y[1] (analytic) = 1.455497110503197 y[1] (numeric) = 1.455497110503198 absolute error = 1e-15 relative error = 6.870504879630288e-14 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.996 y[1] (analytic) = 1.456336141580996 y[1] (numeric) = 1.456336141580996 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.997 y[1] (analytic) = 1.457175716322607 y[1] (numeric) = 1.457175716322607 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.998 y[1] (analytic) = 1.458015833888457 y[1] (numeric) = 1.458015833888457 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.999 y[1] (analytic) = 1.458856493438428 y[1] (numeric) = 1.458856493438428 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1 y[1] (analytic) = 1.45969769413186 y[1] (numeric) = 1.45969769413186 absolute error = 0 relative error = 0 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = sin(x); Iterations = 1000 Total Elapsed Time = 9 Seconds Elapsed Time(since restart) = 9 Seconds Expected Time Remaining = 39 Seconds Optimized Time Remaining = 39 Seconds Time to Timeout = 14 Minutes 50 Seconds Percent Done = 20.02 % > quit memory used=148.0MB, alloc=4.4MB, time=10.02